Finite Group Databasebeta

← C2×#22573962 #31764263

Subgroups — C2×#22573962 #31764263

Order 17152.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22573962C2132yesmaximal, direct product factor
2C2×#16864114C212yesmaximal, complemented
3C2×#16864101C212yesmaximal, complemented
4C2×#16864086C214yesmaximal, complemented
5C2×#16864085C212yesmaximal, complemented
6C2×#16864081C212yesmaximal, complemented
7C2×#16864075C214yesmaximal, complemented
8C2×#16864027C211yesmaximal, characteristic, complemented
9C2×#16864011C212yesmaximal, complemented
10C2×#16864004C212yesmaximal, complemented
11C2×#16863967C211yesmaximal, characteristic, complemented
12C2×#16863950C212yesmaximal, complemented
13C2×#16863928C212yesmaximal, complemented
14C2×#16863903C211yesmaximal, characteristic
15C22×#14524023C211yesmaximal, characteristic, complemented
16C2×#16863873C211yesmaximal, characteristic, complemented
17C2×#117×D67C211yesmaximal, characteristic, complemented
18C2×#520×C67C211yesmaximal, characteristic, complemented
19C23×Dic134C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21#16864114C22132yescomplemented
22#16864101C22132yescomplemented
23#16864086C22164yescomplemented
24#16864085C22132yescomplemented
25#16864081C22132yescomplemented
26#16864075C22164yescomplemented
27#16864027C22116yescomplemented
28#16864011C22132yescomplemented
29#16864004C22132yescomplemented
30#16863967C22116yescomplemented
31#16863950C22132yescomplemented
32C2×#14524042C2212yescomplemented
33C2×#14524042C2212yescomplemented
34C2×#14524041C2212yescomplemented
35#16863928C22132yescomplemented
36C2×#14524038C2214yes—
37C2×#14524037C2214yes—
38C2×#14524036C2214yescomplemented
39C2×#14524036C2214yescomplemented
40C2×#14524035C2214yescomplemented
41C2×#14524034C2212yescomplemented
42C2×#14524034C2212yescomplemented
43C2×#14524033C2214yescomplemented
44C2×#14524033C2214yescomplemented
45C2×#14524030C2212yescomplemented
46C2×#14524029C2214yes—
47#16863903C22116yes—
48C2×#14524026C2214yes—
49C2×#14524025C2214yes—
50C2×#14524024C2212yes—
51C2×#14524024C2214yes—
52C2×#14524023C2212yes—
53C2×#14524023C2212yes—
54C2×#14524023C2212yes—
55C2×#14524023C2212yes—
56C2×#14524023C22116yescomplemented
57C2×#14524022C2214yes—
58C2×#14524022C2214yescomplemented
59C2×#14524022C2212yescomplemented
60C2×#14524022C2212yescomplemented
61C2×#14524021C2214yes—
62C2×#14524019C2211yescharacteristic
63C2×#14524019C2211yescharacteristic
64C2×#14524014C2211yescharacteristic
65C2×#14524014C2211yescharacteristic
66C2×#14524011C2212yes—
67#16863873C22116yescomplemented
68C2×C4×Dic134C2212yescomplemented
69C2×C4×Dic134C2212yescomplemented
70C2×C4×Dic134C2214yescomplemented
71C2×#14524008C2212yescomplemented
72C2×#14524008C2212yescomplemented
73C2×C4×C22⋊D67C2212yes—
74C2×C4×C22⋊D67C2212yes—
75C2×C4×C22⋊D67C2214yes—
76C2×#14524002C2211yescharacteristic
77C2×#14524002C2211yescharacteristic
78C2×#14524002C2214yescomplemented
