Finite Group Databasebeta

← #7646189

Subgroups — #7646189

Order 512.

4772 conjugacy classes of subgroups.

The subgroup lattice has 1031 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42768C214yesmaximal, complemented
2#42707C214yesmaximal, complemented
3#42604C214yesmaximal, complemented
4#42549C214yesmaximal, complemented
5#40216C214yesmaximal, complemented
6#40127C214yesmaximal, complemented
7#39784C214yesmaximal, complemented
8#39213C214yesmaximal, complemented
9#37462C214yesmaximal, complemented
10#36980C214yesmaximal, complemented
11#36765C214yesmaximal, complemented
12#35545C212yesmaximal, complemented
13#35542C212yesmaximal, complemented
14#35257C212yesmaximal, complemented
15#35167C211yesmaximal, characteristic, complemented
16#35158C211yesmaximal, characteristic, complemented
17#35151C211yesmaximal, characteristic, complemented
18#35150C211yesmaximal, characteristic
19#35083C214yesmaximal, complemented
20#34742C212yesmaximal, complemented
21#34271C211yesmaximal, characteristic, complemented
22C2×#2347C211yesmaximal, characteristic, complemented
23C4×#537C211yesmaximal, characteristic, complemented
24C2×#544C2211yescharacteristic
25C2×#544C2212yes—
26C2×#537C2211yescharacteristic
27C2×#525C2212yes—
28C2×C4×#41C2212yes—
29C22×#117C2211yescharacteristic
30#2857C2214yes—
31#2857C2214yescomplemented
32#2855C2214yes—
33#2854C2214yes—
34#2851C2214yescomplemented
35#2850C2214yes—
36#2838C2218yes—
37#2829C2218yes—
38#2800C2218yes—
39#2798C2218yes—
40#2779C2218yes—
41#2775C2218yescomplemented
42#2770C2218yescomplemented
43#2766C2218yescomplemented
44#2764C2218yescomplemented
45#2759C2218yescomplemented
46#2758C2218yescomplemented
47#2757C2218yescomplemented
48#2754C2218yes—
49#2737C2218yescomplemented
50#2731C2218yes—
51#2718C2218yes—
52#2712C2218yes—
53#2705C2218yes—
54#2663C2218yes—
55#2659C2214yes—
56#2654C2218yescomplemented
57#2653C2218yes—
58#2651C2218yes—
59#2650C2218yescomplemented
60#2639C2214yes—
61#2632C2218yes—
62#2629C2214yescomplemented
63#2628C2214yescomplemented
64#2626C2214yes—
65#2617C2214yes—
66#2563C2214yes—
67#2562C2214yes—
68#2562C2214yes—
69#2552C2214yescomplemented
70#2551C2214yescomplemented
71#2550C2214yescomplemented
72#2550C2214yescomplemented
73#2547C2214yes—
74#2525C2218yes—
75#2514C2214yescomplemented
76#2513C2214yescomplemented
77#2512C2214yescomplemented
78#2512C2214yescomplemented
79#2511C2214yescomplemented
80#2511C2214yescomplemented
81#2510C2218yes—
82#2509C2214yescomplemented
83#2508C2214yescomplemented
84#2497C2214yescomplemented
85#2496C2214yescomplemented
86#2495C2214yescomplemented
87#2494C2214yescomplemented
88#2492C2214yes—
89#2492C2214yescomplemented
90#2491C2214yes—
91#2491C2214yescomplemented
92#2490C2214yes—
93#2490C2214yescomplemented
94#2489C2214yes—
95#2489C2214yescomplemented
96#2488C2218yes—
97#2481C2218yes—
98#2472C2218yes—
99#2461C2218yes—
100#2454C2214yescomplemented
101#2453C2214yescomplemented
102#2452C2214yescomplemented
103#2452C2214yescomplemented
104#2451C2214yescomplemented
105#2451C2214yescomplemented
106#2450C2218yes—
107#2449C2218yes—
108#2448C2214yescomplemented
109#2447C2214yescomplemented
110#2441C2214yes—
111#2441C2214yes—
112#2439C2214yes—
113#2439C2214yes—
114#2423C2212yes—
115#2423C2212yes—
116#2422C2212yes—
117#2422C2212yes—
118#2421C2212yes—
119#2421C2212yes—
120#2420C2212yes—
121#2420C2212yes—
122#2419C2214yes—
123#2419C2214yes—
124#2418C2214yes—
125#2418C2214yes—
126#2415C2214yes—
127#2415C2214yes—
128#2414C2214yes—
129#2414C2214yes—
130#2395C2214yes—
131#2395C2214yes—
132#2370C2214yescomplemented
133#2370C2214yescomplemented
134#2369C2214yescomplemented
135#2365C2214yescomplemented
136#2347C2214yes—
137#2347C2214yes—
138#2347C2214yes—
139#2347C2214yes—
140#2334C2218yescomplemented
141#2332C2218yescomplemented
142#2329C2214yes—
143#2325C2214yes—
144#2324C2214yescomplemented
145#2323C2214yescomplemented
146#2317C2212yes—
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2311C2212yes—
150#2311C2212yes—
151#2311C2212yes—
152C4×C22⋊Q8C2214yes—
153C4×C22⋊Q8C2214yescomplemented
154C4×#123C2214yes—
155C4×#123C2214yes—
156C4×#121C2214yes—
157C4×#121C2214yescomplemented
158#2297C2212yes—
159#2296C2212yes—
