Finite Group Databasebeta

← #17197859

Subgroups — #17197859

Order 4352.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763393C211yesmaximal, characteristic
2#14531971C211yesmaximal, characteristic, complemented
3#14531958C211yesmaximal, characteristic, complemented
4#14531935C211yesmaximal, characteristic, complemented
5#14531926C211yesmaximal, characteristic, complemented
6#14531905C211yesmaximal, characteristic, complemented
7#14531863C211yesmaximal, characteristic, complemented
8#14531835C211yesmaximal, characteristic, complemented
9#14531801C211yesmaximal, characteristic, complemented
10#14531797C211yesmaximal, characteristic, complemented
11#14531785C211yesmaximal, characteristic, complemented
12#14531779C211yesmaximal, characteristic, complemented
13#14531719C211yesmaximal, characteristic, complemented
14#14531716C211yesmaximal, characteristic, complemented
15#14531695C211yesmaximal, characteristic, complemented
16#14531682C211yesmaximal, characteristic, complemented
17#14531596C211yesmaximal, characteristic, complemented
18#14531567C211yesmaximal, characteristic, complemented
19#14531559C211yesmaximal, characteristic, complemented
20#14531559C211yesmaximal, characteristic, complemented
21#14531491C211yesmaximal, characteristic, complemented
22#14531488C211yesmaximal, characteristic, complemented
23#14531476C211yesmaximal, characteristic, complemented
24#14531455C211yesmaximal, characteristic, complemented
25#14531446C211yesmaximal, characteristic, complemented
26#14531443C211yesmaximal, characteristic, complemented
27#14531378C211yesmaximal, characteristic, complemented
28C4×#10587568C211yesmaximal, characteristic, complemented
29C4×#10587623C211yesmaximal, characteristic, complemented
30D17×#385C211yesmaximal, characteristic, complemented
31C17×#2367C211yesmaximal, characteristic, complemented
32C23×C4×D17C2211yescharacteristic
33#11763393C4116yescomplemented
34C2×#10587562C2211yescharacteristic
35C2×#10587565C2211yescharacteristic
36C2×#10587633C2211yescharacteristic
37C2×#10587572C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587632C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587568C2211yescharacteristic
44C2×#10587623C2211yescharacteristic
45C2×C4×D68C2211yescharacteristic
46C2×C4×D68C2211yescharacteristic
47C2×C4×D68C2211yescharacteristic
48C2×C4×D68C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×#10587567C2211yescharacteristic
53C2×#10587567C2211yescharacteristic
54C2×#10587567C2211yescharacteristic, complemented
55C2×#10587578C2211yescharacteristic, complemented
56C22×#63225C2211yescharacteristic, complemented
57C2×C4⋊C4×D17C2211yescharacteristic
58C2×C4⋊C4×D17C2211yescharacteristic
59C2×C22⋊C4×D17C2211yescharacteristic
60C2×C22⋊C4×D17C2211yescharacteristic
61#11762716C2211yescharacteristic, complemented
62#11762716C2211yescharacteristic, complemented
63#11762710C2211yescharacteristic
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic, complemented
67#11762707C2211yescharacteristic, complemented
68#11762707C2211yescharacteristic, complemented
69#11762707C2211yescharacteristic, complemented
70#11762706C2211yescharacteristic, complemented
71#11762706C2211yescharacteristic, complemented
72#11762704C2211yescharacteristic, complemented
73#11762704C2211yescharacteristic, complemented
74#11762704C2211yescharacteristic, complemented
75#11762703C2211yescharacteristic
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762702C2211yescharacteristic
79#11762702C2211yescharacteristic
80#11762702C2211yescharacteristic, complemented
81#11762702C2211yescharacteristic, complemented
82#11762701C2211yescharacteristic
83#11762701C2211yescharacteristic
84#11762701C2211yescharacteristic, complemented
85#11762700C2211yescharacteristic
86#11762700C2211yescharacteristic
87#11762700C2211yescharacteristic
88#11762700C2211yescharacteristic, complemented
89#11762700C2211yescharacteristic, complemented
90#11762700C2211yescharacteristic, complemented
91#11762699C2211yescharacteristic
92#11762699C2211yescharacteristic
93#11762698C2211yescharacteristic
94#11762697C2211yescharacteristic
