Finite Group Databasebeta

← C2×#14541271 #17912905

Subgroups — C2×#14541271 #17912905

Order 4352.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763516C211yesmaximal, characteristic, complemented
2C2×#11763505C211yesmaximal, characteristic
3#14541271C2116yesmaximal, direct product factor
4C2×#11763218C211yesmaximal, characteristic, complemented
5C2×#11763145C211yesmaximal, characteristic, complemented
6C2×#11763128C211yesmaximal, characteristic, complemented
7C2×#11763151C211yesmaximal, characteristic, complemented
8C2×#11763123C211yesmaximal, characteristic, complemented
9C2×#11763117C211yesmaximal, characteristic, complemented
10C2×#11763090C211yesmaximal, characteristic, complemented
11C2×#11763055C211yesmaximal, characteristic, complemented
12C2×#11763038C211yesmaximal, characteristic, complemented
13C2×#11762911C211yesmaximal, characteristic, complemented
14C2×#11762851C211yesmaximal, characteristic, complemented
15C22×#10587489C211yesmaximal, characteristic, complemented
16C2×C17×#435C211yesmaximal, characteristic, complemented
17C22×#63219C2211yescharacteristic
18#11763516—24no—
19#11763516C2218yescomplemented
20#11763505—24no—
21#11763505C2218yes—
22C2×#10587555C2211yescharacteristic
23C2×#10587584—21no—
24C2×#10587556C2211yescharacteristic
25C2×#10587576—21no—
26C2×#10587569—21no—
27C2×#10587610C2211yescharacteristic
28C2×#10587610C2211yescharacteristic
29C2×#10587564—21no—
30C2×#10587564—21no—
31C2×#10587616C2211yescharacteristic
32C2×#10587616C2211yescharacteristic
33C2×#10587625—21no—
34C2×C4×Dic34C2211yescharacteristic
35C2×C4×D68C2211yescharacteristic
36C2×D4×Dic17—21no—
37C2×#10587567—21no—
38C2×#10587612C2211yescharacteristic
39C22×C4⋊Dic17C2211yescharacteristic
40C22×C4⋊Dic17C2211yescharacteristic
41C22×C4⋊Dic17C2211yescharacteristic
42#11763218C2218yescomplemented
43#11763151C2218yescomplemented
44#11763145C2218yescomplemented
45#11763128C2218yescomplemented
46#11763123C2218yescomplemented
47#11763117C2218yescomplemented
48#11763090C2218yescomplemented
49#11763055C2218yescomplemented
50#11763038C2218yescomplemented
51#11762911C2218yescomplemented
52#11762851C2218yescomplemented
53C2×#10587489C2211yescharacteristic
54C2×#10587489C2211yescharacteristic
55C2×#10587489C2211yescharacteristic
56C2×#10587489C2211yescharacteristic
57C2×#10587489C2211yescharacteristic
58C2×#10587489C2211yescharacteristic
59C2×#10587489C2218yescomplemented
60C2×#10587488C2211yescharacteristic
61C2×#10587488C2211yescharacteristic
62C2×#10587488C2211yescharacteristic
63C2×#10587487C2211yescharacteristic
64C2×#10587487C2211yescharacteristic
65C2×#10587487C2211yescharacteristic
66C2×#10587492C2211yescharacteristic
67C2×#10587492C2211yescharacteristic
68C2×#10587492C2211yescharacteristic
69C22×M16×C17C2211yescharacteristic
70C23×C8×C17C2211yescharacteristic
71C2×C4×D4×C17C2211yescharacteristic
72C17×#435C2218yescomplemented
73C2×C17×C4⋊C8C2211yescharacteristic
