Finite Group Databasebeta

← #17068492

Subgroups — #17068492

Order 4352.

1090 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763113C211yesmaximal, characteristic, complemented
2C2×#11762914C211yesmaximal, characteristic, complemented
3#14533706C211yesmaximal, characteristic
4#14529984C211yesmaximal, characteristic, complemented
5#14529977C211yesmaximal, characteristic, complemented
6#14529792C211yesmaximal, characteristic, complemented
7#14529792C211yesmaximal, characteristic, complemented
8#14529754C211yesmaximal, characteristic, complemented
9#14529583C211yesmaximal, characteristic
10#14529096C211yesmaximal, characteristic, complemented
11#14529091C211yesmaximal, characteristic, complemented
12#14528983C211yesmaximal, characteristic, complemented
13#14528977C211yesmaximal, characteristic, complemented
14#14528789C211yesmaximal, characteristic, complemented
15C2×C17×#552C211yesmaximal, characteristic
16C22×#63231C2211yescharacteristic
17C2×#10587610C2211yescharacteristic
18C2×#10587610C2211yescharacteristic
19C2×C4×Dic34C2211yescharacteristic
20#11763113—24no—
21#11762914—24no—
22C2×#10587478C2211yescharacteristic
23C2×#10587479C2211yescharacteristic
24C2×#10587479C2211yescharacteristic
25C2×C4⋊#3622C2211yescharacteristic
26C2×#10587506C2211yescharacteristic
27C2×#10587506C2211yescharacteristic
28C2×#10587506C2211yescharacteristic
29C2×#10587481C2211yescharacteristic
30C2×#10587481C2211yescharacteristic
31C2×#10587481C2211yescharacteristic
32C2×C22⋊#3622C2211yescharacteristic
33C2×C22⋊#3622C2211yescharacteristic
34C2×C22⋊#3622C2211yescharacteristic
35C2×C22⋊#3622C2211yescharacteristic
36C2×#10587474C2211yescharacteristic
37#11762732—21no—
38#11762732—21no—
39#11762712—21no—
40#11762705—21no—
41#11762679C2211yescharacteristic
42#11762669C2211yescharacteristic
43#11762669C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50C17×#552—24no—
51C17×#552—24no—
52C2×C17×#126—21no—
53C2×C17×#125—21no—
54C2×C17×#125C2211yescharacteristic
55C2×C17×#123—21no—
56C2×C17×C22⋊Q8C2211yescharacteristic
57C2×C17×C22⋊Q8C2211yescharacteristic
58C2×C4×Q8×C17C2211yescharacteristic
59C2×C4×D4×C17C2211yescharacteristic
60C2×C17×#117—21no—
61C2×C17×#117C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×Q8×C17C2311yescharacteristic
64C22×D4×C17D411yescharacteristic
65C23×C4×C17—21no—
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C22×Dic34C2311yescharacteristic
69C17×#126—28no—
70C17×#125—28no—
71C17×#125—22no—
72C17×#125D414yes—
73C17×#123—28no—
74C17×C22⋊Q8—22no—
75C17×C22⋊Q8—22no—
76C17×C22⋊Q8—22no—
77C17×C22⋊Q8—22no—
78C4×Q8×C17—22no—
79C4×Q8×C17D414yes—
80C4×D4×C17—22no—
81C4×D4×C17—22no—
82C17×#117—28no—
83C17×#117—22no—
84C17×#117—22no—
85C2×C4⋊C4×C17—21no—
86C2×C4⋊C4×C17—21no—
87C2×C4⋊C4×C17—21no—
88C2×C4⋊C4×C17—21no—
89C2×C4⋊C4×C17—21no—
90C2×C4⋊C4×C17—21no—
91C2×C4⋊C4×C17—22no—
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17D411yescharacteristic
94C2×C4⋊C4×C17C2311yescharacteristic
95C2×C4⋊C4×C17C2311yescharacteristic