95#11762696C2211yescharacteristic, complemented
96#11762696C2211yescharacteristic, complemented
97#11762696C2211yescharacteristic, complemented
98#11762694C2211yescharacteristic, complemented
99#11762694C2211yescharacteristic, complemented
100#11762694C2211yescharacteristic, complemented
101#11762693C2211yescharacteristic, complemented
102#11762693C2211yescharacteristic, complemented
103#11762693C2211yescharacteristic, complemented
104#11762692C2211yescharacteristic, complemented
105#11762690C2211yescharacteristic, complemented
106#11762690C2211yescharacteristic, complemented
107#11762689C2211yescharacteristic
108#11762689C2211yescharacteristic
109#11762688C2211yescharacteristic, complemented
110#11762687C2211yescharacteristic
111#11762687C2211yescharacteristic
112#11762687C2211yescharacteristic
113#11762687C2211yescharacteristic
114#11762686C2211yescharacteristic
115#11762686C2211yescharacteristic
116#11762685C2211yescharacteristic
117#11762685C2211yescharacteristic
118#11762685C2211yescharacteristic
119#11762685C2211yescharacteristic
120#11762685C2211yescharacteristic, complemented
121#11762684C2211yescharacteristic
122#11762684C2211yescharacteristic
123#11762684C2211yescharacteristic, complemented
124#11762684C2211yescharacteristic, complemented
125#11762683C2211yescharacteristic
126#11762683C2211yescharacteristic
127#11762683C2211yescharacteristic
128#11762683C2211yescharacteristic
129#11762682C2211yescharacteristic
130#11762681C2211yescharacteristic
131#11762681C2211yescharacteristic
132#11762680C2211yescharacteristic
133#11762680C2211yescharacteristic
134#11762680C2211yescharacteristic
135#11762680C2211yescharacteristic
136#11762680C2211yescharacteristic
137#11762680C2211yescharacteristic
138#11762680C2211yescharacteristic, complemented
139#11762680C2211yescharacteristic, complemented
140#11762680C2211yescharacteristic, complemented
141#11762678C2211yescharacteristic, complemented
142#11762676C2211yescharacteristic, complemented
143#11762675C2211yescharacteristic, complemented
144#11762675C2211yescharacteristic, complemented
145#11762670C2211yescharacteristic, complemented
146#11762668C2211yescharacteristic
147#11762668C2211yescharacteristic, complemented
148#11762667C2211yescharacteristic, complemented
149#11762666C2211yescharacteristic
150#11762666C2211yescharacteristic, complemented
151#11762664C2211yescharacteristic
152#11762664C2211yescharacteristic
153C4⋊C4×Dic17C2211yescharacteristic, complemented
154C4×#63225C2211yescharacteristic, complemented
155C4×#63225C2211yescharacteristic, complemented
156#11762660C2211yescharacteristic, complemented
157#11762660C2211yescharacteristic, complemented
158C22⋊C4×Dic17C2211yescharacteristic, complemented
159C4×#63227C2211yescharacteristic
160C4×#63227C2211yescharacteristic
161C4×#63227C2211yescharacteristic
162C4×#63227C2211yescharacteristic
163C4×#63227C2211yescharacteristic
164C4×#63227C2211yescharacteristic
165C4×C22⋊Dic17C2211yescharacteristic
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic
168#11762656C2211yescharacteristic, complemented
169#11762655C2211yescharacteristic, complemented
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#124C2211yescharacteristic
174C2×C4×Q8×C17C2211yescharacteristic, complemented
175C2×C4×D4×C17C2211yescharacteristic
176C17×#391C2211yescharacteristic, complemented
177C17×#390C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#388C2211yescharacteristic, complemented
181C17×#388C2211yescharacteristic, complemented
182C17×#385C2211yescharacteristic
183C17×#385C2211yescharacteristic, complemented
184C4×C4⋊C4×C17C2211yescharacteristic, complemented
185C4×C4⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C22×Q8×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C23×Dic17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C22×D68C2311yescharacteristic
201C22×D68C2311yescharacteristic
202C22×C4×D17—42no—
203C22×C4×D17—42no—
204C22×C4×D17—42no—
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C17×#124C2×C418yescomplemented
217C4×Q8×C17—42no—
218C4×D4×C17—42no—
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C42×C17C2311yescharacteristic
