Finite Group Databasebeta

← #7652667

Subgroups — #7652667

Order 512.

6864 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3509C211yesmaximal, characteristic, complemented
3#42877C214yesmaximal, complemented
4#42802C214yesmaximal, complemented
5#42799C214yesmaximal, complemented
6#42795C214yesmaximal, complemented
7#41984C218yesmaximal, complemented
8#39882C214yesmaximal, complemented
9#39879C214yesmaximal, complemented
10#39726C214yesmaximal, complemented
11#39127C214yesmaximal, complemented
12#38429C218yesmaximal, complemented
13#35677C211yesmaximal, characteristic, complemented
14#35677C211yesmaximal, characteristic, complemented
15#35667C211yesmaximal, characteristic, complemented
16#35662C211yesmaximal, characteristic, complemented
17#35617C211yesmaximal, characteristic, complemented
18#35515C211yesmaximal, characteristic, complemented
19#35308C211yesmaximal, characteristic, complemented
20#35256C211yesmaximal, characteristic
21#35153C211yesmaximal, characteristic, complemented
22C2×#2545C211yesmaximal, characteristic, complemented
23#34745C211yesmaximal, characteristic, complemented
24#34745C211yesmaximal, characteristic, complemented
25#34249C211yesmaximal, characteristic, complemented
26#3510—216no—
27#3509—216no—
28C2×#559C2214yes—
29C2×#557C2214yescomplemented
30C2×#556C2214yes—
31C2×#556C2214yescomplemented
32C2×#552C2218yes—
33C2×#551C2218yes—
34C2×#542C2214yes—
35C2×#541C2214yescomplemented
36C2×#537C2211yescharacteristic
37C2×#536C2211yescharacteristic
38C2×#536C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#536C2211yescharacteristic
41C2×#535C2211yescharacteristic
42C2×#535C2211yescharacteristic
43C2×#533C2211yescharacteristic
44C2×#533C2211yescharacteristic
45C2×#533C2214yescomplemented
46C22×C4⋊Q8C2211yescharacteristic
47C2×#529C2214yes—
48C22×#124C2211yescharacteristic
49C22×#124C2211yescharacteristic
50C2×#519C2211yescharacteristic
51C2×#519C2211yescharacteristic
52C2×#519C2211yescharacteristic
53C2×#518C2211yescharacteristic
54C2×C4×#41C2211yescharacteristic
55C2×C4×#41C2211yescharacteristic
56C22×C4×Q8C2211yescharacteristic
57#2857C2212yescomplemented
58#2856C2212yes—
59#2854C2214yes—
60#2850C2212yes—
61#2850C2212yescomplemented
62#2823C2218yescomplemented
63#2820C2218yescomplemented
64#2727C2218yescomplemented
65#2725C2218yescomplemented
66#2725C2218yescomplemented
67#2707C2218yescomplemented
68#2707C2218yescomplemented
69#2707C2218yescomplemented
70#2707C2218yescomplemented
71#2705C2218yescomplemented
72#2705C2218yescomplemented
73#2704C2218yescomplemented
74#2704C2218yescomplemented
75#2702C2218yescomplemented
76#2702C2218yescomplemented
77#2683C2218yescomplemented
78#2681C2218yescomplemented
79#2681C2218yescomplemented
80#2664C2218yescomplemented
81#2662C2218yescomplemented
82#2637C2218yescomplemented
83#2636C2218yescomplemented
84#2629C2218yescomplemented
85#2621C2212yescomplemented
86#2620C2212yes—
87#2620C2218yescomplemented
88#2620C2212yescomplemented
89#2619C2212yes—
90#2618C2214yes—
91#2609C2218yescomplemented
92#2601C2218yescomplemented
93#2601C2218yescomplemented
94#2592C2218yescomplemented
95#2582C2214yescomplemented
96#2581C2214yescomplemented
97#2580C2214yes—
98#2562C2218yescomplemented
99#2548C2214yes—
