Finite Group Databasebeta

← #17198395

Subgroups — #17198395

Order 4352.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763393C211yesmaximal, characteristic
2#14531956C211yesmaximal, characteristic, complemented
3#14531942C211yesmaximal, characteristic, complemented
4#14531937C211yesmaximal, characteristic, complemented
5#14531924C211yesmaximal, characteristic, complemented
6#14531904C211yesmaximal, characteristic, complemented
7#14531904C211yesmaximal, characteristic, complemented
8#14531860C211yesmaximal, characteristic, complemented
9#14531859C211yesmaximal, characteristic, complemented
10#14531823C211yesmaximal, characteristic, complemented
11#14531795C211yesmaximal, characteristic, complemented
12#14531766C211yesmaximal, characteristic, complemented
13#14531754C211yesmaximal, characteristic, complemented
14#14531707C211yesmaximal, characteristic, complemented
15#14531628C211yesmaximal, characteristic, complemented
16#14531627C211yesmaximal, characteristic, complemented
17#14531576C211yesmaximal, characteristic, complemented
18#14531567C211yesmaximal, characteristic, complemented
19#14531561C211yesmaximal, characteristic, complemented
20#14531556C211yesmaximal, characteristic, complemented
21#14531547C211yesmaximal, characteristic, complemented
22#14531539C211yesmaximal, characteristic, complemented
23#14531469C211yesmaximal, characteristic, complemented
24#14531455C211yesmaximal, characteristic, complemented
25#14531447C211yesmaximal, characteristic, complemented
26#14531440C211yesmaximal, characteristic, complemented
27#14531428C211yesmaximal, characteristic, complemented
28#14531311C211yesmaximal, characteristic, complemented
29C4×#10587570C211yesmaximal, characteristic, complemented
30#14531228C211yesmaximal, characteristic, complemented
31C17×#2372C211yesmaximal, characteristic, complemented
32#11763393C4116yescomplemented
33C2×#10587562C2211yescharacteristic
34C2×#10587565C2211yescharacteristic
35C2×#10587633C2211yescharacteristic
36C2×#10587572C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587632C2211yescharacteristic
39C2×#10587570C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587625C2211yescharacteristic
42C2×#10587568C2211yescharacteristic
43C2×#10587623C2211yescharacteristic
44C2×Q8×Dic17C2211yescharacteristic, complemented
45C2×C4×D68C2211yescharacteristic
46C2×C4×D68C2211yescharacteristic
47C2×D4×Dic17C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic, complemented
50C2×#10587567C2211yescharacteristic
51C2×#10587567C2211yescharacteristic
52C2×#10587558C2211yescharacteristic
53C2×#10587558C2211yescharacteristic
54C22×#63225C2211yescharacteristic, complemented
55C22×#63227C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C2×C42×D17C2211yescharacteristic, complemented
59#11762716C2211yescharacteristic, complemented
60#11762712C2211yescharacteristic
61#11762711C2211yescharacteristic
62#11762711C2211yescharacteristic
63#11762710C2211yescharacteristic
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic
68#11762709C2211yescharacteristic, complemented
69#11762707C2211yescharacteristic, complemented
70#11762707C2211yescharacteristic, complemented
71#11762707C2211yescharacteristic, complemented
72#11762706C2211yescharacteristic, complemented
73#11762706C2211yescharacteristic, complemented
74#11762706C2211yescharacteristic, complemented
75#11762703C2211yescharacteristic
76#11762702C2211yescharacteristic
77#11762702C2211yescharacteristic
78#11762702C2211yescharacteristic, complemented
79#11762702C2211yescharacteristic, complemented
80#11762701C2211yescharacteristic
81#11762701C2211yescharacteristic
82#11762701C2211yescharacteristic
83#11762701C2211yescharacteristic
84#11762701C2211yescharacteristic
85#11762701C2211yescharacteristic, complemented
86#11762700C2211yescharacteristic
87#11762700C2211yescharacteristic
88#11762700C2211yescharacteristic
89#11762700C2211yescharacteristic
90#11762700C2211yescharacteristic, complemented
91#11762699C2211yescharacteristic
92#11762698C2211yescharacteristic
93#11762698C2211yescharacteristic
94#11762698C2211yescharacteristic
95#11762698C2211yescharacteristic
96#11762698C2211yescharacteristic
97#11762698C2211yescharacteristic
98#11762698C2211yescharacteristic, complemented
99#11762698C2211yescharacteristic, complemented
100#11762697C2211yescharacteristic
101#11762697C2211yescharacteristic
102#11762697C2211yescharacteristic
