Finite Group Databasebeta

← #17198058

Subgroups — #17198058

Order 4352.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763392C211yesmaximal, characteristic
2#14531977C211yesmaximal, characteristic, complemented
3#14531975C211yesmaximal, characteristic, complemented
4#14531940C211yesmaximal, characteristic, complemented
5#14531938C211yesmaximal, characteristic, complemented
6#14531907C211yesmaximal, characteristic, complemented
7#14531900C211yesmaximal, characteristic, complemented
8#14531803C211yesmaximal, characteristic, complemented
9#14531800C211yesmaximal, characteristic, complemented
10#14531761C211yesmaximal, characteristic, complemented
11#14531761C211yesmaximal, characteristic, complemented
12#14531760C211yesmaximal, characteristic, complemented
13#14531760C211yesmaximal, characteristic, complemented
14#14531726C211yesmaximal, characteristic, complemented
15#14531724C211yesmaximal, characteristic, complemented
16C4⋊C4×C22⋊D17C211yesmaximal, characteristic, complemented
17#14531598C211yesmaximal, characteristic, complemented
18#14531597C211yesmaximal, characteristic, complemented
19#14531577C211yesmaximal, characteristic, complemented
20#14531570C211yesmaximal, characteristic, complemented
21#14531515C211yesmaximal, characteristic, complemented
22#14531492C211yesmaximal, characteristic, complemented
23#14531490C211yesmaximal, characteristic, complemented
24#14531482C211yesmaximal, characteristic, complemented
25#14531453C211yesmaximal, characteristic, complemented
26#14531448C211yesmaximal, characteristic, complemented
27#14531397C211yesmaximal, characteristic, complemented
28#14531316C211yesmaximal, characteristic, complemented
29C4×#10587625C211yesmaximal, characteristic, complemented
30C2×#11762699C211yesmaximal, characteristic, complemented
31D4×C4⋊C4×C17C211yesmaximal, characteristic, complemented
32#11763392C4116yescomplemented
33C2×#10587584C2211yescharacteristic
34C2×#10587562C2211yescharacteristic
35C2×#10587561C2211yescharacteristic
36C2×#10587571C2211yescharacteristic
37C2×#10587580C2211yescharacteristic
38C2×#10587615C2211yescharacteristic
39C2×#10587564C2211yescharacteristic
40C2×#10587616C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587568C2211yescharacteristic
44C2×#10587623C2211yescharacteristic
45C2×#10587573C2211yescharacteristic, complemented
46C2×#10587579C2211yescharacteristic
47C2×#10587579C2211yescharacteristic
48C2×C4×C22⋊D17C2211yescharacteristic
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×C4×C22⋊D17C2211yescharacteristic
53C2×C4×C22⋊D17C2211yescharacteristic, complemented
54C2×C4⋊C4×D17C2211yescharacteristic, complemented
55C22×#63227C2211yescharacteristic
56C22×#63227C2211yescharacteristic
57C22×#63227C2211yescharacteristic
58C2×C22⋊C4×D17C2211yescharacteristic
59C2×C22⋊C4×D17C2211yescharacteristic
60C22×C4×Dic17C2211yescharacteristic
61#11762714C2211yescharacteristic, complemented
62#11762713C2211yescharacteristic, complemented
63#11762713C2211yescharacteristic, complemented
64#11762710C2211yescharacteristic
65#11762710C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic
68#11762709C2211yescharacteristic, complemented
69#11762705C2211yescharacteristic, complemented
70#11762704C2211yescharacteristic, complemented
71#11762704C2211yescharacteristic, complemented
72#11762704C2211yescharacteristic, complemented
73#11762704C2211yescharacteristic, complemented
74#11762704C2211yescharacteristic, complemented
75#11762703C2211yescharacteristic, complemented
76#11762702C2211yescharacteristic, complemented
77#11762702C2211yescharacteristic, complemented
78#11762700C2211yescharacteristic
