Finite Group Databasebeta

← #7634873

Subgroups — #7634873

Order 512.

8770 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3449C212yesmaximal, complemented
2#52167C214yesmaximal, complemented
3#52165C218yesmaximal, complemented
4#52163C214yesmaximal, complemented
5#37419C212yesmaximal, complemented
6#37418C212yesmaximal, complemented
7#37388C214yesmaximal, complemented
8#37386C211yesmaximal, characteristic, complemented
9#37300C214yesmaximal, complemented
10#37297C211yesmaximal, characteristic, complemented
11#37296C212yesmaximal, complemented
12#37190C214yesmaximal, complemented
13#37129C214yesmaximal, complemented
14#36737C218yesmaximal, complemented
15#36624C212yesmaximal, complemented
16#34810C214yesmaximal, complemented
17#34738C214yesmaximal, complemented
18#34633C212yesmaximal, complemented
19C2×#2297C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C23×#41C2212yescomplemented
22#3449—232no—
23C2×#537C2214yes—
24C2×#537C2214yescomplemented
25C2×#536C2212yes—
26C2×#536C2212yescomplemented
27C2×#536C2214yescomplemented
28C2×#535C2212yes—
29C2×#535C2214yes—
30C2×#535C2212yescomplemented
31C2×#534C2214yes—
32C2×#534C2214yescomplemented
33C2×#532C2214yes—
34C2×#532C2212yes—
35C2×#532C2212yes—
36C2×#532C2214yescomplemented
37C2×#525C2214yes—
38C2×#525C2214yes—
39C2×#525C2214yescomplemented
40C2×#525C2214yescomplemented
41C22×#117C2212yescomplemented
42C22×#117C2211yescharacteristic, complemented
43C23×C42C2211yescharacteristic, complemented
44#2857C2212yescomplemented
45#2857C2212yescomplemented
46#2856C2212yescomplemented
47#2856C2212yescomplemented
48#2854C2218yescomplemented
49#2850C2214yescomplemented
50#2850C2214yescomplemented
51#2847C2218yescomplemented
52#2734C2214yescomplemented
53#2733C2214yescomplemented
54#2732C2218yescomplemented
55#2731C2218yescomplemented
56#2730C22116yescomplemented
57#2729C22116yescomplemented
58#2728C2218yescomplemented
59#2724C2214yescomplemented
60#2717C2218yescomplemented
61#2709C2218yescomplemented
62#2708C22116yescomplemented
63#2701C22116yescomplemented
64#2699C2218yescomplemented
65#2697C2218yescomplemented
66#2688C22116yescomplemented
67#2686C22116yescomplemented
68#2684C2218yescomplemented
69#2682C2218yescomplemented
70#2679C2214yescomplemented
71#2678C22116yescomplemented
72#2673C22116yescomplemented
73#2671C22116yescomplemented
74#2669C2218yescomplemented
75#2668C22116yescomplemented
76#2621C2212yescomplemented
77#2621C2212yescomplemented
78#2620C2214yescomplemented
79#2620C2214yescomplemented
80#2619C2212yescomplemented
81#2619C2212yescomplemented
82#2618C2218yescomplemented
83#2617C2218yescomplemented
84#2504C2214yescomplemented
85#2503C2214yescomplemented
86#2502C2214yescomplemented
87#2501C2214yescomplemented
88#2500C2214yescomplemented
89#2500C2214yescomplemented
90#2499C2214yescomplemented
91#2499C2214yescomplemented
92#2498C22116yescomplemented
93#2436C2214yescomplemented
94#2435C2214yescomplemented
95#2434C2214yescomplemented
96#2433C2214yescomplemented
