Finite Group Databasebeta

← #7697191

Subgroups — #7697191

Order 512.

5977 conjugacy classes of subgroups.

The subgroup lattice has 991 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59952C212yesmaximal, complemented
2#59885C212yesmaximal, complemented
3#59822C211yesmaximal, characteristic, complemented
4#59160C214yesmaximal, complemented
5#52270C211yesmaximal, characteristic, complemented
6C2×#2733C212yesmaximal, complemented
7#45408C212yesmaximal, complemented
8#44909C214yesmaximal, complemented
9#43963C218yesmaximal, complemented
10#43198C214yesmaximal, complemented
11#39503C214yesmaximal, complemented
12#39500C212yesmaximal, complemented
13#38286C214yesmaximal, complemented
14#38280C218yesmaximal, complemented
15#36276C211yesmaximal, characteristic, complemented
16D4×#124C212yesmaximal, complemented
17#35903C212yesmaximal, complemented
18#35691C214yesmaximal, complemented
19#34310C212yesmaximal, complemented
20#34261C214yesmaximal, complemented
21C2×#555C2212yescomplemented
22C2×#554C2211yescharacteristic
23C2×D4×Q8C2211yescharacteristic
24C2×D42C2212yes—
25C2×D42C2212yes—
26C2×D42C2212yes—
27C22×#124C2214yescomplemented
28C2×#518C2214yes—
29#2862C2211yescharacteristic, complemented
30#2858C2212yescomplemented
31#2857C2212yescomplemented
32#2850C2214yescomplemented
33#2809C2211yescharacteristic, complemented
34#2808C2212yescomplemented
35#2808C2214yescomplemented
36#2808C2214yescomplemented
37#2803C2214yescomplemented
38#2803C2218yescomplemented
39#2803C2218yescomplemented
40#2795C2212yescomplemented
41#2785C2214yescomplemented
42#2783C2214yescomplemented
43#2781C2218yescomplemented
44#2756C2218yescomplemented
45#2756C2218yescomplemented
46#2733C2211yescharacteristic
47#2733C2214yescomplemented
48#2733C2214yescomplemented
49#2733C2214yescomplemented
50#2733C2212yescomplemented
51#2733C2214yescomplemented
52#2733C2218yescomplemented
53#2733C2218yescomplemented
54#2733C2212yescomplemented
55#2731C2212yescomplemented
56#2699C2214yescomplemented
57#2699C2218yescomplemented
58#2686C2218yescomplemented
59#2641C2212yescomplemented
60#2639C2214yescomplemented
61#2619C2214yescomplemented
62#2617C2218yescomplemented
63#2610C2218yescomplemented
64#2610C2218yescomplemented
65#2593C2214yescomplemented
66#2591C2214yescomplemented
67#2572C2214yescomplemented
68#2567C2211yescharacteristic, complemented
69#2562C2212yescomplemented
70#2555C2218yescomplemented
71#2555C2214yescomplemented
72#2550C2214yescomplemented
73#2549C2218yescomplemented
74#2548C2212yescomplemented
75#2548C2212yescomplemented
76#2547C2212yescomplemented
77#2546C2211yescharacteristic, complemented
78#2543C2218yescomplemented
79#2541C2214yescomplemented
80#2537C2212yescomplemented
81#2535C2214yescomplemented
82#2532C2218yescomplemented
83#2513C2218yescomplemented
84#2502C2212yescomplemented
85#2500C2218yescomplemented
86#2491C2214yescomplemented
87#2491C2214yescomplemented
88#2491C2218yescomplemented
89#2491C2214yescomplemented
90#2490C2214yescomplemented
91#2476C2218yescomplemented
92#2474C2218yescomplemented
93#2472C2218yescomplemented
94#2472C2218yescomplemented
95#2472C2218yescomplemented
96#2472C2218yescomplemented
97#2459C2218yescomplemented
98#2459C2218yescomplemented
99#2459C2218yescomplemented
100#2436C2214yescomplemented
101#2435C2214yescomplemented
102#2435C2214yescomplemented
103#2434C2212yescomplemented
104#2428C2214yescomplemented
105#2428C2214yescomplemented
