Finite Group Databasebeta

← C2×#22574693 #31763552

Subgroups — C2×#22574693 #31763552

Order 17152.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574693C2132yesmaximal, direct product factor
2C2×#16864150C214yesmaximal, complemented
3C2×Q8×Dic134C211yesmaximal, characteristic, complemented
4C2×#16864122C212yesmaximal, complemented
5C2×#16864120C212yesmaximal, complemented
6C2×#16864120C211yesmaximal, characteristic, complemented
7C2×#16864119C212yesmaximal, complemented
8C2×#16864106C211yesmaximal, characteristic, complemented
9C2×#16864084C212yesmaximal, complemented
10C2×#16864026C212yesmaximal, complemented
11C2×#16864018C212yesmaximal
12C2×#16864007C212yesmaximal, complemented
13C2×#16864005C214yesmaximal, complemented
14C2×#16864004C212yesmaximal, complemented
15C2×#16863951C211yesmaximal, characteristic, complemented
16C2×#16863950C211yesmaximal, characteristic, complemented
17C2×#16863933C211yesmaximal, characteristic
18C2×#557×C67C211yesmaximal, characteristic, complemented
19#16864150C22164yescomplemented
20Q8×Dic134C22116yescomplemented
21#16864122C22132yescomplemented
22#16864120C22132yescomplemented
23#16864120C22116yescomplemented
24#16864119C22132yescomplemented
25#16864106C22116yescomplemented
26#16864084C22132yescomplemented
27#16864026C22132yescomplemented
28#16864018C22132yes—
29#16864007C22132yescomplemented
30#16864005C22164yescomplemented
31#16864004C22132yescomplemented
32#16863951C22116yescomplemented
33#16863950C22116yescomplemented
34C2×#14524043C2212yes—
35C2×#14524043C2211yescharacteristic
36C2×#14524042C2214yes—
37C2×#14524042C2214yes—
38C2×#14524042C2212yes—
39C2×#14524042C2211yescharacteristic
40C2×#14524041C2211yescharacteristic
41#16863933C22116yes—
42C2×#14524038C2214yes—
43C2×#14524038C2212yes—
44C2×#14524038C2214yes—
45C2×#14524038C2214yes—
46C2×#14524038C2214yes—
47C2×#14524038C2214yes—
48C2×#14524037C2214yes—
49C2×#14524035C2214yes—
50C2×#14524035C2212yes—
51C2×#14524034C2212yes—
52C2×#14524034C2214yes—
53C2×#14524034C2211yescharacteristic
54C2×#14524033C2214yes—
55C2×#14524033C2212yes—
56C2×#14524033C2214yes—
57C2×#14524032C2212yes—
58C2×#14524032C2211yescharacteristic
59C2×#14524031C2214yes—
60C2×#14524028C2212yes—
61C2×#14524028C2214yes—
62C2×#14524023C2212yes—
63C2×#14524023C2212yes—
64C2×#14524023C2214yes—
65C2×#14524023C2211yescharacteristic
66C2×#14524021C2214yes—
67C2×#14524021C2214yes—
68C2×#14524021C2212yes—
69C2×#14524019C2212yes—
