Finite Group Databasebeta

← #7674365

Subgroups — #7674365

Order 512.

10726 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic, complemented
2C2×#3486C211yesmaximal, characteristic, complemented
3C2×#3485C211yesmaximal, characteristic, complemented
4C22×#536C211yesmaximal, characteristic, complemented
5#45332C218yesmaximal, complemented
6#45134C218yesmaximal, complemented
7#39360C214yesmaximal, complemented
8#39357C214yesmaximal, complemented
9#37680C214yesmaximal, complemented
10#37676C214yesmaximal, complemented
11#37654C218yesmaximal, complemented
12#37647C218yesmaximal, complemented
13#35667C211yesmaximal, characteristic, complemented
14#35666C211yesmaximal, characteristic, complemented
15#35617C211yesmaximal, characteristic, complemented
16#35616C211yesmaximal, characteristic, complemented
17#35317C211yesmaximal, characteristic, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35242C211yesmaximal, characteristic, complemented
20#35149C211yesmaximal, characteristic, complemented
21#34633C211yesmaximal, characteristic, complemented
22#34211C211yesmaximal, characteristic, complemented
23#34065C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C22×H(5,𝔽2)C2211yescharacteristic
26C23×#41C2211yescharacteristic
27C24×Q8C2211yescharacteristic, complemented
28#3500—216no—
29#3486—216no—
30#3485—216no—
31C2×D4×Q8C2214yescomplemented
32C2×D4×Q8C2214yescomplemented
33C2×#548C2214yescomplemented
34C2×#548C2214yescomplemented
35C2×#548C2214yescomplemented
36C2×#547C2214yes—
37C2×#547C2214yes—
38C2×#546C2218yes—
39C2×#546C2214yes—
40C2×#546C2214yes—
41C2×#546C2214yescomplemented
42C2×#536—216no—
43C2×#536C2211yescharacteristic
44C2×#536C2211yescharacteristic
45C2×#536C2211yescharacteristic
46C2×#536C2211yescharacteristic
47C2×#536C2211yescharacteristic
48C2×#536C2214yescomplemented
49C2×#536C2218yescomplemented
50C2×#536C2211yescharacteristic, complemented
51C2×#536C2214yescomplemented
52C2×#536C2212yescomplemented
53C2×#536C2214yescomplemented
54C2×#536C2211yescharacteristic, complemented
55C2×#535C2211yescharacteristic
56C2×#535C2212yescomplemented
57C2×#534C2214yes—
58C2×#532C2211yescharacteristic
59C2×#532C2212yescomplemented
60C22×C4⋊Q8C2211yescharacteristic, complemented
61C22×C4⋊Q8C2211yescharacteristic, complemented
62C22×#124C2211yescharacteristic
63C22×#124C2211yescharacteristic
64C22×#124C2212yescomplemented
65C2×#525C2211yescharacteristic
66C2×#525C2211yescharacteristic
67C2×#525C2214yescomplemented
68C2×#525C2211yescharacteristic, complemented
69C22×#123C2214yes—
70C22×#123C2214yescomplemented
71C22×C22⋊Q8C2214yescomplemented
72C2×#519C2211yescharacteristic, complemented
73C2×#518C2211yescharacteristic
74C2×C4×#41C2211yescharacteristic
75C22×#117C2211yescharacteristic, complemented
76#2868C2212yescomplemented
77#2858C2212yescomplemented
78#2857C2214yescomplemented
79#2849C2214yescomplemented
80#2849C2214yescomplemented
81#2681C22116yescomplemented
82#2680C22116yescomplemented
83#2680C22116yescomplemented
84#2678C22116yescomplemented
85#2674C22116yescomplemented
86#2672C22116yescomplemented
87#2672C22116yescomplemented
88#2671C22116yescomplemented
89#2658C2212yescomplemented
90#2658C2212yescomplemented
91#2621C2212yescomplemented
92#2621C2214yescomplemented
93#2620C2212yescomplemented