100#2548C2212yes—
101#2548C2212yes—
102#2547C2214yes—
103#2546C2212yescomplemented
104#2546C2212yescomplemented
105#2545C2212yes—
106#2545C2214yes—
107#2545C2214yes—
108#2545C2214yes—
109#2545C2214yes—
110#2545C2214yes—
111#2545C2212yes—
112#2545C2212yescomplemented
113#2545C2212yescomplemented
114#2544C2214yes—
115#2538C2214yes—
116#2538C2218yescomplemented
117#2454C2214yes—
118#2454C2212yescomplemented
119#2454C2212yescomplemented
120#2453C2212yescomplemented
121#2453C2214yescomplemented
122#2453C2212yescomplemented
123#2452C2214yes—
124#2452C2212yescomplemented
125#2452C2212yescomplemented
126#2451C2212yescomplemented
127#2451C2214yescomplemented
128#2451C2212yescomplemented
129#2450C2214yes—
130#2450C2214yes—
131#2449C2214yes—
132#2449C2214yes—
133#2438C2218yes—
134#2437C2218yes—
135#2429C2214yescomplemented
136#2429C2214yescomplemented
137#2429C2214yescomplemented
138#2429C2214yescomplemented
139#2429C2214yescomplemented
140#2428C2214yes—
141#2427C2214yes—
142#2427C2214yes—
143#2427C2214yescomplemented
144#2426C2214yes—
145#2426C2214yes—
146#2426C2214yes—
147#2426C2214yes—
148#2426C2214yes—
149#2426C2214yescomplemented
150#2426C2214yescomplemented
151#2425C2218yes—
152#2424C2218yes—
153#2413C2218yes—
154#2412C2214yes—
155#2412C2214yes—
156#2411C2214yes—
157#2411C2218yes—
158#2411C2214yes—
159#2396C2214yescomplemented
160#2396C2214yescomplemented
161C2×#396C2214yes—
162#2351C2214yescomplemented
163#2351C2214yescomplemented
164Q8×C4⋊C4C2214yescomplemented
165Q8×C4⋊C4C2214yescomplemented
166#2324C2218yescomplemented
167#2323C2218yescomplemented
168#2317C2214yes—
169#2317C2211yescharacteristic
170#2317C2211yescharacteristic
171#2316C2211yescharacteristic
172#2310C2211yescharacteristic
173#2309C2211yescharacteristic
174C4×C22⋊Q8C2214yescomplemented
175C4×C22⋊Q8C2214yescomplemented
176#2297C2211yescharacteristic
177#2297C2211yescharacteristic
178#2297C2211yescharacteristic
179#2297C2211yescharacteristic
180#2296C2214yes—
181#2296C2211yescharacteristic
182#2296C2211yescharacteristic
183#2296C2211yescharacteristic
184#2296C2211yescharacteristic
185C2×#391C2211yescharacteristic
186C2×#390C2211yescharacteristic
187C2×#388C2214yes—
188C2×C4×C4⋊C4C2211yescharacteristic
189C22×#41C2311yescharacteristic
190C22×#41C2311yescharacteristic
191C23×Q8C2311yescharacteristic
192C23×Q8C2311yescharacteristic
193C23×D4C2311yescharacteristic
194#559—232no—
195#557—232no—
196#556—232no—
197#556—232no—
198#552—264no—
199#551—264no—
200#542—232no—
201#541—232no—
202#537—44no—
203#536—28no—
204#536—28no—
205#536—28no—
206#536—44no—
207#535—28no—
208#535—44no—
209#533—232no—
210#533—28no—
211#533—28no—
212C2×C4⋊Q8—28no—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2312yes—
217C2×C4⋊Q8C2312yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2312yes—
221C2×C4⋊Q8C2312yes—
222C2×#127C2312yes—
223C2×#127C2312yes—
224#529—232no—
225C2×#126C2318yes—
226C2×#126C2318yes—
227C2×#126C2318yes—
228C2×#126C2318yes—
229C2×#125C2318yes—
230C2×#125C2312yes—
231C2×#125C2312yes—
232C2×#125C2318yes—
233C2×#125C2318yes—
234C2×#124—28no—
235C2×#124—44no—
236C2×#124C2318yes—
237C2×#124C2312yes—
238C2×#124C2312yes—
239C2×#124C2312yes—
240C2×#124C2314yes—
241C2×#124C2312yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2314yes—
