Finite Group Databasebeta

← C2×#22574187 #31763945

Subgroups — C2×#22574187 #31763945

Order 17152.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574187C2132yesmaximal, direct product factor
2C2×#16864124C211yesmaximal, characteristic, complemented
3C2×#16864106C211yesmaximal, characteristic, complemented
4C2×#16864103C211yesmaximal, characteristic, complemented
5C2×#16864092C212yesmaximal, complemented
6C2×#16864086C212yesmaximal, complemented
7C2×#16864085C212yesmaximal, complemented
8C2×#16864079C214yesmaximal, complemented
9C2×#16864050C211yesmaximal, characteristic, complemented
10C2×#16864045C212yesmaximal, complemented
11C2×#16864004C212yesmaximal, complemented
12C2×#16863988C214yesmaximal, complemented
13C2×#16863953C211yesmaximal, characteristic, complemented
14C2×#16863930C212yesmaximal, complemented
15C2×#16863930C211yesmaximal, characteristic, complemented
16C22×#14524035C212yesmaximal, complemented
17C2×#16863875C212yesmaximal, complemented
18C2×C4×#41×C67C211yesmaximal, characteristic, complemented
19C22×#11761627C2212yes—
20#16864124C22116yescomplemented
21#16864106C22116yescomplemented
22#16864103C22116yescomplemented
23#16864092C22132yescomplemented
24#16864086C22132yescomplemented
25#16864085C22132yescomplemented
26#16864079C22164yescomplemented
27#16864050C22116yescomplemented
28#16864045C22132yescomplemented
29#16864004C22132yescomplemented
30#16863988C22164yescomplemented
31#16863953C22116yescomplemented
32C2×#14524043C2211yescharacteristic
33C2×#14524043C2211yescharacteristic
34C2×#14524041C2212yes—
35#16863930C22132yescomplemented
36#16863930C22116yescomplemented
37C2×#14524038C2214yes—
38C2×#14524037C2214yes—
39C2×#14524037C2212yes—
40C2×#14524036C2214yes—
41C2×#14524035C2214yes—
42C2×#14524035C2214yes—
43C2×#14524035C2211yescharacteristic
44C2×#14524035C2212yes—
45C2×#14524035C2212yes—
46C2×#14524035C2212yes—
47C2×#14524035C22132yescomplemented
48C2×#14524034C2212yes—
49C2×#14524033C2214yes—
50C2×#14524033C2214yes—
51C2×#14524031C2211yescharacteristic
52C2×#14524027C2214yes—
53C2×#14524026C2214yes—
54C2×#14524026C2212yes—
55C2×#14524025C2214yes—
56C2×#14524024C2214yes—
57C2×#14524023C2212yes—
58C2×#14524022C2212yes—
59C2×#14524022C2211yescharacteristic
60C2×#14524022C2212yes—
61C2×#14524022C2212yes—
62C2×#14524021C2214yes—
63C2×#14524020C2214yes—
64C2×#14524019C2212yes—
65C2×#14524017C2212yes—
66C2×#14524017C2211yescharacteristic
67C2×#14524015C2214yes—
68#16863875C22132yescomplemented
69C2×C4×Dic134C2212yes—
70C2×C4×Dic134C2212yes—
71C2×C4×Dic134C2212yes—
72C2×C4×Dic134C2211yescharacteristic
73C2×#14524008C2212yes—
