Finite Group Databasebeta

← #7677972

Subgroups — #7677972

Order 512.

8068 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C22×#556C211yesmaximal, characteristic, complemented
3#59421C214yesmaximal, complemented
4#59410C214yesmaximal, complemented
5#59134C214yesmaximal, complemented
6#59049C214yesmaximal, complemented
7#45269C214yesmaximal, complemented
8#45268C214yesmaximal, complemented
9#45240C218yesmaximal, complemented
10#38905C214yesmaximal, complemented
11#38031C218yesmaximal, complemented
12#36426C214yesmaximal, complemented
13#35677C212yesmaximal, complemented
14#35676C212yesmaximal, complemented
15#35182C212yesmaximal, complemented
16#35165C211yesmaximal, characteristic, complemented
17#34955C211yesmaximal, characteristic, complemented
18#34952C211yesmaximal, characteristic, complemented
19#34257C212yesmaximal, complemented
20#34209C211yesmaximal, characteristic, complemented
21C4×#535C211yesmaximal, characteristic, complemented
22C22×2−1+4C2212yes—
23#3499—216no—
24C2×#556—216no—
25C2×#556C2214yes—
26C2×#556C2214yes—
27C2×#556C2214yes—
28C2×#556C2214yes—
29C2×D4×Q8C2212yescomplemented
30C2×D4×Q8C2212yescomplemented
31C2×#547C2214yes—
32C2×#547C2214yes—
33C2×#547C2212yescomplemented
34C2×#547C2212yescomplemented
35C2×#536C2212yes—
36C2×#536C2214yescomplemented
37C2×#535C2211yescharacteristic
38C2×#535C2212yes—
39C2×#532C2211yescharacteristic
40C2×#532C2212yescomplemented
41C22×C4⋊Q8C2211yescharacteristic
42C22×C4⋊Q8C2212yescomplemented
43C22×#126C2214yes—
44C22×#124C2212yes—
45C22×C22⋊Q8C2212yes—
46C2×#519C2212yes—
47C2×C4×#41C2211yescharacteristic
48C22×C4×Q8C2212yes—
49C22×C4×Q8C2211yescharacteristic
50C22×C4×D4C2211yescharacteristic
51C22×#117C2212yes—
52#2853C2218yes—
53#2847C2214yes—
54#2716C22116yescomplemented
55#2714C22116yescomplemented
56#2705C22116yescomplemented
57#2702C22116yescomplemented
58#2696C22116yescomplemented
59#2692C22116yescomplemented
60#2623C2218yes—
61#2617C2214yes—
62#2592C2214yescomplemented
63#2591C2214yes—
64#2582C2212yescomplemented
65#2581C2212yescomplemented
66#2580C2212yescomplemented
67#2579C2214yes—
68#2568C2212yescomplemented
69#2560C22116yescomplemented
70#2554C22116yescomplemented
71#2548C2218yes—
72#2548C2212yescomplemented
73#2547C2212yes—
74#2545C2218yes—
75#2544C2214yes—
76#2541C2212yes—
77#2540C2218yescomplemented
78#2538C2212yescomplemented
79#2537C2214yes—
80#2535C2214yes—
81#2504C2212yes—
82#2492C2218yescomplemented
83#2487C2212yes—
84#2481C22116yescomplemented
85#2477C22116yescomplemented
86#2471C22116yescomplemented
87#2467C22116yescomplemented
88#2448C2218yescomplemented
89#2446C2218yescomplemented
90#2439C2218yescomplemented
91#2436C2218yes—
92#2436C2218yes—
93#2436C2212yes—
94#2431C2218yes—
95#2431C2218yes—
96#2427C2218yescomplemented
97#2426C2218yes—
98#2426C2218yes—
99#2423C2218yescomplemented
100#2421C2218yescomplemented
101#2417C2218yescomplemented
102#2414C2218yescomplemented
103#2411C2218yes—
104#2411C2218yes—
105#2409C2212yes—
106#2404C2218yes—
107#2404C2218yes—
108#2398C2214yescomplemented
109#2396C2214yescomplemented
110#2365C2214yescomplemented
