Finite Group Databasebeta

← #62927

Subgroups — #62927

Order 256.

3548 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3560C214yesmaximal, complemented
2#3559C214yesmaximal, complemented
3#3551C214yesmaximal, complemented
4#3547C214yesmaximal, complemented
5#3542C214yesmaximal, complemented
6#3541C214yesmaximal, complemented
7#3539C214yesmaximal, complemented
8#3538C214yesmaximal, complemented
9#3534C214yesmaximal, complemented
10#3520C214yesmaximal, complemented
11#3512C212yesmaximal, complemented
12#3505C214yesmaximal, complemented
13#3497C211yesmaximal, characteristic, complemented
14#3494C214yesmaximal, complemented
15#3493C211yesmaximal, characteristic, complemented
16#3492C211yesmaximal, characteristic, complemented
17#3489C212yesmaximal, complemented
18#3489C212yesmaximal, complemented
19C2×#552C211yesmaximal, characteristic, complemented
20D4×#41C212yesmaximal, complemented
21#3461C211yesmaximal, characteristic, complemented
22#3449C211yesmaximal, characteristic, complemented
23C2×#537C211yesmaximal, characteristic, complemented
24C2×2−1+4C2212yescomplemented
25C22×#41C2212yescomplemented
26C22×#41C2212yescomplemented
27#563C2218yescomplemented
28#563C2218yescomplemented
29#562C2218yescomplemented
30#562C2218yescomplemented
31#560C2218yescomplemented
32#560C2218yescomplemented
33#556C2214yescomplemented
34#555C2214yescomplemented
35#555C2218yescomplemented
36#554C2214yescomplemented
37#554C2218yescomplemented
38#553C2214yescomplemented
39#553C2214yescomplemented
40#553C2218yescomplemented
41#553C2218yescomplemented
42#553C2214yescomplemented
43#553C2218yescomplemented
44#553C2218yescomplemented
45#553C2218yescomplemented
46#553C2214yescomplemented
47#552C2214yescomplemented
48#552C2214yescomplemented
49#552C2214yescomplemented
50#552C2214yescomplemented
51#552C2214yescomplemented
52#552C2214yescomplemented
53#552C2214yescomplemented
54#552C2214yescomplemented
55#551C2218yescomplemented
56#551C2218yescomplemented
57#551C2218yescomplemented
58#551C2218yescomplemented
59#550C2212yescomplemented
60#550C2214yescomplemented
61D4×Q8C2212yescomplemented
62D4×Q8C2214yescomplemented
63D4×Q8C2214yescomplemented
64D4×Q8C2214yescomplemented
65#548C2212yes—
66#548C2212yescomplemented
67#548C2214yescomplemented
68#548C2214yescomplemented
69#548C2214yescomplemented
70#548C2214yescomplemented
71#547C2212yescomplemented
72#547C2214yescomplemented
73#547C2218yescomplemented
74#547C2214yescomplemented
75#547C2214yescomplemented
76#547C2218yescomplemented
77#547C2214yescomplemented
78#546C2212yes—
79#546C2214yescomplemented
80#546C2212yescomplemented
81#546C2214yescomplemented
82#546C2218yescomplemented
83#546C2214yescomplemented
84#546C2218yescomplemented
85#546C2214yescomplemented
86#546C2218yescomplemented
87D42C2214yes—
88D42C2212yescomplemented
89#544C2211yescharacteristic, complemented
90#544C2214yescomplemented
