Finite Group Databasebeta

← C2×#22574032 #31764311

Subgroups — C2×#22574032 #31764311

Order 17152.

6958 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574032C2132yesmaximal, direct product factor
2C2×#16864123C212yesmaximal, complemented
3C2×#16864121C212yesmaximal, complemented
4C2×#16864107C212yesmaximal, complemented
5C2×#16864104C214yesmaximal, complemented
6C2×#16864102C212yesmaximal, complemented
7C2×#16864100C214yesmaximal, complemented
8C2×#16864026C212yesmaximal, complemented
9C2×#16864024C211yesmaximal, characteristic, complemented
10C2×#16864023C212yesmaximal, complemented
11C2×#16863951C212yesmaximal, complemented
12C2×#16863949C211yesmaximal, characteristic, complemented
13C22×#14524034C211yesmaximal, characteristic, complemented
14C2×#125×D67C212yesmaximal, complemented
15C2×#16863877C211yesmaximal, characteristic
16C2×#16863876C211yesmaximal, characteristic
17C2×#16863864C211yesmaximal, characteristic
18C2×#544×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2211yescharacteristic
20#16864123C22132yescomplemented
21#16864121C22132yescomplemented
22#16864107C22132yescomplemented
23#16864104C22164yescomplemented
24#16864102C22132yescomplemented
25#16864100C22164yescomplemented
26#16864026C22132yescomplemented
27#16864024C22116yescomplemented
28#16864023C22132yescomplemented
29#16863951C22132yescomplemented
30#16863949C22116yescomplemented
31C2×#14524043C2212yes—
32C2×#14524042C2211yescharacteristic
33C2×#14524042C2212yes—
34C2×#14524042C2211yescharacteristic
35C2×#14524042C2214yes—
36C2×#14524041C2214yes—
37C2×#14524035C2212yes—
38C2×#14524034C2212yes—
39C2×#14524034C2212yes—
40C2×#14524034C2211yescharacteristic
41C2×#14524034C2212yes—
42C2×#14524034C2212yes—
43C2×#14524034C2212yes—
44C2×#14524034C2211yescharacteristic
45C2×#14524034C22116yescomplemented
46C2×#14524033C2214yes—
47C2×#14524033C2214yes—
48C2×#14524033C2214yes—
49C2×#14524033C2214yes—
50#125×D67C22132yescomplemented
51C2×#14524023C2214yes—
52C2×#14524023C2214yes—
53C2×#14524021C2214yes—
54C2×#14524021C2214yes—
55C2×#14524020C2214yes—
56C2×#14524020C2212yes—
57C2×#14524020C2212yes—
58C2×#14524019C2214yes—
59C2×#14524019C2214yes—
60#16863877C22116yes—
61#16863876C22116yes—
62#16863864C22116yes—
63C2×Q8×Dic67C2214yes—
64C2×C4×Dic134C2212yes—
65C2×C4×Dic134C2212yes—
66C2×C4×Dic134C2212yes—
67C2×#14524008C2211yescharacteristic
68C2×#14524008C2211yescharacteristic
69C2×#14524008C2212yes—
70C2×#14524008C2214yes—
71C2×C4×D268C2212yes—
72C2×#14524005C2211yescharacteristic
