Finite Group Databasebeta

← #7634883

Subgroups — #7634883

Order 512.

4958 conjugacy classes of subgroups.

The subgroup lattice has 939 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52248C214yesmaximal, complemented
2#52247C218yesmaximal, complemented
3#52246C214yesmaximal, complemented
4#37383C212yesmaximal, complemented
5#37382C212yesmaximal, complemented
6#37289C212yesmaximal, complemented
7#37288C214yesmaximal, complemented
8#37287C214yesmaximal, complemented
9#37286C212yesmaximal, complemented
10#37236C214yesmaximal, complemented
11#37124C214yesmaximal, complemented
12#36726C218yesmaximal, complemented
13#36626C212yesmaximal, complemented
14#34816C212yesmaximal, complemented
15#34815C212yesmaximal, complemented
16#34745C212yesmaximal, complemented
17#34744C212yesmaximal, complemented
18#34634C211yesmaximal, characteristic, complemented
19#34633C211yesmaximal, characteristic
20#34065C212yesmaximal, complemented
21C2×#2285C211yesmaximal, characteristic, complemented
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C2×#525C2212yes—
25C2×C4×#41C2212yes—
26C22×#117C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2855C2214yes—
30#2855C2214yes—
31#2854C2214yes—
32#2854C2214yes—
33#2853C2214yes—
34#2853C2214yes—
35#2849C2214yes—
36#2849C2214yes—
37#2795C2214yescomplemented
38#2794C2214yescomplemented
39#2793C2218yescomplemented
40#2792C2214yescomplemented
41#2791C2218yescomplemented
42#2790C2218yescomplemented
43#2789C2214yescomplemented
44#2785C2214yescomplemented
45#2783C2218yescomplemented
46#2782C2214yescomplemented
47#2781C2218yescomplemented
48#2775C2218yescomplemented
49#2769C2214yescomplemented
50#2767C2218yescomplemented
51#2765C2218yescomplemented
52#2746C2218yes—
53#2745C2218yes—
54#2744C2218yes—
55#2744C2218yescomplemented
56#2743C2218yes—
57#2740C2218yes—
58#2739C2218yes—
59#2738C2218yes—
60#2737C2218yes—
61#2721C2218yescomplemented
62#2720C2218yescomplemented
63#2718C2218yescomplemented
64#2707C2218yes—
65#2706C2218yes—
66#2705C2218yes—
67#2696C2218yes—
68#2695C2218yes—
69#2694C2218yes—
70#2693C2218yes—
71#2687C2218yes—
72#2680C2214yescomplemented
73#2629C2212yes—
74#2629C2212yes—
75#2628C2212yes—
76#2628C2212yes—
77#2627C2214yes—
78#2626C2214yes—
79#2621C2211yescharacteristic
80#2621C2211yescharacteristic
81#2620C2212yes—
82#2620C2212yes—
83#2619C2211yescharacteristic
84#2619C2211yescharacteristic
85#2618C2214yes—
86#2617C2214yes—
87#2514C2214yescomplemented
88#2513C2214yescomplemented
89#2512C2214yescomplemented
90#2511C2214yescomplemented
91#2510C2218yes—
92#2509C2214yescomplemented
93#2508C2214yescomplemented
94#2507C2214yescomplemented
95#2506C2214yescomplemented
96#2505C2218yes—
97#2481C2218yes—
98#2473C2218yes—
99#2454C2214yescomplemented
100#2453C2214yescomplemented
101#2452C2214yescomplemented
102#2451C2214yescomplemented
103#2450C2218yes—
104#2449C2218yes—
105#2448C2214yescomplemented
106#2447C2214yescomplemented
107#2446C2214yescomplemented
108#2445C2214yescomplemented
109#2444C2218yes—
110#2443C2218yes—
111#2402C2218yescomplemented
112#2401C2218yescomplemented
113#2396C2214yes—
114#2396C2214yes—
115#2396C2218yescomplemented
116#2395C2218yescomplemented
