Finite Group Databasebeta

← #8093281

Subgroups — #8093281

Order 512.

4890 conjugacy classes of subgroups.

The subgroup lattice has 977 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45728C214yesmaximal, complemented
2#45715C214yesmaximal, complemented
3#45702C214yesmaximal, complemented
4#45654C214yesmaximal, complemented
5#45640C214yesmaximal, complemented
6#45633C214yesmaximal, complemented
7#45595C214yesmaximal, complemented
8#45579C218yesmaximal, complemented
9#45513C214yesmaximal, complemented
10#45485C214yesmaximal, complemented
11#45456C214yesmaximal, complemented
12#36625C212yesmaximal, complemented
13C2×#2854C211yesmaximal, characteristic
14#35584C211yesmaximal, characteristic
15#35566C212yesmaximal, complemented
16#35558C212yesmaximal, complemented
17#35544C212yesmaximal, complemented
18#35543C212yesmaximal, complemented
19#35540C211yesmaximal, characteristic
20#35515C212yesmaximal, complemented
21C2×#563C2214yescomplemented
22C2×#544C2211yescharacteristic
23C2×#533C2212yes—
24C22×#123C2212yes—
25C22×#121C2211yescharacteristic
26C2×#518C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2857C2212yescomplemented
29#2857C2212yescomplemented
30#2857C2212yescomplemented
31#2857C2212yescomplemented
32#2855C2214yes—
33#2855C2214yes—
34#2854C2214yes—
35#2854C2214yes—
36#2854C2214yes—
37#2854C2214yes—
38#2851C2212yescomplemented
39#2851C2212yescomplemented
40#2851C2212yescomplemented
41#2851C2212yescomplemented
42#2848C2214yes—
43#2848C2214yes—
44#2838C2218yescomplemented
45#2831C2218yescomplemented
46#2827C2218yescomplemented
47#2814C2218yescomplemented
48#2793C2218yescomplemented
49#2777C2218yescomplemented
50#2773C2218yescomplemented
51#2770C2218yescomplemented
52#2765C2218yescomplemented
53#2759C2218yescomplemented
54#2745C2218yescomplemented
55#2729C2218yescomplemented
56#2728C2218yescomplemented
57#2725C2218yescomplemented
58#2724C2214yescomplemented
59#2723C2218yescomplemented
60#2718C2218yescomplemented
61#2717C2214yescomplemented
62#2717C2214yescomplemented
63#2716C2218yescomplemented
64#2715C2218yescomplemented
65#2707C2218yescomplemented
66#2702C2218yescomplemented
67#2695C2218yescomplemented
68#2695C2218yescomplemented
69#2690C2218yescomplemented
70#2689C2218yescomplemented
71#2683C2214yescomplemented
72#2680C2218yescomplemented
73#2674C2218yescomplemented
74#2584C2214yescomplemented
75#2584C2214yescomplemented
76#2580C2214yescomplemented
77#2580C2214yescomplemented
78#2571C2214yescomplemented
79#2570C2214yescomplemented
80#2570C2214yescomplemented
81#2567C2214yescomplemented
82#2561C2214yes—
83#2552C2214yescomplemented
84#2552C2214yescomplemented
85#2551C2214yescomplemented
86#2550C2214yescomplemented
87#2550C2214yescomplemented
88#2549C2218yes—
89#2546C2214yescomplemented
90#2538C2214yescomplemented
91#2538C2214yescomplemented
92#2513C2214yescomplemented
93#2513C2214yescomplemented
94#2513C2214yescomplemented
95#2513C2214yescomplemented
96#2512C2214yescomplemented
97#2512C2214yescomplemented
98#2512C2214yescomplemented
99#2512C2214yescomplemented
100#2509C2214yescomplemented
101#2508C2214yescomplemented
102#2507C2214yescomplemented
103#2506C2214yescomplemented
104#2505C2218yes—
105#2497C2214yescomplemented