73C2×#14524005C2211yescharacteristic
74C2×#14524005C2212yes—
75C2×C4×C22⋊D67C2214yes—
76C2×(C22⋊D67)⋊C4C2212yes—
77C2×(C22⋊D67)⋊C4C2212yes—
78C2×(C22⋊D67)⋊C4C2214yes—
79C2×#14524002C2211yescharacteristic
80C2×#14524001C2212yes—
81C2×#14524001C2212yes—
82C2×#14524000C2212yes—
83C22×C4⋊Dic67C2211yescharacteristic
84C22×C4⋊Dic67C2212yes—
85C22×Dic67⋊C4C2212yes—
86C2×C4⋊C4×D67C2212yes—
87C2×C4⋊C4×D67C2212yes—
88C2×C4⋊C4×D67C2214yes—
89C2×C4⋊C4×D67C2214yes—
90C22×C4×Dic67C2211yescharacteristic
91C2×C42×D67C2212yes—
92#544×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2212yes—
94C2×C4⋊Q8×C67C2212yes—
95C2×#125×C67C2212yes—
96C2×#125×C67C2212yes—
97C2×C22⋊Q8×C67C2214yes—
98C2×#117×C67C2211yescharacteristic
99C2×#117×C67C2211yescharacteristic
100C22×C4⋊C4×C67C2211yescharacteristic
101C2×#11761628Q8116yescomplemented
102C2×#11761628C2318yes—
103C22×Dic134C2314yes—
104C22×Dic134C2312yes—
105C22×Dic134C2312yes—
106C22×Dic134C2311yescharacteristic
107C22×D268C2311yescharacteristic
108C22×C22⋊D67C2312yes—
109C23×Dic67C2311yescharacteristic
110C23×Dic67C2311yescharacteristic
111C23×Dic67C2312yes—
112C22×C4×D67C2312yes—
113C22×C4×D67C2312yes—
114C22×C4×D67C2314yes—
115C22×C4×D67C2314yes—
116C22×C4×D67C2312yes—
117#14524043C23116yes—
118#14524042C2318yes—
119#14524042C23116yes—
120#14524042C2318yes—
121#14524042C23132yes—
122#14524041C23132yes—
123#14524035C23116yes—
124#14524034C23116yes—
125#14524034C23116yes—
126#14524034C23116yes—
127#14524034C23116yes—
128#14524034C2318yes—
129#14524034C23116yes—
130#14524034C2318yes—
131#14524033C23132yes—
132#14524033C23132yes—
133#14524033C23132yes—
134#14524033C23132yes—
135#14524023C23132yes—
136#14524023C23132yes—
137#14524021C23132yes—
138#14524021C23132yes—
139#14524020C23132yes—
140#14524020C23116yes—
141#14524020C23116yes—
142#14524019C23132yes—
143#14524019C23132yes—
144Q8×Dic67C23132yes—
145C4×Dic134C23116yes—
146C4×Dic134C23116yes—
147C4×Dic134C23116yes—
148#14524008C23132yes—
149#14524008C2318yes—
150#14524008C2318yes—
151#14524008C23116yes—
152C4×D268C23116yes—
153#14524005C2318yes—
154#14524005C23116yes—
155#14524005C2318yes—
156C4×C22⋊D67C23132yes—
157(C22⋊D67)⋊C4C23116yes—
158(C22⋊D67)⋊C4C23132yes—
159(C22⋊D67)⋊C4C23116yes—
160#14524002C2318yes—
161#14524001C23116yes—
162#14524001C23116yes—
163#14524000C23116yes—
164C2×C4⋊Dic67C2318yes—
165C2×C4⋊Dic67C2311yescharacteristic
166C2×C4⋊Dic67C2312yes—
167C2×C4⋊Dic67C2312yes—
168C2×C4⋊Dic67C2314yes—
169C2×C4⋊Dic67C23116yes—
170C2×C4⋊Dic67C2312yes—
171C2×C4⋊Dic67C2314yes—