79C2×#14524001C2211yescharacteristic
80C2×#14524001C2211yescharacteristic
81C2×#14524000C2212yes—
82C2×#14524000C2214yes—
83C2×#14523999C2212yes—
84C2×#14523999C2214yes—
85#117×D67C22116yescomplemented
86C22×C4⋊Dic67C2212yes—
87C2×C4⋊C4×D67C2211yescharacteristic
88C2×C4⋊C4×D67C2211yescharacteristic
89C22×(C2×D67)⋊C4C2212yes—
90C2×C22⋊C4×D67C2212yes—
91C2×C42×D67C2212yes—
92C22×#41×C67C2211yescharacteristic
93#520×C67C22116yescomplemented
94C2×C4×Q8×C67C2212yescomplemented
95C2×C4×D4×C67C2214yes—
96C2×C4×D4×C67C2212yescomplemented
97C2×#117×C67C2211yescharacteristic
98C2×#117×C67C2212yescomplemented
99C22×C4⋊C4×C67C2211yescharacteristic
100C22×C4⋊C4×C67C2212yescomplemented
101C24×D67C2311yescharacteristic
102C22×Dic134—28no—
103C22×Dic134C2312yes—
104C22×Dic134C2312yes—
105C22×Dic134C2318yes—
106C22×Dic134C2314yes—
107C22×C22⋊D67C2312yes—
108C22×C22⋊D67C2312yes—
109C23×Dic67C2312yes—
110C23×Dic67C2311yescharacteristic
111C22×C4×D67—28no—
112C22×C4×D67C2311yescharacteristic
113C22×C4×D67C2312yes—
114C22×C4×D67C2311yescharacteristic
115C22×C4×D67C2318yes—
116C22×C4×D67C2311yescharacteristic
117C22×C4×D67C2311yescharacteristic
118C22×C4×D67C2312yes—
119#14524042C23116yescomplemented
120#14524042C23116yescomplemented
121#14524041C23116yescomplemented
122#14524038C23132yes—
123#14524037C23132yes—
124#14524036C23132yescomplemented
125#14524036C23132yescomplemented
126#14524035C23132yescomplemented
127#14524034C23116yescomplemented
128#14524034C23116yescomplemented
129#14524033C23132yescomplemented
130#14524033C23132yescomplemented
131#14524030C23116yescomplemented
132#14524029C23132yes—
133#14524026C23132yes—
134#14524025C23132yes—
135#14524024C23132yes—
136#14524024C23116yes—
137#14524023C23116yes—
138#14524023C23116yes—
139#14524023C23116yes—
140#14524023C23116yes—
141#14524022C23132yes—
142#14524022C23132yescomplemented
143#14524022C23116yescomplemented
144#14524022C23116yescomplemented
145#14524021C23132yes—
146#14524019C2318yes—
147#14524019C2318yes—
148#14524014C2318yes—
149#14524014C2318yes—
150#14524011C23116yes—
151C4×Dic134C23116yescomplemented
152C4×Dic134C23116yescomplemented
153C4×Dic134C23132yescomplemented
154#14524008C23116yescomplemented
155#14524008C23116yescomplemented
156C4×C22⋊D67C23132yes—
157C4×C22⋊D67C23116yes—
158C4×C22⋊D67C23116yes—
159#14524002C2318yes—
160#14524002C2318yes—
161#14524002C23132yescomplemented
162#14524001C2318yes—
163#14524001C2318yes—
164#14524000C23116yes—
165#14524000C23132yes—
166#14523999C23132yes—
167#14523999C23116yes—
168C2×C4⋊Dic67C23116yes—
169C2×C4⋊Dic67C2311yescharacteristic
170C2×C4⋊Dic67C2311yescharacteristic
171C2×C4⋊Dic67C2314yes—
172C2×C4⋊Dic67C2314yes—
173C2×C4⋊Dic67C2311yescharacteristic
174C2×C4⋊Dic67C2311yescharacteristic
175C2×C4⋊Dic67C2314yes—
176C2×Dic67⋊C4C2312yes—
177C2×Dic67⋊C4C2312yes—
178C2×Dic67⋊C4C2314yes—
179C2×Dic67⋊C4C2314yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2312yes—
184C2×Dic67⋊C4C2314yes—