79#11762700C2211yescharacteristic
80#11762700C2211yescharacteristic, complemented
81#11762699C2211yescharacteristic
82#11762699C2211yescharacteristic
83#11762699C2211yescharacteristic
84#11762699C2211yescharacteristic
85#11762699C2211yescharacteristic
86#11762699C2211yescharacteristic
87#11762699C2211yescharacteristic
88#11762699C2211yescharacteristic
89#11762699C2211yescharacteristic
90#11762699C2211yescharacteristic
91#11762699C2211yescharacteristic
92#11762699C2211yescharacteristic
93#11762699C2211yescharacteristic, complemented
94#11762699C2211yescharacteristic, complemented
95#11762699C2211yescharacteristic, complemented
96#11762698C2211yescharacteristic
97#11762698C2211yescharacteristic
98#11762697C2211yescharacteristic, complemented
99#11762695C2211yescharacteristic, complemented
100#11762695C2211yescharacteristic, complemented
101#11762694C2211yescharacteristic, complemented
102#11762694C2211yescharacteristic, complemented
103#11762693C2211yescharacteristic, complemented
104#11762691C2211yescharacteristic, complemented
105#11762691C2211yescharacteristic, complemented
106#11762690C2211yescharacteristic, complemented
107#11762690C2211yescharacteristic, complemented
108#11762690C2211yescharacteristic, complemented
109#11762690C2211yescharacteristic, complemented
110#11762690C2211yescharacteristic, complemented
111#11762689C2211yescharacteristic
112#11762689C2211yescharacteristic
113#11762688C2211yescharacteristic
114#11762688C2211yescharacteristic
115#11762688C2211yescharacteristic, complemented
116#11762687C2211yescharacteristic
117#11762687C2211yescharacteristic
118#11762687C2211yescharacteristic
119#11762687C2211yescharacteristic
120#11762686C2211yescharacteristic
121#11762686C2211yescharacteristic
122#11762685C2211yescharacteristic
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic, complemented
125#11762683C2211yescharacteristic
126#11762683C2211yescharacteristic
127#11762683C2211yescharacteristic
128#11762683C2211yescharacteristic
129#11762682C2211yescharacteristic
130#11762682C2211yescharacteristic
131#11762682C2211yescharacteristic, complemented
132#11762680C2211yescharacteristic
133#11762680C2211yescharacteristic
134#11762680C2211yescharacteristic
135#11762680C2211yescharacteristic
136#11762680C2211yescharacteristic
137#11762680C2211yescharacteristic
138#11762680C2211yescharacteristic
139#11762680C2211yescharacteristic
140#11762680C2211yescharacteristic, complemented
141#11762680C2211yescharacteristic, complemented
142#11762680C2211yescharacteristic, complemented
143#11762678C2211yescharacteristic, complemented
144#11762677C2211yescharacteristic, complemented
145#11762676C2211yescharacteristic, complemented
146#11762672C2211yescharacteristic, complemented
147#11762671C2211yescharacteristic, complemented
148#11762669C2211yescharacteristic
149#11762667C2211yescharacteristic
150#11762667C2211yescharacteristic
151#11762666C2211yescharacteristic, complemented
152C4⋊C4×Dic17C2211yescharacteristic, complemented
153C4⋊C4×Dic17C2211yescharacteristic, complemented
154C4×#63225C2211yescharacteristic, complemented
155#11762660C2211yescharacteristic, complemented
156#11762660C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C4×#63227C2211yescharacteristic
162C4×#63227C2211yescharacteristic
163C4×#63227C2211yescharacteristic, complemented
164C4×C22⋊Dic17C2211yescharacteristic, complemented
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic
168#11762656C2211yescharacteristic, complemented
169#11762655C2211yescharacteristic, complemented
170#11762654C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic
172C2×#10587502C2211yescharacteristic
