Finite Group Databasebeta

← C2×#22573964 #31764264

Subgroups — C2×#22573964 #31764264

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#22573964C2132yesmaximal, direct product factor
2C2×#16864120C212yesmaximal, complemented
3C2×#16864107C212yesmaximal, complemented
4C2×#16864088C214yesmaximal, complemented
5C2×#16864084C212yesmaximal, complemented
6C2×#16864084C212yesmaximal, complemented
7C2×#16864073C214yesmaximal, complemented
8C2×#16864020C212yesmaximal, complemented
9C2×#16864009C212yesmaximal, complemented
10C2×#16863972C211yesmaximal, characteristic, complemented
11C2×#16863951C212yesmaximal, complemented
12C2×#16863931C212yesmaximal, complemented
13C2×#16863908C211yesmaximal, characteristic
14C22×#14524023C211yesmaximal, characteristic, complemented
15C2×#16863877C211yesmaximal, characteristic, complemented
16C2×#16863873C211yesmaximal, characteristic, complemented
17C2×#117×D67C211yesmaximal, characteristic, complemented
18C2×#544×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2211yescharacteristic
20C23×Dic134C2211yescharacteristic
21C23×C4×D67C2211yescharacteristic
22#16864120C22132yescomplemented
23#16864107C22132yescomplemented
24#16864088C22164yescomplemented
25#16864084C22132yescomplemented
26#16864084C22132yescomplemented
27#16864073C22164yescomplemented
28#16864020C22132yescomplemented
29#16864009C22132yescomplemented
30#16863972C22116yescomplemented
31#16863951C22132yescomplemented
32C2×#14524043C2212yescomplemented
33#16863931C22132yescomplemented
34C2×#14524038C2214yes—
35C2×#14524038C2214yes—
36C2×#14524038C2214yescomplemented
37C2×#14524038C2214yescomplemented
38C2×#14524034C2214yescomplemented
39C2×#14524034C2214yescomplemented
40C2×#14524034C2214yescomplemented
41C2×#14524032C2214yes—
42C2×#14524031C2212yescomplemented
43#16863908C22116yes—
44C2×#14524028C2214yes—
45C2×#14524028C2214yes—
46C2×#14524027C2214yes—
47C2×#14524027C2212yes—
48C2×#14524023C2211yescharacteristic
49C2×#14524023C2212yes—
50C2×#14524023C2212yes—
51C2×#14524023C2212yes—
52C2×#14524023C2212yes—
53C2×#14524023C2211yescharacteristic
54C2×#14524023C22116yescomplemented
55C2×#14524023C2212yescomplemented
56C2×#14524023C2212yescomplemented
57C2×#14524019C2214yes—
58C2×#14524019C2214yescomplemented
59C2×#14524018C2211yescharacteristic
60C2×#14524018C2211yescharacteristic
61C2×#14524013C2212yes—
62#16863877C22116yescomplemented
63#16863873C22116yescomplemented
64C2×Q8×Dic67C2214yescomplemented
65C2×C4×Dic134C2212yescomplemented
66C2×C4×Dic134C2212yescomplemented
67C2×#14524008C2212yescomplemented
68C2×#14524008C2212yescomplemented
69C2×#14524008C2212yescomplemented
70C2×C4×D268C2212yes—
71C2×C4×D268C2212yes—
72C2×#14524005C2214yes—
73C2×#14524005C2212yescomplemented
74C2×C4×C22⋊D67C2214yes—
75C2×#14524002C2211yescharacteristic
76C2×#14524001C2211yescharacteristic
77C2×#14524001C2211yescharacteristic
78C2×#14524001C2214yes—