70C2×#14524019C2211yescharacteristic
71C2×#14524019C2212yes—
72C2×#14524019C2211yescharacteristic
73C2×#14524018C2211yescharacteristic
74C2×Q8×Dic67C2212yes—
75C2×Q8×Dic67C2212yes—
76C2×Q8×Dic67C2212yes—
77C2×C4×Dic134C2212yes—
78C2×C4×Dic134C2214yes—
79C2×C4×Dic134C2212yes—
80C2×C4×Dic134C2211yescharacteristic
81C2×#14524008C2212yes—
82C2×C4×D268C2212yes—
83C2×C4×D268C2212yes—
84C2×C4×D268C2211yescharacteristic
85C2×#14524001C2214yes—
86C2×#14524001C2212yes—
87C2×#14524001C2212yes—
88C2×#14524000C2212yes—
89C2×#14524000C2212yes—
90C2×C4⋊C4×D67C2212yes—
91C2×C42×D67C2211yescharacteristic
92#557×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2212yes—
94C2×C4⋊Q8×C67C2211yescharacteristic
95C2×#125×C67C2214yes—
96C2×#125×C67C2212yes—
97C2×C4×Q8×C67C2212yes—
98C2×C4×Q8×C67C2212yes—
99C2×C4×Q8×C67C2211yescharacteristic
100C2×C4×Q8×C67C2211yescharacteristic
101C22×Dic134C2311yescharacteristic
102C22×Dic134C2312yes—
103C22×Dic134C2312yes—
104C22×Dic134C2314yes—
105C22×D268C2311yescharacteristic
106C22×D268C2312yes—
107C22×C4×D67C2311yescharacteristic
108C22×C4×D67C2311yescharacteristic
109C22×C4×D67C2312yes—
110C22×C4×D67C2311yescharacteristic
111C22×C4×D67C2314yes—
112#14524043C23116yes—
113#14524043C2318yes—
114#14524042C23132yes—
115#14524042C23116yes—
116#14524042C2318yes—
117#14524042C23132yes—
118#14524041C2318yes—
119#14524038C23132yes—
120#14524038C23116yes—
121#14524038C23132yes—
122#14524038C23132yes—
123#14524038C23132yes—
124#14524038C23132yes—
125#14524037C23132yes—
126#14524035C23132yes—
127#14524035C23116yes—
128#14524034C23116yes—
129#14524034C23132yes—
130#14524034C2318yes—
131#14524033C23132yes—
132#14524033C23116yes—
133#14524033C23132yes—
134#14524032C23116yes—
135#14524032C2318yes—
136#14524031C23132yes—
137#14524028C23132yes—
138#14524028C23116yes—
139#14524023C23116yes—
140#14524023C23132yes—
141#14524023C2318yes—
142#14524023C23116yes—
143#14524021C23132yes—
144#14524021C23132yes—
145#14524021C23116yes—
146#14524019C23116yes—
147#14524019C2318yes—
148#14524019C23116yes—
149#14524019C2318yes—
150#14524018C2318yes—
151Q8×Dic67C23116yes—
152Q8×Dic67C23116yes—
153Q8×Dic67C23116yes—
154C4×Dic134C23116yes—
155C4×Dic134C23132yes—
156C4×Dic134C23116yes—
157C4×Dic134C2318yes—
158#14524008C23116yes—
159C4×D268C23116yes—
160C4×D268C23116yes—
161C4×D268C2318yes—
162#14524001C23132yes—
163#14524001C23116yes—
164#14524001C23116yes—
165#14524000C23116yes—
166#14524000C23116yes—
167C2×C4⋊Dic67C2312yes—