91#544C2218yescomplemented
92#542C2214yescomplemented
93#542C2214yescomplemented
94#542C2214yescomplemented
95#542C2218yescomplemented
96#541C2214yescomplemented
97#541C2214yescomplemented
98#540C2214yescomplemented
99#540C2214yescomplemented
100#540C2214yescomplemented
101#540C2218yescomplemented
102#540C2218yescomplemented
103#539C2214yescomplemented
104#539C2214yescomplemented
105#539C2218yescomplemented
106#539C2218yescomplemented
107#539C2218yescomplemented
108#539C2218yescomplemented
109#538C2214yescomplemented
110#538C2218yescomplemented
111#538C2218yescomplemented
112#538C2218yescomplemented
113#537C2211yescharacteristic
114#537C2212yescomplemented
115#537C2211yescharacteristic, complemented
116#537C2214yescomplemented
117#537C2214yescomplemented
118#537C2214yescomplemented
119#537C2212yescomplemented
120#537C2211yescharacteristic, complemented
121#537C2214yescomplemented
122#537C2214yescomplemented
123#537C2214yescomplemented
124#536C2214yescomplemented
125#536C2212yescomplemented
126#536C2214yescomplemented
127#536C2214yescomplemented
128#535C2214yescomplemented
129#535C2214yescomplemented
130#534C2214yescomplemented
131#534C2218yescomplemented
132#533C2214yescomplemented
133#532C2214yescomplemented
134#532C2212yescomplemented
135#532C2214yescomplemented
136#532C2214yescomplemented
137#529C2214yescomplemented
138#529C2214yescomplemented
139#529C2214yescomplemented
140#529C2214yescomplemented
141#529C2214yescomplemented
142C2×#126C2212yescomplemented
143C2×#125C2211yescharacteristic, complemented
144C2×#125C2212yescomplemented
145#525C2214yes—
146#525C2214yescomplemented
147#525C2214yescomplemented
148#525C2212yescomplemented
149#525C2212yescomplemented
150#525C2214yescomplemented
151#525C2214yescomplemented
152#525C2214yescomplemented
153#525C2214yescomplemented
154C2×#123C2212yes—
155C2×C22⋊Q8C2214yescomplemented
156C2×C22⋊Q8C2211yescharacteristic, complemented
157C2×C22⋊Q8C2211yescharacteristic, complemented
158C2×C22⋊Q8C2214yescomplemented
159C2×C22⋊Q8C2214yescomplemented
160C2×#121C2214yescomplemented
161C2×#121C2214yescomplemented
162#520C2212yescomplemented
163#520C2212yescomplemented
164#520C2214yescomplemented
165#518C2214yescomplemented
166C4×#41C2212yescomplemented
167C2×C4×Q8C2211yescharacteristic, complemented
168C2×C4×D4C2211yescharacteristic
169C2×C4×D4C2214yescomplemented
170C2×#117C2211yescharacteristic, complemented
171C2×#117C2212yescomplemented
172C22×C4⋊C4C2211yescharacteristic, complemented
1732−1+4—48no—
174C2×#41—48no—
175C2×#41—48no—
176C2×#41C2312yes—
177C2×#41C2312yes—
178C2×#41C2312yes—
179C2×#41C2314yes—
180C2×#41C2314yes—
181C2×#41C2312yes—
182C2×#41C2312yes—
183C2×#41C2314yes—
184C2×#41C2314yes—
185C2×#41C2314yes—
186C2×#41C2314yes—
187C2×#41C2318yes—
188C2×#41C2314yes—
189C2×#41C2312yes—
190C2×#41C2312yes—
191C22×Q8C2311yescharacteristic
192C22×Q8C2312yes—