185C2×Dic67⋊C4C2314yes—
186C4⋊C4×D67C2318yes—
187C4⋊C4×D67C2318yes—
188C2×C22⋊Dic67C2312yes—
189C2×C22⋊Dic67C2312yes—
190C2×C22⋊Dic67C2312yes—
191C2×C22⋊Dic67C2314yes—
192C2×C22⋊Dic67C2312yes—
193C2×C22⋊Dic67C2314yes—
194C2×(C2×D67)⋊C4C23116yes—
195C2×(C2×D67)⋊C4C2312yes—
196C2×(C2×D67)⋊C4C2312yes—
197C2×(C2×D67)⋊C4C2314yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×(C2×D67)⋊C4C2312yes—
200C2×(C2×D67)⋊C4C2312yes—
201C22⋊C4×D67C23116yes—
202C2×C4×Dic67C2312yes—
203C2×C4×Dic67C2312yes—
204C2×C4×Dic67C2312yes—
205C2×C4×Dic67C2314yes—
206C2×C4×Dic67C2314yes—
207C2×C4×Dic67C2312yes—
208C42×D67C23116yes—
209C2×#41×C67—28no—
210C2×#41×C67C2318yes—
211C22×Q8×C67C2311yescharacteristic
212C22×D4×C67C2312yes—
213C22×D4×C67C2311yescharacteristic
214C23×C4×C67C2312yes—
215C23×C4×C67C2312yes—
216C23×C4×C67C2314yes—
217C23×C4×C67C2311yescharacteristic
218C4×Q8×C67C23116yescomplemented
219C4×D4×C67C23132yes—
220C4×D4×C67C23116yescomplemented
221#117×C67C2318yes—
222#117×C67C23116yescomplemented
223C2×C4⋊C4×C67C2318yes—
224C2×C4⋊C4×C67C2312yes—
225C2×C4⋊C4×C67C2312yes—
226C2×C4⋊C4×C67C2311yescharacteristic
227C2×C4⋊C4×C67C2314yes—
228C2×C4⋊C4×C67C2311yescharacteristic
229C2×C4⋊C4×C67C23116yescomplemented
230C2×C22⋊C4×C67C2312yes—
231C2×C22⋊C4×C67C2314yes—
232C2×C42×C67C2312yes—
233C2×C42×C67C2314yes—
234C23×D67—24no—
235C23×D67—24no—
236C23×D67—42no—
237C23×D67C2411yescharacteristic
238C23×D67C2414yes—
239C23×D67C2411yescharacteristic
240C2×Dic134—28no—
241C2×Dic134—28no—
242C2×Dic134—232no—
243C2×Dic134—48no—
244C2×Dic134C2418yes—
245C2×Dic134C2418yes—
246C2×Dic134C24116yes—
247C2×C22⋊D67—28no—
248C2×C22⋊D67—44no—
249C2×C22⋊D67C2418yes—
250C2×C22⋊D67C2418yes—
251C22×Dic67—24no—
252C22×Dic67—28no—
253C22×Dic67C2411yescharacteristic
254C22×Dic67C2412yes—
255C22×Dic67C2412yes—
256C22×Dic67C2414yes—
257C22×Dic67C2412yes—
258C22×Dic67C2412yes—
259C22×Dic67C2418yes—
260C22×Dic67C2411yescharacteristic
261C22×Dic67C2414yes—
262C2×C4×D67—28no—
263C2×C4×D67—24no—
264C2×C4×D67—24no—
265C2×C4×D67—24no—
266C2×C4×D67—24no—
267C2×C4×D67—232no—
268C2×C4×D67—44no—
269C2×C4×D67C2414yes—
270C2×C4×D67C2418yes—
271C2×C4×D67C2414yes—
272C2×C4×D67C2414yes—
273C2×C4×D67C2414yes—
274C2×C4×D67C2418yes—
275C4⋊Dic67C2414yes—
276C4⋊Dic67C2414yes—
277C4⋊Dic67C24116yes—
278C4⋊Dic67C24116yes—
279C4⋊Dic67C2414yes—
280C4⋊Dic67C2414yes—
281C4⋊Dic67C24116yes—
282Dic67⋊C4C2418yes—
283Dic67⋊C4C2418yes—
284Dic67⋊C4C24116yes—
285Dic67⋊C4C24116yes—
286Dic67⋊C4C24116yes—
287Dic67⋊C4C24116yes—
288Dic67⋊C4C2418yes—
289Dic67⋊C4C2418yes—
290Dic67⋊C4C24116yes—
291Dic67⋊C4C24116yes—
292C22⋊Dic67C2418yes—
293C22⋊Dic67C2418yes—
294C22⋊Dic67C2418yes—
295C22⋊Dic67C24116yes—
296C22⋊Dic67C2418yes—
297C22⋊Dic67C24116yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C2418yes—
300(C2×D67)⋊C4C24116yes—
301(C2×D67)⋊C4C24116yes—
302(C2×D67)⋊C4C2418yes—
303(C2×D67)⋊C4C2418yes—
304C4×Dic67C2418yes—
305C4×Dic67C2418yes—
306C4×Dic67C2418yes—