96C2×C4⋊C4×C17C2311yescharacteristic
97C2×C22⋊C4×C17—21no—
98C2×C22⋊C4×C17—21no—
99C2×C22⋊C4×C17—21no—
100C2×C22⋊C4×C17D411yescharacteristic
101C2×C22⋊C4×C17D411yescharacteristic
102C2×C42×C17—21no—
103C2×C42×C17—21no—
104C2×C42×C17C2311yescharacteristic
105C2×C22⋊Dic17—21no—
106C2×C22⋊Dic17—21no—
107C2×C22⋊Dic17—21no—
108C2×C22⋊Dic17—21no—
109C2×#63231—22no—
110C2×#63231—22no—
111C2×#63231—22no—
112C2×C4⋊Dic17—21no—
113C2×C4⋊Dic17—21no—
114C2×C4⋊Dic17C2311yescharacteristic
115C2×C4⋊Dic17C2311yescharacteristic
116C2×C4⋊Dic17C2311yescharacteristic
117#10587610—22no—
118#10587610—22no—
119#10587610—41no—
120#10587610—41no—
121C2×#63225—21no—
122C2×#63225—21no—
123C2×#63225—21no—
124C2×C4×Dic17—21no—
125C22×#3622C2311yescharacteristic
126C22×#3622C2311yescharacteristic
127C22×#3622C2311yescharacteristic
128C22×#3622C2311yescharacteristic
129C4×Dic34—22no—
130C4×Dic34—22no—
131#10587506—22no—
132#10587506—41no—
133#10587506—41no—
134#10587502—21no—
135#10587502—21no—
136C22⋊#3622—22no—
137C22⋊#3622—22no—
138C22⋊#3622—41no—
139C22⋊#3622—41no—
140#10587481—22no—
141#10587481—22no—
142#10587481—22no—
143#10587479—22no—
144#10587479—22no—
145#10587478—22no—
146C4⋊#3622—22no—
147#10587474—22no—
148C24×C17C2×D411yescharacteristic
149C24×C17C2×D411yescharacteristic
150C2×Q8×C17—21no—
151C2×Q8×C17—21no—
152C2×Q8×C17—21no—
153C2×Q8×C17—21no—
154C2×Q8×C17—21no—
155C2×Q8×C17C2×D412yes—
156C2×D4×C17—22no—
157C2×D4×C17—22no—
158C2×D4×C17—41no—
159C22×C4×C17—24no—
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—42no—
177C22×C4×C17—42no—
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17C2×D411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2411yescharacteristic
183C22×Dic17—21no—
184C22×Dic17—21no—
185C22×Dic17—21no—
186C22×Dic17—21no—
187C2×Dic34—21no—
188C2×Dic34—21no—
189C2×Dic34—21no—
190C2×Dic34—21no—
191C2×Dic34—21no—
192C2×Dic34#4112yes—
193C4⋊C4×C17—24no—
194C4⋊C4×C17—24no—
195C4⋊C4×C17—24no—
196C4⋊C4×C17—24no—
197C4⋊C4×C17—24no—
198C4⋊C4×C17—22no—
199C4⋊C4×C17—24no—
200C4⋊C4×C17—21no—
201C4⋊C4×C17—21no—
202C4⋊C4×C17—21no—
203C4⋊C4×C17C2×D412yes—
204C4⋊C4×C17C2×D412yes—
205C4⋊C4×C17C2×D412yes—
206C22⋊C4×C17—24no—
207C22⋊C4×C17—24no—
208C22⋊C4×C17—24no—
209C22⋊C4×C17—22no—
210C22⋊C4×C17—22no—
211C42×C17—24no—
212C42×C17—24no—
213C42×C17C2×D412yes—
214C42×C17C2×D412yes—
215C22⋊Dic17—42no—
216C22⋊Dic17—42no—
217C22⋊Dic17—81no—
218C22⋊Dic17—81no—
219#63231—28no—
220C4⋊Dic17—21no—
221C4⋊Dic17—21no—
222C4⋊Dic17—21no—
223C4⋊Dic17—21no—
224C4⋊Dic17—21no—
225C4⋊Dic17—21no—
226C4⋊Dic17—42no—
227C4⋊Dic17—81no—
228#63225—42no—
229#63225—42no—
230#63225—42no—
231C4×Dic17—42no—
232C2×#3622—21no—
233C2×#3622—21no—
234C2×#3622—21no—
235C2×#3622—21no—
236C2×#3622—21no—
237C2×#3622—21no—
238C2×#3622—21no—
239C2×#3622—21no—
240C2×#3622—21no—
241C2×#3622—21no—
242C2×#3622—21no—
243C2×#3622#4112yes—
244#24139—171nomaximal, Sylow
245C23×C17—21no—
246C23×C17—21no—
247C23×C17—21no—
248C23×C17—21no—
249C23×C17—21no—
250C23×C17—21no—
251C23×C17—21no—
