Finite Group Databasebeta

← #7644411

Subgroups — #7644411

Order 512.

5586 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42857C214yesmaximal, complemented
2#42842C214yesmaximal, complemented
3#42634C214yesmaximal, complemented
4#42575C214yesmaximal, complemented
5#40893C218yesmaximal, complemented
6#40754C218yesmaximal, complemented
7#37499C214yesmaximal, complemented
8#37492C214yesmaximal, complemented
9#37371C214yesmaximal, complemented
10#37338C214yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35673C211yesmaximal, characteristic, complemented
13#35621C211yesmaximal, characteristic, complemented
14#35616C211yesmaximal, characteristic, complemented
15#35592C211yesmaximal, characteristic, complemented
16#35574C211yesmaximal, characteristic, complemented
17#35558C211yesmaximal, characteristic, complemented
18#35513C211yesmaximal, characteristic
19#35308C211yesmaximal, characteristic, complemented
20#35254C211yesmaximal, characteristic, complemented
21#34639C211yesmaximal, characteristic, complemented
22C2×#2640C211yesmaximal, characteristic, complemented
23#34268C211yesmaximal, characteristic, complemented
24#34258C211yesmaximal, characteristic, complemented
25#34070C211yesmaximal, characteristic, complemented
26C22×H(5,𝔽2)C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic, complemented
31C2×#535C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic, complemented
34C22×#124C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic, complemented
37C2×C4×#41C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic, complemented
39#2857C2212yescomplemented
40#2854C2214yescomplemented
41#2850C2212yescomplemented
42#2830C2218yescomplemented
43#2829C2218yescomplemented
44#2827C2218yescomplemented
45#2824C2218yescomplemented
46#2808C2218yescomplemented
47#2800C2218yescomplemented
48#2797C2218yescomplemented
49#2788C2218yescomplemented
50#2787C2218yescomplemented
51#2784C2218yescomplemented
52#2779C2218yescomplemented
53#2778C2218yescomplemented
54#2736C2218yescomplemented
55#2735C2218yescomplemented
56#2710C2218yescomplemented
57#2702C2218yescomplemented
58#2697C2218yescomplemented
59#2696C2218yescomplemented
60#2695C2218yescomplemented
61#2684C2218yescomplemented
62#2662C2218yescomplemented
63#2653C2218yescomplemented
64#2653C2218yescomplemented
65#2652C2218yescomplemented
66#2651C2218yescomplemented
67#2648C2218yescomplemented
68#2645C2212yescomplemented
69#2645C2212yescomplemented
70#2644C2212yescomplemented
71#2644C2212yescomplemented
72#2643C2214yescomplemented
73#2643C2214yescomplemented
74#2640C2214yescomplemented
75#2640C2214yescomplemented
76#2640C2214yescomplemented
77#2640C2214yescomplemented
78#2626C2218yescomplemented
79#2624C2214yescomplemented
80#2622C2218yescomplemented
81#2621C2212yescomplemented
82#2620C2212yescomplemented
83#2595C2218yescomplemented
84#2591C2214yescomplemented
85#2589C2218yescomplemented
86#2579C2214yescomplemented
87#2548C2214yescomplemented
88#2547C2212yescomplemented
89#2546C2212yescomplemented
90#2545C2212yescomplemented
91#2545C2214yescomplemented
92#2544C2212yescomplemented
93#2513C2214yescomplemented
94#2513C2214yescomplemented
95#2512C2214yescomplemented
96#2512C2214yescomplemented
97#2498C2218yescomplemented
98#2492C2214yescomplemented
99#2492C2214yescomplemented
100#2491C2214yescomplemented
101#2491C2214yescomplemented
102#2480C2218yescomplemented
103#2480C2218yescomplemented
104#2472C2218yescomplemented
105#2452C2214yescomplemented
106#2451C2214yescomplemented
107#2448C2214yescomplemented