307C4×Dic67C24116yes—
308C4×Dic67C24116yes—
309C4×Dic67C2418yes—
310C24×C67C2412yes—
311C24×C67C2411yescharacteristic
312#41×C67—232no—
313C2×Q8×C67—24no—
314C2×Q8×C67C2414yes—
315C2×D4×C67—28no—
316C2×D4×C67—24no—
317C2×D4×C67C2418yes—
318C2×D4×C67C2414yes—
319C22×C4×C67—28no—
320C22×C4×C67—48no—
321C22×C4×C67—44no—
322C22×C4×C67#4118yes—
323C22×C4×C67C2412yes—
324C22×C4×C67C2412yes—
325C22×C4×C67C2412yes—
326C22×C4×C67C2414yes—
327C22×C4×C67C2418yes—
328C22×C4×C67C2418yes—
329C22×C4×C67C24116yes—
330C22×C4×C67C2411yescharacteristic
331C22×C4×C67C2411yescharacteristic
332C22×C4×C67C2414yes—
333C4⋊C4×C67C2418yes—
334C4⋊C4×C67C2418yes—
335C4⋊C4×C67C2414yes—
336C4⋊C4×C67C24116yes—
337C4⋊C4×C67C2414yes—
338C22⋊C4×C67C2418yes—
339C22⋊C4×C67C24116yes—
340C42×C67C2418yes—
341C42×C67C24116yes—
342C23×C67—22no—
343C23×C67—22no—
344C23×C67—24no—
345C23×C67—24no—
346C23×C67—24no—
347C23×C67C2×#4114yes—
348C23×C67C2514yes—
349C23×C67C2512yes—
350C23×C67C2511yescharacteristic
351C22×D67—22no—
352C22×D67—22no—
353C22×D67—28no—
354C22×D67—22no—
355C22×D67—22no—
356C22×D67—22no—
357C22×D67—28no—
358C22×D67—44no—
359C22×D67—416no—
360C22×D672−1+414yes—
361C22×D67C2512yes—
362C22×D67C2512yes—
363Q8×C67—28no—
364D4×C67—216no—
365D4×C67—28no—
366C2×C4×C67—24no—
367C2×C4×C67—24no—
368C2×C4×C67—24no—
369C2×C4×C67—28no—
370C2×C4×C67—216no—
371C2×C4×C67—48no—
372C2×C4×C67—416no—
373C2×C4×C67C2×#4114yes—
374C2×C4×C67C2×#4114yes—
375C2×C4×C67C2×#41116yes—
376C2×C4×C67C2514yes—
377C2×C4×C67C2514yes—
378C2×C4×C67C2514yes—
379C2×C4×C67C2518yes—
380C2×C4×C67C2512yes—
381C2×C4×C67C2512yes—
382C22⋊D67—216no—
383C22⋊D67—48no—
384C2×Dic67—28no—
385C2×Dic67—22no—
386C2×Dic67—22no—
387C2×Dic67—216no—
388C2×Dic67—28no—
389C2×Dic67—24no—
390C2×Dic67—24no—
391C2×Dic67—24no—
392C2×Dic67—24no—
393C2×Dic67C2512yes—
394C2×Dic67C2514yes—
395C2×Dic67C2514yes—
396C2×Dic67C2518yes—
397C2×Dic67C2514yes—
398C2×Dic67C2514yes—
399C2×Dic67C2512yes—
400C4×D67—216no—
401C4×D67—28no—
402C4×D67—28no—
403C4×D67—28no—
404C4×D67—28no—
405C4×D67—48no—
406Dic134—216no—
407Dic134—216no—
408Dic134—416no—
409C22×C67—22no—
410C22×C67—22no—
411C22×C67—28no—
412C22×C67—24no—
413C22×C67—24no—
414C22×C67—24no—
415C22×C67—48no—
416C22×C67C22×#4114yes—
417C22×C67C22×#4112yes—
418C22×C67C2×2−1+412yes—
419C22×C67#58512yes—
420C22×C67C2611yescharacteristic
421C2×D67—22no—
422C2×D67—22no—
423C2×D67—28no—
424C2×D67—22no—
425C2×D67—22no—
426C2×D67—22no—
427C2×D67—416no—
428C2×D67—44no—
429C2×D67C2×2−1+414yes—
430C4×C67—24no—
431C4×C67—24no—
432C4×C67—28no—
433C4×C67—24no—
434C4×C67C22×#4114yes—
435C4×C67C22×#4114yes—
436Dic67—28no—
437Dic67—22no—
438Dic67—22no—
439Dic67—24no—
440Dic67—24no—
441Dic67—24no—
442Dic67—24no—
443C2×#3495—671nomaximal, Sylow
444C2×C67—24no—
445C2×C67—44no—
446C2×C67#349514yescomplemented
447C2×C67C23×#4111yescharacteristic
448C2×C67C22×2−1+411yescharacteristic
449C2×C67C2×#58511yescharacteristic
450D67—24no—