245C2×#124C2314yes—
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2318yes—
252C2×#123C2318yes—
253C2×#123C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2318yes—
260C2×C22⋊Q8C2318yes—
261C2×C22⋊Q8C2318yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×#121C2314yes—
269C2×#121C2318yes—
270C2×#121C2312yes—
271C2×#121C2312yes—
272C2×#121C2314yes—
273C2×#121C2312yes—
274C2×#121C2312yes—
275C2×#120C2314yes—
276C2×#120C2314yes—
277#519—28no—
278#519—44no—
279#519D4116yescomplemented
280#518—28no—
281C4×#41—28no—
282C4×#41—28no—
283C2×C4×Q8—44no—
284C2×C4×Q8C2318yes—
285C2×C4×Q8C2314yes—
286C2×C4×Q8C2314yes—
287C2×C4×Q8C2314yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2314yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2314yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2314yes—
298C2×C4×Q8C2314yes—
299C2×C4×D4C2318yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2314yes—
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2311yescharacteristic
309C2×#117C2311yescharacteristic
310C2×#117C2318yes—
311C2×#117C2318yes—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2314yes—
315C2×#117C2314yes—
316C2×#117C2311yescharacteristic
317C2×#117C2311yescharacteristic
318C2×#117C2314yes—
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2314yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C22⋊C4C2314yes—
324C22×C22⋊C4C2314yes—
325C22×C22⋊C4C2312yes—
326C22×C22⋊C4C2314yes—
327C22×C22⋊C4C2312yes—
328C22×C42C2312yes—
329C22×C42C2312yes—
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2312yes—
334#400C2314yes—
335#400C2318yes—
336#400C2314yes—
337#399C2314yes—
338#399C2318yes—
339#399C2314yes—
340#398C2314yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2314yes—
345#398C2318yes—
346#398C2318yes—
347#398C2318yes—
348#398C2314yes—
349#398C2314yes—
350#397C2318yes—
351#397C2318yes—
352#397C2318yes—
353#396C2318yes—
354#396C2318yes—
355#396C2318yes—
356#396C2318yes—
357#396C2314yes—
358#396C2318yes—
359#396C2318yes—
360#396C2318yes—
361#396C2318yes—
362#396C2314yes—
363#396C2318yes—
364#396C2318yes—
365#396C2318yes—
366#396C2318yes—
367#396C2314yes—
368#396C2318yes—
369#396C2318yes—
370#396C2318yes—
371#396C2318yes—
372#396C2314yes—
373#395C2314yes—
374#395C2318yes—
375#395C2314yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#394C2318yes—
380#394C2318yes—
381#394C2318yes—
382#394C2318yes—
383#394C2318yes—
384#394C2318yes—
385#394C2318yes—
386#393C2318yes—
387#393C2314yes—
388#393C2314yes—
389#392C2318yes—
390#391C2312yes—
391#391C2312yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2318yes—
396#391C2314yes—
397#391C2311yescharacteristic
398#391C2312yes—
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2312yes—
402#391C2311yescharacteristic
403#391C2312yes—
404#391C2312yes—
405#390C2312yes—
406#390C2314yes—
407#390C2312yes—
408#390C2318yes—
409#390C2318yes—
410#390C2318yes—
411#390C2314yes—
412#390C2318yes—
413#390C2312yes—
414#390C2311yescharacteristic
415#390C2311yescharacteristic
416#390C2318yes—
417#390C2311yescharacteristic
418#390C2312yes—
419#390C2311yescharacteristic
420#390C2318yes—
421#390C2312yes—
422#390C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2318yes—
426#389C2314yes—
