Finite Group Databasebeta

← #7674641

Subgroups — #7674641

Order 512.

7026 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
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3509C211yesmaximal, characteristic, complemented
3#43528C2116yesmaximal, complemented
4#39746C214yesmaximal, complemented
5#39744C214yesmaximal, complemented
6#39741C214yesmaximal, complemented
7#39740C214yesmaximal, complemented
8#37774C218yesmaximal, complemented
9#37773C218yesmaximal, complemented
10#35677C211yesmaximal, characteristic, complemented
11#35667C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic, complemented
13#35617C211yesmaximal, characteristic, complemented
14#35329C211yesmaximal, characteristic
15#35327C211yesmaximal, characteristic, complemented
16#35317C211yesmaximal, characteristic, complemented
17#35316C211yesmaximal, characteristic, complemented
18C2×#2658C211yesmaximal, characteristic, complemented
19#34211C211yesmaximal, characteristic, complemented
20#34209C211yesmaximal, characteristic, complemented
21#34074C211yesmaximal, characteristic, complemented
22#34070C211yesmaximal, characteristic, complemented
23#3510—216no—
24#3509—216no—
25C2×#559C2214yes—
26C2×#557C2214yescomplemented
27C2×#556C2214yes—
28C2×#556C2214yescomplemented
29C2×#552C2218yes—
30C2×#551C2218yes—
31C2×#542C2214yes—
32C2×#541C2214yescomplemented
33C2×#536C2211yescharacteristic
34C2×#536C2211yescharacteristic
35C2×#536C2211yescharacteristic
36C2×#536C2211yescharacteristic
37C2×#536C2211yescharacteristic
38C2×#536C2211yescharacteristic
39C2×#535C2211yescharacteristic
40C2×#535C2211yescharacteristic
41C2×#533C2211yescharacteristic
42C2×#533C2214yescomplemented
43C2×#532C2211yescharacteristic
44C22×C4⋊Q8C2211yescharacteristic
45C22×C4⋊Q8C2211yescharacteristic
46C22×C4⋊Q8C2211yescharacteristic
47C2×#529C2214yes—
48C22×#124C2211yescharacteristic
49C22×#124C2211yescharacteristic
50C22×#124C2211yescharacteristic
51C2×#519C2211yescharacteristic
52C2×#519C2211yescharacteristic
53C2×#519C2211yescharacteristic
54C2×#518C2211yescharacteristic
55C2×C4×#41C2211yescharacteristic
56C2×C4×#41C2211yescharacteristic
57#2868C2212yescomplemented
58#2858C2212yes—
59#2858C2212yes—
60#2858C2212yescomplemented
61#2857C2214yescomplemented
62#2850C2214yes—
63#2732C22116yescomplemented
64#2730C22116yescomplemented
65#2727C22116yescomplemented
66#2721C22116yescomplemented
67#2721C22116yescomplemented
68#2705C22116yescomplemented
69#2694C22116yescomplemented
70#2694C22116yescomplemented
71#2658C2212yes—
72#2658C2214yes—
73#2658C2214yes—
74#2658C2214yes—
75#2658C2214yes—
76#2658C2212yescomplemented
77#2658C2212yescomplemented
78#2657C2212yes—
79#2621C2214yescomplemented
80#2620C2214yes—
81#2548C2214yes—
82#2547C2214yes—
83#2547C2214yescomplemented
84#2546C2214yescomplemented
85#2546C2214yescomplemented
86#2546C2214yescomplemented
87#2545C2214yes—
88#2545C2214yes—
89#2545C2214yescomplemented
90#2545C2214yescomplemented
91#2544C2214yes—
92#2544C2214yes—
93#2542C2218yescomplemented
94#2540C2218yes—
95#2539C2218yes—
96#2534C2218yes—
97#2501C2218yes—
98#2486C2218yes—
99#2479C22116yescomplemented