74C2×C4×D268C2211yescharacteristic
75C2×C4×D268C2212yes—
76C2×D4×Dic67C2212yes—
77C2×C4×C22⋊D67C2214yes—
78C2×C4×C22⋊D67C2212yes—
79C2×(C22⋊D67)⋊C4C2214yes—
80C2×#14524002C2212yes—
81C2×#14524000C2212yes—
82C2×#14524000C2214yes—
83C2×#14523999C2214yes—
84C22×C4⋊Dic67C2212yes—
85C22×C4⋊Dic67C2212yes—
86C22×Dic67⋊C4C2214yes—
87C22×Dic67⋊C4C2214yes—
88C2×C4⋊C4×D67C2212yes—
89C22×#41×C67C2211yescharacteristic
90C4×#41×C67C22116yescomplemented
91C2×C4×Q8×C67C2211yescharacteristic
92C2×C4×Q8×C67C2211yescharacteristic
93C2×C4×D4×C67C2211yescharacteristic
94C2×C4×D4×C67C2211yescharacteristic
95C2×C4×D4×C67C2212yes—
96C2×C4×D4×C67C2212yes—
97C2×#117×C67C2212yes—
98C2×#117×C67C2211yescharacteristic
99C22×C42×C67C2212yes—
100C22×C42×C67C2211yescharacteristic
101C2×#11761627—216no—
102C2×#11761627C23116yes—
103C22×Dic134C2312yes—
104C22×Dic134C2311yescharacteristic
105C22×Dic134C2312yes—
106C22×D268C2311yescharacteristic
107C22×C22⋊D67C2314yes—
108C22×C22⋊D67C2312yes—
109C23×Dic67C2314yes—
110C23×Dic67C2314yes—
111C22×C4×D67C2312yes—
112C22×C4×D67C2314yes—
113#14524043C2318yes—
114#14524043C2318yes—
115#14524041C23116yes—
116#14524038C23132yes—
117#14524037C23132yes—
118#14524037C23116yes—
119#14524036C23132yes—
120#14524035C23132yes—
121#14524035C23132yes—
122#14524035C23116yes—
123#14524035C23116yes—
124#14524035C2318yes—
125#14524035C23116yes—
126#14524034C23116yes—
127#14524033C23132yes—
128#14524033C23132yes—
129#14524031C2318yes—
130#14524027C23132yes—
131#14524026C23132yes—
132#14524026C23116yes—
133#14524025C23132yes—
134#14524024C23132yes—
135#14524023C23116yes—
136#14524022C23116yes—
137#14524022C2318yes—
138#14524022C23116yes—
139#14524022C23116yes—
140#14524021C23132yes—
141#14524020C23132yes—
142#14524019C23116yes—
143#14524017C23116yes—
144#14524017C2318yes—
145#14524015C23132yes—
146C4×Dic134C23116yes—
147C4×Dic134C23116yes—
148C4×Dic134C23116yes—
149C4×Dic134C2318yes—
150#14524008C23116yes—
151C4×D268C2318yes—
152C4×D268C23116yes—
153D4×Dic67C23116yes—
154C4×C22⋊D67C23116yes—
155C4×C22⋊D67C23132yes—
156(C22⋊D67)⋊C4C23132yes—
157#14524002C23116yes—
158#14524000C23116yes—
159#14524000C23132yes—
160#14523999C23132yes—
161C2×C4⋊Dic67C23116yes—
162C2×C4⋊Dic67C23116yes—
163C2×C4⋊Dic67C2312yes—
164C2×C4⋊Dic67C2311yescharacteristic
165C2×C4⋊Dic67C2311yescharacteristic
166C2×C4⋊Dic67C2312yes—
167C2×C4⋊Dic67C2312yes—
168C2×C4⋊Dic67C2314yes—
169C2×C4⋊Dic67C2314yes—
170C2×C4⋊Dic67C2312yes—
171C2×Dic67⋊C4C23132yes—
172C2×Dic67⋊C4C2314yes—
173C2×Dic67⋊C4C2312yes—
174C2×Dic67⋊C4C2312yes—
175C2×Dic67⋊C4C2314yes—
176C2×Dic67⋊C4C2314yes—
177C2×Dic67⋊C4C2314yes—
178C2×Dic67⋊C4C23132yes—