108#2448C2214yescomplemented
109#2446C2214yescomplemented
110#2445C2214yescomplemented
111#2440C2214yescomplemented
112#2439C2214yescomplemented
113#2436C2214yescomplemented
114#2435C2214yes—
115#2435C2214yes—
116#2435C2212yes—
117#2433C2212yes—
118#2432C2214yes—
119#2432C2214yes—
120#2432C2212yes—
121#2431C2212yes—
122#2429C2214yescomplemented
123#2427C2214yescomplemented
124#2426C2214yescomplemented
125#2426C2214yescomplemented
126#2425C2218yescomplemented
127#2425C2218yescomplemented
128#2423C2214yescomplemented
129#2421C2214yescomplemented
130#2418C2218yescomplemented
131#2417C2214yescomplemented
132#2415C2214yescomplemented
133#2411C2214yescomplemented
134#2411C2214yescomplemented
135#2410C2218yes—
136#2409C2214yescomplemented
137#2408C2214yes—
138#2407C2214yes—
139#2405C2214yes—
140#2405C2214yes—
141#2401C2214yescomplemented
142#2401C2214yescomplemented
143C2×#397C2214yescomplemented
144C2×#393C2214yescomplemented
145#2367C2214yescomplemented
146#2365C2214yescomplemented
147#2359C2218yescomplemented
148#2341C2214yes—
149D4×C22⋊C4C2218yes—
150D4×C22⋊C4C2214yes—
151#2328C2212yescomplemented
152#2327C2212yescomplemented
153#2326C2212yescomplemented
154#2326C2212yescomplemented
155#2325C2214yescomplemented
156#2325C2214yescomplemented
157#2323C2214yescomplemented
158#2317C2211yescharacteristic, complemented
159#2316C2211yescharacteristic, complemented
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2311C2212yes—
163#2311C2211yescharacteristic, complemented
164#2309C2211yescharacteristic
165#2309C2211yescharacteristic
166#2309C2212yes—
167C4×C22⋊Q8C2214yescomplemented
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2212yes—
173#2297C2211yescharacteristic, complemented
174#2296C2211yescharacteristic, complemented
175#2296C2211yescharacteristic, complemented
176#2296C2211yescharacteristic, complemented
177C2×#391C2211yescharacteristic, complemented
178C2×#391C2211yescharacteristic, complemented
179C2×#390C2211yescharacteristic
180C2×#390C2211yescharacteristic
181C2×#390C2212yes—
182#2290C2214yescomplemented
183#2290C2214yescomplemented
184#2285C2211yescharacteristic, complemented
185#2274C2211yescharacteristic, complemented
186C2×#376C2211yescharacteristic, complemented
187C2×H(5,𝔽2)—28no—
188C2×H(5,𝔽2)—44no—
189C2×H(5,𝔽2)—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2312yes—
194C22×#41C2312yes—
195C23×Q8C2311yescharacteristic
196C23×Q8C2312yes—
197C23×D4C2311yescharacteristic
198C23×D4C2312yes—
199C23×D4C2314yes—
200C23×D4C2312yes—
201#537—44no—
202#536—28no—
203#536—44no—
204#536—44no—
205#535—44no—
206#532—28no—
207C2×C4⋊Q8—44no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×#127C2311yescharacteristic
215C2×#127C2312yes—
216C2×#126C2318yes—
217C2×#124—44no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2314yes—
224C2×#124C2312yes—
225C2×#124C2312yes—
226C2×#124C2318yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2318yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#121C2314yes—
242C2×#121C2312yes—
243C2×#120C2314yes—
244C2×#120C2318yes—
245#520—44no—
246#519—44no—
247C4×#41—44no—
248C4×#41—44no—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2312yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2312yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2318yes—
277C22×C22⋊C4C2314yes—
278C22×C22⋊C4C2314yes—
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2311yescharacteristic
282C22×C42C2312yes—
283C22×C42C2312yes—
284#401C2314yes—
285#401C2314yes—
286#400C2314yes—
287#400C2318yes—