100#2479C22116yescomplemented
101#2471C22116yescomplemented
102#2467C22116yescomplemented
103#2454C22116yescomplemented
104#2448C22116yescomplemented
105#2441C22116yescomplemented
106#2429C2218yescomplemented
107#2429C2218yescomplemented
108#2427C2218yes—
109#2426C2218yes—
110#2423C22116yescomplemented
111#2413C2218yes—
112#2413C2218yes—
113#2412C2218yes—
114#2411C2218yes—
115C2×#399C2218yes—
116#2367C2218yes—
117#2365C2218yescomplemented
118#2344C2218yes—
119#2342C2218yes—
120#2331C2214yescomplemented
121#2330C2214yescomplemented
122#2329C2218yes—
123#2328C2212yescomplemented
124#2327C2212yescomplemented
125#2327C2214yescomplemented
126#2326C2214yes—
127#2326C2212yescomplemented
128#2326C2212yescomplemented
129#2325C2218yes—
130#2310C2211yescharacteristic
131#2310C2211yescharacteristic
132#2310C2211yescharacteristic
133#2309C2211yescharacteristic
134C4×C4⋊Q8C2214yescomplemented
135C4×#124C2214yes—
136#2297C2211yescharacteristic
137#2297C2211yescharacteristic
138#2296C2211yescharacteristic
139#2296C2211yescharacteristic
140#2295C2214yescomplemented
141#2295C2214yescomplemented
142#2290C2214yescomplemented
143#2290C2214yescomplemented
144#2285C2211yescharacteristic
145#2285C2211yescharacteristic
146C4×#117C2211yescharacteristic
147C4×#117C2211yescharacteristic
148C2×#376C2211yescharacteristic
149C22×#41C2311yescharacteristic
150C22×#41C2311yescharacteristic
151C23×Q8C2311yescharacteristic
152C23×Q8C2311yescharacteristic
153C23×Q8C2311yescharacteristic
154C23×D4C2311yescharacteristic
155#559—232no—
156#557—232no—
157#556—232no—
158#556—232no—
159#552—264no—
160#551—264no—
161#542—232no—
162#541—232no—
163#536—28no—
164#536—28no—
165#536—28no—
166#536—44no—
167#536—44no—
168#536—44no—
169#535—28no—
170#535—44no—
171#533—232no—
172#533D4116yescomplemented
173#532—28no—
174C2×C4⋊Q8—28no—
175C2×C4⋊Q8—28no—
176C2×C4⋊Q8—44no—
177C2×C4⋊Q8C2312yes—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2311yescharacteristic
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2312yes—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2314yes—
187C2×C4⋊Q8C2312yes—
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2312yes—
193C2×#127C2311yescharacteristic
194C2×#127C2312yes—
195C2×#127C2312yes—
196#529—232no—
197C2×#126C2318yes—
198C2×#126C2318yes—
199C2×#126C2318yes—
200C2×#126C2318yes—
201C2×#125C2318yes—
202C2×#125C2318yes—
203C2×#125C2318yes—
204C2×#125C2312yes—
205C2×#124—28no—
206C2×#124—28no—
207C2×#124—44no—
208C2×#124C2312yes—
209C2×#124C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#124C2312yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#124C2312yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#124C2314yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×#124C2318yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2314yes—
230C2×#123C2318yes—
231C2×#123C2318yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2314yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#121C2314yes—
247C2×#120C2314yes—
248C2×#120C2314yes—
249#519—28no—
250#519—28no—
251#519—28no—
252#518—28no—
253C4×#41—28no—
254C4×#41—28no—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2318yes—
