Finite Group Databasebeta

← #7681133

Subgroups — #7681133

Order 512.

8190 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3497C211yesmaximal, characteristic, complemented
3#59110C218yesmaximal, complemented
4#59039C214yesmaximal, complemented
5#59036C214yesmaximal, complemented
6#45303C218yesmaximal, complemented
7#43888C218yesmaximal, complemented
8#38958C212yesmaximal, complemented
9#38952C212yesmaximal, complemented
10#38091C214yesmaximal, complemented
11#38079C214yesmaximal, complemented
12#36412C212yesmaximal, complemented
13#36276C212yesmaximal, complemented
14#35660C212yesmaximal, complemented
15#35530C212yesmaximal, complemented
16#35289C211yesmaximal, characteristic, complemented
17#35273C212yesmaximal, complemented
18C2×#2567C211yesmaximal, characteristic, complemented
19#34937C211yesmaximal, characteristic, complemented
20#34259C212yesmaximal, complemented
21#34141C211yesmaximal, characteristic, complemented
22C4×#536C211yesmaximal, characteristic, complemented
23C22×2−1+4C2212yes—
24#3511—216no—
25#3497—216no—
26C2×#556C2212yes—
27C2×#555C2212yes—
28C2×#554C2212yes—
29C2×#553C2214yes—
30C2×#550C2212yes—
31C2×#550C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×#548C2214yes—
35C2×#548C2214yes—
36C2×#548C2214yes—
37C2×#547C2212yes—
38C2×#542C2214yes—
39C2×#537C2214yes—
40C2×#537C2212yes—
41C2×#537C2212yes—
42C2×#536C2211yescharacteristic
43C2×#533C2212yes—
44C2×#532C2211yescharacteristic
45C2×#532C2214yes—
46C2×#532C2212yes—
47C2×#532C2212yes—
48C2×#532C2211yescharacteristic
49C22×C4⋊Q8C2211yescharacteristic
50C2×#520C2212yes—
51C2×C4×#41C2211yescharacteristic
52C2×C4×#41C2212yes—
53C22×C4×Q8C2211yescharacteristic
54#2862C2212yes—
55#2858C2212yes—
56#2857C2214yes—
57#2856C2214yes—
58#2715C22116yes—
59#2710C22116yes—
60#2700C22116yes—
61#2692C22116yes—
62#2686C22116yes—
63#2672C22116yes—
64#2640C2214yes—
65#2620C2214yes—
66#2620C2214yes—
67#2567C2212yes—
68#2567C2212yes—
69#2567C2214yes—
70#2567C2214yes—
71#2567C2214yes—
72#2563C2214yes—
73#2555C22116yes—
74#2550C2218yes—
75#2549C22116yes—
76#2548C2211yescharacteristic
77#2547C2211yescharacteristic
78#2547C2214yes—
79#2546C2211yescharacteristic
80#2545C2212yes—
81#2544C2212yes—
82#2543C2214yes—
83#2541C2211yescharacteristic
84#2538C2218yes—
85#2537C2218yes—
86#2504C2214yes—
87#2502C2214yes—
88#2501C2214yes—
89#2500C2214yes—
90#2499C2214yes—
91#2466C22116yes—
92#2465C22116yes—
93#2454C2218yes—
94#2445C2218yes—
95#2443C22116yes—
96#2439C2218yes—
97#2436C2214yes—
98#2436C2214yes—
99#2434C2214yes—
100#2432C2214yes—
101#2431C2214yes—
102#2430C22116yes—
103#2430C22116yes—
104#2428C2218yes—
105#2425C22116yes—
106#2423C2218yes—
107#2422C2218yes—
108#2420C2218yes—
109#2416C22116yes—
110#2416C2214yes—
111#2409C2218yes—
112#2407C2218yes—
113#2392C2214yes—
114C2×#395C2214yes—
115#2367C2214yes—
116#2366C2212yes—
117#2365C2212yes—
118#2364C2214yes—
119#2363C2218yes—
120#2361C2214yes—
121#2349C2218yes—
122Q8×C22⋊C4C2218yes—
