Finite Group Databasebeta

← C2×#14532453 #17202963

Subgroups — C2×#14532453 #17202963

Order 4352.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587632C211yesmaximal, characteristic
2C22×#10587578C211yesmaximal, characteristic
3#14532453C2116yesmaximal, direct product factor
4C2×#11762751C211yesmaximal, characteristic, complemented
5C2×#11762742C211yesmaximal, characteristic, complemented
6C2×#11762741C211yesmaximal, characteristic, complemented
7C2×#11762716C211yesmaximal, characteristic, complemented
8C2×#11762704C211yesmaximal, characteristic, complemented
9C2×#11762695C211yesmaximal, characteristic, complemented
10C2×#11762694C211yesmaximal, characteristic, complemented
11C2×#11762683C211yesmaximal, characteristic
12C2×#11762680C211yesmaximal, characteristic
13C2×#11762671C211yesmaximal, characteristic
14C2×#11762666C211yesmaximal, characteristic
15C2×#95×D17C211yesmaximal, characteristic
16C2×C17×#395C211yesmaximal, characteristic, complemented
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C2×#10587632—28no—
21C2×#10587632C2218yes—
22C2×#10587578—28no—
23C2×#10587578C2218yes—
24C22×C4⋊Dic17C2211yescharacteristic
25C22×C4⋊Dic17C2211yescharacteristic
26C22×C4⋊Dic17C2211yescharacteristic
27C22×C4⋊Dic17C2211yescharacteristic
28C22×#63225C2211yescharacteristic
29C22×#63225C2211yescharacteristic
30C22×#63225C2211yescharacteristic
31C22×#63225C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36C22×C4×Dic17C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38#11762751C2218yescomplemented
39#11762742C2218yescomplemented
40#11762741C2218yescomplemented
41#11762716C2218yescomplemented
42#11762704C2218yescomplemented
43#11762695C2218yescomplemented
44#11762694C2218yescomplemented
45#11762683C2218yes—
46#11762680C2218yes—
47#11762671C2218yes—
48#11762666C2218yes—
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C2×#10587502C2211yescharacteristic
60#95×D17C2218yes—
61C23×Q8×C17C2211yescharacteristic
62C22×C4⋊C4×C17C2211yescharacteristic
63C22×C4⋊C4×C17C2211yescharacteristic
64C22×C4⋊C4×C17C2211yescharacteristic
65C17×#395C2218yescomplemented
66C2×C17×#95C2211yescharacteristic
67C2×C17×#95C2211yescharacteristic
68C2×C17×#95C2211yescharacteristic
69C24×D17C2311yescharacteristic
70C22×Q8×C17—24no—
71C22×Q8×C17—24no—
72C22×Q8×C17—42no—
73C22×Q8×C17C2314yes—
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C23×Dic17C2311yescharacteristic
83C23×Dic17C2311yescharacteristic
84C23×Dic17C2311yescharacteristic
85C23×Dic17C2311yescharacteristic
86C23×Dic17C2311yescharacteristic
87C23×Dic17C2311yescharacteristic
88C22×C4×D17—24no—
89C22×C4×D17—24no—
90C22×C4×D17—24no—
91C22×C4×D17—24no—