74C2×C17×C22⋊C8C2211yescharacteristic
75C2×C17×C22⋊C8C2211yescharacteristic
76C2×C17×#97C2211yescharacteristic
77C22×D4×C17D411yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C22×C22⋊D17—21no—
81C22×C22⋊D17—21no—
82C23×Dic17—21no—
83C23×Dic17—21no—
84C23×Dic17—21no—
85C22×D68C2311yescharacteristic
86C22×C4×D17—21no—
87C22×Dic34—21no—
88C22×Dic34C2311yescharacteristic
89C2×M16×C17—24no—
90C2×M16×C17C2314yes—
91C22×C8×C17—24no—
92C22×C8×C17C2314yes—
93C22×C8×C17C2311yescharacteristic
94C22×C8×C17C2311yescharacteristic
95C22×C8×C17C2311yescharacteristic
96C22×C8×C17C2311yescharacteristic
97C4×D4×C17D414yes—
98C4×D4×C17C2314yes—
99C2×C4⋊C4×C17D411yescharacteristic
100C2×C22⋊C4×C17D411yescharacteristic
101C2×C22⋊C4×C17D411yescharacteristic
102C2×C42×C17C2311yescharacteristic
103C2×C22⋊Dic17—21no—
104C2×C22⋊Dic17—21no—
105C2×C22⋊Dic17—21no—
106#10587625—28no—
107D4×Dic17—28no—
108#10587616—22no—
109#10587616—22no—
110#10587616C2314yes—
111#10587616C2314yes—
112C2×#63227—21no—
113C2×#63227—21no—
114C2×#63227—21no—
115#10587612—22no—
116#10587612C2314yes—
117C2×C4⋊Dic17—22no—
118C2×C4⋊Dic17—22no—
119C2×C4⋊Dic17—22no—
120C2×C4⋊Dic17—21no—
121C2×C4⋊Dic17—21no—
122C2×C4⋊Dic17—21no—
123C2×C4⋊Dic17—21no—
124C2×C4⋊Dic17C2314yes—
125C2×C4⋊Dic17C2311yescharacteristic
126C2×C4⋊Dic17C2314yes—
127C2×C4⋊Dic17C2314yes—
128C2×C4⋊Dic17C2311yescharacteristic
129C2×C4⋊Dic17C2311yescharacteristic
130C2×C4⋊Dic17C2311yescharacteristic
131C2×C4⋊Dic17C2311yescharacteristic
132C2×C4⋊Dic17C2311yescharacteristic
133#10587610—22no—
134#10587610—22no—
135#10587610C2314yes—
136#10587610C2314yes—
137C2×#63225—21no—
138C2×#63225—21no—
139C2×#63225—21no—
140C2×#63225—21no—
141C2×#63225—21no—
142C2×C4×Dic17—21no—
143C2×C4×Dic17—21no—
144C2×#63219—24no—
145C2×#63219C2314yes—
146#10587584—28no—
147#10587576—28no—
148#10587569—28no—
149#10587567—28no—
150#10587564—28no—
151#10587564—28no—
152C4×D68—22no—
153C4×D68C2314yes—
154#10587556—22no—
155#10587556C2314yes—
156#10587555—22no—
157#10587555C2314yes—
158C4×Dic34—22no—
159C4×Dic34C2314yes—
160C17×C4⋊C8C2314yes—
161C17×C22⋊C8C2314yes—
162C17×C22⋊C8C2314yes—
163C17×#97C2314yes—
164#10587492C2314yes—
165#10587492C2314yes—
166#10587492C2314yes—
167#10587489C2314yes—
168#10587489C2314yes—
169#10587489C2314yes—
170#10587489C2314yes—
171#10587489C2314yes—
172#10587489C2314yes—
173#10587488C2314yes—
174#10587488C2314yes—
175#10587488C2314yes—
176#10587487C2314yes—
177#10587487C2314yes—
178#10587487C2314yes—
179C24×C17C2×D411yescharacteristic
180C24×C17C2×D411yescharacteristic
181C23×D17—21no—
182C2×D4×C17—24no—
183C2×D4×C17C2×D414yes—
184C22×C4×C17—22no—
185C22×C4×C17—22no—
186C22×C4×C17—22no—
187C22×C4×C17—22no—
188C22×C4×C17C2×D411yescharacteristic
189C22×C4×C17C2×D411yescharacteristic
190C22×C4×C17C2×D411yescharacteristic
191C22×C4×C17C2×D412yes—
192C22×C4×C17C2×D412yes—
193C22×C4×C17C2×D411yescharacteristic
194C22×C4×C17C2412yes—