94#2620C2212yescomplemented
95#2619C2212yescomplemented
96#2618C2214yescomplemented
97#2617C2214yescomplemented
98#2614C2214yescomplemented
99#2613C2214yescomplemented
100#2547C2214yescomplemented
101#2547C2214yescomplemented
102#2546C2214yescomplemented
103#2546C2214yescomplemented
104#2545C2214yescomplemented
105#2544C2214yescomplemented
106#2542C2218yescomplemented
107#2501C2218yescomplemented
108#2486C2218yescomplemented
109#2472C22116yescomplemented
110#2464C22116yescomplemented
111#2455C22116yescomplemented
112#2449C22116yescomplemented
113#2440C22116yescomplemented
114#2437C22116yescomplemented
115#2436C2214yescomplemented
116#2435C2214yescomplemented
117#2435C2214yescomplemented
118#2434C2214yescomplemented
119#2434C2214yescomplemented
120#2434C2214yescomplemented
121#2432C2214yescomplemented
122#2432C2214yescomplemented
123#2432C2214yescomplemented
124#2432C2214yescomplemented
125#2432C2214yescomplemented
126#2431C2214yescomplemented
127#2429C2218yescomplemented
128#2427C2218yescomplemented
129#2422C22116yescomplemented
130#2418C22116yescomplemented
131#2413C2218yescomplemented
132#2412C2218yescomplemented
133#2409C2218yescomplemented
134#2407C2218yescomplemented
135#2406C2218yescomplemented
136#2405C2218yes—
137#2392C2218yescomplemented
138#2367C2218yescomplemented
139#2342C2218yescomplemented
140#2326C2214yescomplemented
141#2324C2214yescomplemented
142#2323C2214yescomplemented
143#2322C2214yescomplemented
144#2321C2214yescomplemented
145#2310C2211yescharacteristic, complemented
146#2310C2211yescharacteristic, complemented
147#2310C2211yescharacteristic, complemented
148#2309C2211yescharacteristic
149C4×#124C2214yescomplemented
150#2297C2211yescharacteristic
151#2297C2211yescharacteristic
152#2297C2211yescharacteristic, complemented
153#2296C2211yescharacteristic, complemented
154#2293C2214yescomplemented
155#2290C2214yescomplemented
156#2285C2211yescharacteristic, complemented
157#2280C2211yescharacteristic, complemented
158C4×#117C2211yescharacteristic, complemented
159C2×2−1+4—28no—
160C2×2−1+4—28no—
161C2×2−1+4—44no—
162C2×H(5,𝔽2)—28no—
163C2×H(5,𝔽2)—28no—
164C2×H(5,𝔽2)—44no—
165C22×#41—28no—
166C22×#41—28no—
167C22×#41—44no—
168C22×#41C2311yescharacteristic
169C22×#41C2311yescharacteristic
170C22×#41C2314yes—
171C22×#41C2314yes—
172C22×#41C2312yes—
173C22×#41C2312yes—
174C22×#41C2314yes—
175C22×#41C2312yes—
176C22×#41C2312yes—
177C22×#41C2311yescharacteristic
178C23×Q8—28no—
179C23×Q8—28no—
180C23×Q8—44no—
181C23×Q8C2311yescharacteristic
182C23×Q8C2311yescharacteristic
183C23×Q8C2312yes—
184C23×Q8C2314yes—
185C23×Q8C2314yes—
186C23×Q8C2312yes—
187C23×Q8C2312yes—
188C23×Q8C2311yescharacteristic
189C23×D4C2312yes—
190C23×D4C2314yes—
191C23×D4C2312yes—
192C23×D4C2312yes—
193C23×D4C2311yescharacteristic
194C24×C4C2312yes—
195C24×C4C2312yes—
196C24×C4C2311yescharacteristic
197D4×Q8—232no—
198D4×Q8—232no—
199#548—232no—
200#548—232no—
201#548—232no—
202#547—232no—
203#547—232no—
204#546—232no—
205#546—232no—
206#546—232no—
207#546—264no—
208#536—28no—
209#536—28no—
210#536—28no—
211#536—232no—
212#536—232no—
213#536—264no—
214#536—216no—
215#536—232no—
216#536—28no—
217#536—28no—
218#536—44no—
219#536—44no—
220#535—28no—
221#535—216no—
222#534—232no—
223#532—216no—
224#532—28no—
225C2×C4⋊Q8—28no—