172C2×C4⋊Dic67C2311yescharacteristic
173C2×C4⋊Dic67C2312yes—
174C2×C4⋊Dic67C2314yes—
175C2×Dic67⋊C4C23116yes—
176C2×Dic67⋊C4C2312yes—
177C2×Dic67⋊C4C2314yes—
178C2×Dic67⋊C4C2314yes—
179C2×Dic67⋊C4C2314yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2312yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2312yes—
188C4⋊C4×D67C23116yes—
189C4⋊C4×D67C23116yes—
190C4⋊C4×D67C23132yes—
191C4⋊C4×D67C23132yes—
192C2×C22⋊Dic67C2312yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×C4×Dic67C2311yescharacteristic
198C2×C4×Dic67C2312yes—
199C2×C4×Dic67C2312yes—
200C2×C4×Dic67C2311yescharacteristic
201C2×C4×Dic67C2311yescharacteristic
202C2×C4×Dic67C2311yescharacteristic
203C2×C4×Dic67C2318yes—
204C2×C4×Dic67C2314yes—
205C2×C4×Dic67C2314yes—
206C2×C4×Dic67C2312yes—
207C42×D67C23116yes—
208C22×Q8×C67C2314yes—
209C23×C4×C67C2312yes—
210C23×C4×C67C2311yescharacteristic
211C4⋊Q8×C67C23116yes—
212C4⋊Q8×C67C23116yes—
213#125×C67C23116yes—
214#125×C67C23116yes—
215C22⋊Q8×C67C23132yes—
216#117×C67C2318yes—
217#117×C67C2318yes—
218C2×C4⋊C4×C67C2312yes—
219C2×C4⋊C4×C67C2312yes—
220C2×C4⋊C4×C67C2318yes—
221C2×C4⋊C4×C67C2311yescharacteristic
222C2×C4⋊C4×C67C2311yescharacteristic
223C2×C4⋊C4×C67C2311yescharacteristic
224C2×C4⋊C4×C67C2311yescharacteristic
225C2×C4⋊C4×C67C2314yes—
226C2×C4⋊C4×C67C2314yes—
227C2×C4⋊C4×C67C2314yes—
228C2×C22⋊C4×C67C2312yes—
229C2×C22⋊C4×C67C2312yes—
230C2×C42×C67C2312yes—
231C2×C42×C67C2312yes—
232C23×D67C2412yes—
233#11761628C2×Q8164yescomplemented
234C2×Dic134—44no—
235C2×Dic134—48no—
236C2×Dic134—44no—
237C2×Dic134C2×Q818yes—
238C2×Dic134C24116yes—
239C2×Dic134C2418yes—
240C2×Dic134C2418yes—
241C2×Dic134C2414yes—
242C2×D268C2×Q818yes—
243C2×D268C2414yes—
244C2×C22⋊D67C2×Q8116yes—
245C2×C22⋊D67C2418yes—
246C22×Dic67—42no—
247C22×Dic67—42no—
248C22×Dic67—44no—
249C22×Dic67C2411yescharacteristic
250C22×Dic67C2411yescharacteristic
251C22×Dic67C2412yes—
252C22×Dic67C2411yescharacteristic
253C22×Dic67C2411yescharacteristic
254C22×Dic67C2414yes—
255C22×Dic67C2412yes—
256C22×Dic67C2414yes—
257C22×Dic67C2414yes—
258C22×Dic67C2418yes—
259C22×Dic67C2412yes—
260C2×C4×D67—44no—
261C2×C4×D67—44no—
262C2×C4×D67—48no—
263C2×C4×D67—48no—
264C2×C4×D67C2×Q8116yes—
265C2×C4×D67C2418yes—
266C2×C4×D67C2418yes—
267C2×C4×D67C24116yes—
268C2×C4×D67C24116yes—
269C2×C4×D67C2418yes—
270C4⋊Dic67C2414yes—
271C4⋊Dic67C2418yes—
272C4⋊Dic67C2418yes—
273C4⋊Dic67C24116yes—
274C4⋊Dic67C2418yes—
275C4⋊Dic67C24116yes—
276C4⋊Dic67C2414yes—
277C4⋊Dic67C2418yes—