79C2×#14524001C2212yescomplemented
80C2×#14524001C2214yescomplemented
81C2×#14524000C2212yes—
82C2×#14523999C2212yes—
83C2×#14523999C2214yes—
84#117×D67C22116yescomplemented
85C22×C4⋊Dic67C2212yes—
86C2×C4⋊C4×D67C2211yescharacteristic
87C2×C4⋊C4×D67C2211yescharacteristic
88C2×C4⋊C4×D67C2212yescomplemented
89C22×(C2×D67)⋊C4C2212yes—
90C2×C22⋊C4×D67C2212yes—
91C2×C42×D67C2212yes—
92#544×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2212yescomplemented
94C2×C4⋊Q8×C67C2212yescomplemented
95C2×#125×C67C2212yescomplemented
96C2×#125×C67C2212yescomplemented
97C2×C22⋊Q8×C67C2214yes—
98C2×#117×C67C2211yescharacteristic
99C2×#117×C67C2211yescharacteristic
100C22×C4⋊C4×C67C2211yescharacteristic
101C24×D67C2311yescharacteristic
102C2×#11761628—28no—
103C2×#11761628C2318yes—
104C22×Dic134—28no—
105C22×Dic134C2312yes—
106C22×Dic134C2311yescharacteristic
107C22×Dic134C2312yes—
108C22×Dic134C2318yes—
109C22×D268C2312yes—
110C22×D268C2311yescharacteristic
111C22×D268C2312yes—
112C22×C22⋊D67C2312yes—
113C23×Dic67C2312yes—
114C23×Dic67C2311yescharacteristic
115C22×C4×D67—28no—
116C22×C4×D67C2311yescharacteristic
117C22×C4×D67C2312yes—
118C22×C4×D67C2311yescharacteristic
119C22×C4×D67C2312yes—
120C22×C4×D67C2318yes—
121C22×C4×D67C2311yescharacteristic
122C22×C4×D67C2311yescharacteristic
123C22×C4×D67C2312yes—
124C22×C4×D67C2314yes—
125#14524043C23116yescomplemented
126#14524038C23132yes—
127#14524038C23132yes—
128#14524038C23132yescomplemented
129#14524038C23132yescomplemented
130#14524034C23132yescomplemented
131#14524034C23132yescomplemented
132#14524034C23132yescomplemented
133#14524032C23132yes—
134#14524031C23116yescomplemented
135#14524028C23132yes—
136#14524028C23132yes—
137#14524027C23132yes—
138#14524027C23116yes—
139#14524023C2318yes—
140#14524023C23116yes—
141#14524023C23116yes—
142#14524023C23116yes—
143#14524023C23116yes—
144#14524023C2318yes—
145#14524023C23116yescomplemented
146#14524023C23116yescomplemented
147#14524019C23132yes—
148#14524019C23132yescomplemented
149#14524018C2318yes—
150#14524018C2318yes—
151#14524013C23116yes—
152Q8×Dic67C23132yescomplemented
153C4×Dic134C23116yescomplemented
154C4×Dic134C23116yescomplemented
155#14524008C23116yescomplemented
156#14524008C23116yescomplemented
157#14524008C23116yescomplemented
158C4×D268C23116yes—
159C4×D268C23116yes—
160#14524005C23132yes—
161#14524005C23116yescomplemented
162C4×C22⋊D67C23132yes—
163#14524002C2318yes—
164#14524001C23132yes—
165#14524001C2318yes—
166#14524001C2318yes—
167#14524001C23132yescomplemented
168#14524001C23116yescomplemented
169#14524000C23116yes—
170#14523999C23132yes—
171#14523999C23116yes—
172C2×C4⋊Dic67C23116yes—
173C2×C4⋊Dic67C2311yescharacteristic
174C2×C4⋊Dic67C2311yescharacteristic
175C2×C4⋊Dic67C2314yes—
176C2×C4⋊Dic67C2314yes—
177C2×C4⋊Dic67C2314yes—
178C2×C4⋊Dic67C2312yes—
179C2×C4⋊Dic67C2312yes—
180C2×C4⋊Dic67C2314yes—
181C2×Dic67⋊C4C2312yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2314yes—