117#2392C2214yes—
118#2392C2214yes—
119#2324C2214yes—
120#2324C2214yes—
121#2323C2214yes—
122#2323C2214yes—
123#2322C2218yes—
124#2321C2218yes—
125C4×#125C2218yescomplemented
126C4×#126C2218yescomplemented
127C4×C22⋊Q8C2218yescomplemented
128C4×#123C2218yes—
129C4×#123C2218yes—
130C4×#123C2218yescomplemented
131#2297C2212yes—
132#2297C2212yes—
133#2297C2212yes—
134#2297C2212yes—
135#2296C2212yes—
136#2296C2212yes—
137#2296C2212yes—
138#2296C2212yes—
139#2293C2214yes—
140#2293C2214yes—
141#2290C2214yes—
142#2290C2214yes—
143#2285C2211yescharacteristic
144#2285C2212yes—
145#2285C2212yes—
146#2285C2212yes—
147#2285C2214yes—
148#2285C2212yes—
149#2285C2211yescharacteristic
150#2285C2212yes—
151#2285C2212yes—
152C2×#384C2212yes—
153C2×#382C2212yes—
154#2280C2212yes—
155C2×#380C2214yes—
156C4×#117C2212yes—
157C2×C4×C4⋊C4C2212yes—
158C2×C4×C4⋊C4C2212yes—
159C22×#41C2312yes—
160C24×C4C2311yescharacteristic
161C24×C4C2312yes—
162#533—44no—
163#532—44no—
164C2×C4⋊Q8C2311yescharacteristic
165C2×C4⋊Q8C2312yes—
166C2×#127C2311yescharacteristic
167C2×#126C2318yes—
168C2×#125C2318yes—
169C2×#125C2312yes—
170C2×#124C2312yes—
171#525—216no—
172C2×#123C2314yes—
173C2×#123C2318yes—
174C2×#123C2318yes—
175C2×#123C2318yes—
176C2×C22⋊Q8C2312yes—
177C2×C22⋊Q8C2312yes—
178C2×C22⋊Q8C2314yes—
179C2×C22⋊Q8C2318yes—
180C2×#121C2312yes—
181C2×#121C2312yes—
182C2×#121C2314yes—
183C2×#120C2314yes—
184C4×#41—48no—
185C2×C4×Q8C2314yes—
186C2×C4×Q8C2314yes—
187C2×C4×D4C2314yes—
188C2×C4×D4C2314yes—
189C2×C4×D4C2318yes—
190C2×C4×D4C2314yes—
191C2×C4×D4C2314yes—
192C2×#117—44no—
193C2×#117—44no—
194C2×#117C2312yes—
195C2×#117C2312yes—
196C2×#117C2312yes—
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2311yescharacteristic
200C2×#117C2311yescharacteristic
201C2×#117C2311yescharacteristic
202C2×#117C2311yescharacteristic
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2314yes—
206C2×#117C2311yescharacteristic
207C2×#117C2312yes—
208C2×#117C2311yescharacteristic
209C22×C4⋊C4C2312yes—
210C22×C4⋊C4C2312yes—
211C22×C4⋊C4C2314yes—
212C22×C4⋊C4C2314yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C42—28no—
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2314yes—
227#401C2318yes—
228#400C2314yes—
229#400C2314yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#399C2314yes—
240#399C2314yes—
241#399C2318yes—
242#399C2318yes—
243#398C2314yes—
244#398C2314yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#397C2314yes—
255#397C2314yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2318yes—
269#395C2314yes—
270#395C2314yes—
271#395C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2314yes—
275#394C2314yes—
276#394C2318yes—
277#394C2318yes—
278#393C2314yes—
279#393C2314yes—
280#393C2318yes—
281#392C2314yes—
282#392C2314yes—
283#391C2314yes—
284#391C2314yes—
285#391C2314yes—
286#391C2312yes—
287#391C2312yes—
288#391C2318yes—
289#390C2318yes—
290#390C2318yes—
291#390C2314yes—
292#390C2314yes—
293#390C2314yes—
294#390C2312yes—
295#390C2312yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2318yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2314yes—
345#386C2314yes—
346#386C2314yes—