123#2339C22116yes—
124#2339C2218yes—
125#2327C2212yes—
126#2326C2212yes—
127#2323C2214yes—
128#2322C2214yes—
129#2317C2211yescharacteristic
130#2311C2214yes—
131#2311C2211yescharacteristic
132#2311C2212yes—
133#2311C2212yes—
134#2310C2211yescharacteristic
135#2310C2214yes—
136C4×C4⋊Q8C2212yes—
137C4×#124C2212yes—
138C4×C22⋊Q8C2214yes—
139C4×#123C2214yes—
140C4×#121C2214yes—
141#2297C2214yes—
142#2297C2212yes—
143#2297C2212yes—
144C2×#391C2212yes—
145C2×#391C2214yes—
146#2293C2212yes—
147C2×#389C2214yes—
148#2290C2214yes—
149C2×#384C2212yes—
150C42×D4C2212yes—
151C4×#117C2211yescharacteristic
152C2×C4×C4⋊C4C2211yescharacteristic
153C2×2−1+4—216no—
154C2×2−1+4—216no—
155C2×2−1+4—48no—
156C22×#41C2312yes—
157C22×#41C2311yescharacteristic
158C22×#41C2314yes—
159C22×#41C2314yes—
160C22×#41C2318yes—
161C22×#41C2312yes—
162C22×#41C2314yes—
163C23×Q8C2314yes—
164C23×Q8C2314yes—
165C23×Q8C2311yescharacteristic
166C23×Q8C2312yes—
167#556—216no—
168#555—216no—
169#554—216no—
170#553—232no—
171#550—216no—
172#550—216no—
173D4×Q8—216no—
174D4×Q8—216no—
175#548—232no—
176#548—232no—
177#548—232no—
178#547—216no—
179#542—232no—
180#537—216no—
181#537—216no—
182#537—232no—
183#536—28no—
184#533—216no—
185#532—216no—
186#532—232no—
187#532—28no—
188#532—48no—
189#532D4116yescomplemented
190C2×C4⋊Q8—28no—
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×#127C2311yescharacteristic
201C2×#127C2314yes—
202C2×#127C2312yes—
203C2×#127C2311yescharacteristic
204C2×#126C2318yes—
205C2×#125C2314yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2314yes—
209C2×#124C2318yes—
210C2×#124C2318yes—
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2318yes—
214C2×#124C2312yes—
215C2×#123C2314yes—
216C2×#123C2318yes—
217C2×#123C23116yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2318yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2314yes—
231C2×#121C2312yes—
232C2×#121C2318yes—
233C2×#121C2318yes—
234C2×#121C2318yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237C2×#121C2314yes—
238C2×#121C2318yes—
239C2×#121C2318yes—
240C2×#121C23116yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243#520—216no—
244C4×#41—28no—
245C4×#41—48no—
246C2×C4×Q8—28no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2314yes—
260C2×C4×D4C2318yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2318yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2314yes—
277C2×#117C2311yescharacteristic
278C2×#117C2312yes—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2314yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2318yes—
288C22×C42C2312yes—
289C22×C42C2312yes—
290C22×C42C2312yes—
291C22×C42C2314yes—
292C22×C42C2311yescharacteristic
293#399C23116yes—
294#398C2314yes—
295#398C23116yes—
296#397C23116yes—
297#397C2314yes—
298#397C23116yes—
299#396C23116yes—
300#396C23116yes—
301#396C2318yes—
302#395C2318yes—
303#395C23116yes—
304#395C2318yes—
305#395C23116yes—
306#394C23116yes—