264C2×C4×Q8C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C2314yes—
273C2×#117C2311yescharacteristic
274C2×#117C2311yescharacteristic
275C2×#117C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2314yes—
278C2×#117C2314yes—
279C2×#117C2314yes—
280C2×#117C2312yes—
281C2×#117C2312yes—
282C2×#117C2318yes—
283C2×#117C2318yes—
284C2×#117C2311yescharacteristic
285C2×#117C2311yescharacteristic
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2314yes—
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2314yes—
291C22×C22⋊C4C2314yes—
292C22×C22⋊C4C2314yes—
293C22×C42C2312yes—
294C22×C42C2312yes—
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298#399C23116yes—
299#399C23116yes—
300#399C23116yes—
301#399C23116yes—
302#399C23116yes—
303#399C23116yes—
304#399C23116yes—
305#398C23116yes—
306#398C23116yes—
307#398C23116yes—
308#397C23116yes—
309#397C23116yes—
310#396C23116yes—
311#396C23116yes—
312#396C23116yes—
313#396C23116yes—
314#394C23116yes—
315#394C23116yes—
316#394C23116yes—
317#392C23116yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2318yes—
327#391C2318yes—
328#390C2314yes—
329#390C2314yes—
330#390C2312yes—
331#390C2312yes—
332#390C23116yes—
333#390C23116yes—
334#390C23116yes—
335#390C23116yes—
336#389C23116yes—
337#389C2318yes—
338#389C2318yes—
339#389C2314yes—
340#389C2314yes—
341#389C23116yes—
342#389C23116yes—
343#389C23116yes—
344#388C2318yes—
345#388C2318yes—
346#388C23116yes—
347#388C23116yes—
348#388C23116yes—
349#388C23116yes—
350#388C23116yes—
351#388C23116yes—
352#387C2318yes—
353#387C2318yes—
354#387C23116yes—
355#387C23116yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#386C2314yes—
361#386C2314yes—
362#386C2318yes—
363#386C2318yes—
364#386C23116yes—
365#386C23116yes—
366#385C2318yes—
367#385C2318yes—
368#385C23116yes—
369#385C2314yes—
370#385C2314yes—
371#384C2312yes—
372#384C2312yes—
373#384C23116yes—
374#382C2312yes—
375#382C2312yes—
376#381C2314yes—
377#381C2314yes—
378#381C2314yes—
379#380C2314yes—
380#380C2314yes—
381#380C23116yes—
382#380C23116yes—
383#379C2314yes—
384C4×C4⋊C4C23116yes—
385C4×C4⋊C4C2314yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2314yes—
388C4×C4⋊C4C2314yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C22⋊C4C2314yes—
392C4×C22⋊C4C2314yes—
393C4×C22⋊C4C23116yes—
394C4×C22⋊C4C2314yes—
395C4×C22⋊C4C2314yes—
396#376C2312yes—
397#376C2312yes—
398#376C2312yes—
399#376C2312yes—
400#376C2312yes—
401#376C2312yes—
402C2×#95C2314yes—
403C43C2312yes—
404C43C2312yes—
405C25C2412yes—
406C2×#41—24no—
407C2×#41—24no—
408C2×#41—24no—
409C2×#41—24no—
410C2×#41—24no—
411C2×#41—24no—
412C22×Q8—24no—
413C22×Q8—24no—
414C22×Q8—24no—
415C22×Q8—24no—
416C22×Q8—24no—
417C22×Q8—24no—
418C22×Q8—24no—
419C22×Q8—24no—
420C22×Q8—24no—
421C22×Q8C2412yes—
422C22×Q8C2412yes—
423C22×Q8C2412yes—
424C22×Q8C2412yes—
425C22×Q8C2412yes—
426C22×Q8C2412yes—
427C22×Q8C2411yescharacteristic
428C22×Q8C2411yescharacteristic
429C22×Q8C2414yes—
430C22×D4—24no—
431C22×D4—24no—
432C22×D4—24no—
433C22×D4C2412yes—
434C22×D4C2412yes—
435C22×D4C2412yes—
436C22×D4C2412yes—
437C22×D4C2411yescharacteristic