111#2365C2214yescomplemented
112#2363C2218yescomplemented
113#2352C2218yescomplemented
114#2344C2214yes—
115#2344C2214yes—
116#2341C2218yescomplemented
117#2341C2218yescomplemented
118Q8×C22⋊C4C2218yescomplemented
119Q8×C22⋊C4C2218yescomplemented
120#2328C2212yes—
121#2327C2214yescomplemented
122#2326C2212yes—
123#2324C2214yes—
124#2321C2214yes—
125#2317C2211yescharacteristic
126#2311C2211yescharacteristic
127#2311C2212yes—
128#2311C2218yes—
129#2310C2212yes—
130#2309C2211yescharacteristic
131C4×C4⋊Q8C2214yescomplemented
132C4×#127C2212yes—
133C4×#124C2212yes—
134C4×#124C2214yescomplemented
135C4×C22⋊Q8C2214yescomplemented
136C4×#121C2214yes—
137C4×#120C2214yes—
138#2297C2218yes—
139#2297C2212yes—
140#2297C2212yes—
141#2297C2212yes—
142#2296C2212yes—
143#2285C2211yescharacteristic
144C4×#117C2211yescharacteristic
145C2×2−1+4—216no—
146C2×2−1+4—216no—
147C2×2−1+4—48no—
148C22×#41C2312yes—
149C22×#41C2318yes—
150C22×#41C2314yes—
151C22×#41C2314yes—
152C22×#41C2311yescharacteristic
153C23×Q8C2314yes—
154C23×Q8C2314yes—
155C23×Q8C2312yes—
156C23×Q8C2311yescharacteristic
157C23×D4C2311yescharacteristic
158C24×C4C2312yes—
159#556—232no—
160#556—232no—
161#556—232no—
162#556—232no—
163D4×Q8—216no—
164D4×Q8—216no—
165#547—216no—
166#547—216no—
167#547—232no—
168#547—232no—
169#536—216no—
170#536—232no—
171#535—28no—
172#535—48no—
173#532—216no—
174#532—28no—
175C2×C4⋊Q8—216no—
176C2×C4⋊Q8D4116yescomplemented
177C2×C4⋊Q8C2311yescharacteristic
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2312yes—
185C2×#127C2312yes—
186C2×#127C2311yescharacteristic
187C2×#127C2314yes—
188C2×#126—232no—
189C2×#126C23116yes—
190C2×#126C23116yes—
191C2×#124—216no—
192C2×#124C2312yes—
193C2×#124C2312yes—
194C2×#124C2318yes—
195C2×#124C2318yes—
196C2×#124C2314yes—
197C2×#124C2314yes—
198C2×#124C2314yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×#123C2318yes—
202C2×C22⋊Q8—216no—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2318yes—
205C2×C22⋊Q8C2318yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C2314yes—
210C2×#121C2314yes—
211C2×#121C2312yes—
212C2×#121C2312yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2318yes—
216C2×#121C2318yes—
217C2×#120C2314yes—
218C2×#120C2318yes—
219#519—48no—
220C4×#41—28no—
221C2×C4×Q8—216no—
222C2×C4×Q8—28no—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2318yes—
230C2×C4×Q8C2318yes—
231C2×C4×Q8C2318yes—
232C2×C4×Q8C2318yes—
233C2×C4×D4—28no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2318yes—
247C2×#117—216no—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2318yes—
254C2×#117C2318yes—
255C2×#117C2318yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2314yes—
266C22×C22⋊C4C2314yes—
267C22×C42C2314yes—
268C22×C42C2312yes—
269C22×C42C2312yes—
270C22×C42C2311yescharacteristic
271#400C2318yes—
272#400C2314yes—
273#400C23116yes—
274#399C2314yes—
275#399C23116yes—
276#398C2318yes—
277#398C23116yes—
278#397C23116yes—
279#397C2318yes—
280#397C2318yes—
281#396C2318yes—
282#396C23116yes—
283#396C23116yes—
284#395C2314yes—
285#394C23116yes—
286#394C2318yes—
287#394C23116yes—