92C22×C4×D17—24no—
93C22×C4×D17—24no—
94C22×C4×D17—42no—
95C22×C4×D17—42no—
96C22×C4×D17Q818yescomplemented
97C22×C4×D17C2314yes—
98C22×C4×D17C2314yes—
99C22×C4×D17C2314yes—
100C2×C4⋊C4×C17—24no—
101C2×C4⋊C4×C17—24no—
102C2×C4⋊C4×C17—42no—
103C2×C4⋊C4×C17C2314yes—
104C2×C4⋊C4×C17C2314yes—
105C2×C4⋊C4×C17C2314yes—
106#10587632—232no—
107C2×#63227—24no—
108C2×#63227—24no—
109C2×#63227—24no—
110C2×#63227D418yes—
111C2×#63227C2314yes—
112C2×#63227C2314yes—
113C2×#63227C2314yes—
114C2×#63227C2314yes—
115C2×C4⋊Dic17—24no—
116C2×C4⋊Dic17—24no—
117C2×C4⋊Dic17—24no—
118C2×C4⋊Dic17—42no—
119C2×C4⋊Dic17C2314yes—
120C2×C4⋊Dic17C2314yes—
121C2×C4⋊Dic17C2314yes—
122C2×C4⋊Dic17C2314yes—
123C2×#63225—24no—
124C2×#63225—24no—
125C2×#63225—24no—
126C2×#63225—42no—
127C2×#63225C2314yes—
128C2×#63225C2314yes—
129C2×#63225C2314yes—
130C2×#63225C2314yes—
131C2×C4×Dic17—24no—
132C2×C4×Dic17—24no—
133C2×C4×Dic17C2314yes—
134C2×C4×Dic17C2314yes—
135#10587578—232no—
136C17×#95C2314yes—
137C17×#95C2314yes—
138C17×#95C2314yes—
139#10587502C2314yes—
140#10587502C2314yes—
141#10587502C2314yes—
142#10587502C2314yes—
143#10587502C2314yes—
144#10587502C2314yes—
145#10587502C2314yes—
146#10587502C2314yes—
147#10587502C2314yes—
148#10587502C2314yes—
149#10587502C2314yes—
150C24×C17C2411yescharacteristic
151C23×D17—22no—
152C23×D17—22no—
153C23×D17—22no—
154C23×D17—22no—
155C23×D17C2×D414yes—
156C23×D17C2×Q814yes—
157C23×D17#4114yes—
158C23×D17C2412yes—
159C2×Q8×C17—28no—
160C2×Q8×C17—28no—
161C2×Q8×C17—44no—
162C2×Q8×C17—416no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17—22no—
166C22×C4×C17—22no—
167C22×C4×C17—22no—
168C22×C4×C17—22no—
169C22×C4×C17—22no—
170C22×C4×C17—22no—
171C22×C4×C17—22no—
172C22×C4×C17—22no—
173C22×C4×C17—22no—
174C22×C4×C17—22no—
175C22×C4×C17—22no—
176C22×C4×C17—22no—
177C22×C4×C17—22no—
178C22×C4×C17—22no—
179C22×C4×C17—22no—
180C22×C4×C17C2×D414yes—
181C22×C4×C17C2×Q814yes—
182C22×C4×C17#4114yes—
183C22×C4×C17#4114yes—
184C22×C4×C17C2412yes—
185C22×C4×C17C2412yes—
186C22×C4×C17C2412yes—
187C22×C4×C17C2412yes—
188C22×C4×C17C2412yes—
189C22×C4×C17C2412yes—
190C22×C4×C17C2412yes—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17—22no—
197C22×Dic17—22no—
198C22×Dic17—22no—
199C22×Dic17—22no—
200C22×Dic17—22no—
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—22no—
204C22×Dic17—22no—
205C22×Dic17—22no—
206C22×Dic17—22no—
207C22×Dic17—22no—
208C22×Dic17—22no—
209C22×Dic17—22no—
210C22×Dic17C2×D414yes—
211C22×Dic17C2×Q814yes—
212C22×Dic17C2412yes—
213C22×Dic17C2412yes—
214C22×Dic17C2412yes—
215C22×Dic17C2412yes—
216C22×Dic17C2412yes—
217C22×Dic17C2412yes—
218C22×Dic17C2412yes—
219C2×C4×D17—232no—
