Finite Group Databasebeta

← #7644242

Subgroups — #7644242

Order 512.

6652 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic, complemented
2C22×#541C211yesmaximal, characteristic, complemented
3#42878C214yesmaximal, complemented
4#42877C214yesmaximal, complemented
5#42803C218yesmaximal, complemented
6#42802C218yesmaximal, complemented
7#42791C214yesmaximal, complemented
8#42790C214yesmaximal, complemented
9#37549C214yesmaximal, complemented
10#37538C214yesmaximal, complemented
11#36971C214yesmaximal, complemented
12#36968C214yesmaximal, complemented
13#35667C212yesmaximal, complemented
14#35661C212yesmaximal, complemented
15#35639C212yesmaximal, complemented
16#35633C212yesmaximal, complemented
17#35179C211yesmaximal, characteristic, complemented
18#35178C211yesmaximal, characteristic, complemented
19#34634C211yesmaximal, characteristic, complemented
20#34633C211yesmaximal, characteristic
21#34182C211yesmaximal, characteristic, complemented
22#3507—216no—
23C2×#559C2212yescomplemented
24C2×#557C2212yescomplemented
25C2×#556C2214yescomplemented
26C2×#556C2212yescomplemented
27C2×#554C2212yescomplemented
28C2×#552C2214yescomplemented
29C2×#541—216no—
30C2×#541C2214yes—
31C2×#541C2214yes—
32C2×#541C2214yes—
33C2×#541C2214yes—
34C2×#539C2214yes—
35C2×#536C2212yes—
36C2×#536C2212yes—
37C2×#533C2211yescharacteristic
38C2×#532C2211yescharacteristic
39C22×C4⋊Q8C2211yescharacteristic
40C2×#529C2214yes—
41C22×#126C2212yes—
42C22×#126C2212yes—
43C22×#125C2211yescharacteristic
44C22×#125C2212yes—
45C22×#125C2212yes—
46C2×#525C2212yes—
47C22×C22⋊Q8C2211yescharacteristic
48C22×C22⋊Q8C2211yescharacteristic
49C2×#520C2212yes—
50C2×#519C2212yes—
51C22×C4×Q8C2211yescharacteristic
52C22×C4×Q8C2211yescharacteristic
53C22×#117C2211yescharacteristic
54#2855C2214yes—
55#2854C2214yes—
56#2823C22116yes—
57#2822C2218yescomplemented
58#2820C2218yescomplemented
59#2727C22116yes—
60#2726C22116yescomplemented
61#2725C22116yes—
62#2725C22116yescomplemented
63#2707C22116yescomplemented
64#2705C22116yes—
65#2704C22116yescomplemented
66#2702C22116yes—
67#2664C2218yes—
68#2664C22116yescomplemented
69#2662C2218yes—
70#2637C2218yes—
71#2636C2218yes—
72#2629C2214yes—
73#2629C22116yescomplemented
74#2628C2212yes—
75#2628C2212yes—
76#2627C2212yes—
77#2627C2212yes—
78#2627C2214yes—
79#2626C2212yes—
80#2626C2212yes—
81#2621C2212yes—
82#2620C2214yes—
83#2619C2212yes—
84#2618C2212yes—
85#2618C2212yes—
86#2618C2214yes—
87#2617C2212yes—
88#2617C2212yes—
89#2601C22116yes—
90#2584C2218yescomplemented
91#2582C2214yescomplemented
92#2581C2214yescomplemented
93#2579C2218yes—
94#2568C2212yescomplemented
95#2567C2212yescomplemented
96#2565C2214yescomplemented
97#2562C2218yescomplemented
98#2548C2212yescomplemented
99#2546C2212yescomplemented
100#2546C2218yescomplemented
101#2545C2214yescomplemented
102#2545C2218yescomplemented
103#2538C2218yes—
104#2538C2214yescomplemented
105#2536C2218yes—
106#2536C2214yescomplemented
107#2534C2218yes—
108#2487C2218yes—
109#2486C2218yes—
110#2454C2218yescomplemented
111#2453C2218yescomplemented
112#2442C2218yescomplemented
113#2441C2218yescomplemented
114#2429C2218yes—
115#2429C2218yes—
116#2429C2218yescomplemented
117#2429C2218yescomplemented
118#2427C2218yes—
119#2426C2218yes—
120#2417C2218yes—
121#2415C2218yes—
122#2413C2218yes—
123#2413C2218yes—
124#2413C2218yes—
125#2411C2218yes—
126#2396C2214yes—
127#2396C2214yes—
128#2392C2214yes—
129#2392C2214yes—
130#2351C2214yescomplemented
131#2351C2214yescomplemented
132Q8×C4⋊C4C2214yescomplemented