179C2×Dic67⋊C4C2314yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2312yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2312yes—
184C2×Dic67⋊C4C2314yes—
185C4⋊C4×D67C23116yes—
186C2×C22⋊Dic67C2314yes—
187C2×C22⋊Dic67C2314yes—
188C2×C22⋊Dic67C2312yes—
189C2×(C2×D67)⋊C4C2312yes—
190C2×(C2×D67)⋊C4C2312yes—
191C2×(C2×D67)⋊C4C2312yes—
192C2×(C2×D67)⋊C4C2314yes—
193C2×(C2×D67)⋊C4C2314yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×C4×Dic67C2314yes—
196C2×C4×Dic67C2314yes—
197C2×C4×Dic67C2312yes—
198C2×#41×C67—28no—
199C2×#41×C67C2318yes—
200C22×Q8×C67C2311yescharacteristic
201C22×D4×C67C2312yes—
202C22×D4×C67C2311yescharacteristic
203C23×C4×C67C2312yes—
204C23×C4×C67C2311yescharacteristic
205C23×C4×C67C2312yes—
206C23×C4×C67C2311yescharacteristic
207C23×C4×C67C2312yes—
208C23×C4×C67C2311yescharacteristic
209C4×Q8×C67C2318yes—
210C4×Q8×C67C2318yes—
211C4×D4×C67C2318yes—
212C4×D4×C67C23116yes—
213C4×D4×C67C2318yes—
214C4×D4×C67C23116yes—
215#117×C67C23116yes—
216#117×C67C2318yes—
217C2×C4⋊C4×C67C2311yescharacteristic
218C2×C4⋊C4×C67C2312yes—
219C2×C4⋊C4×C67C2311yescharacteristic
220C2×C4⋊C4×C67C2312yes—
221C2×C22⋊C4×C67C2312yes—
222C2×C22⋊C4×C67C2312yes—
223C2×C22⋊C4×C67C2312yes—
224C2×C42×C67C2311yescharacteristic
225C2×C42×C67C2312yes—
226C2×C42×C67C2311yescharacteristic
227C2×C42×C67C2311yescharacteristic
228C2×C42×C67C2312yes—
229C2×C42×C67C2311yescharacteristic
230C2×C42×C67C2312yes—
231C2×C42×C67C23116yes—
232C2×C42×C67C2318yes—
233C23×D67C2412yes—
234#11761627—264no—
235C2×Dic134—28no—
236C2×Dic134—24no—
237C2×Dic134—44no—
238C2×Dic134C2418yes—
239C2×Dic134C2414yes—
240C2×Dic134C2418yes—
241C2×D268—24no—
242C2×D268C2414yes—
243C2×C22⋊D67—216no—
244C2×C22⋊D67—44no—
245C2×C22⋊D67C24116yes—
246C2×C22⋊D67C2418yes—
247C22×Dic67—216no—
248C22×Dic67—48no—
249C22×Dic67C2412yes—
250C22×Dic67C2414yes—
251C22×Dic67C2414yes—
252C22×Dic67C2412yes—
253C22×Dic67C2412yes—
254C22×Dic67C24116yes—
255C22×Dic67C24116yes—
256C2×C4×D67—28no—
257C2×C4×D67—48no—
258C2×C4×D67C2418yes—
259C2×C4×D67C24116yes—
260C4⋊Dic67C2418yes—
261C4⋊Dic67C2414yes—
262C4⋊Dic67C2414yes—
263C4⋊Dic67C2418yes—
264C4⋊Dic67C2418yes—
265C4⋊Dic67C24116yes—
266C4⋊Dic67C24116yes—
267C4⋊Dic67C2418yes—
268Dic67⋊C4C24116yes—
269Dic67⋊C4C2418yes—
270Dic67⋊C4C2418yes—
271Dic67⋊C4C24116yes—
272Dic67⋊C4C24116yes—
273Dic67⋊C4C24116yes—
274Dic67⋊C4C24116yes—
275Dic67⋊C4C24116yes—
276Dic67⋊C4C2418yes—
277Dic67⋊C4C24116yes—
278Dic67⋊C4C2418yes—
279Dic67⋊C4C24116yes—
280C22⋊Dic67C24116yes—
281C22⋊Dic67C24116yes—
282C22⋊Dic67C2418yes—
283(C2×D67)⋊C4C2418yes—
284(C2×D67)⋊C4C2418yes—
285(C2×D67)⋊C4C2418yes—