307#394C23116yes—
308#394C2318yes—
309#394C2314yes—
310#394C23116yes—
311#394C23116yes—
312#393C23116yes—
313#393C23116yes—
314#392C2314yes—
315#392C23116yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C23116yes—
324#391C2314yes—
325#391C2318yes—
326#391C2314yes—
327#391C23116yes—
328#391C2318yes—
329#391C2314yes—
330#391C2312yes—
331#390C2318yes—
332#390C2314yes—
333#390C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C23116yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#389C2318yes—
342#389C2318yes—
343#389C2318yes—
344#389C23116yes—
345#389C2314yes—
346#389C23116yes—
347#389C2314yes—
348#389C2314yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C23116yes—
353#388C2318yes—
354#388C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C23116yes—
359#386C2314yes—
360#386C2318yes—
361#386C23116yes—
362#386C2318yes—
363#386C2318yes—
364#386C23116yes—
365#386C2318yes—
366#386C23116yes—
367#386C2318yes—
368#386C23116yes—
369#386C2318yes—
370#385C2314yes—
371#385C2318yes—
372#385C23116yes—
373#385C23116yes—
374#385C2318yes—
375#385C23116yes—
376#384C2312yes—
377#384C2314yes—
378#384C2314yes—
379#384C2318yes—
380#382C2318yes—
381#382C2312yes—
382#381C2314yes—
383#381C23116yes—
384#380C2318yes—
385#380C2318yes—
386#380C2314yes—
387#380C23116yes—
388#380C23116yes—
389#380C2314yes—
390C4×C4⋊C4C2318yes—
391C4×C4⋊C4C2312yes—
392C4×C4⋊C4C2312yes—
393C4×C4⋊C4C2312yes—
394C4×C4⋊C4C2311yescharacteristic
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2311yescharacteristic
397C4×C4⋊C4C2312yes—
398C4×C4⋊C4C2314yes—
399C4×C22⋊C4C2312yes—
400C4×C22⋊C4C23116yes—
401C4×C22⋊C4C2318yes—
402C4×C22⋊C4C2312yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2318yes—
405C4×C22⋊C4C2314yes—
406C4×C22⋊C4C2314yes—
407#376C2312yes—
408C2×#95C23116yes—
409C2×#95C2318yes—
410C2×#95C2312yes—
411C43C2312yes—
4122−1+4—4128no—
413C2×#41—216no—
414C2×#41—216no—
415C2×#41—232no—
416C2×#41—216no—
417C2×#41—216no—
418C2×#41—24no—
419C2×#41—28no—
420C2×#41—216no—
421C2×#41—28no—
422C2×#41—24no—
423C2×#41—232no—
424C2×#41—28no—
425C2×#41—28no—
426C2×#41—24no—
427C2×#41—28no—
428C2×#41—416no—
429C2×#41—48no—
430C2×#41—48no—
431C2×#41—88no—
432C2×#41C2×D4116yes—
433C22×Q8—216no—
434C22×Q8—216no—
435C22×Q8—216no—
436C22×Q8—24no—
437C22×Q8—216no—
438C22×Q8—28no—
439C22×Q8—24no—
440C22×Q8—48no—
441C22×Q8—48no—
442C22×Q8—84no—
443C22×Q8#4118yescomplemented
444C22×Q8C2411yescharacteristic
445C22×Q8C2412yes—
446C22×Q8C2418yes—
447C22×Q8C2412yes—
448C22×Q8C2412yes—
449C22×Q8C2412yes—
450C22×Q8C2414yes—
451C22×Q8C2414yes—
452C22×D4C2412yes—
453C22×D4C2412yes—
454C22×D4C2411yescharacteristic
455C22×D4C2414yes—
456C22×D4C2412yes—
457C22×D4C2418yes—
458C22×D4C2412yes—
459C22×D4C2414yes—
460C22×D4C2412yes—
461C22×D4C2418yes—
462C22×D4C2412yes—
463C22×D4C2418yes—
464C22×D4C2418yes—
465C22×D4C2412yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C23×C4C2418yes—
471C23×C4C2418yes—
472C23×C4C2411yescharacteristic