278C4⋊Dic67C24116yes—
279Dic67⋊C4C2418yes—
280Dic67⋊C4C24116yes—
281Dic67⋊C4C24116yes—
282Dic67⋊C4C24116yes—
283Dic67⋊C4C24116yes—
284Dic67⋊C4C24116yes—
285Dic67⋊C4C24116yes—
286Dic67⋊C4C2418yes—
287Dic67⋊C4C2418yes—
288Dic67⋊C4C2418yes—
289Dic67⋊C4C2418yes—
290Dic67⋊C4C2418yes—
291C22⋊Dic67C2418yes—
292(C2×D67)⋊C4C2418yes—
293(C2×D67)⋊C4C2418yes—
294(C2×D67)⋊C4C24116yes—
295(C2×D67)⋊C4C24116yes—
296C4×Dic67C2414yes—
297C4×Dic67C2418yes—
298C4×Dic67C2418yes—
299C4×Dic67C2414yes—
300C4×Dic67C2414yes—
301C4×Dic67C2414yes—
302C4×Dic67C24116yes—
303C4×Dic67C24116yes—
304C4×Dic67C2418yes—
305C24×C67C2411yescharacteristic
306C2×Q8×C67—48no—
307C2×Q8×C67C24116yes—
308C22×C4×C67—44no—
309C22×C4×C67C2×Q818yes—
310C22×C4×C67C2412yes—
311C22×C4×C67C2412yes—
312C22×C4×C67C2412yes—
313C22×C4×C67C2412yes—
314C22×C4×C67C2414yes—
315C22×C4×C67C2418yes—
316C22×C4×C67C2411yescharacteristic
317C22×C4×C67C2411yescharacteristic
318C22×C4×C67C2414yes—
319C4⋊C4×C67C2418yes—
320C4⋊C4×C67C2418yes—
321C4⋊C4×C67C2414yes—
322C4⋊C4×C67C2414yes—
323C4⋊C4×C67C2414yes—
324C4⋊C4×C67C2414yes—
325C4⋊C4×C67C24116yes—
326C4⋊C4×C67C24116yes—
327C4⋊C4×C67C24116yes—
328C22⋊C4×C67C2418yes—
329C22⋊C4×C67C2418yes—
330C42×C67C2418yes—
331C42×C67C2418yes—
332C23×C67—22no—
333C23×C67—22no—
334C23×C67C22×Q814yes—
335C23×C67C2512yes—
336C23×C67C2511yescharacteristic
337C22×D67—24no—
338C22×D67—24no—
339C22×D67C22×Q818yes—
340C22×D67C2514yes—
341Q8×C67—416no—
342C2×C4×C67—28no—
343C2×C4×C67—24no—
344C2×C4×C67—24no—
345C2×C4×C67—24no—
346C2×C4×C67—24no—
347C2×C4×C67—48no—
348C2×C4×C67C22×Q814yes—
349C2×C4×C67C22×Q814yes—
350C2×C4×C67C22×Q8116yes—
351C2×C4×C67C2514yes—
352C2×C4×C67C2514yes—
353C2×C4×C67C2514yes—
354C2×C4×C67C2514yes—
355C2×C4×C67C2518yes—
356C2×C4×C67C2512yes—
357C2×C4×C67C2512yes—
358C22⋊D67C22×Q8132yes—
359C2×Dic67—22no—
360C2×Dic67—22no—
361C2×Dic67—24no—
362C2×Dic67—28no—
363C2×Dic67—22no—
364C2×Dic67—22no—
365C2×Dic67—24no—
366C2×Dic67—44no—
367C2×Dic67—44no—
368C2×Dic67—48no—
369C2×Dic67C22×Q818yes—
370C2×Dic67C2512yes—
371C2×Dic67C2512yes—
372C2×Dic67C2514yes—
373C2×Dic67C2512yes—
374C2×Dic67C2512yes—
375C2×Dic67C2518yes—
376C2×Dic67C2514yes—
377C2×Dic67C2514yes—
378D268C22×Q8116yes—
379C4×D67—416no—
380C4×D67—416no—
381C4×D67—48no—
382C4×D67—48no—
383C4×D67C22×Q8132yes—
384Dic134—48no—
385Dic134—416no—
386Dic134—48no—
387Dic134C22×Q8116yes—
388C22×C67—22no—
389C22×C67—22no—
390C22×C67—28no—
391C22×C67C23×Q814yes—
392C22×C67C23×Q812yes—
393C22×C67#58512yes—
394C22×C67#58512yes—