220C2×C4×D17—28no—
221C2×C4×D17—28no—
222C2×C4×D17—28no—
223C2×C4×D17—28no—
224C2×C4×D17—28no—
225C2×C4×D17—28no—
226C2×C4×D17—44no—
227C2×C4×D17—44no—
228C2×C4×D17—416no—
229C2×C4×D17—416no—
230C2×C4×D17C2×Q8116yescomplemented
231C4⋊C4×C17—28no—
232C4⋊C4×C17—28no—
233C4⋊C4×C17—44no—
234#63227—28no—
235#63227—28no—
236#63227—28no—
237#63227C2×D4116yes—
238C4⋊Dic17—28no—
239C4⋊Dic17—28no—
240C4⋊Dic17—28no—
241C4⋊Dic17—44no—
242#63225—28no—
243#63225—28no—
244#63225—28no—
245#63225—44no—
246C4×Dic17—28no—
247C4×Dic17—28no—
248C2×#2438—171nomaximal, Sylow
249C23×C17C22×D412yes—
250C23×C17C22×Q812yes—
251C23×C17C2×#4112yes—
252C23×C17C2×#4112yes—
253C23×C17C2×#4112yes—
254C23×C17H(5,𝔽2)12yes—
255C23×C172−1+412yes—
256C23×C17C2511yescharacteristic
257C22×D17—28no—
258C22×D17—28no—
259C22×D17—28no—
260C22×D17—28no—
261C22×D17—28no—
262C22×D17—28no—
263C22×D17—22no—
264C22×D17—22no—
265C22×D17—22no—
266C22×D17—22no—
267C22×D17C22⋊Q8116yes—
268C22×D17C22×D414yes—
269C22×D17C22×Q814yes—
270C22×D17C2×#4114yes—
271Q8×C17—416no—
272C2×C4×C17—28no—
273C2×C4×C17—28no—
274C2×C4×C17—28no—
275C2×C4×C17—28no—
276C2×C4×C17—22no—
277C2×C4×C17—22no—
278C2×C4×C17—22no—
279C2×C4×C17—22no—
280C2×C4×C17—22no—
281C2×C4×C17—22no—
282C2×C4×C17—22no—
283C2×C4×C17—22no—
284C2×C4×C17—22no—
285C2×C4×C17—22no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—22no—
291C2×C4×C17—22no—
292C2×C4×C17—22no—
293C2×C4×C17—44no—
294C2×C4×C17—44no—
295C2×C4×C17—44no—
296C2×C4×C17C22×D414yes—
297C2×C4×C17C22×Q814yes—
298C2×C4×C17C2×#4114yes—
299C2×C4×C17C2×#4114yes—
300C2×Dic17—28no—
301C2×Dic17—28no—
302C2×Dic17—22no—
303C2×Dic17—22no—
304C2×Dic17—22no—
305C2×Dic17—22no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—22no—
314C2×Dic17—22no—
315C2×Dic17—22no—
316C2×Dic17—22no—
317C2×Dic17—22no—
318C2×Dic17—22no—
319C2×Dic17—22no—
320C2×Dic17—22no—
321C2×Dic17—44no—
322C2×Dic17—44no—
323C2×Dic17—44no—
324C2×Dic17—44no—
325C2×Dic17—44no—
326C2×Dic17C22×D414yes—
327C2×Dic17C22×Q814yes—
328C4×D17—232no—
329C4×D17—416no—
330C4×D17—416no—
331C22×C22⋊Q8—171no—
332C22×#117—171no—
333#2438—1716no—
334C2×#400—171no—
335C2×#398—171no—
336C2×#398—171no—
337C2×#395D1711yescharacteristic, complemented
338C2×#391—171no—
339C2×#389—171no—
340C2×#387—171no—
341C2×#387—171no—
342C2×#385—171no—
343C2×#385—171no—
344C2×#381—171no—
345C2×#380—171no—
346C22×#95—171no—
347C22×C17C2×C22⋊Q814yes—
348C22×C17#53314yes—
349C22×C17#54414yes—
350C22×C17#54614yes—
351C22×C17#54714yes—
352C22×C17#55114yes—
353C22×C17#55214yes—
354C22×C17C23×D411yescharacteristic
355C22×C17C23×Q811yescharacteristic
356C22×C17C22×#4111yescharacteristic
357C22×C17C22×#4111yescharacteristic