106#2424C2218yescomplemented
107#2424C2218yescomplemented
108#2414C2214yescomplemented
109#2414C2218yescomplemented
110#2414C2214yescomplemented
111#2414C2218yescomplemented
112#2410C2218yescomplemented
113#2410C2218yescomplemented
114#2408C2218yescomplemented
115#2398C2212yescomplemented
116#2392C2214yescomplemented
117C2×#394C2214yescomplemented
118C2×#392C2218yescomplemented
119#2372C2214yescomplemented
120#2366C2212yescomplemented
121#2363C2214yescomplemented
122#2361C2214yescomplemented
123#2358C2218yescomplemented
124#2357C2214yescomplemented
125#2354C2212yescomplemented
126#2354C2214yescomplemented
127#2353C2218yescomplemented
128#2352C2218yescomplemented
129#2349C2214yes—
130D4×C4⋊C4C2212yes—
131#2347C2214yescomplemented
132#2346C2214yescomplemented
133#2342C2218yescomplemented
134#2342C2218yescomplemented
135D4×C22⋊C4C2214yes—
136D4×C22⋊C4C2214yes—
137D4×C22⋊C4C2214yes—
138D4×C22⋊C4C2214yescomplemented
139#2324C2214yescomplemented
140#2321C2218yescomplemented
141#2319C2214yescomplemented
142#2318C2218yescomplemented
143#2314C2214yescomplemented
144#2312C2218yescomplemented
145C4×C4⋊Q8C2211yescharacteristic, complemented
146C4×#127C2212yescomplemented
147C4×#124C2212yescomplemented
148C4×#121C2214yescomplemented
149#2298C2214yescomplemented
150C2×#391C2212yescomplemented
151#2293C2212yescomplemented
152#2293C2214yescomplemented
153C2×#390C2214yescomplemented
154#2290C2218yescomplemented
155C2×#388C2218yescomplemented
156#2275C2212yes—
157C42×D4C2211yescharacteristic
158C42×D4C2212yes—
159C23×Q8C2312yes—
160C23×D4C2314yes—
161C23×D4C2314yes—
162C23×D4C2314yes—
163C23×D4C2314yes—
164#555—48no—
165#554—44no—
166D4×Q8—44no—
167D42—216no—
168D42—48no—
169D42—48no—
170C2×C4⋊Q8C2311yescharacteristic
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2311yescharacteristic
174C2×C4⋊Q8C2312yes—
175C2×#127C2312yes—
176C2×#127C2312yes—
177C2×#127C2312yes—
178C2×#125C2312yes—
179C2×#124—416no—
180C2×#124C2314yes—
181C2×#124C2312yes—
182C2×#124C2314yes—
183C2×#124C2314yes—
184C2×#124C2318yes—
185C2×#124C2318yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188C2×#124C2318yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2314yes—
193C2×#121C2314yes—
194C2×#121C2314yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2314yes—
199C2×#121C2318yes—
200C2×#121C2318yes—
201C2×#121C2318yes—
202C2×#121C2318yes—
203C2×#120C2318yes—
204C2×#120C2318yes—
205C2×#120C2318yes—
206#518—232no—
207C2×C4×Q8C2311yescharacteristic
208C2×C4×Q8C2311yescharacteristic
209C2×C4×D4C2314yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2314yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2312yes—
224C2×#117C2314yes—
225C2×#117C2314yes—
226C2×#117C2318yes—
227C2×#117C2318yes—
228C22×C4⋊C4C2312yes—
229C22×C4⋊C4C2314yes—
230C22×C22⋊C4C2318yes—
231C22×C22⋊C4C2318yes—
232C22×C22⋊C4C2318yes—
233C22×C22⋊C4C2318yes—
234C22×C22⋊C4C2318yes—
235C22×C42C2314yes—
236C22×C42C2312yes—
237#400C2314yes—
238#400C2312yes—
239#400C2312yes—
240#398C2314yes—
241#398C2314yes—
242#398C2318yes—
243#397C2314yes—
244#397C2318yes—
245#397C2318yes—
246#397C2314yes—
247#397C2318yes—
248#396C2314yes—
249#396C2314yes—
250#395C2314yes—
251#395C2318yes—
252#394C2314yes—
253#394C2314yes—
254#394C2314yes—
255#394C2318yes—
256#394C2314yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2314yes—
263#394C2314yes—
264#394C2318yes—
265#394C2312yes—
266#394C2318yes—
