Finite Group Databasebeta

← #16956944

Subgroups — #16956944

Order 4352.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762702C211yesmaximal, characteristic
2C2×C22⋊C4×Dic17C211yesmaximal, characteristic
3#14527043C211yesmaximal, characteristic, complemented
4#14527040C211yesmaximal, characteristic, complemented
5#14527027C211yesmaximal, characteristic
6#14527027C211yesmaximal, characteristic
7#14527017C211yesmaximal, characteristic, complemented
8#14527015C211yesmaximal, characteristic, complemented
9#14527013C211yesmaximal, characteristic, complemented
10#14527012C211yesmaximal, characteristic, complemented
11#14527010C211yesmaximal, characteristic, complemented
12#14527006C211yesmaximal, characteristic
13#14527006C211yesmaximal, characteristic
14C4×#10587502C211yesmaximal, characteristic, complemented
15C2×C17×#388C211yesmaximal, characteristic
16C24×Dic17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×C22⋊Dic17C2211yescharacteristic
21C22×C22⋊Dic17C2211yescharacteristic
22C22×C22⋊Dic17C2211yescharacteristic
23C22×C4×Dic17C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26#11762702—24no—
27C22⋊C4×Dic17C418yescomplemented
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C22×C4⋊C4×C17C2211yescharacteristic
47C22×C22⋊C4×C17C2211yescharacteristic
48C22×C22⋊C4×C17C2211yescharacteristic
49C22×C22⋊C4×C17C2211yescharacteristic
50C22×C42×C17C2211yescharacteristic
51C17×#388—24no—
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C25×C17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×Dic17—22no—
62C23×Dic17—22no—
63C23×Dic17—41no—
64C23×Dic17—41no—
65C23×Dic17—41no—
66C23×Dic17—41no—
67C23×Dic17C2×C414yes—
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C2×C4⋊C4×C17—22no—
77C2×C4⋊C4×C17—22no—
78C2×C4⋊C4×C17—41no—
79C2×C22⋊C4×C17—22no—
80C2×C22⋊C4×C17—22no—
81C2×C22⋊C4×C17—22no—
82C2×C22⋊C4×C17—22no—
83C2×C22⋊C4×C17—41no—
84C2×C22⋊C4×C17—41no—
85C2×C22⋊C4×C17C2×C414yes—
86C2×C22⋊C4×C17D414yes—
87C2×C22⋊C4×C17Q814yes—
88C2×C42×C17—22no—
89C2×C42×C17—22no—
90C2×C42×C17—41no—
91C2×C22⋊Dic17—22no—
92C2×C22⋊Dic17—22no—
93C2×C22⋊Dic17—22no—
94C2×C22⋊Dic17—22no—
95C2×C22⋊Dic17—22no—
96C2×C22⋊Dic17—22no—
97C2×C22⋊Dic17—41no—
98C2×C22⋊Dic17—41no—
99C2×C22⋊Dic17C2×C414yes—
100C2×C4⋊Dic17—22no—
101C2×C4⋊Dic17—22no—
102C2×C4⋊Dic17—41no—
103C2×#63225—22no—
104C2×#63225—22no—
105C2×#63225—22no—
106C2×#63225—22no—
107C2×#63225—41no—
108C2×#63225—41no—
109C2×C4×Dic17—22no—
110C2×C4×Dic17—22no—
111C2×C4×Dic17—41no—
112C2×C4×Dic17—41no—
113C2×C4×Dic17—41no—
114C2×C4×Dic17—41no—
115C2×C4×Dic17—41no—
116C2×C4×Dic17C2×C414yes—
117C2×C4×Dic17C2×C414yes—
118C17×#95—22no—
119C17×#95—22no—
120#10587502—22no—
121#10587502—22no—
122#10587502—22no—
123#10587502—22no—
124#10587502—22no—
125#10587502—22no—
126#10587502—22no—
127#10587502—22no—
128#10587502—22no—
129#10587502—22no—
130#10587502—41no—
131#10587502—41no—
132#10587502—41no—
133#10587502—41no—
134#10587502—41no—
135#10587502—41no—
136#10587502C2×C414yes—
137#10587502C2×C414yes—
138C24×C17—21no—
139C24×C17—21no—
140C24×C17—21no—
141C24×C17—21no—
142C24×C17—21no—
143C24×C17—21no—
144C24×C17—21no—
145C24×C17—21no—
146C24×C17—21no—
147C24×C17—21no—
148C24×C17—21no—
149C24×C17—21no—
150C24×C17C22×C412yes—