395C22×C67C2611yescharacteristic
396C2×D67—24no—
397C2×D67—24no—
398C2×D67—216no—
399C2×D67C23×Q818yes—
400C4×C67—24no—
401C4×C67—24no—
402C4×C67—24no—
403C4×C67—28no—
404C4×C67—24no—
405C4×C67C23×Q814yes—
406C4×C67C23×Q814yes—
407Dic67—24no—
408Dic67—22no—
409Dic67—22no—
410Dic67—24no—
411Dic67—28no—
412Dic67—22no—
413Dic67—22no—
414Dic67C23×Q818yes—
415C2×#3504—671nomaximal, Sylow
416C2×C67—24no—
417C2×C67#350414yescomplemented
418C2×C67C24×Q811yescharacteristic
419C2×C67C2×#58511yescharacteristic
420C2×C67C2×#58511yescharacteristic
421D67—28no—
422#3504—6732no—
423C2×#557—672no—
424C2×#557—672no—
425C2×#554—672no—
426C2×#554—672no—
427C2×#554—674no—
428C2×#554—674no—
429C2×#544—672no—
430C2×#544—672no—
431C2×#544—671no—
432C2×#544D6711yescharacteristic, complemented
433C2×#533—672no—
434C2×#533—671no—
435C22×#125—672no—
436C22×#125—671no—
437C2×#520—671no—
438C2×#520—671no—
439C2×C4×#41—671no—
440C67C2×#350411yescharacteristic, complemented, Sylow
441C22×#41—671no—
442#557—6732no—
443#557—6732no—
444#554—6732no—
445#554—6732no—
446#554—6764no—
447#554—6764no—
448#544—6732no—
449#544—6732no—
450#544—6716no—
451#544C2×D67116yescomplemented
452#533—6732no—
453#533—6716no—
454C2×C4⋊Q8—674no—
455C2×C4⋊Q8—671no—
456C2×C4⋊Q8—671no—
457C2×C4⋊Q8—674no—
458C2×C4⋊Q8—672no—
459C2×C4⋊Q8—672no—
460C2×C4⋊Q8C2×D6712yes—
461C2×C4⋊Q8C2×D6712yes—
462C2×#125—6732no—
463C2×#125—671no—
464C2×#125—672no—
465C2×#125—672no—
466C2×#125—674no—
467C2×#125—674no—
468C2×#125—672no—
469C2×#125—672no—
470C2×#125—6716no—
471C2×#125—671no—
472C2×#125—674no—
473C2×#125—674no—
474C2×#125—672no—
475C2×#125—672no—
476C2×#125C2×D6712yes—
477C2×#125C2×D6712yes—
478C2×C22⋊Q8—674no—
479C2×C22⋊Q8—674no—
480C2×C22⋊Q8—674no—
481C2×C22⋊Q8—674no—
482C2×C22⋊Q8—674no—
483C2×C22⋊Q8—674no—
484C2×C22⋊Q8—672no—
485C2×C22⋊Q8—672no—
486C2×C22⋊Q8—674no—
487C2×C22⋊Q8C2×D6714yes—
488#520—6716no—
489#520—6716no—
490C4×#41—6716no—
491C2×C4×Q8—674no—
492C2×C4×Q8—671no—
493C2×C4×Q8—671no—
494C2×C4×Q8—672no—
495C2×C4×Q8—674no—
496C2×C4×Q8—672no—
497C2×C4×Q8—672no—
498C2×C4×Q8—672no—
499C2×C4×D4—674no—
500C2×C4×D4—671no—
501C2×C4×D4—671no—
502C2×C4×D4—672no—
503C2×C4×D4—672no—
504C2×C4×D4—672no—
505C2×C4×D4—674no—
506C2×C4×D4—672no—
507C2×#117—671no—
508C2×#117—672no—
509C2×#117—672no—
510C2×#117—672no—
511C2×#117C2×D6711yescharacteristic
512C2×#117C2×D6711yescharacteristic
513C22×C4⋊C4—671no—
514C22×C4⋊C4—672no—
515C22×C4⋊C4—672no—
516C22×C4⋊C4—672no—
517C22×C4⋊C4—672no—
518C22×C4⋊C4—674no—
519C22×C4⋊C4—674no—
