Finite Group Databasebeta

← #7711650

Subgroups — #7711650

Order 512.

7242 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3545C212yesmaximal, complemented
2#59837C218yesmaximal, complemented
3#46149C214yesmaximal, complemented
4#45999C214yesmaximal, complemented
5#39482C214yesmaximal, complemented
6#39446C214yesmaximal, complemented
7#39444C214yesmaximal, complemented
8#39390C218yesmaximal, complemented
9#39354C214yesmaximal, complemented
10#37608C212yesmaximal, complemented
11#37190C212yesmaximal, complemented
12#37129C212yesmaximal, complemented
13#36631C212yesmaximal, complemented
14#36318C218yesmaximal, complemented
15#35153C212yesmaximal, complemented
16#34984C212yesmaximal, complemented
17C2×C4×#124C211yesmaximal, characteristic, complemented
18#3545—232no—
19C2×#563C2212yescomplemented
20C2×#562C2214yes—
21C2×H(3,𝔽4)C2212yescomplemented
22C2×#555C2214yes—
23C2×#551C2218yescomplemented
24C2×#551C2214yescomplemented
25C2×#546C2218yescomplemented
26C2×#542C2218yescomplemented
27C2×#538C2218yescomplemented
28C2×#537C2212yes—
29C2×#536C2214yescomplemented
30C2×#534C2214yes—
31C2×#534C2212yescomplemented
32C2×#529C2214yescomplemented
33C22×#124C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic, complemented
35C22×C4×D4C2211yescharacteristic
36#2861C2214yescomplemented
37#2860C2214yescomplemented
38#2860C2214yescomplemented
39#2859C2212yescomplemented
40#2858C2212yescomplemented
41#2857C2212yescomplemented
42#2856C2212yes—
43#2854C2214yescomplemented
44#2854C2214yescomplemented
45#2854C2214yescomplemented
46#2850C2214yescomplemented
47#2847C2214yes—
48#2822C2212yescomplemented
49#2820C2214yescomplemented
50#2819C2212yescomplemented
51#2734C2212yescomplemented
52#2733C2212yescomplemented
53#2732C2214yescomplemented
54#2731C2214yescomplemented
55#2730C2218yescomplemented
56#2729C2218yescomplemented
57#2728C2214yescomplemented
58#2724C2212yescomplemented
59#2718C2218yescomplemented
60#2710C2218yescomplemented
61#2701C2218yescomplemented
62#2699C2214yes—
63#2697C2214yescomplemented
64#2689C2218yescomplemented
65#2682C2214yes—
66#2681C2218yescomplemented
67#2680C2218yescomplemented
68#2679C2212yescomplemented
69#2678C2218yescomplemented
70#2678C2218yescomplemented
71#2674C2218yescomplemented
72#2669C2218yescomplemented
73#2637C2218yescomplemented
74#2636C2218yescomplemented
75#2618C2214yescomplemented
76#2618C2214yescomplemented
77#2618C2214yescomplemented
78#2617C2214yes—
79#2609C2214yescomplemented
80#2609C2214yescomplemented
81#2564C2218yescomplemented
82#2559C2218yescomplemented
83#2559C2218yescomplemented
84#2557C2218yescomplemented
85#2557C2218yescomplemented
86#2555C2218yescomplemented
87#2553C2218yescomplemented
88#2549C2218yescomplemented
89#2543C2218yescomplemented
90#2539C2218yescomplemented
91#2521C2218yescomplemented
92#2498C2218yescomplemented
93#2488C2218yescomplemented
94#2478C2218yescomplemented
95#2472C2218yescomplemented
96#2472C2218yescomplemented
97#2470C2218yescomplemented
98#2466C2218yescomplemented
99#2464C2218yescomplemented
100#2464C2218yescomplemented
101#2461C2218yescomplemented
102#2455C2218yescomplemented
103#2430C2218yescomplemented
104#2429C2218yescomplemented
105#2429C2218yescomplemented