168C2×C4⋊Dic67C2311yescharacteristic
169C2×C4⋊Dic67C2312yes—
170C2×C4⋊Dic67C2312yes—
171C2×C4⋊Dic67C2311yescharacteristic
172C2×C4⋊Dic67C2312yes—
173C2×C4⋊Dic67C2314yes—
174C2×C4⋊Dic67C2314yes—
175C2×C4⋊Dic67C2314yes—
176C2×Dic67⋊C4C2314yes—
177C2×Dic67⋊C4C2312yes—
178C2×Dic67⋊C4C2312yes—
179C2×Dic67⋊C4C2312yes—
180C2×Dic67⋊C4C2312yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2314yes—
187C4⋊C4×D67C23116yes—
188C2×(C2×D67)⋊C4C2312yes—
189C2×(C2×D67)⋊C4C2312yes—
190C2×(C2×D67)⋊C4C2312yes—
191C2×(C2×D67)⋊C4C2312yes—
192C2×(C2×D67)⋊C4C2312yes—
193C2×(C2×D67)⋊C4C2314yes—
194C2×(C2×D67)⋊C4C2314yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×(C2×D67)⋊C4C2312yes—
199C2×C4×Dic67C2311yescharacteristic
200C2×C4×Dic67C2311yescharacteristic
201C2×C4×Dic67C2311yescharacteristic
202C2×C4×Dic67C2312yes—
203C2×C4×Dic67C2314yes—
204C2×C4×Dic67C2314yes—
205C2×C4×Dic67C2314yes—
206C42×D67C2318yes—
207C22×Q8×C67C2311yescharacteristic
208C22×Q8×C67C2312yes—
209C22×Q8×C67C2311yescharacteristic
210C4⋊Q8×C67C23116yes—
211C4⋊Q8×C67C2318yes—
212#125×C67C23132yes—
213#125×C67C23116yes—
214C4×Q8×C67C23116yes—
215C4×Q8×C67C23116yes—
216C4×Q8×C67C2318yes—
217C4×Q8×C67C2318yes—
218C2×C4⋊C4×C67C2311yescharacteristic
219C2×C4⋊C4×C67C2311yescharacteristic
220C2×C4⋊C4×C67C2312yes—
221C2×C4⋊C4×C67C2314yes—
222C2×C4⋊C4×C67C2312yes—
223C2×C4⋊C4×C67C2312yes—
224C2×C4⋊C4×C67C2314yes—
225C2×C4⋊C4×C67C2314yes—
226C2×C4⋊C4×C67C2312yes—
227C2×C42×C67C2312yes—
228C2×C42×C67C2314yes—
229C2×C42×C67C2311yescharacteristic
230C2×C42×C67C2312yes—
231C23×D67C2411yescharacteristic
232C23×D67C2412yes—
233C2×Dic134—24no—
234C2×Dic134—44no—
235C2×Dic134—44no—
236C2×Dic134—48no—
237C2×Dic134C2414yes—
238C2×Dic134C2418yes—
239C2×Dic134C2418yes—
240C2×Dic134C24116yes—
241C2×D268—24no—
242C2×D268—44no—
243C2×D268C2414yes—
244C2×D268C2418yes—
245C22×Dic67C2411yescharacteristic
246C22×Dic67C2412yes—
247C22×Dic67C2412yes—
248C22×Dic67C2411yescharacteristic
249C22×Dic67C2412yes—
250C22×Dic67C2411yescharacteristic
251C22×Dic67C2414yes—
252C2×C4×D67—24no—
253C2×C4×D67—24no—
254C2×C4×D67—28no—
255C2×C4×D67—48no—
256C2×C4×D67—42no—
257C2×C4×D67C2414yes—
258C2×C4×D67C2414yes—
259C2×C4×D67C2418yes—
260C2×C4×D67C2414yes—
261C2×C4×D67C24116yes—
262C4⋊Dic67C2418yes—
263C4⋊Dic67C2414yes—
264C4⋊Dic67C2418yes—
265C4⋊Dic67C2418yes—
266C4⋊Dic67C2414yes—
267C4⋊Dic67C2418yes—
268C4⋊Dic67C24116yes—
269C4⋊Dic67C24116yes—
270C4⋊Dic67C24116yes—