237C2×C42×C17C2311yescharacteristic
238C2×C42×C17C2311yescharacteristic
239C2×C42×C17C2311yescharacteristic
240C2×C42×C17C2311yescharacteristic
241C2×C42×C17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250#10587633C2×C418yescomplemented
251#10587632C2×C418yescomplemented
252#10587625C2×C418yescomplemented
253#10587623C2×C418yescomplemented
254C4×C22⋊D17—42no—
255C4×C22⋊D17—42no—
256C4×C22⋊D17—42no—
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×C4⋊Dic17C2311yescharacteristic
288C2×C4⋊Dic17C2311yescharacteristic
289C2×#63225—42no—
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
317#10587578—42no—
318C4⋊C4×D17—42no—
319C4⋊C4×D17—42no—
320#10587572C2×C418yescomplemented
321#10587570C2×C418yescomplemented
322#10587570C2×C418yescomplemented
323#10587569C2×C418yescomplemented
324#10587568C2×C418yescomplemented
325#10587567—42no—
326#10587567—42no—
327#10587567C2×C418yescomplemented
328C22⋊C4×D17—42no—
329C22⋊C4×D17C2×C418yescomplemented
330#10587565C2×C418yescomplemented
331#10587562C2×C418yescomplemented
332C4×D68—42no—
333C4×D68—42no—
334C4×D68—42no—
335C4×D68C2×C418yescomplemented
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C23×D17—22no—
379C23×D17—22no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17C22×C414yes—
385C23×D17C2411yescharacteristic
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C2×Q8×C17—41no—
389C2×Q8×C17—41no—
390C2×Q8×C17C22×C414yescomplemented
391C2×D4×C17—41no—
392C2×D4×C17—41no—
393C2×D4×C17C22×C414yes—
394C22×C4×C17—22no—
395C22×C4×C17—22no—
396C22×C4×C17—22no—
397C22×C4×C17—41no—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C2×C22⋊D17—22no—
414C2×C22⋊D17—22no—
415C2×C22⋊D17—41no—
416C2×C22⋊D17—41no—
417C2×C22⋊D17—41no—
418C2×C22⋊D17—41no—
419C2×C22⋊D17—41no—
420C2×C22⋊D17—41no—
421C2×C22⋊D17C22×C414yes—
422C2×C22⋊D17C22×C414yes—
423C2×C22⋊D17C22×C414yes—
424C2×C22⋊D17C22×C414yescomplemented
425C22×Dic17—41no—
426C22×Dic17—41no—
427C22×Dic17—41no—
428C22×Dic17—41no—
429C22×Dic17—41no—
430C22×Dic17—41no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17C22×C414yescomplemented
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C2×D68—22no—
448C2×D68—22no—
449C2×D68—41no—
450C2×D68—41no—
451C2×D68C22×C414yes—
452C2×D68C22×C414yes—
453C2×C4×D17—22no—
454C2×C4×D17—22no—
455C2×C4×D17—22no—
456C2×C4×D17—22no—
457C2×C4×D17—22no—
458C2×C4×D17—22no—
459C2×C4×D17—22no—
460C2×C4×D17—22no—
461C2×C4×D17—22no—
462C2×C4×D17—41no—
463C2×C4×D17—41no—
464C2×C4×D17—41no—
465C2×C4×D17—41no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—416no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17C22×C414yes—
485C2×C4×D17C22×C414yes—
486C2×C4×D17C22×C414yescomplemented
487C4⋊C4×C17—22no—
488C4⋊C4×C17—22no—
489C4⋊C4×C17—22no—
490C4⋊C4×C17—41no—
491C4⋊C4×C17—41no—
492C4⋊C4×C17—41no—
493C22⋊C4×C17—22no—
494C22⋊C4×C17—41no—
495C22⋊C4×C17—41no—
496C22⋊C4×C17—41no—
497C22⋊C4×C17—41no—
498C22⋊C4×C17—41no—
499C22⋊C4×C17C22×C414yes—
500C22⋊C4×C17C22×C414yes—
501C22⋊C4×C17C22×C414yescomplemented
502C22⋊C4×C17C22×C414yescomplemented
503C42×C17—22no—
504C42×C17—41no—
505C42×C17—41no—
506C42×C17—41no—
507C42×C17—41no—
508C42×C17—41no—
509C42×C17C22×C414yescomplemented
510C22⋊Dic17—41no—
511C22⋊Dic17—41no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17—41no—
515C22⋊Dic17—41no—
516C22⋊Dic17C22×C414yes—
517C22⋊Dic17C22×C414yes—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—22no—
522#63227—22no—
523#63227—41no—
524#63227—41no—
525#63227—41no—
526#63227—41no—
527#63227—41no—
528#63227—41no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227C22×C414yes—
535#63227C22×C414yes—
536#63227C22×C414yes—
537#63227C22×C414yes—
538#63227C22×C414yes—
539#63227C22×C414yes—
540#63227C22×C414yescomplemented
541#63227C22×C414yescomplemented
542C4⋊Dic17—41no—
543C4⋊Dic17—41no—
544C4⋊Dic17—41no—
545C4⋊Dic17—41no—
546C4⋊Dic17—41no—
547C4⋊Dic17—41no—
548C4⋊Dic17C22×C414yescomplemented
549C4⋊Dic17C22×C414yescomplemented
550#63225—22no—
551#63225—22no—
552#63225—22no—
553#63225—41no—
554#63225—41no—
555#63225—41no—
556#63225—41no—