160C2×#389C2211yescharacteristic
161C2×#389C2211yescharacteristic
162C2×#388C2212yes—
163C2×#388C2212yes—
164#2285C2212yes—
165C2×#383C2212yes—
166#2280C2212yes—
167C2×#380C2211yescharacteristic
168#2274C2212yes—
169C2×C4×C4⋊C4C2212yes—
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2211yescharacteristic
173C22×#41C2312yes—
174C24×C4C2311yescharacteristic
175#544—28no—
176#544—48no—
177#537—28no—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2314yes—
182C2×#126C2318yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#124C2314yes—
187C2×#124C2318yes—
188#525—48no—
189C2×#123C2314yes—
190C2×#123C2314yes—
191C2×#123C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2318yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2312yes—
201C2×#121C2312yes—
202C2×#120C2314yes—
203C4×#41—48no—
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2312yes—
206C2×C4×Q8C2314yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2314yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2312yes—
213C2×C4×D4C2314yes—
214C2×#117—28no—
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2314yes—
235C22×C42C2312yes—
236C22×C42C2312yes—
237#401C2318yes—
238#400C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2318yes—
243#400C2314yes—
244#400C2318yes—
245#400C2314yes—
246#400C2318yes—
247#399C2318yes—
248#399C2314yes—
249#399C2318yes—
250#399C2314yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2314yes—
255#398C2314yes—
256#398C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2314yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2314yes—
264#397C2318yes—
265#397C2314yes—
266#397C2314yes—
267#397C2314yes—
268#397C2314yes—
269#397C2318yes—
270#396C2318yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#395C2318yes—
276#395C2318yes—
277#395C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2314yes—
281#394C2314yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2314yes—
286#394C2314yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2318yes—
291#393C2318yes—
292#392C2318yes—
293#391C2314yes—
294#391C2314yes—
295#391C2314yes—
296#391C2318yes—
297#391C2318yes—
298#391C2318yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2318yes—
303#391C2314yes—
304#391C2312yes—
305#391C2312yes—
306#390C2318yes—
307#390C2314yes—
308#390C2314yes—
309#390C2314yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2314yes—
314#390C2312yes—
315#390C2312yes—
316#389C2314yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2318yes—
324#389C2318yes—
325#389C2318yes—
326#389C2312yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2312yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2312yes—
339#389C2312yes—
340#389C2314yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2314yes—
359#388C2314yes—
360#388C2314yes—
361#388C2314yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2314yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2314yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2314yes—
376#387C2314yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2314yes—
382#386C2314yes—
383#386C2314yes—
384#386C2314yes—
385#385C2318yes—
386#385C2318yes—
387#385C2314yes—
388#385C2314yes—
389#385C2318yes—
390#385C2318yes—
391#385C2314yes—
392#385C2314yes—
393#384C2314yes—
394#384C2314yes—
395#384C2312yes—
396#384C2312yes—
397#383C2318yes—
398#383C2318yes—
399#383C2318yes—
400#382C2318yes—
401#382C2314yes—
402#382C2314yes—
403#382C2312yes—
404#382C2312yes—
405#381C2314yes—
406#381C2314yes—
407#381C2314yes—
408#380C2314yes—
409#380C2312yes—
410#380C2312yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2312yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2318yes—
423#380C2314yes—
424#380C2312yes—
425#379C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C22⋊C4C2318yes—
446C4×C22⋊C4C2318yes—
447C4×C22⋊C4C2312yes—
448C4×C22⋊C4C2312yes—
449C4×C22⋊C4C2312yes—
450C4×C22⋊C4C2312yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C2×#95C2312yes—
456C2×#95C2312yes—
457C2×#95C2311yescharacteristic
458C2×#95C2311yescharacteristic
459C2×#95C2312yes—
460C2×#95C2312yes—
461C2×#95C2312yes—
462C25C2411yescharacteristic
463C2×#41—28no—
464C2×#41—28no—
465C2×#41—28no—
466C22×Q8C2412yes—
467C22×Q8C2414yes—