286(C2×D67)⋊C4C24116yes—
287(C2×D67)⋊C4C24116yes—
288(C2×D67)⋊C4C2418yes—
289C4×Dic67C24116yes—
290C4×Dic67C24116yes—
291C4×Dic67C2418yes—
292C24×C67C2411yescharacteristic
293C24×C67C2412yes—
294#41×C67—232no—
295C2×Q8×C67—24no—
296C2×Q8×C67C2414yes—
297C2×D4×C67—28no—
298C2×D4×C67#4118yes—
299C2×D4×C67C2418yes—
300C2×D4×C67C2414yes—
301C22×C4×C67—28no—
302C22×C4×C67—24no—
303C22×C4×C67—28no—
304C22×C4×C67—24no—
305C22×C4×C67—44no—
306C22×C4×C67—42no—
307C22×C4×C67C2411yescharacteristic
308C22×C4×C67C2411yescharacteristic
309C22×C4×C67C2411yescharacteristic
310C22×C4×C67C2412yes—
311C22×C4×C67C2412yes—
312C22×C4×C67C2411yescharacteristic
313C22×C4×C67C2412yes—
314C22×C4×C67C2418yes—
315C22×C4×C67C2414yes—
316C22×C4×C67C2418yes—
317C22×C4×C67C2414yes—
318C22×C4×C67C2418yes—
319C22×C4×C67C2414yes—
320C22×C4×C67C2411yescharacteristic
321C22×C4×C67C2411yescharacteristic
322C4⋊C4×C67C2414yes—
323C4⋊C4×C67C2418yes—
324C4⋊C4×C67C2414yes—
325C4⋊C4×C67C2418yes—
326C22⋊C4×C67C2418yes—
327C22⋊C4×C67C2418yes—
328C22⋊C4×C67C2418yes—
329C42×C67C2414yes—
330C42×C67C2418yes—
331C42×C67C2414yes—
332C42×C67C2414yes—
333C42×C67C2418yes—
334C42×C67C2414yes—
335C42×C67C2418yes—
336C23×C67—24no—
337C23×C67—24no—
338C23×C67—22no—
339C23×C67—22no—
340C23×C67—22no—
341C23×C67C2×#4118yes—
342C23×C67C2512yes—
343C23×C67C2514yes—
344C23×C67C2511yescharacteristic
345C22×D67—24no—
346C22×D67—24no—
347C22×D67—24no—
348C22×D67C2514yes—
349Q8×C67—28no—
350D4×C67—216no—
351D4×C67C2×#41116yes—
352C2×C4×C67—22no—
353C2×C4×C67—24no—
354C2×C4×C67—216no—
355C2×C4×C67—22no—
356C2×C4×C67—24no—
357C2×C4×C67—22no—
358C2×C4×C67—24no—
359C2×C4×C67—22no—
360C2×C4×C67—28no—
361C2×C4×C67—216no—
362C2×C4×C67—28no—
363C2×C4×C67—44no—
364C2×C4×C67—48no—
365C2×C4×C67C2×#4114yes—
366C2×C4×C672−1+414yes—
367C2×C4×C67C2512yes—
368C2×C4×C67C2512yes—
369C2×C4×C67C2512yes—
370C2×C4×C67C2514yes—
371C2×C4×C67C2514yes—
372C2×C4×C67C2512yes—
373C2×C4×C67C2514yes—
374C2×C4×C67C2512yes—
375C2×C4×C67C2512yes—
376C22⋊D67—232no—
377C22⋊D67—48no—
378C2×Dic67—24no—
379C2×Dic67—28no—
380C2×Dic67—232no—
381C2×Dic67—24no—
382C2×Dic67—28no—
383C2×Dic67—24no—
384C2×Dic67—416no—
385C2×Dic67C2514yes—
386C2×Dic67C2518yes—
387C2×Dic67C2518yes—
388C2×Dic67C2514yes—
389C2×Dic67C2514yes—
390D268—28no—
391C4×D67—216no—
392C4×D67—416no—
393Dic134—216no—
394Dic134—28no—
395Dic134—48no—
396C22×C67—24no—
397C22×C67—24no—
398C22×C67—216no—
399C22×C67—22no—
400C22×C67—22no—
401C22×C67—22no—
402C22×C67—44no—
403C22×C67C22×#4118yes—
404C22×C67C22×#4112yes—
405C22×C67C2×2−1+412yes—
406C22×C67#58512yes—
407C22×C67C2611yescharacteristic
408C2×D67—24no—
409C2×D67—24no—