557#63225—41no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225C22×C414yescomplemented
563#63225C22×C414yescomplemented
564#63225C22×C414yescomplemented
565#63225C22×C414yescomplemented
566C4×Dic17—22no—
567C4×Dic17—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573C4×Dic17—41no—
574C4×Dic17—41no—
575C4×Dic17—41no—
576C4×Dic17C22×C414yescomplemented
577#34416—171nomaximal, Sylow
578C23×C17—21no—
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17C23×C412yes—
591C23×C17C23×C412yes—
592C23×C17C2511yescharacteristic
593C22×D17—21no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—21no—
609C22×D17—28no—
610C22×D17—44no—
611C22×D17—44no—
612C22×D17—44no—
613C22×D17—44no—
614C22×D17—44no—
615C22×D17—44no—
616C22×D17C23×C412yes—
617C22×D17C23×C412yes—
618C22×D17C23×C412yes—
619C22×D17H(5,𝔽2)12yes—
620C22×D172−1+412yes—
621Q8×C17—44no—
622D4×C17—44no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—44no—
656C2×C4×C17—82no—
657C2×C4×C17C23×C412yes—
658C2×C4×C17C23×C412yes—
659C2×C4×C17C23×C412yes—
660C2×C4×C17C23×C412yes—
661C2×C4×C17C23×C412yes—
662C2×C4×C17H(5,𝔽2)12yes—
663C2×C4×C17H(5,𝔽2)12yes—
664C22⋊D17—28no—
665C22⋊D17—44no—
666C22⋊D17—44no—
667C22⋊D17—44no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—44no—
703C2×Dic17—44no—
704C2×Dic17—82no—
705C2×Dic17C23×C412yes—
706C2×Dic17C23×C412yes—
707C2×Dic17C23×C412yes—
708C2×Dic17C23×C412yes—
709C2×Dic17C23×C412yes—
710D68—28no—
711D68—44no—
712C4×D17—44no—
713C4×D17—44no—
714C4×D17—44no—
715C4×D17—44no—
716C4×D17—44no—
717C4×D17—44no—
718C4×D17—44no—
719C4×D17—82no—
720C4×D17—82no—
721C4×D17—82no—
722C4×D17—82no—
723C2×#538—171no—
724#2383—171no—
725#2379—171no—
726#2377—171no—
727#2376—171no—
728#2373—171no—
729#2368—171no—
730#2367D1711yescharacteristic, complemented
731#2364—171no—
732#2361—171no—
733#2361—171no—
734#2360—171no—
735#2359—171no—
736#2353—171no—
737#2352—171no—
738#2349—171no—
739D4×C4⋊C4—171no—
740#2337—171no—
741#2335—171no—
742#2334—171no—
743#2334—171no—
744#2326—171no—
745#2325—171no—
746#2324—171no—
747#2322—171no—
748#2321—171no—
749#2321—171no—
750#2312—171no—
751C4×#120—171no—
752C4×#120—171no—
753C2×#385—171no—
754C22×C17—22no—
755C22×C17—22no—
756C22×C17—22no—
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—41no—
761C22×C17—41no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17—41no—
767C22×C17—41no—
768C22×C17C24×C411yescharacteristic
769C22×C17C2×H(5,𝔽2)11yescharacteristic
770C22×C17C2×H(5,𝔽2)11yescharacteristic
771C22×C17C2×H(5,𝔽2)11yescharacteristic
772C22×C17C2×2−1+411yescharacteristic
773C22×C17#58511yescharacteristic
774C22×C17#58511yescharacteristic
775C2×D17—22no—
776C2×D17—22no—
777C2×D17—22no—
778C2×D17—22no—
779C2×D17—22no—
780C2×D17—22no—
781C2×D17—22no—
782C2×D17—22no—
783C2×D17—22no—
784C2×D17—22no—
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—416no—
788C2×D17—41no—
789C2×D17—41no—
790C2×D17—41no—
791C2×D17—41no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—41no—
796C2×D17#52014yes—
797C4×C17—22no—
798C4×C17—22no—
799C4×C17—22no—
800C4×C17—22no—
801C4×C17—22no—
802C4×C17—22no—
803C4×C17—22no—
804C4×C17—41no—
805C4×C17—41no—
806C4×C17—41no—
807C4×C17—41no—
808C4×C17—41no—
809C4×C17—41no—
810Dic17—22no—
811Dic17—22no—
812Dic17—22no—
813Dic17—22no—
814Dic17—22no—
815Dic17—41no—
816Dic17—41no—
817Dic17—41no—
818Dic17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822Dic17—41no—
823C24×C4—171no—
824#538—1716no—
825C2×#126—171no—
826C2×#126—171no—
827C2×#124—171no—
828C2×#124C2×D1711yescharacteristic
829C2×#123—171no—
830C2×#123—171no—
831C2×C22⋊Q8—171no—
832C2×#121—171no—
833C2×#121—171no—
834C2×#121—171no—
835C2×#120—171no—
836C2×#120—171no—
837C2×C4×Q8C2×D1711yescharacteristic, complemented
838C2×C4×D4—171no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4—171no—
842C2×C4×D4—171no—
843C2×C4×D4—171no—
844C2×C4×D4—171no—
845C2×C4×D4—171no—
846C2×C4×D4—171no—
847C2×C4×D4—171no—
848C2×C4×D4C2×D1711yescharacteristic
849C2×#117—171no—
850C22×C4⋊C4—171no—
851C22×C4⋊C4—171no—
852C22×C4⋊C4—171no—
853C22×C22⋊C4—171no—
854C22×C22⋊C4—171no—
855#391—171no—
856#391—171no—