267#394C2318yes—
268#394C2314yes—
269#394C2314yes—
270#394C2312yes—
271#394C2314yes—
272#394C2318yes—
273#394C2318yes—
274#394C2314yes—
275#393C2318yes—
276#393C2318yes—
277#393C2318yes—
278#393C2314yes—
279#392C2318yes—
280#392C2318yes—
281#392C2318yes—
282#392C2318yes—
283#392C2318yes—
284#392C2314yes—
285#392C2318yes—
286#392C2318yes—
287#392C2318yes—
288#392C2318yes—
289#391C2311yescharacteristic
290#391C2311yescharacteristic
291#391C2312yes—
292#391C2312yes—
293#391C2314yes—
294#391C2312yes—
295#391C2312yes—
296#391C2314yes—
297#391C2312yes—
298#391C2318yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2314yes—
303#390C2314yes—
304#390C2318yes—
305#390C2314yes—
306#390C2314yes—
307#390C2314yes—
308#390C2314yes—
309#390C2312yes—
310#390C2314yes—
311#390C2314yes—
312#390C2318yes—
313#390C2318yes—
314#390C2318yes—
315#390C2318yes—
316#390C2318yes—
317#390C2314yes—
318#390C2312yes—
319#390C2312yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2318yes—
325#389C2312yes—
326#389C2312yes—
327#388C2318yes—
328#388C2314yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2314yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2314yes—
348#388C2314yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2314yes—
354#388C2314yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2314yes—
359#387C2318yes—
360#387C2318yes—
361#387C2314yes—
362#387C2314yes—
363#387C2314yes—
364#387C2314yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#384C2312yes—
383#384C2311yescharacteristic
384#384C2312yes—
385#383C2318yes—
386#382C2314yes—
387#382C2318yes—
388#382C2312yes—
389#381C2318yes—
390#381C2318yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2318yes—
395#380C2314yes—
396#380C2318yes—
397#380C2318yes—
398#379C2318yes—
399#379C2318yes—
400#379C2318yes—
401C4×C4⋊C4C2312yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2311yescharacteristic
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C22⋊C4C2318yes—
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2314yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2312yes—
423#376C2312yes—
424#376C2318yes—
425C2×#95C2314yes—
426C2×#95C2318yes—
427C43C2311yescharacteristic
428C43C2312yes—
429C25C2418yes—
430C22×Q8—28no—
431C22×Q8—44no—
432C22×Q8—82no—
433C22×Q8C2411yescharacteristic
434C22×Q8C2414yes—
435C22×Q8C2412yes—
436C22×Q8C2412yes—
437C22×Q8C2411yescharacteristic
438C22×D4—216no—
439C22×D4—216no—
440C22×D4—216no—
441C22×D4—216no—
442C22×D4—48no—
443C22×D4—48no—
444C22×D4—48no—
445C22×D4—84no—
446C22×D4—84no—
447C22×D4—84no—
448C22×D4—88no—
449C22×D4C2418yes—
450C22×D4C2414yes—
451C22×D4C2414yes—
452C22×D4C2414yes—
453C22×D4C2412yes—
454C22×D4C2412yes—
455C22×D4C2418yes—
456C22×D4C2414yes—
457C22×D4C2412yes—
458C22×D4C2414yes—
459C22×D4C2414yes—
460C22×D4C2418yes—
461C22×D4C2418yes—
462C22×D4C2414yes—
463C22×D4C2411yescharacteristic
464C23×C4C2414yes—
465C23×C4C2412yes—
466C23×C4C2414yes—
467C23×C4C2418yes—
468C23×C4C2414yes—
469C23×C4C2418yes—
470C23×C4C2418yes—
471C23×C4C2414yes—
472C4⋊Q8—24no—
473C4⋊Q8—44no—
474C4⋊Q8—42no—
475C4⋊Q8—42no—
476C4⋊Q8—82no—
477#127—28no—
478#127—44no—
479#127—44no—
480#125—44no—
481#124—28no—
482#124—216no—
483#124—48no—
484#124—48no—
485#124—416no—
486#124—416no—
487#124—48no—
488#124—88no—
489#124—84no—
490C22⋊Q8—44no—
491C22⋊Q8—48no—
492C22⋊Q8—44no—
493C22⋊Q8—48no—
494#121—216no—
495#121—216no—
496#121—416no—
497#121—48no—
498#121—48no—