185C2×Dic67⋊C4C2314yes—
186C4⋊C4×D67C2318yes—
187C4⋊C4×D67C2318yes—
188C4⋊C4×D67C23116yescomplemented
189C2×C22⋊Dic67C2312yes—
190C2×(C2×D67)⋊C4C23116yes—
191C2×(C2×D67)⋊C4C2312yes—
192C2×(C2×D67)⋊C4C2312yes—
193C2×(C2×D67)⋊C4C2314yes—
194C2×(C2×D67)⋊C4C2314yes—
195C2×(C2×D67)⋊C4C2312yes—
196C2×(C2×D67)⋊C4C2312yes—
197C2×(C2×D67)⋊C4C2314yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×(C2×D67)⋊C4C2314yes—
200C2×(C2×D67)⋊C4C2312yes—
201C2×(C2×D67)⋊C4C2312yes—
202C22⋊C4×D67C23116yes—
203C2×C4×Dic67C2312yes—
204C2×C4×Dic67C2312yes—
205C2×C4×Dic67C2312yes—
206C2×C4×Dic67C2314yes—
207C2×C4×Dic67C2314yes—
208C2×C4×Dic67C2314yes—
209C42×D67C23116yes—
210C22×Q8×C67C2314yes—
211C23×C4×C67C2312yes—
212C23×C4×C67C2311yescharacteristic
213C4⋊Q8×C67C23116yescomplemented
214C4⋊Q8×C67C23116yescomplemented
215#125×C67C23116yescomplemented
216#125×C67C23116yescomplemented
217C22⋊Q8×C67C23132yes—
218#117×C67C2318yes—
219#117×C67C2318yes—
220C2×C4⋊C4×C67C2312yes—
221C2×C4⋊C4×C67C2312yes—
222C2×C4⋊C4×C67C2318yes—
223C2×C4⋊C4×C67C2311yescharacteristic
224C2×C4⋊C4×C67C2311yescharacteristic
225C2×C4⋊C4×C67C2311yescharacteristic
226C2×C4⋊C4×C67C2311yescharacteristic
227C2×C4⋊C4×C67C2314yes—
228C2×C4⋊C4×C67C2314yes—
229C2×C4⋊C4×C67C2314yes—
230C2×C22⋊C4×C67C2312yes—
231C2×C22⋊C4×C67C2312yes—
232C2×C42×C67C2312yes—
233C2×C42×C67C2312yes—
234C23×D67—24no—
235C23×D67—24no—
236C23×D67—42no—
237C23×D67C2411yescharacteristic
238C23×D67C2412yes—
239C23×D67C2414yes—
240C23×D67C2411yescharacteristic
241#11761628—232no—
242C2×Dic134—28no—
243C2×Dic134—28no—
244C2×Dic134—232no—
245C2×Dic134—24no—
246C2×Dic134C2418yes—
247C2×Dic134C2414yes—
248C2×Dic134C2418yes—
249C2×D268—28no—
250C2×D268—24no—
251C2×D268—44no—
252C2×D268C2418yes—
253C2×D268C2414yes—
254C2×D268C2418yes—
255C2×C22⋊D67—28no—
256C2×C22⋊D67C2418yes—
257C22×Dic67—24no—
258C22×Dic67—28no—
259C22×Dic67C2412yes—
260C22×Dic67C2411yescharacteristic
261C22×Dic67C2412yes—
262C22×Dic67C2414yes—
263C22×Dic67C2412yes—
264C22×Dic67C2411yescharacteristic
265C22×Dic67C2418yes—
266C22×Dic67C2414yes—
267C2×C4×D67—28no—
268C2×C4×D67—24no—
269C2×C4×D67—24no—
270C2×C4×D67—24no—
271C2×C4×D67—24no—
272C2×C4×D67—232no—
273C2×C4×D67—28no—
274C2×C4×D67—48no—
275C2×C4×D67—44no—
276C2×C4×D67C2414yes—
277C2×C4×D67C2418yes—
278C2×C4×D67C2414yes—
279C2×C4×D67C2418yes—
280C2×C4×D67C2414yes—
281C2×C4×D67C2414yes—
282C2×C4×D67C2418yes—
283C2×C4×D67C24116yes—
284C4⋊Dic67C2414yes—
285C4⋊Dic67C2414yes—
286C4⋊Dic67C24116yes—
287C4⋊Dic67C24116yes—
288C4⋊Dic67C24116yes—
289C4⋊Dic67C2418yes—
290C4⋊Dic67C2418yes—
291C4⋊Dic67C24116yes—
292Dic67⋊C4C2418yes—
293Dic67⋊C4C2418yes—
294Dic67⋊C4C24116yes—
295Dic67⋊C4C24116yes—
296Dic67⋊C4C24116yes—
297C22⋊Dic67C2418yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C2418yes—
300(C2×D67)⋊C4C24116yes—
301(C2×D67)⋊C4C24116yes—
302(C2×D67)⋊C4C2418yes—