173C2×C4×D4×C17C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C4×D4×C17C2211yescharacteristic
176C22×C4⋊C4×C17C2211yescharacteristic
177C22×C4⋊C4×C17C2211yescharacteristic, complemented
178C17×#389C2211yescharacteristic, complemented
179C17×#389C2211yescharacteristic, complemented
180C17×#385C2211yescharacteristic
181C17×#385C2211yescharacteristic
182C17×#385C2211yescharacteristic, complemented
183C17×#385C2211yescharacteristic, complemented
184C17×#384C2211yescharacteristic, complemented
185C17×#380C2211yescharacteristic
186C17×#380C2211yescharacteristic, complemented
187C4×C4⋊C4×C17C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C22×D68C2311yescharacteristic
204C22×D68C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×Dic34C2311yescharacteristic
213C4×D4×C17—42no—
214C4×D4×C17—42no—
215C4×D4×C17C2×C418yescomplemented
216C2×C4⋊C4×C17—42no—
217C2×C4⋊C4×C17—42no—
218C2×C4⋊C4×C17C2311yescharacteristic
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×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C42×C17C2311yescharacteristic
238C2×C42×C17C2311yescharacteristic
239C2×C42×C17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248#10587625C2×C418yescomplemented
249#10587623C2×C418yescomplemented
250#10587616C2×C418yescomplemented
251#10587615C2×C418yescomplemented
252C4×C22⋊D17—42no—
253C4×C22⋊D17—42no—
254C4×C22⋊D17—42no—
255C4×C22⋊D17—42no—
256C4×C22⋊D17—42no—
257C4×C22⋊D17C2×C418yescomplemented
258C2×#63227—42no—
259C2×#63227—42no—
260C2×#63227C2×C418yescomplemented
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×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
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×Dic17—42no—
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
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322#10587584C2×C418yescomplemented
323#10587580C2×C418yescomplemented
324#10587579—42no—
325#10587579—42no—
326C4⋊C4×D17—42no—
327#10587573—42no—
328#10587571C2×C418yescomplemented
329#10587570C2×C418yescomplemented
330#10587568C2×C418yescomplemented
331C22⋊C4×D17—42no—
332C22⋊C4×D17—42no—
333#10587564C2×C418yescomplemented
334#10587562C2×C418yescomplemented
335#10587561C2×C418yescomplemented
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
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×D4×C17—22no—
389C2×D4×C17—22no—
390C2×D4×C17C22×C414yes—
391C22×C4×C17—22no—
392C22×C4×C17—22no—
393C22×C4×C17—22no—
394C22×C4×C17—22no—
395C22×C4×C17—41no—
396C22×C4×C17—41no—
397C22×C4×C17—41no—
398C22×C4×C17—41no—
399C22×C4×C17—41no—
400C22×C4×C17—41no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17C22×C414yes—
408C22×C4×C17C22×C414yes—
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C2×C22⋊D17—22no—
423C2×C22⋊D17—22no—
424C2×C22⋊D17—41no—
425C2×C22⋊D17—41no—
426C2×C22⋊D17—41no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17—41no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17C22×C414yes—
431C2×C22⋊D17C22×C414yes—
432C2×C22⋊D17C22×C414yes—
433C2×C22⋊D17C22×C414yes—
434C22×Dic17—22no—
435C22×Dic17—22no—
436C22×Dic17—22no—
437C22×Dic17—41no—
438C22×Dic17—41no—
439C22×Dic17—41no—
440C22×Dic17—41no—
441C22×Dic17—41no—
442C22×Dic17C22×C414yes—
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C2×D68—41no—
457C2×D68—41no—
458C2×D68—41no—
459C2×D68—41no—
460C2×D68C22×C414yes—
461C2×D68C22×C414yes—
462C2×C4×D17—22no—
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—41no—
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×D17C22×C414yes—
483C2×Dic34—41no—
484C2×Dic34—41no—
485C2×Dic34C22×C414yes—
486C4⋊C4×C17—22no—
487C4⋊C4×C17—22no—
488C4⋊C4×C17—22no—