857#391C2×D1711yescharacteristic, complemented
858#390—171no—
859#390—171no—
860#390—171no—
861#390—171no—
862#390C2×D1711yescharacteristic
863#389—171no—
864#389—171no—
865#389—171no—
866#389—171no—
867#389—171no—
868#389—171no—
869#389—171no—
870#389—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388—171no—
879#388—171no—
880#388—171no—
881#388—171no—
882#388—171no—
883#388—171no—
884#388—171no—
885#388—171no—
886#388—171no—
887#388—171no—
888#388—171no—
889#388—171no—
890#388—171no—
891#388C2×D1711yescharacteristic
892#388C2×D1711yescharacteristic
893#388C2×D1711yescharacteristic, complemented
894#388C2×D1711yescharacteristic, complemented
895#387—171no—
896#387—171no—
897#387—171no—
898#387—171no—
899#387—171no—
900#387—171no—
901#387—171no—
902#387—171no—
903#387—171no—
904#387—171no—
905#387—171no—
906#387—171no—
907#386—171no—
908#386—171no—
909#386—171no—
910#386—171no—
911#386—171no—
912#386—171no—
913#386—171no—
914#386—171no—
915#386—171no—
916#386—171no—
917#386—171no—
918#386—171no—
919#386—171no—
920#386—171no—
921#385—171no—
922#385—171no—
923#385—171no—
924#385—171no—
925#385—171no—
926#385—171no—
927#385—171no—
928#385—171no—
929#385—171no—
930#385—171no—
931#385—171no—
932#385—171no—
933#385—171no—
934#385—171no—
935#385—171no—
936#385—171no—
937#385—171no—
938#385—171no—
939#385—171no—
940#385—171no—
941#385C2×D1711yescharacteristic
942#385C2×D1711yescharacteristic, complemented
943#384—171no—
944#383—171no—
945#382—171no—
946#382—171no—
947#381—171no—
948#380—171no—
949#380—171no—
950#380—171no—
951#380—171no—
952#380—171no—
953#379—171no—
954#379—171no—
955C4×C4⋊C4—171no—
956C4×C4⋊C4—171no—
957C4×C4⋊C4—171no—
958C4×C4⋊C4—171no—
959C4×C4⋊C4—171no—
960C4×C4⋊C4C2×D1711yescharacteristic, complemented
961C4×C4⋊C4C2×D1711yescharacteristic, complemented
962C4×C22⋊C4—171no—
963C4×C22⋊C4—171no—
964C4×C22⋊C4—171no—
965C4×C22⋊C4—171no—
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4—171no—
971C4×C22⋊C4—171no—
972C4×C22⋊C4—171no—
973C4×C22⋊C4C2×D1711yescharacteristic
974C4×C22⋊C4C2×D1711yescharacteristic, complemented
975#376—171no—
976C2×#95—171no—
977C2×#95—171no—
978C2×#95—171no—
979C2×C17—42no—
980C2×C17—42no—
981C2×C17C2×#52011yescharacteristic
982C2×C17C4×H(5,𝔽2)11yescharacteristic
983C2×C17C4×H(5,𝔽2)11yescharacteristic
984C2×C17#353211yescharacteristic
985C2×C17#353311yescharacteristic
986C2×C17#354111yescharacteristic
987C2×C17#354111yescharacteristic
988D17—24no—
989D17—42no—
990D17—42no—
991C25—171no—
992C22×Q8C22×D1711yescharacteristic
993C22×D4—171no—
994C22×D4—171no—
995C22×D4—171no—
996C22×D4—171no—
997C22×D4—171no—
998C22×D4—171no—
999C22×D4C22×D1711yescharacteristic
1000C23×C4—171no—
1001C23×C4—171no—
1002C23×C4—171no—
1003C23×C4—171no—
1004C23×C4—171no—
1005C23×C4—171no—
1006C23×C4—171no—
1007C23×C4—171no—
1008C23×C4—171no—
1009C23×C4—171no—
1010C23×C4—171no—
1011C23×C4—171no—
1012C23×C4—171no—
1013C23×C4—171no—
1014C23×C4—682no—
1015C23×C4—682no—
1016C23×C4—682no—
1017C23×C4C22×D1711yescharacteristic
1018C23×C4C22×D1711yescharacteristic
1019#126—178no—
1020#126—178no—
1021#124—178no—
1022#124C4×D1718yescomplemented
1023#123—178no—
1024#123—178no—
1025C22⋊Q8—178no—
1026#121—178no—
1027#121—178no—
1028#121—178no—
1029#120—178no—
1030#120—178no—
1031C4×Q8—42no—
1032C4×D4—42no—
1033C4×D4—178no—
1034C4×D4—178no—
1035C4×D4—682no—
1036C4×D4—682no—
1037C4×D4—682no—
1038C4×D4—682no—
1039C4×D4—682no—
1040C4×D4—682no—
1041C4×D4—682no—
1042C4×D4—682no—
1043#117—682no—
1044C2×C4⋊C4—171no—
1045C2×C4⋊C4—171no—
1046C2×C4⋊C4—171no—
1047C2×C4⋊C4—171no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—171no—
1064C2×C4⋊C4—171no—
1065C2×C4⋊C4—171no—
1066C2×C4⋊C4—171no—
1067C2×C4⋊C4—171no—
1068C2×C4⋊C4—682no—
1069C2×C4⋊C4—682no—
1070C2×C4⋊C4—682no—
1071C2×C4⋊C4C22×D1711yescharacteristic
1072C2×C4⋊C4C22×D1711yescharacteristic
1073C2×C4⋊C4C22×D1711yescharacteristic
1074C2×C4⋊C4C22×D1711yescharacteristic
1075C2×C4⋊C4C22×D1711yescharacteristic
1076C2×C4⋊C4C22×D1711yescharacteristic
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—171no—