520C22×C4⋊C4C2×D6711yescharacteristic
521C22×C42—671no—
522C22×C42—672no—
523C2×#41—6716no—
524C2×#41—678no—
525C22×Q8—672no—
526C22×Q8—674no—
527C22×Q8—672no—
528C22×Q8—671no—
529C22×Q8C22×D6714yes—
530C22×D4—672no—
531C22×D4—671no—
532C23×C4—672no—
533C23×C4—671no—
534C23×C4—671no—
535C23×C4—674no—
536C23×C4—674no—
537C23×C4—672no—
538C23×C4—672no—
539C23×C4—672no—
540C23×C4C22×D6712yes—
541C23×C4C22×D6711yescharacteristic
542C4⋊Q8—6732no—
543C4⋊Q8—678no—
544C4⋊Q8—678no—
545C4⋊Q8—6732no—
546C4⋊Q8—6716no—
547C4⋊Q8—6716no—
548C4⋊Q8C22×D67116yes—
549C4⋊Q8C22×D67116yes—
550#125—678no—
551#125—6716no—
552#125—6716no—
553#125—6732no—
554#125—6732no—
555#125—6716no—
556#125—6716no—
557#125—678no—
558#125—6732no—
559#125—6732no—
560#125—6716no—
561#125—6716no—
562#125C22×D67116yes—
563#125C22×D67116yes—
564C22⋊Q8—6732no—
565C22⋊Q8—6732no—
566C22⋊Q8—6732no—
567C22⋊Q8—6732no—
568C22⋊Q8—6732no—
569C22⋊Q8—6732no—
570C22⋊Q8—6716no—
571C22⋊Q8—6716no—
572C22⋊Q8—6732no—
573C22⋊Q8C22×D67132yes—
574C4×Q8—6732no—
575C4×Q8—678no—
576C4×Q8—678no—
577C4×Q8—6716no—
578C4×Q8—6732no—
579C4×Q8—6716no—
580C4×Q8—6716no—
581C4×Q8—6716no—
582C4×D4—6732no—
583C4×D4—678no—
584C4×D4—678no—
585C4×D4—6716no—
586C4×D4—6716no—
587C4×D4—6716no—
588C4×D4—6732no—
589C4×D4—6716no—
590#117—678no—
591#117—6716no—
592#117—6716no—
593#117—6716no—
594#117C22×D6718yes—
595#117C22×D6718yes—
596C2×C4⋊C4—672no—
597C2×C4⋊C4—671no—
598C2×C4⋊C4—674no—
599C2×C4⋊C4—672no—
600C2×C4⋊C4—674no—
601C2×C4⋊C4—672no—
602C2×C4⋊C4—674no—
603C2×C4⋊C4—674no—
604C2×C4⋊C4—672no—
605C2×C4⋊C4—678no—
606C2×C4⋊C4—674no—
607C2×C4⋊C4—674no—
608C2×C4⋊C4—674no—
609C2×C4⋊C4—674no—
610C2×C4⋊C4—6716no—
611C2×C4⋊C4—6716no—
612C2×C4⋊C4—671no—
613C2×C4⋊C4—672no—
614C2×C4⋊C4—672no—
615C2×C4⋊C4—672no—
616C2×C4⋊C4—672no—
617C2×C4⋊C4—672no—
618C2×C4⋊C4—672no—
619C2×C4⋊C4—674no—
620C2×C4⋊C4—6716no—
621C2×C4⋊C4—6716no—
622C2×C4⋊C4—6732no—
623C2×C4⋊C4—6732no—
624C2×C4⋊C4C22×D6711yescharacteristic
625C2×C4⋊C4C22×D6712yes—
626C2×C4⋊C4C22×D6714yes—
627C2×C4⋊C4C22×D6714yes—
628C2×C4⋊C4C22×D6712yes—
629C2×C4⋊C4C22×D6718yes—
630C2×C4⋊C4C22×D6711yescharacteristic
631C2×C4⋊C4C22×D6711yescharacteristic
632C2×C4⋊C4C22×D6711yescharacteristic
633C2×C4⋊C4C22×D6714yes—
634C2×C22⋊C4—672no—
635C2×C22⋊C4—674no—
636C2×C22⋊C4—672no—
637C2×C22⋊C4—672no—
638C2×C22⋊C4—674no—
639C2×C22⋊C4C22×D6712yes—
640C2×C22⋊C4C22×D6712yes—
641C2×C42—671no—
642C2×C42—674no—
643C2×C42—674no—
644C2×C42—672no—
645C2×C42—672no—
646C2×C42—672no—
647C2×C42—671no—
648C2×C42—671no—
649C2×C42—678no—