288#400C2314yes—
289#400C2318yes—
290#400C2314yes—
291#400C2314yes—
292#400C2314yes—
293#400C2314yes—
294#399C2318yes—
295#399C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2314yes—
306#397C2314yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#396C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2314yes—
324#396C2314yes—
325#395C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#393C2318yes—
340#393C2318yes—
341#393C2318yes—
342#393C2318yes—
343#393C2318yes—
344#393C2318yes—
345#393C2318yes—
346#392C2318yes—
347#392C2318yes—
348#391C2311yescharacteristic
349#391C2312yes—
350#391C2312yes—
351#391C2312yes—
352#391C2312yes—
353#391C2312yes—
354#391C2312yes—
355#391C2318yes—
356#391C2318yes—
357#391C2312yes—
358#391C2314yes—
359#391C2311yescharacteristic
360#391C2314yes—
361#391C2312yes—
362#391C2312yes—
363#391C2312yes—
364#391C2312yes—
365#390C2311yescharacteristic
366#390C2312yes—
367#390C2312yes—
368#390C2312yes—
369#390C2312yes—
370#390C2318yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2312yes—
375#390C2312yes—
376#390C2318yes—
377#390C2312yes—
378#390C2312yes—
379#390C2314yes—
380#390C2318yes—
381#390C2311yescharacteristic
382#390C2312yes—
383#390C2314yes—
384#390C2312yes—
385#390C2312yes—
386#390C2312yes—
387#390C2312yes—
388#390C2318yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2312yes—
393#389C2318yes—
394#389C2318yes—
395#389C2318yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#388C2314yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#387C2318yes—
421#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2318yes—
428#387C2318yes—
429#386C2314yes—
430#386C2314yes—
431#386C2318yes—
432#386C2314yes—
433#386C2314yes—
434#386C2318yes—
435#386C2312yes—
436#386C2312yes—
437#386C2312yes—
438#386C2312yes—
439#386C2314yes—
440#386C2314yes—
441#386C2314yes—
442#386C2312yes—
443#386C2314yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2312yes—
449#386C2314yes—
450#385C2318yes—
451#385C2314yes—
452#385C2314yes—
453#385C2312yes—
454#385C2318yes—
455#385C2314yes—
456#385C2314yes—
457#385C2314yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2314yes—
462#385C2312yes—
463#385C2314yes—
464#384C2312yes—
465#384C2312yes—
466#382C2312yes—
467#382C2312yes—
468#380C2314yes—
469#380C2314yes—
470#380C2318yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2318yes—
475#380C2318yes—
476#379C2314yes—
477#379C2318yes—
478#379C2314yes—
479#379C2318yes—
480#379C2318yes—
481#379C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499#376C2312yes—
500#376C2312yes—
501#376C2312yes—
502#376C2312yes—
503C2×#95C2312yes—
504C2×#95C2312yes—
505C2×#95C2314yes—
506C2×#95C2314yes—
507C25C2412yes—
508C25C2414yes—
509H(5,𝔽2)—464no—
510C2×#41—28no—
511C2×#41—24no—
512C2×#41—28no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—44no—
521C2×#41—44no—
522C2×#41—44no—
523C2×#41—44no—
524C2×#41#4118yes—
525C22×Q8—24no—
526C22×Q8—24no—
527C22×Q8—24no—
528C22×Q8—44no—
529C22×Q8—84no—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2418yes—
536C22×D4—216no—
537C22×D4—28no—
538C22×D4—28no—
539C22×D4—24no—
540C22×D4—24no—
541C22×D4—24no—
542C22×D4—44no—
543C22×D4—44no—
544C22×D4—44no—
545C22×D4—44no—
546C22×D4—48no—
547C22×D4—48no—
548C22×D4C2412yes—
549C22×D4C2411yescharacteristic
550C22×D4C2412yes—
551C22×D4C2412yes—
552C22×D4C2411yescharacteristic
553C22×D4C2412yes—
554C22×D4C2412yes—
555C22×D4C2411yescharacteristic
556C22×D4C2414yes—
557C22×D4C2414yes—
558C22×D4C2414yes—
559C22×D4C2414yes—