106#2426C2218yescomplemented
107#2426C2218yescomplemented
108#2425C2218yescomplemented
109#2425C2218yescomplemented
110#2424C2218yescomplemented
111#2424C2218yescomplemented
112#2424C2218yescomplemented
113#2412C2218yescomplemented
114#2410C2218yescomplemented
115#2364C2218yescomplemented
116#2359C2218yescomplemented
117#2358C2218yescomplemented
118#2342C2218yescomplemented
119#2316C2212yescomplemented
120#2315C2212yescomplemented
121C4×C4⋊Q8C2212yescomplemented
122C4×#127C2212yescomplemented
123C4×#124C2214yescomplemented
124C4×#124C2214yescomplemented
125C4×#124C2214yescomplemented
126C4×#124C2214yescomplemented
127C4×#124C2214yescomplemented
128C4×#121C2214yescomplemented
129C4×#121C2214yescomplemented
130#2297C2214yescomplemented
131C2×#391C2211yescharacteristic, complemented
132#2293C2214yescomplemented
133#2293C2214yescomplemented
134C2×#390C2211yescharacteristic
135C2×#388C2214yescomplemented
136C2×#386C2214yescomplemented
137C2×#382C2211yescharacteristic, complemented
138C2×C4×C22⋊C4C2214yescomplemented
139C2×C43C2211yescharacteristic, complemented
140C22×#41C2314yes—
141C23×Q8C2311yescharacteristic
142C23×D4C2314yes—
143C23×D4C2311yescharacteristic
144C24×C4C2312yes—
145#563—216no—
146#562—232no—
147H(3,𝔽4)—216no—
148#555—232no—
149#551—232no—
150#551—264no—
151#546—264no—
152#542—264no—
153#538—264no—
154#537—48no—
155#536—232no—
156#534—232no—
157#534—48no—
158C2×C4⋊Q8C2314yes—
159C2×C4⋊Q8C2314yes—
160C2×C4⋊Q8C2312yes—
161C2×#127C2312yes—
162#529—232no—
163C2×#126C2318yes—
164C2×#126C2318yes—
165C2×#126C2318yes—
166C2×#125C2314yes—
167C2×#124D4116yescomplemented
168C2×#124C2314yes—
169C2×#124C2318yes—
170C2×#124C2314yes—
171C2×#124C2314yes—
172C2×#124C2318yes—
173C2×#124C2314yes—
174C2×#124C2314yes—
175C2×#124C2312yes—
176C2×#124C2312yes—
177C2×#123C2318yes—
178C2×#123C2318yes—
179C2×#123C2314yes—
180C2×#123C2314yes—
181C2×#123C2318yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×#123C2318yes—
185C2×#123C2318yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2318yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2318yes—
195C2×#121C2318yes—
196C2×#121C2318yes—
197C2×#121C2318yes—
198C2×#121C2314yes—
199C2×#121C2318yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2318yes—
203C2×#120C2318yes—
204C2×#120C2318yes—
205C2×#120C2314yes—
206C2×#120C2314yes—
207C2×#120C2318yes—
208C2×#120C2318yes—
209C2×C4×Q8—44no—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2314yes—
212C2×C4×Q8C2314yes—
213C2×C4×D4—44no—
214C2×C4×D4C2314yes—
215C2×C4×D4C2318yes—
216C2×C4×D4C2318yes—
217C2×C4×D4C2318yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×#117C2314yes—
223C2×#117C2318yes—
224C2×#117C2318yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2314yes—
230C22×C22⋊C4C2318yes—
231C22×C22⋊C4C2318yes—
232C22×C22⋊C4C2314yes—
233C22×C22⋊C4C2314yes—
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237C22×C42C2312yes—
238C22×C42C2312yes—
239C22×C42C2311yescharacteristic
240#400C2318yes—
241#400C2318yes—
242#399C2318yes—
243#399C2318yes—
244#398C2314yes—
245#398C2314yes—
246#398C2318yes—
247#398C2314yes—
248#398C2314yes—
249#398C2318yes—
250#398C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#395C2318yes—