226C2×C4⋊Q8—28no—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2314yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2318yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×#127C2311yescharacteristic
242C2×#127C2312yes—
243C2×#124—28no—
244C2×#124—216no—
245C2×#124D4116yescomplemented
246C2×#124C2312yes—
247C2×#124C2312yes—
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2314yes—
251C2×#124C2314yes—
252C2×#124C2318yes—
253C2×#124C2312yes—
254C2×#124C2312yes—
255C2×#124C2318yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2312yes—
263#525—28no—
264#525—28no—
265#525—232no—
266#525D4116yescomplemented
267C2×#123—232no—
268C2×#123—232no—
269C2×#123C2312yes—
270C2×#123C2314yes—
271C2×#123C2312yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2318yes—
276C2×#123C2318yes—
277C2×#123C23116yes—
278C2×#123C23116yes—
279C2×#123C2314yes—
280C2×#123C2318yes—
281C2×#123C2318yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2312yes—
285C2×C22⋊Q8—232no—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C23116yes—
292C2×C22⋊Q8C23116yes—
293C2×C22⋊Q8C2318yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2318yes—
296C2×C22⋊Q8C2318yes—
297C2×C22⋊Q8C2318yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2318yes—
307C2×#121C2318yes—
308C2×#121C2318yes—
309C2×#121C2318yes—
310C2×#121C2318yes—
311C2×#121C2312yes—
312C2×#120C2312yes—
313C2×#120C2314yes—
314C2×#120C2312yes—
315C2×#120C2318yes—
316C2×#120C2318yes—
317C2×#120C2312yes—
318#519—28no—
319#518—28no—
320C4×#41—28no—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2314yes—
323C2×C4×Q8C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2318yes—
332C2×C4×D4C2318yes—
333C2×C4×D4C2318yes—
334C2×C4×D4C2314yes—
335C2×#117—28no—
336C2×#117C2311yescharacteristic
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2311yescharacteristic
340C2×#117C2314yes—
341C2×#117C2314yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2311yescharacteristic
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2314yes—
348C22×C4⋊C4C2314yes—
349C22×C4⋊C4C2318yes—
350C22×C22⋊C4C2312yes—
351C22×C22⋊C4C2314yes—
352C22×C22⋊C4C2314yes—
353C22×C22⋊C4C2318yes—
354C22×C22⋊C4C2318yes—
355C22×C22⋊C4C2314yes—
356C22×C42C2312yes—
357C22×C42C2311yescharacteristic
358C22×C42C2311yescharacteristic
359#399C23116yes—
360#399C23116yes—
361#398C2318yes—
362#398C23116yes—
363#398C23116yes—
364#397C2318yes—
365#397C23116yes—
366#397C23116yes—
367#396C2318yes—
368#396C2318yes—
369#396C23116yes—
370#395C23116yes—
371#395C23116yes—
372#394C23116yes—
373#394C2318yes—
374#394C2318yes—
375#394C2318yes—
376#394C23116yes—
377#394C23116yes—
378#394C23116yes—
379#394C23116yes—
380#393C23116yes—
381#392C23116yes—
382#392C2318yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2314yes—
389#391C2312yes—
390#391C2312yes—
391#391C2312yes—
392#390C2314yes—
393#390C2314yes—
394#390C2318yes—
395#390C2312yes—
396#390C23116yes—
397#390C2312yes—
398#390C2312yes—
399#389C2318yes—
400#389C2314yes—
401#389C23116yes—
402#389C23116yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C23116yes—
407#388C23116yes—
408#388C23116yes—
409#387C2318yes—
410#386C2314yes—
411#386C2318yes—
412#386C23116yes—
413#386C23116yes—
414#386C2314yes—
415#386C2314yes—
416#386C23116yes—
417#385C2314yes—