560C22×D4C2418yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2411yescharacteristic
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2411yescharacteristic
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2411yescharacteristic
576C4⋊Q8—24no—
577C4⋊Q8—28no—
578C4⋊Q8—48no—
579C4⋊Q8—48no—
580C4⋊Q8—44no—
581C4⋊Q8—44no—
582#127—24no—
583#127—44no—
584#126—88no—
585#124—24no—
586#124—24no—
587#124—28no—
588#124—48no—
589#124—48no—
590#124—44no—
591#124—44no—
592#124—44no—
593#124—88no—
594#123—216no—
595#123—48no—
596#123—48no—
597#123—88no—
598C22⋊Q8—216no—
599C22⋊Q8—44no—
600C22⋊Q8—44no—
601C22⋊Q8—48no—
602C22⋊Q8—44no—
603C22⋊Q8—44no—
604C22⋊Q8—88no—
605#121—216no—
606#121—48no—
607#121—44no—
608#121—44no—
609#121—48no—
610#120—48no—
611#120—88no—
612C4×Q8—44no—
613C4×Q8—44no—
614C4×Q8—48no—
615C4×Q8—48no—
616C4×Q8—44no—
617C4×D4—216no—
618C4×D4—44no—
619C4×D4—44no—
620C4×D4—44no—
621C4×D4—48no—
622C4×D4—48no—
623C4×D4—48no—
624#117—24no—
625#117—24no—
626#117—24no—
627#117—24no—
628#117—24no—
629#117—44no—
630#117—44no—
631#117—48no—
632#117—44no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—44no—
636C2×C4⋊C4—44no—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C22⋊C4—44no—
669C2×C22⋊C4—44no—
670C2×C22⋊C4—84no—
671C2×C22⋊C4—88no—
672C2×C22⋊C4—84no—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2418yes—
713C2×C42—24no—
714C2×C42—24no—
715C2×C42—24no—
716C2×C42—44no—
717C2×C42—44no—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2414yes—
732C2×C42C2418yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2418yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772C24—28no—
773C24—24no—
774C24—24no—
775C24—24no—
776C24—44no—
777C24—44no—
778C24—44no—
779C24—44no—
780C24—48no—
781C24—48no—
782C24C2512yes—
783C24C2514yes—
784C24C2512yes—
785C24C2512yes—
786C24C2511yescharacteristic
787#41—232no—
788#41—432no—
789#41—432no—
790#41—416no—
791#41—416no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—22no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—24no—
799C2×Q8—22no—
800C2×Q8—24no—
801C2×Q8—24no—
802C2×Q8—22no—
803C2×Q8—22no—
804C2×Q8—24no—
805C2×Q8—22no—
806C2×Q8—48no—
807C2×Q8—48no—
808C2×Q8—48no—
809C2×Q8—416no—
810C2×Q8—816no—
811C2×Q8C2×#4114yes—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—28no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—28no—
822C2×D4—22no—
823C2×D4—28no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—22no—
831C2×D4—24no—
832C2×D4—22no—
833C2×D4—24no—
834C2×D4—24no—
835C2×D4—22no—
836C2×D4—24no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—432no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—48no—
845C2×D4—48no—
846C2×D4—48no—
847C2×D4—44no—
848C2×D4—48no—
849C2×D4—464no—
850C2×D4—432no—
851C2×D4—416no—
852C2×D4C2×#4118yes—
853C2×D4C2×#4114yes—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—28no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—24no—
871C22×C4—24no—
872C22×C4—42no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—42no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—48no—
889C22×C4—44no—
890C22×C4C2×#4118yes—
891C22×C4C2×#4114yes—
892C22×C4H(5,𝔽2)14yes—
893C22×C4H(5,𝔽2)14yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2512yes—
897C22×C4C2512yes—
898C22×C4C2512yes—
899C22×C4C2512yes—
900C22×C4C2512yes—
901C22×C4C2514yes—
902C22×C4C2512yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C4⋊C4—24no—
915C4⋊C4—28no—
916C4⋊C4—216no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—44no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—48no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—48no—