195C22×C4×C17C2412yes—
196C22×C4×C17C2411yescharacteristic
197C2×C22⋊D17—24no—
198C2×C22⋊D17—24no—
199C2×C22⋊D17—44no—
200C2×C22⋊D17—82no—
201C22×Dic17—21no—
202C22×Dic17—21no—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—24no—
209C22×Dic17—24no—
210C22×Dic17—24no—
211C22×Dic17—82no—
212C22×Dic17—82no—
213C22×Dic17—82no—
214C2×D68—22no—
215C2×D68—22no—
216C2×D68—21no—
217C2×D68C2412yes—
218C2×C4×D17—24no—
219C2×C4×D17—82no—
220C2×Dic34—22no—
221C2×Dic34—22no—
222C2×Dic34—21no—
223C2×Dic34—24no—
224C2×Dic34—82no—
225C2×Dic34C2412yes—
226M16×C17—28no—
227C2×C8×C17—22no—
228C2×C8×C17—22no—
229C2×C8×C17—22no—
230C2×C8×C17—28no—
231C2×C8×C17#4114yes—
232C2×C8×C17C2412yes—
233C2×C8×C17C2412yes—
234C2×C8×C17C2412yes—
235C2×C8×C17C2412yes—
236C4⋊C4×C17C2×D414yes—
237C22⋊C4×C17C2×D414yes—
238C22⋊C4×C17C2×D414yes—
239C42×C17C2×D412yes—
240C42×C17C2412yes—
241C22⋊Dic17—24no—
242C22⋊Dic17—24no—
243C22⋊Dic17—24no—
244#63227—24no—
245#63227—24no—
246#63227—24no—
247C4⋊Dic17—21no—
248C4⋊Dic17—21no—
249C4⋊Dic17—21no—
250C4⋊Dic17—24no—
251C4⋊Dic17—21no—
252C4⋊Dic17—21no—
253C4⋊Dic17—21no—
254C4⋊Dic17—24no—
255C4⋊Dic17—24no—
256C4⋊Dic17—24no—
257C4⋊Dic17C2412yes—
258C4⋊Dic17C2412yes—
259C4⋊Dic17C2412yes—
260C4⋊Dic17C2412yes—
261C4⋊Dic17C2412yes—
262C4⋊Dic17C2412yes—
263#63225—24no—
264#63225—24no—
265#63225—24no—
266#63225—24no—
267#63225—24no—
268C4×Dic17—24no—
269C4×Dic17—24no—
270#63219—28no—
271C2×#3346—171nomaximal, Sylow
272C23×C17—22no—
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—22no—
276C23×C17—22no—
277C23×C17#13714yes—
278C23×C17C22×D412yes—
279C23×C17C22×D412yes—
280C23×C17C22×D411yescharacteristic
281C22×D17—22no—
282C22×D17—42no—
283C22×D17—42no—
284C22×D17—42no—
285D4×C17—28no—
286C2×C4×C17—22no—
287C2×C4×C17—22no—
288C2×C4×C17—22no—
289C2×C4×C17—22no—
290C2×C4×C17—24no—
291C2×C4×C17—24no—
292C2×C4×C17—22no—
293C2×C4×C17—22no—
294C2×C4×C17—22no—
295C2×C4×C17—22no—
296C2×C4×C17C22×D412yes—
297C2×C4×C17C22×D412yes—
298C2×C4×C17C22×D412yes—
299C2×C4×C17C22×D412yes—
300C2×C4×C17C22×D411yescharacteristic
301C2×C4×C17C2×#4112yes—
302C2×C4×C172−1+412yes—
303C2×C4×C17C2511yescharacteristic
304C22⋊D17—48no—
305C22⋊D17—84no—
306C2×Dic17—22no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—22no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—22no—
313C2×Dic17—42no—
314C2×Dic17—42no—
315C2×Dic17—42no—
316C2×Dic17—42no—
317C2×Dic17—42no—
318C2×Dic17—42no—
319C2×Dic17—42no—
320C2×Dic17—84no—
321C2×Dic17—84no—
322C2×Dic17—84no—
323D68—22no—
324D68—22no—
325D68—42no—
326C4×D17—84no—
327Dic34—22no—
328Dic34—22no—
329Dic34—42no—
330Dic34—84no—
331C8×C17—22no—
332C8×C17—22no—
333C8×C17—22no—
334C8×C17C2×#4114yes—
335C2×#554—171no—
336C2×#553—171no—
337#3346—1716no—
338C2×#501—171no—
339C2×#484—171no—
340C2×#481—171no—
341C2×#485—171no—
342C2×#480—171no—
343C2×#479—171no—
344C2×#474—171no—
345C2×#468—171no—
346C2×#465—171no—
347C2×#440—171no—