151C24×C17C2×D412yes—
152C24×C17C2×Q812yes—
153C24×C17C2411yescharacteristic
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17C22×C412yes—
189C22×C4×C17C22×C412yes—
190C22×C4×C17C2×D412yes—
191C22×C4×C17C2×D412yes—
192C22×C4×C17C2×Q812yes—
193C22×C4×C17C2×Q812yes—
194C22×C4×C17#4112yes—
195C22×C4×C17#4112yes—
196C22×Dic17—21no—
197C22×Dic17—21no—
198C22×Dic17—21no—
199C22×Dic17—21no—
200C22×Dic17—21no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—28no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17—21no—
243C22×Dic17—44no—
244C22×Dic17—44no—
245C22×Dic17—44no—
246C22×Dic17—44no—
247C22×Dic17—44no—
248C22×Dic17—44no—
249C22×Dic17C22×C412yes—
250C22×Dic17C22×C412yes—
251C22×Dic17C22×C412yes—
252C22×Dic17C22×C412yes—
253C22×Dic17#4112yes—
254C22×Dic17#4112yes—
255C22×Dic17#4112yes—
256C22×Dic17#4112yes—
257C22×Dic17#4112yes—
258C22×Dic17#4112yes—
259C4⋊C4×C17—44no—
260C22⋊C4×C17—44no—
261C22⋊C4×C17—44no—
262C22⋊C4×C17C4⋊C4116yescomplemented
263C42×C17—44no—
264C22⋊Dic17—28no—
265C22⋊Dic17—44no—
266C22⋊Dic17—44no—
267C4⋊Dic17—44no—
268#63225—44no—
269#63225—44no—
270C4×Dic17—44no—
271C4×Dic17—44no—
272C4×Dic17—44no—
273#13948—171nomaximal, Sylow
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17—22no—
278C23×C17—22no—
279C23×C17—22no—
280C23×C17—22no—
281C23×C17—22no—
282C23×C17—22no—
283C23×C17—22no—
284C23×C17—22no—
285C23×C17—22no—
286C23×C17—22no—
287C23×C17—22no—
288C23×C17—22no—
289C23×C17—22no—
290C23×C17—22no—
291C23×C17—22no—
292C23×C17—41no—
293C23×C17—41no—
294C23×C17—41no—
295C23×C17—41no—
296C23×C17—41no—
297C23×C17—41no—
298C23×C17—41no—
299C23×C17—41no—
300C23×C17—41no—
301C23×C17—41no—
302C23×C17—41no—
303C23×C17—41no—
304C23×C17—41no—
305C23×C17—41no—
306C23×C17—41no—
307C23×C17—41no—
308C23×C17C2×C4⋊C414yes—
309C23×C17C23×C411yescharacteristic
310C23×C17C22×D411yescharacteristic
311C23×C17C22×Q811yescharacteristic
312C23×C17C2×#4111yescharacteristic
313C23×C17C2×#4111yescharacteristic
314C23×C17C2×#4111yescharacteristic
315C23×C17C2×#4111yescharacteristic
316C23×C17C2×#4111yescharacteristic
317C23×C17C2×#4111yescharacteristic
318C23×C17C2×#4111yescharacteristic
319C23×C17C2×#4111yescharacteristic
320C23×C17H(5,𝔽2)11yescharacteristic
321C23×C17H(5,𝔽2)11yescharacteristic
322C23×C17H(5,𝔽2)11yescharacteristic
323C23×C17H(5,𝔽2)11yescharacteristic
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17—41no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17C2×C4⋊C414yes—
365C2×C4×C17C2×C4⋊C414yes—
366C2×Dic17—22no—
367C2×Dic17—22no—
368C2×Dic17—22no—
369C2×Dic17—22no—
370C2×Dic17—22no—
371C2×Dic17—22no—
372C2×Dic17—22no—
373C2×Dic17—22no—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—22no—
379C2×Dic17—22no—
380C2×Dic17—22no—
381C2×Dic17—22no—
382C2×Dic17—22no—
383C2×Dic17—22no—
384C2×Dic17—22no—
385C2×Dic17—22no—
386C2×Dic17—22no—
387C2×Dic17—22no—
388C2×Dic17—22no—
389C2×Dic17—22no—
390C2×Dic17—416no—
391C2×Dic17—41no—
392C2×Dic17—41no—
393C2×Dic17—41no—
394C2×Dic17—41no—
395C2×Dic17—41no—
396C2×Dic17—41no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17—41no—
421C2×Dic17#11714yes—
422C2×Dic17#11714yes—
423C2×#388—171no—
424C2×#388D1711yescharacteristic
425C2×C4×C22⋊C4—171no—
426#1442—171no—
427#1442—171no—
428#1439—171no—