941C4⋊C4—48no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C22⋊C4—24no—
946C22⋊C4—28no—
947C22⋊C4—216no—
948C22⋊C4—24no—
949C22⋊C4—24no—
950C22⋊C4—24no—
951C22⋊C4—24no—
952C22⋊C4—28no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—44no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—48no—
973C22⋊C4—44no—
974C22⋊C4—48no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—48no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—48no—
982C22⋊C4—48no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C42—24no—
986C42—22no—
987C42—22no—
988C42—24no—
989C42—22no—
990C42—22no—
991C42—24no—
992C42—24no—
993C42—24no—
994C42—24no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—44no—
999C42—44no—
1000C42—44no—
1001C42—48no—
1002C42—48no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—24no—
1008C23—24no—
1009C23—22no—
1010C23—24no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—24no—
1015C23—22no—
1016C23—22no—
1017C23—24no—
1018C23—28no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—28no—
1023C23—24no—
1024C23—416no—
1025C23—48no—
1026C23—88no—
1027C23—84no—
1028C23—88no—
1029C23—84no—
1030C23—816no—
1031C23—164no—
1032C23—168no—
1033C23—164no—
1034C23C22×#4114yes—
1035C23C22×#4112yes—
1036C23C2×H(5,𝔽2)12yes—
1037C23C2×H(5,𝔽2)12yes—
1038C23C2611yescharacteristic
1039Q8—28no—
1040Q8—48no—
1041Q8—48no—
1042Q8—44no—
1043Q8—44no—
1044Q8—816no—
1045D4—216no—
1046D4—28no—
1047D4—416no—
1048D4—416no—
1049D4—48no—
1050D4—48no—
1051D4—48no—
1052D4—44no—
1053D4—48no—
1054D4—44no—
1055D4—88no—
1056D4—164no—
1057D4—168no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—216no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—28no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—28no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—416no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—48no—
1112C2×C4—48no—
1113C2×C4—48no—
1114C2×C4—84no—
1115C2×C4—84no—
1116C2×C4—84no—
1117C2×C4—84no—
1118C2×C4—88no—
1119C2×C4—88no—
1120C2×C4—164no—
1121C2×C4#538116yes—
1122C2×C4C22×#4114yes—
1123C2×C4C22×#4112yes—
1124C2×C4C22×#4112yes—
1125C2×C4C2×H(5,𝔽2)12yes—
1126C2×C4C2×H(5,𝔽2)12yes—
1127C2×C4C2×H(5,𝔽2)12yes—
1128C2×C4C2×H(5,𝔽2)12yes—
1129C22—24no—
1130C22—22no—
1131C22—24no—
1132C22—22no—
1133C22—28no—
1134C22—24no—
1135C22—42no—
1136C22—44no—
1137C22—42no—
1138C22—44no—
1139C22—48no—
1140C22—44no—
1141C22—42no—
1142C22—42no—
1143C22—44no—
1144C22—44no—
1145C22—48no—
1146C22—44no—
1147C22—42no—
1148C22—44no—
1149C22—42no—
1150C22—44no—
1151C22—42no—
1152C22—42no—
1153C22—168no—
1154C22—1616no—
1155C22C2×#53814yes—
1156C22C23×#4111yescharacteristic
1157C22C22×H(5,𝔽2)11yescharacteristic
1158C22C22×H(5,𝔽2)11yescharacteristic
1159C22H(7,𝔽2)12yes—
1160C222−1+612yes—
1161C4—24no—
1162C4—44no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—44no—
1167C4—44no—
1168C4—42no—
1169C4—44no—
1170C4—44no—
1171C4—42no—
1172C4—42no—
1173C4—44no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—44no—
1179C4C2×#53814yes—
1180C4C2×#53814yes—
1181C2—24no—
1182C2—44no—
1183C2—82no—
1184C2—82no—
1185C2—84no—
1186C2C22×#53811yescharacteristic
1187C2#6285712yes—
1188C2#6287611yescharacteristic
1189C2#6287812yes—
1190C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35513C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42857C2semidirect
2. #42842C2semidirect
3. #42634C2semidirect
4. #42575C2semidirect
5. #40893C2semidirect
6. #40754C2semidirect
7. #37499C2semidirect
