Finite Group Databasebeta

← #8093067

Subgroups — #8093067

Order 512.

5533 conjugacy classes of subgroups.

The subgroup lattice has 979 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52989C212yesmaximal, complemented
2#52988C212yesmaximal, complemented
3#52987C211yesmaximal, characteristic, complemented
4#52986C211yesmaximal, characteristic, complemented
5#52985C212yesmaximal, complemented
6#52971C214yesmaximal, complemented
7#52963C214yesmaximal, complemented
8#52891C214yesmaximal, complemented
9#52762C214yesmaximal, complemented
10#52669C214yesmaximal, complemented
11#52422C214yesmaximal, complemented
12#52163C214yesmaximal, complemented
13#52096C214yesmaximal, complemented
14#36676C214yesmaximal, complemented
15#36670C214yesmaximal, complemented
16#34963C212yesmaximal, complemented
17#34937C212yesmaximal, complemented
18#34788C214yesmaximal, complemented
19#34681C214yesmaximal, complemented
20#34621C212yesmaximal, complemented
21#34547C211yesmaximal, characteristic, complemented
22C2×#532C2212yes—
23C2×#532C2214yescomplemented
24C2×#525C2218yescomplemented
25C2×C4×#41C2211yescharacteristic
26C2×C4×#41C2211yescharacteristic, complemented
27C22×C4×D4C2212yescomplemented
28#2842C2214yescomplemented
29#2834C2214yescomplemented
30#2833C2214yescomplemented
31#2832C2214yescomplemented
32#2831C2218yescomplemented
33#2830C2214yescomplemented
34#2829C2218yescomplemented
35#2828C2214yes—
36#2827C2218yescomplemented
37#2827C2218yescomplemented
38#2827C2218yescomplemented
39#2827C2218yescomplemented
40#2826C2214yes—
41#2826C2218yescomplemented
42#2826C2218yescomplemented
43#2825C2218yescomplemented
44#2825C2218yescomplemented
45#2824C2218yescomplemented
46#2812C2214yes—
47#2812C2218yescomplemented
48#2732C2218yescomplemented
49#2728C2214yes—
50#2728C2214yescomplemented
51#2724C2214yescomplemented
52#2708C2218yescomplemented
53#2708C2218yescomplemented
54#2697C2218yescomplemented
55#2679C2214yes—
56#2677C2214yescomplemented
57#2676C2218yescomplemented
58#2675C2214yes—
59#2674C2218yescomplemented
60#2673C2218yescomplemented
61#2672C2218yescomplemented
62#2671C2218yescomplemented
63#2670C2214yes—
64#2669C2218yescomplemented
65#2668C2218yes—
66#2668C2214yescomplemented
67#2668C2218yescomplemented
68#2651C2218yescomplemented
69#2648C2218yescomplemented
70#2647C2212yescomplemented
71#2644C2214yescomplemented
72#2641C2212yes—
73#2629C2212yescomplemented
74#2624C2214yescomplemented
75#2619C2212yes—
76#2598C2214yes—
77#2598C2214yescomplemented
78#2580C2214yescomplemented
79#2548C2212yes—
80#2547C2212yescomplemented
81#2546C2212yescomplemented
82#2545C2214yescomplemented
83#2544C2214yescomplemented
84#2543C2214yescomplemented
85#2543C2214yescomplemented
86#2541C2212yes—
87#2535C2214yes—
88#2525C2218yescomplemented
89#2516C2218yescomplemented
90#2513C2214yescomplemented
91#2510C2218yescomplemented
92#2509C2214yescomplemented
93#2504C2214yescomplemented
94#2494C2214yescomplemented
95#2490C2214yes—
96#2487C2212yes—
97#2487C2212yescomplemented
98#2487C2214yescomplemented
99#2482C2214yescomplemented
100#2472C2218yescomplemented
101#2464C2218yescomplemented
102#2461C2218yescomplemented
103#2452C2214yescomplemented