438C22×D4C2411yescharacteristic
439C22×D4C2418yes—
440C22×D4C2414yes—
441C22×D4C2418yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2412yes—
448C23×C4C2418yes—
449C23×C4C2414yes—
450C23×C4C2414yes—
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2411yescharacteristic
454C4⋊Q8—28no—
455C4⋊Q8—28no—
456C4⋊Q8—216no—
457C4⋊Q8—28no—
458C4⋊Q8—28no—
459C4⋊Q8—28no—
460C4⋊Q8—216no—
461C4⋊Q8—28no—
462C4⋊Q8—28no—
463C4⋊Q8—24no—
464C4⋊Q8—48no—
465C4⋊Q8—48no—
466C4⋊Q8—44no—
467C4⋊Q8—44no—
468C4⋊Q8—44no—
469C4⋊Q8C2×D4116yes—
470#127—28no—
471#127—24no—
472#127—44no—
473#126—232no—
474#126—232no—
475#126—232no—
476#126—232no—
477#125—232no—
478#125—232no—
479#125—232no—
480#125C2×D4116yes—
481#124—232no—
482#124—28no—
483#124—28no—
484#124—216no—
485#124—28no—
486#124—28no—
487#124—28no—
488#124—28no—
489#124—216no—
490#124—28no—
491#124—28no—
492#124—24no—
493#124—24no—
494#124—48no—
495#124—48no—
496#124—44no—
497#124—44no—
498#124—44no—
499#124—44no—
500#123—232no—
501#123—232no—
502#123—216no—
503#123—216no—
504#123—216no—
505#123—48no—
506#123—48no—
507#123—48no—
508C22⋊Q8—232no—
509C22⋊Q8—232no—
510C22⋊Q8—216no—
511C22⋊Q8—216no—
512C22⋊Q8—216no—
513C22⋊Q8—48no—
514C22⋊Q8—48no—
515C22⋊Q8—48no—
516C22⋊Q8C2×D4132yes—
517#121—216no—
518#121—216no—
519#121—48no—
520#120—216no—
521#120—48no—
522C4×Q8—232no—
523C4×Q8—216no—
524C4×Q8—216no—
525C4×Q8—216no—
526C4×Q8—28no—
527C4×Q8—28no—
528C4×Q8—216no—
529C4×Q8—216no—
530C4×Q8—216no—
531C4×Q8C2×D4132yes—
532C4×D4—216no—
533C4×D4—216no—
534C4×D4—216no—
535C4×D4—232no—
536C4×D4—28no—
537C4×D4—28no—
538C4×D4—216no—
539C4×D4—216no—
540#117—24no—
541#117—24no—
542#117—24no—
543#117—24no—
544#117—232no—
545#117—232no—
546#117—216no—
547#117—216no—
548#117—216no—
549#117—28no—
550#117—28no—
551#117C2×D418yes—
552#117C2×D418yes—
553C2×C4⋊C4—216no—
554C2×C4⋊C4—216no—
555C2×C4⋊C4—48no—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C24116yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C22⋊C4—216no—
587C2×C22⋊C4—216no—
588C2×C22⋊C4—216no—
589C2×C22⋊C4—48no—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2412yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C24116yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C24116yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C42—24no—
618C2×C42—28no—
619C2×C42—28no—
620C2×C42C2×D418yes—
621C2×C42#4118yes—
622C2×C42C2412yes—
623C2×C42C2418yes—
624C2×C42C2414yes—
625C2×C42C2412yes—
626C2×C42C2418yes—
627C2×C42C2418yes—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2414yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2418yes—
634C2×C42C2418yes—
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2412yes—
638C2×C42C2412yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C24116yes—
652#95C2418yes—
653#95C24116yes—
654#95C2418yes—
655#95C24116yes—
656#95C2418yes—
657#95C2418yes—
658C24—24no—
659C24—24no—
660C24—24no—
661C24—48no—
662C24C2514yes—
663C24C2512yes—
664C24C2512yes—
665C24C2511yescharacteristic
666#41—416no—
667#41—416no—
668C2×Q8—24no—
669C2×Q8—24no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—22no—
673C2×Q8—24no—