288#394C23116yes—
289#393C23116yes—
290#393C2314yes—
291#393C2318yes—
292#393C23116yes—
293#392C2318yes—
294#392C23116yes—
295#392C23116yes—
296#391C23116yes—
297#391C2318yes—
298#391C2318yes—
299#391C2312yes—
300#391C2314yes—
301#391C2314yes—
302#391C2314yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C23116yes—
307#390C23116yes—
308#390C2312yes—
309#390C2312yes—
310#390C2318yes—
311#390C2314yes—
312#390C2312yes—
313#390C23116yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2314yes—
318#390C23116yes—
319#390C2314yes—
320#390C23116yes—
321#389C2318yes—
322#389C2318yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#388C2318yes—
328#388C2318yes—
329#388C23116yes—
330#388C2318yes—
331#388C2318yes—
332#388C23116yes—
333#388C23116yes—
334#388C23116yes—
335#387C23116yes—
336#387C2318yes—
337#387C23116yes—
338#387C23116yes—
339#387C23116yes—
340#386C23116yes—
341#386C2314yes—
342#386C2314yes—
343#386C2314yes—
344#386C2318yes—
345#386C2318yes—
346#386C2314yes—
347#386C2318yes—
348#386C2314yes—
349#386C2314yes—
350#386C2314yes—
351#386C23116yes—
352#386C23116yes—
353#386C23116yes—
354#386C23116yes—
355#385C2314yes—
356#385C2318yes—
357#385C2314yes—
358#385C2314yes—
359#385C2318yes—
360#384C2312yes—
361#384C2312yes—
362#382C2314yes—
363#382C2312yes—
364#382C2312yes—
365#381C2318yes—
366#380C2314yes—
367#380C23116yes—
368#380C2318yes—
369#380C23116yes—
370#380C2312yes—
371#380C2312yes—
372#380C2318yes—
373#380C2314yes—
374#379C2314yes—
375C4×C4⋊C4C2318yes—
376C4×C4⋊C4C2318yes—
377C4×C4⋊C4C2312yes—
378C4×C4⋊C4C2312yes—
379C4×C4⋊C4C2312yes—
380C4×C4⋊C4C2312yes—
381C4×C4⋊C4C2318yes—
382C4×C22⋊C4C23116yes—
383C4×C22⋊C4C2312yes—
384C4×C22⋊C4C23116yes—
385C4×C22⋊C4C2318yes—
386C4×C22⋊C4C2318yes—
387C4×C22⋊C4C2312yes—
388C4×C22⋊C4C2318yes—
389C4×C22⋊C4C2318yes—
390#376C2312yes—
391C43C2312yes—
392C25C2412yes—
3932−1+4—4128no—
394C2×#41—216no—
395C2×#41—216no—
396C2×#41—232no—
397C2×#41—216no—
398C2×#41—24no—
399C2×#41—28no—
400C2×#41—232no—
401C2×#41—216no—
402C2×#41—28no—
403C2×#41—24no—
404C2×#41—28no—
405C2×#41—416no—
406C2×#41—48no—
407C2×#41—48no—
408C2×#41#4118yes—
409C22×Q8—216no—
410C22×Q8—216no—
411C22×Q8—216no—
412C22×Q8—24no—
413C22×Q8—28no—
414C22×Q8—216no—
415C22×Q8—28no—
416C22×Q8—44no—
417C22×Q8—48no—
418C22×Q8—48no—
419C22×Q8C2×D4116yes—
420C22×Q8C2412yes—
421C22×Q8C2412yes—
422C22×Q8C2418yes—
423C22×Q8C2414yes—
424C22×Q8C2414yes—
425C22×Q8C2411yescharacteristic
426C22×Q8C2412yes—
427C22×D4—24no—
428C22×D4—24no—
429C22×D4—24no—
430C22×D4C2412yes—
431C22×D4C2412yes—
432C22×D4C2412yes—
433C22×D4C2414yes—
434C22×D4C2412yes—
435C22×D4C2418yes—
436C22×D4C2412yes—
437C22×D4C2411yescharacteristic
438C22×D4C2412yes—
439C22×D4C2418yes—
440C22×D4C24116yes—
441C23×C4—28no—
442C23×C4—48no—
443C23×C4C2412yes—
444C23×C4C2414yes—
445C23×C4C2414yes—
446C23×C4C2418yes—
447C23×C4C2418yes—
448C23×C4C2414yes—
449C23×C4C2411yescharacteristic
450C23×C4C2412yes—
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C4⋊Q8—216no—
459C4⋊Q8—216no—
460C4⋊Q8—216no—
461C4⋊Q8—24no—
462C4⋊Q8C2×D4116yes—
463C4⋊Q8C2×D4116yes—
464C4⋊Q8C2×D4116yes—
