Finite Group Databasebeta

← C2×#22574091 #31764272

Subgroups — C2×#22574091 #31764272

Order 17152.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574091C2132yesmaximal, direct product factor
2C2×#16864123C214yesmaximal, complemented
3C2×#16864113C214yesmaximal, complemented
4C2×#16864082C214yesmaximal, complemented
5C2×#16864078C214yesmaximal, complemented
6C2×#16864009C211yesmaximal, characteristic, complemented
7C2×#16864008C211yesmaximal, characteristic, complemented
8C2×#16864007C211yesmaximal, characteristic, complemented
9C2×#16863969C212yesmaximal
10C2×#16863952C211yesmaximal, characteristic, complemented
11C2×#16863950C212yesmaximal, complemented
12C2×#16863948C212yesmaximal, complemented
13C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
14C2×#16863872C212yesmaximal, complemented
15C2×#16863864C211yesmaximal, characteristic
16C2×#541×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2211yescharacteristic
18C22×Q8×D67C2212yes—
19#16864123C22164yescomplemented
20#16864113C22164yescomplemented
21#16864082C22164yescomplemented
22#16864078C22164yescomplemented
23#16864009C22116yescomplemented
24#16864008C22116yescomplemented
25#16864007C22116yescomplemented
26#16863969C22132yes—
27#16863952C22116yescomplemented
28#16863950C22132yescomplemented
29#16863948C22132yescomplemented
30C2×#14524043C2211yescharacteristic
31C2×#14524042C2214yes—
32C2×#14524042C2212yes—
33C2×#14524042C2214yes—
34C2×#14524041C2212yes—
35C4⋊Q8×D67C22116yescomplemented
36C2×#14524038C2214yes—
37C2×#14524038C2214yes—
38C2×#14524036C2214yes—
39C2×#14524035C2211yescharacteristic
40C2×#14524034C2214yes—
41C2×#14524033C2214yes—
42C2×#14524033C2214yes—
43C2×#14524033C2214yes—
44C2×#14524033C2214yes—
45C2×#14524029C2214yes—
46C2×#14524028C2214yes—
47C2×#14524025C2214yes—
48C2×#14524023C2212yes—
49C2×#14524022C2212yes—
50C2×#14524021C2214yes—
51C2×#14524021C2214yes—
52C2×#14524020C2214yes—
53C2×#14524019C2212yes—
54#16863872C22132yescomplemented
55#16863864C22116yes—
56C2×Q8×Dic67C2212yes—
57C2×C4×Dic134C2212yes—
58C2×C4×Dic134C2214yes—
59C2×C4×Dic134C2214yes—
60C2×#14524008C2212yes—
61C2×#14524008C2212yes—
62C2×#14524008C2214yes—
63C2×#14524008C2214yes—
64C2×#14524008C2214yes—
65C2×#14524005C2212yes—
66C2×(C22⋊D67)⋊C4C2212yes—
67C2×(C22⋊D67)⋊C4C2212yes—
68C2×#14524001C2214yes—
69C2×#14524001C2212yes—
70C2×#14524000C2211yescharacteristic
71C2×#14524000C2211yescharacteristic
72C2×#14524000C2214yes—
73C2×#14524000C2214yes—
74C2×#14523999C2214yes—