103#11762696C2211yescharacteristic, complemented
104#11762696C2211yescharacteristic, complemented
105#11762694C2211yescharacteristic, complemented
106#11762694C2211yescharacteristic, complemented
107#11762694C2211yescharacteristic, complemented
108#11762693C2211yescharacteristic, complemented
109#11762693C2211yescharacteristic, complemented
110#11762692C2211yescharacteristic, complemented
111#11762691C2211yescharacteristic, complemented
112#11762691C2211yescharacteristic, complemented
113#11762691C2211yescharacteristic, complemented
114#11762690C2211yescharacteristic, complemented
115#11762688C2211yescharacteristic
116#11762688C2211yescharacteristic
117#11762687C2211yescharacteristic
118#11762687C2211yescharacteristic
119#11762687C2211yescharacteristic
120#11762687C2211yescharacteristic
121#11762686C2211yescharacteristic
122#11762686C2211yescharacteristic
123#11762686C2211yescharacteristic, complemented
124#11762685C2211yescharacteristic
125#11762685C2211yescharacteristic
126#11762685C2211yescharacteristic, complemented
127#11762684C2211yescharacteristic
128#11762684C2211yescharacteristic, complemented
129#11762683C2211yescharacteristic
130#11762683C2211yescharacteristic
131#11762683C2211yescharacteristic
132#11762683C2211yescharacteristic, complemented
133#11762683C2211yescharacteristic, complemented
134#11762682C2211yescharacteristic
135#11762682C2211yescharacteristic
136#11762681C2211yescharacteristic
137#11762680C2211yescharacteristic
138#11762680C2211yescharacteristic, complemented
139#11762673C2211yescharacteristic, complemented
140#11762673C2211yescharacteristic, complemented
141#11762671C2211yescharacteristic
142#11762671C2211yescharacteristic
143#11762671C2211yescharacteristic, complemented
144#11762670C2211yescharacteristic, complemented
145#11762668C2211yescharacteristic
146#11762668C2211yescharacteristic, complemented
147#11762667C2211yescharacteristic, complemented
148#11762666C2211yescharacteristic
149#11762664C2211yescharacteristic
150#11762664C2211yescharacteristic
151C4⋊C4×Dic17C2211yescharacteristic, complemented
152C4⋊C4×Dic17C2211yescharacteristic, complemented
153C4×#63225C2211yescharacteristic, complemented
154C4×#63225C2211yescharacteristic, complemented
155C4×#63225C2211yescharacteristic, complemented
156C4×#63225C2211yescharacteristic, complemented
157C4×C4⋊Dic17C2211yescharacteristic, complemented
158C4×C4⋊Dic17C2211yescharacteristic, complemented
159#11762660C2211yescharacteristic, complemented
160#11762660C2211yescharacteristic, complemented
161C22⋊C4×Dic17C2211yescharacteristic
162C22⋊C4×Dic17C2211yescharacteristic
163C22⋊C4×Dic17C2211yescharacteristic, complemented
164C22⋊C4×Dic17C2211yescharacteristic, complemented
165C4×#63227C2211yescharacteristic
166C4×#63227C2211yescharacteristic
167C4×#63227C2211yescharacteristic
168C4×#63227C2211yescharacteristic, complemented
169#11762656C2211yescharacteristic
170#11762656C2211yescharacteristic
171#11762656C2211yescharacteristic
172#11762656C2211yescharacteristic, complemented
173C2×C17×#124C2211yescharacteristic
174C17×#391C2211yescharacteristic, complemented
175C17×#391C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic
177C17×#388C2211yescharacteristic
178C17×#388C2211yescharacteristic, complemented
179C17×#388C2211yescharacteristic, complemented
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C4×C22⋊C4×C17C2211yescharacteristic
183C4×C22⋊C4×C17C2211yescharacteristic
184C4×C22⋊C4×C17C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C17×#376C2211yescharacteristic, complemented
187C17×#376C2211yescharacteristic, 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×D17C2311yescharacteristic
203C22×C4×D17C2311yescharacteristic
204C22×C4×D17C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C17×#124C2×C418yescomplemented
210C2×C4⋊C4×C17C2311yescharacteristic
211C2×C4⋊C4×C17C2311yescharacteristic
212C2×C22⋊C4×C17C2311yescharacteristic
213C2×C22⋊C4×C17C2311yescharacteristic
214C2×C22⋊C4×C17C2311yescharacteristic
215C2×C22⋊C4×C17C2311yescharacteristic
216C2×C22⋊C4×C17C2311yescharacteristic
217C2×C22⋊C4×C17C2311yescharacteristic
218C2×C22⋊C4×C17C2311yescharacteristic
219C2×C22⋊C4×C17C2311yescharacteristic
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C42×C17C2311yescharacteristic
223C2×C42×C17C2311yescharacteristic
224C2×C42×C17C2311yescharacteristic
225C2×C42×C17C2311yescharacteristic
226C2×C42×C17C2311yescharacteristic