133Q8×C4⋊C4C2214yescomplemented
134#2317C2212yes—
135#2316C2212yes—
136#2316C2214yes—
137#2311C2212yes—
138#2310C2212yes—
139#2297C2212yes—
140#2296C2212yes—
141#2285C2211yescharacteristic
142#2285C2211yescharacteristic
143#2285C2214yes—
144#2280C2212yes—
145C22×#41C2312yes—
146C23×Q8C2311yescharacteristic
147C23×Q8C2311yescharacteristic
148C24×C4C2311yescharacteristic
149#559—216no—
150#557—216no—
151#556—216no—
152#556—232no—
153#554—216no—
154#552—232no—
155#541—232no—
156#541—232no—
157#541—232no—
158#541—232no—
159#539—232no—
160#536—216no—
161#536—48no—
162#533—28no—
163#532—28no—
164C2×C4⋊Q8—28no—
165C2×C4⋊Q8C2311yescharacteristic
166C2×C4⋊Q8C2311yescharacteristic
167C2×C4⋊Q8C2311yescharacteristic
168C2×C4⋊Q8C2314yes—
169C2×C4⋊Q8C2314yes—
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2314yes—
172C2×#127C2311yescharacteristic
173#529—232no—
174C2×#126—216no—
175C2×#126—216no—
176C2×#126C2318yes—
177C2×#126C2318yes—
178C2×#126C2318yes—
179C2×#126C2318yes—
180C2×#126C2318yes—
181C2×#126C2318yes—
182C2×#125—28no—
183C2×#125—216no—
184C2×#125—216no—
185C2×#125C2318yes—
186C2×#125C2312yes—
187C2×#125C2314yes—
188C2×#125C2318yes—
189C2×#125C2314yes—
190C2×#125C2318yes—
191C2×#125C2318yes—
192C2×#125C2314yes—
193C2×#125C2318yes—
194C2×#124C2314yes—
195C2×#124C2312yes—
196C2×#124C2314yes—
197C2×#124C2314yes—
198#525—48no—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×#123C2318yes—
202C2×#123C2314yes—
203C2×C22⋊Q8—28no—
204C2×C22⋊Q8—28no—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2312yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2318yes—
216C2×#121C2312yes—
217C2×#121C2312yes—
218C2×#121C2314yes—
219C2×#120C2314yes—
220#520—216no—
221#519—48no—
222C2×C4×Q8—28no—
223C2×C4×Q8D4116yescomplemented
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2318yes—
233C2×C4×Q8C2318yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2318yes—
244C2×#117—28no—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2318yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2314yes—
254C2×#117C2318yes—
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2311yescharacteristic
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2312yes—
272C22×C42C2312yes—
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276#400C2314yes—
277#400C2318yes—
278#400C23116yes—
279#400C2314yes—
280#399C23116yes—
281#399C2314yes—
282#399C2314yes—
283#398C23116yes—
284#398C2314yes—
285#398C2318yes—
286#398C23116yes—
287#398C23116yes—
288#398C23116yes—
289#398C23116yes—
290#398C23116yes—
291#398C2314yes—
292#398C2318yes—
293#398C2318yes—
294#397C23116yes—
295#397C2314yes—
296#397C2314yes—
297#396C23116yes—
298#396C23116yes—
299#396C2318yes—
300#396C23116yes—
301#396C23116yes—
302#396C23116yes—
303#396C23116yes—
304#396C23116yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#395C2314yes—
309#395C2318yes—
310#395C2314yes—
311#394C2314yes—
312#394C2318yes—
313#394C2318yes—
314#394C23116yes—
315#394C23116yes—
316#394C2318yes—
317#394C2314yes—
318#393C2314yes—
319#393C2314yes—
320#392C2314yes—
321#392C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2318yes—
325#391C2314yes—
326#391C2318yes—
327#391C2314yes—
328#390C2314yes—
329#390C2318yes—
330#390C23116yes—
331#390C2314yes—
332#389C2318yes—
333#389C2318yes—
334#389C2318yes—
335#389C23116yes—
336#389C23116yes—
337#389C2318yes—
338#389C23116yes—
339#389C23116yes—
340#389C23116yes—
341#389C23116yes—
342#389C2318yes—
343#389C23116yes—
344#389C2314yes—
345#389C2314yes—