468C22×Q8C2418yes—
469C22×D4C2414yes—
470C22×D4C2412yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2414yes—
480C23×C4C2411yescharacteristic
481C23×C4C2411yescharacteristic
482C23×C4C2411yescharacteristic
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2414yes—
489C23×C4C2414yes—
490C23×C4C2412yes—
491C23×C4C2411yescharacteristic
492C4⋊Q8—216no—
493C4⋊Q8—48no—
494C4⋊Q8—48no—
495C4⋊Q8—84no—
496#126—416no—
497#125—216no—
498#125—48no—
499#125—48no—
500#124—84no—
501#124—88no—
502#123—48no—
503#123—48no—
504#123—48no—
505C22⋊Q8—216no—
506C22⋊Q8—216no—
507C22⋊Q8—416no—
508C22⋊Q8—416no—
509C22⋊Q8—44no—
510C22⋊Q8—44no—
511#121—216no—
512#121—216no—
513#121—44no—
514#121—44no—
515#120—48no—
516C4×Q8—44no—
517C4×Q8—44no—
518C4×Q8—84no—
519C4×D4—44no—
520C4×D4—44no—
521C4×D4—48no—
522C4×D4—48no—
523C4×D4—48no—
524C4×D4—48no—
525C4×D4—84no—
526#117—28no—
527#117—28no—
528#117—28no—
529#117—216no—
530#117—216no—
531#117—48no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—44no—
536C2×C4⋊C4—44no—
537C2×C4⋊C4#4118yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C22⋊C4—28no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—82no—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2412yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C42—28no—
611C2×C42—24no—
612C2×C42—24no—
613C2×C42—48no—
614C2×C42—82no—
615C2×C42—82no—
616C2×C42C2412yes—
617C2×C42C2414yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2414yes—
626C2×C42C2414yes—
627C2×C42C2414yes—
628C2×C42C2418yes—
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2418yes—
632C2×C42C2414yes—
633#95C2411yescharacteristic
634#95C2411yescharacteristic
635#95C2411yescharacteristic
636#95C2411yescharacteristic
637#95C2412yes—
638#95C2412yes—
639#95C2414yes—
640#95C2414yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2418yes—
665#95C2418yes—
666#95C2414yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—41no—
677C24—41no—
678C24—41no—
679C24—41no—
680C24C2512yes—
681C24C2514yes—
682C24C2511yescharacteristic
683#41—432no—
684C2×Q8—24no—
685C2×Q8—28no—
686C2×Q8—24no—
687C2×Q8—24no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—48no—
691C2×Q8—48no—
692C2×Q8—48no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—24no—
697C2×D4—28no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C22×C4—22no—
709C22×C4—24no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—24no—
716C22×C4—22no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—28no—
721C22×C4—28no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—28no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—28no—
730C22×C4—41no—
731C22×C4—42no—
732C22×C4—41no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—41no—
747C22×C4—44no—
748C22×C4—41no—
749C22×C4—416no—
750C22×C4C2×#4118yes—
751C22×C4C2×#4114yes—
752C22×C4H(5,𝔽2)14yes—
753C22×C42−1+414yes—
754C22×C4C2512yes—
755C22×C4C2511yescharacteristic
756C22×C4C2511yescharacteristic
757C22×C4C2514yes—
758C22×C4C2511yescharacteristic
759C22×C4C2514yes—
760C22×C4C2512yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2514yes—
766C22×C4C2514yes—
767C22×C4C2514yes—
768C22×C4C2514yes—
769C22×C4C2511yescharacteristic
770C22×C4C2514yes—
771C22×C4C2511yescharacteristic
772C22×C4C2511yescharacteristic
773C22×C4C2512yes—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—28no—
778C4⋊C4—28no—
779C4⋊C4—216no—
780C4⋊C4—28no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—28no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—48no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C4⋊C4—48no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—48no—
810C4⋊C4—44no—
811C4⋊C4C2×#41116yes—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—28no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—48no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C22⋊C4—44no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—44no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C42—28no—
843C42—28no—
844C42—28no—
845C42—24no—
846C42—24no—
847C42—28no—
848C42—28no—
849C42—24no—
850C42—24no—
851C42—44no—
852C42—44no—
853C42—44no—
854C42—44no—
855C42—44no—
856C42—44no—
857C42—48no—