473C23×C4C2414yes—
474C23×C4C2412yes—
475C23×C4C2412yes—
476C23×C4C2414yes—
477C23×C4C2418yes—
478C23×C4C2418yes—
479C23×C4C2412yes—
480C23×C4C2411yescharacteristic
481C23×C4C2411yescharacteristic
482C4⋊Q8—28no—
483C4⋊Q8—216no—
484C4⋊Q8—28no—
485C4⋊Q8—28no—
486C4⋊Q8—28no—
487C4⋊Q8—28no—
488C4⋊Q8—24no—
489C4⋊Q8—44no—
490C4⋊Q8C2×D418yes—
491#127—216no—
492#127—24no—
493#127—44no—
494#127C2×D418yes—
495#126—232no—
496#125—216no—
497#124—28no—
498#124—216no—
499#124—232no—
500#124—232no—
501#124—28no—
502#124—44no—
503#124—44no—
504#124—88no—
505#124C2×D4116yes—
506#123—216no—
507#123—232no—
508#123—816no—
509C22⋊Q8—216no—
510C22⋊Q8—216no—
511C22⋊Q8—216no—
512C22⋊Q8—216no—
513C22⋊Q8—216no—
514C22⋊Q8—216no—
515C22⋊Q8—232no—
516C22⋊Q8—232no—
517C22⋊Q8—232no—
518#121—232no—
519#121—216no—
520#121—216no—
521#121—216no—
522#121—232no—
523#121—232no—
524#121—28no—
525#121—28no—
526#121—216no—
527#121—216no—
528#121—216no—
529#121—232no—
530#121—416no—
531#121—816no—
532#121C2×D4116yes—
533#121C2×D4116yes—
534C4×Q8—216no—
535C4×Q8—216no—
536C4×Q8—28no—
537C4×Q8—28no—
538C4×Q8—28no—
539C4×Q8—28no—
540C4×Q8—24no—
541C4×Q8—24no—
542C4×Q8—48no—
543C4×D4—216no—
544C4×D4—232no—
545C4×D4—216no—
546C4×D4—216no—
547C4×D4—28no—
548C4×D4—28no—
549C4×D4—216no—
550C4×D4—216no—
551C4×D4—232no—
552C4×D4—24no—
553C4×D4—24no—
554C4×D4—28no—
555C4×D4—28no—
556C4×D4—48no—
557C4×D4—416no—
558C4×D4—416no—
559C4×D4C2×D4116yes—
560C4×D4C2×D4116yes—
561#117—24no—
562#117—216no—
563#117—24no—
564#117—24no—
565#117—216no—
566#117—28no—
567#117—48no—
568C2×C4⋊C4—28no—
569C2×C4⋊C4—24no—
570C2×C4⋊C4—28no—
571C2×C4⋊C4—216no—
572C2×C4⋊C4—28no—
573C2×C4⋊C4—28no—
574C2×C4⋊C4—88no—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C24116yes—
598C2×C4⋊C4C24116yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2412yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C24116yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C24116yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C42—28no—
631C2×C42—28no—
632C2×C42—28no—
633C2×C42—48no—
634C2×C42C2×D418yes—
635C2×C42C2412yes—
636C2×C42C2412yes—
637C2×C42C2418yes—
638C2×C42C2412yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2412yes—
645C2×C42C2414yes—
646C2×C42C2412yes—
647C2×C42C2418yes—
648C2×C42C2414yes—
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653#95C2418yes—
654#95C24116yes—
655#95C2418yes—
656#95C2412yes—
657#95C2414yes—
658#95C2412yes—
659#95C24116yes—
660#95C24116yes—
661#95C2414yes—
662#95C2414yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C24116yes—
670C24C2512yes—
671C24C2514yes—
672C24C2514yes—
673C24C2511yescharacteristic
674#41—264no—
675#41—4128no—
676#41—464no—
677#41—464no—
678#41—416no—
679#41—432no—
680#41—832no—
681C2×Q8—232no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—22no—
685C2×Q8—28no—
686C2×Q8—216no—
687C2×Q8—24no—
688C2×Q8—28no—
689C2×Q8—24no—
690C2×Q8—22no—
691C2×Q8—216no—
692C2×Q8—24no—