346#388C23116yes—
347#388C23116yes—
348#388C23116yes—
349#388C23116yes—
350#388C23116yes—
351#388C23116yes—
352#387C23116yes—
353#387C23116yes—
354#386C2318yes—
355#386C2314yes—
356#386C23116yes—
357#386C2314yes—
358#385C2318yes—
359#385C2314yes—
360#385C23116yes—
361#385C2314yes—
362#384C2314yes—
363#384C2318yes—
364#384C2312yes—
365#384C2312yes—
366#382C2318yes—
367#382C2314yes—
368#382C2312yes—
369#382C2312yes—
370#381C2318yes—
371#381C2314yes—
372#380C23116yes—
373#380C23116yes—
374#380C2318yes—
375#380C2318yes—
376#380C2312yes—
377#380C2312yes—
378#380C2312yes—
379#380C2312yes—
380#380C2314yes—
381#380C2314yes—
382#379C2314yes—
383C4×C4⋊C4C2318yes—
384C4×C4⋊C4C2312yes—
385C4×C4⋊C4C2312yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2312yes—
388C4×C4⋊C4C2312yes—
389C4×C4⋊C4C2318yes—
390C4×C22⋊C4C2318yes—
391C4×C22⋊C4C2318yes—
392C25C2411yescharacteristic
393C2×#41—28no—
394C2×#41—28no—
395C2×#41—28no—
396C22×Q8—24no—
397C22×Q8—24no—
398C22×Q8—24no—
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8C2×D418yes—
402C22×Q8C2412yes—
403C22×Q8C2412yes—
404C22×Q8C2412yes—
405C22×Q8C2412yes—
406C22×Q8C2412yes—
407C22×Q8C2412yes—
408C22×Q8C2412yes—
409C22×D4C2414yes—
410C22×D4C2412yes—
411C22×D4C2412yes—
412C22×D4C2412yes—
413C22×D4C2418yes—
414C23×C4—24no—
415C23×C4—24no—
416C23×C4—24no—
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419C23×C4C2414yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2412yes—
426C23×C4C2418yes—
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C4⋊Q8—216no—
432C4⋊Q8—216no—
433C4⋊Q8—216no—
434C4⋊Q8—24no—
435C4⋊Q8—24no—
436C4⋊Q8—24no—
437C4⋊Q8—48no—
438#127—24no—
439#126—232no—
440#126—232no—
441#126—232no—
442#126—232no—
443#126—232no—
444#126—232no—
445#125—216no—
446#125—216no—
447#125—232no—
448#125—232no—
449#125—232no—
450#125—232no—
451#125—232no—
452#125—216no—
453#125—28no—
454#124—216no—
455#124—216no—
456#124—28no—
457#124—48no—
458#123—232no—
459#123—232no—
460#123—48no—
461#123—416no—
462C22⋊Q8—216no—
463C22⋊Q8—216no—
464C22⋊Q8—216no—
465C22⋊Q8—216no—
466C22⋊Q8—28no—
467C22⋊Q8—28no—
468C22⋊Q8—216no—
469C22⋊Q8—216no—
470C22⋊Q8—232no—
471C22⋊Q8—48no—
472C22⋊Q8—416no—
473#121—28no—
474#121—28no—
475#121—48no—
476#120—48no—
477C4×Q8—216no—
478C4×Q8—28no—
479C4×Q8—28no—
480C4×Q8—28no—
481C4×Q8—28no—
482C4×Q8—216no—
483C4×Q8—28no—
484C4×Q8—28no—
485C4×Q8—416no—
486C4×Q8—416no—
487C4×Q8C2×D4116yes—
488C4×Q8C2×D4116yes—
489C4×Q8C2×D4116yes—
490C4×Q8C2×D4116yes—
491C4×D4—232no—
492C4×D4—216no—
493C4×D4—216no—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—416no—
497#117—28no—
498#117—28no—
499#117—28no—
500#117—216no—
501#117—28no—
502#117—28no—
503#117—28no—
504#117—28no—
505#117—232no—
506#117—416no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—28no—
511C2×C4⋊C4—28no—
512C2×C4⋊C4—28no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—28no—
515C2×C4⋊C4—28no—
516C2×C4⋊C4—28no—
517C2×C4⋊C4—216no—
518C2×C4⋊C4C2×D418yes—
519C2×C4⋊C4C2×D4116yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C24116yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C24116yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C24116yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C24116yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—28no—
565C2×C22⋊C4—28no—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C24116yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C24116yes—
588C2×C42—24no—
589C2×C42—28no—
590C2×C42C2×D418yes—
591C2×C42C2×D4116yes—