227C2×C42×C17C2311yescharacteristic
228C2×C42×C17C2311yescharacteristic
229C2×C22⋊Dic17C2311yescharacteristic
230C2×C22⋊Dic17C2311yescharacteristic
231C2×C22⋊Dic17C2311yescharacteristic
232C2×C22⋊Dic17C2311yescharacteristic
233C2×C22⋊Dic17C2311yescharacteristic
234C2×C22⋊Dic17C2311yescharacteristic
235C2×C22⋊Dic17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237#10587633C2×C418yescomplemented
238#10587632C2×C418yescomplemented
239Q8×Dic17—42no—
240#10587625C2×C418yescomplemented
241#10587623C2×C418yescomplemented
242D4×Dic17—42no—
243C4×C22⋊D17—42no—
244C4×C22⋊D17—42no—
245C2×#63227—42no—
246C2×#63227C2311yescharacteristic
247C2×#63227C2311yescharacteristic
248C2×#63227C2311yescharacteristic
249C2×#63227C2311yescharacteristic
250C2×#63227C2311yescharacteristic
251C2×#63227C2311yescharacteristic
252C2×#63227C2311yescharacteristic
253C2×#63227C2311yescharacteristic
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
275C2×C4⋊Dic17C2311yescharacteristic
276C2×C4⋊Dic17C2311yescharacteristic
277C2×C4⋊Dic17C2311yescharacteristic
278C2×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×#63225—42no—
283C2×#63225C2311yescharacteristic
284C2×#63225C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×#63225C2311yescharacteristic
298C2×#63225C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314#10587572C2×C418yescomplemented
315#10587570C2×C418yescomplemented
316#10587570C2×C418yescomplemented
317#10587569C2×C418yescomplemented
318#10587568C2×C418yescomplemented
319#10587567—42no—
320#10587567C2×C418yescomplemented
321C22⋊C4×D17—42no—
322C22⋊C4×D17C2×C418yescomplemented
323#10587565C2×C418yescomplemented
324#10587562C2×C418yescomplemented
325C4×D68—42no—
326C4×D68C2×C418yescomplemented
327#10587558—42no—
328#10587558—42no—
329C42×D17—42no—
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
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
370C24×C17C2411yescharacteristic
371C24×C17C2411yescharacteristic
372C23×D17—41no—
373C23×D17—41no—
374C23×D17—41no—
375C23×D17—41no—
376C23×D17—41no—
377C23×D17—41no—
378C23×D17C22×C414yes—
379C23×D17C2411yescharacteristic
380C23×D17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C2×Q8×C17—41no—
383C2×Q8×C17—41no—
384C2×Q8×C17C22×C414yes—
385C2×D4×C17—41no—
386C2×D4×C17—41no—
387C2×D4×C17C22×C414yes—
388C22×C4×C17—22no—
389C22×C4×C17—41no—
390C22×C4×C17—41no—
391C22×C4×C17—41no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17C2411yescharacteristic
395C22×C4×C17C2411yescharacteristic
396C22×C4×C17C2411yescharacteristic
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C2×C22⋊D17—41no—
408C2×C22⋊D17—41no—
409C2×C22⋊D17—41no—
410C2×C22⋊D17—41no—
411C2×C22⋊D17—41no—
412C2×C22⋊D17—41no—
413C2×C22⋊D17—41no—
414C2×C22⋊D17—41no—
415C2×C22⋊D17C22×C414yes—
416C2×C22⋊D17C22×C414yes—
417C2×C22⋊D17C22×C414yes—
418C2×C22⋊D17C22×C414yes—
419C22×Dic17—22no—
420C22×Dic17—41no—
421C22×Dic17—41no—
422C22×Dic17—41no—
423C22×Dic17—41no—
424C22×Dic17—41no—
425C22×Dic17—41no—
426C22×Dic17—41no—
427C22×Dic17C22×C414yes—
428C22×Dic17C2411yescharacteristic
429C22×Dic17C2411yescharacteristic
430C22×Dic17C2411yescharacteristic
431C22×Dic17C2411yescharacteristic
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C2×D68—41no—
442C2×D68—41no—
443C2×D68—41no—
444C2×D68—41no—
445C2×D68C22×C414yes—
446C2×D68C22×C414yes—
447C2×C4×D17—22no—
448C2×C4×D17—22no—
449C2×C4×D17—22no—
450C2×C4×D17—41no—
451C2×C4×D17—41no—
452C2×C4×D17—41no—
453C2×C4×D17—41no—
454C2×C4×D17—41no—
455C2×C4×D17—41no—
456C2×C4×D17—41no—
457C2×C4×D17—41no—
458C2×C4×D17—41no—
459C2×C4×D17—41no—
460C2×C4×D17—41no—
461C2×C4×D17—41no—
462C2×C4×D17—41no—
463C2×C4×D17—41no—
464C2×C4×D17—41no—
465C2×C4×D17C22×C414yes—
466C2×C4×D17C22×C414yes—
467C2×C4×D17C22×C414yes—
468C4⋊C4×C17—41no—
469C4⋊C4×C17—41no—
470C22⋊C4×C17—22no—
471C22⋊C4×C17—41no—
472C22⋊C4×C17—41no—
473C22⋊C4×C17—41no—
474C22⋊C4×C17—41no—
475C22⋊C4×C17—41no—
476C22⋊C4×C17C22×C414yes—
477C22⋊C4×C17C22×C414yes—
478C22⋊C4×C17C22×C414yes—
479C22⋊C4×C17C22×C414yes—
480C42×C17—22no—
481C42×C17—41no—
482C42×C17—41no—
483C42×C17—41no—
484C42×C17—41no—
485C42×C17—41no—
486C42×C17C22×C414yes—
487C22⋊Dic17—22no—
488C22⋊Dic17—41no—
489C22⋊Dic17—41no—
490C22⋊Dic17—41no—
491C22⋊Dic17—41no—
492C22⋊Dic17—41no—
493C22⋊Dic17C22×C414yes—
494C22⋊Dic17C22×C414yes—
495#63227—22no—
496#63227—22no—
497#63227—22no—
498#63227—41no—
499#63227—41no—
500#63227—41no—
501#63227—41no—