499#121—48no—
500#121—48no—
501#121—88no—
502#121—88no—
503#121—88no—
504#120—232no—
505#120—416no—
506#120—416no—
507C4×Q8—42no—
508C4×Q8—42no—
509C4×D4—216no—
510C4×D4—28no—
511C4×D4—28no—
512C4×D4—24no—
513C4×D4—232no—
514C4×D4—216no—
515C4×D4—232no—
516C4×D4—216no—
517C4×D4—28no—
518C4×D4—48no—
519C4×D4—44no—
520C4×D4—44no—
521C4×D4—84no—
522C4×D4—84no—
523C4×D4#41116yes—
524#117—216no—
525#117—216no—
526#117—416no—
527#117—88no—
528C2×C4⋊C4—44no—
529C2×C4⋊C4—84no—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2411yescharacteristic
538C2×C4⋊C4C2411yescharacteristic
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2411yescharacteristic
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2412yes—
558C2×C22⋊C4—232no—
559C2×C22⋊C4—232no—
560C2×C22⋊C4—416no—
561C2×C22⋊C4—416no—
562C2×C22⋊C4—88no—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C42—48no—
601C2×C42—82no—
602C2×C42C2414yes—
603C2×C42C2414yes—
604C2×C42C2418yes—
605C2×C42C2411yescharacteristic
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2411yescharacteristic
609C2×C42C2412yes—
610C2×C42C2414yes—
611C2×C42C2414yes—
612C2×C42C2418yes—
613C2×C42C2412yes—
614C2×C42C2414yes—
615C2×C42C2412yes—
616C2×C42C2418yes—
617C2×C42C2412yes—
618C2×C42C2411yescharacteristic
619C2×C42C2412yes—
620#95C2412yes—
621#95C2414yes—
622#95C2418yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2414yes—
629#95C2418yes—
630#95C2412yes—
631#95C2418yes—
632#95C2414yes—
633#95C2414yes—
634#95C2418yes—
635#95C2414yes—
636#95C2414yes—
637#95C2412yes—
638#95C2414yes—
639#95C2418yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2418yes—
646C24—216no—
647C24—216no—
648C24—216no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24C2514yes—
654C24C2518yes—
655C24C2512yes—
656C2×Q8—22no—
657C2×Q8—24no—
658C2×Q8—28no—
659C2×Q8—41no—
660C2×Q8—41no—
661C2×Q8—41no—
662C2×Q8—42no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—41no—
666C2×Q8—42no—
667C2×Q8—42no—
668C2×Q8—44no—
669C2×Q8—816no—
670C2×Q8H(5,𝔽2)14yes—
671C2×D4—216no—
672C2×D4—216no—
673C2×D4—216no—
674C2×D4—28no—
675C2×D4—24no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—216no—
680C2×D4—28no—
681C2×D4—24no—
682C2×D4—28no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—44no—
704C2×D4—48no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—44no—
710C2×D4—464no—
711C2×D4—832no—
712C2×D4—832no—
713C2×D4—832no—
714C2×D4C2×#4118yes—
715C2×D4H(5,𝔽2)14yes—
716C22×C4—24no—
717C22×C4—28no—
718C22×C4—216no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—24no—
724C22×C4—28no—
725C22×C4—216no—
726C22×C4—216no—
727C22×C4—44no—
728C22×C4—42no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—48no—
732C22×C4—48no—
733C22×C4—48no—
734C22×C4—48no—
735C22×C4—48no—
736C22×C4—48no—
737C22×C4—48no—
738C22×C4C2×#41116yes—
739C22×C4C2514yes—
740C22×C4C2512yes—
741C22×C4C2514yes—
742C22×C4C2514yes—
743C22×C4C2514yes—
744C22×C4C2514yes—
745C22×C4C2518yes—
746C22×C4C2511yescharacteristic
747C22×C4C2512yes—
748C22×C4C2512yes—
749C22×C4C2512yes—
750C22×C4C2512yes—
751C22×C4C2514yes—
752C22×C4C2512yes—
753C22×C4C2512yes—
754C22×C4C2511yescharacteristic
755C22×C4C2511yescharacteristic
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—24no—
760C4⋊C4—28no—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—22no—
764C4⋊C4—41no—
765C4⋊C4—44no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4—48no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—48no—