418#385C2318yes—
419#385C23116yes—
420#385C23116yes—
421#385C23116yes—
422#385C23116yes—
423#385C23116yes—
424#385C23116yes—
425#384C2312yes—
426#384C23116yes—
427#382C2312yes—
428#381C2314yes—
429#381C2314yes—
430#381C2314yes—
431#381C2312yes—
432#380C2314yes—
433#380C2314yes—
434#380C23116yes—
435#380C23116yes—
436#379C2314yes—
437#379C2312yes—
438#379C23116yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C23116yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448#376C2312yes—
449C43C2312yes—
450C25C2414yes—
451C25C2412yes—
452C25C2411yescharacteristic
4532−1+4—464no—
454H(5,𝔽2)—464no—
455C2×#41—28no—
456C2×#41—28no—
457C2×#41—28no—
458C2×#41—216no—
459C2×#41—28no—
460C2×#41—216no—
461C2×#41—216no—
462C2×#41—28no—
463C2×#41—28no—
464C2×#41—24no—
465C2×#41—24no—
466C2×#41—24no—
467C2×#41—24no—
468C2×#41—24no—
469C2×#41—216no—
470C2×#41—216no—
471C2×#41—216no—
472C2×#41—28no—
473C2×#41—28no—
474C2×#41—24no—
475C2×#41—24no—
476C2×#41—24no—
477C2×#41—48no—
478C2×#41—48no—
479C2×#41—48no—
480C2×#41—44no—
481C2×#41—44no—
482C2×#41—44no—
483C2×#41—44no—
484C2×#41—464no—
485C2×#41C2×D418yes—
486C22×Q8—28no—
487C22×Q8—216no—
488C22×Q8—216no—
489C22×Q8—28no—
490C22×Q8—28no—
491C22×Q8—24no—
492C22×Q8—28no—
493C22×Q8—24no—
494C22×Q8—24no—
495C22×Q8—28no—
496C22×Q8—24no—
497C22×Q8—24no—
498C22×Q8—216no—
499C22×Q8—216no—
500C22×Q8—28no—
501C22×Q8—24no—
502C22×Q8—24no—
503C22×Q8—24no—
504C22×Q8—44no—
505C22×Q8—48no—
506C22×Q8—48no—
507C22×Q8—44no—
508C22×Q8—44no—
509C22×Q8—464no—
510C22×Q8C2×D418yes—
511C22×Q8C2412yes—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×Q8C2411yescharacteristic
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2418yes—
518C22×Q8C2414yes—
519C22×Q8C2412yes—
520C22×Q8C2411yescharacteristic
521C22×Q8C2412yes—
522C22×D4—28no—
523C22×D4—28no—
524C22×D4—216no—
525C22×D4—216no—
526C22×D4—28no—
527C22×D4—28no—
528C22×D4—28no—
529C22×D4—24no—
530C22×D4—28no—
531C22×D4—24no—
532C22×D4—44no—
533C22×D4—44no—
534C22×D4—44no—
535C22×D4—48no—
536C22×D4C2×D418yes—
537C22×D4C2412yes—
538C22×D4C2412yes—
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C22×D4C2418yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C22×D4C2412yes—
546C22×D4C2412yes—
547C22×D4C2411yescharacteristic
548C22×D4C2412yes—
549C22×D4C2414yes—
550C22×D4C2414yes—
551C22×D4C2418yes—
552C22×D4C2414yes—
553C22×D4C2414yes—
554C23×C4—24no—
555C23×C4—24no—
556C23×C4—28no—
557C23×C4—28no—
558C23×C4—28no—
559C23×C4—28no—
560C23×C4—44no—
561C23×C4—44no—
562C23×C4C2×D418yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2414yes—
568C23×C4C2418yes—
569C23×C4C2414yes—
570C23×C4C2414yes—
571C23×C4C2418yes—
572C23×C4C2412yes—
573C23×C4C2411yescharacteristic
574C23×C4C2412yes—
575C23×C4C2412yes—
576C23×C4C2412yes—
577C23×C4C2412yes—
578C23×C4C2418yes—
579C23×C4C2414yes—
580C23×C4C2412yes—
581C23×C4C2411yescharacteristic
582C4⋊Q8—216no—
583C4⋊Q8—216no—
584C4⋊Q8—28no—
585C4⋊Q8—28no—
586C4⋊Q8—28no—
587C4⋊Q8—232no—
588C4⋊Q8—28no—
589C4⋊Q8—28no—
590C4⋊Q8—216no—
591C4⋊Q8—24no—
592C4⋊Q8—28no—
593C4⋊Q8—28no—
594C4⋊Q8—44no—
595C4⋊Q8—44no—
596#127—28no—
597#127—24no—
598#124—28no—
599#124—28no—
600#124—216no—
601#124—216no—
602#124—28no—
603#124—28no—
604#124—232no—
605#124—232no—
606#124—24no—
607#124—24no—
608#124—28no—
609#124—28no—