104#2445C2214yes—
105#2444C2218yescomplemented
106#2442C2214yescomplemented
107#2440C2214yescomplemented
108#2433C2214yes—
109#2428C2214yes—
110#2424C2218yescomplemented
111#2422C2214yescomplemented
112#2416C2214yes—
113#2416C2214yes—
114#2416C2214yescomplemented
115#2416C2214yescomplemented
116#2408C2212yes—
117#2408C2214yescomplemented
118#2408C2212yescomplemented
119#2404C2214yes—
120#2401C2218yescomplemented
121#2399C2211yescharacteristic, complemented
122#2398C2211yescharacteristic
123#2398C2214yescomplemented
124#2398C2211yescharacteristic, complemented
125#2397C2214yes—
126#2397C2211yescharacteristic
127#2396C2212yescomplemented
128#2396C2212yescomplemented
129#2395C2212yescomplemented
130#2395C2218yescomplemented
131#2395C2212yescomplemented
132#2395C2218yescomplemented
133#2392C2212yes—
134#2392C2218yescomplemented
135#2392C2218yescomplemented
136#2392C2214yescomplemented
137#2392C2214yescomplemented
138#2392C2212yescomplemented
139#2392C2214yescomplemented
140#2388C2212yes—
141#2388C2218yescomplemented
142#2388C2212yescomplemented
143C4×#127C2212yes—
144C4×#125C2212yescomplemented
145C4×#121C2214yes—
146C4×#121C2214yescomplemented
147C4×#121C2214yescomplemented
148C4×#121C2218yescomplemented
149C4×#120C2214yes—
150C4×#120C2218yescomplemented
151C4×#120C2214yescomplemented
152#2297C2214yescomplemented
153#2293C2214yescomplemented
154#2290C2218yescomplemented
155#2283C2212yescomplemented
156C42×D4C2214yescomplemented
157C4×#117C2211yescharacteristic, complemented
158C2×C4×C4⋊C4C2212yescomplemented
159C22×#41C2311yescharacteristic
160C22×#41C2314yes—
161C22×#41C2311yescharacteristic
162C23×D4C2312yes—
163C24×C4C2314yes—
164#532—48no—
165#532—416no—
166C2×C4⋊Q8C2314yes—
167C2×C4⋊Q8C2312yes—
168C2×#127C2312yes—
169C2×#127C2314yes—
170C2×#127C2312yes—
171C2×#125C2312yes—
172C2×#124C2314yes—
173C2×#124C2314yes—
174C2×#124C2314yes—
175#525—432no—
176C2×#123C2318yes—
177C2×#123C2318yes—
178C2×C22⋊Q8C2318yes—
179C2×C22⋊Q8C2318yes—
180C2×#121C2314yes—
181C2×#121C2314yes—
182C2×#121C2314yes—
183C2×#121C2314yes—
184C2×#121C2318yes—
185C2×#121C2318yes—
186C2×#121C2318yes—
187C2×#121C2318yes—
188C2×#121C2318yes—
189C2×#121C2314yes—
190C2×#120C2314yes—
191C2×#120C2314yes—
192C2×#120C2318yes—
193C2×#120C2318yes—
194C2×#120C2318yes—
195C4×#41—44no—
196C4×#41—44no—
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2311yescharacteristic
200C2×C4×Q8C2311yescharacteristic
201C2×C4×D4—48no—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2318yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2311yescharacteristic
213C2×C4×D4C2314yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2314yes—
219C2×C4×D4C2318yes—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117C2312yes—
223C2×#117C2311yescharacteristic
224C2×#117C2312yes—
225C2×#117C2312yes—
226C2×#117C2311yescharacteristic
227C2×#117C2318yes—
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2314yes—
230C22×C22⋊C4C2314yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2312yes—
234C22×C42C2314yes—
235#401C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2314yes—
240#400C2318yes—
241#400C2312yes—
242#400C2314yes—
243#400C2318yes—