427#389C2314yes—
428#389C2318yes—
429#389C2318yes—
430#389C2318yes—
431#389C2318yes—
432#389C2318yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2318yes—
437#389C2318yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2318yes—
443#389C2314yes—
444#389C2312yes—
445#389C2314yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#388C2318yes—
452#388C2318yes—
453#388C2318yes—
454#388C2318yes—
455#388C2318yes—
456#388C2318yes—
457#388C2318yes—
458#388C2318yes—
459#388C2318yes—
460#387C2314yes—
461#387C2318yes—
462#387C2318yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#386C2318yes—
467#386C2318yes—
468#386C2318yes—
469#386C2312yes—
470#386C2312yes—
471#386C2318yes—
472#386C2312yes—
473#386C2312yes—
474#386C2314yes—
475#386C2314yes—
476#385C2312yes—
477#385C2312yes—
478#385C2314yes—
479#385C2314yes—
480#385C2314yes—
481#385C2318yes—
482#385C2318yes—
483#385C2314yes—
484#385C2314yes—
485#385C2314yes—
486#385C2314yes—
487#385C2312yes—
488#385C2312yes—
489#385C2314yes—
490#384C2318yes—
491#384C2312yes—
492#384C2312yes—
493#382C2318yes—
494#382C2312yes—
495#382C2312yes—
496#381C2314yes—
497#380C2314yes—
498#380C2318yes—
499#380C2318yes—
500#380C2318yes—
501#380C2314yes—
502#380C2314yes—
503#380C2318yes—
504#379C2314yes—
505C4×C4⋊C4C2318yes—
506C4×C4⋊C4C2318yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C2×#95C2314yes—
522C2×#95C2312yes—
523C25C2412yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—24no—
534C22×Q8—24no—
535C22×Q8C2×D418yes—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2411yescharacteristic
539C22×Q8C2411yescharacteristic
540C22×Q8C2414yes—
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×Q8C2414yes—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4C2412yes—
548C22×D4C2412yes—
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C22×D4C2418yes—
554C22×D4C2414yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2414yes—
562C23×C4C2412yes—
563C23×C4C2411yescharacteristic
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2411yescharacteristic
567C23×C4C2418yes—
568C23×C4C2414yes—
569C23×C4C2411yescharacteristic
570C4⋊Q8—28no—
571C4⋊Q8—28no—
572C4⋊Q8—216no—
573C4⋊Q8—28no—
574C4⋊Q8—28no—
575C4⋊Q8—28no—
576C4⋊Q8—28no—
577C4⋊Q8—28no—
578C4⋊Q8—44no—
579#127—28no—
580#127—44no—
581#126—232no—
582#126—232no—
583#126—232no—
584#126—232no—
585#125—28no—
586#125—28no—
587#125—232no—
588#125—232no—
589#125—232no—
590#124—28no—
591#124—28no—
592#124—216no—
593#124—28no—
594#124—28no—
595#124—28no—
596#124—28no—
597#124—232no—
598#124—48no—
599#124—48no—
600#124—44no—
601#124—44no—
602#123—216no—
603#123—216no—
604#123—232no—
605#123—232no—
606#123—216no—
607#123—48no—
608C22⋊Q8—216no—
609C22⋊Q8—216no—
610C22⋊Q8—216no—
611C22⋊Q8—232no—
612C22⋊Q8—232no—
613C22⋊Q8—216no—
614C22⋊Q8—216no—
615C22⋊Q8—416no—
616C22⋊Q8—48no—
617C22⋊Q8—48no—
618C22⋊Q8—44no—
619C22⋊Q8—44no—
620C22⋊Q8—44no—
621C22⋊Q8—44no—
622#121—216no—
623#121—416no—
624#121—44no—
625#121—44no—
626#121—44no—
627#121—44no—
628#121—48no—
629#120—216no—
630#120—48no—
631C4×Q8—28no—
632C4×Q8—28no—
633C4×Q8—216no—
634C4×Q8—216no—
635C4×Q8—232no—
636C4×Q8—216no—
637C4×Q8—216no—
638C4×Q8—48no—
639C4×Q8—48no—
640C4×Q8—44no—
641C4×Q8—44no—
642C4×Q8—44no—
643C4×Q8—44no—