303(C2×D67)⋊C4C2418yes—
304(C2×D67)⋊C4C24116yes—
305(C2×D67)⋊C4C24116yes—
306(C2×D67)⋊C4C24116yes—
307(C2×D67)⋊C4C2418yes—
308(C2×D67)⋊C4C2418yes—
309C4×Dic67C2418yes—
310C4×Dic67C2418yes—
311C4×Dic67C2418yes—
312C4×Dic67C24116yes—
313C4×Dic67C24116yes—
314C4×Dic67C24116yes—
315C24×C67C2411yescharacteristic
316C2×Q8×C67—48no—
317C2×Q8×C67C24116yes—
318C22×C4×C67—44no—
319C22×C4×C67#4118yes—
320C22×C4×C67C2412yes—
321C22×C4×C67C2412yes—
322C22×C4×C67C2412yes—
323C22×C4×C67C2412yes—
324C22×C4×C67C2414yes—
325C22×C4×C67C2418yes—
326C22×C4×C67C2411yescharacteristic
327C22×C4×C67C2411yescharacteristic
328C22×C4×C67C2414yes—
329C4⋊C4×C67C2418yes—
330C4⋊C4×C67C2418yes—
331C4⋊C4×C67C2414yes—
332C4⋊C4×C67C2414yes—
333C4⋊C4×C67C2414yes—
334C4⋊C4×C67C2414yes—
335C4⋊C4×C67C24116yes—
336C4⋊C4×C67C24116yes—
337C4⋊C4×C67C24116yes—
338C22⋊C4×C67C2418yes—
339C22⋊C4×C67C2418yes—
340C42×C67C2418yes—
341C42×C67C2418yes—
342C23×C67—22no—
343C23×C67—22no—
344C23×C67C2×#4114yes—
345C23×C67C2512yes—
346C23×C67C2511yescharacteristic
347C22×D67—22no—
348C22×D67—22no—
349C22×D67—28no—
350C22×D67—22no—
351C22×D67—24no—
352C22×D67—24no—
353C22×D67—22no—
354C22×D67—24no—
355C22×D67—22no—
356C22×D67—28no—
357C22×D67—44no—
358C22×D67—416no—
359C22×D672−1+414yes—
360C22×D67C2512yes—
361C22×D67C2514yes—
362C22×D67C2512yes—
363Q8×C67—416no—
364C2×C4×C67—24no—
365C2×C4×C67—24no—
366C2×C4×C67—28no—
367C2×C4×C67—24no—
368C2×C4×C67—24no—
369C2×C4×C67—48no—
370C2×C4×C67C2×#4114yes—
371C2×C4×C67C2×#4114yes—
372C2×C4×C67C2×#41116yes—
373C2×C4×C67C2514yes—
374C2×C4×C67C2514yes—
375C2×C4×C67C2514yes—
376C2×C4×C67C2514yes—
377C2×C4×C67C2518yes—
378C2×C4×C67C2512yes—
379C2×C4×C67C2512yes—
380C22⋊D67—216no—
381C2×Dic67—28no—
382C2×Dic67—22no—
383C2×Dic67—22no—
384C2×Dic67—24no—
385C2×Dic67—216no—
386C2×Dic67—28no—
387C2×Dic67—24no—
388C2×Dic67—24no—
389C2×Dic67C2514yes—
390C2×Dic67C2512yes—
391C2×Dic67C2514yes—
392C2×Dic67C2518yes—
393C2×Dic67C2514yes—
394C2×Dic67C2512yes—
395D268—216no—
396D268—28no—
397D268—48no—
398C4×D67—216no—
399C4×D67—28no—
400C4×D67—28no—
401C4×D67—28no—
402C4×D67—28no—
403C4×D67—216no—
404C4×D67—416no—
405C4×D67—48no—
406Dic134—216no—
407Dic134—216no—
408Dic134—28no—
409C22×C67—22no—
410C22×C67—22no—
411C22×C67—28no—
412C22×C67C22×#4114yes—
413C22×C67C22×#4112yes—
414C22×C67C2×2−1+412yes—
415C22×C67#58512yes—
416C22×C67C2611yescharacteristic
417C2×D67—22no—
418C2×D67—22no—
419C2×D67—28no—
420C2×D67—22no—
421C2×D67—24no—
422C2×D67—24no—
423C2×D67—22no—
424C2×D67—24no—
425C2×D67—22no—
426C2×D67—416no—
427C2×D67—48no—
428C2×D67—44no—
429C2×D67C2×2−1+414yes—
430C4×C67—24no—
431C4×C67—24no—
432C4×C67—28no—
433C4×C67—24no—
434C4×C67—24no—
435C4×C67C22×#4114yes—
436C4×C67C22×#4114yes—
437Dic67—28no—
438Dic67—24no—
439Dic67—22no—
440Dic67—22no—
441Dic67—24no—
442Dic67—24no—
443C2×#3495—671nomaximal, Sylow
444C2×C67—24no—
445C2×C67#349514yescomplemented
446C2×C67C23×#4111yescharacteristic