348C2×#435D1711yescharacteristic, complemented
349C2×#428—171no—
350C22×#107—171no—
351C22×C17—28no—
352C22×C17—22no—
353C22×C17—22no—
354C22×C17—22no—
355C22×C17—22no—
356C22×C17—22no—
357C22×C17—44no—
358C22×C17#54712yes—
359C22×C17C2×#13714yes—
360C22×C17C2×#13712yes—
361C22×C17#57612yes—
362C22×C17C23×D411yescharacteristic
363C2×D17—42no—
364C2×D17—42no—
365C2×D17—42no—
366C2×D17—84no—
367C4×C17—22no—
368C4×C17—22no—
369C4×C17—22no—
370C4×C17—22no—
371C4×C17#54712yes—
372C4×C17C22×#4111yescharacteristic
373C4×C17C2×2−1+411yescharacteristic
374Dic17—42no—
375Dic17—42no—
376Dic17—42no—
377Dic17—42no—
378Dic17—42no—
379Dic17—42no—
380Dic17—42no—
381C22×SD16—171no—
382C22×M16C2×D1711yescharacteristic
383C23×C8C2×D1711yescharacteristic
384#554—178no—
385#554—344no—
386#553—178no—
387#553—344no—
388C2×C4⋊Q8—171no—
389C2×#126—341no—
390C2×#125—171no—
391C2×#125—341no—
392C2×#123—341no—
393C2×C22⋊Q8—171no—
394C2×C22⋊Q8—171no—
395C2×C22⋊Q8—341no—
396C2×C22⋊Q8—341no—
397C2×#121—171no—
398C2×#121—171no—
399C2×#121—341no—
400C2×C4×Q8—171no—
401C2×C4×D4—171no—
402C2×C4×D4—341no—
403C2×C4×D4—341no—
404C2×C4×D4C2×D1711yescharacteristic
405C2×#117—171no—
406C22×C4⋊C4—171no—
407C22×C4⋊C4—171no—
408C22×C4⋊C4—171no—
409#501—178no—
410#485—178no—
411#484—178no—
412#481—178no—
413#480—178no—
414#479—178no—
415#474—178no—
416#468—178no—
417#465—178no—
418#440—178no—
419#435C2×D1718yescomplemented
420#428—178no—
421C2×#107—171no—
422C2×#107—171no—
423C2×#107—171no—
424C2×#107—171no—
425C2×#107—178no—
426C2×#107—171no—
427C2×#107—171no—
428C2×#106—171no—
429C2×#106—171no—
430C2×#106—171no—
431C2×C4⋊C8C2×D1711yescharacteristic
432C2×#103—171no—
433C2×#103—171no—
434C2×#103—171no—
435C2×#102—171no—
436C2×#102—171no—
437C2×#102—171no—
438C2×C22⋊C8C2×D1711yescharacteristic
439C2×C22⋊C8C2×D1711yescharacteristic
440C2×#97C2×D1711yescharacteristic
441C2×C17—24no—
442C2×C17—42no—
443C2×C17#334614yescomplemented
444C2×C17C2×#54711yescharacteristic
445C2×C17C22×#13711yescharacteristic
446C2×C17C2×#57611yescharacteristic
447D17—82no—
448C22×Q8—171no—
449C22×Q8—341no—
450C22×D4—171no—
451C22×D4—341no—
452C22×D4—341no—
453C22×D4D6811yescharacteristic
454C23×C4—341no—
455C23×C4—341no—
456C23×C4—341no—
457C23×C4—341no—
458C23×C4C22×D1711yescharacteristic
459C23×C4C22×D1711yescharacteristic
460C2×SD16—174no—
461C2×SD16—344no—
462C2×M16—24no—
463C2×M16C22×D1714yes—
464C22×C8—24no—
465C22×C8C22×D1711yescharacteristic
466C22×C8C22×D1714yes—
467C22×C8C22×D1711yescharacteristic
468C22×C8C22×D1711yescharacteristic
469C22×C8C22×D1711yescharacteristic
470C4⋊Q8—174no—
471C4⋊Q8—342no—
472#126—348no—
473#125—174no—
474#125—348no—
475#125—342no—
476#123—348no—
477C22⋊Q8—174no—
478C22⋊Q8—174no—
479C22⋊Q8—342no—
480C22⋊Q8—342no—
481C22⋊Q8—348no—
482C22⋊Q8—348no—
483#121—174no—
484#121—174no—
485#121—348no—
486#121—342no—
487#121—342no—
488C4×Q8—174no—
489C4×Q8—342no—
490C4×D4—174no—
491C4×D4—348no—