650C2×C42—671no—
651C2×C42—6716no—
652C2×C42C22×D6712yes—
653C2×C42C22×D6712yes—
654C24—672no—
655C24C23×D6711yescharacteristic
656#41—6764no—
657C2×Q8—48no—
658C2×Q8—2684no—
659C2×Q8—2684no—
660C2×Q8—2688no—
661C2×Q8—678no—
662C2×Q8—678no—
663C2×Q8—6716no—
664C2×Q8—678no—
665C2×Q8—674no—
666C2×Q8C23×D67116yes—
667C2×D4—6716no—
668C2×D4—678no—
669C2×D4—678no—
670C2×D4—674no—
671C22×C4—44no—
672C22×C4—2688no—
673C22×C4—2684no—
674C22×C4—2688no—
675C22×C4—2684no—
676C22×C4—2682no—
677C22×C4—2682no—
678C22×C4—2684no—
679C22×C4—674no—
680C22×C4—674no—
681C22×C4—678no—
682C22×C4—678no—
683C22×C4—678no—
684C22×C4—6716no—
685C22×C4—6716no—
686C22×C4—672no—
687C22×C4—6716no—
688C22×C4—678no—
689C22×C4—671no—
690C22×C4—671no—
691C22×C4—672no—
692C22×C4—671no—
693C22×C4—671no—
694C22×C4—672no—
695C22×C4—674no—
696C22×C4Q8×D6718yes—
697C22×C4C23×D6712yes—
698C22×C4C23×D6712yes—
699C22×C4C23×D6712yes—
700C22×C4C23×D6714yes—
701C22×C4C23×D6712yes—
702C22×C4C23×D6718yes—
703C22×C4C23×D6714yes—
704C22×C4C23×D6711yescharacteristic
705C22×C4C23×D6711yescharacteristic
706C4⋊C4—678no—
707C4⋊C4—674no—
708C4⋊C4—6716no—
709C4⋊C4—678no—
710C4⋊C4—6716no—
711C4⋊C4—678no—
712C4⋊C4—6716no—
713C4⋊C4—6716no—
714C4⋊C4—678no—
715C4⋊C4—6716no—
716C4⋊C4—6716no—
717C4⋊C4—6716no—
718C4⋊C4—6716no—
719C4⋊C4—674no—
720C4⋊C4—678no—
721C4⋊C4—678no—
722C4⋊C4—678no—
723C4⋊C4—678no—
724C4⋊C4—678no—
725C4⋊C4—678no—
726C4⋊C4—6716no—
727C4⋊C4C23×D6714yes—
728C4⋊C4C23×D6718yes—
729C4⋊C4C23×D67116yes—
730C4⋊C4C23×D67116yes—
731C4⋊C4C23×D6718yes—
732C4⋊C4C23×D6714yes—
733C4⋊C4C23×D6714yes—
734C4⋊C4C23×D6714yes—
735C4⋊C4C23×D67116yes—
736C22⋊C4—678no—
737C22⋊C4—6716no—
738C22⋊C4—678no—
739C22⋊C4—678no—
740C22⋊C4—6716no—
741C22⋊C4C23×D6718yes—
742C22⋊C4C23×D6718yes—
743C42—674no—
744C42—674no—
745C42—678no—
746C42—678no—
747C42—674no—
748C42—674no—
749C42—6716no—
750C42—6716no—
751C42—678no—
752C42C23×D6718yes—
753C42C23×D6718yes—
754C23—22no—
755C23—22no—
756C23—678no—
757C23—674no—
758C23—1344no—
759C23—1344no—
760C23C2×Q8×D6714yes—
761C23C24×D6712yes—
762C23C24×D6711yescharacteristic
763Q8—416no—
764Q8—2688no—
765Q8—2688no—
766Q8—26816no—
767Q8—6716no—
768D4—6732no—
769D4—6716no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—48no—
776C2×C4—26816no—
777C2×C4—2688no—
778C2×C4—26816no—
779C2×C4—2688no—
780C2×C4—2684no—
781C2×C4—2684no—
782C2×C4—2688no—
783C2×C4—678no—
784C2×C4—674no—
785C2×C4—6732no—
786C2×C4—672no—
787C2×C4—672no—
788C2×C4—674no—
789C2×C4—672no—
790C2×C4—672no—
791C2×C4—674no—