674C2×Q8—24no—
675C2×Q8—22no—
676C2×Q8—24no—
677C2×Q8—24no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—24no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—24no—
685C2×Q8—24no—
686C2×Q8—24no—
687C2×Q8—24no—
688C2×Q8—22no—
689C2×Q8—24no—
690C2×Q8—24no—
691C2×Q8—22no—
692C2×Q8—48no—
693C2×Q8—416no—
694C2×Q8—416no—
695C2×Q8—416no—
696C2×Q8C22×D4116yes—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—22no—
705C2×D4—24no—
706C2×D4—22no—
707C2×D4—216no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—28no—
713C2×D4—24no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—22no—
717C2×D4—48no—
718C2×D4—416no—
719C2×D4—48no—
720C2×D4—416no—
721C2×D4—416no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—28no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—28no—
740C22×C4—216no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—48no—
744C22×C4—44no—
745C22×C4—416no—
746C22×C4—48no—
747C22×C4C22×D418yes—
748C22×C4C22×D414yes—
749C22×C4C2×#4118yes—
750C22×C4C2×#4114yes—
751C22×C4H(5,𝔽2)14yes—
752C22×C4C2514yes—
753C22×C4C2514yes—
754C22×C4C2514yes—
755C22×C4C2514yes—
756C22×C4C2514yes—
757C22×C4C2514yes—
758C22×C4C2514yes—
759C22×C4C2514yes—
760C22×C4C2512yes—
761C22×C4C2512yes—
762C22×C4C2512yes—
763C22×C4C2514yes—
764C22×C4C2514yes—
765C22×C4C2512yes—
766C22×C4C2512yes—
767C22×C4C2512yes—
768C22×C4C2511yescharacteristic
769C22×C4C2511yescharacteristic
770C4⋊C4—216no—
771C4⋊C4—216no—
772C4⋊C4—24no—
773C4⋊C4—24no—
774C4⋊C4—28no—
775C4⋊C4—28no—
776C4⋊C4—216no—
777C4⋊C4—216no—
778C4⋊C4—216no—
779C4⋊C4—216no—
780C4⋊C4—216no—
781C4⋊C4—216no—
782C4⋊C4—216no—
783C4⋊C4—216no—
784C4⋊C4—28no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—416no—
788C4⋊C4—48no—
789C4⋊C4—48no—
790C4⋊C4—48no—
791C4⋊C4—48no—
792C4⋊C4—48no—
793C4⋊C4—48no—
794C4⋊C4—48no—
795C4⋊C4C22×D4116yes—
796C4⋊C4C22×D4116yes—
797C4⋊C4C22×D418yes—
798C4⋊C4C22×D418yes—
799C4⋊C4C22×D4116yes—
800C22⋊C4—24no—
801C22⋊C4—24no—
802C22⋊C4—24no—
803C22⋊C4—24no—
804C22⋊C4—216no—
805C22⋊C4—216no—
806C22⋊C4—216no—
807C22⋊C4—28no—
808C22⋊C4—28no—
809C22⋊C4—216no—
810C22⋊C4—216no—
811C22⋊C4—216no—
812C22⋊C4—216no—
813C22⋊C4—216no—
814C22⋊C4—216no—
815C22⋊C4—28no—
816C22⋊C4—28no—
817C22⋊C4—416no—
818C22⋊C4—416no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—48no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4C22×D418yes—
826C22⋊C4C22×D418yes—
827C42—24no—
828C42—28no—
829C42—24no—
830C42—28no—
831C42—216no—
832C42—216no—
833C42—216no—
834C42—24no—
835C42—24no—
836C42—24no—
837C42—24no—
838C42—48no—
839C42—48no—
840C42C22×D414yes—
841C42C22×D414yes—
842C42C22×D418yes—
843C42C22×D418yes—
844C42C22×D418yes—
845C42C2×#4118yes—
846C42C2×#4114yes—
847C42C2×#4114yes—
848C23—24no—
849C23—22no—
850C23—24no—
851C23—22no—
852C23—24no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—24no—
857C23—22no—
858C23—28no—
859C23—28no—
860C23—216no—
861C23—48no—
862C23—88no—
863C23—88no—
864C23—88no—
865C23C23×D412yes—
866C23C22×#4112yes—
867C23C2×H(5,𝔽2)12yes—
868C23C2611yescharacteristic
869Q8—416no—
870Q8—48no—
871Q8—48no—
872Q8—48no—
873Q8—48no—
874Q8—48no—
875Q8—48no—
876Q8—44no—
877Q8—44no—