492C4×D4—348no—
493C4×D4—342no—
494C4×D4D6814yes—
495C4×D4C22×D1714yes—
496#117—174no—
497#117—342no—
498C2×C4⋊C4—171no—
499C2×C4⋊C4—171no—
500C2×C4⋊C4—171no—
501C2×C4⋊C4—171no—
502C2×C4⋊C4—171no—
503C2×C4⋊C4—174no—
504C2×C4⋊C4—174no—
505C2×C4⋊C4—174no—
506C2×C4⋊C4—171no—
507C2×C4⋊C4—341no—
508C2×C4⋊C4—341no—
509C2×C4⋊C4—341no—
510C2×C4⋊C4—342no—
511C2×C4⋊C4—342no—
512C2×C4⋊C4—342no—
513C2×C4⋊C4—341no—
514C2×C4⋊C4—341no—
515C2×C4⋊C4—341no—
516C2×C4⋊C4—341no—
517C2×C4⋊C4—341no—
518C2×C4⋊C4—341no—
519C2×C4⋊C4D6811yescharacteristic
520C2×C22⋊C4—341no—
521C2×C22⋊C4—341no—
522C2×C22⋊C4—341no—
523C2×C22⋊C4—341no—
524C2×C22⋊C4—341no—
525C2×C22⋊C4—341no—
526C2×C22⋊C4D6811yescharacteristic
527C2×C22⋊C4D6811yescharacteristic
528C2×C42—341no—
529C2×C42—341no—
530C2×C42C22×D1711yescharacteristic
531#107—174no—
532#107—174no—
533#107—174no—
534#107—174no—
535#107—174no—
536#107—174no—
537#106—174no—
538#106—174no—
539#106—174no—
540C4⋊C8C22×D1714yes—
541#103—174no—
542#103—174no—
543#103—174no—
544#102—174no—
545#102—174no—
546#102—174no—
547C22⋊C8C22×D1714yes—
548C22⋊C8C22×D1714yes—
549#97C22×D1714yes—
550C17C2×#334611yescharacteristic, complemented, Sylow
551C24—341no—
552C24C2×D6811yescharacteristic
553C24C2×D6811yescharacteristic
554C2×Q8—172no—
555C2×Q8—341no—
556C2×Q8—344no—
557C2×Q8—342no—
558C2×Q8—342no—
559C2×Q8—1362no—
560C2×D4—24no—
561C2×D4—172no—
562C2×D4—344no—
563C2×D4—344no—
564C2×D4—341no—
565C2×D4—342no—
566C2×D4—342no—
567C2×D4—684no—
568C2×D4—1362no—
569C2×D4C2×D6814yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—341no—
575C22×C4—341no—
576C22×C4—341no—
577C22×C4—341no—
578C22×C4—341no—
579C22×C4—341no—
580C22×C4—341no—
581C22×C4—344no—
582C22×C4—344no—
583C22×C4—344no—
584C22×C4—344no—
585C22×C4—1362no—
586C22×C4—1362no—
587C22×C4—1362no—
588C22×C4—1362no—
589C22×C4C2×D6812yes—
590C22×C4C2×D6812yes—
591C22×C4C2×D6811yescharacteristic
592C22×C4C2×D6811yescharacteristic
593C22×C4C2×D6811yescharacteristic
594C22×C4C2×D6811yescharacteristic
595C22×C4C23×D1712yes—
596C22×C4C23×D1712yes—
597C22×C4C23×D1711yescharacteristic
598SD16—348no—
599M16—28no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—28no—
604C2×C8#6325414yes—
605C2×C8C23×D1712yes—
606C2×C8C23×D1712yes—
607C2×C8C23×D1712yes—
608C2×C8C23×D1712yes—
609C4⋊C4—172no—
610C4⋊C4—172no—
611C4⋊C4—172no—
612C4⋊C4—172no—
613C4⋊C4—172no—
614C4⋊C4—172no—
615C4⋊C4—341no—
616C4⋊C4—341no—
617C4⋊C4—341no—
618C4⋊C4—344no—
619C4⋊C4—344no—
620C4⋊C4—341no—
621C4⋊C4—341no—
622C4⋊C4—344no—
623C4⋊C4—341no—
624C4⋊C4—344no—
625C4⋊C4—344no—
626C4⋊C4—344no—
627C4⋊C4—344no—
628C4⋊C4—344no—
629C4⋊C4—344no—
630C4⋊C4C2×D6814yes—
631C22⋊C4—344no—
632C22⋊C4—344no—
633C22⋊C4—344no—
634C22⋊C4—344no—
635C22⋊C4—344no—
636C22⋊C4—344no—
637C22⋊C4C2×D6814yes—
638C22⋊C4C2×D6814yes—
639C42—344no—
640C42—344no—
641C42C2×D6812yes—
642C42C23×D1712yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—342no—