75C2×C4⋊C4×D67C2214yes—
76C22×C4×Dic67C2211yescharacteristic
77C2×C42×D67C2211yescharacteristic
78C2×C42×D67C2211yescharacteristic
79#541×C67C22116yescomplemented
80C2×C4⋊Q8×C67C2211yescharacteristic
81C2×#126×C67C2214yes—
82C2×#125×C67C2211yescharacteristic
83C2×#125×C67C2214yes—
84C2×C22⋊Q8×C67C2212yes—
85C2×C4×Q8×C67C2212yes—
86C2×#117×C67C2211yescharacteristic
87C2×#11761628—28no—
88C2×#11761628C2318yes—
89C22×Dic134C2314yes—
90C22×Dic134C2311yescharacteristic
91C22×Dic134C2312yes—
92C22×Dic134C2314yes—
93C2×Q8×D67—216no—
94C2×Q8×D67C23116yes—
95C22×D268C2311yescharacteristic
96C22×C22⋊D67C2311yescharacteristic
97C22×C22⋊D67C2311yescharacteristic
98C23×Dic67C2312yes—
99C22×C4×D67C2312yes—
100C22×C4×D67C2312yes—
101C22×C4×D67C2311yescharacteristic
102C22×C4×D67C2314yes—
103C22×C4×D67C2311yescharacteristic
104#14524043C2318yes—
105#14524042C23132yes—
106#14524042C23132yes—
107#14524042C23116yes—
108#14524041C23116yes—
109#14524038C23132yes—
110#14524038C23132yes—
111#14524036C23132yes—
112#14524035C2318yes—
113#14524034C23132yes—
114#14524033C23132yes—
115#14524033C23132yes—
116#14524033C23132yes—
117#14524033C23132yes—
118#14524029C23132yes—
119#14524028C23132yes—
120#14524025C23132yes—
121#14524023C23116yes—
122#14524022C23116yes—
123#14524021C23132yes—
124#14524021C23132yes—
125#14524020C23132yes—
126#14524019C23116yes—
127Q8×Dic67C23116yes—
128C4×Dic134C23116yes—
129C4×Dic134C23132yes—
130C4×Dic134C23132yes—
131#14524008C23116yes—
132#14524008C23132yes—
133#14524008C23132yes—
134#14524008C23132yes—
135#14524008C23116yes—
136#14524005C23116yes—
137(C22⋊D67)⋊C4C23116yes—
138(C22⋊D67)⋊C4C23116yes—
139#14524001C23132yes—
140#14524001C23116yes—
141#14524000C2318yes—
142#14524000C23132yes—
143#14524000C23132yes—
144#14524000C2318yes—
145#14523999C23132yes—
146C2×C4⋊Dic67C2314yes—
147C2×C4⋊Dic67C2312yes—
148C2×C4⋊Dic67C2314yes—
149C2×C4⋊Dic67C2314yes—
150C2×Dic67⋊C4C2314yes—
151C2×Dic67⋊C4C2314yes—
152C2×Dic67⋊C4C2314yes—
153C2×Dic67⋊C4C2312yes—
154C2×Dic67⋊C4C2312yes—
155C2×Dic67⋊C4C2314yes—
156C2×Dic67⋊C4C2314yes—
157C2×Dic67⋊C4C2314yes—
158C2×Dic67⋊C4C2314yes—
159C2×Dic67⋊C4C2314yes—
160C4⋊C4×D67C23132yes—
161C2×C22⋊Dic67C2314yes—
162C2×(C2×D67)⋊C4C2312yes—
163C2×(C2×D67)⋊C4C2314yes—
164C2×(C2×D67)⋊C4C2312yes—
165C2×(C2×D67)⋊C4C2314yes—
166C2×(C2×D67)⋊C4C2314yes—
167C2×C4×Dic67C2311yescharacteristic
168C2×C4×Dic67C2312yes—
169C2×C4×Dic67C2312yes—
170C2×C4×Dic67C2311yescharacteristic
171C2×C4×Dic67C2312yes—