97#2432C2214yescomplemented
98#2432C2214yescomplemented
99#2431C2214yescomplemented
100#2431C2214yescomplemented
101#2430C22116yescomplemented
102#2412C22116yescomplemented
103#2410C22116yescomplemented
104#2395C22116yescomplemented
105#2392C2218yescomplemented
106#2392C2218yescomplemented
107#2388C22116yescomplemented
108C4×#123C22116yescomplemented
109C4×#121C2218yescomplemented
110C4×#121C2218yescomplemented
111C4×#120C22116yescomplemented
112#2297C2211yescharacteristic
113#2297C2211yescharacteristic
114#2297C2212yes—
115#2297C2214yescomplemented
116#2297C2214yescomplemented
117#2297C2211yescharacteristic, complemented
118#2297C2214yescomplemented
119#2297C2211yescharacteristic, complemented
120#2297C2214yescomplemented
121#2297C2212yescomplemented
122C2×#391C2212yescomplemented
123C2×#390C2212yes—
124C2×#386C2214yescomplemented
125#2285C2212yescomplemented
126#2285C2212yescomplemented
127C2×C4×C22⋊C4C2214yescomplemented
128C22×#41—216no—
129C22×#41—44no—
130C22×#41—44no—
131C22×#41—48no—
132C22×#41—48no—
133C22×#41D4116yescomplemented
134C22×#41C2314yes—
135C22×#41C2314yes—
136C22×#41C2314yes—
137C22×#41C2314yes—
138C22×#41C2311yescharacteristic
139C22×#41C2312yes—
140C22×#41C2311yescharacteristic
141C22×#41C2311yescharacteristic
142C22×#41C2312yes—
143C22×#41C2311yescharacteristic
144C23×Q8C2312yes—
145C23×Q8C2311yescharacteristic
146C23×D4C2314yes—
147C23×D4C2312yes—
148C23×D4C2311yescharacteristic
149C23×D4C2312yes—
150C24×C4C2312yes—
151C24×C4C2311yescharacteristic
152C24×C4C2314yes—
153C24×C4C2312yes—
154#537—232no—
155#537—232no—
156#536—216no—
157#536—216no—
158#536—232no—
159#535—216no—
160#535—216no—
161#535—232no—
162#534—232no—
163#534—232no—
164#532—232no—
165#532—232no—
166#532—48no—
167#532—48no—
168C2×C4⋊Q8C2314yes—
169C2×C4⋊Q8C2314yes—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2312yes—
172C2×#127C2314yes—
173C2×#127C2314yes—
174C2×#127C2312yes—
175C2×#127C2312yes—
176C2×#124C2314yes—
177C2×#124C2314yes—
178C2×#124C2314yes—
179C2×#124C2314yes—
180C2×#124C2314yes—
181C2×#124C2314yes—
182#525—232no—
183#525—232no—
184#525—232no—
185#525—232no—
186C2×#123C2318yes—
187C2×#123C2314yes—
188C2×#123C2318yes—
189C2×#123C2314yes—
190C2×#123C2314yes—
191C2×#123C2314yes—
192C2×#123C23116yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2318yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2318yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2318yes—
205C2×#121C2318yes—
206C2×#121C2318yes—
207C2×#121C2318yes—
208C2×#121C2318yes—
209C2×#121C2318yes—
210C2×#121C2318yes—
211C2×#121C2318yes—
212C2×#121C2318yes—
213C2×#120C2318yes—
214C2×#120C2318yes—
215C2×#120C2314yes—
216C2×#120C2314yes—
217C2×#120C2314yes—
218C2×#120C2314yes—
219C2×#120C23116yes—
220C2×C4×D4C2318yes—
221C2×C4×D4C2318yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2318yes—
225C2×C4×D4C2318yes—
226C2×#117—216no—
227C2×#117—44no—
228C2×#117C2314yes—
229C2×#117C2314yes—
230C2×#117C2314yes—
