Finite Group Databasebeta

← #7652671

Subgroups — #7652671

Order 512.

5440 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42903C214yesmaximal, complemented
2#42847C214yesmaximal, complemented
3#42842C214yesmaximal, complemented
4#42834C214yesmaximal, complemented
5#42012C218yesmaximal, complemented
6#40200C214yesmaximal, complemented
7#40098C214yesmaximal, complemented
8#39790C214yesmaximal, complemented
9#39227C214yesmaximal, complemented
10#38468C218yesmaximal, complemented
11#35677C211yesmaximal, characteristic, complemented
12#35676C211yesmaximal, characteristic
13#35673C211yesmaximal, characteristic, complemented
14#35666C211yesmaximal, characteristic, complemented
15#35617C211yesmaximal, characteristic, complemented
16#35541C211yesmaximal, characteristic, complemented
17#35312C211yesmaximal, characteristic, complemented
18#35264C211yesmaximal, characteristic, complemented
19#35154C211yesmaximal, characteristic, complemented
20C2×#2545C211yesmaximal, characteristic, complemented
21#34816C211yesmaximal, characteristic, complemented
22#34816C211yesmaximal, characteristic, complemented
23#34257C211yesmaximal, characteristic, complemented
24#34211C211yesmaximal, characteristic, complemented
25#34209C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#535C2211yescharacteristic
31C2×#535C2211yescharacteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C22×#124C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#518C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2862C2212yescomplemented
40#2861C2212yes—
41#2861C2212yescomplemented
42#2858C2212yes—
43#2855C2214yes—
44#2831C2218yescomplemented
45#2829C2218yescomplemented
46#2803C2218yescomplemented
47#2803C2218yescomplemented
48#2797C2218yescomplemented
49#2788C2218yescomplemented
50#2786C2218yescomplemented
51#2784C2218yescomplemented
52#2781C2218yescomplemented
53#2780C2218yescomplemented
54#2779C2218yescomplemented
55#2775C2218yescomplemented
56#2759C2218yescomplemented
57#2750C2218yescomplemented
58#2745C2218yescomplemented
59#2715C2218yescomplemented
60#2710C2218yescomplemented
61#2695C2218yescomplemented
62#2665C2218yescomplemented
63#2662C2218yescomplemented
64#2653C2218yescomplemented
65#2650C2218yescomplemented
66#2649C2218yescomplemented
67#2648C2218yescomplemented
68#2642C2212yescomplemented
69#2641C2212yes—
70#2640C2212yes—
71#2640C2212yescomplemented
72#2627C2214yes—
73#2597C2218yescomplemented
74#2595C2218yescomplemented
75#2578C2218yescomplemented
76#2576C2218yescomplemented
77#2574C2218yescomplemented
78#2554C2218yescomplemented
79#2548C2214yes—
80#2547C2214yes—
81#2545C2214yes—
82#2545C2214yes—
83#2545C2214yes—
84#2545C2214yes—
85#2545C2214yes—
86#2544C2214yes—
87#2514C2212yescomplemented
88#2514C2212yescomplemented
89#2513C2212yescomplemented
90#2513C2212yescomplemented
91#2512C2212yescomplemented
92#2512C2212yescomplemented
93#2511C2212yescomplemented
94#2511C2212yescomplemented
95#2510C2214yes—
96#2510C2214yes—
97#2498C2218yes—
98#2492C2214yescomplemented
99#2491C2214yes—
100#2490C2214yes—
101#2489C2214yescomplemented
102#2488C2218yes—
103#2481C2214yes—
104#2481C2214yes—
105#2472C2218yes—
106#2453C2214yescomplemented
107#2453C2214yescomplemented
108#2451C2214yescomplemented
109#2451C2214yescomplemented
110#2448C2214yescomplemented
111#2447C2214yes—
112#2446C2214yescomplemented
113#2445C2214yes—
114#2436C2214yes—
115#2436C2212yes—
116#2436C2212yes—
117#2434C2212yescomplemented
118#2434C2214yescomplemented