347#386C2314yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2314yes—
356#385C2314yes—
357#385C2314yes—
358#385C2314yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#384C2312yes—
366#384C2312yes—
367#384C2312yes—
368#384C2314yes—
369#384C2314yes—
370#384C2312yes—
371#384C2312yes—
372#384C2312yes—
373#383C2318yes—
374#382C2318yes—
375#382C2311yescharacteristic
376#382C2311yescharacteristic
377#382C2312yes—
378#382C2312yes—
379#382C2314yes—
380#382C2314yes—
381#382C2312yes—
382#382C2312yes—
383#382C2312yes—
384#381C2314yes—
385#381C2318yes—
386#381C2318yes—
387#381C2318yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2318yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#379C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2318yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427#376C2314yes—
428C2×#95C2314yes—
429C2×#95C2314yes—
430C43C2314yes—
431C25C2411yescharacteristic
432C2×#41—28no—
433C2×#41—28no—
434C2×#41—28no—
435C22×Q8C2412yes—
436C22×Q8C2414yes—
437C22×D4C2414yes—
438C22×D4C2412yes—
439C22×D4C2414yes—
440C22×D4C2414yes—
441C22×D4C2414yes—
442C23×C4—24no—
443C23×C4—24no—
444C23×C4—28no—
445C23×C4—48no—
446C23×C4#4118yes—
447C23×C4C2412yes—
448C23×C4C2414yes—
449C23×C4C2414yes—
450C23×C4C2414yes—
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2414yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2418yes—
461C23×C4C2411yescharacteristic
462C4⋊Q8—44no—
463C4⋊Q8—42no—
464#127—42no—
465#126—416no—
466#125—44no—
467#125—416no—
468#124—44no—
469#123—216no—
470#123—416no—
471#123—416no—
472#123—416no—
473C22⋊Q8—28no—
474C22⋊Q8—28no—
475C22⋊Q8—48no—
476C22⋊Q8—416no—
477#121—28no—
478#121—28no—
479#121—48no—
480#120—216no—
481C4×Q8—48no—
482C4×Q8—48no—
483C4×D4—216no—
484C4×D4—216no—
485C4×D4—48no—
486C4×D4—48no—
487C4×D4—416no—
488#117—28no—
489#117—28no—
490#117—28no—
491#117—42no—
492#117—44no—
493#117—42no—
494#117—44no—
495#117—44no—
496#117—44no—
497#117—44no—
498#117—42no—
499#117—42no—
500#117—42no—
501#117—42no—
502#117—48no—
503C2×C4⋊C4—48no—
504C2×C4⋊C4—48no—
505C2×C4⋊C4—44no—
506C2×C4⋊C4—44no—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2414yes—
511C2×C4⋊C4C2414yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2418yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2414yes—
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⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C22⋊C4—44no—
543C2×C22⋊C4—44no—
544C2×C22⋊C4C2414yes—
545C2×C22⋊C4C2414yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2418yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2412yes—
557C2×C22⋊C4C2412yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2418yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C42—24no—
571C2×C42—28no—
572C2×C42—28no—
573C2×C42—28no—
574C2×C42—28no—
575C2×C42—28no—
576C2×C42—24no—
577C2×C42—28no—
578C2×C42—24no—
579C2×C42—24no—
580C2×C42—48no—
581C2×C42C2414yes—
582C2×C42C2411yescharacteristic
583C2×C42C2411yescharacteristic
584C2×C42C2411yescharacteristic
585C2×C42C2411yescharacteristic
586C2×C42C2414yes—
587C2×C42C2412yes—
588C2×C42C2412yes—
589C2×C42C2412yes—
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2412yes—
593C2×C42C2412yes—