592C2×C42C2418yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2414yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C24116yes—
601C2×C42C2411yescharacteristic
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2414yes—
606C2×C42C2414yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2414yes—
612#95C2414yes—
613#95C2418yes—
614#95C24116yes—
615#95C2414yes—
616#95C2414yes—
617#95C2418yes—
618#95C24116yes—
619#95C24116yes—
620#95C24116yes—
621#95C24116yes—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—42no—
626C24—42no—
627C24C2512yes—
628C24C2514yes—
629C24C2511yescharacteristic
630#41—432no—
631C2×Q8—232no—
632C2×Q8—24no—
633C2×Q8—24no—
634C2×Q8—24no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—24no—
638C2×Q8—24no—
639C2×Q8—24no—
640C2×Q8—24no—
641C2×Q8—24no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—24no—
645C2×Q8—24no—
646C2×Q8—24no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—416no—
650C2×Q8C22×D418yes—
651C2×Q8C22×D418yes—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—44no—
661C2×D4—48no—
662C2×D4—44no—
663C2×D4—48no—
664C2×D4—48no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—24no—
674C22×C4—22no—
675C22×C4—24no—
676C22×C4—28no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—28no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—28no—
685C22×C4—216no—
686C22×C4—42no—
687C22×C4—44no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—44no—
691C22×C4—42no—
692C22×C4—416no—
693C22×C4—416no—
694C22×C4C22×D418yes—
695C22×C4C22×D414yes—
696C22×C4C22×D414yes—
697C22×C4C22×D418yes—
698C22×C4C22×D414yes—
699C22×C4H(5,𝔽2)14yes—
700C22×C42−1+414yes—
701C22×C4C2518yes—
702C22×C4C2514yes—
703C22×C4C2518yes—
704C22×C4C2514yes—
705C22×C4C2512yes—
706C22×C4C2512yes—
707C22×C4C2514yes—
708C22×C4C2514yes—
709C22×C4C2514yes—
710C22×C4C2512yes—
711C22×C4C2511yescharacteristic
712C22×C4C2511yescharacteristic
713C22×C4C2511yescharacteristic
714C22×C4C2514yes—
715C22×C4C2511yescharacteristic
716C22×C4C2514yes—
717C22×C4C2511yescharacteristic
718C22×C4C2511yescharacteristic
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—24no—
724C4⋊C4—216no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—216no—
730C4⋊C4—216no—
731C4⋊C4—216no—
732C4⋊C4—216no—
733C4⋊C4—216no—
734C4⋊C4—216no—
735C4⋊C4—24no—
736C4⋊C4—28no—
737C4⋊C4—216no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—24no—
741C4⋊C4—28no—
742C4⋊C4—216no—
743C4⋊C4—24no—
744C4⋊C4—28no—
745C4⋊C4—28no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—416no—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—416no—
754C4⋊C4—416no—
755C4⋊C4—48no—
756C4⋊C4—416no—
757C4⋊C4C22×D418yes—
758C4⋊C4C22×D418yes—
759C4⋊C4C22×D4116yes—
760C4⋊C4C22×D4116yes—
761C22⋊C4—28no—
762C22⋊C4—28no—
763C22⋊C4—28no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—216no—
769C22⋊C4—216no—
770C22⋊C4—28no—
771C22⋊C4—216no—
772C22⋊C4—216no—
773C22⋊C4—28no—
774C22⋊C4—216no—
775C22⋊C4—416no—
776C22⋊C4—48no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—48no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—416no—
783C42—24no—
784C42—24no—
785C42—28no—
786C42—28no—
787C42—216no—
788C42—28no—
789C42—28no—
790C42—28no—
791C42—416no—
792C42C22×D414yes—
793C42C22×D414yes—
794C42C22×D414yes—
795C42C22×D414yes—
796C42C22×D4116yes—
797C42C22×D4116yes—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—24no—
802C23—24no—
803C23—22no—
804C23—22no—
805C23—24no—
806C23—28no—
807C23—24no—
808C23—24no—
809C23—28no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—84no—