644C4×Q8C2×D4132yes—
645C4×Q8C2×D4132yes—
646C4×D4—28no—
647C4×D4—28no—
648C4×D4—216no—
649C4×D4—216no—
650C4×D4—216no—
651C4×D4—216no—
652C4×D4—232no—
653#117—24no—
654#117—24no—
655#117—24no—
656#117—24no—
657#117—216no—
658#117—28no—
659#117—28no—
660#117—232no—
661#117—232no—
662#117—48no—
663#117C2×D418yes—
664#117C2×D418yes—
665#117C2×D4132yes—
666C2×C4⋊C4—216no—
667C2×C4⋊C4—24no—
668C2×C4⋊C4—44no—
669C2×C4⋊C4—44no—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2418yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2418yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2418yes—
716C2×C22⋊C4—216no—
717C2×C22⋊C4—216no—
718C2×C22⋊C4—48no—
719C2×C22⋊C4—44no—
720C2×C22⋊C4—44no—
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2418yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2412yes—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2412yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2418yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2412yes—
756C2×C42—24no—
757C2×C42—24no—
758C2×C42—24no—
759C2×C42—28no—
760C2×C42—28no—
761C2×C42—44no—
762C2×C42C2414yes—
763C2×C42C2418yes—
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2412yes—
767C2×C42C2412yes—
768C2×C42C2412yes—
769C2×C42C2412yes—
770C2×C42C2412yes—
771C2×C42C2414yes—
772C2×C42C2412yes—
773C2×C42C2412yes—
774C2×C42C2412yes—
775C2×C42C2411yescharacteristic
776C2×C42C2411yescharacteristic
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2418yes—
780C2×C42C2418yes—
781C2×C42C2412yes—
782C2×C42C2412yes—
783#95C2412yes—
784#95C2412yes—
785#95C2412yes—
786#95C2412yes—
787#95C2418yes—
788#95C2418yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2418yes—
803#95C2414yes—
804#95C2414yes—
805#95C2418yes—
806#95C2414yes—
807#95C2418yes—
808#95C2418yes—
809#95C2418yes—
810C24—24no—
811C24—24no—
812C24—24no—
813C24—44no—
814C24—44no—
815C24C2514yes—
816C24C2512yes—
817C24C2512yes—
818C24C2511yescharacteristic
819#41—416no—
820#41—416no—
821C2×Q8—232no—
822C2×Q8—28no—
823C2×Q8—24no—
824C2×Q8—22no—
825C2×Q8—24no—
826C2×Q8—22no—
827C2×Q8—28no—
828C2×Q8—24no—
829C2×Q8—24no—
830C2×Q8—24no—
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—24no—
834C2×Q8—24no—
835C2×Q8—24no—
836C2×Q8—24no—
837C2×Q8—24no—
838C2×Q8—22no—
839C2×Q8—22no—
840C2×Q8—28no—
841C2×Q8—44no—
842C2×Q8—44no—
843C2×Q8—44no—
844C2×Q8—416no—
845C2×Q8C22×D418yes—
846C2×Q8C22×D418yes—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—22no—
855C2×D4—24no—
856C2×D4—22no—
857C2×D4—216no—
858C2×D4—24no—
859C2×D4—22no—
860C2×D4—22no—
861C2×D4—24no—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—48no—
867C2×D4—48no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—48no—
872C2×D4—48no—
873C2×D4—48no—
874C2×D4—416no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—28no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—28no—
894C22×C4—28no—
895C22×C4—216no—
896C22×C4—42no—
897C22×C4—44no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—44no—
901C22×C4—42no—
902C22×C4—48no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—48no—
906C22×C4—42no—
907C22×C4C22×D418yes—
908C22×C4C22×D414yes—
909C22×C4H(5,𝔽2)14yes—
910C22×C42−1+414yes—
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2512yes—