489C4⋊C4×C17—41no—
490C4⋊C4×C17—41no—
491C4⋊C4×C17—41no—
492C4⋊C4×C17—41no—
493C4⋊C4×C17—41no—
494C4⋊C4×C17—41no—
495C4⋊C4×C17—41no—
496C4⋊C4×C17—41no—
497C4⋊C4×C17—41no—
498C4⋊C4×C17C22×C414yes—
499C22⋊C4×C17—22no—
500C22⋊C4×C17—22no—
501C22⋊C4×C17—41no—
502C22⋊C4×C17—41no—
503C22⋊C4×C17C22×C414yes—
504C22⋊C4×C17C22×C414yes—
505C42×C17—41no—
506C42×C17—41no—
507C42×C17C22×C414yes—
508C22⋊Dic17—22no—
509C22⋊Dic17—22no—
510C22⋊Dic17—22no—
511C22⋊Dic17—41no—
512C22⋊Dic17—41no—
513C22⋊Dic17—41no—
514C22⋊Dic17C22×C414yes—
515C22⋊Dic17C22×C414yes—
516#63227—22no—
517#63227—22no—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—41no—
522#63227—41no—
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×C414yes—
541#63227C22×C414yes—
542#63227C22×C414yes—
543#63227C22×C414yes—
544C4⋊Dic17—41no—
545C4⋊Dic17—41no—
546C4⋊Dic17C22×C414yes—
547#63225—22no—
548#63225—41no—
549#63225—41no—
550#63225—41no—
551#63225—41no—
552#63225—41no—
553#63225—41no—
554#63225—41no—
555#63225—41no—
556#63225—41no—
557#63225C22×C414yes—
558#63225C22×C414yes—
559#63225C22×C414yes—
560#63225C22×C414yes—
561C4×Dic17—22no—
562C4×Dic17—22no—
563C4×Dic17—22no—
564C4×Dic17—22no—
565C4×Dic17—41no—
566C4×Dic17—41no—
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×Dic17C22×C414yes—
576#34426—171nomaximal, Sylow
577C23×C17—21no—
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×C17C23×C412yes—
588C23×C17C23×C412yes—
589C23×C17H(5,𝔽2)12yes—
590C23×C172−1+412yes—
591C23×C17C2511yescharacteristic
592C22×D17—21no—
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—21no—
610C22×D17—28no—
611C22×D17—44no—
612C22×D17—44no—
613C22×D17—82no—
614C22×D17—82no—
615C22×D17—82no—
616C22×D17—82no—
617C22×D17C23×C412yes—
618C22×D17C23×C412yes—
619C22×D17C23×C412yes—
620D4×C17—28no—
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—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—44no—
655C2×C4×C17—44no—
656C2×C4×C17—44no—
657C2×C4×C17—82no—
658C2×C4×C17—82no—
659C2×C4×C17—82no—
660C2×C4×C17C23×C412yes—
661C2×C4×C17C23×C412yes—
662C2×C4×C17C23×C412yes—
663C2×C4×C17C23×C412yes—
664C2×C4×C17C23×C412yes—
665C2×C4×C17H(5,𝔽2)12yes—
666C22⋊D17—28no—
667C22⋊D17—44no—
668C22⋊D17—44no—
669C22⋊D17—44no—
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—21no—
703C2×Dic17—44no—
704C2×Dic17—44no—
705C2×Dic17—82no—
706C2×Dic17C23×C412yes—
707C2×Dic17C23×C412yes—
708C2×Dic17C23×C412yes—
709C2×Dic17C23×C412yes—
710C2×Dic17C23×C412yes—
711C2×Dic17H(5,𝔽2)12yes—
712D68—44no—
713D68—44no—
714C4×D17—44no—
715C4×D17—82no—
716C4×D17—82no—
717C4×D17—82no—
718C4×D17—82no—
719C4×D17—82no—
720C4×D17—82no—
721Dic34—44no—
722C2×#538—171no—
723#2383—171no—
724#2383—171no—
725#2377—171no—
726#2377—171no—
727#2373—171no—
728#2373—171no—
729#2361—171no—
730#2361—171no—
731#2358—171no—
732#2358—171no—
733#2358—171no—
734#2358—171no—
735#2353—171no—
736#2353—171no—
737D4×C4⋊C4—171no—
738D4×C4⋊C4D1711yescharacteristic, complemented
739#2337—171no—
740#2337—171no—
741#2335—171no—
742#2335—171no—
743#2329—171no—
744#2326—171no—
745#2326—171no—
746#2325—171no—
747#2322—171no—
748#2322—171no—
749#2315—171no—
750C4×C22⋊Q8—171no—
751C4×#121—171no—
752C2×#388—171no—
753C22×C17—22no—
754C22×C17—22no—
755C22×C17—22no—
756C22×C17—22no—
757C22×C17—22no—
758C22×C17—22no—
759C22×C17—22no—
760C22×C17—22no—
761C22×C17—22no—
762C22×C17—41no—
763C22×C17—41no—
764C22×C17—41no—
765C22×C17—41no—
766C22×C17#52014yes—
767C22×C17C24×C411yescharacteristic
768C22×C17C2×H(5,𝔽2)11yescharacteristic
769C22×C17C2×H(5,𝔽2)11yescharacteristic
770C22×C17C2×H(5,𝔽2)11yescharacteristic
771C22×C17C2×2−1+411yescharacteristic
772C22×C17#58511yescharacteristic