231C2×#117C2312yes—
232C2×#117C2312yes—
233C2×#117C2311yescharacteristic
234C2×#117C2312yes—
235C2×#117C2311yescharacteristic
236C2×#117C2312yes—
237C2×#117C2312yes—
238C22×C4⋊C4C2314yes—
239C22×C4⋊C4C2312yes—
240C22×C22⋊C4C2314yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2318yes—
243C22×C42—44no—
244C22×C42C2312yes—
245C22×C42C2314yes—
246C22×C42C2312yes—
247C22×C42C2311yescharacteristic
248C22×C42C2312yes—
249C22×C42C2312yes—
250C22×C42C2311yescharacteristic
251C22×C42C2312yes—
252C22×C42C2312yes—
253#400C23116yes—
254#399C23116yes—
255#398C2318yes—
256#398C2318yes—
257#398C23116yes—
258#397C2318yes—
259#397C2318yes—
260#397C23116yes—
261#397C23116yes—
262#397C23116yes—
263#396C23116yes—
264#396C23116yes—
265#395C23116yes—
266#394C23116yes—
267#394C23116yes—
268#394C2318yes—
269#394C2318yes—
270#394C23116yes—
271#394C23116yes—
272#394C23116yes—
273#394C23116yes—
274#394C23116yes—
275#393C23116yes—
276#392C2318yes—
277#392C2318yes—
278#392C23116yes—
279#392C23116yes—
280#392C23116yes—
281#391C2314yes—
282#391C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2312yes—
286#391C2318yes—
287#391C2312yes—
288#391C2312yes—
289#391C2312yes—
290#390C2314yes—
291#390C2314yes—
292#390C2318yes—
293#390C2318yes—
294#390C2314yes—
295#390C2314yes—
296#390C2318yes—
297#390C2312yes—
298#390C2312yes—
299#390C2312yes—
300#390C2312yes—
301#389C2318yes—
302#389C2318yes—
303#388C23116yes—
304#388C23116yes—
305#388C23116yes—
306#388C23116yes—
307#387C23116yes—
308#387C23116yes—
309#386C23116yes—
310#386C23116yes—
311#386C23116yes—
312#386C23116yes—
313#386C23116yes—
314#386C23116yes—
315#386C2318yes—
316#386C23116yes—
317#386C23116yes—
318#386C2314yes—
319#386C2314yes—
320#386C2318yes—
321#386C2314yes—
322#386C2314yes—
323#385C23116yes—
324#385C23116yes—
325#385C23116yes—
326#385C23116yes—
327#384C2312yes—
328#384C2312yes—
329#384C2314yes—
330#382C2314yes—
331#382C2312yes—
332#382C2312yes—
333#381C23116yes—
334#380C2318yes—
335#380C2318yes—
336#380C2318yes—
337#380C2318yes—
338#379C23116yes—
339C4×C4⋊C4C2318yes—
340C4×C4⋊C4C2318yes—
341C4×C22⋊C4C2318yes—
342C4×C22⋊C4C23116yes—
343C4×C22⋊C4C23116yes—
344C4×C22⋊C4C2318yes—
345C4×C22⋊C4C2314yes—
346C4×C22⋊C4C2314yes—
347C4×C22⋊C4C2314yes—
348C4×C22⋊C4C2314yes—
349C2×#95C2318yes—
350C25C2412yes—
351C25C2411yescharacteristic
352C25C2414yes—
353C2×#41—216no—
354C2×#41—216no—
355C2×#41—216no—
356C2×#41—216no—
357C2×#41—216no—
358C2×#41—216no—
359C2×#41—464no—
360C2×#41—42no—
361C2×#41—44no—
362C2×#41—42no—
363C2×#41—44no—
364C2×#41—42no—
365C2×#41—42no—
366C2×#41—42no—
367C2×#41—44no—
368C2×#41—42no—
369C2×#41—44no—
370C2×#41—42no—
371C2×#41—42no—
372C2×#41—48no—
373C2×#41—48no—
374C2×#41—48no—
375C2×#41—48no—
376C2×#41—48no—
377C2×#41—48no—
378C2×#41—4128no—
379C2×#41C2×D418yes—
380C2×#41C2×D4116yes—
381C2×#41C2×D418yes—
382C2×#41C2×D418yes—
383C2×#41C2×D4116yes—
384C2×#41C2×D418yes—
385C22×Q8—28no—
386C22×Q8—42no—
387C22×Q8—42no—
388C22×Q8—44no—
389C22×Q8—44no—
390C22×Q8C2×D418yes—