252C23×C17—21no—
253C23×C17—21no—
254C23×C17—21no—
255C23×C17—21no—
256C23×C17—21no—
257C23×C17—21no—
258C23×C17#13712yes—
259C23×C17C22×D411yescharacteristic
260Q8×C17—22no—
261Q8×C17—22no—
262Q8×C17—41no—
263Q8×C17—41no—
264D4×C17—44no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—21no—
268C2×C4×C17—21no—
269C2×C4×C17—21no—
270C2×C4×C17—22no—
271C2×C4×C17—22no—
272C2×C4×C17—22no—
273C2×C4×C17—21no—
274C2×C4×C17—22no—
275C2×C4×C17—21no—
276C2×C4×C17—21no—
277C2×C4×C17—21no—
278C2×C4×C17—21no—
279C2×C4×C17—48no—
280C2×C4×C17—41no—
281C2×C4×C17—41no—
282C2×C4×C17—41no—
283C2×C4×C17—41no—
284C2×C4×C17—41no—
285C2×C4×C17—41no—
286C2×C4×C17—41no—
287C2×C4×C17—41no—
288C2×C4×C17—41no—
289C2×C4×C17—41no—
290C2×C4×C17—41no—
291C2×C4×C17—41no—
292C2×C4×C17—41no—
293C2×C4×C17—41no—
294C2×C4×C17—41no—
295C2×C4×C17—41no—
296C2×C4×C17#12012yes—
297C2×C4×C17#12012yes—
298C2×C4×C17C22×D411yescharacteristic
299C2×C4×C17C22×D411yescharacteristic
300C2×C4×C17C2×#4111yescharacteristic
301C2×C4×C17C2×#4111yescharacteristic
302C2×C4×C17H(5,𝔽2)11yescharacteristic
303C2×C4×C172−1+411yescharacteristic
304C2×Dic17—22no—
305C2×Dic17—41no—
306C2×Dic17—41no—
307C2×Dic17—41no—
308C2×Dic17—41no—
309C2×Dic17—41no—
310C2×Dic17—41no—
311C2×Dic17—41no—
312C2×Dic17—41no—
313C2×Dic17—41no—
314C2×Dic17—41no—
315C2×Dic17—41no—
316Dic34—22no—
317Dic34—22no—
318Dic34—41no—
319Dic34—41no—
320#3622—22no—
321#3622—41no—
322#3622—41no—
323#3622—41no—
324C2×#552D1711yescharacteristic
325C2×#479—171no—
326C2×#441—171no—
327#2538—171no—
328#2036—171no—
329#2035—171no—
330#2001—171no—
331#2001—171no—
332#1992—171no—
333#1955—171no—
334#1873—171no—
335#1872—171no—
336#1854—171no—
337#1853—171no—
338#1803—171no—
339C22×C17—22no—
340C22×C17—22no—
341C22×C17—22no—
342C22×C17—41no—
343C22×C17—41no—
344C22×C17—41no—
345C22×C17—41no—
346C22×C17—41no—
347C22×C17—41no—
348C22×C17—41no—
349C22×C17—41no—
350C22×C17—41no—
351C22×C17—41no—
352C22×C17—41no—
353C22×C17C2×#12011yescharacteristic
354C22×C17#54611yescharacteristic
355C22×C17#54711yescharacteristic
356C22×C17C2×#13711yescharacteristic
357C22×C17#57511yescharacteristic
358C22×C17#57711yescharacteristic
359C22×C17#57811yescharacteristic
360C4×C17—22no—
361C4×C17—22no—
362C4×C17—41no—
363C4×C17—41no—
364C4×C17—42no—
365C4×C17—42no—
366C4×C17—42no—
367C4×C17—42no—
368C4×C17#52511yescharacteristic
369C4×C17#53711yescharacteristic
370C4×C17#54811yescharacteristic
371C4×C17#55011yescharacteristic
372Dic17—42no—
373Dic17—81no—
374Dic17—81no—
375Dic17—81no—
376C22×Q16—171no—
377#552—24no—
378#552—24no—
379C2×#126—21no—
380C2×#125—21no—
381C2×#125C2×D1711yescharacteristic
382C2×#123—21no—
383C2×C22⋊Q8—171no—
384C2×C22⋊Q8—171no—
385C2×C22⋊Q8C2×D1711yescharacteristic
386C2×C22⋊Q8C2×D1711yescharacteristic
387C2×C4×Q8—171no—
388C2×C4×Q8C2×D1711yescharacteristic
389C2×C4×D4C2×D1711yescharacteristic
390C2×#117—21no—
391C2×#117C2×D1711yescharacteristic
392C22×C4⋊C4C2×D1711yescharacteristic
393#479—344no—
394#441—344no—
395C2×#107—171no—