773C22×C17#58511yescharacteristic
774C2×D17—22no—
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—41no—
784C2×D17—41no—
785C2×D17—41no—
786C2×D17—41no—
787C2×D17—41no—
788C2×D17—41no—
789C2×D17—41no—
790C2×D17—41no—
791C2×D17—41no—
792C2×D17—41no—
793C2×D17—41no—
794C2×D17—41no—
795C2×D17—88no—
796C4×C17—22no—
797C4×C17—22no—
798C4×C17—22no—
799C4×C17—22no—
800C4×C17—22no—
801C4×C17—22no—
802C4×C17—41no—
803C4×C17—41no—
804C4×C17—41no—
805C4×C17—41no—
806C4×C17—41no—
807C4×C17—41no—
808C4×C17—41no—
809Dic17—22no—
810Dic17—22no—
811Dic17—22no—
812Dic17—22no—
813Dic17—22no—
814Dic17—22no—
815Dic17—41no—
816Dic17—41no—
817Dic17—41no—
818Dic17—41no—
819Dic17—41no—
820Dic17—41no—
821Dic17—41no—
822#538—1716no—
823C2×#126—171no—
824C2×#126—171no—
825C2×#124—171no—
826C2×#124—171no—
827C2×#123—171no—
828C2×#123—171no—
829C2×C22⋊Q8—171no—
830C2×#121—171no—
831C2×#121—171no—
832C2×#121—171no—
833C2×#120—171no—
834C2×#120—171no—
835C2×C4×Q8—171no—
836C2×C4×D4—171no—
837C2×C4×D4—171no—
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×D4C2×D1711yescharacteristic
845C2×C4×D4C2×D1711yescharacteristic
846C2×C4×D4C2×D1711yescharacteristic
847C22×C4⋊C4—171no—
848C22×C4⋊C4C2×D1711yescharacteristic
849C22×C4⋊C4C2×D1711yescharacteristic, complemented
850C22×C22⋊C4—171no—
851C22×C22⋊C4—171no—
852C22×C22⋊C4—171no—
853C22×C22⋊C4—171no—
854C22×C22⋊C4—171no—
855C22×C42—171no—
856#391—171no—
857#391—171no—
858#391—171no—
859#390—171no—
860#390—171no—
861#390—171no—
862#390—171no—
863#390—171no—
864#389—171no—
865#389—171no—
866#389—171no—
867#389—171no—
868#389—171no—
869#389—171no—
870#389C2×D1711yescharacteristic, complemented
871#389C2×D1711yescharacteristic, complemented
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#388—171no—
892#388—171no—
893#388—171no—
894#388—171no—
895#388—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#387—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#386—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#385C2×D1711yescharacteristic
941#385C2×D1711yescharacteristic
942#385C2×D1711yescharacteristic, complemented
943#385C2×D1711yescharacteristic, complemented
944#384—171no—
945#384C2×D1711yescharacteristic, complemented
946#383—171no—
947#383—171no—
948#381—171no—
949#381—171no—
950#380—171no—
951#380—171no—
952#380—171no—
953#380—171no—
954#380C2×D1711yescharacteristic
955#380C2×D1711yescharacteristic, complemented
956C4×C4⋊C4—171no—
957C4×C4⋊C4—171no—
958C4×C4⋊C4—171no—
959C4×C4⋊C4—171no—
960C4×C4⋊C4—171no—
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⋊C4—171no—
974#376—171no—
975#376—171no—
976C2×#95—171no—
977C2×#95—171no—
978C2×C17—24no—
979C2×C17—42no—
980C2×C17C2×#52011yescharacteristic
981C2×C17C4×H(5,𝔽2)11yescharacteristic
982C2×C17C4×H(5,𝔽2)11yescharacteristic
983C2×C17#353511yescharacteristic
984C2×C17#353711yescharacteristic
985C2×C17#356011yescharacteristic
986C2×C17#356111yescharacteristic
987D17—42no—
988D17—42no—
989D17—42no—
990C25—171no—
991C22×Q8—171no—
992C22×D4—171no—
993C22×D4—171no—
994C22×D4—171no—
995C22×D4—171no—
996C22×D4—171no—
997C22×D4—171no—
998C22×D4C22×D1711yescharacteristic
999C23×C4—171no—
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×C4C22×D1711yescharacteristic
1010C23×C4C22×D1711yescharacteristic
1011C23×C4C22×D1711yescharacteristic
1012C23×C4C22×D1711yescharacteristic
1013C23×C4C22×D1711yescharacteristic
1014C23×C4C22×D1711yescharacteristic
1015#126—178no—
1016#126—178no—
1017#124—178no—
1018#124—178no—
1019#123—178no—
1020#123—178no—
1021C22⋊Q8—178no—
1022#121—178no—
1023#121—178no—
1024#121—178no—
1025#120—178no—
1026#120—178no—
1027C4×Q8—682no—