8. #37492C2semidirect
9. #37371C2semidirect
10. #37338C2semidirect
11. #35677C2semidirect
12. #35673C2semidirect
13. #35621C2semidirect
14. #35616C2semidirect
15. #35592C2semidirect
16. #35574C2semidirect
17. #35558C2semidirect
19. #35308C2semidirect
20. #35254C2semidirect
21. #34639C2semidirect
22. C2×#2640C2semidirect
23. #34268C2semidirect
24. #34258C2semidirect
25. #34070C2semidirect
30. C2×#536C22semidirect
33. C22×C4⋊Q8C22semidirect
36. C2×#519C22semidirect
38. C2×C4×#41C22semidirect
39. #2857C22semidirect
40. #2854C22semidirect
41. #2850C22semidirect
42. #2830C22semidirect
43. #2829C22semidirect
44. #2827C22semidirect
45. #2824C22semidirect
46. #2808C22semidirect
47. #2800C22semidirect
48. #2797C22semidirect
49. #2788C22semidirect
50. #2787C22semidirect
51. #2784C22semidirect
52. #2779C22semidirect
53. #2778C22semidirect
54. #2736C22semidirect
55. #2735C22semidirect
56. #2710C22semidirect
57. #2702C22semidirect
58. #2697C22semidirect
59. #2696C22semidirect
60. #2695C22semidirect
61. #2684C22semidirect
62. #2662C22semidirect
63. #2653C22semidirect
64. #2653C22semidirect
65. #2652C22semidirect
66. #2651C22semidirect
67. #2648C22semidirect
68. #2645C22semidirect
69. #2645C22semidirect
70. #2644C22semidirect
71. #2644C22semidirect
72. #2643C22semidirect
73. #2643C22semidirect
74. #2640C22semidirect
75. #2640C22semidirect
76. #2640C22semidirect
77. #2640C22semidirect
78. #2626C22semidirect
79. #2624C22semidirect
80. #2622C22semidirect
81. #2621C22semidirect
82. #2620C22semidirect
83. #2595C22semidirect
84. #2591C22semidirect
85. #2589C22semidirect
86. #2579C22semidirect
87. #2548C22semidirect
88. #2547C22semidirect
89. #2546C22semidirect
90. #2545C22semidirect
91. #2545C22semidirect
92. #2544C22semidirect
93. #2513C22semidirect
94. #2513C22semidirect
95. #2512C22semidirect
96. #2512C22semidirect
97. #2498C22semidirect
98. #2492C22semidirect
99. #2492C22semidirect
100. #2491C22semidirect
101. #2491C22semidirect
102. #2480C22semidirect
103. #2480C22semidirect
104. #2472C22semidirect
105. #2452C22semidirect
106. #2451C22semidirect
107. #2448C22semidirect
108. #2448C22semidirect
109. #2446C22semidirect
110. #2445C22semidirect
111. #2440C22semidirect
112. #2439C22semidirect
113. #2436C22semidirect
122. #2429C22semidirect
123. #2427C22semidirect
124. #2426C22semidirect
125. #2426C22semidirect
126. #2425C22semidirect
127. #2425C22semidirect
128. #2423C22semidirect
129. #2421C22semidirect
130. #2418C22semidirect
131. #2417C22semidirect
132. #2415C22semidirect
133. #2411C22semidirect
134. #2411C22semidirect
136. #2409C22semidirect
141. #2401C22semidirect
142. #2401C22semidirect
143. C2×#397C22semidirect
144. C2×#393C22semidirect
145. #2367C22semidirect
146. #2365C22semidirect
147. #2359C22semidirect
151. #2328C22semidirect
152. #2327C22semidirect
153. #2326C22semidirect
154. #2326C22semidirect
155. #2325C22semidirect
156. #2325C22semidirect
157. #2323C22semidirect
158. #2317C22semidirect
159. #2316C22semidirect
163. #2311C22semidirect
167. C4×C22⋊Q8C22semidirect
173. #2297C22semidirect
174. #2296C22semidirect
175. #2296C22semidirect
176. #2296C22semidirect
177. C2×#391C22semidirect
178. C2×#391C22semidirect
182. #2290C22semidirect
183. #2290C22semidirect
184. #2285C22semidirect
185. #2274C22semidirect
186. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
#428572
#428422
#426342
#425752
#408932
#407542
#374992
#374922
#373712
#373382
#356772
#356732
#356212
#356162
#355922
#355742
#355582
#355132
#353082
#352542
#346392
C2×#26402
#342682
#342582
#340702