271Dic67⋊C4C24116yes—
272Dic67⋊C4C2418yes—
273Dic67⋊C4C2418yes—
274Dic67⋊C4C2418yes—
275Dic67⋊C4C2418yes—
276Dic67⋊C4C24116yes—
277Dic67⋊C4C2418yes—
278Dic67⋊C4C24116yes—
279Dic67⋊C4C2418yes—
280Dic67⋊C4C2418yes—
281Dic67⋊C4C24116yes—
282(C2×D67)⋊C4C2418yes—
283(C2×D67)⋊C4C2418yes—
284(C2×D67)⋊C4C2418yes—
285(C2×D67)⋊C4C2418yes—
286(C2×D67)⋊C4C2418yes—
287(C2×D67)⋊C4C24116yes—
288(C2×D67)⋊C4C24116yes—
289(C2×D67)⋊C4C24116yes—
290(C2×D67)⋊C4C24116yes—
291(C2×D67)⋊C4C2418yes—
292(C2×D67)⋊C4C2418yes—
293C4×Dic67C2414yes—
294C4×Dic67C2414yes—
295C4×Dic67C2414yes—
296C4×Dic67C2418yes—
297C4×Dic67C24116yes—
298C4×Dic67C24116yes—
299C4×Dic67C24116yes—
300C2×Q8×C67—28no—
301C2×Q8×C67—24no—
302C2×Q8×C67—24no—
303C2×Q8×C67C2414yes—
304C2×Q8×C67C2418yes—
305C2×Q8×C67C2414yes—
306C22×C4×C67C2412yes—
307C22×C4×C67C2412yes—
308C22×C4×C67C2411yescharacteristic
309C22×C4×C67C2412yes—
310C22×C4×C67C2412yes—
311C22×C4×C67C2414yes—
312C22×C4×C67C2411yescharacteristic
313C22×C4×C67C2411yescharacteristic
314C4⋊C4×C67C2414yes—
315C4⋊C4×C67C2414yes—
316C4⋊C4×C67C2418yes—
317C4⋊C4×C67C24116yes—
318C4⋊C4×C67C2418yes—
319C4⋊C4×C67C2418yes—
320C4⋊C4×C67C24116yes—
321C4⋊C4×C67C24116yes—
322C4⋊C4×C67C2418yes—
323C42×C67C2418yes—
324C42×C67C24116yes—
325C42×C67C2414yes—
326C42×C67C2418yes—
327C23×C67C2511yescharacteristic
328C22×D67—22no—
329C22×D67—22no—
330C22×D67—24no—
331C22×D67—24no—
332C22×D67—24no—
333C22×D67—22no—
334C22×D67C2512yes—
335C22×D67C2514yes—
336Q8×C67—216no—
337Q8×C67—28no—
338Q8×C67—28no—
339C2×C4×C67—24no—
340C2×C4×C67—28no—
341C2×C4×C67—24no—
342C2×C4×C67—24no—
343C2×C4×C67—22no—
344C2×C4×C67—24no—
345C2×C4×C672−1+414yes—
346C2×C4×C672−1+414yes—
347C2×C4×C67C2514yes—
348C2×C4×C67C2514yes—
349C2×C4×C67C2512yes—
350C2×C4×C67C2514yes—
351C2×C4×C67C2514yes—
352C2×C4×C67C2518yes—
353C2×C4×C67C2512yes—
354C2×C4×C67C2512yes—
355C2×Dic67—22no—
356C2×Dic67—22no—
357C2×Dic67—24no—
358C2×Dic67—24no—
359C2×Dic67—28no—
360C2×Dic67—22no—
361C2×Dic67—24no—
362C2×Dic67C2512yes—
363C2×Dic67C2514yes—
364C2×Dic67C2514yes—
365C2×Dic67C2512yes—
366C2×Dic67C2514yes—
367C2×Dic67C2512yes—
368C2×Dic67C2518yes—
369D268—28no—
370D268—48no—
371C4×D67—28no—
372C4×D67—28no—
373C4×D67—216no—
374C4×D67—44no—
375C4×D67—416no—
376Dic134—28no—
377Dic134—416no—
378Dic134—48no—
379Dic134—48no—
380C22×C67C2×2−1+412yes—
381C22×C67C2×2−1+412yes—
382C22×C67#58512yes—
383C22×C67C2611yescharacteristic
384C2×D67—22no—
385C2×D67—22no—
386C2×D67—24no—