106#2497C2214yescomplemented
107#2496C2214yescomplemented
108#2496C2214yescomplemented
109#2495C2214yescomplemented
110#2495C2214yescomplemented
111#2494C2214yescomplemented
112#2494C2214yescomplemented
113#2493C2218yes—
114#2491C2214yes—
115#2491C2214yes—
116#2490C2214yes—
117#2490C2214yes—
118#2483C2214yes—
119#2480C2218yes—
120#2480C2218yes—
121#2480C2218yes—
122#2473C2218yes—
123#2454C2214yescomplemented
124#2454C2214yescomplemented
125#2452C2214yescomplemented
126#2452C2214yescomplemented
127#2440C2218yes—
128#2437C2218yes—
129#2437C2218yes—
130#2435C2214yes—
131#2422C2214yes—
132#2422C2214yes—
133#2420C2214yes—
134#2420C2214yes—
135#2405C2214yes—
136#2383C2218yescomplemented
137#2379C2214yescomplemented
138#2378C2218yescomplemented
139#2376C2214yescomplemented
140#2376C2214yescomplemented
141#2317C2212yes—
142#2317C2212yes—
143#2317C2212yes—
144#2316C2212yes—
145#2309C2212yes—
146#2309C2211yescharacteristic
147C4×C22⋊Q8C2214yescomplemented
148C4×C22⋊Q8C2214yescomplemented
149C4×C22⋊Q8C2214yescomplemented
150C4×C22⋊Q8C2214yescomplemented
151#2296C2212yes—
152#2296C2212yes—
153C2×#390C2212yes—
154C2×#389C2212yes—
155C2×#388C2214yes—
156C2×#386C2212yes—
157#2285C2212yes—
158#2280C2212yes—
159#2280C2212yes—
160C2×#380C2211yescharacteristic
161#2274C2211yescharacteristic
162#2274C2212yes—
163C23×D4C2311yescharacteristic
164C23×D4C2312yes—
165C24×C4C2311yescharacteristic
166C24×C4C2311yescharacteristic
167C24×C4C2311yescharacteristic
168#563—416no—
169#544—44no—
170#533—48no—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2318yes—
175C2×#126C2318yes—
176C2×#126C2318yes—
177C2×#126C2318yes—
178C2×#125C2314yes—
179C2×#125C2312yes—
180C2×#125C2312yes—
181C2×#125C2318yes—
182C2×#124C2314yes—
183C2×#124C2314yes—
184C2×#123—48no—
185C2×#123C2314yes—
186C2×#123C2318yes—
187C2×#123C2314yes—
188C2×#123C2314yes—
189C2×#123C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2318yes—
199C2×#121—44no—
200C2×#121C2314yes—
201C2×#121C2314yes—
202#518—44no—
203C2×C4×Q8C2314yes—
204C2×C4×Q8C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×#117C2312yes—
208C2×#117C2312yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2314yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2314yes—
216C22×C22⋊C4C2314yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2314yes—
219C22×C42—44no—
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2312yes—
225C22×C42C2312yes—
226#401C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#399C2318yes—
235#399C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2318yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#395C2318yes—
264#395C2318yes—
265#395C2318yes—
266#395C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#393C2318yes—
272#393C2318yes—
273#393C2318yes—
274#391C2318yes—
275#391C2314yes—
276#391C2314yes—
277#391C2314yes—
278#391C2314yes—
279#391C2318yes—
280#390C2314yes—
281#390C2314yes—
282#390C2314yes—
283#390C2314yes—
284#390C2314yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#390C2314yes—
289#390C2314yes—
290#390C2314yes—
291#390C2314yes—
292#389C2312yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2318yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2312yes—
308#389C2312yes—