792C2×C4—678no—
793C2×C4—1342no—
794C2×C4—1344no—
795C2×C4—1342no—
796C2×C4—1342no—
797C2×C4—1348no—
798C2×C4—1342no—
799C2×C4—1344no—
800C2×C4C2×Q8×D6714yes—
801C2×C4C2×Q8×D6714yes—
802C2×C4C2×Q8×D67116yes—
803C2×C4C24×D6714yes—
804C2×C4C24×D6714yes—
805C2×C4C24×D6714yes—
806C2×C4C24×D6718yes—
807C2×C4C24×D6714yes—
808C2×C4C24×D6712yes—
809C2×C4C24×D6712yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—678no—
814C22—1344no—
815C22—1344no—
816C22—13416no—
817C22C22×Q8×D6714yes—
818C22C22×Q8×D6712yes—
819C22#1686423112yes—
820C22#1686423312yes—
821C22C25×D6711yescharacteristic
822C4—28no—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—678no—
828C4—1342no—
829C4—1344no—
830C4—1342no—
831C4—1342no—
832C4—1348no—
833C4—1342no—
834C4—1344no—
835C4C22×Q8×D6714yes—
836C4C22×Q8×D6714yes—
837C2—24no—
838C2—1348no—
839C2#2257403214yesdirect product factor
840C2C23×Q8×D6711yescharacteristic
841C2C2×#1686423111yescharacteristic
842C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#544×C67C2
socleC23×C67C25
prime radicalC22×#11761628C22
hypercenterC2×#544D67
hypocenterC67C2×#3504
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #22574032C2direct (N × H)
2. C2×#16864123C2semidirect
3. C2×#16864121C2semidirect
4. C2×#16864107C2semidirect
5. C2×#16864104C2semidirect
6. C2×#16864102C2semidirect
7. C2×#16864100C2semidirect
8. C2×#16864026C2semidirect
9. C2×#16864024C2semidirect
10. C2×#16864023C2semidirect
11. C2×#16863951C2semidirect
12. C2×#16863949C2semidirect
13. C22×#14524034C2semidirect
14. C2×#125×D67C2semidirect
18. C2×#544×C67C2semidirect
20. #16864123C22semidirect
21. #16864121C22semidirect
22. #16864107C22semidirect
23. #16864104C22semidirect
24. #16864102C22semidirect
25. #16864100C22semidirect
26. #16864026C22semidirect
27. #16864024C22semidirect
28. #16864023C22semidirect
29. #16863951C22semidirect
30. #16863949C22semidirect
45. C2×#14524034C22semidirect
50. #125×D67C22semidirect
92. #544×C67C22semidirect
101. C2×#11761628Q8semidirect
233. #11761628C2×Q8semidirect
417. C2×C67#3504semidirect
432. C2×#544D67semidirect
440. C67C2×#3504semidirect
451. #544C2×D67semidirect
839. C2#22574032direct (N × H)

Maximal subgroups

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

subgroupindex
#225740322
C2×#168641232
C2×#168641212
C2×#168641072
C2×#168641042
C2×#168641022
C2×#168641002
C2×#168640262
C2×#168640242
C2×#168640232
C2×#168639512
C2×#168639492
C22×#145240342
C2×#125×D672
C2×#168638772
C2×#168638762
C2×#168638642
C2×#544×C672
C2×#350467