1028C4×D4—42no—
1029C4×D4—42no—
1030C4×D4—178no—
1031C4×D4—682no—
1032C4×D4—682no—
1033C4×D4—682no—
1034C4×D4—682no—
1035C4×D4—682no—
1036C4×D4—682no—
1037C4×D4—682no—
1038C4×D4C4×D1718yescomplemented
1039C2×C4⋊C4—42no—
1040C2×C4⋊C4—42no—
1041C2×C4⋊C4—171no—
1042C2×C4⋊C4—171no—
1043C2×C4⋊C4—171no—
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—682no—
1059C2×C4⋊C4C22×D1711yescharacteristic
1060C2×C4⋊C4C22×D1711yescharacteristic
1061C2×C4⋊C4C22×D1711yescharacteristic
1062C2×C4⋊C4C22×D1711yescharacteristic
1063C2×C4⋊C4C22×D1711yescharacteristic
1064C2×C4⋊C4C22×D1711yescharacteristic
1065C2×C4⋊C4C22×D1711yescharacteristic
1066C2×C4⋊C4C22×D1711yescharacteristic
1067C2×C4⋊C4C22×D1711yescharacteristic
1068C2×C4⋊C4C22×D1711yescharacteristic
1069C2×C4⋊C4C22×D1711yescharacteristic
1070C2×C4⋊C4C22×D1711yescharacteristic
1071C2×C4⋊C4C22×D1711yescharacteristic
1072C2×C22⋊C4—171no—
1073C2×C22⋊C4—171no—
1074C2×C22⋊C4—178no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
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—171no—
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—682no—
1110C2×C22⋊C4—682no—
1111C2×C22⋊C4—682no—
1112C2×C22⋊C4—682no—
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×C42—171no—
1120C2×C42—171no—
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×C42—171no—
1133C2×C42—171no—
1134C2×C42—682no—
1135C2×C42C22×D1711yescharacteristic
1136C2×C42C22×D1711yescharacteristic
1137C2×C42C22×D1711yescharacteristic
1138#95—171no—
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#95—171no—
1172#95C22×D1711yescharacteristic
1173#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178C17#3442611yescharacteristic, complemented, Sylow
1179C24—171no—
1180C24—171no—
1181C24—171no—
1182C24—174no—
1183C24—342no—
1184C24—342no—
1185C24—681no—
1186C24—681no—
1187C24—681no—
1188C24—681no—
1189C24C23×D1711yescharacteristic
1190C24C23×D1711yescharacteristic
1191C2×Q8—174no—
1192C2×Q8—681no—
1193C2×Q8—681no—
1194C2×D4—22no—
1195C2×D4—22no—
1196C2×D4—174no—
1197C2×D4—174no—
1198C2×D4—174no—
1199C2×D4—174no—
1200C2×D4—174no—
1201C2×D4—174no—
1202C2×D4—342no—
1203C2×D4—342no—
1204C2×D4—681no—
1205C2×D4—681no—
1206C2×D4—681no—
1207C2×D4—681no—
1208C2×D4—681no—
1209C2×D4—681no—
1210C2×D4—681no—
1211C2×D4—681no—
1212C2×D4—681no—
1213C2×D4—681no—
1214C2×D4C2×C4×D1714yes—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—171no—
1232C22×C4—171no—
1233C22×C4—171no—
1234C22×C4—171no—
1235C22×C4—171no—
1236C22×C4—171no—
1237C22×C4—174no—
1238C22×C4—174no—
1239C22×C4—171no—
1240C22×C4—171no—
1241C22×C4—171no—
1242C22×C4—171no—
1243C22×C4—171no—
1244C22×C4—171no—
1245C22×C4—171no—
1246C22×C4—342no—
1247C22×C4—342no—
1248C22×C4—342no—
1249C22×C4—342no—
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—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4C2×C4×D1714yes—
1275C22×C4C2×C4×D1714yes—
1276C22×C4C23×D1711yescharacteristic
1277C22×C4C23×D1711yescharacteristic
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
1289C4⋊C4—22no—
1290C4⋊C4—22no—
1291C4⋊C4—22no—
1292C4⋊C4—41no—
1293C4⋊C4—41no—
1294C4⋊C4—41no—
1295C4⋊C4—41no—
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—41no—
1299C4⋊C4—41no—
1300C4⋊C4—41no—
1301C4⋊C4—174no—
1302C4⋊C4—174no—
1303C4⋊C4—174no—
1304C4⋊C4—174no—
1305C4⋊C4—174no—
1306C4⋊C4—342no—
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⋊C4C2×C4×D1714yes—
1319C22⋊C4—22no—
1320C22⋊C4—22no—
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—174no—
1324C22⋊C4—174no—
1325C22⋊C4—174no—
1326C22⋊C4—174no—
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—342no—
1336C22⋊C4—342no—
1337C22⋊C4—342no—