309#389C2314yes—
310#389C2312yes—
311#389C2312yes—
312#389C2314yes—
313#389C2318yes—
314#389C2318yes—
315#389C2318yes—
316#389C2318yes—
317#389C2312yes—
318#389C2312yes—
319#389C2312yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#387C2314yes—
347#387C2314yes—
348#387C2314yes—
349#387C2314yes—
350#387C2314yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#386C2314yes—
355#386C2314yes—
356#386C2318yes—
357#386C2314yes—
358#386C2314yes—
359#385C2314yes—
360#385C2314yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#385C2314yes—
372#385C2314yes—
373#385C2314yes—
374#385C2314yes—
375#385C2314yes—
376#385C2314yes—
377#385C2314yes—
378#385C2318yes—
379#384C2318yes—
380#384C2312yes—
381#384C2314yes—
382#384C2314yes—
383#384C2314yes—
384#384C2312yes—
385#383C2318yes—
386#382C2314yes—
387#382C2312yes—
388#382C2314yes—
389#382C2312yes—
390#382C2318yes—
391#382C2314yes—
392#381C2314yes—
393#381C2314yes—
394#381C2318yes—
395#380C2318yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2312yes—
403#380C2312yes—
404#380C2312yes—
405#380C2312yes—
406#380C2312yes—
407#380C2312yes—
408#380C2312yes—
409#380C2312yes—
410#380C2314yes—
411#380C2314yes—
412#380C2318yes—
413#380C2318yes—
414#379C2318yes—
415#379C2314yes—
416#379C2314yes—
417#379C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2318yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C2×#95C2312yes—
437C2×#95C2314yes—
438C25C2411yescharacteristic
439C25C2412yes—
440C22×Q8C2414yes—
441C22×Q8C2414yes—
442C22×Q8C2414yes—
443C22×D4—24no—
444C22×D4—28no—
445C22×D4—44no—
446C22×D4—44no—
447C22×D4—44no—
448C22×D4C2414yes—
449C22×D4C2414yes—
450C22×D4C2414yes—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—28no—
454C23×C4—44no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—42no—
458C23×C4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2414yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2411yescharacteristic
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C4⋊Q8—44no—
475C4⋊Q8—44no—
476C4⋊Q8—48no—
477C4⋊Q8—416no—
478#126—416no—
479#126—416no—
480#126—416no—
481#125—44no—
482#125—44no—
483#125—48no—
484#125—416no—
485#124—48no—
486#124—48no—
487#123—216no—
488#123—48no—
489#123—48no—
490#123—416no—
491#123—48no—
492C22⋊Q8—216no—
493C22⋊Q8—48no—
494C22⋊Q8—48no—
495C22⋊Q8—48no—
496C22⋊Q8—48no—
497C22⋊Q8—416no—
498C22⋊Q8—416no—
499C22⋊Q8—48no—
500C22⋊Q8—48no—
501#121—48no—
502#121—48no—
503C4×Q8—48no—
504C4×Q8—48no—
505C4×D4—48no—
506C4×D4—48no—
507#117—28no—
508#117—28no—
509#117—28no—
510#117—28no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—28no—
513C2×C4⋊C4—48no—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C22⋊C4—48no—
556C2×C22⋊C4—48no—
557C2×C22⋊C4—48no—
558C2×C22⋊C4—44no—
559C2×C22⋊C4—44no—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C42—28no—
588C2×C42—44no—
589C2×C42—44no—
590C2×C42—44no—
591C2×C42—44no—
592C2×C42—44no—
593C2×C42C2414yes—
594C2×C42C2414yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603C2×C42C2418yes—
604C2×C42C2418yes—
605C2×C42C2412yes—
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2412yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—24no—
647C24—24no—
648C24—28no—
649C24—42no—
650C24—42no—
651C24—44no—