358C22×C17C22×#4111yescharacteristic
359C22×C17C2×H(5,𝔽2)11yescharacteristic
360C22×C17C2×2−1+411yescharacteristic
361C2×D17—24no—
362C2×D17—24no—
363C2×D17—232no—
364C2×D17—24no—
365C2×D17—24no—
366C2×D17—24no—
367C2×D17—24no—
368C2×D17C2×C22⋊Q818yes—
369C4×C17—24no—
370C4×C17—24no—
371C4×C17—24no—
372C4×C17—24no—
373C4×C17—42no—
374C4×C17—42no—
375C4×C17—42no—
376Dic17—24no—
377Dic17—24no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381Dic17—42no—
382Dic17—42no—
383C23×Q8C2×D1711yescharacteristic
384C24×C4—171no—
385C24×C4—171no—
386C24×C4—171no—
387C2×C22⋊Q8—178no—
388C2×C22⋊Q8—348no—
389C2×#117—178no—
390C2×#117—348no—
391C22×C4⋊C4—171no—
392C22×C4⋊C4—171no—
393C22×C4⋊C4—171no—
394C22×C4⋊C4—171no—
395C22×C4⋊C4—171no—
396C22×C4⋊C4—171no—
397C22×C4⋊C4—171no—
398C22×C4⋊C4—171no—
399C22×C4⋊C4C2×D1711yescharacteristic
400C22×C4⋊C4C2×D1711yescharacteristic
401C22×C4⋊C4C2×D1711yescharacteristic
402C22×C22⋊C4—171no—
403C22×C22⋊C4—171no—
404C22×C22⋊C4—171no—
405C22×C22⋊C4—171no—
406C22×C42—171no—
407C22×C42—171no—
408#400—178no—
409#398—178no—
410#398—178no—
411#395C2×D1718yescomplemented
412#391—178no—
413#389—178no—
414#387—178no—
415#387—178no—
416#385—178no—
417#385—178no—
418#381—178no—
419#380—178no—
420C2×#95—171no—
421C2×#95—171no—
422C2×#95—171no—
423C2×#95—171no—
424C2×#95—171no—
425C2×#95—171no—
426C2×#95—171no—
427C2×#95—171no—
428C2×#95—171no—
429C2×#95—171no—
430C2×#95—171no—
431C2×#95—178no—
432C2×#95C2×D1711yescharacteristic
433C2×#95C2×D1711yescharacteristic
434C2×#95C2×D1711yescharacteristic
435C2×C17#243818yescomplemented
436C2×C17C22×C22⋊Q811yescharacteristic
437C2×C17C2×#53311yescharacteristic
438C2×C17C2×#54411yescharacteristic
439C2×C17C2×#54611yescharacteristic
440C2×C17C2×#54711yescharacteristic
441C2×C17C2×#55111yescharacteristic
442C2×C17C2×#55211yescharacteristic
443D17—28no—
444C25—171no—
445C22×Q8—24no—
446C22×Q8—24no—
447C22×Q8—42no—
448C22×Q8C22×D1714yes—
449C23×C4—171no—
450C23×C4—171no—
451C23×C4—178no—
452C23×C4—174no—
453C23×C4—171no—
454C23×C4—171no—
455C23×C4—171no—
456C23×C4—171no—
457C23×C4—171no—
458C23×C4—174no—
459C23×C4—174no—
460C23×C4—344no—
461C23×C4—344no—
462C23×C4—344no—
463C23×C4—344no—
464C23×C4—344no—
465C23×C4—344no—
466C23×C4—682no—
467C23×C4—682no—
468C23×C4C22×D1711yescharacteristic
469C23×C4C22×D1711yescharacteristic
470C23×C4C22×D1711yescharacteristic
471C23×C4C22×D1711yescharacteristic
472C23×C4C22×D1711yescharacteristic
473C23×C4C22×D1711yescharacteristic
474C23×C4C22×D1711yescharacteristic
475C22⋊Q8—3432no—
476#117—3432no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—174no—
481C2×C4⋊C4—174no—
482C2×C4⋊C4—174no—
483C2×C4⋊C4—174no—