429#1439—171no—
430#1436—171no—
431#1436—171no—
432C4⋊#95—171no—
433C4⋊#95—171no—
434#1434—171no—
435C22⋊#95—171no—
436C22⋊#95—171no—
437C4×#95—171no—
438C22×C17—24no—
439C22×C17—24no—
440C22×C17—24no—
441C22×C17—42no—
442C22×C17—42no—
443C22×C17—42no—
444C22×C17—42no—
445C22×C17—42no—
446C22×C17—42no—
447C22×C17—42no—
448C22×C17—42no—
449C22×C17—42no—
450C22×C17—42no—
451C22×C17—42no—
452C22×C17—42no—
453C22×C17C22×C4⋊C411yescharacteristic
454C22×C17C2×#11711yescharacteristic
455C22×C17C2×#11711yescharacteristic
456C22×C17C4×#4111yescharacteristic
457C22×C17C4×#4111yescharacteristic
458C22×C17#51811yescharacteristic
459C22×C17#51811yescharacteristic
460C22×C17#52911yescharacteristic
461C22×C17#52911yescharacteristic
462C22×C17#52911yescharacteristic
463C22×C17#52911yescharacteristic
464C22×C17#53211yescharacteristic
465C22×C17#53211yescharacteristic
466C22×C17#53311yescharacteristic
467C22×C17#53311yescharacteristic
468C22×C17#53811yescharacteristic
469C22×C17#53811yescharacteristic
470C22×C17#53811yescharacteristic
471C22×C17#53811yescharacteristic
472C22×C17#54611yescharacteristic
473C22×C17#54611yescharacteristic
474C22×C17#54611yescharacteristic
475C22×C17#54611yescharacteristic
476C22×C17#55111yescharacteristic
477C22×C17#55111yescharacteristic
478C22×C17#55311yescharacteristic
479C22×C17#55311yescharacteristic
480C22×C17#55311yescharacteristic
481C22×C17#55311yescharacteristic
482C22×C17#55411yescharacteristic
483C22×C17#55411yescharacteristic
484C22×C17#55411yescharacteristic
485C22×C17#55411yescharacteristic
486C22×C17#55911yescharacteristic
487C22×C17#55911yescharacteristic
488C4×C17—24no—
489C4×C17—24no—
490C4×C17—42no—
491C4×C17—42no—
492C4×C17—81no—
493C4×C17—81no—
494Dic17—24no—
495Dic17—24no—
496Dic17—42no—
497Dic17—42no—
498Dic17—42no—
499Dic17—42no—
500Dic17—81no—
501Dic17—81no—
502C24×C4—171no—
503C22×C4⋊C4—171no—
504C22×C4⋊C4—171no—
505C22×C4⋊C4—171no—
506C22×C4⋊C4C2×D1711yescharacteristic
507C22×C22⋊C4—171no—
508C22×C22⋊C4—171no—
509C22×C22⋊C4—171no—
510C22×C22⋊C4C2×D1711yescharacteristic
511C22×C22⋊C4C2×D1711yescharacteristic
512C22×C22⋊C4C2×D1711yescharacteristic
513C22×C42—171no—
514C22×C42—171no—
515C22×C42—171no—
516C22×C42C2×D1711yescharacteristic
517#388—24no—
518#388—344no—
519C4×C22⋊C4—178no—
520C2×#95—171no—
521C2×#95—171no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×#95—171no—
528C2×#95—171no—
529C2×#95—171no—
530C2×#95—171no—
531C2×#95—171no—
532C2×#95—171no—
533C2×#95—171no—
534C2×#95—171no—
535C2×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95C2×D1711yescharacteristic
539C2×#95C2×D1711yescharacteristic
540C2×C17—44no—
541C2×C17#228511yescharacteristic
542C2×C17#229811yescharacteristic
543C2×C17#231211yescharacteristic
544C2×C17#234911yescharacteristic
545C2×C17#234911yescharacteristic
546C2×C17#235311yescharacteristic
547C2×C17#235711yescharacteristic
548C2×C17#255711yescharacteristic
549C2×C17#255711yescharacteristic
550C2×C17#255911yescharacteristic
551C2×C17#255911yescharacteristic
552C2×C17#258711yescharacteristic
553C2×C17#258711yescharacteristic
554C2×C17#258911yescharacteristic
555C2×C17#258911yescharacteristic
556C25C22×D1711yescharacteristic
557C23×C4—171no—
558C23×C4—171no—
559C23×C4—171no—