772C4⋊C4—42no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—41no—
776C4⋊C4—42no—
777C4⋊C4—42no—
778C4⋊C4—44no—
779C4⋊C4—48no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—42no—
783C4⋊C4C2×#4118yes—
784C22⋊C4—216no—
785C22⋊C4—28no—
786C22⋊C4—28no—
787C22⋊C4—24no—
788C22⋊C4—216no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—216no—
792C22⋊C4—216no—
793C22⋊C4—28no—
794C22⋊C4—216no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—216no—
798C22⋊C4—216no—
799C22⋊C4—48no—
800C22⋊C4—48no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—44no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C22⋊C4—48no—
809C22⋊C4—44no—
810C22⋊C4—44no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—48no—
815C22⋊C4—44no—
816C22⋊C4—44no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—44no—
820C22⋊C4C2×#41116yes—
821C42—216no—
822C42—28no—
823C42—24no—
824C42—28no—
825C42—24no—
826C42—24no—
827C42—22no—
828C42—22no—
829C42—48no—
830C42—41no—
831C42—44no—
832C42—42no—
833C42—44no—
834C42—44no—
835C42—48no—
836C42—42no—
837C42—42no—
838C42C2×#4118yes—
839C23—22no—
840C23—24no—
841C23—22no—
842C23—24no—
843C23—28no—
844C23—24no—
845C23—28no—
846C23—24no—
847C23—28no—
848C23—24no—
849C23—28no—
850C23—24no—
851C23—28no—
852C23—28no—
853C23—28no—
854C23—24no—
855C23—24no—
856C23—432no—
857C23—816no—
858C23—816no—
859C23—816no—
860C23—816no—
861C23—816no—
862C23—816no—
863C23C22×#4118yes—
864C23C2×H(5,𝔽2)14yes—
865C23C2611yescharacteristic
866Q8—44no—
867Q8—82no—
868Q8—88no—
869Q8—84no—
870Q8—162no—
871D4—416no—
872D4—48no—
873D4—48no—
874D4—48no—
875D4—432no—
876D4—416no—
877D4—88no—
878D4—816no—
879D4—88no—
880D4—88no—
881D4—816no—
882D4—816no—
883D4—164no—
884D4—164no—
885D4#555116yescomplemented
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—24no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—28no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—28no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—416no—
926C2×C4—416no—
927C2×C4—48no—
928C2×C4—416no—
929C2×C4—816no—
930C2×C4—816no—
931C2×C4—816no—
932C2×C4—88no—
933C2×C4C22×#4118yes—
934C2×C4C22×#4114yes—
935C2×C4C22×#4114yes—
936C2×C4C22×#4114yes—
937C2×C4C2×H(5,𝔽2)14yes—
938C2×C4C2×H(5,𝔽2)12yes—
939C2×C4C2×H(5,𝔽2)12yes—
940C22—28no—
941C22—24no—
942C22—28no—
943C22—24no—
944C22—48no—
945C22—48no—
946C22—44no—
947C22—44no—
948C22—44no—
949C22—48no—
950C22—48no—
951C22—44no—
952C22—48no—
953C22—44no—
954C22—44no—
955C22—48no—
956C22—44no—
957C22—48no—
958C22—1632no—
959C22C2×#55518yes—
960C22C23×#4112yes—
961C22C22×H(5,𝔽2)11yescharacteristic
962C22C22×H(5,𝔽2)11yescharacteristic
963C22H(7,𝔽2)12yes—
964C22H(7,𝔽2)11yescharacteristic
965C4—24no—
966C4—24no—
967C4—28no—
968C4—24no—
969C4—22no—
970C4—44no—
971C4—48no—
972C4—42no—
973C4—44no—
974C4—42no—
975C4—41no—
976C4—44no—
977C4—44no—
978C4—42no—
979C4—42no—
980C4—44no—
981C4C2×#55514yes—
982C2—28no—
983C2—88no—
984C2—84no—
985C2C22×#55511yescharacteristic
986C2#6284612yes—
987C2#6289211yescharacteristic
988C2#6298612yes—
989C2#6304511yescharacteristic
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. #59952C2semidirect
2. #59885C2semidirect
3. #59822C2semidirect
4. #59160C2semidirect
5. #52270C2semidirect
6. C2×#2733C2semidirect
7. #45408C2semidirect
8. #44909C2semidirect
9. #43963C2semidirect
10. #43198C2semidirect
11. #39503C2semidirect