193C22×Q8C2314yes—
194C22×Q8C2314yes—
195C22×Q8C2312yes—
196C22×D4C2311yescharacteristic
197C22×D4C2314yes—
198C22×D4C2314yes—
199C22×D4C2314yes—
200C22×D4C2312yes—
201C22×D4C2314yes—
202C22×D4C2312yes—
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2312yes—
206C23×C4C2314yes—
207C23×C4C2314yes—
208C4⋊Q8C2314yes—
209C4⋊Q8C2312yes—
210C4⋊Q8C2314yes—
211C4⋊Q8C2314yes—
212C4⋊Q8C2314yes—
213C4⋊Q8C2314yes—
214C4⋊Q8C2318yes—
215C4⋊Q8C2318yes—
216#127C2314yes—
217#127C2314yes—
218#127C2314yes—
219#127C2312yes—
220#126C2318yes—
221#126C2318yes—
222#126C2318yes—
223#126C2318yes—
224#126C2318yes—
225#126C2318yes—
226#126C2318yes—
227#126C2318yes—
228#126C2318yes—
229#126C2318yes—
230#126C2318yes—
231#125C2314yes—
232#125C2318yes—
233#125C2314yes—
234#125C2318yes—
235#125C2314yes—
236#125C2314yes—
237#125C2314yes—
238#125C2318yes—
239#125C2318yes—
240#125C2318yes—
241#125C2318yes—
242#124C2312yes—
243#124C2312yes—
244#124C2314yes—
245#124C2314yes—
246#124C2314yes—
247#124C2318yes—
248#124C2318yes—
249#124C2314yes—
250#124C2314yes—
251#124C2318yes—
252#124C2318yes—
253#124C2318yes—
254#123C2318yes—
255#123C2318yes—
256#123C2314yes—
257#123C2314yes—
258#123C2314yes—
259#123C2318yes—
260#123C2318yes—
261#123C2318yes—
262#123C2314yes—
263#123C2314yes—
264#123C2318yes—
265#123C2318yes—
266#123C2314yes—
267#123C2318yes—
268#123C2318yes—
269#123C2318yes—
270#123C2318yes—
271#123C2318yes—
272#123C2318yes—
273#123C2318yes—
274#123C2318yes—
275#123C2318yes—
276#123C2318yes—
277#123C2318yes—
278#123C2318yes—
279C22⋊Q8C2312yes—
280C22⋊Q8C2314yes—
281C22⋊Q8C2312yes—
282C22⋊Q8C2314yes—
283C22⋊Q8C2314yes—
284C22⋊Q8C2314yes—
285C22⋊Q8C2314yes—
286C22⋊Q8C2314yes—
287C22⋊Q8C2314yes—
288C22⋊Q8C2314yes—
289C22⋊Q8C2314yes—
290C22⋊Q8C2318yes—
291C22⋊Q8C2314yes—
292C22⋊Q8C2314yes—
293C22⋊Q8C2318yes—
294C22⋊Q8C2318yes—
295C22⋊Q8C2318yes—
296C22⋊Q8C2318yes—
297C22⋊Q8C2318yes—
298C22⋊Q8C2314yes—
299C22⋊Q8C2314yes—
300C22⋊Q8C2314yes—
301C22⋊Q8C2312yes—
302C22⋊Q8C2312yes—
303C22⋊Q8C2314yes—
304C22⋊Q8C2314yes—
305C22⋊Q8C2314yes—
306C22⋊Q8C2314yes—
307C22⋊Q8C2314yes—
308C22⋊Q8C2318yes—
309C22⋊Q8C2318yes—
310C22⋊Q8C2318yes—
311C22⋊Q8C2318yes—
312C22⋊Q8C2318yes—
313C22⋊Q8C2318yes—
314#121C2314yes—
315#121C2314yes—
316#121C2314yes—
317#121C2314yes—
318#121C2318yes—
319#121C2314yes—
320#121C2314yes—
321#121C2318yes—
322#121C2314yes—
323#121C2314yes—
324#121C2318yes—
325#121C2318yes—
326#121C2314yes—
327#121C2314yes—
328#121C2312yes—
329#121C2312yes—
330#121C2314yes—
331#121C2314yes—
332#121C2314yes—
333#121C2314yes—
334#121C2312yes—
335#121C2312yes—
336#121C2314yes—
337#121C2314yes—
338#121C2314yes—
339#121C2314yes—
340#121C2318yes—
341#121C2314yes—
342#121C2314yes—
343#121C2314yes—
344#121C2314yes—
345#121C2314yes—
346#121C2318yes—
347#121C2318yes—
348#121C2318yes—
349#121C2318yes—
350#121C2318yes—
351#121C2318yes—
352#121C2318yes—
353#121C2318yes—