451D67—42no—
452#3495—6732no—
453C2×#556—672no—
454C2×#554—672no—
455C2×#552—674no—
456C2×#552—672no—
457C2×#552—672no—
458C2×#551—674no—
459C2×#544—671no—
460C2×#542—672no—
461C2×#541—672no—
462C2×#536—671no—
463C2×#533—672no—
464C2×#529—672no—
465C2×#525—671no—
466C22×C22⋊Q8—671no—
467C2×#520D6711yescharacteristic, complemented
468C2×#519—671no—
469C22×#117—671no—
470C67C2×#349511yescharacteristic, complemented, Sylow
471C22×#41C2×D6711yescharacteristic
472C23×Q8—671no—
473C24×C4—671no—
474#556—6732no—
475#554—6732no—
476#552—6764no—
477#552—6732no—
478#552—6732no—
479#551—6764no—
480#544—6716no—
481#542—6732no—
482#541—6732no—
483#536—6716no—
484#533—6732no—
485C2×C4⋊Q8—672no—
486C2×C4⋊Q8—672no—
487C2×C4⋊Q8—672no—
488#529—6732no—
489C2×#126—674no—
490C2×#126—674no—
491C2×#126—674no—
492C2×#126—674no—
493C2×#125—672no—
494C2×#125—674no—
495C2×#125—674no—
496C2×#125—672no—
497C2×#125—674no—
498C2×#124—672no—
499C2×#124—674no—
500#525—6716no—
501C2×#123—672no—
502C2×#123—674no—
503C2×#123—674no—
504C2×#123—674no—
505C2×C22⋊Q8—671no—
506C2×C22⋊Q8—671no—
507C2×C22⋊Q8—672no—
508C2×C22⋊Q8—672no—
509C2×C22⋊Q8—674no—
510C2×C22⋊Q8—674no—
511C2×C22⋊Q8—672no—
512C2×C22⋊Q8—672no—
513C2×C22⋊Q8—672no—
514C2×C22⋊Q8—672no—
515C2×C22⋊Q8—6716no—
516C2×C22⋊Q8—674no—
517C2×#121—671no—
518C2×#121—671no—
519C2×#120—672no—
520#520C2×D67116yescomplemented
521#519—6716no—
522C2×C4×Q8—672no—
523C2×C4×Q8—672no—
524C2×C4×Q8—672no—
525C2×C4×Q8—672no—
526C2×C4×Q8—674no—
527C2×C4×Q8C2×D6712yescomplemented
528C2×C4×D4—672no—
529C2×C4×D4—672no—
530C2×C4×D4—674no—
531C2×C4×D4C2×D6714yes—
532C2×C4×D4C2×D6712yescomplemented
533C2×#117—671no—
534C2×#117—671no—
535C2×#117—674no—
536C2×#117—6716no—
537C2×#117—671no—
538C2×#117—671no—
539C2×#117—672no—
540C2×#117—674no—
541C2×#117—672no—
542C2×#117—674no—
543C2×#117C2×D6711yescharacteristic
544C2×#117C2×D6712yescomplemented
545C22×C4⋊C4—672no—
546C22×C4⋊C4—671no—
547C22×C4⋊C4—671no—
548C22×C4⋊C4C2×D6711yescharacteristic
549C22×C4⋊C4C2×D6712yescomplemented
550C22×C22⋊C4—672no—
551C22×C22⋊C4—672no—
552C22×C42—672no—
553C25—671no—
554C2×#41—28no—
555C2×#41C22×D6718yes—
556C22×Q8—674no—
557C22×Q8—672no—
558C22×Q8—672no—
559C22×Q8—678no—
560C22×Q8—1348no—
561C22×Q8C22×D6711yescharacteristic
562C22×D4—672no—
563C22×D4—672no—
564C22×D4C22×D6712yes—
565C22×D4C22×D6711yescharacteristic
566C23×C4—672no—
567C23×C4—672no—
568C23×C4—671no—
569C23×C4—672no—
570C23×C4—671no—
571C23×C4—671no—
572C23×C4—671no—
573C23×C4—678no—
574C23×C4—671no—
575C23×C4—1348no—
576C23×C4C22×D6712yes—
577C23×C4C22×D6712yes—
578C23×C4C22×D6714yes—
579C23×C4C22×D6711yescharacteristic
580C4⋊Q8—6716no—
581C4⋊Q8—6716no—
582C4⋊Q8—6716no—
583#126—6732no—
584#126—6732no—
585#126—6732no—
586#126—6732no—
587#125—6716no—
588#125—6732no—
589#125—6732no—
590#125—6716no—
591#125—6732no—
592#124—6716no—
593#124—6732no—
594#123—6716no—
595#123—6732no—
596#123—6732no—
597#123—6732no—
598C22⋊Q8—678no—