172C2×C4×Dic67C2318yes—
173C2×C4×Dic67C2314yes—
174C2×C4×Dic67C2314yes—
175C2×C4×Dic67C2314yes—
176C2×C4×Dic67C2314yes—
177C42×D67C2318yes—
178C42×D67C2318yes—
179C22×Q8×C67C2312yes—
180C23×C4×C67C2311yescharacteristic
181C4⋊Q8×C67C2318yes—
182#126×C67C23132yes—
183#125×C67C2318yes—
184#125×C67C23132yes—
185C22⋊Q8×C67C23116yes—
186C4×Q8×C67C23116yes—
187#117×C67C2318yes—
188C2×C4⋊C4×C67C2312yes—
189C2×C4⋊C4×C67C2312yes—
190C2×C4⋊C4×C67C2314yes—
191C2×C4⋊C4×C67C2314yes—
192C2×C4⋊C4×C67C2314yes—
193C2×C4⋊C4×C67C2314yes—
194C2×C22⋊C4×C67C2312yes—
195C2×C22⋊C4×C67C2314yes—
196C2×C42×C67C2311yescharacteristic
197C2×C42×C67C2311yescharacteristic
198C2×C42×C67C2314yes—
199C23×D67C2411yescharacteristic
200C23×D67C2411yescharacteristic
201#11761628—232no—
202C2×Dic134—28no—
203C2×Dic134—216no—
204C2×Dic134—24no—
205C2×Dic134—216no—
206C2×Dic134C24116yes—
207C2×Dic134C2414yes—
208C2×Dic134C2418yes—
209C2×Dic134C24116yes—
210Q8×D67—264no—
211C2×D268—24no—
212C2×D268C2414yes—
213C2×C22⋊D67—24no—
214C2×C22⋊D67—24no—
215C2×C22⋊D67C2414yes—
216C2×C22⋊D67C2414yes—
217C22×Dic67—28no—
218C22×Dic67C2412yes—
219C22×Dic67C2414yes—
220C22×Dic67C2414yes—
221C22×Dic67C2411yescharacteristic
222C22×Dic67C2418yes—
223C22×Dic67C2411yescharacteristic
224C22×Dic67C2412yes—
225C2×C4×D67—216no—
226C2×C4×D67—24no—
227C2×C4×D67—28no—
228C2×C4×D67—28no—
229C2×C4×D67#4118yes—
230C2×C4×D67C2418yes—
231C2×C4×D67C2418yes—
232C2×C4×D67C2414yes—
233C2×C4×D67C24116yes—
234C2×C4×D67C2414yes—
235C4⋊Dic67C24116yes—
236C4⋊Dic67C2418yes—
237C4⋊Dic67C24116yes—
238C4⋊Dic67C24116yes—
239Dic67⋊C4C24116yes—
240Dic67⋊C4C24116yes—
241Dic67⋊C4C24116yes—
242Dic67⋊C4C2418yes—
243Dic67⋊C4C2418yes—
244Dic67⋊C4C24116yes—
245Dic67⋊C4C24116yes—
246Dic67⋊C4C24116yes—
247Dic67⋊C4C24116yes—
248Dic67⋊C4C24116yes—
249C22⋊Dic67C24116yes—
250(C2×D67)⋊C4C2418yes—
251(C2×D67)⋊C4C24116yes—
252(C2×D67)⋊C4C2418yes—
253(C2×D67)⋊C4C24116yes—
254(C2×D67)⋊C4C24116yes—
255C4×Dic67C2414yes—
256C4×Dic67C2418yes—
257C4×Dic67C2418yes—
258C4×Dic67C2414yes—
259C4×Dic67C2418yes—
260C4×Dic67C24116yes—
261C4×Dic67C24116yes—
262C4×Dic67C24116yes—
263C4×Dic67C24116yes—
264C24×C67C2411yescharacteristic
265C2×Q8×C67—28no—
266C2×Q8×C67C2418yes—
267C22×C4×C67—24no—
268C22×C4×C67C2412yes—
269C22×C4×C67C2414yes—
270C22×C4×C67C2412yes—
271C22×C4×C67C2414yes—
272C22×C4×C67C2411yescharacteristic
273C22×C4×C67C2414yes—
274C22×C4×C67C2411yescharacteristic
275C4⋊C4×C67C2418yes—
276C4⋊C4×C67C2418yes—
277C4⋊C4×C67C24116yes—