447C2×C67C22×2−1+411yescharacteristic
448C2×C67C2×#58511yescharacteristic
449D67—24no—
450D67—44no—
451D67—42no—
452#3495—6732no—
453C2×#556—672no—
454C2×#554—672no—
455C2×#552—672no—
456C2×#552—672no—
457C2×#552—674no—
458C2×#551—674no—
459C2×#544D6711yescharacteristic, complemented
460C2×#542—672no—
461C2×#541—672no—
462C2×#536—671no—
463C2×#533—672no—
464C2×#529—672no—
465C2×#525—671no—
466C22×C22⋊Q8—671no—
467C2×#520—671no—
468C2×#519—671no—
469C22×#117—671no—
470C67C2×#349511yescharacteristic, complemented, Sylow
471C22×#41—671no—
472C23×Q8—671no—
473C24×C4—671no—
474#556—6732no—
475#554—6732no—
476#552—6732no—
477#552—6732no—
478#552—6764no—
479#551—6764no—
480#544C2×D67116yescomplemented
481#542—6732no—
482#541—6732no—
483#536—6716no—
484#533—6732no—
485C2×C4⋊Q8—672no—
486C2×C4⋊Q8C2×D6712yescomplemented
487C2×C4⋊Q8C2×D6712yescomplemented
488#529—6732no—
489C2×#126—674no—
490C2×#126—674no—
491C2×#126—674no—
492C2×#126—674no—
493C2×#125—674no—
494C2×#125—674no—
495C2×#125—674no—
496C2×#125C2×D6712yescomplemented
497C2×#125C2×D6712yescomplemented
498C2×#124—674no—
499C2×#124—672no—
500#525—6716no—
501C2×#123—674no—
502C2×#123—674no—
503C2×#123—672no—
504C2×#123—674no—
505C2×C22⋊Q8—674no—
506C2×C22⋊Q8—674no—
507C2×C22⋊Q8—672no—
508C2×C22⋊Q8—672no—
509C2×C22⋊Q8—672no—
510C2×C22⋊Q8—672no—
511C2×C22⋊Q8—6716no—
512C2×C22⋊Q8—671no—
513C2×C22⋊Q8—671no—
514C2×C22⋊Q8—672no—
515C2×C22⋊Q8—672no—
516C2×C22⋊Q8C2×D6714yes—
517C2×#121—671no—
518C2×#121—671no—
519C2×#120—672no—
520#520—6716no—
521#519—6716no—
522C2×C4×Q8—674no—
523C2×C4×Q8—672no—
524C2×C4×Q8—672no—
525C2×C4×Q8—672no—
526C2×C4×Q8—672no—
527C2×C4×Q8—672no—
528C2×C4×D4—674no—
529C2×C4×D4—672no—
530C2×C4×D4—674no—
531C2×C4×D4—672no—
532C2×C4×D4—672no—
533C2×#117—671no—
534C2×#117—6716no—
535C2×#117—671no—
536C2×#117—671no—
537C2×#117—672no—
538C2×#117—674no—
539C2×#117—674no—
540C2×#117—672no—
541C2×#117—674no—
542C2×#117—672no—
543C2×#117C2×D6711yescharacteristic
544C2×#117C2×D6711yescharacteristic
545C22×C4⋊C4—672no—
546C22×C4⋊C4—671no—
547C22×C4⋊C4—671no—
548C22×C4⋊C4—672no—
549C22×C4⋊C4C2×D6711yescharacteristic
550C22×C22⋊C4—672no—
551C22×C22⋊C4—672no—
552C22×C42—672no—
553C25—671no—
554C2×#41—678no—
555C2×#41—1348no—
556C22×Q8—672no—
557C22×Q8—672no—
558C22×Q8—671no—
559C22×Q8—678no—
560C22×Q8—1348no—
561C22×Q8C22×D6714yes—
562C22×D4—672no—
563C22×D4—672no—
564C22×D4—672no—
565C22×D4—671no—
566C23×C4—672no—
567C23×C4—674no—
568C23×C4—672no—
569C23×C4—671no—
570C23×C4—672no—
571C23×C4—671no—
572C23×C4—672no—
573C23×C4—671no—
574C23×C4—671no—
575C23×C4—678no—
576C23×C4—671no—
577C23×C4—1348no—
578C23×C4C22×D6712yes—
579C23×C4C22×D6711yescharacteristic
580C4⋊Q8—6716no—
581C4⋊Q8C22×D67116yescomplemented
582C4⋊Q8C22×D67116yescomplemented
583#126—6732no—
584#126—6732no—
585#126—6732no—
586#126—6732no—
587#125—6732no—
588#125—6732no—
589#125—6732no—
590#125C22×D67116yescomplemented