119#2434C2212yescomplemented
120#2432C2214yescomplemented
121#2432C2212yescomplemented
122#2432C2212yescomplemented
123#2431C2212yes—
124#2431C2212yes—
125#2431C2214yes—
126#2427C2214yes—
127#2427C2214yes—
128#2426C2214yes—
129#2426C2214yes—
130#2423C2214yescomplemented
131#2422C2214yes—
132#2421C2214yescomplemented
133#2420C2214yes—
134#2412C2214yes—
135#2412C2218yes—
136#2412C2214yes—
137#2411C2214yes—
138#2411C2214yes—
139#2406C2218yes—
140#2404C2218yes—
141#2401C2214yescomplemented
142#2401C2214yescomplemented
143C2×#396C2214yes—
144#2367C2214yes—
145#2367C2214yes—
146#2365C2214yescomplemented
147#2365C2214yescomplemented
148#2344C2218yes—
149#2342C2218yes—
150#2341C2214yescomplemented
151#2341C2214yescomplemented
152Q8×C22⋊C4C2214yescomplemented
153Q8×C22⋊C4C2214yescomplemented
154#2337C2218yescomplemented
155#2335C2218yescomplemented
156#2327C2214yescomplemented
157#2326C2214yes—
158#2316C2211yescharacteristic
159#2311C2214yes—
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2310C2211yescharacteristic
163#2310C2211yescharacteristic
164#2310C2211yescharacteristic
165#2309C2211yescharacteristic
166C4×C4⋊Q8C2214yescomplemented
167C4×#126C2214yescomplemented
168C4×#126C2214yescomplemented
169C4×#124C2214yes—
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2214yes—
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#390C2211yescharacteristic
181C2×#388C2214yes—
182#2285C2211yescharacteristic
183#2285C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2314yes—
193C22×#41C2312yes—
194C22×#41C2312yes—
195C23×Q8C2311yescharacteristic
196C23×Q8C2311yescharacteristic
197C23×Q8C2312yes—
198C23×Q8C2312yes—
199C23×D4C2311yescharacteristic
200#544—44no—
201#536—44no—
202#536—44no—
203#535—44no—
204#535—44no—
205C2×C4⋊Q8—28no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×#127C2312yes—
214C2×#127C2312yes—
215C2×#126C2314yes—
216C2×#126C2314yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#124—28no—
220C2×#124—44no—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#124C2318yes—
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2312yes—
230C2×#124C2312yes—
231C2×#123C2318yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×#121C2314yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#120C2314yes—
242C2×#120C2314yes—
243#519—44no—
244#519—44no—
245#518—44no—
246C2×C4×Q8—44no—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2314yes—
262C2×#117C2314yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C22⋊C4C2314yes—
268C22×C22⋊C4C2314yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2314yes—
271C22×C22⋊C4C2312yes—
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276#401C2314yes—
277#401C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2318yes—
281#400C2318yes—
282#400C2314yes—
283#400C2318yes—
284#400C2318yes—
285#400C2314yes—
286#400C2314yes—
287#400C2314yes—
288#399C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#397C2314yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2314yes—
299#397C2318yes—
300#397C2314yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2314yes—
305#396C2314yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2314yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#393C2318yes—
327#393C2318yes—
328#393C2318yes—
329#393C2318yes—
330#392C2318yes—
331#392C2318yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2318yes—
342#391C2312yes—
343#391C2312yes—
344#391C2318yes—
345#391C2318yes—
346#391C2318yes—
347#391C2312yes—