610#124—44no—
611#124—44no—
612#124C2×D4116yes—
613#124C2×D4116yes—
614#124C2×D4132yes—
615#123—216no—
616#123—216no—
617#123—28no—
618#123—28no—
619#123—216no—
620#123—232no—
621#123—216no—
622#123—264no—
623#123—264no—
624#123—232no—
625#123—216no—
626#123—232no—
627#123—232no—
628#123—48no—
629#123—48no—
630#123C2×D4116yes—
631C22⋊Q8—216no—
632C22⋊Q8—28no—
633C22⋊Q8—28no—
634C22⋊Q8—216no—
635C22⋊Q8—216no—
636C22⋊Q8—216no—
637C22⋊Q8—232no—
638C22⋊Q8—216no—
639C22⋊Q8—264no—
640C22⋊Q8—264no—
641C22⋊Q8—232no—
642C22⋊Q8—232no—
643C22⋊Q8—232no—
644C22⋊Q8—48no—
645C22⋊Q8—48no—
646C22⋊Q8C2×D4116yes—
647#121—232no—
648#121—232no—
649#121—216no—
650#121—28no—
651#121—28no—
652#121—216no—
653#121—232no—
654#121—232no—
655#121—232no—
656#121C2×D4116yes—
657#120—28no—
658#120—28no—
659#120—216no—
660#120—232no—
661#120—232no—
662#120C2×D4116yes—
663C4×Q8—216no—
664C4×Q8—28no—
665C4×Q8—216no—
666C4×D4—232no—
667C4×D4—216no—
668C4×D4—216no—
669C4×D4—216no—
670C4×D4—216no—
671C4×D4—232no—
672C4×D4—232no—
673C4×D4—28no—
674C4×D4—216no—
675C4×D4—216no—
676C4×D4C2×D4132yes—
677#117—24no—
678#117—24no—
679#117—24no—
680#117—24no—
681#117—216no—
682#117—28no—
683#117—28no—
684#117—216no—
685#117—28no—
686#117C2×D418yes—
687C2×C4⋊C4—28no—
688C2×C4⋊C4—216no—
689C2×C4⋊C4—216no—
690C2×C4⋊C4—232no—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C24116yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2412yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2418yes—
707C2×C4⋊C4C2418yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2418yes—
710C2×C4⋊C4C2418yes—
711C2×C4⋊C4C2418yes—
712C2×C4⋊C4C2418yes—
713C2×C4⋊C4C2418yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2412yes—
716C2×C22⋊C4—216no—
717C2×C22⋊C4—28no—
718C2×C22⋊C4—216no—
719C2×C22⋊C4—232no—
720C2×C22⋊C4—232no—
721C2×C22⋊C4C2×D4132yes—
722C2×C22⋊C4C2412yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2418yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C24116yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2412yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2412yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2418yes—
743C2×C22⋊C4C2418yes—
744C2×C22⋊C4C2418yes—
745C2×C22⋊C4C2418yes—
746C2×C22⋊C4C24116yes—
747C2×C22⋊C4C2418yes—
748C2×C22⋊C4C2418yes—
749C2×C22⋊C4C2418yes—
750C2×C22⋊C4C2412yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2418yes—
753C2×C22⋊C4C2418yes—
754C2×C22⋊C4C2414yes—
755C2×C42—24no—
756C2×C42—28no—
757C2×C42C2×D418yes—
758C2×C42C2412yes—
759C2×C42C2412yes—
760C2×C42C2412yes—
761C2×C42C2412yes—
762C2×C42C2412yes—
763C2×C42C2418yes—
764C2×C42C2412yes—
765C2×C42C2414yes—
766C2×C42C2418yes—
767C2×C42C2411yescharacteristic
768C2×C42C2412yes—
769C2×C42C2411yescharacteristic
770C2×C42C2412yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2418yes—
775#95C24116yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C24116yes—
780#95C24116yes—
781C24—22no—
782C24—22no—
783C24—24no—
784C24—24no—
785C24—28no—
786C24—28no—
787C24—44no—
788C24—48no—
789C24—44no—
790C24—416no—
791C24C22×D418yes—
792C24C22×D414yes—
793C24C2512yes—
794C24C2512yes—
795C24C2512yes—
796C24C2514yes—
797C24C2512yes—
798C24C2511yescharacteristic
799#41—232no—
800#41—464no—
801#41—464no—
802#41—432no—
803#41—464no—
804#41—432no—