693C2×Q8—24no—
694C2×Q8—24no—
695C2×Q8—24no—
696C2×Q8—22no—
697C2×Q8—24no—
698C2×Q8—48no—
699C2×Q8—48no—
700C2×Q8—48no—
701C2×Q8—464no—
702C2×Q8—464no—
703C2×Q8—816no—
704C2×Q8C22×D418yes—
705C2×Q8C2×#4118yes—
706C2×Q8C2×#4118yes—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—24no—
710C2×D4—28no—
711C2×D4—216no—
712C2×D4—24no—
713C2×D4—28no—
714C2×D4—24no—
715C2×D4—28no—
716C2×D4—216no—
717C2×D4—216no—
718C2×D4—24no—
719C2×D4—22no—
720C2×D4—24no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—216no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—22no—
728C2×D4—24no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—216no—
732C2×D4—48no—
733C2×D4—44no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—416no—
737C2×D4—416no—
738C2×D4—44no—
739C2×D4C22×D418yes—
740C2×D4C22×D4116yes—
741C2×D4C22×D418yes—
742C2×D4C22×D418yes—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—24no—
748C22×C4—216no—
749C22×C4—28no—
750C22×C4—24no—
751C22×C4—28no—
752C22×C4—216no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—216no—
757C22×C4—28no—
758C22×C4—24no—
759C22×C4—216no—
760C22×C4—216no—
761C22×C4—28no—
762C22×C4—24no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—216no—
767C22×C4—44no—
768C22×C4—48no—
769C22×C4—48no—
770C22×C4—42no—
771C22×C4—44no—
772C22×C4—48no—
773C22×C4—44no—
774C22×C4—48no—
775C22×C4—48no—
776C22×C4—416no—
777C22×C4C22×D414yes—
778C22×C4C22×D4116yes—
779C22×C4C22×D414yes—
780C22×C4C22×D414yes—
781C22×C4C2×#4118yes—
782C22×C4C2×#4114yes—
783C22×C4H(5,𝔽2)14yes—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2518yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C22×C4C2511yescharacteristic
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C4⋊C4—22no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—216no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—28no—
812C4⋊C4—22no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—216no—
817C4⋊C4—24no—
818C4⋊C4—216no—
819C4⋊C4—24no—
820C4⋊C4—216no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—416no—
825C4⋊C4—416no—
826C4⋊C4—48no—
827C4⋊C4—48no—
828C4⋊C4—48no—
829C4⋊C4C22×D418yes—
830C4⋊C4C22×D418yes—
831C4⋊C42−1+418yescomplemented
832C22⋊C4—24no—
833C22⋊C4—216no—
834C22⋊C4—216no—
835C22⋊C4—216no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—216no—
841C22⋊C4—28no—
842C22⋊C4—216no—
843C22⋊C4—28no—
844C22⋊C4—216no—
845C22⋊C4—216no—
846C22⋊C4—216no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—416no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—416no—
855C22⋊C4C22×D4116yes—
856C22⋊C4C22×D4116yes—
857C42—24no—
858C42—24no—
859C42—28no—
860C42—28no—
861C42—24no—
862C42—216no—
863C42—24no—
864C42—24no—
865C42—24no—
866C42—28no—
867C42—24no—
868C42—28no—
869C42—48no—
870C42—44no—
871C42C22×D414yes—
872C42C22×D414yes—
873C42C22×D414yes—
874C42C22×D414yes—
875C23—22no—
876C23—22no—
877C23—24no—
878C23—24no—
879C23—28no—
880C23—28no—
881C23—22no—
882C23—24no—