354#121C2318yes—
355#121C2318yes—
356#121C2318yes—
357#120C2314yes—
358#120C2314yes—
359#120C2314yes—
360#120C2318yes—
361#120C2318yes—
362#120C2318yes—
363#120C2318yes—
364#120C2314yes—
365#120C2314yes—
366#120C2314yes—
367C4×Q8C2314yes—
368C4×Q8C2314yes—
369C4×Q8C2312yes—
370C4×Q8C2312yes—
371C4×Q8C2314yes—
372C4×Q8C2314yes—
373C4×Q8C2314yes—
374C4×Q8C2314yes—
375C4×D4C2312yes—
376C4×D4C2312yes—
377C4×D4C2312yes—
378C4×D4C2312yes—
379C4×D4C2314yes—
380C4×D4C2314yes—
381C4×D4C2314yes—
382C4×D4C2314yes—
383C4×D4C2314yes—
384C4×D4C2314yes—
385C4×D4C2314yes—
386C4×D4C2312yes—
387C4×D4C2314yes—
388C4×D4C2314yes—
389C4×D4C2312yes—
390C4×D4C2314yes—
391C4×D4C2318yes—
392C4×D4C2314yes—
393C4×D4C2318yes—
394C4×D4C2314yes—
395C4×D4C2314yes—
396C4×D4C2314yes—
397C4×D4C2318yes—
398C4×D4C2318yes—
399C4×D4C2318yes—
400C4×D4C2314yes—
401C4×D4C2314yes—
402C4×D4C2314yes—
403C4×D4C2314yes—
404C4×D4C2314yes—
405C4×D4C2314yes—
406C4×D4C2318yes—
407C4×D4C2318yes—
408C4×D4C2318yes—
409C4×D4C2318yes—
410C4×D4C2318yes—
411C4×D4C2318yes—
412#117C2314yes—
413#117C2314yes—
414#117C2314yes—
415#117C2314yes—
416#117C2314yes—
417#117C2314yes—
418#117C2312yes—
419#117C2314yes—
420#117C2314yes—
421#117C2314yes—
422#117C2314yes—
423#117C2318yes—
424#117C2318yes—
425#117C2318yes—
426#117C2318yes—
427C2×C4⋊C4C2311yescharacteristic
428C2×C4⋊C4C2311yescharacteristic
429C2×C4⋊C4C2314yes—
430C2×C4⋊C4C2312yes—
431C2×C4⋊C4C2314yes—
432C2×C4⋊C4C2311yescharacteristic
433C2×C4⋊C4C2312yes—
434C2×C4⋊C4C2312yes—
435C2×C4⋊C4C2311yescharacteristic
436C2×C4⋊C4C2314yes—
437C2×C4⋊C4C2312yes—
438C2×C4⋊C4C2314yes—
439C2×C4⋊C4C2314yes—
440C2×C4⋊C4C2314yes—
441C2×C4⋊C4C2318yes—
442C2×C4⋊C4C2312yes—
443C2×C4⋊C4C2318yes—
444C2×C4⋊C4C2312yes—
445C2×C22⋊C4C2311yescharacteristic
446C2×C22⋊C4C2312yes—
447C2×C22⋊C4C2312yes—
448C2×C22⋊C4C2311yescharacteristic
449C2×C22⋊C4C2314yes—
450C2×C22⋊C4C2314yes—
451C2×C22⋊C4C2318yes—
452C2×C22⋊C4C2318yes—
453C2×C22⋊C4C2312yes—
454C2×C22⋊C4C2318yes—
455C2×C42C2312yes—
456C2×C42C2312yes—
457C2×C42C2311yescharacteristic
458C2×C42C2314yes—
459C24C2411yescharacteristic
460C24C2411yescharacteristic
461C24C2414yes—
462C24C2414yes—
463#41—28no—
464#41—28no—
465#41—28no—
466#41—48no—
467#41—48no—
468#41—48no—
469#41—48no—
470#41—48no—
471#41—416no—
472#41—44no—
473#41—44no—
474#41—44no—
475#41—44no—
476#41—48no—
477#41—48no—
478C2×Q8—24no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—48no—
482C2×Q8—48no—
483C2×Q8C2414yes—
484C2×Q8C2412yes—
485C2×Q8C2412yes—
486C2×Q8C2412yes—
487C2×Q8C2414yes—
488C2×Q8C2414yes—
489C2×Q8C2418yes—
490C2×Q8C2414yes—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—48no—
494C2×D4—42no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4C2414yes—
499C2×D4C2412yes—
500C2×D4C2414yes—
501C2×D4C2414yes—
502C2×D4C2414yes—
503C2×D4C2412yes—
504C2×D4C2412yes—
505C2×D4C2412yes—
506C2×D4C2414yes—