410C2×D67—24no—
411C2×D67—48no—
412C4×C67—22no—
413C4×C67—24no—
414C4×C67—22no—
415C4×C67—24no—
416C4×C67—22no—
417C4×C67—24no—
418C4×C67—22no—
419C4×C67C22×#4114yes—
420C4×C67C2×2−1+414yes—
421Dic67—28no—
422Dic67—24no—
423Dic67—24no—
424Dic67—28no—
425Dic67—24no—
426C2×#3515—671nomaximal, Sylow
427C2×C67—28no—
428C2×C67—42no—
429C2×C67#351514yescomplemented
430C2×C67C23×#4111yescharacteristic
431C2×C67C22×2−1+411yescharacteristic
432C2×C67C2×#58511yescharacteristic
433D67—44no—
434#3515—6732no—
435C2×#557—671no—
436C2×#554—671no—
437C2×#554—671no—
438C2×#553—672no—
439C2×#552—672no—
440C2×#552—674no—
441C2×#552—672no—
442C2×#547—672no—
443C2×#547—671no—
444C2×#541—672no—
445C2×#539—674no—
446C2×#533—671no—
447C2×#529—671no—
448C2×#529—672no—
449C22×#125—672no—
450C2×#520—672no—
451C2×C4×#41D6711yescharacteristic, complemented
452C67C2×#351511yescharacteristic, complemented, Sylow
453C22×#41—672no—
454C22×#41C2×D6711yescharacteristic
455#557—6716no—
456#554—6716no—
457#554—6716no—
458#553—6732no—
459#552—6732no—
460#552—6764no—
461#552—6732no—
462#547—6732no—
463#547—6716no—
464#541—6732no—
465#539—6764no—
466#533—6716no—
467C2×C4⋊Q8—672no—
468C2×C4⋊Q8—671no—
469C2×C4⋊Q8—671no—
470#529—6732no—
471#529—6716no—
472C2×#126—674no—
473C2×#126—674no—
474C2×#126—674no—
475C2×#126—672no—
476C2×#125—674no—
477C2×#125—674no—
478C2×#125—672no—
479C2×#125—671no—
480C2×#125—672no—
481C2×#125—674no—
482C2×#125—674no—
483C2×#125—672no—
484C2×#125—672no—
485C2×#125—6732no—
486C2×#124—671no—
487C2×#123—674no—
488C2×#123—672no—
489C2×#123—674no—
490C2×#123—674no—
491C2×#123—674no—
492C2×C22⋊Q8—672no—
493C2×C22⋊Q8—671no—
494C2×C22⋊Q8—672no—
495C2×C22⋊Q8—672no—
496C2×C22⋊Q8—672no—
497C2×C22⋊Q8—674no—
498C2×C22⋊Q8—672no—
499C2×C22⋊Q8—674no—
500C2×#121—674no—
501C2×#121—672no—
502C2×#121—671no—
503#520—6732no—
504C4×#41C2×D67116yescomplemented
505C2×C4×Q8—672no—
506C2×C4×Q8—672no—
507C2×C4×Q8—672no—
508C2×C4×Q8—671no—
509C2×C4×Q8—672no—
510C2×C4×Q8C2×D6711yescharacteristic
511C2×C4×Q8C2×D6711yescharacteristic
512C2×C4×D4—672no—
513C2×C4×D4—674no—
514C2×C4×D4—672no—
515C2×C4×D4—674no—
516C2×C4×D4—671no—
517C2×C4×D4—672no—
518C2×C4×D4C2×D6711yescharacteristic
519C2×C4×D4C2×D6712yes—
520C2×C4×D4C2×D6711yescharacteristic
521C2×C4×D4C2×D6712yes—
522C2×#117—672no—
523C2×#117—674no—
524C2×#117—672no—
525C2×#117—674no—
526C2×#117C2×D6711yescharacteristic
527C2×#117C2×D6712yes—
528C22×C4⋊C4—674no—
529C22×C4⋊C4—674no—
530C22×C4⋊C4—672no—
531C22×C4⋊C4—672no—
532C22×C4⋊C4—672no—
533C22×C42C2×D6712yes—
534C22×C42C2×D6711yescharacteristic
535C2×#41—28no—
536C2×#41—6716no—
537C2×#41—13416no—