278C4⋊C4×C67C24116yes—
279C4⋊C4×C67C24116yes—
280C4⋊C4×C67C24116yes—
281C22⋊C4×C67C2418yes—
282C22⋊C4×C67C24116yes—
283C42×C67C2414yes—
284C42×C67C2414yes—
285C42×C67C24116yes—
286C23×C67—22no—
287C23×C67—24no—
288C23×C67C2512yes—
289C23×C67C2511yescharacteristic
290C22×D67—24no—
291C22×D67—22no—
292C22×D67—24no—
293C22×D67C2×#4114yes—
294C22×D67C2512yes—
295C22×D67C2512yes—
296Q8×C67—216no—
297C2×C4×C67—22no—
298C2×C4×C67—28no—
299C2×C4×C67—24no—
300C2×C4×C67—24no—
301C2×C4×C67—28no—
302C2×C4×C67—28no—
303C2×C4×C67C2×#4114yes—
304C2×C4×C67C2514yes—
305C2×C4×C67C2518yes—
306C2×C4×C67C2514yes—
307C2×C4×C67C2518yes—
308C2×C4×C67C2512yes—
309C2×C4×C67C2512yes—
310C22⋊D67—28no—
311C22⋊D67—28no—
312C2×Dic67—22no—
313C2×Dic67—28no—
314C2×Dic67—24no—
315C2×Dic67—28no—
316C2×Dic67—216no—
317C2×Dic67C2×#4114yes—
318C2×Dic672−1+418yes—
319C2×Dic67C2514yes—
320C2×Dic67C2518yes—
321C2×Dic67C2518yes—
322C2×Dic67C2512yes—
323C2×Dic67C2512yes—
324C2×Dic67C2514yes—
325D268—28no—
326C4×D67—232no—
327C4×D67—28no—
328C4×D67—216no—
329C4×D67—216no—
330C4×D67C2×#41116yes—
331Dic134—216no—
332Dic134—232no—
333Dic134—28no—
334Dic134—232no—
335C22×C67—22no—
336C22×C67—24no—
337C22×C67—44no—
338C22×C67C22×#4112yes—
339C22×C67C2×2−1+414yes—
340C22×C67C2611yescharacteristic
341C2×D67—24no—
342C2×D67—28no—
343C2×D67—22no—
344C2×D67—24no—
345C2×D67—44no—
346C2×D67C22×#4114yes—
347C4×C67—28no—
348C4×C67—22no—
349C4×C67—28no—
350C4×C67—24no—
351C4×C67—24no—
352C4×C67C22×#4114yes—
353Dic67—28no—
354Dic67—22no—
355Dic67—28no—
356Dic67—24no—
357Dic67C22×#4114yes—
358Dic67C2×2−1+418yes—
359C2×#3509—671nomaximal, Sylow
360C2×C67—42no—
361C2×C67#350914yescomplemented
362C2×C67C23×#4111yescharacteristic
363C2×C67C22×2−1+412yes—
364D67—24no—
365D67—42no—
366#3509—6732no—
367C2×#557—674no—
368C2×#556—674no—
369C2×#552—674no—
370C2×#552—674no—
371C2×#541—671no—
372C2×#541—671no—
373C2×#541—671no—
374C2×#541D6711yescharacteristic, complemented
375C2×#536—672no—
376C2×#533—671no—
377C2×#533—672no—
378C2×#533—672no—
379C22×C4⋊Q8—671no—
380C2×#519—672no—
381C2×C4×#41—671no—
382C67C2×#350911yescharacteristic, complemented, Sylow
383C22×#41—671no—
384C23×Q8—672no—
385#557—6764no—
386#556—6764no—
387#552—6764no—
388#552—6764no—
389#541—6716no—
390#541—6716no—
391#541—6716no—
392#541C2×D67116yescomplemented
393#536—6732no—
394#533—6716no—
395#533—6732no—
396#533—6732no—
397C2×C4⋊Q8—672no—
398C2×C4⋊Q8—6716no—
399C2×C4⋊Q8—674no—
400C2×C4⋊Q8—672no—
401C2×C4⋊Q8—674no—