387C2×D67—24no—
388C2×D67—24no—
389C2×D67—22no—
390C2×D67—44no—
391C2×D67—48no—
392C4×C67—24no—
393C4×C67—28no—
394C4×C67—24no—
395C4×C67—22no—
396C4×C67—24no—
397C4×C67—24no—
398C4×C67C2×2−1+414yes—
399C4×C67C2×2−1+414yes—
400Dic67—24no—
401Dic67—22no—
402Dic67—22no—
403Dic67—24no—
404Dic67—24no—
405Dic67—28no—
406Dic67—22no—
407C2×#3555—671nomaximal, Sylow
408C2×C67#355514yescomplemented
409C2×C67C22×2−1+411yescharacteristic
410C2×C67C22×2−1+411yescharacteristic
411C2×C67C2×#58511yescharacteristic
412D67—42no—
413D67—44no—
414#3555—6732no—
415C2×#563—674no—
416C2×Q82—671no—
417C2×#557—672no—
418C2×#557D6711yescharacteristic, complemented
419C2×#556—672no—
420C2×#556—671no—
421C2×#556—672no—
422C2×#554—671no—
423C2×#552—672no—
424C2×#544—672no—
425C2×#542—672no—
426C2×#541—672no—
427C2×#541—674no—
428C2×#541—672no—
429C2×#533—671no—
430C2×#533—671no—
431C2×#529—671no—
432C67C2×#355511yescharacteristic, complemented, Sylow
433#563—6764no—
434Q82—6716no—
435#557—6732no—
436#557C2×D67116yescomplemented
437#556—6732no—
438#556—6716no—
439#556—6732no—
440#554—6716no—
441#552—6732no—
442#544—6732no—
443#542—6732no—
444#541—6732no—
445#541—6764no—
446#541—6732no—
447#533—6716no—
448#533—6716no—
449C2×C4⋊Q8—671no—
450C2×C4⋊Q8—671no—
451C2×C4⋊Q8—674no—
452C2×C4⋊Q8—672no—
453C2×C4⋊Q8—674no—
454C2×C4⋊Q8—671no—
455C2×C4⋊Q8—672no—
456C2×C4⋊Q8C2×D6711yescharacteristic
457C2×C4⋊Q8C2×D6712yes—
458#529—6716no—
459C2×#126—672no—
460C2×#126—674no—
461C2×#126—674no—
462C2×#126—674no—
463C2×#126—674no—
464C2×#126—674no—
465C2×#126—674no—
466C2×#125—671no—
467C2×#125—672no—
468C2×#125—672no—
469C2×#125—674no—
470C2×#125—674no—
471C2×#125—674no—
472C2×#125—672no—
473C2×#125—674no—
474C2×#125C2×D6714yes—
475C2×#125C2×D6712yes—
476C2×#124—671no—
477C2×#124—672no—
478C2×#124—674no—
479C2×#123—672no—
480C2×#123—674no—
481C2×C22⋊Q8—671no—
482C2×C22⋊Q8—672no—
483C2×C22⋊Q8—671no—
484C2×C22⋊Q8—672no—
485C2×C22⋊Q8—671no—
486C2×C22⋊Q8—672no—
487C2×C22⋊Q8—672no—
488C2×C22⋊Q8—674no—
489C2×C22⋊Q8—672no—
490C2×C22⋊Q8—674no—
491C2×C22⋊Q8—674no—
492C2×#121—671no—
493C2×C4×Q8—672no—
494C2×C4×Q8—672no—
495C2×C4×Q8—672no—
496C2×C4×Q8—672no—
497C2×C4×Q8—672no—
498C2×C4×Q8—671no—
499C2×C4×Q8—672no—
500C2×C4×Q8—674no—
501C2×C4×Q8C2×D6711yescharacteristic
502C2×C4×Q8C2×D6711yescharacteristic
503C2×C4×Q8C2×D6712yes—
504C2×C4×Q8C2×D6712yes—
505C2×C4×D4—672no—
506C2×C4×D4—671no—
507C2×C4×D4—672no—
508C2×#117—672no—
509C2×#117—674no—