538C2×#41C22×D6718yes—
539C22×Q8—672no—
540C22×Q8—671no—
541C22×Q8—672no—
542C22×Q8C22×D6711yescharacteristic
543C22×D4—672no—
544C22×D4—674no—
545C22×D4—671no—
546C22×D4C22×D6712yes—
547C22×D4C22×D6711yescharacteristic
548C23×C4—674no—
549C23×C4—674no—
550C23×C4—674no—
551C23×C4—672no—
552C23×C4C22×D6712yes—
553C23×C4C22×D6712yes—
554C23×C4C22×D6711yescharacteristic
555C23×C4C22×D6711yescharacteristic
556C23×C4C22×D6712yes—
557C23×C4C22×D6711yescharacteristic
558C4⋊Q8—6716no—
559C4⋊Q8—678no—
560C4⋊Q8—678no—
561#126—6732no—
562#126—6732no—
563#126—6732no—
564#126—6716no—
565#125—6732no—
566#125—6732no—
567#125—6716no—
568#125—678no—
569#125—6716no—
570#125—6732no—
571#125—6732no—
572#125—6716no—
573#125—6716no—
574#124—678no—
575#123—6732no—
576#123—6716no—
577#123—6732no—
578#123—6732no—
579#123—6732no—
580C22⋊Q8—6716no—
581C22⋊Q8—678no—
582C22⋊Q8—6716no—
583C22⋊Q8—6716no—
584C22⋊Q8—6716no—
585C22⋊Q8—6732no—
586C22⋊Q8—6716no—
587C22⋊Q8—6732no—
588#121—6732no—
589#121—6716no—
590#121—678no—
591C4×Q8—6716no—
592C4×Q8—6716no—
593C4×Q8—6716no—
594C4×Q8—678no—
595C4×Q8—6716no—
596C4×Q8C22×D6718yes—
597C4×Q8C22×D6718yes—
598C4×D4—6716no—
599C4×D4—6732no—
600C4×D4—6716no—
601C4×D4—6732no—
602C4×D4—678no—
603C4×D4—6716no—
604C4×D4C22×D6718yes—
605C4×D4C22×D67116yes—
606C4×D4C22×D6718yes—
607C4×D4C22×D67116yes—
608#117—6716no—
609#117—6732no—
610#117—6716no—
611#117—6732no—
612#117C22×D6718yes—
613#117C22×D67116yes—
614C2×C4⋊C4—674no—
615C2×C4⋊C4—672no—
616C2×C4⋊C4—671no—
617C2×C4⋊C4—672no—
618C2×C4⋊C4—671no—
619C2×C4⋊C4—672no—
620C2×C4⋊C4—672no—
621C2×C4⋊C4—674no—
622C2×C4⋊C4—672no—
623C2×C4⋊C4—674no—
624C2×C4⋊C4—674no—
625C2×C4⋊C4—6732no—
626C2×C4⋊C4—674no—
627C2×C4⋊C4—674no—
628C2×C4⋊C4—674no—
629C2×C4⋊C4—674no—
630C2×C4⋊C4—6732no—
631C2×C4⋊C4—6716no—
632C2×C4⋊C4—6716no—
633C2×C4⋊C4—672no—
634C2×C4⋊C4—674no—
635C2×C4⋊C4—672no—
636C2×C4⋊C4—672no—
637C2×C4⋊C4—674no—
638C2×C4⋊C4—6716no—
639C2×C4⋊C4C22×D6711yescharacteristic
640C2×C4⋊C4C22×D6712yes—
641C2×C4⋊C4C22×D6711yescharacteristic
642C2×C4⋊C4C22×D6712yes—
643C2×C22⋊C4—674no—
644C2×C22⋊C4—674no—
645C2×C22⋊C4—672no—
646C2×C22⋊C4—672no—
647C2×C22⋊C4—672no—
648C2×C22⋊C4—672no—
649C2×C22⋊C4—674no—
650C2×C22⋊C4—674no—
651C2×C22⋊C4—672no—
652C2×C22⋊C4C22×D6712yes—
653C2×C22⋊C4C22×D6712yes—
654C2×C22⋊C4C22×D6712yes—
655C2×C42—674no—
656C2×C42—674no—
657C2×C42—672no—
658C2×C42C22×D6712yes—
659C2×C42C22×D6711yescharacteristic
660C2×C42C22×D6711yescharacteristic
661C2×C42C22×D6712yes—
662C2×C42C22×D6711yescharacteristic
663C2×C42C22×D6712yes—
664C2×C42C22×D67116yes—
665C2×C42C22×D6718yes—
666C2×C42C22×D6711yescharacteristic