591#125C22×D67116yescomplemented
592#124—6732no—
593#124—6716no—
594#123—6732no—
595#123—6732no—
596#123—6716no—
597#123—6732no—
598C22⋊Q8—6732no—
599C22⋊Q8—6732no—
600C22⋊Q8—6716no—
601C22⋊Q8—6716no—
602C22⋊Q8—6716no—
603C22⋊Q8—6716no—
604C22⋊Q8—678no—
605C22⋊Q8—678no—
606C22⋊Q8—6716no—
607C22⋊Q8—6716no—
608C22⋊Q8C22×D67132yes—
609#121—678no—
610#121—678no—
611#120—6716no—
612C4×Q8—6732no—
613C4×Q8—6716no—
614C4×Q8—6716no—
615C4×Q8—6716no—
616C4×Q8—6716no—
617C4×Q8—6716no—
618C4×D4—6732no—
619C4×D4—6716no—
620C4×D4—6732no—
621C4×D4—6716no—
622C4×D4—6716no—
623#117—678no—
624#117—678no—
625#117—678no—
626#117—6716no—
627#117—6732no—
628#117—6732no—
629#117—6716no—
630#117—6732no—
631#117—6716no—
632#117C22×D6718yes—
633#117C22×D6718yes—
634C2×C4⋊C4—671no—
635C2×C4⋊C4—671no—
636C2×C4⋊C4—672no—
637C2×C4⋊C4—672no—
638C2×C4⋊C4—674no—
639C2×C4⋊C4—674no—
640C2×C4⋊C4—674no—
641C2×C4⋊C4—6716no—
642C2×C4⋊C4—674no—
643C2×C4⋊C4—674no—
644C2×C4⋊C4—674no—
645C2×C4⋊C4—672no—
646C2×C4⋊C4—672no—
647C2×C4⋊C4—674no—
648C2×C4⋊C4—678no—
649C2×C4⋊C4—678no—
650C2×C4⋊C4—6716no—
651C2×C4⋊C4C22×D6712yes—
652C2×C4⋊C4C22×D6711yescharacteristic
653C2×C4⋊C4C22×D6711yescharacteristic
654C2×C4⋊C4C22×D6712yes—
655C2×C4⋊C4C22×D6718yes—
656C2×C4⋊C4C22×D6714yes—
657C2×C4⋊C4C22×D6714yes—
658C2×C4⋊C4C22×D6711yescharacteristic
659C2×C4⋊C4C22×D6711yescharacteristic
660C2×C4⋊C4C22×D6714yes—
661C2×C22⋊C4—672no—
662C2×C22⋊C4—672no—
663C2×C22⋊C4—672no—
664C2×C22⋊C4—674no—
665C2×C22⋊C4—674no—
666C2×C22⋊C4—6716no—
667C2×C22⋊C4—672no—
668C2×C22⋊C4—672no—
669C2×C22⋊C4—674no—
670C2×C22⋊C4—674no—
671C2×C22⋊C4—672no—
672C2×C22⋊C4—672no—
673C2×C22⋊C4—674no—
674C2×C22⋊C4—6716no—
675C2×C22⋊C4C22×D6712yes—
676C2×C22⋊C4C22×D6712yes—
677C2×C42—672no—
678C2×C42—672no—
679C2×C42—674no—
680C2×C42—674no—
681C2×C42—674no—
682C2×C42—672no—
683C2×C42—6716no—
684C2×C42C22×D6712yes—
685C2×C42C22×D6712yes—
686C24—2682no—
687C24—674no—
688C24—671no—
689C24—671no—
690C24—672no—
691C24—1344no—
692C24—1344no—
693C24C23×D6711yescharacteristic
694#41—13432no—
695C2×Q8—48no—
696C2×Q8—678no—
697C2×Q8—678no—
698C2×Q8—674no—
699C2×Q8—1348no—
700C2×Q8—1348no—
701C2×Q8—13432no—
702C2×Q8—1344no—
703C2×Q8C23×D67116yes—
704C2×D4—2684no—
705C2×D4—678no—
706C2×D4—678no—
707C2×D4—678no—
708C2×D4—674no—
709C2×D4—1348no—
710C2×D4—1348no—
711C2×D4—1344no—
712C22×C4—44no—
713C22×C4—2688no—
714C22×C4—2684no—
715C22×C4—678no—
716C22×C4—6716no—
717C22×C4—678no—
718C22×C4—674no—
719C22×C4—672no—
720C22×C4—671no—
721C22×C4—672no—
722C22×C4—674no—
723C22×C4—672no—
724C22×C4—671no—
725C22×C4—674no—
726C22×C4—678no—
727C22×C4—674no—
728C22×C4—678no—
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—1348no—
740C22×C4#1176162918yes—
741C22×C4C23×D6712yes—
742C22×C4C23×D6712yes—
743C22×C4C23×D6712yes—
744C22×C4C23×D6712yes—
745C22×C4C23×D6714yes—
746C22×C4C23×D6718yes—
747C22×C4C23×D6714yes—
748C22×C4C23×D6711yescharacteristic