244#400C2312yes—
245#399C2312yes—
246#399C2312yes—
247#399C2318yes—
248#399C2318yes—
249#399C2314yes—
250#399C2318yes—
251#399C2314yes—
252#398C2312yes—
253#398C2318yes—
254#398C2314yes—
255#398C2318yes—
256#398C2318yes—
257#398C2318yes—
258#398C2314yes—
259#398C2314yes—
260#398C2312yes—
261#397C2318yes—
262#397C2318yes—
263#397C2314yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2314yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2314yes—
275#397C2312yes—
276#397C2318yes—
277#397C2312yes—
278#396C2314yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2314yes—
287#395C2312yes—
288#395C2318yes—
289#395C2312yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2314yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2314yes—
302#394C2314yes—
303#394C2318yes—
304#394C2318yes—
305#394C2314yes—
306#394C2318yes—
307#394C2318yes—
308#394C2314yes—
309#394C2318yes—
310#394C2312yes—
311#394C2314yes—
312#394C2312yes—
313#394C2314yes—
314#393C2312yes—
315#393C2318yes—
316#393C2318yes—
317#393C2312yes—
318#392C2318yes—
319#392C2318yes—
320#392C2314yes—
321#392C2314yes—
322#392C2314yes—
323#392C2318yes—
324#392C2318yes—
325#392C2314yes—
326#392C2318yes—
327#392C2318yes—
328#392C2314yes—
329#392C2312yes—
330#392C2312yes—
331#391C2314yes—
332#391C2314yes—
333#390C2314yes—
334#390C2318yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2318yes—
342#390C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2314yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2314yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#385C2318yes—
379#385C2314yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2314yes—
387#384C2312yes—
388#383C2314yes—
389#382C2312yes—
390#382C2314yes—
391#381C2314yes—
392#380C2314yes—
393#380C2312yes—
394#380C2312yes—
395#380C2314yes—
396#380C2318yes—
397#380C2314yes—
398#379C2314yes—
399#379C2318yes—
400#379C2314yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2314yes—
412C4×C22⋊C4C2312yes—
413C4×C22⋊C4C2314yes—
414C4×C22⋊C4C2314yes—
415C4×C22⋊C4C2312yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425#376C2311yescharacteristic
426#376C2311yescharacteristic
427#376C2314yes—
428C2×#95C2314yes—
429C43C2312yes—
430C25C2414yes—
431C2×#41—28no—
432C2×#41—216no—
433C2×#41—42no—
434C2×#41—42no—
435C2×#41—48no—
436C2×#41—48no—
437C2×#41—44no—
438C22×Q8C2411yescharacteristic
439C22×Q8C2414yes—
440C22×Q8C2411yescharacteristic
441C22×D4—44no—
442C22×D4—48no—
443C22×D4C2414yes—
444C22×D4C2414yes—
445C22×D4C2411yescharacteristic
446C22×D4C2411yescharacteristic
447C22×D4C2412yes—
448C22×D4C2412yes—
449C22×D4C2418yes—
450C22×D4C2418yes—
451C22×D4C2414yes—
452C22×D4C2418yes—
453C22×D4C2414yes—
454C22×D4C2414yes—
455C22×D4C2418yes—
456C22×D4C2418yes—
457C23×C4—48no—
458C23×C4—416no—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2418yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2411yescharacteristic
468C23×C4C2412yes—
469C23×C4C2414yes—
470C23×C4C2418yes—
471C23×C4C2418yes—
472C4⋊Q8—44no—
473C4⋊Q8—48no—
474#127—44no—
475#127—44no—
476#127—48no—
477#125—44no—
478#124—48no—
479#124—48no—
480#124—48no—
481#123—416no—
482#123—416no—
483C22⋊Q8—416no—
484C22⋊Q8—416no—