599C22⋊Q8—678no—
600C22⋊Q8—6716no—
601C22⋊Q8—6716no—
602C22⋊Q8—6732no—
603C22⋊Q8—6732no—
604C22⋊Q8—6716no—
605C22⋊Q8—6716no—
606C22⋊Q8—6716no—
607C22⋊Q8—6716no—
608C22⋊Q8—6732no—
609#121—678no—
610#121—678no—
611#120—6716no—
612C4×Q8—6716no—
613C4×Q8—6716no—
614C4×Q8—6716no—
615C4×Q8—6716no—
616C4×Q8—6732no—
617C4×Q8C22×D67116yescomplemented
618C4×D4—6716no—
619C4×D4—6716no—
620C4×D4—6732no—
621C4×D4C22×D67132yes—
622C4×D4C22×D67116yescomplemented
623#117—678no—
624#117—678no—
625#117—6732no—
626#117—678no—
627#117—678no—
628#117—6716no—
629#117—6732no—
630#117—6716no—
631#117—6732no—
632#117C22×D6718yes—
633#117C22×D67116yescomplemented
634C2×C4⋊C4—672no—
635C2×C4⋊C4—671no—
636C2×C4⋊C4—671no—
637C2×C4⋊C4—672no—
638C2×C4⋊C4—674no—
639C2×C4⋊C4—674no—
640C2×C4⋊C4—6716no—
641C2×C4⋊C4—671no—
642C2×C4⋊C4—671no—
643C2×C4⋊C4—674no—
644C2×C4⋊C4—674no—
645C2×C4⋊C4—674no—
646C2×C4⋊C4—674no—
647C2×C4⋊C4—674no—
648C2×C4⋊C4—672no—
649C2×C4⋊C4—672no—
650C2×C4⋊C4—674no—
651C2×C4⋊C4—674no—
652C2×C4⋊C4—678no—
653C2×C4⋊C4—678no—
654C2×C4⋊C4C22×D6711yescharacteristic
655C2×C4⋊C4C22×D6711yescharacteristic
656C2×C4⋊C4C22×D6712yes—
657C2×C4⋊C4C22×D6712yes—
658C2×C4⋊C4C22×D6718yes—
659C2×C4⋊C4C22×D6714yes—
660C2×C4⋊C4C22×D67116yescomplemented
661C2×C22⋊C4—672no—
662C2×C22⋊C4—672no—
663C2×C22⋊C4—672no—
664C2×C22⋊C4—674no—
665C2×C22⋊C4—672no—
666C2×C22⋊C4—674no—
667C2×C22⋊C4—672no—
668C2×C22⋊C4—672no—
669C2×C22⋊C4—674no—
670C2×C22⋊C4—674no—
671C2×C22⋊C4—6716no—
672C2×C22⋊C4—672no—
673C2×C22⋊C4—672no—
674C2×C22⋊C4—6716no—
675C2×C22⋊C4C22×D6712yes—
676C2×C22⋊C4C22×D6714yes—
677C2×C42—672no—
678C2×C42—674no—
679C2×C42—674no—
680C2×C42—672no—
681C2×C42—672no—
682C2×C42—672no—
683C2×C42—6716no—
684C2×C42C22×D6712yes—
685C2×C42C22×D6714yes—
686C24—2682no—
687C24—674no—
688C24—671no—
689C24—671no—
690C24—1344no—
691C24—1344no—
692C24C23×D6712yes—
693C24C23×D6711yescharacteristic
694#41—232no—
695C2×Q8—24no—
696C2×Q8—2688no—
697C2×Q8—6716no—
698C2×Q8—678no—
699C2×Q8—678no—
700C2×Q8—1348no—
701C2×Q8—1348no—
702C2×Q8—13432no—
703C2×Q8C23×D6714yes—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—2684no—
707C2×D4—678no—
708C2×D4—678no—
709C2×D4—1348no—
710C2×D4C23×D6718yes—
711C2×D4C23×D6714yes—
712C22×C4—28no—
713C22×C4—48no—
714C22×C4—44no—
715C22×C4—2684no—
716C22×C4—678no—
717C22×C4—678no—
718C22×C4—674no—
719C22×C4—671no—
720C22×C4—672no—
721C22×C4—672no—
722C22×C4—672no—
723C22×C4—674no—
724C22×C4—672no—
725C22×C4—671no—
726C22×C4—674no—
727C22×C4—678no—
728C22×C4—674no—
729C22×C4—674no—
730C22×C4—674no—
731C22×C4—1348no—
732C22×C4—1344no—
733C22×C4—1348no—
734C22×C4—1344no—
735C22×C4—1344no—
736C22×C4—1344no—
737C22×C4—1344no—
738C22×C4—13432no—
739C22×C4#1176162818yes—
740C22×C4C23×D6718yes—
741C22×C4C23×D6712yes—
742C22×C4C23×D6712yes—
743C22×C4C23×D6712yes—
744C22×C4C23×D6714yes—
745C22×C4C23×D6718yes—
746C22×C4C23×D67116yes—
747C22×C4C23×D6714yes—
748C22×C4C23×D6711yescharacteristic