1083C2×C22⋊C4—171no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—178no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—682no—
1111C2×C22⋊C4C22×D1711yescharacteristic
1112C2×C22⋊C4C22×D1711yescharacteristic
1113C2×C22⋊C4C22×D1711yescharacteristic
1114C2×C22⋊C4C22×D1711yescharacteristic
1115C2×C22⋊C4C22×D1711yescharacteristic
1116C2×C22⋊C4C22×D1711yescharacteristic
1117C2×C22⋊C4C22×D1711yescharacteristic
1118C2×C22⋊C4C22×D1711yescharacteristic
1119C2×C22⋊C4C22×D1711yescharacteristic
1120C2×C22⋊C4C22×D1711yescharacteristic
1121C2×C42—171no—
1122C2×C42—171no—
1123C2×C42—171no—
1124C2×C42—171no—
1125C2×C42—171no—
1126C2×C42—171no—
1127C2×C42—171no—
1128C2×C42—171no—
1129C2×C42—171no—
1130C2×C42—171no—
1131C2×C42—171no—
1132C2×C42C22×D1711yescharacteristic
1133C2×C42C22×D1711yescharacteristic
1134C2×C42C22×D1711yescharacteristic
1135C2×C42C22×D1711yescharacteristic
1136C2×C42C22×D1711yescharacteristic
1137C2×C42C22×D1711yescharacteristic
1138C2×C42C22×D1711yescharacteristic
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95C22×D1711yescharacteristic
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
1179C17#3441611yescharacteristic, complemented, Sylow
1180C24—171no—
1181C24—171no—
1182C24—171no—
1183C24—174no—
1184C24—342no—
1185C24—342no—
1186C24—681no—
1187C24—681no—
1188C24—681no—
1189C24—681no—
1190C24C23×D1711yescharacteristic
1191C24C23×D1711yescharacteristic
1192C2×Q8—41no—
1193C2×Q8—41no—
1194C2×Q8C2×C4×D1714yescomplemented
1195C2×D4—41no—
1196C2×D4—41no—
1197C2×D4—174no—
1198C2×D4—174no—
1199C2×D4—174no—
1200C2×D4—174no—
1201C2×D4—174no—
1202C2×D4—174no—
1203C2×D4—342no—
1204C2×D4—342no—
1205C2×D4—342no—
1206C2×D4—342no—
1207C2×D4—681no—
1208C2×D4—681no—
1209C2×D4—681no—
1210C2×D4—681no—
1211C2×D4—681no—
1212C2×D4—681no—
1213C2×D4—681no—
1214C2×D4—681no—
1215C2×D4C2×C4×D1714yes—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—171no—
1223C22×C4—171no—
1224C22×C4—171no—
1225C22×C4—171no—
1226C22×C4—171no—
1227C22×C4—174no—
1228C22×C4—174no—
1229C22×C4—174no—
1230C22×C4—174no—
1231C22×C4—171no—
1232C22×C4—171no—
1233C22×C4—171no—
1234C22×C4—171no—
1235C22×C4—171no—
1236C22×C4—171no—
1237C22×C4—171no—
1238C22×C4—171no—
1239C22×C4—342no—
1240C22×C4—342no—
1241C22×C4—342no—
1242C22×C4—342no—
1243C22×C4—342no—
1244C22×C4—342no—
1245C22×C4—342no—
1246C22×C4—342no—
1247C22×C4—342no—
1248C22×C4—681no—
1249C22×C4—681no—
1250C22×C4—681no—
1251C22×C4—681no—
1252C22×C4—681no—
1253C22×C4—681no—
1254C22×C4—681no—
1255C22×C4—681no—
1256C22×C4—681no—
1257C22×C4—681no—
1258C22×C4—681no—
1259C22×C4—681no—
1260C22×C4—681no—
1261C22×C4—681no—
1262C22×C4—681no—
1263C22×C4—681no—
1264C22×C4—681no—
1265C22×C4—681no—
1266C22×C4—681no—
1267C22×C4—681no—
1268C22×C4—681no—
1269C22×C4—6816no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—681no—
1278C22×C4C23×D1711yescharacteristic
1279C22×C4C23×D1711yescharacteristic
1280C22×C4C23×D1711yescharacteristic
1281C22×C4C23×D1711yescharacteristic
1282C22×C4C23×D1711yescharacteristic
1283C22×C4C23×D1711yescharacteristic
1284C22×C4C23×D1711yescharacteristic
1285C22×C4C23×D1711yescharacteristic
1286C22×C4C23×D1711yescharacteristic
1287C22×C4C23×D1711yescharacteristic
1288C22×C4C23×D1711yescharacteristic
1289C22×C4C23×D1711yescharacteristic
1290C22×C4C23×D1711yescharacteristic
1291C4⋊C4—22no—
1292C4⋊C4—22no—
1293C4⋊C4—22no—
1294C4⋊C4—41no—
1295C4⋊C4—41no—
1296C4⋊C4—41no—
1297C4⋊C4—174no—
1298C4⋊C4—174no—
1299C4⋊C4—174no—
1300C4⋊C4—174no—
1301C4⋊C4—174no—
1302C4⋊C4—174no—
1303C4⋊C4—342no—
1304C4⋊C4—342no—
1305C4⋊C4—342no—
1306C4⋊C4—681no—
1307C4⋊C4—681no—
1308C4⋊C4—681no—
1309C4⋊C4—681no—
1310C4⋊C4—681no—
1311C4⋊C4—681no—
1312C4⋊C4—681no—
1313C4⋊C4—681no—
1314C4⋊C4—681no—
1315C4⋊C4—681no—
1316C4⋊C4—681no—
1317C4⋊C4—681no—
1318C4⋊C4—681no—
1319C4⋊C4—681no—
1320C4⋊C4—681no—
1321C22⋊C4—22no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—41no—
1326C22⋊C4—41no—
1327C22⋊C4—174no—
1328C22⋊C4—174no—
1329C22⋊C4—174no—
1330C22⋊C4—174no—
1331C22⋊C4—174no—
1332C22⋊C4—174no—
1333C22⋊C4—174no—
1334C22⋊C4—174no—
1335C22⋊C4—174no—
1336C22⋊C4—174no—
1337C22⋊C4—342no—
1338C22⋊C4—342no—
1339C22⋊C4—342no—
1340C22⋊C4—342no—