805#41—432no—
806#41—432no—
807#41—416no—
808#41—416no—
809C2×Q8—232no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—22no—
813C2×Q8—216no—
814C2×Q8—28no—
815C2×Q8—216no—
816C2×Q8—24no—
817C2×Q8—24no—
818C2×Q8—24no—
819C2×Q8—24no—
820C2×Q8—28no—
821C2×Q8—22no—
822C2×Q8—22no—
823C2×Q8—22no—
824C2×Q8—24no—
825C2×Q8—24no—
826C2×Q8—22no—
827C2×Q8—24no—
828C2×Q8—24no—
829C2×Q8—24no—
830C2×Q8—24no—
831C2×Q8—22no—
832C2×Q8—24no—
833C2×Q8—24no—
834C2×Q8—24no—
835C2×Q8—24no—
836C2×Q8—22no—
837C2×Q8—22no—
838C2×Q8—48no—
839C2×Q8—44no—
840C2×Q8—432no—
841C2×Q8—464no—
842C2×Q8—464no—
843C2×Q8—432no—
844C2×Q8—432no—
845C2×Q8—416no—
846C2×Q8—416no—
847C2×Q8C22×D418yes—
848C2×Q8C22×D414yes—
849C2×Q8C22×D418yes—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—28no—
853C2×D4—24no—
854C2×D4—216no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—28no—
858C2×D4—28no—
859C2×D4—24no—
860C2×D4—28no—
861C2×D4—28no—
862C2×D4—216no—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—28no—
866C2×D4—216no—
867C2×D4—232no—
868C2×D4—24no—
869C2×D4—22no—
870C2×D4—24no—
871C2×D4—28no—
872C2×D4—28no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—22no—
876C2×D4—22no—
877C2×D4—28no—
878C2×D4—24no—
879C2×D4—24no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—22no—
883C2×D4—432no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—48no—
887C2×D4—48no—
888C2×D4—48no—
889C2×D4—44no—
890C2×D4—48no—
891C2×D4—48no—
892C2×D4—416no—
893C2×D4—432no—
894C2×D4—464no—
895C2×D4—432no—
896C2×D4C22×D418yes—
897C2×D4C22×D418yes—
898C2×D4C22×D414yes—
899C2×D4C22×D418yes—
900C2×D4C22×D4116yes—
901C22×C4—22no—
902C22×C4—24no—
903C22×C4—22no—
904C22×C4—24no—
905C22×C4—232no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—216no—
916C22×C4—28no—
917C22×C4—28no—
918C22×C4—216no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—28no—
924C22×C4—216no—
925C22×C4—28no—
926C22×C4—28no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—28no—
931C22×C4—24no—
932C22×C4—216no—
933C22×C4—24no—
934C22×C4—24no—
935C22×C4—28no—
936C22×C4—216no—
937C22×C4—48no—
938C22×C4—48no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—416no—
945C22×C4—48no—
946C22×C4—432no—
947C22×C4—432no—
948C22×C4C22×D418yes—
949C22×C4C22×D418yes—
950C22×C4C22×D418yes—
951C22×C4C22×D418yes—
952C22×C4C22×D414yes—
953C22×C4C22×D418yes—
954C22×C4C22×D414yes—
955C22×C4C22×D414yes—
956C22×C4H(5,𝔽2)14yes—
957C22×C4C2514yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2514yes—
961C22×C4C2514yes—
962C22×C4C2514yes—
963C22×C4C2512yes—
964C22×C4C2514yes—
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2514yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—216no—
978C4⋊C4—216no—
979C4⋊C4—232no—
980C4⋊C4—216no—
981C4⋊C4—216no—
982C4⋊C4—24no—
983C4⋊C4—28no—
984C4⋊C4—24no—
985C4⋊C4—216no—
986C4⋊C4—24no—
987C4⋊C4—216no—
988C4⋊C4—28no—
989C4⋊C4—216no—
990C4⋊C4—28no—
991C4⋊C4—216no—
992C4⋊C4—24no—
993C4⋊C4—48no—
994C4⋊C4—48no—
995C4⋊C4—48no—
996C4⋊C4—48no—
997C4⋊C4C22×D4116yes—
998C4⋊C4C22×D418yes—
999C22⋊C4—24no—
1000C22⋊C4—216no—
1001C22⋊C4—216no—
1002C22⋊C4—232no—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—216no—
1008C22⋊C4—24no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—216no—
1014C22⋊C4—216no—
1015C22⋊C4—216no—