402C2×C4⋊Q8—671no—
403C2×C4⋊Q8C2×D6711yescharacteristic
404C2×#126—674no—
405C2×#126—674no—
406C2×#126—674no—
407C2×#126C2×D6714yes—
408C2×#125—674no—
409C2×#125—674no—
410C2×#125—674no—
411C2×#125—674no—
412C2×#125—674no—
413C2×#125—671no—
414C2×#125C2×D6711yescharacteristic
415C2×#125C2×D6714yes—
416C2×#124—674no—
417C2×#123—674no—
418C2×#123—674no—
419C2×C22⋊Q8—672no—
420C2×C22⋊Q8—672no—
421C2×C22⋊Q8—672no—
422C2×C22⋊Q8—674no—
423C2×C22⋊Q8—674no—
424C2×C22⋊Q8—674no—
425C2×C22⋊Q8C2×D6712yes—
426#519—6732no—
427C4×#41—6716no—
428C2×C4×Q8—672no—
429C2×C4×Q8—672no—
430C2×C4×Q8—672no—
431C2×C4×Q8—674no—
432C2×C4×Q8—674no—
433C2×C4×Q8—674no—
434C2×C4×Q8—672no—
435C2×C4×Q8—674no—
436C2×C4×Q8—674no—
437C2×C4×Q8C2×D6712yes—
438C2×C4×D4—672no—
439C2×C4×D4—672no—
440C2×C4×D4—672no—
441C2×#117—672no—
442C2×#117—674no—
443C2×#117—674no—
444C2×#117—671no—
445C2×#117—671no—
446C2×#117—674no—
447C2×#117—674no—
448C2×#117C2×D6711yescharacteristic
449C22×C4⋊C4—674no—
450C22×C42—671no—
451C22×C42—671no—
452C22×C42—671no—
453C2×#41—678no—
454C2×#41—1348no—
455C22×Q8—6716no—
456C22×Q8—674no—
457C22×Q8—672no—
458C22×Q8—674no—
459C22×Q8—671no—
460C22×Q8—13416no—
461C22×Q8C22×D6712yes—
462C22×D4—671no—
463C22×D4—671no—
464C22×D4—671no—
465C23×C4—671no—
466C23×C4—672no—
467C23×C4—674no—
468C23×C4—672no—
469C23×C4—672no—
470C23×C4—671no—
471C23×C4C22×D6711yescharacteristic
472C4⋊Q8—6716no—
473C4⋊Q8—6732no—
474C4⋊Q8—6716no—
475C4⋊Q8—6732no—
476C4⋊Q8—678no—
477C4⋊Q8C22×D6718yes—
478#126—6732no—
479#126—6732no—
480#126—6732no—
481#126C22×D67132yes—
482#125—6732no—
483#125—6732no—
484#125—6732no—
485#125—6732no—
486#125—6732no—
487#125—678no—
488#125C22×D6718yes—
489#125C22×D67132yes—
490#124—6732no—
491#123—6732no—
492#123—6732no—
493C22⋊Q8—6716no—
494C22⋊Q8—6716no—
495C22⋊Q8—6716no—
496C22⋊Q8—6732no—
497C22⋊Q8—6732no—
498C22⋊Q8—6732no—
499C22⋊Q8C22×D67116yes—
500C4×Q8—6716no—
501C4×Q8—6716no—
502C4×Q8—6716no—
503C4×Q8—6732no—
504C4×Q8—6732no—
505C4×Q8—6732no—
506C4×Q8—6716no—
507C4×Q8—6732no—
508C4×Q8—6732no—
509C4×Q8C22×D67116yes—
510C4×D4—6716no—
511C4×D4—6716no—
512C4×D4—6716no—
513#117—6716no—
514#117—6732no—
515#117—6732no—
516#117—678no—
517#117—678no—
518#117—6732no—
519#117—6732no—
520#117C22×D6718yes—
521C2×C4⋊C4—674no—
522C2×C4⋊C4—674no—
523C2×C4⋊C4—674no—
524C2×C4⋊C4—674no—
525C2×C4⋊C4—672no—
526C2×C4⋊C4—672no—
527C2×C4⋊C4—672no—
528C2×C4⋊C4—674no—
529C2×C4⋊C4—674no—
530C2×C4⋊C4—674no—
531C2×C4⋊C4—674no—
532C2×C4⋊C4—674no—
533C2×C4⋊C4—674no—