652C24—42no—
653C24C2514yes—
654C24C2511yescharacteristic
655C24C2511yescharacteristic
656C24C2511yescharacteristic
657C2×Q8—28no—
658C2×Q8—28no—
659C2×Q8—44no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—416no—
676C2×D4—816no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—28no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—41no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—48no—
716C22×C4—44no—
717C22×C4—416no—
718C22×C4—416no—
719C22×C4—416no—
720C22×C4H(5,𝔽2)14yes—
721C22×C4H(5,𝔽2)14yes—
722C22×C42−1+418yes—
723C22×C4C2512yes—
724C22×C4C2514yes—
725C22×C4C2514yes—
726C22×C4C2512yes—
727C22×C4C2518yes—
728C22×C4C2514yes—
729C22×C4C2514yes—
730C22×C4C2514yes—
731C22×C4C2514yes—
732C22×C4C2512yes—
733C22×C4C2514yes—
734C22×C4C2514yes—
735C22×C4C2514yes—
736C22×C4C2512yes—
737C22×C4C2512yes—
738C22×C4C2512yes—
739C4⋊C4—28no—
740C4⋊C4—216no—
741C4⋊C4—24no—
742C4⋊C4—24no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—24no—
754C4⋊C4—28no—
755C4⋊C4—28no—
756C4⋊C4—28no—
757C4⋊C4—48no—
758C4⋊C4—44no—
759C4⋊C4—44no—
760C4⋊C4—44no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—48no—
774C4⋊C4—48no—
775C4⋊C4—48no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—48no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—28no—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—216no—
790C22⋊C4—216no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—44no—
795C22⋊C4—48no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C22⋊C4—48no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C42—24no—
808C42—24no—
809C42—24no—
810C42—24no—
811C42—28no—
812C42—28no—
813C42—28no—
814C42—28no—
815C42—42no—
816C42—42no—
817C42—42no—
818C42—42no—
819C42—44no—
820C42—44no—
821C42—48no—
822C42—48no—
823C23—21no—
824C23—22no—
825C23—21no—
826C23—28no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—21no—
835C23—24no—
836C23—24no—
837C23—28no—
838C23—28no—
839C23—24no—
840C23—48no—
841C23—48no—
842C23—44no—
843C23—44no—
844C23—48no—
845C23—84no—
846C23—84no—
847C23—88no—
848C23—88no—
849C23C2×H(5,𝔽2)12yes—
850C23C2×H(5,𝔽2)12yes—
851C23C2×2−1+414yes—
852C23#58512yes—
853C23C2611yescharacteristic
854Q8—88no—
855Q8—88no—
856Q8—164no—
857D4—416no—
858D4—88no—
859D4—88no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—28no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—24no—
883C2×C4—28no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—28no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—48no—
906C2×C4—48no—
907C2×C4—48no—
908C2×C4—48no—
909C2×C4—44no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—48no—
913C2×C4—48no—
914C2×C4—88no—
915C2×C4—84no—
916C2×C4—164no—
917C2×C4—164no—
918C2×C4#563116yescomplemented
919C2×C4C2×H(5,𝔽2)14yes—
920C2×C4C2×H(5,𝔽2)14yes—
921C2×C4C2×2−1+414yes—
922C2×C4C2×2−1+414yes—
923C2×C4#58514yes—
924C22—22no—
925C22—22no—
926C22—24no—
927C22—24no—
928C22—22no—
929C22—22no—
930C22—24no—
931C22—24no—
932C22—416no—
933C22—41no—
934C22—41no—
935C22—42no—
936C22—42no—
937C22—41no—
938C22—41no—
939C22—44no—
940C22—44no—
941C22—48no—
942C22—48no—
943C22—44no—
944C22—168no—
945C22C2×#56314yes—
946C22C22×H(5,𝔽2)11yescharacteristic
947C22C22×H(5,𝔽2)11yescharacteristic
948C22C22×2−1+412yes—