485#121—48no—
486#121—416no—
487#121—416no—
488#121—416no—
489#121—416no—
490#121—416no—
491#121—48no—
492#121—48no—
493#121—48no—
494#121—48no—
495#120—416no—
496#120—416no—
497#120—48no—
498#120—48no—
499#120—416no—
500C4×Q8—42no—
501C4×Q8—42no—
502C4×Q8—42no—
503C4×Q8—42no—
504C4×D4—216no—
505C4×D4—232no—
506C4×D4—216no—
507C4×D4—48no—
508C4×D4—48no—
509C4×D4—48no—
510C4×D4—48no—
511C4×D4—42no—
512C4×D4—42no—
513C4×D4—44no—
514C4×D4—44no—
515C4×D4—42no—
516C4×D4—42no—
517C4×D4—44no—
518C4×D4—44no—
519C4×D4—416no—
520C4×D4—416no—
521C4×D4—48no—
522C4×D4—416no—
523C4×D4—48no—
524#117—44no—
525#117—42no—
526#117—42no—
527#117—44no—
528#117—44no—
529#117—416no—
530C2×C4⋊C4—48no—
531C2×C4⋊C4—44no—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2411yescharacteristic
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2411yescharacteristic
544C2×C4⋊C4C2411yescharacteristic
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2411yescharacteristic
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C22⋊C4—48no—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C42—28no—
596C2×C42—24no—
597C2×C42—28no—
598C2×C42—48no—
599C2×C42C2412yes—
600C2×C42C2411yescharacteristic
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2411yescharacteristic
605C2×C42C2412yes—
606C2×C42C2412yes—
607C2×C42C2414yes—
608C2×C42C2412yes—
609C2×C42C2411yescharacteristic
610C2×C42C2418yes—
611C2×C42C2412yes—
612C2×C42C2414yes—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2411yescharacteristic
616#95C2418yes—
617#95C2414yes—
618#95C2414yes—
619#95C2412yes—
620#95C2412yes—
621#95C2412yes—
622#95C2412yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643C24—28no—
644C24—44no—
645C24—48no—
646C24—48no—
647C24—44no—
648C24C2518yes—
649C24C2511yescharacteristic
650C24C2512yes—
651C24C2512yes—
652#41—416no—
653#41—416no—
654#41—832no—
655C2×Q8—24no—
656C2×Q8—28no—
657C2×Q8—41no—
658C2×Q8—41no—
659C2×Q8—42no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×D4—28no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—28no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—216no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—24no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—44no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—41no—
680C2×D4—41no—
681C2×D4—44no—
682C2×D4—48no—
683C2×D4—42no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—44no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—48no—
700C2×D4—432no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—216no—
712C22×C4—28no—
713C22×C4—216no—
714C22×C4—216no—
715C22×C4—24no—
716C22×C4—28no—
717C22×C4—24no—
718C22×C4—28no—
719C22×C4—24no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—48no—
723C22×C4—44no—
724C22×C4—48no—
725C22×C4—48no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—832no—
732C22×C4H(5,𝔽2)18yes—
733C22×C4C2512yes—
734C22×C4C2511yescharacteristic
735C22×C4C2512yes—
736C22×C4C2512yes—
737C22×C4C2518yes—
738C22×C4C2514yes—
739C22×C4C2518yes—
740C22×C4C2514yes—
741C22×C4C2512yes—
742C22×C4C2511yescharacteristic
743C22×C4C2512yes—
744C22×C4C2518yes—
745C22×C4C2511yescharacteristic