348#391C2312yes—
349#391C2311yescharacteristic
350#391C2312yes—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2312yes—
354#391C2311yescharacteristic
355#391C2312yes—
356#391C2312yes—
357#391C2314yes—
358#390C2314yes—
359#390C2312yes—
360#390C2312yes—
361#390C2318yes—
362#390C2312yes—
363#390C2312yes—
364#390C2318yes—
365#390C2318yes—
366#390C2312yes—
367#390C2312yes—
368#390C2318yes—
369#390C2311yescharacteristic
370#390C2312yes—
371#390C2311yescharacteristic
372#390C2312yes—
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2318yes—
376#390C2312yes—
377#390C2312yes—
378#390C2314yes—
379#389C2318yes—
380#389C2318yes—
381#389C2314yes—
382#389C2314yes—
383#389C2318yes—
384#389C2312yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#386C2312yes—
425#386C2312yes—
426#386C2314yes—
427#386C2314yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2314yes—
436#386C2314yes—
437#386C2314yes—
438#386C2314yes—
439#386C2312yes—
440#386C2312yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2312yes—
449#385C2312yes—
450#385C2312yes—
451#385C2312yes—
452#384C2312yes—
453#384C2312yes—
454#383C2314yes—
455#383C2314yes—
456#382C2318yes—
457#382C2312yes—
458#382C2312yes—
459#381C2314yes—
460#381C2314yes—
461#381C2314yes—
462#381C2318yes—
463#380C2314yes—
464#380C2314yes—
465#380C2318yes—
466#380C2318yes—
467#380C2314yes—
468#380C2318yes—
469#380C2318yes—
470#380C2314yes—
471#380C2314yes—
472#379C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2318yes—
496C4×C22⋊C4C2318yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501#376C2312yes—
502#376C2312yes—
503C2×#95C2314yes—
504C2×#95C2312yes—
505C43C2312yes—
506C43C2312yes—
507C25C2412yes—
5082−1+4—464no—
509C2×#41—28no—
510C2×#41—28no—
511C2×#41—216no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—48no—
519C2×#41—48no—
520C2×#41—44no—
521C2×#41—44no—
522C2×#41—44no—
523C2×#41—44no—
524C22×Q8—28no—
525C22×Q8—28no—
526C22×Q8—24no—
527C22×Q8—24no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—44no—
532C22×Q8—44no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8#4118yes—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2411yescharacteristic
539C22×Q8C2411yescharacteristic
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×Q8C2414yes—
543C22×Q8C2414yes—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4C2412yes—
548C22×D4C2412yes—
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C22×D4C2414yes—
554C22×D4C2418yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2411yescharacteristic
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2411yescharacteristic
566C23×C4C2414yes—
567C23×C4C2414yes—
568C23×C4C2418yes—
569C23×C4C2411yescharacteristic
570C4⋊Q8—28no—
571C4⋊Q8—28no—
572C4⋊Q8—216no—
573C4⋊Q8—44no—
574C4⋊Q8—44no—
575C4⋊Q8—44no—
576C4⋊Q8—44no—
577#127—44no—
578#127—44no—
579#126—48no—
580#126—48no—
581#125—44no—
582#125—44no—
583#124—28no—
584#124—216no—
585#124—28no—
586#124—416no—
587#124—48no—
588#124—48no—
589#124—44no—
590#124—44no—
591#124—44no—
592#124—44no—
593#123—416no—
594#123—48no—
595#123—48no—
596C22⋊Q8—48no—
597C22⋊Q8—48no—
598C22⋊Q8—44no—
599C22⋊Q8—44no—
600#121—48no—
601#121—44no—
602#121—44no—
603#120—48no—
604#120—48no—
605C4×Q8—48no—
606C4×Q8—48no—
607C4×Q8—48no—
608C4×Q8—48no—
609C4×Q8—48no—
610C4×Q8—48no—
611C4×D4—48no—
612C4×D4—48no—
613#117—24no—
614#117—24no—
615#117—24no—
616#117—24no—
617#117—24no—
618#117—24no—
619#117—48no—
620#117—48no—