263#395C2318yes—
264#394C2314yes—
265#394C2314yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2314yes—
270#394C2314yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#393C2318yes—
278#393C2318yes—
279#392C2318yes—
280#392C2318yes—
281#392C2318yes—
282#392C2318yes—
283#392C2318yes—
284#391C2314yes—
285#391C2314yes—
286#391C2318yes—
287#391C2312yes—
288#391C2314yes—
289#391C2312yes—
290#390C2314yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2314yes—
295#390C2318yes—
296#390C2314yes—
297#390C2314yes—
298#390C2314yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2312yes—
303#390C2318yes—
304#390C2312yes—
305#389C2314yes—
306#389C2314yes—
307#389C2318yes—
308#389C2318yes—
309#389C2314yes—
310#389C2314yes—
311#389C2318yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#386C2318yes—
339#386C2318yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#384C2312yes—
361#384C2312yes—
362#382C2312yes—
363#382C2314yes—
364#382C2312yes—
365#382C2314yes—
366#381C2318yes—
367#380C2314yes—
368#380C2314yes—
369#380C2314yes—
370#380C2318yes—
371#380C2314yes—
372#379C2318yes—
373C4×C4⋊C4C2314yes—
374C4×C4⋊C4C2314yes—
375C4×C22⋊C4C2318yes—
376C4×C22⋊C4C2318yes—
377C4×C22⋊C4C2318yes—
378C4×C22⋊C4C2318yes—
379C4×C22⋊C4C2318yes—
380C4×C22⋊C4C2318yes—
381C4×C22⋊C4C2318yes—
382C4×C22⋊C4C2318yes—
383C2×#95C2314yes—
384C2×#95C2318yes—
385C2×#95C2314yes—
386C43C2312yes—
387C43C2312yes—
388C43C2312yes—
389C43C2312yes—
390C25C2412yes—
391C25C2414yes—
392C2×#41—216no—
393C2×#41—48no—
394C2×#41—48no—
395C22×Q8—42no—
396C22×Q8—42no—
397C22×Q8C2×D418yes—
398C22×Q8C2414yes—
399C22×Q8C2414yes—
400C22×Q8C2412yes—
401C22×Q8C2412yes—
402C22×D4—216no—
403C22×D4—42no—
404C22×D4—42no—
405C22×D4—48no—
406C22×D4—48no—
407C22×D4C2×D418yes—
408C22×D4C2418yes—
409C22×D4C2418yes—
410C22×D4C2418yes—
411C22×D4C2414yes—
412C22×D4C2414yes—
413C22×D4C2414yes—
414C22×D4C2414yes—
415C22×D4C2418yes—
416C22×D4C2414yes—
417C22×D4C2414yes—
418C22×D4C2412yes—
419C22×D4C2412yes—
420C23×C4—48no—
421C23×C4—44no—
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2418yes—
428C23×C4C2412yes—
429C23×C4C2418yes—
430C23×C4C2418yes—
431C23×C4C2418yes—
432C23×C4C2414yes—
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C4⋊Q8—216no—
436C4⋊Q8—216no—
437C4⋊Q8—44no—
438#127—44no—
439#126—232no—
440#126—232no—
441#126—232no—
442#125—216no—
443#124—216no—
444#124—216no—
445#124—232no—
446#124—232no—
447#124—216no—
448#124—48no—
449#124C2×D4132yes—
450#124C2×D4116yes—
451#124C2×D4116yes—
452#123—216no—
453#123—216no—
454#123—232no—
455#123—232no—
456#123—232no—
457#123—232no—
458#123—232no—
459#123—416no—
460#123—416no—
461C22⋊Q8—232no—
462C22⋊Q8—232no—
463C22⋊Q8—216no—
464C22⋊Q8—232no—
465C22⋊Q8—232no—
466C22⋊Q8—416no—
467#121—232no—
468#121—232no—
469#121—216no—
470#121—216no—
471#121—232no—
472#121—232no—
473#121—416no—
474#121—416no—
475#121—48no—
476#121—48no—
477#121—48no—
478#120—232no—
479#120—216no—
480#120—216no—
481#120—232no—
482#120—416no—
483#120—416no—
484C4×Q8—216no—
485C4×Q8—48no—
486C4×Q8—48no—
487C4×D4—232no—
488C4×D4—232no—
489C4×D4—232no—
490C4×D4—216no—
491C4×D4—48no—
492C4×D4—48no—
493C4×D4—48no—
494C4×D4—48no—
495#117—216no—
496#117—232no—