746C22×C4C2511yescharacteristic
747C22×C4C2512yes—
748C22×C4C2511yescharacteristic
749C22×C4C2511yescharacteristic
750C4⋊C4—28no—
751C4⋊C4—216no—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—48no—
756C4⋊C4—44no—
757C4⋊C4—44no—
758C4⋊C4—42no—
759C4⋊C4—42no—
760C4⋊C4—41no—
761C4⋊C4—42no—
762C4⋊C4—42no—
763C4⋊C4—41no—
764C4⋊C4—41no—
765C4⋊C4—41no—
766C4⋊C4—48no—
767C4⋊C4—48no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—48no—
772C4⋊C4—48no—
773C4⋊C4—48no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C22⋊C4—28no—
777C22⋊C4—216no—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—216no—
781C22⋊C4—28no—
782C22⋊C4—216no—
783C22⋊C4—48no—
784C22⋊C4—44no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C22⋊C4—42no—
789C22⋊C4—42no—
790C22⋊C4—42no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—44no—
807C22⋊C4—48no—
808C22⋊C4—48no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C42—24no—
813C42—24no—
814C42—22no—
815C42—22no—
816C42—24no—
817C42—24no—
818C42—22no—
819C42—24no—
820C42—24no—
821C42—216no—
822C42—28no—
823C42—24no—
824C42—24no—
825C42—44no—
826C42—44no—
827C42—44no—
828C42H(5,𝔽2)14yes—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—28no—
838C23—28no—
839C23—21no—
840C23—28no—
841C23—22no—
842C23—28no—
843C23—22no—
844C23—28no—
845C23—28no—
846C23—28no—
847C23—22no—
848C23—416no—
849C23—88no—
850C23—816no—
851C23—88no—
852C23—816no—
853C23C2×H(5,𝔽2)14yes—
854C23#58514yes—
855C23C2611yescharacteristic
856Q8—44no—
857Q8—44no—
858Q8—88no—
859D4—48no—
860D4—416no—
861D4—44no—
862D4—44no—
863D4—48no—
864D4—416no—
865D4—416no—
866D4—88no—
867D4—816no—
868D4—816no—
869D4—816no—
870D4—88no—
871D4—816no—
872D4—816no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—216no—
877C2×C4—22no—
878C2×C4—21no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—22no—
893C2×C4—28no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—28no—
900C2×C4—22no—
901C2×C4—28no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—28no—
907C2×C4—22no—
908C2×C4—28no—
909C2×C4—48no—
910C2×C4—44no—
911C2×C4—48no—
912C2×C4—44no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—432no—
916C2×C4—44no—
917C2×C4—84no—
918C2×C4—816no—
919C2×C4—816no—
920C2×C4—88no—
921C2×C4C2×H(5,𝔽2)12yes—
922C2×C4C2×H(5,𝔽2)14yes—
923C2×C4C2×H(5,𝔽2)12yes—
924C2×C4C2×H(5,𝔽2)14yes—
925C2×C4C2×H(5,𝔽2)12yes—
926C2×C4#58514yes—
927C22—24no—
928C22—24no—
929C22—28no—
930C22—28no—
931C22—42no—
932C22—42no—
933C22—44no—
934C22—44no—
935C22—42no—
936C22—42no—
937C22—48no—
938C22—41no—
939C22—41no—
940C22—48no—
941C22—44no—
942C22—48no—
943C22—48no—
944C22—48no—
945C22—48no—
946C22—41no—
947C22—48no—
948C22—832no—
949C22C22×H(5,𝔽2)11yescharacteristic
950C22C22×H(5,𝔽2)12yes—
951C22C2×#58512yes—
952C22C2×#58512yes—
953C4—24no—
954C4—22no—
955C4—42no—
956C4—48no—
957C4—41no—
958C4—42no—
959C4—41no—
960C4—42no—
961C4—48no—
962C4—48no—
963C4—44no—
964C4—44no—
965C4—42no—
966C4—41no—
967C4—42no—
968C4#352914yes—
969C4#353714yes—
970C2—44no—
971C2—44no—
972C2—81no—
973C2—88no—
974C2C2×#352911yescharacteristic
975C2C2×#353711yescharacteristic
976C2#6272911yescharacteristic
977C2#6274814yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52989C2semidirect