510C2×#117—672no—
511C2×#117—672no—
512C2×#117—672no—
513C22×C4⋊C4—672no—
514C22×C42—671no—
515C22×Q8—672no—
516C22×Q8—672no—
517C22×Q8—674no—
518C22×Q8—671no—
519C22×Q8C22×D6712yes—
520C22×Q8C22×D6711yescharacteristic
521C22×Q8C22×D6711yescharacteristic
522C22×D4—672no—
523C22×D4—671no—
524C23×C4—674no—
525C23×C4—671no—
526C23×C4—672no—
527C23×C4—671no—
528C23×C4—671no—
529C4⋊Q8—678no—
530C4⋊Q8—678no—
531C4⋊Q8—6732no—
532C4⋊Q8—6716no—
533C4⋊Q8—6732no—
534C4⋊Q8—678no—
535C4⋊Q8—6716no—
536C4⋊Q8C22×D6718yes—
537C4⋊Q8C22×D67116yes—
538#126—6716no—
539#126—6732no—
540#126—6732no—
541#126—6732no—
542#126—6732no—
543#126—6732no—
544#126—6732no—
545#125—678no—
546#125—6716no—
547#125—6716no—
548#125—6732no—
549#125—6732no—
550#125—6732no—
551#125—6716no—
552#125—6732no—
553#125C22×D67132yes—
554#125C22×D67116yes—
555#124—678no—
556#124—6716no—
557#124—6732no—
558#123—6716no—
559#123—6732no—
560C22⋊Q8—678no—
561C22⋊Q8—6716no—
562C22⋊Q8—678no—
563C22⋊Q8—6716no—
564C22⋊Q8—678no—
565C22⋊Q8—6716no—
566C22⋊Q8—6716no—
567C22⋊Q8—6732no—
568C22⋊Q8—6716no—
569C22⋊Q8—6732no—
570C22⋊Q8—6732no—
571#121—678no—
572C4×Q8—6716no—
573C4×Q8—6716no—
574C4×Q8—6716no—
575C4×Q8—6716no—
576C4×Q8—6716no—
577C4×Q8—678no—
578C4×Q8—6716no—
579C4×Q8—6732no—
580C4×Q8C22×D6718yes—
581C4×Q8C22×D6718yes—
582C4×Q8C22×D67116yes—
583C4×Q8C22×D67116yes—
584C4×D4—6716no—
585C4×D4—678no—
586C4×D4—6716no—
587#117—6716no—
588#117—6732no—
589#117—6716no—
590#117—6716no—
591#117—6716no—
592C2×C4⋊C4—672no—
593C2×C4⋊C4—674no—
594C2×C4⋊C4—672no—
595C2×C4⋊C4—671no—
596C2×C4⋊C4—672no—
597C2×C4⋊C4—672no—
598C2×C4⋊C4—672no—
599C2×C4⋊C4—672no—
600C2×C4⋊C4—671no—
601C2×C4⋊C4—672no—
602C2×C4⋊C4—672no—
603C2×C4⋊C4—672no—
604C2×C4⋊C4—674no—
605C2×C4⋊C4—674no—
606C2×C4⋊C4—674no—
607C2×C4⋊C4—674no—
608C2×C4⋊C4—672no—
609C2×C4⋊C4—672no—
610C2×C4⋊C4—674no—
611C2×C4⋊C4—674no—
612C2×C4⋊C4—6716no—
613C2×C4⋊C4C22×D6711yescharacteristic
614C2×C4⋊C4C22×D6712yes—
615C2×C4⋊C4C22×D6714yes—
616C2×C4⋊C4C22×D6712yes—
617C2×C4⋊C4C22×D6711yescharacteristic
618C2×C4⋊C4C22×D6712yes—
619C2×C4⋊C4C22×D6714yes—
620C2×C4⋊C4C22×D6712yes—
621C2×C4⋊C4C22×D6714yes—
622C2×C22⋊C4—672no—
623C2×C22⋊C4—672no—
624C2×C22⋊C4—672no—
625C2×C22⋊C4—674no—
626C2×C22⋊C4—672no—
627C2×C22⋊C4—674no—
628C2×C22⋊C4—672no—
629C2×C22⋊C4—674no—
630C2×C22⋊C4—672no—
631C2×C22⋊C4—674no—
632C2×C22⋊C4—672no—
633C2×C42—674no—
634C2×C42—671no—
635C2×C42—672no—
636C2×C42—674no—
637C2×C42—674no—
638C2×C42—671no—