497#117—232no—
498C2×C4⋊C4—28no—
499C2×C4⋊C4—42no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4C2418yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2418yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2414yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2414yes—
525C2×C22⋊C4—216no—
526C2×C22⋊C4—28no—
527C2×C22⋊C4—232no—
528C2×C22⋊C4—416no—
529C2×C22⋊C4—48no—
530C2×C22⋊C4C2×D4132yes—
531C2×C22⋊C4C2418yes—
532C2×C22⋊C4C2418yes—
533C2×C22⋊C4C2418yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2418yes—
539C2×C22⋊C4C2418yes—
540C2×C22⋊C4C2418yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2418yes—
559C2×C42—24no—
560C2×C42—44no—
561C2×C42—44no—
562C2×C42—44no—
563C2×C42—42no—
564C2×C42C2×D418yes—
565C2×C42C2414yes—
566C2×C42C2418yes—
567C2×C42C2414yes—
568C2×C42C2412yes—
569C2×C42C2412yes—
570C2×C42C2412yes—
571C2×C42C2412yes—
572C2×C42C2412yes—
573C2×C42C2412yes—
574C2×C42C2418yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2412yes—
578C2×C42C2411yescharacteristic
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2411yescharacteristic
582C2×C42C2411yescharacteristic
583C2×C42C2412yes—
584C2×C42C2411yescharacteristic
585#95C2418yes—
586#95C2418yes—
587#95C2418yes—
588#95C2418yes—
589#95C2418yes—
590#95C2418yes—
591#95C2418yes—
592#95C2418yes—
593#95C2418yes—
594#95C2418yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C2418yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2414yes—
603C24—24no—
604C24—24no—
605C24—28no—
606C24—44no—
607C24—44no—
608C24—44no—
609C24—48no—
610C24—48no—
611C24—44no—
612C24C22×D418yes—
613C24C2518yes—
614C24C2514yes—
615C24C2511yescharacteristic
616#41—832no—
617C2×Q8—28no—
618C2×Q8—28no—
619C2×Q8—42no—
620C2×Q8—42no—
621C2×Q8—416no—
622C2×Q8—42no—
623C2×Q8—42no—
624C2×Q8—44no—
625C2×Q8—44no—
626C2×Q8—44no—
627C2×Q8—44no—
628C2×Q8C22×D418yes—
629C2×Q8C22×D418yes—
630C2×D4—216no—
631C2×D4—216no—
632C2×D4—216no—
633C2×D4—216no—
634C2×D4—216no—
635C2×D4—216no—
636C2×D4—28no—
637C2×D4—28no—
638C2×D4—28no—
639C2×D4—28no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—416no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—48no—
649C2×D4—44no—
650C2×D4—44no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—48no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—48no—
658C2×D4—44no—
659C2×D4—44no—
660C2×D4—48no—
661C2×D4—44no—
662C2×D4—48no—
663C2×D4—832no—
664C2×D4C22×D418yes—
665C2×D4C22×D418yes—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—24no—
669C22×C4—22no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—216no—
674C22×C4—28no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—216no—
679C22×C4—216no—
680C22×C4—216no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—44no—
686C22×C4—48no—
687C22×C4—48no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4—48no—
691C22×C4—44no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—48no—
697C22×C4—816no—
698C22×C4C22×D414yes—
699C22×C4C22×D418yes—
700C22×C4C22×D418yes—
701C22×C4H(5,𝔽2)14yes—
702C22×C4C2514yes—
703C22×C4C2512yes—
704C22×C4C2514yes—
705C22×C4C2518yes—
706C22×C4C2518yes—
707C22×C4C2518yes—
708C22×C4C2512yes—
709C22×C4C2512yes—
710C22×C4C2514yes—
711C22×C4C2511yescharacteristic