667C24—672no—
668C24C23×D6711yescharacteristic
669C24C23×D6712yes—
670#41—232no—
671#41—13464no—
672C2×Q8—24no—
673C2×Q8—2684no—
674C2×Q8—678no—
675C2×Q8—674no—
676C2×Q8—678no—
677C2×Q8—1348no—
678C2×Q8—1344no—
679C2×Q8C23×D6714yes—
680C2×D4—28no—
681C2×D4—2684no—
682C2×D4—678no—
683C2×D4—6716no—
684C2×D4—674no—
685C2×D4—13416no—
686C2×D4—1344no—
687C2×D4#1176162818yes—
688C2×D4C23×D6718yes—
689C2×D4C23×D6714yes—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—28no—
693C22×C4—24no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—2688no—
697C22×C4—2688no—
698C22×C4—6716no—
699C22×C4—6716no—
700C22×C4—6716no—
701C22×C4—672no—
702C22×C4—674no—
703C22×C4—674no—
704C22×C4—672no—
705C22×C4—672no—
706C22×C4—678no—
707C22×C4—13416no—
708C22×C4—1348no—
709C22×C4C23×D6718yes—
710C22×C4C23×D6718yes—
711C22×C4C23×D6714yes—
712C22×C4C23×D6714yes—
713C22×C4C23×D6711yescharacteristic
714C22×C4C23×D6712yes—
715C22×C4C23×D6711yescharacteristic
716C22×C4C23×D6711yescharacteristic
717C22×C4C23×D6712yes—
718C22×C4C23×D6711yescharacteristic
719C22×C4C23×D6712yes—
720C22×C4C23×D6718yes—
721C22×C4C23×D6714yes—
722C22×C4C23×D6711yescharacteristic
723C22×C4C23×D6711yescharacteristic
724C4⋊C4—6716no—
725C4⋊C4—678no—
726C4⋊C4—674no—
727C4⋊C4—678no—
728C4⋊C4—674no—
729C4⋊C4—678no—
730C4⋊C4—678no—
731C4⋊C4—6716no—
732C4⋊C4—678no—
733C4⋊C4—6716no—
734C4⋊C4—6716no—
735C4⋊C4—6716no—
736C4⋊C4—6716no—
737C4⋊C4—6716no—
738C4⋊C4—6716no—
739C4⋊C4—678no—
740C4⋊C4—6716no—
741C4⋊C4—678no—
742C4⋊C4—678no—
743C4⋊C4—6716no—
744C4⋊C4C23×D6714yes—
745C4⋊C4C23×D6718yes—
746C4⋊C4C23×D6714yes—
747C4⋊C4C23×D6718yes—
748C22⋊C4—6716no—
749C22⋊C4—6716no—
750C22⋊C4—678no—
751C22⋊C4—678no—
752C22⋊C4—678no—
753C22⋊C4—678no—
754C22⋊C4—6716no—
755C22⋊C4—6716no—
756C22⋊C4—678no—
757C22⋊C4C23×D6718yes—
758C22⋊C4C23×D6718yes—
759C22⋊C4C23×D6718yes—
760C42—6716no—
761C42—6716no—
762C42—678no—
763C42C23×D6714yes—
764C42C23×D6718yes—
765C42C23×D6714yes—
766C42C23×D6714yes—
767C42C23×D6718yes—
768C42C23×D6714yes—
769C42C23×D6718yes—
770C23—24no—
771C23—24no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—674no—
776C23—1344no—
777C23—1344no—
778C23—1344no—
779C23C2×#1176162818yes—
780C23C24×D6712yes—
781C23C24×D6714yes—
782C23C24×D6711yescharacteristic
783Q8—28no—
784Q8—2688no—
785Q8—13416no—
786Q8—1348no—
787D4—216no—
788D4—2688no—
789D4—13432no—
790D4—1348no—
791D4C2×#11761628116yes—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—216no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—216no—
802C2×C4—28no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—26816no—
806C2×C4—26816no—
807C2×C4—674no—