396C2×#106—171no—
397C2×#106—171no—
398C2×C4⋊C8—171no—
399C2×#103—171no—
400C2×#103—171no—
401C2×#103—171no—
402C2×#103—171no—
403C2×#103—171no—
404C2×#103—171no—
405C2×C22⋊C8—171no—
406C2×C22⋊C8—171no—
407C2×C22⋊C8—171no—
408C2×C22⋊C8—171no—
409C2×#97—171no—
410#396—341no—
411#396—341no—
412#390—341no—
413#389—341no—
414#384—171no—
415#380—171no—
416#380—171no—
417#340—171no—
418#340—171no—
419#340—171no—
420#340—171no—
421#340—171no—
422#340—171no—
423C2×C17—42no—
424C2×C17—81no—
425C2×C17#240711yescharacteristic
426C2×C17#300711yescharacteristic
427C2×C17#301311yescharacteristic
428C2×C17#331211yescharacteristic
429C2×C17#331711yescharacteristic
430C2×C17#334411yescharacteristic
431C2×C17#334911yescharacteristic
432C22×Q8—171no—
433C22×Q8C22×D1711yescharacteristic
434C22×D4C22⋊D1711yescharacteristic
435C23×C4—21no—
436C23×C4C22×D1711yescharacteristic
437C23×C4C22×D1711yescharacteristic
438C2×Q16—342no—
439C2×Q16—342no—
440C2×Q16—342no—
441C22×C8—171no—
442C22×C8—171no—
443C22×C8—171no—
444C22×C8—171no—
445#126—28no—
446#125—28no—
447#125—22no—
448#125C22⋊D1714yes—
449#123—28no—
450C22⋊Q8—22no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—342no—
455C22⋊Q8—342no—
456C22⋊Q8—681no—
457C22⋊Q8—681no—
458C4×Q8—22no—
459C4×Q8—342no—
460C4×Q8—342no—
461C4×Q8C22⋊D1714yes—
462C4×D4—22no—
463C4×D4—22no—
464#117—28no—
465#117—22no—
466#117—22no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—171no—
476C2×C4⋊C4—171no—
477C2×C4⋊C4—171no—
478C2×C4⋊C4—341no—
479C2×C4⋊C4—341no—
480C2×C4⋊C4—341no—
481C2×C4⋊C4—341no—
482C2×C4⋊C4—341no—
483C2×C4⋊C4C22⋊D1711yescharacteristic
484C2×C4⋊C4C22×D1711yescharacteristic
485C2×C4⋊C4C22×D1711yescharacteristic
486C2×C4⋊C4C22×D1711yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—341no—
491C2×C22⋊C4—341no—
492C2×C22⋊C4—341no—
493C2×C22⋊C4—341no—
494C2×C22⋊C4C22⋊D1711yescharacteristic
495C2×C22⋊C4C22⋊D1711yescharacteristic
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—341no—
499C2×C42C22×D1711yescharacteristic
500#107—342no—
501#106—342no—
502#106—342no—
503C4⋊C8—342no—
504#103—342no—
505#103—342no—
506#103—342no—
507#103—342no—
508#103—681no—
509#103—681no—
510C22⋊C8—342no—
511C22⋊C8—342no—
512C22⋊C8—681no—
513C22⋊C8—681no—
514#97—342no—
515#95—341no—
516#95—341no—
517C17#2413911yescharacteristic, complemented, Sylow
518C24C2×C22⋊D1711yescharacteristic
519C24C2×C22⋊D1711yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—172no—
526C2×Q8—341no—
527C2×Q8—341no—
528C2×Q8—341no—
529C2×Q8—341no—
530C2×Q8—341no—
531C2×Q8C2×C22⋊D1712yes—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—41no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—341no—
555C22×C4—341no—
556C22×C4—341no—
557C22×C4—341no—
558C22×C4C2×C22⋊D1711yescharacteristic
559C22×C4C2×C22⋊D1711yescharacteristic
560C22×C4C2×C22⋊D1711yescharacteristic
561C22×C4C2×C22⋊D1711yescharacteristic
562C22×C4C23×D1711yescharacteristic
563Q16—348no—
564C2×C8—172no—
565C2×C8—341no—
566C2×C8—341no—
567C2×C8—341no—
568C2×C8—341no—