712C22×C4C2511yescharacteristic
713C22×C4C2512yes—
714C22×C4C2512yes—
715C22×C4C2512yes—
716C4⋊C4—216no—
717C4⋊C4—216no—
718C4⋊C4—216no—
719C4⋊C4—216no—
720C4⋊C4—216no—
721C4⋊C4—216no—
722C4⋊C4—28no—
723C4⋊C4—28no—
724C4⋊C4—216no—
725C4⋊C4—216no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4—42no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C4⋊C4—48no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—48no—
739C4⋊C4—44no—
740C22⋊C4—216no—
741C22⋊C4—216no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—216no—
745C22⋊C4—216no—
746C22⋊C4—216no—
747C22⋊C4—216no—
748C22⋊C4—216no—
749C22⋊C4—216no—
750C22⋊C4—216no—
751C22⋊C4—216no—
752C22⋊C4—216no—
753C22⋊C4—216no—
754C22⋊C4—216no—
755C22⋊C4—216no—
756C22⋊C4—216no—
757C22⋊C4—48no—
758C22⋊C4—48no—
759C22⋊C4—48no—
760C22⋊C4—48no—
761C22⋊C4—48no—
762C22⋊C4—48no—
763C22⋊C4—48no—
764C22⋊C4—48no—
765C22⋊C4—48no—
766C22⋊C4C22×D4132yes—
767C22⋊C4C22×D4132yes—
768C42—28no—
769C42—216no—
770C42—28no—
771C42—24no—
772C42—24no—
773C42—24no—
774C42—24no—
775C42—24no—
776C42—24no—
777C42—42no—
778C42—42no—
779C42—42no—
780C42—42no—
781C42—41no—
782C42—42no—
783C42—41no—
784C42—48no—
785C42C22×D414yes—
786C42C22×D418yes—
787C42C22×D414yes—
788C23—22no—
789C23—22no—
790C23—24no—
791C23—28no—
792C23—28no—
793C23—24no—
794C23—216no—
795C23—28no—
796C23—28no—
797C23—28no—
798C23—28no—
799C23—28no—
800C23—28no—
801C23—28no—
802C23—416no—
803C23—84no—
804C23—88no—
805C23—84no—
806C23—88no—
807C23—816no—
808C23—816no—
809C23—164no—
810C23—164no—
811C23C23×D418yes—
812C23C23×D412yes—
813C23C2×H(5,𝔽2)12yes—
814C23#58512yes—
815C23C2611yescharacteristic
816Q8—48no—
817Q8—48no—
818Q8—88no—
819Q8—88no—
820D4—48no—
821D4—48no—
822D4—432no—
823D4—88no—
824D4—88no—
825D4—88no—
826D4—88no—
827D4—816no—
828D4—816no—
829D4—816no—
830D4—164no—
831D4—164no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—24no—
849C2×C4—28no—
850C2×C4—216no—
851C2×C4—28no—
852C2×C4—28no—
853C2×C4—28no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—28no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—28no—
867C2×C4—48no—
868C2×C4—44no—
869C2×C4—48no—
870C2×C4—816no—
871C2×C4—816no—
872C2×C4—816no—
873C2×C4—816no—
874C2×C4—84no—
875C2×C4—84no—
876C2×C4—88no—
877C2×C4C23×D414yes—
878C2×C4C23×D418yes—
879C2×C4C23×D412yes—
880C2×C4C23×D412yes—
881C2×C4C23×D414yes—
882C2×C4C2×H(5,𝔽2)14yes—
883C2×C4#58514yes—
884C2×C4#58514yes—
885C22—24no—
886C22—24no—
887C22—22no—
888C22—22no—
889C22—28no—
890C22—216no—
891C22—48no—
892C22—44no—
893C22—44no—
894C22—48no—
895C22—48no—
896C22—48no—
897C22—48no—
898C22—48no—
899C22—48no—
900C22—48no—
901C22—816no—
902C22—1616no—
903C22#349614yes—
904C22C24×D411yescharacteristic
905C22C22×H(5,𝔽2)11yescharacteristic
906C22C2×#58511yescharacteristic
907C22C2×#58512yes—
908C22C2×#58512yes—
909C4—24no—
910C4—28no—
911C4—22no—
912C4—22no—
913C4—24no—
914C4—24no—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—48no—
919C4—48no—
920C4—48no—
921C4—44no—
922C4—44no—
923C2—24no—
924C2—48no—
925C2—88no—
926C2#6275512yes—
927C2C2×#349611yescharacteristic
928C2#6281212yes—
929C2#6282211yescharacteristic
930C2#6282411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3545C2semidirect