391C22×Q8C2414yes—
392C22×Q8C2414yes—
393C22×Q8C2411yescharacteristic
394C22×Q8C2412yes—
395C22×Q8C2411yescharacteristic
396C22×D4—216no—
397C22×D4—28no—
398C22×D4—44no—
399C22×D4—44no—
400C22×D4—42no—
401C22×D4—42no—
402C22×D4—44no—
403C22×D4—44no—
404C22×D4—48no—
405C22×D4—48no—
406C22×D4C2×D418yes—
407C22×D4C2×D4116yes—
408C22×D4C2418yes—
409C22×D4C2414yes—
410C22×D4C2418yes—
411C22×D4C2418yes—
412C22×D4C2418yes—
413C22×D4C2418yes—
414C22×D4C2418yes—
415C22×D4C2418yes—
416C22×D4C2414yes—
417C22×D4C2418yes—
418C22×D4C2411yescharacteristic
419C22×D4C2412yes—
420C22×D4C2412yes—
421C22×D4C2412yes—
422C22×D4C2412yes—
423C22×D4C2411yescharacteristic
424C22×D4C2412yes—
425C23×C4—24no—
426C23×C4—28no—
427C23×C4—28no—
428C23×C4—24no—
429C23×C4—216no—
430C23×C4—48no—
431C23×C4—48no—
432C23×C4—48no—
433C23×C4—44no—
434C23×C4C2×D4116yes—
435C23×C4C2×D418yes—
436C23×C4C2418yes—
437C23×C4C2414yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2414yes—
450C23×C4C2418yes—
451C23×C4C2418yes—
452C23×C4C2414yes—
453C23×C4C2414yes—
454C23×C4C2412yes—
455C23×C4C2411yescharacteristic
456C4⋊Q8—216no—
457C4⋊Q8—216no—
458C4⋊Q8—44no—
459C4⋊Q8—44no—
460#127—216no—
461#127—216no—
462#127—44no—
463#127—44no—
464#124—216no—
465#124—216no—
466#124—216no—
467#124—216no—
468#124—48no—
469#124—48no—
470#123—216no—
471#123—216no—
472#123—216no—
473#123—216no—
474#123—232no—
475#123—232no—
476#123—432no—
477C22⋊Q8—232no—
478C22⋊Q8—232no—
479C22⋊Q8—216no—
480C22⋊Q8—216no—
481C22⋊Q8—216no—
482C22⋊Q8—216no—
483#121—232no—
484#121—232no—
485#121—232no—
486#121—232no—
487#121—232no—
488#121—232no—
489#121—216no—
490#121—216no—
491#121—216no—
492#121—216no—
493#121—416no—
494#121—416no—
495#121—416no—
496#121—416no—
497#120—232no—
498#120—232no—
499#120—216no—
500#120—216no—
501#120—216no—
502#120—216no—
503#120—432no—
504C4×D4—232no—
505C4×D4—232no—
506C4×D4—232no—
507C4×D4—232no—
508C4×D4—416no—
509C4×D4—416no—
510#117—216no—
511#117—216no—
512#117—28no—
513#117—28no—
514#117—216no—
515#117—44no—
516#117—44no—
517#117—42no—
518#117—44no—
519#117—42no—
520C2×C4⋊C4—216no—
521C2×C4⋊C4—44no—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C24116yes—
537C2×C22⋊C4—216no—
538C2×C22⋊C4—416no—
539C2×C22⋊C4—44no—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2414yes—
542C2×C22⋊C4C2414yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2418yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2418yes—
547C2×C22⋊C4C2418yes—
548C2×C22⋊C4C2418yes—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C24116yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C24116yes—
560C2×C22⋊C4C24116yes—
561C2×C22⋊C4C24116yes—
562C2×C22⋊C4C24116yes—
563C2×C22⋊C4C24116yes—
564C2×C42—216no—
565C2×C42—28no—
566C2×C42—28no—
567C2×C42—44no—
568C2×C42—44no—
569C2×C42—42no—
570C2×C42—44no—
571C2×C42—42no—
572C2×C42—44no—
573C2×C42C2414yes—
574C2×C42C2414yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2412yes—
579C2×C42C2418yes—
580C2×C42C2414yes—