1338C22⋊C4—342no—
1339C22⋊C4—342no—
1340C22⋊C4—342no—
1341C22⋊C4—342no—
1342C22⋊C4—342no—
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—
1361C42—41no—
1362C42—41no—
1363C42—174no—
1364C42—342no—
1365C42—342no—
1366C42—342no—
1367C42—342no—
1368C42—681no—
1369C42—681no—
1370C42—681no—
1371C42—681no—
1372C42—681no—
1373C42—681no—
1374C42—681no—
1375C42—681no—
1376C42—681no—
1377C42—681no—
1378C42C2×C4×D1714yes—
1379C23—21no—
1380C23—21no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—172no—
1390C23—172no—
1391C23—172no—
1392C23—341no—
1393C23—341no—
1394C23—341no—
1395C23—341no—
1396C23—341no—
1397C23—341no—
1398C23—341no—
1399C23—341no—
1400C23—341no—
1401C23—341no—
1402C23—341no—
1403C23—341no—
1404C23—341no—
1405C23—341no—
1406C23—341no—
1407C23—341no—
1408C23—341no—
1409C23—341no—
1410C23—348no—
1411C23—684no—
1412C23—684no—
1413C23—1362no—
1414C23—1362no—
1415C23—1362no—
1416C23—1362no—
1417C23C22×C4×D1712yes—
1418C23C22×C4×D1712yes—
1419C23#1058769112yes—
1420C23#1058769412yes—
1421C23C24×D1711yescharacteristic
1422Q8—684no—
1423D4—28no—
1424D4—348no—
1425D4—684no—
1426D4—684no—
1427D4—684no—
1428D4—684no—
1429D4—684no—
1430C2×C4—21no—
1431C2×C4—21no—
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—44no—
1464C2×C4—44no—
1465C2×C4—44no—
1466C2×C4—82no—
1467C2×C4—82no—
1468C2×C4—82no—
1469C2×C4—172no—
1470C2×C4—172no—
1471C2×C4—172no—
1472C2×C4—172no—
1473C2×C4—172no—
1474C2×C4—172no—
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—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—684no—
1509C2×C4—684no—
1510C2×C4—684no—
1511C2×C4—1362no—
1512C2×C4—1362no—
1513C2×C4—1362no—
1514C2×C4—1362no—
1515C2×C4—1362no—
1516C2×C4—1362no—
1517C2×C4—1362no—
1518C2×C4C22×C4×D1712yes—
1519C2×C4C22×C4×D1712yes—
1520C2×C4C22×C4×D1712yes—
1521C2×C4C22×C4×D1712yes—
1522C2×C4C22×C4×D1712yes—
1523C2×C4#1058769112yes—
1524C22—22no—
1525C22—22no—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—41no—
1534C22—41no—
1535C22—41no—
1536C22—41no—
1537C22—342no—
1538C22—342no—
1539C22—342no—
1540C22—342no—
1541C22—342no—
1542C22—342no—
1543C22—342no—
1544C22—342no—
1545C22—342no—
1546C22—681no—
1547C22—681no—
1548C22—681no—
1549C22—681no—
1550C22—681no—
1551C22—681no—
1552C22—681no—
1553C22—681no—
1554C22—681no—
1555C22—681no—
1556C22—681no—
1557C22—681no—
1558C22—1368no—
1559C22#1176329014yes—
1560C22C23×C4×D1711yescharacteristic
1561C22H(5,𝔽2)×D1711yescharacteristic
1562C22C2×#1058769111yescharacteristic
1563C22C2×#1058769111yescharacteristic
1564C22C2×#1058769411yescharacteristic
1565C22#1176364511yescharacteristic
1566C22#1176364611yescharacteristic
1567C4—22no—
1568C4—22no—
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—41no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—342no—
1581C4—342no—
1582C4—342no—
1583C4—342no—
1584C4—342no—
1585C4—342no—
1586C4—681no—
1587C4—681no—
1588C4—681no—
1589C4—681no—
1590C4—681no—
1591C4—681no—
1592C4—681no—
1593C2—24no—
1594C2—42no—
1595C2—682no—
1596C2—682no—
1597C2—682no—
1598C2C2×#1176329011yescharacteristic
1599C2C4×#1058769111yescharacteristic
1600C2#1454199011yescharacteristic
1601C2#1454298811yescharacteristic
1602C2#1454301411yescharacteristic
1603C2#1454333211yescharacteristic
1604C2#1454335011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingD4×C4⋊C4×C17C2
socle, cosocleC23×C17C25
prime radicalC2×#11763392C2
hypercenterD4×C4⋊C4D17
hypocenterC17#34426
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14531977C2semidirect
3. #14531975C2semidirect
4. #14531940C2semidirect
5. #14531938C2semidirect
6. #14531907C2semidirect
7. #14531900C2semidirect
8. #14531803C2semidirect