1016C22⋊C4—28no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—216no—
1020C22⋊C4—48no—
1021C22⋊C4—416no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C22⋊C4—48no—
1025C22⋊C4—48no—
1026C22⋊C4—48no—
1027C22⋊C4C22×D418yes—
1028C22⋊C4C22×D4116yes—
1029C22⋊C4C22×D4132yes—
1030C22⋊C4C22×D4132yes—
1031C22⋊C4C22×D4116yes—
1032C42—24no—
1033C42—24no—
1034C42—24no—
1035C42—28no—
1036C42—24no—
1037C42—216no—
1038C42—24no—
1039C42—24no—
1040C42—48no—
1041C42C22×D414yes—
1042C42C22×D414yes—
1043C42C22×D418yes—
1044C42C22×D418yes—
1045C23—24no—
1046C23—22no—
1047C23—22no—
1048C23—24no—
1049C23—22no—
1050C23—22no—
1051C23—24no—
1052C23—24no—
1053C23—28no—
1054C23—216no—
1055C23—24no—
1056C23—28no—
1057C23—216no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—28no—
1065C23—28no—
1066C23—48no—
1067C23—416no—
1068C23—416no—
1069C23—48no—
1070C23—48no—
1071C23—88no—
1072C23—88no—
1073C23—816no—
1074C23—816no—
1075C23—168no—
1076C23C23×D414yes—
1077C23C23×D418yes—
1078C23C23×D414yes—
1079C23C23×D412yes—
1080C23C23×D412yes—
1081C23C2×H(5,𝔽2)12yes—
1082C23C2611yescharacteristic
1083Q8—216no—
1084Q8—216no—
1085Q8—28no—
1086Q8—432no—
1087Q8—416no—
1088Q8—48no—
1089Q8—48no—
1090Q8—44no—
1091Q8—48no—
1092Q8—48no—
1093Q8—44no—
1094D4—216no—
1095D4—216no—
1096D4—216no—
1097D4—28no—
1098D4—416no—
1099D4—416no—
1100D4—416no—
1101D4—416no—
1102D4—432no—
1103D4—416no—
1104D4—48no—
1105D4—48no—
1106D4—44no—
1107D4—44no—
1108D4—88no—
1109D4—88no—
1110D4—816no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—28no—
1119C2×C4—24no—
1120C2×C4—28no—
1121C2×C4—216no—
1122C2×C4—216no—
1123C2×C4—216no—
1124C2×C4—216no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—28no—
1143C2×C4—24no—
1144C2×C4—28no—
1145C2×C4—24no—
1146C2×C4—28no—
1147C2×C4—28no—
1148C2×C4—48no—
1149C2×C4—416no—
1150C2×C4—432no—
1151C2×C4—432no—
1152C2×C4—416no—
1153C2×C4—416no—
1154C2×C4—48no—
1155C2×C4—48no—
1156C2×C4—48no—
1157C2×C4—48no—
1158C2×C4—48no—
1159C2×C4—88no—
1160C2×C4—816no—
1161C2×C4D42116yes—
1162C2×C4C23×D414yes—
1163C2×C4C23×D418yes—
1164C2×C4C23×D414yes—
1165C2×C4C23×D414yes—
1166C2×C4C23×D418yes—
1167C2×C4C23×D414yes—
1168C2×C4C23×D412yes—
1169C2×C4C23×D412yes—
1170C2×C4C23×D412yes—
1171C2×C4C23×D412yes—
1172C2×C4C2×H(5,𝔽2)12yes—
1173C2×C4C2×H(5,𝔽2)12yes—
1174C22—24no—
1175C22—24no—
1176C22—24no—
1177C22—24no—
1178C22—28no—
1179C22—24no—
1180C22—216no—
1181C22—24no—
1182C22—24no—
1183C22—28no—
1184C22—416no—
1185C22—48no—
1186C22—44no—
1187C22—44no—
1188C22—44no—
1189C22—48no—
1190C22—44no—
1191C22—44no—
1192C22—44no—
1193C22—44no—
1194C22—44no—
1195C22—44no—
1196C22—44no—
1197C22—42no—
1198C22—42no—
1199C22—816no—
1200C22—1616no—
1201C22C2×D4214yes—
1202C22C24×D411yescharacteristic
1203C22C24×D411yescharacteristic
1204C22C22×H(5,𝔽2)11yescharacteristic
1205C222−1+614yes—
1206C4—24no—
1207C4—24no—
1208C4—28no—
1209C4—24no—
1210C4—24no—
1211C4—28no—
1212C4—44no—
1213C4—44no—
1214C4—44no—
1215C4—44no—
1216C4—44no—
1217C4—42no—
1218C4—44no—
1219C4—42no—
1220C4—44no—
1221C4C2×D4214yes—
1222C4C2×D4214yes—
1223C2—24no—
1224C2—44no—
1225C2—48no—
1226C2—44no—
1227C2—82no—
1228C2—82no—
1229C2C22×D4211yescharacteristic
1230C2#6285912yes—
1231C2#6285912yes—
1232C2#6288712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3500C2semidirect
2. C2×#3486C2semidirect