594C2×C42C2414yes—
595C2×C42C2412yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2418yes—
600C2×C42C2418yes—
601C2×C42C2418yes—
602#95C2414yes—
603#95C2414yes—
604#95C2414yes—
605#95C2414yes—
606#95C2414yes—
607#95C2414yes—
608#95C2414yes—
609#95C2414yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633#95C2418yes—
634C24—22no—
635C24—22no—
636C24—44no—
637C24C2×#4114yes—
638C24C2514yes—
639C24C2511yescharacteristic
640C24C2511yescharacteristic
641C24C2511yescharacteristic
642#41—432no—
643C2×Q8—24no—
644C2×Q8—24no—
645C2×Q8—24no—
646C2×Q8—44no—
647C2×Q8—48no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—44no—
657C2×D4—48no—
658C2×D4—48no—
659C2×D4—48no—
660C22×C4—24no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—232no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—28no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—24no—
676C22×C4—28no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—28no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—48no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—432no—
695C22×C4C2×#4114yes—
696C22×C4C2×#4114yes—
697C22×C4C2×#4114yes—
698C22×C4C2×#4114yes—
699C22×C4C2×#4114yes—
700C22×C4C2×#4114yes—
701C22×C4H(5,𝔽2)14yes—
702C22×C42−1+414yes—
703C22×C4C2514yes—
704C22×C4C2514yes—
705C22×C4C2518yes—
706C22×C4C2514yes—
707C22×C4C2514yes—
708C22×C4C2514yes—
709C22×C4C2512yes—
710C22×C4C2512yes—
711C22×C4C2518yes—
712C22×C4C2514yes—
713C22×C4C2512yes—
714C22×C4C2512yes—
715C22×C4C2511yescharacteristic
716C22×C4C2511yescharacteristic
717C22×C4C2514yes—
718C22×C4C2511yescharacteristic
719C22×C4C2511yescharacteristic
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—28no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—216no—
731C4⋊C4—216no—
732C4⋊C4—44no—
733C4⋊C4—44no—
734C4⋊C4—44no—
735C4⋊C4—44no—
736C4⋊C4—42no—
737C4⋊C4—44no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—48no—
744C4⋊C4—44no—
745C4⋊C4—48no—
746C4⋊C4—44no—
747C4⋊C4—48no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C22⋊C4—28no—
756C22⋊C4—28no—
757C22⋊C4—28no—
758C22⋊C4—28no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—216no—
763C22⋊C4—216no—
764C22⋊C4—42no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—48no—
772C22⋊C4—48no—
773C22⋊C4—48no—
774C22⋊C4—48no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C42—24no—
782C42—24no—
783C42—28no—
784C42—28no—
785C42—24no—
786C42—24no—
787C42—28no—
788C42—24no—
789C42—24no—
790C42—24no—
791C42—28no—
792C42—24no—
793C42—22no—
794C42—22no—
795C42—22no—
796C42—22no—
797C42—28no—
798C42—28no—
799C42—48no—
800C42—48no—
801C42—48no—
802C23—24no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—24no—
808C23—24no—
809C23—28no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—28no—
814C23—28no—
815C23—48no—
816C23—48no—
817C23—48no—
818C23C22×#4112yes—
819C23C22×#4112yes—
820C23C22×#4112yes—
821C23C2×H(5,𝔽2)12yes—
822C23C2×2−1+412yes—
823C23C2611yescharacteristic
824Q8—48no—
825Q8—88no—
826D4—416no—
827D4—48no—
828D4—88no—
829D4—88no—
830D4—88no—
831C2×C4—216no—
832C2×C4—24no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—24no—
838C2×C4—28no—
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—28no—