949C22C2×#58511yescharacteristic
950C22C2×#58512yes—
951C4—24no—
952C4—24no—
953C4—42no—
954C4—44no—
955C4—44no—
956C4—44no—
957C4—42no—
958C4—44no—
959C4—44no—
960C4—44no—
961C4—44no—
962C4—44no—
963C4—44no—
964C4—48no—
965C4—42no—
966C4C2×#56318yes—
967C2—24no—
968C2—42no—
969C2—42no—
970C2—84no—
971C2C22×#56311yescharacteristic
972C2#6281811yescharacteristic
973C2#6282111yescharacteristic
974C2#6283112yes—
975C2#6283512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45728C2semidirect
2. #45715C2semidirect
3. #45702C2semidirect
4. #45654C2semidirect
5. #45640C2semidirect
6. #45633C2semidirect
7. #45595C2semidirect
8. #45579C2semidirect
9. #45513C2semidirect
10. #45485C2semidirect
11. #45456C2semidirect
12. #36625C2semidirect
15. #35566C2semidirect
16. #35558C2semidirect
17. #35544C2semidirect
18. #35543C2semidirect
20. #35515C2semidirect
21. C2×#563C22semidirect
28. #2857C22semidirect
29. #2857C22semidirect
30. #2857C22semidirect
31. #2857C22semidirect
38. #2851C22semidirect
39. #2851C22semidirect
40. #2851C22semidirect
41. #2851C22semidirect
44. #2838C22semidirect
45. #2831C22semidirect
46. #2827C22semidirect
47. #2814C22semidirect
48. #2793C22semidirect
49. #2777C22semidirect
50. #2773C22semidirect
51. #2770C22semidirect
52. #2765C22semidirect
53. #2759C22semidirect
54. #2745C22semidirect
55. #2729C22semidirect
56. #2728C22semidirect
57. #2725C22semidirect
58. #2724C22semidirect
59. #2723C22semidirect
60. #2718C22semidirect
61. #2717C22semidirect
62. #2717C22semidirect
63. #2716C22semidirect
64. #2715C22semidirect
65. #2707C22semidirect
66. #2702C22semidirect
67. #2695C22semidirect
68. #2695C22semidirect
69. #2690C22semidirect
70. #2689C22semidirect
71. #2683C22semidirect
72. #2680C22semidirect
73. #2674C22semidirect
74. #2584C22semidirect
75. #2584C22semidirect
76. #2580C22semidirect
77. #2580C22semidirect
78. #2571C22semidirect
79. #2570C22semidirect
80. #2570C22semidirect
81. #2567C22semidirect
83. #2552C22semidirect
84. #2552C22semidirect
85. #2551C22semidirect
86. #2550C22semidirect
87. #2550C22semidirect
89. #2546C22semidirect
90. #2538C22semidirect
91. #2538C22semidirect
92. #2513C22semidirect
93. #2513C22semidirect
94. #2513C22semidirect
95. #2513C22semidirect
96. #2512C22semidirect
97. #2512C22semidirect
98. #2512C22semidirect
99. #2512C22semidirect
100. #2509C22semidirect
101. #2508C22semidirect
102. #2507C22semidirect
103. #2506C22semidirect
105. #2497C22semidirect
106. #2497C22semidirect
107. #2496C22semidirect
108. #2496C22semidirect
109. #2495C22semidirect
110. #2495C22semidirect
111. #2494C22semidirect
112. #2494C22semidirect
123. #2454C22semidirect
124. #2454C22semidirect
125. #2452C22semidirect
126. #2452C22semidirect
136. #2383C22semidirect
137. #2379C22semidirect
138. #2378C22semidirect
139. #2376C22semidirect
140. #2376C22semidirect
147. C4×C22⋊Q8C22semidirect
148. C4×C22⋊Q8C22semidirect
149. C4×C22⋊Q8C22semidirect
150. C4×C22⋊Q8C22semidirect
918. C2×C4#563semidirect

Maximal subgroups

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

subgroupindex
#457282
#457152
#457022
#456542
#456402
#456332
#455952
#455792
#455132
#454852
#454562
#366252
C2×#28542
#355842
#355662
#355582
#355442
#355432
#355402
#355152