484C2×C4⋊C4—174no—
485C2×C4⋊C4—174no—
486C2×C4⋊C4—174no—
487C2×C4⋊C4—174no—
488C2×C4⋊C4—344no—
489C2×C4⋊C4—344no—
490C2×C4⋊C4—344no—
491C2×C4⋊C4—344no—
492C2×C4⋊C4—344no—
493C2×C4⋊C4—344no—
494C2×C4⋊C4—682no—
495C2×C4⋊C4—682no—
496C2×C4⋊C4C22×D1714yes—
497C2×C4⋊C4C22×D1714yes—
498C2×C4⋊C4C22×D1714yes—
499C2×C22⋊C4—178no—
500C2×C22⋊C4—174no—
501C2×C22⋊C4—174no—
502C2×C22⋊C4—174no—
503C2×C22⋊C4—174no—
504C2×C22⋊C4—344no—
505C2×C22⋊C4—344no—
506C2×C22⋊C4—344no—
507C2×C42—174no—
508C2×C42—174no—
509C2×C42—344no—
510C2×C42—344no—
511#95—174no—
512#95—174no—
513#95—174no—
514#95—174no—
515#95—174no—
516#95—174no—
517#95—174no—
518#95—174no—
519#95—174no—
520#95—174no—
521#95—174no—
522#95C22×D1714yes—
523#95C22×D1714yes—
524#95C22×D1714yes—
525C17C2×#243811yescharacteristic, complemented, Sylow
526C24—174no—
527C24—174no—
528C24—174no—
529C24—172no—
530C24—342no—
531C24—342no—
532C24—342no—
533C24—342no—
534C24C23×D1711yescharacteristic
535C2×Q8—28no—
536C2×Q8—28no—
537C2×Q8—44no—
538C2×Q8—416no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—174no—
557C22×C4—174no—
558C22×C4—172no—
559C22×C4—172no—
560C22×C4—1716no—
561C22×C4—172no—
562C22×C4—172no—
563C22×C4—172no—
564C22×C4—172no—
565C22×C4—172no—
566C22×C4—348no—
567C22×C4—3432no—
568C22×C4—348no—
569C22×C4—348no—
570C22×C4—348no—
571C22×C4—342no—
572C22×C4—342no—
573C22×C4—342no—
574C22×C4—342no—
575C22×C4—342no—
576C22×C4—342no—
577C22×C4—342no—
578C22×C4—342no—
579C22×C4—342no—
580C22×C4—342no—
581C22×C4—342no—
582C22×C4—342no—
583C22×C4—342no—
584C22×C4—342no—
585C22×C4—342no—
586C22×C4—342no—
587C22×C4—342no—
588C22×C4—342no—
589C22×C4—342no—
590C22×C4—348no—
591C22×C4—348no—
592C22×C4—684no—
593C22×C4—684no—
594C22×C4—6816no—
595C22×C4—6816no—
596C22×C4D4×D1714yes—
597C22×C4#6325414yes—
598C22×C4Q8×D1714yes—
599C22×C4#6325614yes—
600C22×C4C23×D1712yes—
601C22×C4C23×D1712yes—
602C22×C4C23×D1712yes—
603C22×C4C23×D1712yes—
604C22×C4C23×D1712yes—
605C22×C4C23×D1712yes—
606C22×C4C23×D1712yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—348no—
611C4⋊C4—348no—
612C4⋊C4—348no—
613C4⋊C4—348no—
614C4⋊C4—348no—
615C4⋊C4—348no—
616C4⋊C4—684no—
617C4⋊C4—684no—
618C22⋊C4—1716no—
619C22⋊C4—348no—
620C22⋊C4—348no—
621C22⋊C4—348no—
622C42—348no—
623C42—348no—
624C23—1716no—
625C23—174no—
626C23—174no—
627C23—174no—
628C23—348no—
629C23—348no—
630C23—348no—
631C23—348no—
632C23—342no—
633C23—342no—
634C23—342no—
635C23—342no—
636C23—348no—
637C23—348no—
638C23C2×D4×D1712yes—
639C23C2×#6325412yes—
640C23#1058769112yes—
641C23C2×Q8×D1712yes—
642C23C2×#6325612yes—
643C23#1058769412yes—
644C23#41×D1712yes—
645C23C24×D1711yescharacteristic