534C2×C4⋊C4—674no—
535C2×C4⋊C4—6732no—
536C2×C4⋊C4C22×D6714yes—
537C2×C4⋊C4C22×D6712yes—
538C2×C4⋊C4C22×D6714yes—
539C2×C4⋊C4C22×D6712yes—
540C2×C4⋊C4C22×D6714yes—
541C2×C4⋊C4C22×D6714yes—
542C2×C22⋊C4—674no—
543C2×C22⋊C4—672no—
544C2×C22⋊C4—674no—
545C2×C22⋊C4—672no—
546C2×C22⋊C4—674no—
547C2×C22⋊C4—674no—
548C2×C22⋊C4C22×D6714yes—
549C2×C22⋊C4C22×D6712yes—
550C2×C42—671no—
551C2×C42—674no—
552C2×C42—674no—
553C2×C42—674no—
554C2×C42—674no—
555C2×C42—672no—
556C2×C42—672no—
557C2×C42—672no—
558C2×C42—678no—
559C2×C42—671no—
560C2×C42—678no—
561C2×C42—678no—
562C2×C42C22×D6714yes—
563C2×C42C22×D6711yescharacteristic
564C2×C42C22×D6711yescharacteristic
565C24—671no—
566C24—671no—
567C24C23×D6711yescharacteristic
568#41—13432no—
569C2×Q8—28no—
570C2×Q8—6716no—
571C2×Q8—678no—
572C2×Q8—6716no—
573C2×Q8—674no—
574C2×Q8—13416no—
575C2×Q8—1344no—
576C2×Q8—13416no—
577C2×Q8—13464no—
578C2×Q8—1348no—
579C2×Q8C23×D6718yes—
580C2×D4—674no—
581C2×D4—674no—
582C2×D4—674no—
583C2×D4—1344no—
584C2×D4—1344no—
585C2×D4—1344no—
586C22×C4—24no—
587C22×C4—671no—
588C22×C4—672no—
589C22×C4—678no—
590C22×C4—674no—
591C22×C4—678no—
592C22×C4—672no—
593C22×C4—674no—
594C22×C4—674no—
595C22×C4—671no—
596C22×C4—678no—
597C22×C4—678no—
598C22×C4—674no—
599C22×C4—6716no—
600C22×C4—1348no—
601C22×C4—1348no—
602C22×C4—13416no—
603C22×C4—1348no—
604C22×C4—1344no—
605C22×C4C23×D6714yes—
606C22×C4C23×D6712yes—
607C22×C4C23×D6714yes—
608C22×C4C23×D6711yescharacteristic
609C22×C4C23×D6712yes—
610C22×C4C23×D6714yes—
611C22×C4C23×D6711yescharacteristic
612C4⋊C4—6716no—
613C4⋊C4—6716no—
614C4⋊C4—6716no—
615C4⋊C4—6716no—
616C4⋊C4—678no—
617C4⋊C4—678no—
618C4⋊C4—678no—
619C4⋊C4—6716no—
620C4⋊C4—6716no—
621C4⋊C4—6716no—
622C4⋊C4—6716no—
623C4⋊C4—6716no—
624C4⋊C4—6716no—
625C4⋊C4—6716no—
626C4⋊C4C23×D67116yes—
627C4⋊C4C23×D6718yes—
628C4⋊C4C23×D67116yes—
629C4⋊C4C23×D6718yes—
630C4⋊C4C23×D67116yes—
631C4⋊C4C23×D67116yes—
632C22⋊C4—6716no—
633C22⋊C4—678no—
634C22⋊C4—6716no—
635C22⋊C4—678no—
636C22⋊C4—6716no—
637C22⋊C4—6716no—
638C22⋊C4C23×D67116yes—
639C22⋊C4C23×D6718yes—
640C42—674no—
641C42—674no—
642C42—678no—
643C42—678no—
644C42—678no—
645C42—6716no—
646C42—6716no—
647C42—6716no—
648C42—6716no—
649C42C23×D6714yes—
650C42C23×D6714yes—
651C42C23×D67116yes—
652C23—22no—
653C23—24no—
654C23—674no—
655C23—672no—
656C23—672no—
657C23—1342no—
658C23—1344no—
659C23—1344no—
660C23C24×D6712yes—
661C23C24×D6711yescharacteristic
662Q8—216no—
663Q8—13432no—
664Q8—1348no—