465C4⋊Q8C2×D4116yes—
466#127—28no—
467#127—24no—
468#127—48no—
469#126—264no—
470#126—264no—
471#124—232no—
472#124—232no—
473#124—216no—
474#124—28no—
475#124—28no—
476#124—48no—
477#124—48no—
478#123—232no—
479#123—232no—
480#123—232no—
481C22⋊Q8—216no—
482C22⋊Q8—216no—
483C22⋊Q8—232no—
484C22⋊Q8—232no—
485C22⋊Q8—232no—
486C22⋊Q8—232no—
487C22⋊Q8—48no—
488#121—28no—
489#121—28no—
490#121—216no—
491#121—216no—
492#121—216no—
493#121—416no—
494#121—416no—
495#120—216no—
496#120—416no—
497C4×Q8—232no—
498C4×Q8—232no—
499C4×Q8—28no—
500C4×Q8—28no—
501C4×Q8—28no—
502C4×Q8—28no—
503C4×Q8—24no—
504C4×Q8—24no—
505C4×Q8—416no—
506C4×Q8—416no—
507C4×D4—28no—
508C4×D4—28no—
509C4×D4—216no—
510C4×D4—216no—
511C4×D4—28no—
512C4×D4—28no—
513C4×D4—28no—
514C4×D4—28no—
515C4×D4—24no—
516C4×D4—24no—
517C4×D4—28no—
518C4×D4—28no—
519C4×D4—416no—
520#117—24no—
521#117—24no—
522#117—24no—
523#117—28no—
524#117—232no—
525#117—232no—
526#117—28no—
527#117—416no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—216no—
531C2×C4⋊C4—28no—
532C2×C4⋊C4—216no—
533C2×C4⋊C4—216no—
534C2×C4⋊C4C2×D4116yes—
535C2×C4⋊C4C2×D4116yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C24116yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2411yescharacteristic
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C24116yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C22⋊C4—216no—
565C2×C22⋊C4—28no—
566C2×C22⋊C4—216no—
567C2×C22⋊C4C24116yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C24116yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C24116yes—
585C2×C22⋊C4C24116yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C42—216no—
594C2×C42—28no—
595C2×C42—28no—
596C2×C42C2×D418yes—
597C2×C42C24116yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2414yes—
601C2×C42C2412yes—
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2414yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C24116yes—
608C2×C42C2414yes—
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613#95C2414yes—
614#95C2414yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C24116yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2414yes—
625#95C2414yes—
626#95C2418yes—
627#95C24116yes—
628#95C24116yes—
629#95C2418yes—
630C24—24no—
631C24—24no—
632C24—24no—
633C24—44no—
634C24—44no—
635C24C2514yes—
636C24C2514yes—
637C24C2512yes—
638C24C2511yescharacteristic
639#41—232no—
640#41—4128no—
641#41—464no—
642#41—464no—
643#41—432no—
644C2×Q8—264no—
645C2×Q8—22no—
646C2×Q8—24no—
647C2×Q8—24no—
648C2×Q8—216no—
649C2×Q8—24no—
650C2×Q8—28no—
651C2×Q8—28no—
652C2×Q8—216no—
653C2×Q8—24no—
654C2×Q8—28no—
655C2×Q8—28no—
656C2×Q8—22no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×Q8—24no—
660C2×Q8—48no—
661C2×Q8—44no—
662C2×Q8—464no—
663C2×Q8—416no—
664C2×Q8—464no—
665C2×Q8C22×D4116yes—
666C2×Q8C22×D4116yes—
667C2×Q8C2×#4114yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—28no—
671C2×D4—216no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—216no—
675C2×D4—22no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—216no—