646Q8—416no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—174no—
672C2×C4—174no—
673C2×C4—3432no—
674C2×C4—348no—
675C2×C4—348no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—342no—
684C2×C4—342no—
685C2×C4—342no—
686C2×C4—342no—
687C2×C4—342no—
688C2×C4—342no—
689C2×C4—342no—
690C2×C4—342no—
691C2×C4—342no—
692C2×C4—342no—
693C2×C4—342no—
694C2×C4—342no—
695C2×C4—6816no—
696C2×C4—6816no—
697C2×C4—684no—
698C2×C4—684no—
699C2×C4—684no—
700C2×C4—684no—
701C2×C4—684no—
702C2×C4C2×D4×D1714yes—
703C2×C4C2×#6325414yes—
704C2×C4C2×Q8×D1714yes—
705C2×C4C2×#6325614yes—
706C22—178no—
707C22—3432no—
708C22—344no—
709C22—344no—
710C22—344no—
711C22—344no—
712C22—344no—
713C22—344no—
714C22C22⋊Q8×D1714yes—
715C22#1176336414yes—
716C22#1176343614yes—
717C22#1176344614yes—
718C22#1176346214yes—
719C22#1176348614yes—
720C22#1176349314yes—
721C22C22×D4×D1711yescharacteristic
722C22C22×Q8×D1711yescharacteristic
723C22C2×#41×D1711yescharacteristic
724C22C22×#6325411yescharacteristic
725C22C22×#6325611yescharacteristic
726C22C2×#1058769111yescharacteristic
727C22C2×#1058769411yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—344no—
736C4—344no—
737C4—682no—
738C4—682no—
739C4—682no—
740C4—682no—
741C4—682no—
742C2—348no—
743C2#1453245318yesdirect product factor
744C2C2×C22⋊Q8×D1711yescharacteristic
745C2C2×#1176336411yescharacteristic
746C2C2×#1176343611yescharacteristic
747C2C2×#1176344611yescharacteristic
748C2C2×#1176346211yescharacteristic
749C2C2×#1176348611yescharacteristic
750C2C2×#1176349311yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#395C2
socleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×#395D17
hypocenterC17C2×#2438
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. #14532453C2direct (N × H)
4. C2×#11762751C2semidirect
5. C2×#11762742C2semidirect
6. C2×#11762741C2semidirect
7. C2×#11762716C2semidirect
8. C2×#11762704C2semidirect
9. C2×#11762695C2semidirect
10. C2×#11762694C2semidirect
16. C2×C17×#395C2semidirect
38. #11762751C22semidirect
39. #11762742C22semidirect
40. #11762741C22semidirect
41. #11762716C22semidirect
42. #11762704C22semidirect
43. #11762695C22semidirect
44. #11762694C22semidirect
65. C17×#395C22semidirect
96. C22×C4×D17Q8semidirect
230. C2×C4×D17C2×Q8semidirect
337. C2×#395D17semidirect
411. #395C2×D17semidirect
435. C2×C17#2438semidirect
525. C17C2×#2438semidirect
743. C2#14532453direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876322
C22×#105875782
#145324532
C2×#117627512
C2×#117627422
C2×#117627412
C2×#117627162
C2×#117627042
C2×#117626952
C2×#117626942
C2×#117626832
C2×#117626802
C2×#117626712
C2×#117626662
C2×#95×D172
C2×C17×#3952
C2×#243817