749C22×C4C23×D6711yescharacteristic
750C4⋊C4—674no—
751C4⋊C4—674no—
752C4⋊C4—678no—
753C4⋊C4—678no—
754C4⋊C4—6716no—
755C4⋊C4—6716no—
756C4⋊C4—6716no—
757C4⋊C4—6716no—
758C4⋊C4—6716no—
759C4⋊C4—6716no—
760C4⋊C4—678no—
761C4⋊C4—678no—
762C4⋊C4—6716no—
763C4⋊C4C23×D6718yes—
764C4⋊C4C23×D6714yes—
765C4⋊C4C23×D6714yes—
766C4⋊C4C23×D6718yes—
767C4⋊C4C23×D67116yes—
768C4⋊C4C23×D67116yes—
769C4⋊C4C23×D6714yes—
770C4⋊C4C23×D6714yes—
771C4⋊C4C23×D67116yes—
772C22⋊C4—678no—
773C22⋊C4—678no—
774C22⋊C4—678no—
775C22⋊C4—6716no—
776C22⋊C4—6716no—
777C22⋊C4—678no—
778C22⋊C4—678no—
779C22⋊C4—6716no—
780C22⋊C4—6716no—
781C22⋊C4—678no—
782C22⋊C4—678no—
783C22⋊C4—6716no—
784C22⋊C4C23×D6718yes—
785C22⋊C4C23×D6718yes—
786C42—678no—
787C42—678no—
788C42—678no—
789C42—6716no—
790C42—6716no—
791C42—6716no—
792C42C23×D6718yes—
793C42C23×D6718yes—
794C23—22no—
795C23—22no—
796C23—26816no—
797C23—2684no—
798C23—674no—
799C23—672no—
800C23—672no—
801C23—674no—
802C23—1348no—
803C23—1348no—
804C23—1342no—
805C23—1344no—
806C23—1344no—
807C23—1342no—
808C23—1344no—
809C23—1342no—
810C23—1342no—
811C23—1342no—
812C23C2×#1176162914yes—
813C23C24×D6712yes—
814C23C24×D6711yescharacteristic
815Q8—416no—
816Q8—13416no—
817Q8—13416no—
818Q8—1348no—
819D4—2688no—
820D4—13416no—
821D4—13416no—
822D4—1348no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—48no—
829C2×C4—26816no—
830C2×C4—2688no—
831C2×C4—674no—
832C2×C4—672no—
833C2×C4—674no—
834C2×C4—678no—
835C2×C4—674no—
836C2×C4—672no—
837C2×C4—13416no—
838C2×C4—1348no—
839C2×C4—1342no—
840C2×C4—1342no—
841C2×C4—1344no—
842C2×C4—13416no—
843C2×C4—1348no—
844C2×C4—1344no—
845C2×C4—1344no—
846C2×C4—1348no—
847C2×C4—1348no—
848C2×C4—1348no—
849C2×C4—1348no—
850C2×C4—13416no—
851C2×C4C2×#1176162914yes—
852C2×C4C2×#1176162914yes—
853C2×C4C2×#11761629116yes—
854C2×C4C24×D6714yes—
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—26816no—
865C22—2684no—
866C22—2688no—
867C22—674no—
868C22—1342no—
869C22—1344no—
870C22—1344no—
871C22—1342no—
872C22—1344no—
873C22—1342no—
874C22—1348no—
875C22—1342no—
876C22—1342no—
877C22C22×#1176162914yes—
878C22C22×#1176162912yes—
879C222−1+4×D6712yes—
880C22#1686423112yes—
881C22C25×D6711yescharacteristic
882C4—24no—
883C4—24no—
884C4—28no—
885C4—24no—
886C4—24no—
887C4—1342no—
888C4—1342no—
889C4—1344no—
890C4—1348no—
891C4—1344no—
892C4—1344no—
893C4C22×#1176162914yes—
894C4C22×#1176162914yes—
895C2—24no—
896C2—2682no—
897C2—2684no—
898C2—1344no—
899C2#2257396414yesdirect product factor
900C2C23×#1176162911yescharacteristic
901C2C2×2−1+4×D6711yescharacteristic
902C2C2×#1686423111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#544×C67C2
socleC23×C67C25
prime radicalC2×#16863908C2
hypercenterC2×#544D67
hypocenterC67C2×#3495
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #22573964C2direct (N × H)
2. C2×#16864120C2semidirect
3. C2×#16864107C2semidirect
4. C2×#16864088C2semidirect