3. C2×#3485C2semidirect
4. C22×#536C2semidirect
5. #45332C2semidirect
6. #45134C2semidirect
7. #39360C2semidirect
8. #39357C2semidirect
9. #37680C2semidirect
10. #37676C2semidirect
11. #37654C2semidirect
12. #37647C2semidirect
13. #35667C2semidirect
14. #35666C2semidirect
15. #35617C2semidirect
16. #35616C2semidirect
17. #35317C2semidirect
18. #35316C2semidirect
19. #35242C2semidirect
20. #35149C2semidirect
21. #34633C2semidirect
22. #34211C2semidirect
23. #34065C2semidirect
27. C24×Q8C22semidirect
31. C2×D4×Q8C22semidirect
32. C2×D4×Q8C22semidirect
33. C2×#548C22semidirect
34. C2×#548C22semidirect
35. C2×#548C22semidirect
41. C2×#546C22semidirect
48. C2×#536C22semidirect
49. C2×#536C22semidirect
50. C2×#536C22semidirect
51. C2×#536C22semidirect
52. C2×#536C22semidirect
53. C2×#536C22semidirect
54. C2×#536C22semidirect
56. C2×#535C22semidirect
59. C2×#532C22semidirect
60. C22×C4⋊Q8C22semidirect
61. C22×C4⋊Q8C22semidirect
64. C22×#124C22semidirect
67. C2×#525C22semidirect
68. C2×#525C22semidirect
70. C22×#123C22semidirect
71. C22×C22⋊Q8C22semidirect
72. C2×#519C22semidirect
75. C22×#117C22semidirect
76. #2868C22semidirect
77. #2858C22semidirect
78. #2857C22semidirect
79. #2849C22semidirect
80. #2849C22semidirect
81. #2681C22semidirect
82. #2680C22semidirect
83. #2680C22semidirect
84. #2678C22semidirect
85. #2674C22semidirect
86. #2672C22semidirect
87. #2672C22semidirect
88. #2671C22semidirect
89. #2658C22semidirect
90. #2658C22semidirect
91. #2621C22semidirect
92. #2621C22semidirect
93. #2620C22semidirect
94. #2620C22semidirect
95. #2619C22semidirect
96. #2618C22semidirect
97. #2617C22semidirect
98. #2614C22semidirect
99. #2613C22semidirect
100. #2547C22semidirect
101. #2547C22semidirect
102. #2546C22semidirect
103. #2546C22semidirect
104. #2545C22semidirect
105. #2544C22semidirect
106. #2542C22semidirect
107. #2501C22semidirect
108. #2486C22semidirect
109. #2472C22semidirect
110. #2464C22semidirect
111. #2455C22semidirect
112. #2449C22semidirect
113. #2440C22semidirect
114. #2437C22semidirect
115. #2436C22semidirect
116. #2435C22semidirect
117. #2435C22semidirect
118. #2434C22semidirect
119. #2434C22semidirect
120. #2434C22semidirect
121. #2432C22semidirect
122. #2432C22semidirect
123. #2432C22semidirect
124. #2432C22semidirect
125. #2432C22semidirect
126. #2431C22semidirect
127. #2429C22semidirect
128. #2427C22semidirect
129. #2422C22semidirect
130. #2418C22semidirect
131. #2413C22semidirect
132. #2412C22semidirect
133. #2409C22semidirect
134. #2407C22semidirect
135. #2406C22semidirect
137. #2392C22semidirect
138. #2367C22semidirect
139. #2342C22semidirect
140. #2326C22semidirect
141. #2324C22semidirect
142. #2323C22semidirect
143. #2322C22semidirect
144. #2321C22semidirect
145. #2310C22semidirect
146. #2310C22semidirect
147. #2310C22semidirect
149. C4×#124C22semidirect
152. #2297C22semidirect
153. #2296C22semidirect
154. #2293C22semidirect
155. #2290C22semidirect
156. #2285C22semidirect
157. #2280C22semidirect
158. C4×#117C22semidirect
245. C2×#124D4semidirect
266. #525D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×#34862
C2×#34852
C22×#5362
#453322
#451342
#393602
#393572
#376802
#376762
#376542
#376472
#356672
#356662
#356172
#356162
#353172
#353162
#352422
#351492
#346332
#342112
#340652