858C42—48no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—22no—
864C23—24no—
865C23—22no—
866C23—24no—
867C23—22no—
868C23—24no—
869C23—24no—
870C23—22no—
871C23—22no—
872C23—24no—
873C23—22no—
874C23—24no—
875C23—22no—
876C23—24no—
877C23—44no—
878C23—44no—
879C23—44no—
880C23—82no—
881C23—82no—
882C23—82no—
883C23—82no—
884C23C22×#4112yes—
885C23C2×H(5,𝔽2)12yes—
886C23C2×2−1+412yes—
887C23C2611yescharacteristic
888Q8—48no—
889Q8—88no—
890Q8—168no—
891D4—416no—
892D4—48no—
893D4—88no—
894D4—88no—
895D4—88no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—24no—
900C2×C4—21no—
901C2×C4—24no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—24no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—24no—
938C2×C4—21no—
939C2×C4—24no—
940C2×C4—21no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—48no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—48no—
954C2×C4—44no—
955C2×C4—48no—
956C2×C4—48no—
957C2×C4—416no—
958C2×C4—88no—
959C2×C4—84no—
960C2×C4—84no—
961C2×C4—82no—
962C2×C4—82no—
963C2×C4—88no—
964C2×C4#542116yes—
965C2×C4C22×#4118yes—
966C2×C4C22×#4114yes—
967C2×C4C2×H(5,𝔽2)14yes—
968C2×C4C2×2−1+414yes—
969C2×C4#58512yes—
970C2×C4#58512yes—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—44no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—44no—
986C22—42no—
987C22—44no—
988C22—42no—
989C22—44no—
990C22—42no—
991C22—88no—
992C22C2×#54214yes—
993C22C23×#4111yescharacteristic
994C22C22×H(5,𝔽2)11yescharacteristic
995C22C22×2−1+411yescharacteristic
996C22C2×#58511yescharacteristic
997C22C2×#58511yescharacteristic
998C22H(7,𝔽2)11yescharacteristic
999C222−1+611yescharacteristic
1000C4—28no—
1001C4—22no—
1002C4—22no—
1003C4—44no—
1004C4—44no—
1005C4—44no—
1006C4—41no—
1007C4—41no—
1008C4—44no—
1009C4—41no—
1010C4—44no—
1011C4—44no—
1012C4—44no—
1013C4—41no—
1014C4—44no—
1015C4—42no—
1016C4—44no—
1017C4—42no—
1018C4—44no—
1019C4C2×#54218yes—
1020C2—24no—
1021C2—84no—
1022C2—82no—
1023C2C22×#54211yescharacteristic
1024C2#6279311yescharacteristic
1025C2#6284711yescharacteristic
1026C2#6295711yescharacteristic
1027C2#6295811yescharacteristic
1028C2#6295911yescharacteristic
1029C2#6296011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35150C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42768C2semidirect
2. #42707C2semidirect
3. #42604C2semidirect
4. #42549C2semidirect
5. #40216C2semidirect
6. #40127C2semidirect
7. #39784C2semidirect
8. #39213C2semidirect
9. #37462C2semidirect
10. #36980C2semidirect
11. #36765C2semidirect
12. #35545C2semidirect
13. #35542C2semidirect
14. #35257C2semidirect
15. #35167C2semidirect
16. #35158C2semidirect
17. #35151C2semidirect
19. #35083C2semidirect
20. #34742C2semidirect
21. #34271C2semidirect
22. C2×#2347C2semidirect
23. C4×#537C2semidirect
31. #2857C22semidirect
34. #2851C22semidirect
41. #2775C22semidirect
42. #2770C22semidirect
43. #2766C22semidirect
44. #2764C22semidirect
45. #2759C22semidirect
46. #2758C22semidirect
47. #2757C22semidirect
49. #2737C22semidirect
56. #2654C22semidirect
59. #2650C22semidirect
62. #2629C22semidirect
63. #2628C22semidirect
69. #2552C22semidirect
70. #2551C22semidirect
71. #2550C22semidirect
72. #2550C22semidirect
75. #2514C22semidirect
76. #2513C22semidirect
77. #2512C22semidirect
78. #2512C22semidirect
79. #2511C22semidirect
80. #2511C22semidirect
82. #2509C22semidirect
83. #2508C22semidirect
84. #2497C22semidirect
85. #2496C22semidirect
86. #2495C22semidirect
87. #2494C22semidirect
89. #2492C22semidirect
91. #2491C22semidirect
93. #2490C22semidirect
95. #2489C22semidirect
100. #2454C22semidirect
101. #2453C22semidirect
102. #2452C22semidirect
103. #2452C22semidirect
104. #2451C22semidirect
105. #2451C22semidirect
108. #2448C22semidirect
109. #2447C22semidirect
132. #2370C22semidirect
133. #2370C22semidirect
134. #2369C22semidirect
135. #2365C22semidirect
140. #2334C22semidirect
141. #2332C22semidirect
144. #2324C22semidirect
145. #2323C22semidirect
153. C4×C22⋊Q8C22semidirect
157. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#427682
#427072
#426042
#425492
#402162
#401272
#397842
#392132
#374622
#369802
#367652
#355452
#355422
#352572
#351672
#351582
#351512
#351502
#350832
#347422
#342712
C2×#23472
C4×#5372