639C2×C42—671no—
640C2×C42—678no—
641C2×C42C22×D6712yes—
642C2×C42C22×D6712yes—
643C2×C42C22×D6711yescharacteristic
644C2×C42C22×D6714yes—
645C24—671no—
646C24—672no—
647C2×Q8—28no—
648C2×Q8—24no—
649C2×Q8—24no—
650C2×Q8—2684no—
651C2×Q8—2684no—
652C2×Q8—2688no—
653C2×Q8—678no—
654C2×Q8—678no—
655C2×Q8—6716no—
656C2×Q8—674no—
657C2×Q8—1344no—
658C2×Q8C23×D6718yes—
659C2×Q8C23×D6714yes—
660C2×Q8C23×D6714yes—
661C2×D4—2684no—
662C2×D4—678no—
663C2×D4—674no—
664C2×D4—1344no—
665C22×C4—2688no—
666C22×C4—2682no—
667C22×C4—674no—
668C22×C4—6716no—
669C22×C4—671no—
670C22×C4—672no—
671C22×C4—672no—
672C22×C4—671no—
673C22×C4—672no—
674C22×C4—674no—
675C22×C4—671no—
676C22×C4—674no—
677C22×C4—674no—
678C22×C4—678no—
679C22×C4—1344no—
680C22×C4—1348no—
681C22×C4—1344no—
682C22×C4C23×D6714yes—
683C22×C4C23×D6712yes—
684C22×C4C23×D6711yescharacteristic
685C22×C4C23×D6712yes—
686C22×C4C23×D6712yes—
687C22×C4C23×D6712yes—
688C22×C4C23×D6711yescharacteristic
689C22×C4C23×D6711yescharacteristic
690C4⋊C4—678no—
691C4⋊C4—6716no—
692C4⋊C4—678no—
693C4⋊C4—674no—
694C4⋊C4—678no—
695C4⋊C4—678no—
696C4⋊C4—678no—
697C4⋊C4—678no—
698C4⋊C4—674no—
699C4⋊C4—678no—
700C4⋊C4—678no—
701C4⋊C4—678no—
702C4⋊C4—6716no—
703C4⋊C4—6716no—
704C4⋊C4—6716no—
705C4⋊C4—6716no—
706C4⋊C4—678no—
707C4⋊C4—678no—
708C4⋊C4—6716no—
709C4⋊C4—6716no—
710C4⋊C4C23×D6714yes—
711C4⋊C4C23×D6718yes—
712C4⋊C4C23×D67116yes—
713C4⋊C4C23×D6718yes—
714C4⋊C4C23×D6714yes—
715C4⋊C4C23×D6718yes—
716C4⋊C4C23×D67116yes—
717C4⋊C4C23×D6718yes—
718C4⋊C4C23×D67116yes—
719C22⋊C4—678no—
720C22⋊C4—678no—
721C22⋊C4—678no—
722C22⋊C4—6716no—
723C22⋊C4—678no—
724C22⋊C4—6716no—
725C22⋊C4—678no—
726C22⋊C4—6716no—
727C22⋊C4—678no—
728C22⋊C4—6716no—
729C22⋊C4—678no—
730C42—674no—
731C42—674no—
732C42—674no—
733C42—6716no—
734C42—678no—
735C42—6716no—
736C42—6716no—
737C42C23×D6714yes—
738C42C23×D6718yes—
739C42C23×D6718yes—
740C42C23×D67116yes—
741C23—672no—
742C23—674no—
743C23—1342no—
744C23—1344no—
745C23—1342no—
746C23—1344no—
747C23—1344no—
748C23—1342no—
749C23C24×D6711yescharacteristic
750Q8—216no—
751Q8—28no—
752Q8—28no—
753Q8—2688no—
754Q8—2688no—
755Q8—26816no—
756Q8—1348no—
757D4—2688no—
758D4—1348no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—26816no—
766C2×C4—2684no—
767C2×C4—672no—
768C2×C4—674no—
769C2×C4—674no—
770C2×C4—672no—
771C2×C4—674no—
772C2×C4—672no—
773C2×C4—678no—
774C2×C4—1342no—
775C2×C4—1342no—
776C2×C4—1344no—
777C2×C4—1344no—
778C2×C4—1348no—