1341C22⋊C4—342no—
1342C22⋊C4—681no—
1343C22⋊C4—681no—
1344C22⋊C4—681no—
1345C22⋊C4—681no—
1346C22⋊C4—681no—
1347C22⋊C4—681no—
1348C22⋊C4—681no—
1349C22⋊C4—681no—
1350C22⋊C4—681no—
1351C22⋊C4—681no—
1352C22⋊C4—681no—
1353C22⋊C4—681no—
1354C22⋊C4—681no—
1355C22⋊C4—681no—
1356C22⋊C4—681no—
1357C22⋊C4—681no—
1358C22⋊C4—681no—
1359C22⋊C4C2×C4×D1714yes—
1360C22⋊C4C2×C4×D1714yes—
1361C22⋊C4C2×C4×D1714yescomplemented
1362C22⋊C4C2×C4×D1714yescomplemented
1363C42—22no—
1364C42—41no—
1365C42—41no—
1366C42—41no—
1367C42—41no—
1368C42—41no—
1369C42—174no—
1370C42—342no—
1371C42—681no—
1372C42—681no—
1373C42—681no—
1374C42—681no—
1375C42—681no—
1376C42—681no—
1377C42—681no—
1378C42—681no—
1379C42—681no—
1380C42C2×C4×D1714yescomplemented
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—172no—
1394C23—172no—
1395C23—172no—
1396C23—172no—
1397C23—172no—
1398C23—348no—
1399C23—341no—
1400C23—341no—
1401C23—341no—
1402C23—341no—
1403C23—341no—
1404C23—341no—
1405C23—341no—
1406C23—341no—
1407C23—341no—
1408C23—341no—
1409C23—341no—
1410C23—341no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—684no—
1416C23—684no—
1417C23—684no—
1418C23—684no—
1419C23—684no—
1420C23—684no—
1421C23C22×C4×D1712yes—
1422C23C22×C4×D1712yes—
1423C23C24×D1711yescharacteristic
1424Q8—44no—
1425D4—44no—
1426D4—348no—
1427D4—348no—
1428D4—684no—
1429D4—684no—
1430D4—684no—
1431D4—684no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—44no—
1465C2×C4—82no—
1466C2×C4—172no—
1467C2×C4—172no—
1468C2×C4—172no—
1469C2×C4—172no—
1470C2×C4—172no—
1471C2×C4—341no—
1472C2×C4—341no—
1473C2×C4—341no—
1474C2×C4—341no—
1475C2×C4—341no—
1476C2×C4—341no—
1477C2×C4—341no—
1478C2×C4—341no—
1479C2×C4—341no—
1480C2×C4—341no—
1481C2×C4—341no—
1482C2×C4—341no—
1483C2×C4—341no—
1484C2×C4—341no—
1485C2×C4—341no—
1486C2×C4—341no—
1487C2×C4—341no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—684no—
1506C2×C4—684no—
1507C2×C4—684no—
1508C2×C4—684no—
1509C2×C4—684no—
1510C2×C4—684no—
1511C2×C4—684no—
1512C2×C4—684no—
1513C2×C4—684no—
1514C2×C4—1362no—
1515C2×C4—1362no—
1516C2×C4—1362no—
1517C2×C4—1362no—
1518C2×C4—1362no—
1519C2×C4C22×C4×D1712yes—
1520C2×C4C22×C4×D1712yes—
1521C2×C4C22×C4×D1712yes—
1522C2×C4C22×C4×D1712yes—
1523C2×C4C22×C4×D1712yes—
1524C2×C4#1058769112yes—
1525C2×C4#1058769612yes—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—41no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—174no—
1541C22—342no—
1542C22—342no—
1543C22—342no—
1544C22—342no—
1545C22—342no—
1546C22—342no—
1547C22—342no—
1548C22—342no—
1549C22—342no—
1550C22—342no—
1551C22—342no—
1552C22—342no—
1553C22—6816no—
1554C22—681no—
1555C22—681no—
1556C22—681no—
1557C22—681no—
1558C22—681no—
1559C22—681no—
1560C22—681no—
1561C22—681no—
1562C22C23×C4×D1711yescharacteristic
1563C22H(5,𝔽2)×D1711yescharacteristic
1564C22C2×#1058769111yescharacteristic
1565C22C2×#1058769611yescharacteristic
1566C222−1+4×D1711yescharacteristic
1567C22#1176364511yescharacteristic
1568C22#1176364511yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—22no—
1575C4—22no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—41no—
1582C4—342no—
1583C4—342no—
1584C4—342no—
1585C4—342no—
1586C4—342no—
1587C4—681no—
1588C4—681no—
1589C4—681no—
1590C4—681no—
1591C4—681no—
1592C4—681no—
1593C4—681no—
1594C4—681no—
1595C2—42no—
1596C2—42no—
1597C2—344no—
1598C2—682no—
1599C2—682no—
1600C2D17×#52011yescharacteristic
1601C2C4×#1058769111yescharacteristic
1602C2C4×#1058769611yescharacteristic
1603C2#1454293311yescharacteristic
1604C2#1454295811yescharacteristic
1605C2#1454307511yescharacteristic
1606C2#1454308411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2367C2
socle, cosocleC23×C17C25
prime radicalC2×#11763393C2
hypercenter#2367D17
hypocenterC17#34416
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2367

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14531971C2semidirect
3. #14531958C2semidirect
4. #14531935C2semidirect
5. #14531926C2semidirect
6. #14531905C2semidirect
7. #14531863C2semidirect
8. #14531835C2semidirect
9. #14531801C2semidirect
10. #14531797C2semidirect
11. #14531785C2semidirect