507C2×D4C2418yes—
508C2×D4C2414yes—
509C2×D4C2414yes—
510C2×D4C2414yes—
511C2×D4C2414yes—
512C2×D4C2414yes—
513C2×D4C2412yes—
514C2×D4C2418yes—
515C2×D4C2414yes—
516C2×D4C2414yes—
517C2×D4C2414yes—
518C2×D4C2418yes—
519C2×D4C2414yes—
520C2×D4C2414yes—
521C2×D4C2414yes—
522C2×D4C2414yes—
523C2×D4C2414yes—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—44no—
529C22×C4C2411yescharacteristic
530C22×C4C2412yes—
531C22×C4C2414yes—
532C22×C4C2414yes—
533C22×C4C2411yescharacteristic
534C22×C4C2412yes—
535C22×C4C2412yes—
536C22×C4C2414yes—
537C22×C4C2414yes—
538C22×C4C2412yes—
539C22×C4C2412yes—
540C22×C4C2411yescharacteristic
541C22×C4C2412yes—
542C22×C4C2412yes—
543C22×C4C2414yes—
544C22×C4C2411yescharacteristic
545C22×C4C2414yes—
546C22×C4C2414yes—
547C22×C4C2412yes—
548C22×C4C2418yes—
549C22×C4C2418yes—
550C22×C4C2414yes—
551C22×C4C2418yes—
552C22×C4C2418yes—
553C22×C4C2414yes—
554C22×C4C2414yes—
555C22×C4C2414yes—
556C22×C4C2414yes—
557C22×C4C2414yes—
558C22×C4C2411yescharacteristic
559C4⋊C4C2414yes—
560C4⋊C4C2414yes—
561C4⋊C4C2414yes—
562C4⋊C4C2412yes—
563C4⋊C4C2414yes—
564C4⋊C4C2418yes—
565C4⋊C4C2414yes—
566C4⋊C4C2412yes—
567C4⋊C4C2412yes—
568C4⋊C4C2418yes—
569C4⋊C4C2418yes—
570C4⋊C4C2414yes—
571C4⋊C4C2414yes—
572C4⋊C4C2414yes—
573C4⋊C4C2414yes—
574C4⋊C4C2418yes—
575C4⋊C4C2418yes—
576C4⋊C4C2418yes—
577C4⋊C4C2414yes—
578C4⋊C4C2412yes—
579C4⋊C4C2414yes—
580C4⋊C4C2414yes—
581C4⋊C4C2414yes—
582C4⋊C4C2418yes—
583C4⋊C4C2418yes—
584C4⋊C4C2418yes—
585C4⋊C4C2418yes—
586C4⋊C4C2414yes—
587C4⋊C4C2418yes—
588C4⋊C4C2414yes—
589C4⋊C4C2414yes—
590C4⋊C4C2414yes—
591C4⋊C4C2414yes—
592C4⋊C4C2414yes—
593C22⋊C4C2411yescharacteristic
594C22⋊C4C2414yes—
595C22⋊C4C2414yes—
596C22⋊C4C2412yes—
597C22⋊C4C2418yes—
598C22⋊C4C2414yes—
599C22⋊C4C2418yes—
600C22⋊C4C2411yescharacteristic
601C22⋊C4C2411yescharacteristic
602C22⋊C4C2411yescharacteristic
603C22⋊C4C2414yes—
604C22⋊C4C2418yes—
605C22⋊C4C2414yes—
606C22⋊C4C2418yes—
607C22⋊C4C2418yes—
608C22⋊C4C2418yes—
609C22⋊C4C2418yes—
610C22⋊C4C2414yes—
611C22⋊C4C2414yes—
612C22⋊C4C2412yes—
613C22⋊C4C2414yes—
614C22⋊C4C2418yes—
615C22⋊C4C2418yes—
616C22⋊C4C2414yes—
617C22⋊C4C2414yes—
618C22⋊C4C2414yes—
619C22⋊C4C2414yes—
620C22⋊C4C2414yes—
621C22⋊C4C2414yes—
622C22⋊C4C2418yes—
623C22⋊C4C2418yes—
624C22⋊C4C2418yes—
625C22⋊C4C2414yes—
626C22⋊C4C2418yes—
627C22⋊C4C2414yes—
628C22⋊C4C2414yes—
629C42C2412yes—
630C42C2414yes—
631C42C2414yes—
632C42C2414yes—
633C42C2414yes—
634C42C2414yes—
635C42C2412yes—
636C42C2414yes—
637C42C2414yes—
638C42C2418yes—
639C42C2418yes—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—28no—
644C23—41no—
645C23—44no—
646C23—44no—
647C23—41no—
648C23—44no—
649C23—41no—
650C23—44no—
651C23—44no—
652C23C2512yes—
653C23C2514yes—
654C23C2511yescharacteristic
655C23C2514yes—
656C23C2514yes—
657C23C2511yescharacteristic
658C23C2511yescharacteristic
659Q8—28no—
660Q8—24no—