649C23—682no—
650C23—682no—
651C23—682no—
652C23#1058759514yes—
653C23C22×D6812yes—
654C23C22×D6812yes—
655C23C22×D6811yescharacteristic
656Q8—342no—
657Q8—342no—
658Q8—682no—
659Q8—1364no—
660D4—28no—
661D4—342no—
662D4—342no—
663D4—688no—
664D4—682no—
665D4—1364no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—342no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—342no—
680C2×C4—342no—
681C2×C4—342no—
682C2×C4—342no—
683C2×C4—682no—
684C2×C4—682no—
685C2×C4—682no—
686C2×C4—682no—
687C2×C4—682no—
688C2×C4—682no—
689C2×C4—682no—
690C2×C4—1364no—
691C2×C4—1364no—
692C2×C4—1364no—
693C2×C4—1364no—
694C2×C4C22×D6812yes—
695C2×C4C22×D6812yes—
696C2×C4C22×D6812yes—
697C2×C4C22×D6812yes—
698C2×C4C22×D6811yescharacteristic
699C2×C4C2×#6325412yes—
700C2×C4#1058769712yes—
701C2×C4C24×D1711yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#6325414yes—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—682no—
714C22—682no—
715C22—682no—
716C22—1364no—
717C22#1176346312yes—
718C22C2×#1058759514yes—
719C22C2×#1058759512yes—
720C22#1176361412yes—
721C22C23×D6811yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—682no—
727C4—682no—
728C4—682no—
729C4—682no—
730C4—682no—
731C4—682no—
732C4—682no—
733C4#1176346312yes—
734C4C22×#6325411yescharacteristic
735C4C2×#1058769711yescharacteristic
736C2—24no—
737C2—42no—
738C2—1362no—
739C2#1454127114yesdirect product factor
740C2C2×#1176346311yescharacteristic
741C2C22×#1058759511yescharacteristic
742C2C2×#1176361411yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C17×#435C2
socleC23×C17C22×D4
prime radicalC2×#11763505C2
hypercenterC2×#435D17
hypocenterC17C2×#3346
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#11763516C2semidirect
3. #14541271C2direct (N × H)
4. C2×#11763218C2semidirect
5. C2×#11763145C2semidirect
6. C2×#11763128C2semidirect
7. C2×#11763151C2semidirect
8. C2×#11763123C2semidirect
9. C2×#11763117C2semidirect
10. C2×#11763090C2semidirect
11. C2×#11763055C2semidirect
12. C2×#11763038C2semidirect
13. C2×#11762911C2semidirect
14. C2×#11762851C2semidirect
15. C22×#10587489C2semidirect
16. C2×C17×#435C2semidirect
19. #11763516C22semidirect
42. #11763218C22semidirect
43. #11763151C22semidirect
44. #11763145C22semidirect
45. #11763128C22semidirect
46. #11763123C22semidirect
47. #11763117C22semidirect
48. #11763090C22semidirect
49. #11763055C22semidirect
50. #11763038C22semidirect
51. #11762911C22semidirect
52. #11762851C22semidirect
59. C2×#10587489C22semidirect
72. C17×#435C22semidirect
348. C2×#435D17semidirect
419. #435C2×D17semidirect
443. C2×C17#3346semidirect
550. C17C2×#3346semidirect
739. C2#14541271direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635162
C2×#117635052
#145412712
C2×#117632182
C2×#117631452
C2×#117631282
C2×#117631512
C2×#117631232
C2×#117631172
C2×#117630902
C2×#117630552
C2×#117630382
C2×#117629112
C2×#117628512
C22×#105874892
C2×C17×#4352
C2×#334617