914C22×C4C2512yes—
915C22×C4C2512yes—
916C22×C4C2512yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2512yes—
920C22×C4C2514yes—
921C22×C4C2512yes—
922C22×C4C2512yes—
923C22×C4C2512yes—
924C22×C4C2514yes—
925C22×C4C2512yes—
926C22×C4C2514yes—
927C22×C4C2514yes—
928C22×C4C2514yes—
929C22×C4C2512yes—
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C4⋊C4—216no—
933C4⋊C4—216no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—24no—
937C4⋊C4—28no—
938C4⋊C4—28no—
939C4⋊C4—24no—
940C4⋊C4—216no—
941C4⋊C4—216no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—216no—
945C4⋊C4—216no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—24no—
955C4⋊C4—24no—
956C4⋊C4—28no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—48no—
960C4⋊C4—44no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—44no—
964C4⋊C4—44no—
965C4⋊C4—44no—
966C4⋊C4—48no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—48no—
970C4⋊C4—44no—
971C4⋊C4—48no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4C22×D418yes—
976C4⋊C4C22×D418yes—
977C4⋊C4C22×D4132yes—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—24no—
982C22⋊C4—216no—
983C22⋊C4—216no—
984C22⋊C4—216no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—216no—
988C22⋊C4—216no—
989C22⋊C4—216no—
990C22⋊C4—216no—
991C22⋊C4—216no—
992C22⋊C4—28no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—48no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4C22×D418yes—
1012C22⋊C4C22×D418yes—
1013C42—22no—
1014C42—22no—
1015C42—28no—
1016C42—22no—
1017C42—22no—
1018C42—24no—
1019C42—28no—
1020C42—24no—
1021C42—216no—
1022C42—24no—
1023C42—24no—
1024C42—24no—
1025C42—24no—
1026C42—24no—
1027C42—24no—
1028C42—48no—
1029C42—44no—
1030C42—44no—
1031C42C22×D418yes—
1032C42C22×D418yes—
1033C42C22×D4132yes—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—24no—
1038C23—22no—
1039C23—22no—
1040C23—24no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—24no—
1045C23—28no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—28no—
1051C23—48no—
1052C23—88no—
1053C23—84no—
1054C23—84no—
1055C23—88no—
1056C23C23×D412yes—
1057C23C2×H(5,𝔽2)12yes—
1058C23C2×2−1+412yes—
1059C23C2611yescharacteristic
1060Q8—216no—
1061Q8—216no—
1062Q8—416no—
1063Q8—48no—
1064Q8—48no—
1065Q8—44no—
1066Q8—44no—
1067Q8—88no—
1068D4—48no—
1069D4—48no—
1070D4—48no—
1071D4—48no—
1072D4—44no—
1073D4—44no—
1074D4—816no—
1075D4—164no—
1076D4—164no—
1077D4—164no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—216no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—416no—
1128C2×C4—48no—
1129C2×C4—44no—
1130C2×C4—44no—
1131C2×C4—48no—
1132C2×C4—48no—
1133C2×C4—48no—
1134C2×C4—88no—
1135C2×C4—816no—
1136C2×C4—84no—
1137C2×C4—84no—
1138C2×C4#537116yes—
1139C2×C4C23×D418yes—
1140C2×C4C23×D418yes—
1141C2×C4C23×D418yes—
1142C2×C4C23×D412yes—
1143C2×C4C23×D412yes—
1144C2×C4C2×H(5,𝔽2)12yes—
1145C2×C4C2×H(5,𝔽2)12yes—
1146C2×C4C2×2−1+412yes—
1147C2×C4C2×2−1+412yes—
1148C2×C4#58514yes—
1149C22—24no—
1150C22—22no—
1151C22—22no—
1152C22—24no—
1153C22—44no—
1154C22—44no—
1155C22—48no—
1156C22—42no—
1157C22—42no—
1158C22—44no—
1159C22—42no—
1160C22—44no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—44no—
1165C22—44no—
1166C22—44no—
1167C22—48no—
1168C22—168no—