749C22×C4C23×D6711yescharacteristic
750C4⋊C4—678no—
751C4⋊C4—674no—
752C4⋊C4—674no—
753C4⋊C4—678no—
754C4⋊C4—6716no—
755C4⋊C4—6716no—
756C4⋊C4—674no—
757C4⋊C4—674no—
758C4⋊C4—6716no—
759C4⋊C4—6716no—
760C4⋊C4—6716no—
761C4⋊C4—6716no—
762C4⋊C4—6716no—
763C4⋊C4—678no—
764C4⋊C4—678no—
765C4⋊C4—6716no—
766C4⋊C4—6716no—
767C4⋊C4C23×D6714yes—
768C4⋊C4C23×D6714yes—
769C4⋊C4C23×D6718yes—
770C4⋊C4C23×D6718yes—
771C4⋊C4C23×D67116yes—
772C22⋊C4—678no—
773C22⋊C4—678no—
774C22⋊C4—678no—
775C22⋊C4—6716no—
776C22⋊C4—678no—
777C22⋊C4—6716no—
778C22⋊C4—678no—
779C22⋊C4—678no—
780C22⋊C4—6716no—
781C22⋊C4—6716no—
782C22⋊C4—678no—
783C22⋊C4—678no—
784C22⋊C4C23×D6718yes—
785C22⋊C4C23×D67116yes—
786C42—678no—
787C42—678no—
788C42—678no—
789C42—6716no—
790C42—6716no—
791C42—678no—
792C42C23×D6718yes—
793C42C23×D67116yes—
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—26816no—
800C23—2684no—
801C23—674no—
802C23—672no—
803C23—672no—
804C23—1348no—
805C23—1348no—
806C23—1342no—
807C23—1342no—
808C23—1342no—
809C23—1342no—
810C23—1342no—
811C23C2×#1176162814yes—
812C23C24×D6714yes—
813C23C24×D6712yes—
814C23C24×D6711yescharacteristic
815Q8—28no—
816Q8—26816no—
817Q8—13416no—
818Q8—13416no—
819D4—216no—
820D4—28no—
821D4—2688no—
822D4—13416no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—28no—
827C2×C4—216no—
828C2×C4—416no—
829C2×C4—48no—
830C2×C4—2688no—
831C2×C4—672no—
832C2×C4—674no—
833C2×C4—674no—
834C2×C4—674no—
835C2×C4—678no—
836C2×C4—674no—
837C2×C4—672no—
838C2×C4—13416no—
839C2×C4—1348no—
840C2×C4—1342no—
841C2×C4—1342no—
842C2×C4—13416no—
843C2×C4—1348no—
844C2×C4—1344no—
845C2×C4—1344no—
846C2×C4—1344no—
847C2×C4—1344no—
848C2×C4—1348no—
849C2×C4—1348no—
850C2×C4—1348no—
851C2×C4—1348no—
852C2×C4C2×#1176162814yes—
853C2×C4C2×#1176162814yes—
854C2×C4C2×#11761628116yes—
855C2×C4C24×D6714yes—
856C2×C4C24×D6714yes—
857C2×C4C24×D6714yes—
858C2×C4C24×D6718yes—
859C2×C4C24×D6712yes—
860C2×C4C24×D6712yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—26816no—
869C22—2684no—
870C22—674no—
871C22—1342no—
872C22—1342no—
873C22—1342no—
874C22—1348no—
875C22—1342no—
876C22—1342no—
877C22C22×#1176162814yes—
878C22C22×#1176162812yes—
879C222−1+4×D6712yes—
880C22#1686423112yes—
881C22C25×D6711yescharacteristic
882C4—24no—
883C4—24no—
884C4—24no—
885C4—28no—
886C4—1342no—
887C4—1342no—
888C4—1348no—
889C4—1344no—
890C4—1344no—
891C4—1344no—
892C4—1344no—
893C4C22×#1176162814yes—
894C4C22×#1176162814yes—
895C2—24no—
896C2—44no—
897C2—2682no—
898C2—1344no—
899C2#2257396214yesdirect product factor
900C2C23×#1176162811yescharacteristic
901C2C2×2−1+4×D6711yescharacteristic
902C2C2×#1686423111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#520×C67C2
socleC23×C67C25
prime radicalC2×#16863903C2
hypercenterC2×#520D67
hypocenterC67C2×#3495
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22573962C2direct (N × H)
2. C2×#16864114C2semidirect
3. C2×#16864101C2semidirect
4. C2×#16864086C2semidirect