502#63227—41no—
503#63227—41no—
504#63227—41no—
505#63227—41no—
506#63227—41no—
507#63227—41no—
508#63227—41no—
509#63227—41no—
510#63227—41no—
511#63227—41no—
512#63227—41no—
513#63227—41no—
514#63227—41no—
515#63227C22×C414yes—
516#63227C22×C414yes—
517#63227C22×C414yes—
518#63227C22×C414yes—
519#63227C22×C414yes—
520#63227C22×C414yes—
521#63227C22×C414yes—
522#63227C22×C414yes—
523C4⋊Dic17—22no—
524C4⋊Dic17—22no—
525C4⋊Dic17—41no—
526C4⋊Dic17—41no—
527C4⋊Dic17—41no—
528C4⋊Dic17—41no—
529C4⋊Dic17C22×C414yes—
530C4⋊Dic17C22×C414yes—
531#63225—22no—
532#63225—22no—
533#63225—22no—
534#63225—41no—
535#63225—41no—
536#63225—41no—
537#63225—41no—
538#63225—41no—
539#63225—41no—
540#63225—41no—
541#63225—41no—
542#63225—41no—
543#63225C22×C414yes—
544#63225C22×C414yes—
545#63225C22×C414yes—
546#63225C22×C414yes—
547C4×Dic17—22no—
548C4×Dic17—22no—
549C4×Dic17—41no—
550C4×Dic17—41no—
551C4×Dic17—41no—
552C4×Dic17—41no—
553C4×Dic17—41no—
554C4×Dic17—41no—
555C4×Dic17—41no—
556C4×Dic17—41no—
557C4×Dic17—41no—
558C4×Dic17—41no—
559C4×Dic17—41no—
560C4×Dic17—41no—
561C4×Dic17C22×C414yes—
562#34441—171nomaximal, Sylow
563C23×C17—21no—
564C23×C17—21no—
565C23×C17—21no—
566C23×C17—21no—
567C23×C17—21no—
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17—21no—
573C23×C17—21no—
574C23×C17—21no—
575C23×C17C23×C412yes—
576C23×C17C23×C412yes—
577C23×C17C2511yescharacteristic
578C22×D17—21no—
579C22×D17—21no—
580C22×D17—21no—
581C22×D17—21no—
582C22×D17—21no—
583C22×D17—21no—
584C22×D17—21no—
585C22×D17—21no—
586C22×D17—21no—
587C22×D17—21no—
588C22×D17—21no—
589C22×D17—21no—
590C22×D17—21no—
591C22×D17—21no—
592C22×D17—21no—
593C22×D17—21no—
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—44no—
597C22×D17—44no—
598C22×D17—44no—
599C22×D17—82no—
600C22×D17—82no—
601C22×D17—82no—
602C22×D17—82no—
603C22×D17C23×C412yes—
604C22×D17C23×C412yes—
605C22×D17C23×C412yes—
606Q8×C17—44no—
607D4×C17—44no—
608C2×C4×C17—21no—
609C2×C4×C17—21no—
610C2×C4×C17—21no—
611C2×C4×C17—21no—
612C2×C4×C17—21no—
613C2×C4×C17—21no—
614C2×C4×C17—21no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
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—82no—
642C2×C4×C17—82no—
643C2×C4×C17C23×C412yes—
644C2×C4×C17C23×C412yes—
645C2×C4×C17C23×C412yes—
646C2×C4×C17C23×C412yes—
647C2×C4×C17C23×C412yes—
648C2×C4×C17H(5,𝔽2)12yes—
649C22⋊D17—44no—
650C22⋊D17—44no—
651C22⋊D17—44no—
652C22⋊D17—44no—
653C2×Dic17—21no—
654C2×Dic17—21no—
655C2×Dic17—21no—
656C2×Dic17—21no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—21no—
662C2×Dic17—21no—
663C2×Dic17—21no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
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—44no—
687C2×Dic17—82no—
688C2×Dic17—82no—
689C2×Dic17C23×C412yes—
690C2×Dic17C23×C412yes—
691C2×Dic17C23×C412yes—
692C2×Dic17C23×C412yes—
693C2×Dic17C23×C412yes—
694C2×Dic17H(5,𝔽2)12yes—
695D68—44no—
696D68—44no—
697C4×D17—44no—
698C4×D17—44no—
699C4×D17—44no—
700C4×D17—44no—
701C4×D17—44no—
702C4×D17—82no—
703C4×D17—82no—
704C2×#538—171no—
705#2379—171no—
706#2377—171no—
707#2377—171no—
708#2375—171no—
709#2373—171no—
710#2373—171no—
711#2372D1711yescharacteristic, complemented
712#2367—171no—
713#2367—171no—
714#2363—171no—
715#2361—171no—
716#2358—171no—
717#2357—171no—
718#2352—171no—
719#2342—171no—
720#2342—171no—
721#2335—171no—
722#2335—171no—
723#2334—171no—
724#2334—171no—
725#2333—171no—
726#2332—171no—
727#2323—171no—
728#2322—171no—
729#2321—171no—
730#2321—171no—
731#2319—171no—
732C4×#123—171no—
733C4×#121—171no—
734#2290—171no—
735C22×C17—22no—
736C22×C17—22no—
737C22×C17—22no—
738C22×C17—22no—
739C22×C17—22no—
740C22×C17—22no—
741C22×C17—41no—
742C22×C17—41no—
743C22×C17—41no—
744C22×C17—41no—
745C22×C17—41no—
746C22×C17—41no—
747C22×C17—41no—
748C22×C17—41no—
749C22×C17C24×C411yescharacteristic
750C22×C17C2×H(5,𝔽2)11yescharacteristic
751C22×C17C2×H(5,𝔽2)11yescharacteristic
752C22×C17#58511yescharacteristic
753C22×C17#58511yescharacteristic
754C22×C17#58511yescharacteristic
755C22×C17#58511yescharacteristic
756C2×D17—22no—
757C2×D17—22no—
758C2×D17—22no—
759C2×D17—22no—
760C2×D17—22no—
761C2×D17—22no—
762C2×D17—22no—
763C2×D17—22no—
764C2×D17—22no—
765C2×D17—41no—
766C2×D17—41no—
767C2×D17—41no—
768C2×D17—41no—
769C2×D17—41no—
770C2×D17—41no—
771C2×D17—41no—
772C2×D17—41no—
773C2×D17—41no—
774C2×D17—41no—
775C2×D17—41no—
776C2×D17—41no—
777C2×D17—88no—
778C4×C17—22no—