814C23—84no—
815C23C23×D412yes—
816C23C2×H(5,𝔽2)12yes—
817C23C2×2−1+412yes—
818C23C2611yescharacteristic
819Q8—216no—
820Q8—216no—
821Q8—48no—
822Q8—48no—
823Q8—48no—
824Q8—48no—
825Q8—84no—
826D4—48no—
827D4—416no—
828D4—48no—
829D4—84no—
830D4—816no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—22no—
834C2×C4—28no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—216no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—28no—
848C2×C4—28no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—28no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—44no—
865C2×C4—48no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—48no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—48no—
873C2×C4—48no—
874C2×C4—416no—
875C2×C4—816no—
876C2×C4#537116yes—
877C2×C4C23×D412yes—
878C2×C4C23×D412yes—
879C2×C4C23×D418yes—
880C2×C4C23×D412yes—
881C2×C4C23×D412yes—
882C2×C4C23×D418yes—
883C2×C4C23×D412yes—
884C2×C4C23×D412yes—
885C2×C4C2×H(5,𝔽2)12yes—
886C2×C4C2×H(5,𝔽2)12yes—
887C2×C4C2×2−1+412yes—
888C2×C4C2×2−1+412yes—
889C22—22no—
890C22—22no—
891C22—24no—
892C22—24no—
893C22—44no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—44no—
898C22—48no—
899C22—48no—
900C22—44no—
901C22—42no—
902C22—44no—
903C22—88no—
904C22C2×#53714yes—
905C22C24×D411yescharacteristic
906C22C22×H(5,𝔽2)11yescharacteristic
907C22C22×2−1+411yescharacteristic
908C222−1+612yes—
909C222−1+612yes—
910C4—22no—
911C4—22no—
912C4—28no—
913C4—22no—
914C4—22no—
915C4—28no—
916C4—42no—
917C4—44no—
918C4—44no—
919C4—42no—
920C4—44no—
921C4—48no—
922C4—48no—
923C4—42no—
924C4—44no—
925C4—44no—
926C4C2×#53714yes—
927C4C2×#53714yes—
928C2—24no—
929C2—84no—
930C2—82no—
931C2C22×#53711yescharacteristic
932C2#6284811yescharacteristic
933C2#6285911yescharacteristic
934C2#6288812yes—
935C2#6288912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34633C2
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×#3507C2semidirect
2. C22×#541C2semidirect
3. #42878C2semidirect
4. #42877C2semidirect
5. #42803C2semidirect
6. #42802C2semidirect
7. #42791C2semidirect
8. #42790C2semidirect
9. #37549C2semidirect
10. #37538C2semidirect
11. #36971C2semidirect
12. #36968C2semidirect
13. #35667C2semidirect
14. #35661C2semidirect
15. #35639C2semidirect
16. #35633C2semidirect
17. #35179C2semidirect
18. #35178C2semidirect
19. #34634C2semidirect
21. #34182C2semidirect
23. C2×#559C22semidirect
24. C2×#557C22semidirect
25. C2×#556C22semidirect
26. C2×#556C22semidirect
27. C2×#554C22semidirect
28. C2×#552C22semidirect
57. #2822C22semidirect
58. #2820C22semidirect
60. #2726C22semidirect
62. #2725C22semidirect
63. #2707C22semidirect
65. #2704C22semidirect
68. #2664C22semidirect
73. #2629C22semidirect
90. #2584C22semidirect
91. #2582C22semidirect
92. #2581C22semidirect
94. #2568C22semidirect
95. #2567C22semidirect
96. #2565C22semidirect
97. #2562C22semidirect
98. #2548C22semidirect
99. #2546C22semidirect
100. #2546C22semidirect
101. #2545C22semidirect
102. #2545C22semidirect
104. #2538C22semidirect
106. #2536C22semidirect
110. #2454C22semidirect
111. #2453C22semidirect
112. #2442C22semidirect
113. #2441C22semidirect
116. #2429C22semidirect
117. #2429C22semidirect
130. #2351C22semidirect
131. #2351C22semidirect
132. Q8×C4⋊C4C22semidirect
133. Q8×C4⋊C4C22semidirect
223. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
C22×#5412
#428782
#428772
#428032
#428022
#427912
#427902
#375492
#375382
#369712
#369682
#356672
#356612
#356392
#356332
#351792
#351782
#346342
#346332
#341822