581C2×C42C2414yes—
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585#95C2418yes—
586#95C2418yes—
587#95C2418yes—
588#95C2418yes—
589#95C24116yes—
590#95C24116yes—
591#95C24116yes—
592#95C24116yes—
593#95C2418yes—
594#95C24116yes—
595#95C2418yes—
596C24—22no—
597C24—22no—
598C24—24no—
599C24—24no—
600C24—28no—
601C24—44no—
602C24—48no—
603C24—44no—
604C24—44no—
605C24—416no—
606C24C22×D418yes—
607C24C22×D414yes—
608C24C2518yes—
609C24C2512yes—
610C24C2511yescharacteristic
611C24C2511yescharacteristic
612C24C2512yes—
613C24C2511yescharacteristic
614#41—416no—
615#41—432no—
616#41—416no—
617#41—432no—
618#41—416no—
619#41—416no—
620#41—464no—
621#41—464no—
622#41—464no—
623#41—464no—
624C2×Q8—28no—
625C2×Q8—28no—
626C2×Q8—28no—
627C2×Q8—28no—
628C2×Q8—416no—
629C2×Q8—41no—
630C2×Q8—42no—
631C2×Q8—41no—
632C2×Q8—41no—
633C2×Q8—42no—
634C2×Q8—41no—
635C2×Q8—44no—
636C2×Q8—44no—
637C2×Q8—432no—
638C2×Q8C22×D414yes—
639C2×Q8C22×D418yes—
640C2×Q8C22×D414yes—
641C2×D4—216no—
642C2×D4—216no—
643C2×D4—216no—
644C2×D4—216no—
645C2×D4—216no—
646C2×D4—216no—
647C2×D4—216no—
648C2×D4—216no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—216no—
654C2×D4—416no—
655C2×D4—432no—
656C2×D4—41no—
657C2×D4—42no—
658C2×D4—41no—
659C2×D4—41no—
660C2×D4—42no—
661C2×D4—41no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—432no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—416no—
678C2×D4—416no—
679C2×D4—48no—
680C2×D4—416no—
681C2×D4—416no—
682C2×D4—416no—
683C2×D4—464no—
684C2×D4C22×D414yes—
685C2×D4C22×D418yes—
686C2×D4C22×D418yes—
687C2×D4C22×D418yes—
688C2×D4C22×D414yes—
689C2×D4C22×D418yes—
690C2×D4C22×D418yes—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—232no—
696C22×C4—264no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—216no—
716C22×C4—28no—
717C22×C4—216no—
718C22×C4—216no—
719C22×C4—216no—
720C22×C4—216no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—42no—
725C22×C4—44no—
726C22×C4—42no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—48no—
733C22×C4—48no—
734C22×C4—48no—
735C22×C4—416no—
736C22×C4—464no—
737C22×C4—432no—
738C22×C4C22×D418yes—
739C22×C4C22×D418yes—
740C22×C4C22×D418yes—
741C22×C4C22×D418yes—
742C22×C4C22×D418yes—
743C22×C4C22×D414yes—
744C22×C4C22×D414yes—
745C22×C4C22×D414yes—
746C22×C4C22×D414yes—
747C22×C4C22×D414yes—
748C22×C4C22×D414yes—
749C22×C4H(5,𝔽2)14yes—
750C22×C4H(5,𝔽2)14yes—
751C22×C4C2514yes—
752C22×C4C2514yes—
753C22×C4C2514yes—
754C22×C4C2518yes—
755C22×C4C2518yes—
756C22×C4C2518yes—
757C22×C4C2512yes—
758C22×C4C2512yes—
759C22×C4C2511yescharacteristic
760C22×C4C2511yescharacteristic
761C22×C4C2514yes—
762C22×C4C2511yescharacteristic
763C22×C4C2511yescharacteristic
764C4⋊C4—216no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—216no—
768C4⋊C4—216no—
769C4⋊C4—216no—
770C4⋊C4—216no—
771C4⋊C4—216no—
772C4⋊C4—42no—
773C4⋊C4—44no—
774C4⋊C4—42no—
775C4⋊C4—48no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—416no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—216no—