779C4×C17—22no—
780C4×C17—22no—
781C4×C17—22no—
782C4×C17—22no—
783C4×C17—22no—
784C4×C17—41no—
785C4×C17—41no—
786C4×C17—41no—
787C4×C17—41no—
788C4×C17—41no—
789C4×C17—41no—
790C4×C17—41no—
791Dic17—22no—
792Dic17—22no—
793Dic17—22no—
794Dic17—22no—
795Dic17—22no—
796Dic17—22no—
797Dic17—41no—
798Dic17—41no—
799Dic17—41no—
800Dic17—41no—
801Dic17—41no—
802Dic17—41no—
803Dic17—41no—
804#538—1716no—
805C2×#126—171no—
806C2×#126—171no—
807C2×#124—171no—
808C2×#124C2×D1711yescharacteristic
809C2×#123—171no—
810C2×#123—171no—
811C2×C22⋊Q8—171no—
812C2×#121—171no—
813C2×#121—171no—
814C2×#121—171no—
815C2×#120—171no—
816C2×#120—171no—
817C2×C4×Q8—171no—
818C2×C4×D4—171no—
819C2×C4×D4—171no—
820C2×C4×D4—171no—
821C2×C4×D4—171no—
822C2×C4×D4—171no—
823C2×C4×D4—171no—
824C2×C4×D4—171no—
825C2×#117—171no—
826C2×#117—171no—
827C22×C4⋊C4—171no—
828C22×C22⋊C4—171no—
829C22×C22⋊C4—171no—
830C22×C22⋊C4—171no—
831C22×C42—171no—
832#391—171no—
833#391C2×D1711yescharacteristic, complemented
834#391C2×D1711yescharacteristic, complemented
835#390—171no—
836#390—171no—
837#390—171no—
838#390—171no—
839#390—171no—
840#390—171no—
841#390—171no—
842#390—171no—
843#390—171no—
844#389—171no—
845#389—171no—
846#389—171no—
847#389—171no—
848#389—171no—
849#389—171no—
850#388—171no—
851#388—171no—
852#388—171no—
853#388—171no—
854#388—171no—
855#388—171no—
856#388—171no—
857#388—171no—
858#388—171no—
859#388—171no—
860#388—171no—
861#388—171no—
862#388—171no—
863#388—171no—
864#388—171no—
865#388—171no—
866#388—171no—
867#388—171no—
868#388—171no—
869#388—171no—
870#388—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388—171no—
878#388C2×D1711yescharacteristic
879#388C2×D1711yescharacteristic
880#388C2×D1711yescharacteristic, complemented
881#388C2×D1711yescharacteristic, complemented
882#387—171no—
883#387—171no—
884#387—171no—
885#387—171no—
886#387—171no—
887#387—171no—
888#387—171no—
889#387—171no—
890#387—171no—
891#387—171no—
892#387—171no—
893#387—171no—
894#386—171no—
895#386—171no—
896#386—171no—
897#386—171no—
898#386—171no—
899#386—171no—
900#386—171no—
901#386—171no—
902#386—171no—
903#386—171no—
904#386—171no—
905#386—171no—
906#386C2×D1711yescharacteristic
907#386C2×D1711yescharacteristic
908#385—171no—
909#385—171no—
910#385—171no—
911#385—171no—
912#385—171no—
913#385—171no—
914#385—171no—
915#385—171no—
916#385—171no—
917#385—171no—
918#385—171no—
919#385—171no—
920#382—171no—
921#382—171no—
922#381—171no—
923#381—171no—
924#381—171no—
925#381—171no—
926#380—171no—
927#380—171no—
928#380—171no—
929#380—171no—
930#379—171no—
931#379—171no—
932C4×C4⋊C4—171no—
933C4×C4⋊C4—171no—
934C4×C4⋊C4—171no—
935C4×C4⋊C4—171no—
936C4×C4⋊C4—171no—
937C4×C4⋊C4—171no—
938C4×C4⋊C4—171no—
939C4×C4⋊C4—171no—
940C4×C4⋊C4—171no—
941C4×C4⋊C4—171no—
942C4×C22⋊C4—171no—
943C4×C22⋊C4—171no—
944C4×C22⋊C4—171no—
945C4×C22⋊C4—171no—
946C4×C22⋊C4—171no—
947C4×C22⋊C4—171no—
948C4×C22⋊C4—171no—
949C4×C22⋊C4—171no—
950C4×C22⋊C4—171no—
951C4×C22⋊C4—171no—
952C4×C22⋊C4—171no—
953C4×C22⋊C4—171no—
954C4×C22⋊C4C2×D1711yescharacteristic
955C4×C22⋊C4C2×D1711yescharacteristic
956C4×C22⋊C4C2×D1711yescharacteristic, complemented
957C4×C22⋊C4C2×D1711yescharacteristic, complemented
958#376C2×D1711yescharacteristic, complemented
959#376C2×D1711yescharacteristic, complemented
960C2×C17—42no—
961C2×C17—42no—
962C2×C17#342811yescharacteristic
963C2×C17C4×H(5,𝔽2)11yescharacteristic
964C2×C17C4×H(5,𝔽2)11yescharacteristic
965C2×C17#353411yescharacteristic
966C2×C17#354011yescharacteristic
967C2×C17#356211yescharacteristic
968C2×C17#356611yescharacteristic
969D17—42no—
970D17—42no—
971D17—42no—
972C25—171no—
973C22×Q8C22×D1711yescharacteristic
974C22×D4—171no—
975C22×D4—171no—
976C22×D4—171no—
977C22×D4—171no—
978C22×D4—171no—
979C22×D4—171no—
980C22×D4C22×D1711yescharacteristic
981C23×C4—171no—
982C23×C4—171no—
983C23×C4—171no—
984C23×C4—171no—
985C23×C4—171no—
986C23×C4—171no—
987C23×C4—171no—
988C23×C4—171no—
989C23×C4—171no—
990C23×C4—171no—
991C23×C4C22×D1711yescharacteristic
992C23×C4C22×D1711yescharacteristic
993#126—178no—
994#126—178no—
995#124—178no—
996#124C4×D1718yescomplemented
997#123—178no—
998#123—178no—
999C22⋊Q8—178no—
1000#121—178no—
1001#121—178no—
1002#121—178no—
1003#120—178no—
1004#120—178no—
1005C4×Q8—682no—
1006C4×D4—178no—
1007C4×D4—178no—
1008C4×D4—682no—
1009C4×D4—682no—
1010C4×D4—682no—
1011C4×D4—682no—
1012C4×D4—682no—
1013#117—682no—