2. #59837C2semidirect
3. #46149C2semidirect
4. #45999C2semidirect
5. #39482C2semidirect
6. #39446C2semidirect
7. #39444C2semidirect
8. #39390C2semidirect
9. #39354C2semidirect
10. #37608C2semidirect
11. #37190C2semidirect
12. #37129C2semidirect
13. #36631C2semidirect
14. #36318C2semidirect
15. #35153C2semidirect
16. #34984C2semidirect
17. C2×C4×#124C2semidirect
19. C2×#563C22semidirect
21. C2×H(3,𝔽4)C22semidirect
23. C2×#551C22semidirect
24. C2×#551C22semidirect
25. C2×#546C22semidirect
26. C2×#542C22semidirect
27. C2×#538C22semidirect
29. C2×#536C22semidirect
31. C2×#534C22semidirect
32. C2×#529C22semidirect
34. C22×C4×Q8C22semidirect
36. #2861C22semidirect
37. #2860C22semidirect
38. #2860C22semidirect
39. #2859C22semidirect
40. #2858C22semidirect
41. #2857C22semidirect
43. #2854C22semidirect
44. #2854C22semidirect
45. #2854C22semidirect
46. #2850C22semidirect
48. #2822C22semidirect
49. #2820C22semidirect
50. #2819C22semidirect
51. #2734C22semidirect
52. #2733C22semidirect
53. #2732C22semidirect
54. #2731C22semidirect
55. #2730C22semidirect
56. #2729C22semidirect
57. #2728C22semidirect
58. #2724C22semidirect
59. #2718C22semidirect
60. #2710C22semidirect
61. #2701C22semidirect
63. #2697C22semidirect
64. #2689C22semidirect
66. #2681C22semidirect
67. #2680C22semidirect
68. #2679C22semidirect
69. #2678C22semidirect
70. #2678C22semidirect
71. #2674C22semidirect
72. #2669C22semidirect
73. #2637C22semidirect
74. #2636C22semidirect
75. #2618C22semidirect
76. #2618C22semidirect
77. #2618C22semidirect
79. #2609C22semidirect
80. #2609C22semidirect
81. #2564C22semidirect
82. #2559C22semidirect
83. #2559C22semidirect
84. #2557C22semidirect
85. #2557C22semidirect
86. #2555C22semidirect
87. #2553C22semidirect
88. #2549C22semidirect
89. #2543C22semidirect
90. #2539C22semidirect
91. #2521C22semidirect
92. #2498C22semidirect
93. #2488C22semidirect
94. #2478C22semidirect
95. #2472C22semidirect
96. #2472C22semidirect
97. #2470C22semidirect
98. #2466C22semidirect
99. #2464C22semidirect
100. #2464C22semidirect
101. #2461C22semidirect
102. #2455C22semidirect
103. #2430C22semidirect
104. #2429C22semidirect
105. #2429C22semidirect
106. #2426C22semidirect
107. #2426C22semidirect
108. #2425C22semidirect
109. #2425C22semidirect
110. #2424C22semidirect
111. #2424C22semidirect
112. #2424C22semidirect
113. #2412C22semidirect
114. #2410C22semidirect
115. #2364C22semidirect
116. #2359C22semidirect
117. #2358C22semidirect
118. #2342C22semidirect
119. #2316C22semidirect
120. #2315C22semidirect
121. C4×C4⋊Q8C22semidirect
122. C4×#127C22semidirect
123. C4×#124C22semidirect
124. C4×#124C22semidirect
125. C4×#124C22semidirect
126. C4×#124C22semidirect
127. C4×#124C22semidirect
128. C4×#121C22semidirect
129. C4×#121C22semidirect
130. #2297C22semidirect
131. C2×#391C22semidirect
132. #2293C22semidirect
133. #2293C22semidirect
135. C2×#388C22semidirect
136. C2×#386C22semidirect
137. C2×#382C22semidirect
138. C2×C4×C22⋊C4C22semidirect
139. C2×C43C22semidirect
167. C2×#124D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35452
#598372
#461492
#459992
#394822
#394462
#394442
#393902
#393542
#376082
#371902
#371292
#366312
#363182
#351532
#349842
C2×C4×#1242