681C2×D4—24no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—22no—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—28no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—416no—
695C2×D4—416no—
696C2×D4—416no—
697C2×D4—416no—
698C2×D4C2×#4118yes—
699C2×D4C2×#4114yes—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—216no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—216no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—216no—
715C22×C4—28no—
716C22×C4—216no—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—216no—
721C22×C4—48no—
722C22×C4—44no—
723C22×C4—42no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—432no—
730C22×C4C22×D4116yes—
731C22×C4C22×D414yes—
732C22×C4C22×D414yes—
733C22×C4C22×D414yes—
734C22×C4C2×#4118yes—
735C22×C4C2×#4114yes—
736C22×C4H(5,𝔽2)14yes—
737C22×C4C2514yes—
738C22×C4C2518yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2514yes—
743C22×C4C2512yes—
744C22×C4C2514yes—
745C22×C4C2512yes—
746C22×C4C2511yescharacteristic
747C22×C4C2511yescharacteristic
748C22×C4C2518yes—
749C22×C4C2511yescharacteristic
750C22×C4C2512yes—
751C22×C4C2511yescharacteristic
752C22×C4C2511yescharacteristic
753C22×C4C2511yescharacteristic
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—24no—
758C4⋊C4—24no—
759C4⋊C4—24no—
760C4⋊C4—232no—
761C4⋊C4—28no—
762C4⋊C4—28no—
763C4⋊C4—216no—
764C4⋊C4—216no—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—44no—
774C4⋊C4—48no—
775C4⋊C4—416no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4C22×D4116yes—
779C4⋊C4C22×D4116yes—
780C4⋊C4C22×D4116yes—
781C4⋊C4C22×D4116yes—
782C22⋊C4—24no—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—28no—
786C22⋊C4—232no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—232no—
790C22⋊C4—24no—
791C22⋊C4—24no—
792C22⋊C4—216no—
793C22⋊C4—216no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—216no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—416no—
804C22⋊C4—416no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C42—232no—
809C42—24no—
810C42—24no—
811C42—24no—
812C42—28no—
813C42—28no—
814C42—24no—
815C42—24no—
816C42—28no—
817C42—28no—
818C42—44no—
819C42—416no—
820C42C22×D414yes—
821C42C22×D414yes—
822C42C22×D414yes—
823C42C22×D414yes—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—28no—
837C23—28no—
838C23—28no—
839C23—28no—
840C23—48no—
841C23—48no—
842C23—48no—
843C23—88no—
844C23—88no—
845C23C23×D412yes—
846C23C22×#4114yes—
847C23C22×#4112yes—
848C23C2×H(5,𝔽2)12yes—
849C23C2611yescharacteristic
850Q8—232no—
851Q8—232no—
852Q8—28no—
853Q8—432no—
854Q8—48no—
855Q8—48no—
856Q8—48no—
857D4—216no—
858D4—28no—
859D4—432no—
860D4—48no—
861D4—416no—
862D4—48no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—816no—
867D4—1616no—
868C2×C4—22no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—232no—
876C2×C4—216no—
877C2×C4—28no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—28no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—28no—
902C2×C4—44no—
903C2×C4—432no—
904C2×C4—432no—
905C2×C4—48no—
906C2×C4—416no—
907C2×C4—48no—
908C2×C4—48no—
909C2×C4—48no—
910C2×C4—416no—
911C2×C4—48no—
912C2×C4—416no—