782C22⋊C4—216no—
783C22⋊C4—216no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—216no—
787C22⋊C4—216no—
788C22⋊C4—216no—
789C22⋊C4—216no—
790C22⋊C4—216no—
791C22⋊C4—216no—
792C22⋊C4—232no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—42no—
796C22⋊C4—44no—
797C22⋊C4—42no—
798C22⋊C4—416no—
799C22⋊C4—416no—
800C22⋊C4—416no—
801C22⋊C4—416no—
802C22⋊C4—416no—
803C42—216no—
804C42—28no—
805C42—28no—
806C42—28no—
807C42—24no—
808C42—24no—
809C42—28no—
810C42—24no—
811C42—24no—
812C42—42no—
813C42—44no—
814C42—42no—
815C23—24no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—28no—
825C23—28no—
826C23—24no—
827C23—24no—
828C23—28no—
829C23—216no—
830C23—28no—
831C23—28no—
832C23—28no—
833C23—216no—
834C23—216no—
835C23—48no—
836C23—416no—
837C23—48no—
838C23—48no—
839C23—416no—
840C23—88no—
841C23—88no—
842C23—816no—
843C23—816no—
844C23—816no—
845C23C23×D414yes—
846C23C23×D412yes—
847C23C23×D412yes—
848C23C23×D414yes—
849C23C23×D412yes—
850C23C2×H(5,𝔽2)12yes—
851C23C2×H(5,𝔽2)12yes—
852C23C2611yescharacteristic
853Q8—44no—
854Q8—48no—
855Q8—44no—
856Q8—416no—
857Q8—416no—
858D4—48no—
859D4—48no—
860D4—48no—
861D4—48no—
862D4—44no—
863D4—48no—
864D4—44no—
865D4—416no—
866D4—432no—
867D4—432no—
868D4—416no—
869D4—816no—
870D4—816no—
871D4—816no—
872D4—816no—
873D4—816no—
874D4—816no—
875C2×C4—24no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—24no—
885C2×C4—28no—
886C2×C4—216no—
887C2×C4—216no—
888C2×C4—216no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—28no—
893C2×C4—216no—
894C2×C4—216no—
895C2×C4—28no—
896C2×C4—28no—
897C2×C4—28no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—28no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—28no—
905C2×C4—216no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—216no—
909C2×C4—48no—
910C2×C4—416no—
911C2×C4—416no—
912C2×C4—432no—
913C2×C4—416no—
914C2×C4—48no—
915C2×C4—432no—
916C2×C4—88no—
917C2×C4—816no—
918C2×C4#534116yes—
919C2×C4C23×D414yes—
920C2×C4C23×D412yes—
921C2×C4C23×D412yes—
922C2×C4C23×D414yes—
923C2×C4C23×D412yes—
924C2×C4C23×D412yes—
925C2×C4C2×H(5,𝔽2)12yes—
926C2×C4C2×H(5,𝔽2)12yes—
927C2×C4C2×H(5,𝔽2)12yes—
928C2×C4C2×H(5,𝔽2)12yes—
929C2×C4#58518yes—
930C22—24no—
931C22—24no—
932C22—24no—
933C22—28no—
934C22—24no—
935C22—24no—
936C22—28no—
937C22—24no—
938C22—24no—
939C22—22no—
940C22—22no—
941C22—416no—
942C22—42no—
943C22—42no—
944C22—44no—
945C22—44no—
946C22—42no—
947C22—42no—
948C22—44no—
949C22—44no—
950C22—416no—
951C22—416no—
952C22—48no—
953C22—48no—
954C22—48no—
955C22—816no—
956C22—832no—
957C22C2×#53414yes—
958C22C24×D411yescharacteristic
959C22C22×H(5,𝔽2)11yescharacteristic
960C22C22×H(5,𝔽2)11yescharacteristic
961C22C2×#58514yes—
962C4—28no—
963C4—24no—
964C4—24no—
965C4—22no—
966C4—22no—
967C4—44no—
968C4—44no—
969C4—44no—
970C4—48no—
971C4—48no—
972C4—48no—
973C4C2×#53414yes—
974C4C2×#53414yes—
975C2—24no—
976C2—42no—
977C2—42no—
978C2—44no—
979C2—44no—
980C2—88no—