621C2×C4⋊C4—216no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—44no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C22⋊C4—216no—
660C2×C22⋊C4—48no—
661C2×C22⋊C4—48no—
662C2×C22⋊C4—44no—
663C2×C22⋊C4—44no—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C42—24no—
700C2×C42—24no—
701C2×C42—24no—
702C2×C42—44no—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2412yes—
718C2×C42C2418yes—
719C2×C42C2418yes—
720C2×C42C2418yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724#95C2412yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763C24—24no—
764C24—24no—
765C24—24no—
766C24—44no—
767C24—44no—
768C24C2514yes—
769C24C2512yes—
770C24C2512yes—
771C24C2511yescharacteristic
772#41—464no—
773#41—432no—
774#41—432no—
775#41—416no—
776#41—416no—
777C2×Q8—232no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—22no—
793C2×Q8—22no—
794C2×Q8—22no—
795C2×Q8—44no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—48no—
799C2×Q8—432no—
800C2×Q8—432no—
801C2×Q8—416no—
802C2×Q8C2×#4118yes—
803C2×Q8C2×#4118yes—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—28no—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—48no—
826C2×D4—44no—
827C2×D4—44no—
828C2×D4—48no—
829C2×D4—48no—
830C2×D4—48no—
831C2×D4—48no—
832C2×D4—416no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—28no—
844C22×C4—28no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4C2×#4118yes—
866C22×C4C2×#4114yes—
867C22×C4H(5,𝔽2)14yes—
868C22×C4H(5,𝔽2)14yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2514yes—
878C22×C4C2514yes—
879C22×C4C2514yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2512yes—
885C22×C4C2514yes—
886C22×C4C2514yes—
887C22×C4C2512yes—
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C4⋊C4—216no—
891C4⋊C4—216no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—22no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—28no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—48no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—48no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—216no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C42—22no—
960C42—22no—
961C42—24no—
962C42—22no—
963C42—24no—
964C42—22no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—28no—
974C42—48no—
975C42—44no—
976C42—44no—
977C42—48no—
978C42—48no—
979C42—44no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—22no—
984C23—22no—
985C23—24no—
986C23—22no—
987C23—22no—
988C23—24no—
989C23—22no—
990C23—22no—
991C23—24no—
992C23—24no—
993C23—28no—
994C23—24no—
995C23—24no—
996C23—28no—
997C23—48no—
998C23—88no—
999C23—84no—
1000C23—84no—
1001C23—88no—
1002C23C22×#4112yes—
1003C23C2×H(5,𝔽2)12yes—
1004C23C2×H(5,𝔽2)12yes—
1005C23C2611yescharacteristic
1006Q8—216no—
1007Q8—216no—
1008Q8—416no—
1009Q8—48no—
1010Q8—48no—
1011Q8—44no—
1012Q8—44no—
1013Q8—164no—
1014D4—416no—
1015D4—48no—
1016D4—48no—
1017D4—48no—
1018D4—48no—
1019D4—44no—
1020D4—44no—
1021D4—164no—
1022D4—164no—
1023D4—168no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—216no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—28no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—22no—
1075C2×C4—48no—
1076C2×C4—416no—
1077C2×C4—416no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—48no—
1081C2×C4—48no—
1082C2×C4—48no—
1083C2×C4—84no—
1084C2×C4—84no—
1085C2×C4—168no—
1086C2×C4#538116yes—
1087C2×C4C22×#4118yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×H(5,𝔽2)12yes—
1094C2×C4#58514yes—
1095C22—24no—
1096C22—22no—
1097C22—22no—
1098C22—24no—