661Q8—24no—
662Q8—24no—
663Q8—48no—
664Q8—44no—
665Q8—44no—
666Q8—44no—
667D4—28no—
668D4—28no—
669D4—28no—
670D4—24no—
671D4—28no—
672D4—24no—
673D4—24no—
674D4—24no—
675D4—48no—
676D4—44no—
677D4—44no—
678D4—42no—
679D4—44no—
680D4—44no—
681D4—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685D4—44no—
686D4—44no—
687D4—44no—
688D4—48no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—48no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—48no—
717C2×C4—41no—
718C2×C4—44no—
719C2×C4—48no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4H(5,𝔽2)14yes—
723C2×C4C2511yescharacteristic
724C2×C4C2511yescharacteristic
725C2×C4C2514yes—
726C2×C4C2514yes—
727C2×C4C2514yes—
728C2×C4C2514yes—
729C2×C4C2512yes—
730C2×C4C2511yescharacteristic
731C2×C4C2511yescharacteristic
732C2×C4C2514yes—
733C2×C4C2514yes—
734C2×C4C2514yes—
735C2×C4C2514yes—
736C2×C4C2514yes—
737C2×C4C2512yes—
738C2×C4C2512yes—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—21no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—21no—
749C22—24no—
750C22—24no—
751C22—22no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—21no—
756C22—24no—
757C22—22no—
758C22—44no—
759C22—88no—
760C22—82no—
761C22—88no—
762C22C2×H(5,𝔽2)12yes—
763C22#58512yes—
764C22C2611yescharacteristic
765C4—21no—
766C4—22no—
767C4—21no—
768C4—24no—
769C4—24no—
770C4—24no—
771C4—24no—
772C4—24no—
773C4—24no—
774C4—22no—
775C4—24no—
776C4—21no—
777C4—24no—
778C4—24no—
779C4—21no—
780C4C2×H(5,𝔽2)14yes—
781C2—22no—
782C2—22no—
783C2—41no—
784C2—44no—
785C2—44no—
786C2—44no—
787C2—42no—
788C2C22×H(5,𝔽2)11yescharacteristic
789C2C2×#58511yescharacteristic
790C22−1+611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC22C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #3560C2semidirect
2. #3559C2semidirect
3. #3551C2semidirect
4. #3547C2semidirect
5. #3542C2semidirect
6. #3541C2semidirect
7. #3539C2semidirect
8. #3538C2semidirect
9. #3534C2semidirect
10. #3520C2semidirect
11. #3512C2semidirect
12. #3505C2semidirect
13. #3497C2semidirect
14. #3494C2semidirect
15. #3493C2semidirect
16. #3492C2semidirect
17. #3489C2semidirect
18. #3489C2semidirect
19. C2×#552C2semidirect
20. D4×#41C2semidirect
21. #3461C2semidirect
22. #3449C2semidirect
23. C2×#537C2semidirect
24. C2×2−1+4C22semidirect
25. C22×#41C22semidirect
26. C22×#41C22semidirect
27. #563C22semidirect
28. #563C22semidirect
29. #562C22semidirect
30. #562C22semidirect
31. #560C22semidirect
32. #560C22semidirect
33. #556C22semidirect
34. #555C22semidirect
35. #555C22semidirect
36. #554C22semidirect
37. #554C22semidirect
38. #553C22semidirect
39. #553C22semidirect
40. #553C22semidirect
41. #553C22semidirect
42. #553C22semidirect
43. #553C22semidirect
44. #553C22semidirect
45. #553C22semidirect
46. #553C22semidirect
47. #552C22semidirect
48. #552C22semidirect
49. #552C22semidirect
50. #552C22semidirect