5. C2×#16864084C2semidirect
6. C2×#16864084C2semidirect
7. C2×#16864073C2semidirect
8. C2×#16864020C2semidirect
9. C2×#16864009C2semidirect
10. C2×#16863972C2semidirect
11. C2×#16863951C2semidirect
12. C2×#16863931C2semidirect
14. C22×#14524023C2semidirect
15. C2×#16863877C2semidirect
16. C2×#16863873C2semidirect
17. C2×#117×D67C2semidirect
18. C2×#544×C67C2semidirect
22. #16864120C22semidirect
23. #16864107C22semidirect
24. #16864088C22semidirect
25. #16864084C22semidirect
26. #16864084C22semidirect
27. #16864073C22semidirect
28. #16864020C22semidirect
29. #16864009C22semidirect
30. #16863972C22semidirect
31. #16863951C22semidirect
32. C2×#14524043C22semidirect
33. #16863931C22semidirect
36. C2×#14524038C22semidirect
37. C2×#14524038C22semidirect
38. C2×#14524034C22semidirect
39. C2×#14524034C22semidirect
40. C2×#14524034C22semidirect
42. C2×#14524031C22semidirect
54. C2×#14524023C22semidirect
55. C2×#14524023C22semidirect
56. C2×#14524023C22semidirect
58. C2×#14524019C22semidirect
62. #16863877C22semidirect
63. #16863873C22semidirect
64. C2×Q8×Dic67C22semidirect
65. C2×C4×Dic134C22semidirect
66. C2×C4×Dic134C22semidirect
67. C2×#14524008C22semidirect
68. C2×#14524008C22semidirect
69. C2×#14524008C22semidirect
73. C2×#14524005C22semidirect
79. C2×#14524001C22semidirect
80. C2×#14524001C22semidirect
84. #117×D67C22semidirect
88. C2×C4⋊C4×D67C22semidirect
92. #544×C67C22semidirect
93. C2×C4⋊Q8×C67C22semidirect
94. C2×C4⋊Q8×C67C22semidirect
95. C2×#125×C67C22semidirect
96. C2×#125×C67C22semidirect
125. #14524043C23semidirect
128. #14524038C23semidirect
129. #14524038C23semidirect
130. #14524034C23semidirect
131. #14524034C23semidirect
132. #14524034C23semidirect
134. #14524031C23semidirect
145. #14524023C23semidirect
146. #14524023C23semidirect
148. #14524019C23semidirect
152. Q8×Dic67C23semidirect
153. C4×Dic134C23semidirect
154. C4×Dic134C23semidirect
155. #14524008C23semidirect
156. #14524008C23semidirect
157. #14524008C23semidirect
161. #14524005C23semidirect
167. #14524001C23semidirect
168. #14524001C23semidirect
188. C4⋊C4×D67C23semidirect
213. C4⋊Q8×C67C23semidirect
214. C4⋊Q8×C67C23semidirect
215. #125×C67C23semidirect
216. #125×C67C23semidirect
445. C2×C67#3495semidirect
459. C2×#544D67semidirect
470. C67C2×#3495semidirect
480. #544C2×D67semidirect
486. C2×C4⋊Q8C2×D67semidirect
487. C2×C4⋊Q8C2×D67semidirect
496. C2×#125C2×D67semidirect
497. C2×#125C2×D67semidirect
581. C4⋊Q8C22×D67semidirect
582. C4⋊Q8C22×D67semidirect
590. #125C22×D67semidirect
591. #125C22×D67semidirect
899. C2#22573964direct (N × H)

Maximal subgroups

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

subgroupindex
#225739642
C2×#168641202
C2×#168641072
C2×#168640882
C2×#168640842
C2×#168640732
C2×#168640202
C2×#168640092
C2×#168639722
C2×#168639512
C2×#168639312
C2×#168639082
C22×#145240232
C2×#168638772
C2×#168638732
C2×#117×D672
C2×#544×C672
C2×#349567