560C23×C4—171no—
561C23×C4—171no—
562C23×C4—171no—
563C23×C4—174no—
564C23×C4—171no—
565C23×C4—171no—
566C23×C4—342no—
567C23×C4—342no—
568C23×C4—681no—
569C23×C4—681no—
570C23×C4—681no—
571C23×C4—681no—
572C23×C4C22×D1711yescharacteristic
573C23×C4C22×D1711yescharacteristic
574C23×C4C22×D1711yescharacteristic
575C23×C4C22×D1711yescharacteristic
576C23×C4C22×D1711yescharacteristic
577C23×C4C22×D1711yescharacteristic
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—342no—
582C2×C4⋊C4—342no—
583C2×C4⋊C4—342no—
584C2×C4⋊C4—342no—
585C2×C4⋊C4—342no—
586C2×C4⋊C4—342no—
587C2×C4⋊C4—681no—
588C2×C4⋊C4—681no—
589C2×C4⋊C4—681no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—174no—
597C2×C22⋊C4—342no—
598C2×C22⋊C4—342no—
599C2×C22⋊C4—342no—
600C2×C22⋊C4—342no—
601C2×C22⋊C4—342no—
602C2×C22⋊C4—342no—
603C2×C22⋊C4—681no—
604C2×C22⋊C4—681no—
605C2×C22⋊C4Dic3414yes—
606C2×C22⋊C4C4×D1714yes—
607C2×C22⋊C4C22⋊D1714yes—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—41no—
611C2×C42—174no—
612C2×C42—174no—
613C2×C42—342no—
614C2×C42—342no—
615C2×C42—681no—
616C2×C42—681no—
617C2×C42—681no—
618C2×C42—681no—
619C2×C42—681no—
620#95—22no—
621#95—22no—
622#95—174no—
623#95—174no—
624#95—342no—
625#95—342no—
626#95—342no—
627#95—342no—
628#95—342no—
629#95—342no—
630#95—342no—
631#95—342no—
632#95—342no—
633#95—342no—
634#95—681no—
635#95—681no—
636#95—681no—
637#95—681no—
638#95—681no—
639#95—681no—
640C17#1394811yescharacteristic, complemented, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×Dic3412yes—
654C24C2×C4×D1712yes—
655C24C2×C22⋊D1712yes—
656C24C23×D1711yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—172no—
692C22×C4—172no—
693C22×C4—172no—
694C22×C4—172no—
695C22×C4—172no—
696C22×C4—172no—
697C22×C4—172no—
698C22×C4—172no—
699C22×C4—172no—
700C22×C4—172no—
701C22×C4—348no—
702C22×C4—341no—
703C22×C4—341no—
704C22×C4—341no—
705C22×C4—341no—
706C22×C4—341no—
707C22×C4—341no—
708C22×C4—341no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—684no—
749C22×C4—684no—
750C22×C4—684no—
751C22×C4—684no—
752C22×C4—684no—
753C22×C4—684no—
754C22×C4C2×Dic3412yes—
755C22×C4C2×Dic3412yes—
756C22×C4C2×C4×D1712yes—
757C22×C4C2×C4×D1712yes—
758C22×C4#6325412yes—
759C22×C4#6325412yes—
760C22×C4C2×C22⋊D1712yes—
761C22×C4C2×C22⋊D1712yes—
762C4⋊C4—44no—
763C4⋊C4—684no—
764C4⋊C4—684no—
765C4⋊C4—684no—
766C22⋊C4—44no—
767C22⋊C4—44no—
768C22⋊C4—348no—
769C22⋊C4—684no—
770C22⋊C4—684no—
771C22⋊C4#63225116yescomplemented
772C42—44no—
773C42—684no—
774C42—684no—
775C42—684no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×#6322514yes—
811C23C22×Dic3411yescharacteristic
812C23C22×C4×D1711yescharacteristic
813C23C2×#6325411yescharacteristic
814C23C2×#6325411yescharacteristic
815C23#1058769111yescharacteristic
816C23#1058769111yescharacteristic
817C23#41×D1711yescharacteristic
818C23#41×D1711yescharacteristic
819C23#41×D1711yescharacteristic
820C23#41×D1711yescharacteristic
821C23#41×D1711yescharacteristic
822C23#41×D1711yescharacteristic
823C23#1058769611yescharacteristic
824C23#1058769611yescharacteristic
825C23C22×C22⋊D1711yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—174no—
867C2×C4—174no—
868C2×C4—342no—
869C2×C4—342no—
870C2×C4—342no—
871C2×C4—342no—
872C2×C4—342no—