1014#117—682no—
1015C2×C4⋊C4—171no—
1016C2×C4⋊C4—171no—
1017C2×C4⋊C4—171no—
1018C2×C4⋊C4—171no—
1019C2×C4⋊C4—171no—
1020C2×C4⋊C4—171no—
1021C2×C4⋊C4—171no—
1022C2×C4⋊C4—171no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—171no—
1031C2×C4⋊C4—171no—
1032C2×C4⋊C4—171no—
1033C2×C4⋊C4—171no—
1034C2×C4⋊C4—171no—
1035C2×C4⋊C4—171no—
1036C2×C4⋊C4—171no—
1037C2×C4⋊C4—171no—
1038C2×C4⋊C4—171no—
1039C2×C4⋊C4—682no—
1040C2×C4⋊C4C22×D1711yescharacteristic
1041C2×C4⋊C4C22×D1711yescharacteristic
1042C2×C22⋊C4—171no—
1043C2×C22⋊C4—171no—
1044C2×C22⋊C4—171no—
1045C2×C22⋊C4—171no—
1046C2×C22⋊C4—171no—
1047C2×C22⋊C4—171no—
1048C2×C22⋊C4—171no—
1049C2×C22⋊C4—171no—
1050C2×C22⋊C4—171no—
1051C2×C22⋊C4—171no—
1052C2×C22⋊C4—178no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—171no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4—171no—
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—171no—
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—682no—
1080C2×C22⋊C4—682no—
1081C2×C22⋊C4C22×D1711yescharacteristic
1082C2×C22⋊C4C22×D1711yescharacteristic
1083C2×C22⋊C4C22×D1711yescharacteristic
1084C2×C22⋊C4C22×D1711yescharacteristic
1085C2×C22⋊C4C22×D1711yescharacteristic
1086C2×C22⋊C4C22×D1711yescharacteristic
1087C2×C22⋊C4C22×D1711yescharacteristic
1088C2×C22⋊C4C22×D1711yescharacteristic
1089C2×C22⋊C4C22×D1711yescharacteristic
1090C2×C22⋊C4C22×D1711yescharacteristic
1091C2×C42—171no—
1092C2×C42—171no—
1093C2×C42—171no—
1094C2×C42—171no—
1095C2×C42—171no—
1096C2×C42—171no—
1097C2×C42—171no—
1098C2×C42—171no—
1099C2×C42—171no—
1100C2×C42—171no—
1101C2×C42—171no—
1102C2×C42—171no—
1103C2×C42—171no—
1104C2×C42—171no—
1105C2×C42—171no—
1106C2×C42—682no—
1107C2×C42C22×D1711yescharacteristic
1108C2×C42C22×D1711yescharacteristic
1109C2×C42C22×D1711yescharacteristic
1110C2×C42C22×D1711yescharacteristic
1111C2×C42C22×D1711yescharacteristic
1112C2×C42C22×D1711yescharacteristic
1113C2×C42C22×D1711yescharacteristic
1114#95—171no—
1115#95—171no—
1116#95—171no—
1117#95—171no—
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95C22×D1711yescharacteristic
1143#95C22×D1711yescharacteristic
1144#95C22×D1711yescharacteristic
1145#95C22×D1711yescharacteristic
1146#95C22×D1711yescharacteristic
1147#95C22×D1711yescharacteristic
1148#95C22×D1711yescharacteristic
1149#95C22×D1711yescharacteristic
1150#95C22×D1711yescharacteristic
1151#95C22×D1711yescharacteristic
1152#95C22×D1711yescharacteristic
1153#95C22×D1711yescharacteristic
1154C17#3444111yescharacteristic, complemented, Sylow
1155C24—171no—
1156C24—171no—
1157C24—171no—
1158C24—174no—
1159C24—681no—
1160C24—681no—
1161C24—681no—
1162C24—681no—
1163C24—681no—
1164C24—681no—
1165C24C23×D1711yescharacteristic
1166C24C23×D1711yescharacteristic
1167C2×Q8—41no—
1168C2×Q8—41no—
1169C2×Q8C2×C4×D1714yes—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—174no—
1173C2×D4—174no—
1174C2×D4—174no—
1175C2×D4—174no—
1176C2×D4—174no—
1177C2×D4—174no—
1178C2×D4—681no—
1179C2×D4—681no—
1180C2×D4—681no—
1181C2×D4—681no—
1182C2×D4—681no—
1183C2×D4—681no—
1184C2×D4—681no—
1185C2×D4—681no—
1186C2×D4—681no—
1187C2×D4—681no—
1188C2×D4—681no—
1189C2×D4—681no—
1190C2×D4C2×C4×D1714yes—
1191C22×C4—22no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—171no—
1198C22×C4—171no—
1199C22×C4—171no—
1200C22×C4—171no—
1201C22×C4—171no—
1202C22×C4—171no—
1203C22×C4—174no—
1204C22×C4—174no—
1205C22×C4—174no—
1206C22×C4—174no—
1207C22×C4—171no—
1208C22×C4—171no—
1209C22×C4—171no—
1210C22×C4—171no—
1211C22×C4—171no—
1212C22×C4—171no—
1213C22×C4—171no—
1214C22×C4—342no—
1215C22×C4—342no—
1216C22×C4—342no—
1217C22×C4—342no—
1218C22×C4—681no—
1219C22×C4—681no—
1220C22×C4—681no—
1221C22×C4—681no—
1222C22×C4—681no—
1223C22×C4—681no—
1224C22×C4—681no—
1225C22×C4—681no—
1226C22×C4—681no—
1227C22×C4—681no—
1228C22×C4—681no—
1229C22×C4—681no—
1230C22×C4—681no—
1231C22×C4—681no—
1232C22×C4—681no—
1233C22×C4—681no—
1234C22×C4—681no—
1235C22×C4—681no—
1236C22×C4—681no—
1237C22×C4—681no—
1238C22×C4—681no—
1239C22×C4—681no—
1240C22×C4C23×D1711yescharacteristic
1241C22×C4C23×D1711yescharacteristic
1242C22×C4C23×D1711yescharacteristic
1243C22×C4C23×D1711yescharacteristic
1244C22×C4C23×D1711yescharacteristic
1245C22×C4C23×D1711yescharacteristic
1246C22×C4C23×D1711yescharacteristic
1247C22×C4C23×D1711yescharacteristic
1248C22×C4C23×D1711yescharacteristic
1249C22×C4C23×D1711yescharacteristic
1250C22×C4C23×D1711yescharacteristic