842C2×C4—28no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—28no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—24no—
865C2×C4—28no—
866C2×C4—24no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—416no—
874C2×C4—416no—
875C2×C4—48no—
876C2×C4—416no—
877C2×C4—88no—
878C2×C4—84no—
879C2×C4—84no—
880C2×C4—816no—
881C2×C4#539116yes—
882C2×C4C22×#4112yes—
883C2×C4C22×#4112yes—
884C2×C4C22×#4112yes—
885C2×C4C22×#4112yes—
886C2×C4C2×H(5,𝔽2)12yes—
887C2×C4C2×H(5,𝔽2)12yes—
888C2×C4C2×2−1+412yes—
889C2×C4C2×2−1+412yes—
890C2×C4#58518yes—
891C22—24no—
892C22—24no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—22no—
897C22—22no—
898C22—416no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—48no—
904C22—48no—
905C22—44no—
906C22—44no—
907C22—44no—
908C22C2×#53914yes—
909C22C23×#4111yescharacteristic
910C22C22×H(5,𝔽2)11yescharacteristic
911C22C22×2−1+411yescharacteristic
912C22C2×#58514yes—
913C4—28no—
914C4—22no—
915C4—22no—
916C4—42no—
917C4—44no—
918C4—42no—
919C4—44no—
920C4—42no—
921C4—48no—
922C4—42no—
923C4—48no—
924C4—44no—
925C4—44no—
926C4—44no—
927C4—44no—
928C4C2×#53914yes—
929C4C2×#53914yes—
930C2—24no—
931C2—42no—
932C2—42no—
933C2—84no—
934C2C22×#53911yescharacteristic
935C2#6275912yes—
936C2#6276112yes—
937C2#6281412yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radical#34633C2
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. #52248C2semidirect
2. #52247C2semidirect
3. #52246C2semidirect
4. #37383C2semidirect
5. #37382C2semidirect
6. #37289C2semidirect
7. #37288C2semidirect
8. #37287C2semidirect
9. #37286C2semidirect
10. #37236C2semidirect
11. #37124C2semidirect
12. #36726C2semidirect
13. #36626C2semidirect
14. #34816C2semidirect
15. #34815C2semidirect
16. #34745C2semidirect
17. #34744C2semidirect
18. #34634C2semidirect
20. #34065C2semidirect
21. C2×#2285C2semidirect
37. #2795C22semidirect
38. #2794C22semidirect
39. #2793C22semidirect
40. #2792C22semidirect
41. #2791C22semidirect
42. #2790C22semidirect
43. #2789C22semidirect
44. #2785C22semidirect
45. #2783C22semidirect
46. #2782C22semidirect
47. #2781C22semidirect
48. #2775C22semidirect
49. #2769C22semidirect
50. #2767C22semidirect
51. #2765C22semidirect
55. #2744C22semidirect
61. #2721C22semidirect
62. #2720C22semidirect
63. #2718C22semidirect
72. #2680C22semidirect
87. #2514C22semidirect
88. #2513C22semidirect
89. #2512C22semidirect
90. #2511C22semidirect
92. #2509C22semidirect
93. #2508C22semidirect
94. #2507C22semidirect
95. #2506C22semidirect
99. #2454C22semidirect
100. #2453C22semidirect
101. #2452C22semidirect
102. #2451C22semidirect
105. #2448C22semidirect
106. #2447C22semidirect
107. #2446C22semidirect
108. #2445C22semidirect
111. #2402C22semidirect
112. #2401C22semidirect
115. #2396C22semidirect
116. #2395C22semidirect
125. C4×#125C22semidirect
126. C4×#126C22semidirect
127. C4×C22⋊Q8C22semidirect
130. C4×#123C22semidirect

Maximal subgroups

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

subgroupindex
#522482
#522472
#522462
#373832
#373822
#372892
#372882
#372872
#372862
#372362
#371242
#367262
#366262
#348162
#348152
#347452
#347442
#346342
#346332
#340652
C2×#22852