2. #52988C2semidirect
3. #52987C2semidirect
4. #52986C2semidirect
5. #52985C2semidirect
6. #52971C2semidirect
7. #52963C2semidirect
8. #52891C2semidirect
9. #52762C2semidirect
10. #52669C2semidirect
11. #52422C2semidirect
12. #52163C2semidirect
13. #52096C2semidirect
14. #36676C2semidirect
15. #36670C2semidirect
16. #34963C2semidirect
17. #34937C2semidirect
18. #34788C2semidirect
19. #34681C2semidirect
20. #34621C2semidirect
21. #34547C2semidirect
23. C2×#532C22semidirect
24. C2×#525C22semidirect
26. C2×C4×#41C22semidirect
27. C22×C4×D4C22semidirect
28. #2842C22semidirect
29. #2834C22semidirect
30. #2833C22semidirect
31. #2832C22semidirect
32. #2831C22semidirect
33. #2830C22semidirect
34. #2829C22semidirect
36. #2827C22semidirect
37. #2827C22semidirect
38. #2827C22semidirect
39. #2827C22semidirect
41. #2826C22semidirect
42. #2826C22semidirect
43. #2825C22semidirect
44. #2825C22semidirect
45. #2824C22semidirect
47. #2812C22semidirect
48. #2732C22semidirect
50. #2728C22semidirect
51. #2724C22semidirect
52. #2708C22semidirect
53. #2708C22semidirect
54. #2697C22semidirect
56. #2677C22semidirect
57. #2676C22semidirect
59. #2674C22semidirect
60. #2673C22semidirect
61. #2672C22semidirect
62. #2671C22semidirect
64. #2669C22semidirect
66. #2668C22semidirect
67. #2668C22semidirect
68. #2651C22semidirect
69. #2648C22semidirect
70. #2647C22semidirect
71. #2644C22semidirect
73. #2629C22semidirect
74. #2624C22semidirect
77. #2598C22semidirect
78. #2580C22semidirect
80. #2547C22semidirect
81. #2546C22semidirect
82. #2545C22semidirect
83. #2544C22semidirect
84. #2543C22semidirect
85. #2543C22semidirect
88. #2525C22semidirect
89. #2516C22semidirect
90. #2513C22semidirect
91. #2510C22semidirect
92. #2509C22semidirect
93. #2504C22semidirect
94. #2494C22semidirect
97. #2487C22semidirect
98. #2487C22semidirect
99. #2482C22semidirect
100. #2472C22semidirect
101. #2464C22semidirect
102. #2461C22semidirect
103. #2452C22semidirect
105. #2444C22semidirect
106. #2442C22semidirect
107. #2440C22semidirect
110. #2424C22semidirect
111. #2422C22semidirect
114. #2416C22semidirect
115. #2416C22semidirect
117. #2408C22semidirect
118. #2408C22semidirect
120. #2401C22semidirect
121. #2399C22semidirect
123. #2398C22semidirect
124. #2398C22semidirect
127. #2396C22semidirect
128. #2396C22semidirect
129. #2395C22semidirect
130. #2395C22semidirect
131. #2395C22semidirect
132. #2395C22semidirect
134. #2392C22semidirect
135. #2392C22semidirect
136. #2392C22semidirect
137. #2392C22semidirect
138. #2392C22semidirect
139. #2392C22semidirect
141. #2388C22semidirect
142. #2388C22semidirect
144. C4×#125C22semidirect
146. C4×#121C22semidirect
147. C4×#121C22semidirect
148. C4×#121C22semidirect
150. C4×#120C22semidirect
151. C4×#120C22semidirect
152. #2297C22semidirect
153. #2293C22semidirect
154. #2290C22semidirect
155. #2283C22semidirect
156. C42×D4C22semidirect
157. C4×#117C22semidirect
158. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#529892
#529882
#529872
#529862
#529852
#529712
#529632
#528912
#527622
#526692
#524222
#521632
#520962
#366762
#366702
#349632
#349372
#347882
#346812
#346212
#345472