1251C22×C4C23×D1711yescharacteristic
1252C22×C4C23×D1711yescharacteristic
1253C4⋊C4—41no—
1254C4⋊C4—41no—
1255C4⋊C4—174no—
1256C4⋊C4—174no—
1257C4⋊C4—174no—
1258C4⋊C4—174no—
1259C4⋊C4—174no—
1260C4⋊C4—174no—
1261C4⋊C4—342no—
1262C4⋊C4—342no—
1263C4⋊C4—342no—
1264C4⋊C4—342no—
1265C4⋊C4—342no—
1266C4⋊C4—681no—
1267C4⋊C4—681no—
1268C4⋊C4—681no—
1269C4⋊C4—681no—
1270C4⋊C4—681no—
1271C4⋊C4—681no—
1272C4⋊C4—681no—
1273C4⋊C4—681no—
1274C4⋊C4—681no—
1275C4⋊C4—681no—
1276C4⋊C4—681no—
1277C4⋊C4—681no—
1278C4⋊C4—681no—
1279C22⋊C4—22no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—174no—
1286C22⋊C4—174no—
1287C22⋊C4—174no—
1288C22⋊C4—174no—
1289C22⋊C4—174no—
1290C22⋊C4—174no—
1291C22⋊C4—174no—
1292C22⋊C4—174no—
1293C22⋊C4—174no—
1294C22⋊C4—174no—
1295C22⋊C4—342no—
1296C22⋊C4—342no—
1297C22⋊C4—342no—
1298C22⋊C4—342no—
1299C22⋊C4—681no—
1300C22⋊C4—681no—
1301C22⋊C4—681no—
1302C22⋊C4—681no—
1303C22⋊C4—681no—
1304C22⋊C4—681no—
1305C22⋊C4—681no—
1306C22⋊C4—681no—
1307C22⋊C4—681no—
1308C22⋊C4—681no—
1309C22⋊C4—681no—
1310C22⋊C4—681no—
1311C22⋊C4—681no—
1312C22⋊C4—681no—
1313C22⋊C4—681no—
1314C22⋊C4—681no—
1315C22⋊C4—681no—
1316C22⋊C4—681no—
1317C22⋊C4—681no—
1318C22⋊C4—681no—
1319C22⋊C4—681no—
1320C22⋊C4—681no—
1321C22⋊C4C2×C4×D1714yes—
1322C22⋊C4C2×C4×D1714yes—
1323C22⋊C4C2×C4×D1714yes—
1324C22⋊C4C2×C4×D1714yes—
1325C42—22no—
1326C42—41no—
1327C42—41no—
1328C42—41no—
1329C42—41no—
1330C42—41no—
1331C42—174no—
1332C42—342no—
1333C42—342no—
1334C42—681no—
1335C42—681no—
1336C42—681no—
1337C42—681no—
1338C42—681no—
1339C42—681no—
1340C42—681no—
1341C42—681no—
1342C42—681no—
1343C42—681no—
1344C42—681no—
1345C42—681no—
1346C42C2×C4×D1714yes—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—172no—
1360C23—172no—
1361C23—172no—
1362C23—341no—
1363C23—341no—
1364C23—341no—
1365C23—341no—
1366C23—341no—
1367C23—341no—
1368C23—341no—
1369C23—341no—
1370C23—341no—
1371C23—341no—
1372C23—341no—
1373C23—341no—
1374C23—341no—
1375C23—341no—
1376C23—341no—
1377C23—341no—
1378C23—341no—
1379C23—341no—
1380C23—684no—
1381C23—684no—
1382C23—684no—
1383C23—1362no—
1384C23—1362no—
1385C23—1362no—
1386C23—1362no—
1387C23C22×C4×D1712yes—
1388C23C22×C4×D1712yes—
1389C23C24×D1711yescharacteristic
1390Q8—44no—
1391D4—44no—
1392D4—684no—
1393D4—684no—
1394D4—684no—
1395D4—684no—
1396D4—684no—
1397D4—684no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—82no—
1432C2×C4—82no—
1433C2×C4—172no—
1434C2×C4—172no—
1435C2×C4—172no—
1436C2×C4—172no—
1437C2×C4—172no—
1438C2×C4—172no—
1439C2×C4—341no—
1440C2×C4—341no—
1441C2×C4—341no—
1442C2×C4—341no—
1443C2×C4—341no—
1444C2×C4—341no—
1445C2×C4—341no—
1446C2×C4—341no—
1447C2×C4—341no—
1448C2×C4—341no—
1449C2×C4—341no—
1450C2×C4—341no—
1451C2×C4—341no—
1452C2×C4—341no—
1453C2×C4—341no—
1454C2×C4—341no—
1455C2×C4—341no—
1456C2×C4—341no—
1457C2×C4—341no—
1458C2×C4—341no—
1459C2×C4—341no—
1460C2×C4—341no—
1461C2×C4—341no—
1462C2×C4—341no—
1463C2×C4—341no—
1464C2×C4—341no—
1465C2×C4—341no—
1466C2×C4—341no—
1467C2×C4—341no—
1468C2×C4—341no—
1469C2×C4—341no—
1470C2×C4—341no—
1471C2×C4—341no—
1472C2×C4—684no—
1473C2×C4—684no—
1474C2×C4—684no—
1475C2×C4—684no—
1476C2×C4—684no—
1477C2×C4—684no—
1478C2×C4—1362no—
1479C2×C4—1362no—
1480C2×C4—1362no—
1481C2×C4—1362no—
1482C2×C4C22×C4×D1712yes—
1483C2×C4C22×C4×D1712yes—
1484C2×C4C22×C4×D1712yes—
1485C2×C4C22×C4×D1712yes—
1486C2×C4C22×C4×D1712yes—
1487C2×C4#1058769612yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—41no—
1495C22—41no—
1496C22—41no—
1497C22—41no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—342no—
1503C22—342no—
1504C22—342no—
1505C22—342no—
1506C22—342no—
1507C22—342no—
1508C22—342no—
1509C22—342no—
1510C22—342no—
1511C22—681no—
1512C22—681no—
1513C22—681no—
1514C22—681no—
1515C22—681no—
1516C22—681no—
1517C22—681no—
1518C22—681no—
1519C22—681no—
1520C22—681no—
1521C22—681no—
1522C22—681no—
1523C22—1368no—
1524C22C23×C4×D1711yescharacteristic
1525C22H(5,𝔽2)×D1711yescharacteristic
1526C22C2×#1058769611yescharacteristic
1527C22#1176364411yescharacteristic
1528C22#1176364511yescharacteristic
1529C22#1176364511yescharacteristic
1530C22#1176364511yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—22no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—41no—
1544C4—342no—
1545C4—342no—
1546C4—342no—
1547C4—342no—
1548C4—342no—
1549C4—342no—
1550C4—681no—
1551C4—681no—
1552C4—681no—
1553C4—681no—
1554C4—681no—
1555C4—681no—