12. #14531779C2semidirect
13. #14531719C2semidirect
14. #14531716C2semidirect
15. #14531695C2semidirect
16. #14531682C2semidirect
17. #14531596C2semidirect
18. #14531567C2semidirect
19. #14531559C2semidirect
20. #14531559C2semidirect
21. #14531491C2semidirect
22. #14531488C2semidirect
23. #14531476C2semidirect
24. #14531455C2semidirect
25. #14531446C2semidirect
26. #14531443C2semidirect
27. #14531378C2semidirect
28. C4×#10587568C2semidirect
29. C4×#10587623C2semidirect
30. D17×#385C2semidirect
31. C17×#2367C2semidirect
33. #11763393C4semidirect
54. C2×#10587567C22semidirect
55. C2×#10587578C22semidirect
56. C22×#63225C22semidirect
61. #11762716C22semidirect
62. #11762716C22semidirect
66. #11762709C22semidirect
67. #11762707C22semidirect
68. #11762707C22semidirect
69. #11762707C22semidirect
70. #11762706C22semidirect
71. #11762706C22semidirect
72. #11762704C22semidirect
73. #11762704C22semidirect
74. #11762704C22semidirect
80. #11762702C22semidirect
81. #11762702C22semidirect
84. #11762701C22semidirect
88. #11762700C22semidirect
89. #11762700C22semidirect
90. #11762700C22semidirect
95. #11762696C22semidirect
96. #11762696C22semidirect
97. #11762696C22semidirect
98. #11762694C22semidirect
99. #11762694C22semidirect
100. #11762694C22semidirect
101. #11762693C22semidirect
102. #11762693C22semidirect
103. #11762693C22semidirect
104. #11762692C22semidirect
105. #11762690C22semidirect
106. #11762690C22semidirect
109. #11762688C22semidirect
120. #11762685C22semidirect
123. #11762684C22semidirect
124. #11762684C22semidirect
138. #11762680C22semidirect
139. #11762680C22semidirect
140. #11762680C22semidirect
141. #11762678C22semidirect
142. #11762676C22semidirect
143. #11762675C22semidirect
144. #11762675C22semidirect
145. #11762670C22semidirect
147. #11762668C22semidirect
148. #11762667C22semidirect
150. #11762666C22semidirect
153. C4⋊C4×Dic17C22semidirect
154. C4×#63225C22semidirect
155. C4×#63225C22semidirect
156. #11762660C22semidirect
157. #11762660C22semidirect
158. C22⋊C4×Dic17C22semidirect
168. #11762656C22semidirect
169. #11762655C22semidirect
172. #95×D17C22semidirect
174. C2×C4×Q8×C17C22semidirect
176. C17×#391C22semidirect
180. C17×#388C22semidirect
181. C17×#388C22semidirect
183. C17×#385C22semidirect
184. C4×C4⋊C4×C17C22semidirect
185. C4×C4⋊C4×C17C22semidirect
187. C4×C22⋊C4×C17C22semidirect
216. C17×#124C2×C4semidirect
250. #10587633C2×C4semidirect
251. #10587632C2×C4semidirect
252. #10587625C2×C4semidirect
253. #10587623C2×C4semidirect
320. #10587572C2×C4semidirect
321. #10587570C2×C4semidirect
322. #10587570C2×C4semidirect
323. #10587569C2×C4semidirect
324. #10587568C2×C4semidirect
327. #10587567C2×C4semidirect
329. C22⋊C4×D17C2×C4semidirect
330. #10587565C2×C4semidirect
331. #10587562C2×C4semidirect
335. C4×D68C2×C4semidirect
390. C2×Q8×C17C22×C4semidirect
424. C2×C22⋊D17C22×C4semidirect
433. C22×Dic17C22×C4semidirect
486. C2×C4×D17C22×C4semidirect
501. C22⋊C4×C17C22×C4semidirect
502. C22⋊C4×C17C22×C4semidirect
509. C42×C17C22×C4semidirect
540. #63227C22×C4semidirect
541. #63227C22×C4semidirect
548. C4⋊Dic17C22×C4semidirect
549. C4⋊Dic17C22×C4semidirect
562. #63225C22×C4semidirect
563. #63225C22×C4semidirect
564. #63225C22×C4semidirect
565. #63225C22×C4semidirect
576. C4×Dic17C22×C4semidirect
730. #2367D17semidirect
837. C2×C4×Q8C2×D17semidirect
857. #391C2×D17semidirect
893. #388C2×D17semidirect
894. #388C2×D17semidirect
942. #385C2×D17semidirect
960. C4×C4⋊C4C2×D17semidirect
961. C4×C4⋊C4C2×D17semidirect
974. C4×C22⋊C4C2×D17semidirect
1022. #124C4×D17semidirect
1179. C17#34416semidirect
1194. C2×Q8C2×C4×D17semidirect
1361. C22⋊C4C2×C4×D17semidirect
1362. C22⋊C4C2×C4×D17semidirect
1380. C42C2×C4×D17semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633932
#145319712
#145319582
#145319352
#145319262
#145319052
#145318632
#145318352
#145318012
#145317972
#145317852
#145317792
#145317192
#145317162
#145316952
#145316822
#145315962
#145315672
#145315592
#145314912
#145314882
#145314762
#145314552
#145314462
#145314432
#145313782
C4×#105875682
C4×#105876232
D17×#3852
C17×#23672
#3441617