569C2×C8—341no—
570C2×C8—341no—
571C2×C8—341no—
572C2×C8—341no—
573C2×C8—341no—
574C2×C8—341no—
575C2×C8—341no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—341no—
587C4⋊C4—341no—
588C4⋊C4—341no—
589C4⋊C4—341no—
590C4⋊C4—341no—
591C4⋊C4—341no—
592C4⋊C4—682no—
593C4⋊C4—682no—
594C4⋊C4—682no—
595C4⋊C4—682no—
596C4⋊C4—1361no—
597C4⋊C4C2×C22⋊D1712yes—
598C4⋊C4C2×C22⋊D1712yes—
599C4⋊C4C2×C22⋊D1712yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—682no—
606C22⋊C4—682no—
607C22⋊C4—1361no—
608C22⋊C4—1361no—
609C42—24no—
610C42—24no—
611C42—682no—
612C42C2×C22⋊D1712yes—
613C42C2×C22⋊D1712yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23#1058763712yes—
628C23C22×C22⋊D1711yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—342no—
634Q8—342no—
635Q8—681no—
636Q8—681no—
637D4—44no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—48no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—342no—
670C2×C4—681no—
671C2×C4—681no—
672C2×C4—681no—
673C2×C4—681no—
674C2×C4—681no—
675C2×C4—681no—
676C2×C4—681no—
677C2×C4—681no—
678C2×C4—681no—
679C2×C4—681no—
680C2×C4—681no—
681C2×C4#1058763912yes—
682C2×C4#1058763912yes—
683C2×C4#41×D1711yescharacteristic
684C2×C4#41×D1711yescharacteristic
685C2×C4#1058769611yescharacteristic
686C2×C4#1058769711yescharacteristic
687C2×C4C22×C22⋊D1711yescharacteristic
688C2×C4C22×C22⋊D1711yescharacteristic
689C8—342no—
690C8—681no—
691C8—681no—
692C8—681no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22C2×#1058763911yescharacteristic
708C22#1176344711yescharacteristic
709C22#1176345811yescharacteristic
710C22C2×#1058763711yescharacteristic
711C22#1176360711yescharacteristic
712C22#1176361711yescharacteristic
713C22#1176362411yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—682no—
723C4—1361no—
724C4—1361no—
725C4—1361no—
726C4#1176331611yescharacteristic
727C4#1176338711yescharacteristic
728C4#1176346611yescharacteristic
729C4#1176347811yescharacteristic
730C2—42no—
731C2—81no—
732C2#1453212311yescharacteristic
733C2#1453804411yescharacteristic
734C2#1453809911yescharacteristic
735C2#1454082911yescharacteristic
736C2#1454090411yescharacteristic
737C2#1454123911yescharacteristic
738C2#1454131411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#552C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
hypercenterC2×#552D17
hypocenterC17#24139
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#11763113C2semidirect
2. C2×#11762914C2semidirect
4. #14529984C2semidirect
5. #14529977C2semidirect
6. #14529792C2semidirect
7. #14529792C2semidirect
8. #14529754C2semidirect
10. #14529096C2semidirect
11. #14529091C2semidirect
12. #14528983C2semidirect
13. #14528977C2semidirect
14. #14528789C2semidirect
517. C17#24139semidirect

Maximal subgroups

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

subgroupindex
C2×#117631132
C2×#117629142
#145337062
#145299842
#145299772
#145297922
#145297542
#145295832
#145290962
#145290912
#145289832
#145289772
#145287892
C2×C17×#5522
#2413917