1169C22C2×#53714yes—
1170C22C24×D411yescharacteristic
1171C22C22×H(5,𝔽2)11yescharacteristic
1172C22C22×2−1+411yescharacteristic
1173C22C2×#58512yes—
1174C222−1+612yes—
1175C4—24no—
1176C4—28no—
1177C4—28no—
1178C4—28no—
1179C4—42no—
1180C4—42no—
1181C4—44no—
1182C4—42no—
1183C4—44no—
1184C4—42no—
1185C4—42no—
1186C4—44no—
1187C4—42no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—44no—
1194C4C2×#53714yes—
1195C4C2×#53714yes—
1196C2—24no—
1197C2—82no—
1198C2—82no—
1199C2—84no—
1200C2C22×#53711yescharacteristic
1201C2#6283611yescharacteristic
1202C2#6288711yescharacteristic
1203C2#6293212yes—
1204C2#6300212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35256C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3510C2semidirect
2. C2×#3509C2semidirect
3. #42877C2semidirect
4. #42802C2semidirect
5. #42799C2semidirect
6. #42795C2semidirect
7. #41984C2semidirect
8. #39882C2semidirect
9. #39879C2semidirect
10. #39726C2semidirect
11. #39127C2semidirect
12. #38429C2semidirect
13. #35677C2semidirect
14. #35677C2semidirect
15. #35667C2semidirect
16. #35662C2semidirect
17. #35617C2semidirect
18. #35515C2semidirect
19. #35308C2semidirect
21. #35153C2semidirect
22. C2×#2545C2semidirect
23. #34745C2semidirect
24. #34745C2semidirect
25. #34249C2semidirect
29. C2×#557C22semidirect
31. C2×#556C22semidirect
35. C2×#541C22semidirect
45. C2×#533C22semidirect
57. #2857C22semidirect
61. #2850C22semidirect
62. #2823C22semidirect
63. #2820C22semidirect
64. #2727C22semidirect
65. #2725C22semidirect
66. #2725C22semidirect
67. #2707C22semidirect
68. #2707C22semidirect
69. #2707C22semidirect
70. #2707C22semidirect
71. #2705C22semidirect
72. #2705C22semidirect
73. #2704C22semidirect
74. #2704C22semidirect
75. #2702C22semidirect
76. #2702C22semidirect
77. #2683C22semidirect
78. #2681C22semidirect
79. #2681C22semidirect
80. #2664C22semidirect
81. #2662C22semidirect
82. #2637C22semidirect
83. #2636C22semidirect
84. #2629C22semidirect
85. #2621C22semidirect
87. #2620C22semidirect
88. #2620C22semidirect
91. #2609C22semidirect
92. #2601C22semidirect
93. #2601C22semidirect
94. #2592C22semidirect
95. #2582C22semidirect
96. #2581C22semidirect
98. #2562C22semidirect
103. #2546C22semidirect
104. #2546C22semidirect
112. #2545C22semidirect
113. #2545C22semidirect
116. #2538C22semidirect
118. #2454C22semidirect
119. #2454C22semidirect
120. #2453C22semidirect
121. #2453C22semidirect
122. #2453C22semidirect
124. #2452C22semidirect
125. #2452C22semidirect
126. #2451C22semidirect
127. #2451C22semidirect
128. #2451C22semidirect
135. #2429C22semidirect
136. #2429C22semidirect
137. #2429C22semidirect
138. #2429C22semidirect
139. #2429C22semidirect
143. #2427C22semidirect
149. #2426C22semidirect
150. #2426C22semidirect
159. #2396C22semidirect
160. #2396C22semidirect
162. #2351C22semidirect
163. #2351C22semidirect
164. Q8×C4⋊C4C22semidirect
165. Q8×C4⋊C4C22semidirect
166. #2324C22semidirect
167. #2323C22semidirect
174. C4×C22⋊Q8C22semidirect
175. C4×C22⋊Q8C22semidirect
279. #519D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#35092
#428772
#428022
#427992
#427952
#419842
#398822
#398792
#397262
#391272
#384292
#356772
#356672
#356622
#356172
#355152
#353082
#352562
#351532
C2×#25452
#347452
#342492