779C2×C4—1342no—
780C2×C4—1344no—
781C2×C4—1348no—
782C2×C4—1348no—
783C2×C4—13416no—
784C2×C4#1452409014yes—
785C2×C4#1452409114yes—
786C2×C4C24×D6718yes—
787C2×C4C24×D6714yes—
788C2×C4C24×D6712yes—
789C2×C4C24×D6714yes—
790C2×C4C24×D6714yes—
791C2×C4C24×D6714yes—
792C2×C4C24×D6712yes—
793C2×C4C24×D6712yes—
794C22—2684no—
795C22—2688no—
796C22—1342no—
797C22—1344no—
798C22—1342no—
799C22—1344no—
800C22—1344no—
801C22—1342no—
802C22C2×#1452409012yes—
803C22C2×#1452409112yes—
804C22#1686423312yes—
805C22C25×D6711yescharacteristic
806C4—28no—
807C4—24no—
808C4—24no—
809C4—24no—
810C4—22no—
811C4—24no—
812C4—1342no—
813C4—1342no—
814C4—1344no—
815C4—1344no—
816C4—1348no—
817C4—1342no—
818C4—1344no—
819C4C2×#1452409014yes—
820C4C2×#1452409114yes—
821C2—2682no—
822C2—2684no—
823C2#2257469314yesdirect product factor
824C2C22×#1452409011yescharacteristic
825C2C22×#1452409111yescharacteristic
826C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#557×C67C2
socleC23×C67C25
prime radicalC2×#14524018C22
hypercenterC2×#557D67
hypocenterC67C2×#3555
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22574693C2direct (N × H)
2. C2×#16864150C2semidirect
3. C2×Q8×Dic134C2semidirect
4. C2×#16864122C2semidirect
5. C2×#16864120C2semidirect
6. C2×#16864120C2semidirect
7. C2×#16864119C2semidirect
8. C2×#16864106C2semidirect
9. C2×#16864084C2semidirect
10. C2×#16864026C2semidirect
12. C2×#16864007C2semidirect
13. C2×#16864005C2semidirect
14. C2×#16864004C2semidirect
15. C2×#16863951C2semidirect
16. C2×#16863950C2semidirect
18. C2×#557×C67C2semidirect
19. #16864150C22semidirect
20. Q8×Dic134C22semidirect
21. #16864122C22semidirect
22. #16864120C22semidirect
23. #16864120C22semidirect
24. #16864119C22semidirect
25. #16864106C22semidirect
26. #16864084C22semidirect
27. #16864026C22semidirect
29. #16864007C22semidirect
30. #16864005C22semidirect
31. #16864004C22semidirect
32. #16863951C22semidirect
33. #16863950C22semidirect
92. #557×C67C22semidirect
408. C2×C67#3555semidirect
418. C2×#557D67semidirect
432. C67C2×#3555semidirect
436. #557C2×D67semidirect
823. C2#22574693direct (N × H)

Maximal subgroups

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

subgroupindex
#225746932
C2×#168641502
C2×Q8×Dic1342
C2×#168641222
C2×#168641202
C2×#168641192
C2×#168641062
C2×#168640842
C2×#168640262
C2×#168640182
C2×#168640072
C2×#168640052
C2×#168640042
C2×#168639512
C2×#168639502
C2×#168639332
C2×#557×C672
C2×#355567