1099C22—44no—
1100C22—44no—
1101C22—48no—
1102C22—42no—
1103C22—44no—
1104C22—42no—
1105C22—42no—
1106C22—44no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—44no—
1111C22—48no—
1112C22—44no—
1113C22—44no—
1114C22—168no—
1115C22C2×#53814yes—
1116C22C23×#4111yescharacteristic
1117C22C22×H(5,𝔽2)11yescharacteristic
1118C22C22×H(5,𝔽2)11yescharacteristic
1119C22C2×#58512yes—
1120C222−1+612yes—
1121C4—24no—
1122C4—28no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—44no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—44no—
1136C4—44no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4C2×#53814yes—
1141C4C2×#53814yes—
1142C2—24no—
1143C2—82no—
1144C2—82no—
1145C2—84no—
1146C2C22×#53811yescharacteristic
1147C2#6283611yescharacteristic
1148C2#6288711yescharacteristic
1149C2#6293112yes—
1150C2#6300512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35676C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42903C2semidirect
2. #42847C2semidirect
3. #42842C2semidirect
4. #42834C2semidirect
5. #42012C2semidirect
6. #40200C2semidirect
7. #40098C2semidirect
8. #39790C2semidirect
9. #39227C2semidirect
10. #38468C2semidirect
11. #35677C2semidirect
13. #35673C2semidirect
14. #35666C2semidirect
15. #35617C2semidirect
16. #35541C2semidirect
17. #35312C2semidirect
18. #35264C2semidirect
19. #35154C2semidirect
20. C2×#2545C2semidirect
21. #34816C2semidirect
22. #34816C2semidirect
23. #34257C2semidirect
24. #34211C2semidirect
25. #34209C2semidirect
39. #2862C22semidirect
41. #2861C22semidirect
44. #2831C22semidirect
45. #2829C22semidirect
46. #2803C22semidirect
47. #2803C22semidirect
48. #2797C22semidirect
49. #2788C22semidirect
50. #2786C22semidirect
51. #2784C22semidirect
52. #2781C22semidirect
53. #2780C22semidirect
54. #2779C22semidirect
55. #2775C22semidirect
56. #2759C22semidirect
57. #2750C22semidirect
58. #2745C22semidirect
59. #2715C22semidirect
60. #2710C22semidirect
61. #2695C22semidirect
62. #2665C22semidirect
63. #2662C22semidirect
64. #2653C22semidirect
65. #2650C22semidirect
66. #2649C22semidirect
67. #2648C22semidirect
68. #2642C22semidirect
71. #2640C22semidirect
73. #2597C22semidirect
74. #2595C22semidirect
75. #2578C22semidirect
76. #2576C22semidirect
77. #2574C22semidirect
78. #2554C22semidirect
87. #2514C22semidirect
88. #2514C22semidirect
89. #2513C22semidirect
90. #2513C22semidirect
91. #2512C22semidirect
92. #2512C22semidirect
93. #2511C22semidirect
94. #2511C22semidirect
98. #2492C22semidirect
101. #2489C22semidirect
106. #2453C22semidirect
107. #2453C22semidirect
108. #2451C22semidirect
109. #2451C22semidirect
110. #2448C22semidirect
112. #2446C22semidirect
117. #2434C22semidirect
118. #2434C22semidirect
119. #2434C22semidirect
120. #2432C22semidirect
121. #2432C22semidirect
122. #2432C22semidirect
130. #2423C22semidirect
132. #2421C22semidirect
141. #2401C22semidirect
142. #2401C22semidirect
146. #2365C22semidirect
147. #2365C22semidirect
150. #2341C22semidirect
151. #2341C22semidirect
152. Q8×C22⋊C4C22semidirect
153. Q8×C22⋊C4C22semidirect
154. #2337C22semidirect
155. #2335C22semidirect
156. #2327C22semidirect
166. C4×C4⋊Q8C22semidirect
167. C4×#126C22semidirect
168. C4×#126C22semidirect

Maximal subgroups

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

subgroupindex
#429032
#428472
#428422
#428342
#420122
#402002
#400982
#397902
#392272
#384682
#356772
#356762
#356732
#356662
#356172
#355412
#353122
#352642
#351542
C2×#25452
#348162
#342572
#342112
#342092