1556C4—681no—
1557C2—42no—
1558C2—42no—
1559C2—682no—
1560C2—682no—
1561C2—682no—
1562C2#1454198311yescharacteristic
1563C2#1454198811yescharacteristic
1564C2C4×#1058769611yescharacteristic
1565C2#1454297711yescharacteristic
1566C2#1454305411yescharacteristic
1567C2#1454336511yescharacteristic
1568C2#1454343811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2372C2
socle, cosocleC23×C17C25
prime radicalC2×#11763393C2
hypercenter#2372D17
hypocenterC17#34441
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2372

Complements

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

NH ≅ G/Ntype
2. #14531956C2semidirect
3. #14531942C2semidirect
4. #14531937C2semidirect
5. #14531924C2semidirect
6. #14531904C2semidirect
7. #14531904C2semidirect
8. #14531860C2semidirect
9. #14531859C2semidirect
10. #14531823C2semidirect
11. #14531795C2semidirect
12. #14531766C2semidirect
13. #14531754C2semidirect
14. #14531707C2semidirect
15. #14531628C2semidirect
16. #14531627C2semidirect
17. #14531576C2semidirect
18. #14531567C2semidirect
19. #14531561C2semidirect
20. #14531556C2semidirect
21. #14531547C2semidirect
22. #14531539C2semidirect
23. #14531469C2semidirect
24. #14531455C2semidirect
25. #14531447C2semidirect
26. #14531440C2semidirect
27. #14531428C2semidirect
28. #14531311C2semidirect
29. C4×#10587570C2semidirect
30. #14531228C2semidirect
31. C17×#2372C2semidirect
32. #11763393C4semidirect
44. C2×Q8×Dic17C22semidirect
49. C2×C4×C22⋊D17C22semidirect
54. C22×#63225C22semidirect
58. C2×C42×D17C22semidirect
59. #11762716C22semidirect
68. #11762709C22semidirect
69. #11762707C22semidirect
70. #11762707C22semidirect
71. #11762707C22semidirect
72. #11762706C22semidirect
73. #11762706C22semidirect
74. #11762706C22semidirect
78. #11762702C22semidirect
79. #11762702C22semidirect
85. #11762701C22semidirect
90. #11762700C22semidirect
98. #11762698C22semidirect
99. #11762698C22semidirect
103. #11762696C22semidirect
104. #11762696C22semidirect
105. #11762694C22semidirect
106. #11762694C22semidirect
107. #11762694C22semidirect
108. #11762693C22semidirect
109. #11762693C22semidirect
110. #11762692C22semidirect
111. #11762691C22semidirect
112. #11762691C22semidirect
113. #11762691C22semidirect
114. #11762690C22semidirect
123. #11762686C22semidirect
126. #11762685C22semidirect
128. #11762684C22semidirect
132. #11762683C22semidirect
133. #11762683C22semidirect
138. #11762680C22semidirect
139. #11762673C22semidirect
140. #11762673C22semidirect
143. #11762671C22semidirect
144. #11762670C22semidirect
146. #11762668C22semidirect
147. #11762667C22semidirect
151. C4⋊C4×Dic17C22semidirect
152. C4⋊C4×Dic17C22semidirect
153. C4×#63225C22semidirect
154. C4×#63225C22semidirect
155. C4×#63225C22semidirect
156. C4×#63225C22semidirect
157. C4×C4⋊Dic17C22semidirect
158. C4×C4⋊Dic17C22semidirect
159. #11762660C22semidirect
160. #11762660C22semidirect
163. C22⋊C4×Dic17C22semidirect
164. C22⋊C4×Dic17C22semidirect
168. C4×#63227C22semidirect
172. #11762656C22semidirect
174. C17×#391C22semidirect
175. C17×#391C22semidirect
178. C17×#388C22semidirect
179. C17×#388C22semidirect
184. C4×C22⋊C4×C17C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C17×#376C22semidirect
187. C17×#376C22semidirect
209. C17×#124C2×C4semidirect
237. #10587633C2×C4semidirect
238. #10587632C2×C4semidirect
240. #10587625C2×C4semidirect
241. #10587623C2×C4semidirect
314. #10587572C2×C4semidirect
315. #10587570C2×C4semidirect
316. #10587570C2×C4semidirect
317. #10587569C2×C4semidirect
318. #10587568C2×C4semidirect
320. #10587567C2×C4semidirect
322. C22⋊C4×D17C2×C4semidirect
323. #10587565C2×C4semidirect
324. #10587562C2×C4semidirect
326. C4×D68C2×C4semidirect
711. #2372D17semidirect
833. #391C2×D17semidirect
834. #391C2×D17semidirect
880. #388C2×D17semidirect
881. #388C2×D17semidirect
956. C4×C22⋊C4C2×D17semidirect
957. C4×C22⋊C4C2×D17semidirect
958. #376C2×D17semidirect
959. #376C2×D17semidirect
996. #124C4×D17semidirect
1154. C17#34441semidirect

Maximal subgroups

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

subgroupindex
C2×#117633932
#145319562
#145319422
#145319372
#145319242
#145319042
#145318602
#145318592
#145318232
#145317952
#145317662
#145317542
#145317072
#145316282
#145316272
#145315762
#145315672
#145315612
#145315562
#145315472
#145315392
#145314692
#145314552
#145314472
#145314402
#145314282
#145313112
C4×#105875702
#145312282
C17×#23722
#3444117