5. C2×#16864085C2semidirect
6. C2×#16864081C2semidirect
7. C2×#16864075C2semidirect
8. C2×#16864027C2semidirect
9. C2×#16864011C2semidirect
10. C2×#16864004C2semidirect
11. C2×#16863967C2semidirect
12. C2×#16863950C2semidirect
13. C2×#16863928C2semidirect
15. C22×#14524023C2semidirect
16. C2×#16863873C2semidirect
17. C2×#117×D67C2semidirect
18. C2×#520×C67C2semidirect
21. #16864114C22semidirect
22. #16864101C22semidirect
23. #16864086C22semidirect
24. #16864085C22semidirect
25. #16864081C22semidirect
26. #16864075C22semidirect
27. #16864027C22semidirect
28. #16864011C22semidirect
29. #16864004C22semidirect
30. #16863967C22semidirect
31. #16863950C22semidirect
32. C2×#14524042C22semidirect
33. C2×#14524042C22semidirect
34. C2×#14524041C22semidirect
35. #16863928C22semidirect
38. C2×#14524036C22semidirect
39. C2×#14524036C22semidirect
40. C2×#14524035C22semidirect
41. C2×#14524034C22semidirect
42. C2×#14524034C22semidirect
43. C2×#14524033C22semidirect
44. C2×#14524033C22semidirect
45. C2×#14524030C22semidirect
56. C2×#14524023C22semidirect
58. C2×#14524022C22semidirect
59. C2×#14524022C22semidirect
60. C2×#14524022C22semidirect
67. #16863873C22semidirect
68. C2×C4×Dic134C22semidirect
69. C2×C4×Dic134C22semidirect
70. C2×C4×Dic134C22semidirect
71. C2×#14524008C22semidirect
72. C2×#14524008C22semidirect
78. C2×#14524002C22semidirect
85. #117×D67C22semidirect
93. #520×C67C22semidirect
94. C2×C4×Q8×C67C22semidirect
96. C2×C4×D4×C67C22semidirect
98. C2×#117×C67C22semidirect
100. C22×C4⋊C4×C67C22semidirect
119. #14524042C23semidirect
120. #14524042C23semidirect
121. #14524041C23semidirect
124. #14524036C23semidirect
125. #14524036C23semidirect
126. #14524035C23semidirect
127. #14524034C23semidirect
128. #14524034C23semidirect
129. #14524033C23semidirect
130. #14524033C23semidirect
131. #14524030C23semidirect
142. #14524022C23semidirect
143. #14524022C23semidirect
144. #14524022C23semidirect
151. C4×Dic134C23semidirect
152. C4×Dic134C23semidirect
153. C4×Dic134C23semidirect
154. #14524008C23semidirect
155. #14524008C23semidirect
161. #14524002C23semidirect
218. C4×Q8×C67C23semidirect
220. C4×D4×C67C23semidirect
222. #117×C67C23semidirect
229. C2×C4⋊C4×C67C23semidirect
446. C2×C67#3495semidirect
467. C2×#520D67semidirect
470. C67C2×#3495semidirect
520. #520C2×D67semidirect
527. C2×C4×Q8C2×D67semidirect
532. C2×C4×D4C2×D67semidirect
544. C2×#117C2×D67semidirect
549. C22×C4⋊C4C2×D67semidirect
617. C4×Q8C22×D67semidirect
622. C4×D4C22×D67semidirect
633. #117C22×D67semidirect
660. C2×C4⋊C4C22×D67semidirect
899. C2#22573962direct (N × H)

Maximal subgroups

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

subgroupindex
#225739622
C2×#168641142
C2×#168641012
C2×#168640862
C2×#168640852
C2×#168640812
C2×#168640752
C2×#168640272
C2×#168640112
C2×#168640042
C2×#168639672
C2×#168639502
C2×#168639282
C2×#168639032
C22×#145240232
C2×#168638732
C2×#117×D672
C2×#520×C672
C2×#349567