665Q8—13432no—
666Q8—13416no—
667D4—1348no—
668D4—1348no—
669D4—1348no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—674no—
677C2×C4—678no—
678C2×C4—672no—
679C2×C4—674no—
680C2×C4—6716no—
681C2×C4—674no—
682C2×C4—678no—
683C2×C4—678no—
684C2×C4—672no—
685C2×C4—13416no—
686C2×C4—13416no—
687C2×C4—13432no—
688C2×C4—13416no—
689C2×C4—1342no—
690C2×C4—1348no—
691C2×C4—1344no—
692C2×C4—1348no—
693C2×C4—1348no—
694C2×C4#41×D6714yes—
695C2×C4C24×D6714yes—
696C2×C4C24×D6718yes—
697C2×C4C24×D6712yes—
698C2×C4C24×D6714yes—
699C2×C4C24×D6718yes—
700C2×C4C24×D6712yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—2684no—
705C22—674no—
706C22—1342no—
707C22—1344no—
708C22—1348no—
709C22—1344no—
710C22C2×#41×D6712yes—
711C222−1+4×D6714yes—
712C22C25×D6711yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—674no—
719C4—678no—
720C4—1342no—
721C4—1348no—
722C4—1344no—
723C4—1348no—
724C4C2×#41×D6714yes—
725C2—42no—
726C2—2682no—
727C2—1344no—
728C2#2257409114yesdirect product factor
729C2C22×#41×D6711yescharacteristic
730C2C2×2−1+4×D6712yes—
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#541×C67C2
socleC23×C67C25
prime radicalC22×#11761628C22
hypercenterC2×#541D67
hypocenterC67C2×#3509
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #22574091C2direct (N × H)
2. C2×#16864123C2semidirect
3. C2×#16864113C2semidirect
4. C2×#16864082C2semidirect
5. C2×#16864078C2semidirect
6. C2×#16864009C2semidirect
7. C2×#16864008C2semidirect
8. C2×#16864007C2semidirect
10. C2×#16863952C2semidirect
11. C2×#16863950C2semidirect
12. C2×#16863948C2semidirect
13. C2×C4⋊Q8×D67C2semidirect
14. C2×#16863872C2semidirect
16. C2×#541×C67C2semidirect
19. #16864123C22semidirect
20. #16864113C22semidirect
21. #16864082C22semidirect
22. #16864078C22semidirect
23. #16864009C22semidirect
24. #16864008C22semidirect
25. #16864007C22semidirect
27. #16863952C22semidirect
28. #16863950C22semidirect
29. #16863948C22semidirect
35. C4⋊Q8×D67C22semidirect
54. #16863872C22semidirect
79. #541×C67C22semidirect
361. C2×C67#3509semidirect
374. C2×#541D67semidirect
382. C67C2×#3509semidirect
392. #541C2×D67semidirect
728. C2#22574091direct (N × H)

Maximal subgroups

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

subgroupindex
#225740912
C2×#168641232
C2×#168641132
C2×#168640822
C2×#168640782
C2×#168640092
C2×#168640082
C2×#168640072
C2×#168639692
C2×#168639522
C2×#168639502
C2×#168639482
C2×C4⋊Q8×D672
C2×#168638722
C2×#168638642
C2×#541×C672
C2×#350967