883C23—22no—
884C23—24no—
885C23—22no—
886C23—24no—
887C23—28no—
888C23—24no—
889C23—28no—
890C23—24no—
891C23C23×D418yes—
892C23C23×D412yes—
893C23C22×#4112yes—
894C23C2×H(5,𝔽2)12yes—
895C23C2611yescharacteristic
896Q8—216no—
897Q8—216no—
898Q8—216no—
899Q8—432no—
900Q8—416no—
901Q8—48no—
902Q8—44no—
903Q8—88no—
904D4—232no—
905D4—216no—
906D4—216no—
907D4—48no—
908D4—432no—
909D4—48no—
910D4—416no—
911D4—44no—
912D4—48no—
913D4—48no—
914D4—84no—
915D4—816no—
916D4—816no—
917D4—816no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—216no—
928C2×C4—232no—
929C2×C4—28no—
930C2×C4—22no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—28no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—216no—
952C2×C4—28no—
953C2×C4—44no—
954C2×C4—432no—
955C2×C4—416no—
956C2×C4—432no—
957C2×C4—48no—
958C2×C4—416no—
959C2×C4—48no—
960C2×C4—48no—
961C2×C4—816no—
962C2×C4—84no—
963C2×C4—88no—
964C2×C4—816no—
965C2×C4#546116yes—
966C2×C4C23×D412yes—
967C2×C4C23×D412yes—
968C2×C4C23×D418yes—
969C2×C4C23×D412yes—
970C2×C4C23×D412yes—
971C2×C4C23×D412yes—
972C2×C4C23×D412yes—
973C2×C4C22×#4118yes—
974C2×C4C22×#4112yes—
975C2×C4C22×#4112yes—
976C2×C4C2×H(5,𝔽2)12yes—
977C2×C4C2×H(5,𝔽2)12yes—
978C2×C4C2×2−1+418yes—
979C2×C4C2×2−1+414yes—
980C22—24no—
981C22—22no—
982C22—22no—
983C22—24no—
984C22—28no—
985C22—28no—
986C22—28no—
987C22—48no—
988C22—48no—
989C22—44no—
990C22—48no—
991C22—42no—
992C22—44no—
993C22—42no—
994C22—44no—
995C22—44no—
996C22—48no—
997C22—44no—
998C22—42no—
999C22C2×#54614yes—
1000C22C24×D411yescharacteristic
1001C22C23×#4111yescharacteristic
1002C22C22×H(5,𝔽2)11yescharacteristic
1003C22C22×2−1+412yes—
1004C22H(7,𝔽2)12yes—
1005C4—22no—
1006C4—22no—
1007C4—22no—
1008C4—28no—
1009C4—28no—
1010C4—28no—
1011C4—44no—
1012C4—42no—
1013C4—42no—
1014C4—48no—
1015C4—44no—
1016C4—44no—
1017C4—44no—
1018C4—44no—
1019C4—42no—
1020C4C2×#54614yes—
1021C4C2×#54614yes—
1022C4#349914yes—
1023C2—24no—
1024C2—48no—
1025C2—82no—
1026C2—84no—
1027C2C22×#54611yescharacteristic
1028C2C2×#349911yescharacteristic
1029C2#6285211yescharacteristic
1030C2#6294412yes—
1031C2#6299912yes—
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×#3511C2semidirect
2. C2×#3497C2semidirect
3. #59110C2semidirect
4. #59039C2semidirect
5. #59036C2semidirect
6. #45303C2semidirect
7. #43888C2semidirect
8. #38958C2semidirect
9. #38952C2semidirect
10. #38091C2semidirect
11. #38079C2semidirect
12. #36412C2semidirect
13. #36276C2semidirect
14. #35660C2semidirect
15. #35530C2semidirect
16. #35289C2semidirect
17. #35273C2semidirect
18. C2×#2567C2semidirect
19. #34937C2semidirect
20. #34259C2semidirect
21. #34141C2semidirect
22. C4×#536C2semidirect
189. #532D4semidirect
443. C22×Q8#41semidirect
831. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#34972
#591102
#590392
#590362
#453032
#438882
#389582
#389522
#380912
#380792
#364122
#362762
#356602
#355302
#352892
#352732
C2×#25672
#349372
#342592
#341412
C4×#5362