873C2×C4—342no—
874C2×C4—342no—
875C2×C4—342no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—342no—
884C2×C4—342no—
885C2×C4—342no—
886C2×C4—342no—
887C2×C4—342no—
888C2×C4—342no—
889C2×C4—342no—
890C2×C4—342no—
891C2×C4—342no—
892C2×C4—6816no—
893C2×C4—681no—
894C2×C4—681no—
895C2×C4—681no—
896C2×C4—681no—
897C2×C4—681no—
898C2×C4—681no—
899C2×C4—681no—
900C2×C4—681no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—681no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4C2×#6322514yes—
924C2×C4C2×#6322514yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×#6322511yescharacteristic
941C22#117×D1711yescharacteristic
942C22#117×D1711yescharacteristic
943C22C4×#6325411yescharacteristic
944C22C4×#6325411yescharacteristic
945C22#1176328111yescharacteristic
946C22#1176328111yescharacteristic
947C22#1176333611yescharacteristic
948C22#1176333811yescharacteristic
949C22#1176334011yescharacteristic
950C22#1176334211yescharacteristic
951C22#1176335511yescharacteristic
952C22#1176335511yescharacteristic
953C22#1176336211yescharacteristic
954C22#1176336211yescharacteristic
955C22#1176339111yescharacteristic
956C22#1176339311yescharacteristic
957C22#1176339511yescharacteristic
958C22#1176339811yescharacteristic
959C22#1176344711yescharacteristic
960C22#1176344711yescharacteristic
961C22#1176345311yescharacteristic
962C22#1176345311yescharacteristic
963C22#1176348211yescharacteristic
964C22#1176348911yescharacteristic
965C22#1176350211yescharacteristic
966C22#1176350611yescharacteristic
967C22#1176351011yescharacteristic
968C22#1176351011yescharacteristic
969C22#1176351611yescharacteristic
970C22#1176351611yescharacteristic
971C22#1176351811yescharacteristic
972C22#1176351811yescharacteristic
973C22#1176354111yescharacteristic
974C22#1176354311yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—344no—
982C4—344no—
983C4—682no—
984C4—682no—
985C4—682no—
986C4—682no—
987C4—1361no—
988C4—1361no—
989C2—44no—
990C2#1453118711yescharacteristic
991C2#1453127811yescharacteristic
992C2#1453137811yescharacteristic
993C2#1453168911yescharacteristic
994C2#1453168911yescharacteristic
995C2#1453171911yescharacteristic
996C2#1453175411yescharacteristic
997C2#1453387911yescharacteristic
998C2#1453388111yescharacteristic
999C2#1453390911yescharacteristic
1000C2#1453391111yescharacteristic
1001C2#1453420111yescharacteristic
1002C2#1453420311yescharacteristic
1003C2#1453423111yescharacteristic
1004C2#1453423311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#388C2
socle, cosocleC24×C17C24
prime radicalC25×C17C23
hypercenterC2×#388D17
hypocenterC17#13948
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. #14527043C2semidirect
4. #14527040C2semidirect
7. #14527017C2semidirect
8. #14527015C2semidirect
9. #14527013C2semidirect
10. #14527012C2semidirect
11. #14527010C2semidirect
14. C4×#10587502C2semidirect
27. C22⋊C4×Dic17C4semidirect
262. C22⋊C4×C17C4⋊C4semidirect
640. C17#13948semidirect
771. C22⋊C4#63225semidirect

Maximal subgroups

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

subgroupindex
C2×#117627022
C2×C22⋊C4×Dic172
#145270432
#145270402
#145270272
#145270172
#145270152
#145270132
#145270122
#145270102
#145270062
C4×#105875022
C2×C17×#3882
#1394817