913C2×C4#546116yes—
914C2×C4C23×D412yes—
915C2×C4C23×D4116yes—
916C2×C4C23×D412yes—
917C2×C4C23×D412yes—
918C2×C4C23×D412yes—
919C2×C4C23×D412yes—
920C2×C4C23×D412yes—
921C2×C4C22×#4114yes—
922C2×C4C22×#4112yes—
923C2×C4C22×#4112yes—
924C2×C4C2×H(5,𝔽2)12yes—
925C2×C4C2×H(5,𝔽2)12yes—
926C2×C4#58514yes—
927C22—24no—
928C22—22no—
929C22—22no—
930C22—24no—
931C22—28no—
932C22—24no—
933C22—42no—
934C22—42no—
935C22—44no—
936C22—48no—
937C22—48no—
938C22—44no—
939C22—44no—
940C22—44no—
941C22—44no—
942C22—48no—
943C22—48no—
944C22—44no—
945C22—44no—
946C22—816no—
947C22C2×#54614yes—
948C22C24×D411yescharacteristic
949C22C23×#4111yescharacteristic
950C22C22×H(5,𝔽2)11yescharacteristic
951C22C2×#58512yes—
952C222−1+612yes—
953C4—22no—
954C4—22no—
955C4—22no—
956C4—24no—
957C4—216no—
958C4—44no—
959C4—42no—
960C4—44no—
961C4—44no—
962C4—44no—
963C4—42no—
964C4—44no—
965C4—48no—
966C4—44no—
967C4C2×#54614yes—
968C4C2×#54614yes—
969C4#348714yes—
970C2—24no—
971C2—44no—
972C2—84no—
973C2—84no—
974C2C22×#54611yescharacteristic
975C2C2×#348711yescharacteristic
976C2#6284811yescharacteristic
977C2#6293112yes—
978C2#6299512yes—
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×#3499C2semidirect
2. C22×#556C2semidirect
3. #59421C2semidirect
4. #59410C2semidirect
5. #59134C2semidirect
6. #59049C2semidirect
7. #45269C2semidirect
8. #45268C2semidirect
9. #45240C2semidirect
10. #38905C2semidirect
11. #38031C2semidirect
12. #36426C2semidirect
13. #35677C2semidirect
14. #35676C2semidirect
15. #35182C2semidirect
16. #35165C2semidirect
17. #34955C2semidirect
18. #34952C2semidirect
19. #34257C2semidirect
20. #34209C2semidirect
21. C4×#535C2semidirect
29. C2×D4×Q8C22semidirect
30. C2×D4×Q8C22semidirect
33. C2×#547C22semidirect
34. C2×#547C22semidirect
36. C2×#536C22semidirect
40. C2×#532C22semidirect
42. C22×C4⋊Q8C22semidirect
54. #2716C22semidirect
55. #2714C22semidirect
56. #2705C22semidirect
57. #2702C22semidirect
58. #2696C22semidirect
59. #2692C22semidirect
62. #2592C22semidirect
64. #2582C22semidirect
65. #2581C22semidirect
66. #2580C22semidirect
68. #2568C22semidirect
69. #2560C22semidirect
70. #2554C22semidirect
72. #2548C22semidirect
77. #2540C22semidirect
78. #2538C22semidirect
82. #2492C22semidirect
84. #2481C22semidirect
85. #2477C22semidirect
86. #2471C22semidirect
87. #2467C22semidirect
88. #2448C22semidirect
89. #2446C22semidirect
90. #2439C22semidirect
96. #2427C22semidirect
99. #2423C22semidirect
100. #2421C22semidirect
101. #2417C22semidirect
102. #2414C22semidirect
108. #2398C22semidirect
109. #2396C22semidirect
110. #2365C22semidirect
111. #2365C22semidirect
112. #2363C22semidirect
113. #2352C22semidirect
116. #2341C22semidirect
117. #2341C22semidirect
118. Q8×C22⋊C4C22semidirect
119. Q8×C22⋊C4C22semidirect
121. #2327C22semidirect
131. C4×C4⋊Q8C22semidirect
134. C4×#124C22semidirect
135. C4×C22⋊Q8C22semidirect
176. C2×C4⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C22×#5562
#594212
#594102
#591342
#590492
#452692
#452682
#452402
#389052
#380312
#364262
#356772
#356762
#351822
#351652
#349552
#349522
#342572
#342092
C4×#5352