808C2×C4—678no—
809C2×C4—678no—
810C2×C4—674no—
811C2×C4—674no—
812C2×C4—1344no—
813C2×C4—1348no—
814C2×C4—13432no—
815C2×C4—1344no—
816C2×C4—1344no—
817C2×C4—1348no—
818C2×C4—13416no—
819C2×C4C2×#1176162814yes—
820C2×C4#1452409014yes—
821C2×C4C24×D6712yes—
822C2×C4C24×D6714yes—
823C2×C4C24×D6712yes—
824C2×C4C24×D6712yes—
825C2×C4C24×D6714yes—
826C2×C4C24×D6712yes—
827C2×C4C24×D6714yes—
828C2×C4C24×D6712yes—
829C2×C4C24×D6712yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—2688no—
838C22—1344no—
839C22—1344no—
840C22—1344no—
841C22C22×#1176162818yes—
842C22C22×#1176162812yes—
843C22C2×#1452409012yes—
844C22#1686423212yes—
845C22C25×D6711yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—1344no—
854C4—1348no—
855C4—1344no—
856C4—1344no—
857C4—1348no—
858C4C22×#1176162814yes—
859C4C2×#1452409014yes—
860C2—28no—
861C2—42no—
862C2—2684no—
863C2#2257418714yesdirect product factor
864C2C23×#1176162811yescharacteristic
865C2C22×#1452409011yescharacteristic
866C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×C4×#41×C67C2
socleC23×C67C25
hypercenterC2×C4×#41D67
hypocenterC67C2×#3515
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22574187C2direct (N × H)
2. C2×#16864124C2semidirect
3. C2×#16864106C2semidirect
4. C2×#16864103C2semidirect
5. C2×#16864092C2semidirect
6. C2×#16864086C2semidirect
7. C2×#16864085C2semidirect
8. C2×#16864079C2semidirect
9. C2×#16864050C2semidirect
10. C2×#16864045C2semidirect
11. C2×#16864004C2semidirect
12. C2×#16863988C2semidirect
13. C2×#16863953C2semidirect
14. C2×#16863930C2semidirect
15. C2×#16863930C2semidirect
16. C22×#14524035C2semidirect
17. C2×#16863875C2semidirect
18. C2×C4×#41×C67C2semidirect
20. #16864124C22semidirect
21. #16864106C22semidirect
22. #16864103C22semidirect
23. #16864092C22semidirect
24. #16864086C22semidirect
25. #16864085C22semidirect
26. #16864079C22semidirect
27. #16864050C22semidirect
28. #16864045C22semidirect
29. #16864004C22semidirect
30. #16863988C22semidirect
31. #16863953C22semidirect
35. #16863930C22semidirect
36. #16863930C22semidirect
47. C2×#14524035C22semidirect
68. #16863875C22semidirect
90. C4×#41×C67C22semidirect
429. C2×C67#3515semidirect
451. C2×C4×#41D67semidirect
452. C67C2×#3515semidirect
504. C4×#41C2×D67semidirect
863. C2#22574187direct (N × H)

Maximal subgroups

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

subgroupindex
#225741872
C2×#168641242
C2×#168641062
C2×#168641032
C2×#168640922
C2×#168640862
C2×#168640852
C2×#168640792
C2×#168640502
C2×#168640452
C2×#168640042
C2×#168639882
C2×#168639532
C2×#168639302
C22×#145240352
C2×#168638752
C2×C4×#41×C672
C2×#351567