51. #552C22semidirect
52. #552C22semidirect
53. #552C22semidirect
54. #552C22semidirect
55. #551C22semidirect
56. #551C22semidirect
57. #551C22semidirect
58. #551C22semidirect
59. #550C22semidirect
60. #550C22semidirect
61. D4×Q8C22semidirect
62. D4×Q8C22semidirect
63. D4×Q8C22semidirect
64. D4×Q8C22semidirect
66. #548C22semidirect
67. #548C22semidirect
68. #548C22semidirect
69. #548C22semidirect
70. #548C22semidirect
71. #547C22semidirect
72. #547C22semidirect
73. #547C22semidirect
74. #547C22semidirect
75. #547C22semidirect
76. #547C22semidirect
77. #547C22semidirect
79. #546C22semidirect
80. #546C22semidirect
81. #546C22semidirect
82. #546C22semidirect
83. #546C22semidirect
84. #546C22semidirect
85. #546C22semidirect
86. #546C22semidirect
88. D42C22semidirect
89. #544C22semidirect
90. #544C22semidirect
91. #544C22semidirect
92. #542C22semidirect
93. #542C22semidirect
94. #542C22semidirect
95. #542C22semidirect
96. #541C22semidirect
97. #541C22semidirect
98. #540C22semidirect
99. #540C22semidirect
100. #540C22semidirect
101. #540C22semidirect
102. #540C22semidirect
103. #539C22semidirect
104. #539C22semidirect
105. #539C22semidirect
106. #539C22semidirect
107. #539C22semidirect
108. #539C22semidirect
109. #538C22semidirect
110. #538C22semidirect
111. #538C22semidirect
112. #538C22semidirect
114. #537C22semidirect
115. #537C22semidirect
116. #537C22semidirect
117. #537C22semidirect
118. #537C22semidirect
119. #537C22semidirect
120. #537C22semidirect
121. #537C22semidirect
122. #537C22semidirect
123. #537C22semidirect
124. #536C22semidirect
125. #536C22semidirect
126. #536C22semidirect
127. #536C22semidirect
128. #535C22semidirect
129. #535C22semidirect
130. #534C22semidirect
131. #534C22semidirect
132. #533C22semidirect
133. #532C22semidirect
134. #532C22semidirect
135. #532C22semidirect
136. #532C22semidirect
137. #529C22semidirect
138. #529C22semidirect
139. #529C22semidirect
140. #529C22semidirect
141. #529C22semidirect
142. C2×#126C22semidirect
143. C2×#125C22semidirect
144. C2×#125C22semidirect
146. #525C22semidirect
147. #525C22semidirect
148. #525C22semidirect
149. #525C22semidirect
150. #525C22semidirect
151. #525C22semidirect
152. #525C22semidirect
153. #525C22semidirect
155. C2×C22⋊Q8C22semidirect
156. C2×C22⋊Q8C22semidirect
157. C2×C22⋊Q8C22semidirect
158. C2×C22⋊Q8C22semidirect
159. C2×C22⋊Q8C22semidirect
160. C2×#121C22semidirect
161. C2×#121C22semidirect
162. #520C22semidirect
163. #520C22semidirect
164. #520C22semidirect
165. #518C22semidirect
166. C4×#41C22semidirect
167. C2×C4×Q8C22semidirect
169. C2×C4×D4C22semidirect
170. C2×#117C22semidirect
171. C2×#117C22semidirect
172. C22×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#35602
#35592
#35512
#35472
#35422
#35412
#35392
#35382
#35342
#35202
#35122
#35052
#34972
#34942
#34932
#34922
#34892
C2×#5522
D4×#412
#34612
#34492
C2×#5372