9. #14531800C2semidirect
10. #14531761C2semidirect
11. #14531761C2semidirect
12. #14531760C2semidirect
13. #14531760C2semidirect
14. #14531726C2semidirect
15. #14531724C2semidirect
16. C4⋊C4×C22⋊D17C2semidirect
17. #14531598C2semidirect
18. #14531597C2semidirect
19. #14531577C2semidirect
20. #14531570C2semidirect
21. #14531515C2semidirect
22. #14531492C2semidirect
23. #14531490C2semidirect
24. #14531482C2semidirect
25. #14531453C2semidirect
26. #14531448C2semidirect
27. #14531397C2semidirect
28. #14531316C2semidirect
29. C4×#10587625C2semidirect
30. C2×#11762699C2semidirect
31. D4×C4⋊C4×C17C2semidirect
32. #11763392C4semidirect
45. C2×#10587573C22semidirect
53. C2×C4×C22⋊D17C22semidirect
54. C2×C4⋊C4×D17C22semidirect
61. #11762714C22semidirect
62. #11762713C22semidirect
63. #11762713C22semidirect
68. #11762709C22semidirect
69. #11762705C22semidirect
70. #11762704C22semidirect
71. #11762704C22semidirect
72. #11762704C22semidirect
73. #11762704C22semidirect
74. #11762704C22semidirect
75. #11762703C22semidirect
76. #11762702C22semidirect
77. #11762702C22semidirect
80. #11762700C22semidirect
93. #11762699C22semidirect
94. #11762699C22semidirect
95. #11762699C22semidirect
98. #11762697C22semidirect
99. #11762695C22semidirect
100. #11762695C22semidirect
101. #11762694C22semidirect
102. #11762694C22semidirect
103. #11762693C22semidirect
104. #11762691C22semidirect
105. #11762691C22semidirect
106. #11762690C22semidirect
107. #11762690C22semidirect
108. #11762690C22semidirect
109. #11762690C22semidirect
110. #11762690C22semidirect
115. #11762688C22semidirect
124. #11762685C22semidirect
131. #11762682C22semidirect
140. #11762680C22semidirect
141. #11762680C22semidirect
142. #11762680C22semidirect
143. #11762678C22semidirect
144. #11762677C22semidirect
145. #11762676C22semidirect
146. #11762672C22semidirect
147. #11762671C22semidirect
151. #11762666C22semidirect
152. C4⋊C4×Dic17C22semidirect
153. C4⋊C4×Dic17C22semidirect
154. C4×#63225C22semidirect
155. #11762660C22semidirect
156. #11762660C22semidirect
163. C4×#63227C22semidirect
164. C4×C22⋊Dic17C22semidirect
165. C4×C22⋊Dic17C22semidirect
168. #11762656C22semidirect
169. #11762655C22semidirect
170. #11762654C22semidirect
177. C22×C4⋊C4×C17C22semidirect
178. C17×#389C22semidirect
179. C17×#389C22semidirect
182. C17×#385C22semidirect
183. C17×#385C22semidirect
184. C17×#384C22semidirect
186. C17×#380C22semidirect
187. C4×C4⋊C4×C17C22semidirect
215. C4×D4×C17C2×C4semidirect
248. #10587625C2×C4semidirect
249. #10587623C2×C4semidirect
250. #10587616C2×C4semidirect
251. #10587615C2×C4semidirect
257. C4×C22⋊D17C2×C4semidirect
260. C2×#63227C2×C4semidirect
322. #10587584C2×C4semidirect
323. #10587580C2×C4semidirect
328. #10587571C2×C4semidirect
329. #10587570C2×C4semidirect
330. #10587568C2×C4semidirect
333. #10587564C2×C4semidirect
334. #10587562C2×C4semidirect
335. #10587561C2×C4semidirect
738. D4×C4⋊C4D17semidirect
849. C22×C4⋊C4C2×D17semidirect
870. #389C2×D17semidirect
871. #389C2×D17semidirect
942. #385C2×D17semidirect
943. #385C2×D17semidirect
945. #384C2×D17semidirect
955. #380C2×D17semidirect
961. C4×C4⋊C4C2×D17semidirect
1038. C4×D4C4×D17semidirect
1178. C17#34426semidirect

Maximal subgroups

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

subgroupindex
C2×#117633922
#145319772
#145319752
#145319402
#145319382
#145319072
#145319002
#145318032
#145318002
#145317612
#145317602
#145317262
#145317242
C4⋊C4×C22⋊D172
#145315982
#145315972
#145315772
#145315702
#145315152
#145314922
#145314902
#145314822
#145314532
#145314482
#145313972
#145313162
C4×#105876252
C2×#117626992
D4×C4⋊C4×C172
#3442617