12. #39500C2semidirect
13. #38286C2semidirect
14. #38280C2semidirect
15. #36276C2semidirect
16. D4×#124C2semidirect
17. #35903C2semidirect
18. #35691C2semidirect
19. #34310C2semidirect
20. #34261C2semidirect
21. C2×#555C22semidirect
27. C22×#124C22semidirect
29. #2862C22semidirect
30. #2858C22semidirect
31. #2857C22semidirect
32. #2850C22semidirect
33. #2809C22semidirect
34. #2808C22semidirect
35. #2808C22semidirect
36. #2808C22semidirect
37. #2803C22semidirect
38. #2803C22semidirect
39. #2803C22semidirect
40. #2795C22semidirect
41. #2785C22semidirect
42. #2783C22semidirect
43. #2781C22semidirect
44. #2756C22semidirect
45. #2756C22semidirect
47. #2733C22semidirect
48. #2733C22semidirect
49. #2733C22semidirect
50. #2733C22semidirect
51. #2733C22semidirect
52. #2733C22semidirect
53. #2733C22semidirect
54. #2733C22semidirect
55. #2731C22semidirect
56. #2699C22semidirect
57. #2699C22semidirect
58. #2686C22semidirect
59. #2641C22semidirect
60. #2639C22semidirect
61. #2619C22semidirect
62. #2617C22semidirect
63. #2610C22semidirect
64. #2610C22semidirect
65. #2593C22semidirect
66. #2591C22semidirect
67. #2572C22semidirect
68. #2567C22semidirect
69. #2562C22semidirect
70. #2555C22semidirect
71. #2555C22semidirect
72. #2550C22semidirect
73. #2549C22semidirect
74. #2548C22semidirect
75. #2548C22semidirect
76. #2547C22semidirect
77. #2546C22semidirect
78. #2543C22semidirect
79. #2541C22semidirect
80. #2537C22semidirect
81. #2535C22semidirect
82. #2532C22semidirect
83. #2513C22semidirect
84. #2502C22semidirect
85. #2500C22semidirect
86. #2491C22semidirect
87. #2491C22semidirect
88. #2491C22semidirect
89. #2491C22semidirect
90. #2490C22semidirect
91. #2476C22semidirect
92. #2474C22semidirect
93. #2472C22semidirect
94. #2472C22semidirect
95. #2472C22semidirect
96. #2472C22semidirect
97. #2459C22semidirect
98. #2459C22semidirect
99. #2459C22semidirect
100. #2436C22semidirect
101. #2435C22semidirect
102. #2435C22semidirect
103. #2434C22semidirect
104. #2428C22semidirect
105. #2428C22semidirect
106. #2424C22semidirect
107. #2424C22semidirect
108. #2414C22semidirect
109. #2414C22semidirect
110. #2414C22semidirect
111. #2414C22semidirect
112. #2410C22semidirect
113. #2410C22semidirect
114. #2408C22semidirect
115. #2398C22semidirect
116. #2392C22semidirect
117. C2×#394C22semidirect
118. C2×#392C22semidirect
119. #2372C22semidirect
120. #2366C22semidirect
121. #2363C22semidirect
122. #2361C22semidirect
123. #2358C22semidirect
124. #2357C22semidirect
125. #2354C22semidirect
126. #2354C22semidirect
127. #2353C22semidirect
128. #2352C22semidirect
131. #2347C22semidirect
132. #2346C22semidirect
133. #2342C22semidirect
134. #2342C22semidirect
138. D4×C22⋊C4C22semidirect
139. #2324C22semidirect
140. #2321C22semidirect
141. #2319C22semidirect
142. #2318C22semidirect
143. #2314C22semidirect
144. #2312C22semidirect
145. C4×C4⋊Q8C22semidirect
146. C4×#127C22semidirect
147. C4×#124C22semidirect
148. C4×#121C22semidirect
149. #2298C22semidirect
150. C2×#391C22semidirect
151. #2293C22semidirect
152. #2293C22semidirect
153. C2×#390C22semidirect
154. #2290C22semidirect
155. C2×#388C22semidirect
885. D4#555semidirect

Maximal subgroups

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

subgroupindex
#599522
#598852
#598222
#591602
#522702
C2×#27332
#454082
#449092
#439632
#431982
#395032
#395002
#382862
#382802
#362762
D4×#1242
#359032
#356912
#343102
#342612