981C2C22×#53411yescharacteristic
982C2#6272912yes—
983C2#6275912yes—
984C2#6281212yes—
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. C2×#3449C2semidirect
2. #52167C2semidirect
3. #52165C2semidirect
4. #52163C2semidirect
5. #37419C2semidirect
6. #37418C2semidirect
7. #37388C2semidirect
8. #37386C2semidirect
9. #37300C2semidirect
10. #37297C2semidirect
11. #37296C2semidirect
12. #37190C2semidirect
13. #37129C2semidirect
14. #36737C2semidirect
15. #36624C2semidirect
16. #34810C2semidirect
17. #34738C2semidirect
18. #34633C2semidirect
19. C2×#2297C2semidirect
21. C23×#41C22semidirect
24. C2×#537C22semidirect
26. C2×#536C22semidirect
27. C2×#536C22semidirect
30. C2×#535C22semidirect
32. C2×#534C22semidirect
36. C2×#532C22semidirect
39. C2×#525C22semidirect
40. C2×#525C22semidirect
41. C22×#117C22semidirect
42. C22×#117C22semidirect
43. C23×C42C22semidirect
44. #2857C22semidirect
45. #2857C22semidirect
46. #2856C22semidirect
47. #2856C22semidirect
48. #2854C22semidirect
49. #2850C22semidirect
50. #2850C22semidirect
51. #2847C22semidirect
52. #2734C22semidirect
53. #2733C22semidirect
54. #2732C22semidirect
55. #2731C22semidirect
56. #2730C22semidirect
57. #2729C22semidirect
58. #2728C22semidirect
59. #2724C22semidirect
60. #2717C22semidirect
61. #2709C22semidirect
62. #2708C22semidirect
63. #2701C22semidirect
64. #2699C22semidirect
65. #2697C22semidirect
66. #2688C22semidirect
67. #2686C22semidirect
68. #2684C22semidirect
69. #2682C22semidirect
70. #2679C22semidirect
71. #2678C22semidirect
72. #2673C22semidirect
73. #2671C22semidirect
74. #2669C22semidirect
75. #2668C22semidirect
76. #2621C22semidirect
77. #2621C22semidirect
78. #2620C22semidirect
79. #2620C22semidirect
80. #2619C22semidirect
81. #2619C22semidirect
82. #2618C22semidirect
83. #2617C22semidirect
84. #2504C22semidirect
85. #2503C22semidirect
86. #2502C22semidirect
87. #2501C22semidirect
88. #2500C22semidirect
89. #2500C22semidirect
90. #2499C22semidirect
91. #2499C22semidirect
92. #2498C22semidirect
93. #2436C22semidirect
94. #2435C22semidirect
95. #2434C22semidirect
96. #2433C22semidirect
97. #2432C22semidirect
98. #2432C22semidirect
99. #2431C22semidirect
100. #2431C22semidirect
101. #2430C22semidirect
102. #2412C22semidirect
103. #2410C22semidirect
104. #2395C22semidirect
105. #2392C22semidirect
106. #2392C22semidirect
107. #2388C22semidirect
108. C4×#123C22semidirect
109. C4×#121C22semidirect
110. C4×#121C22semidirect
111. C4×#120C22semidirect
115. #2297C22semidirect
116. #2297C22semidirect
117. #2297C22semidirect
118. #2297C22semidirect
119. #2297C22semidirect
120. #2297C22semidirect
121. #2297C22semidirect
122. C2×#391C22semidirect
124. C2×#386C22semidirect
125. #2285C22semidirect
126. #2285C22semidirect
127. C2×C4×C22⋊C4C22semidirect
133. C22×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34492
#521672
#521652
#521632
#374192
#374182
#373882
#373862
#373002
#372972
#372962
#371902
#371292
#367372
#366242
#348102
#347382
#346332
C2×#22972