878D4—48no—
879D4—48no—
880D4—48no—
881D4—48no—
882D4—44no—
883D4—44no—
884D4—816no—
885D4—88no—
886D4—168no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—28no—
890C2×C4—28no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—22no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—28no—
919C2×C4—48no—
920C2×C4—48no—
921C2×C4—416no—
922C2×C4—48no—
923C2×C4—48no—
924C2×C4—48no—
925C2×C4—48no—
926C2×C4—48no—
927C2×C4—48no—
928C2×C4—88no—
929C2×C4—816no—
930C2×C4#550116yes—
931C2×C4C23×D418yes—
932C2×C4C23×D414yes—
933C2×C4C23×D414yes—
934C2×C4C23×D418yes—
935C2×C4C23×D412yes—
936C2×C4C23×D412yes—
937C2×C4C22×#4114yes—
938C2×C4C22×#4114yes—
939C2×C4C22×#4112yes—
940C2×C4C22×#4112yes—
941C2×C4C2×H(5,𝔽2)12yes—
942C2×C4C2×H(5,𝔽2)12yes—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—44no—
947C22—44no—
948C22—48no—
949C22—44no—
950C22—44no—
951C22—48no—
952C22—44no—
953C22—48no—
954C22—44no—
955C22—42no—
956C22—42no—
957C22—44no—
958C22—168no—
959C22C2×#55014yes—
960C22C24×D411yescharacteristic
961C22C23×#4111yescharacteristic
962C22C22×H(5,𝔽2)11yescharacteristic
963C222−1+614yes—
964C4—24no—
965C4—24no—
966C4—28no—
967C4—28no—
968C4—24no—
969C4—24no—
970C4—44no—
971C4—44no—
972C4—44no—
973C4—44no—
974C4—44no—
975C4—42no—
976C4—42no—
977C4—44no—
978C4—44no—
979C4—44no—
980C4C2×#55014yes—
981C4C2×#55014yes—
982C2—24no—
983C2—82no—
984C2—82no—
985C2—84no—
986C2C22×#55011yescharacteristic
987C2#6285912yes—
988C2#6286012yes—
989C2#6288712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35329C2
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×#3510C2semidirect
2. C2×#3509C2semidirect
3. #43528C2semidirect
4. #39746C2semidirect
5. #39744C2semidirect
6. #39741C2semidirect
7. #39740C2semidirect
8. #37774C2semidirect
9. #37773C2semidirect
10. #35677C2semidirect
11. #35667C2semidirect
12. #35667C2semidirect
13. #35617C2semidirect
15. #35327C2semidirect
16. #35317C2semidirect
17. #35316C2semidirect
18. C2×#2658C2semidirect
19. #34211C2semidirect
20. #34209C2semidirect
21. #34074C2semidirect
22. #34070C2semidirect
26. C2×#557C22semidirect
28. C2×#556C22semidirect
32. C2×#541C22semidirect
42. C2×#533C22semidirect
57. #2868C22semidirect
60. #2858C22semidirect
61. #2857C22semidirect
63. #2732C22semidirect
64. #2730C22semidirect
65. #2727C22semidirect
66. #2721C22semidirect
67. #2721C22semidirect
68. #2705C22semidirect
69. #2694C22semidirect
70. #2694C22semidirect
76. #2658C22semidirect
77. #2658C22semidirect
79. #2621C22semidirect
83. #2547C22semidirect
84. #2546C22semidirect
85. #2546C22semidirect
86. #2546C22semidirect
89. #2545C22semidirect
90. #2545C22semidirect
93. #2542C22semidirect
99. #2479C22semidirect
100. #2479C22semidirect
101. #2471C22semidirect
102. #2467C22semidirect
103. #2454C22semidirect
104. #2448C22semidirect
105. #2441C22semidirect
106. #2429C22semidirect
107. #2429C22semidirect
110. #2423C22semidirect
117. #2365C22semidirect
120. #2331C22semidirect
121. #2330C22semidirect
123. #2328C22semidirect
124. #2327C22semidirect
125. #2327C22semidirect
127. #2326C22semidirect
128. #2326C22semidirect
134. C4×C4⋊Q8C22semidirect
140. #2295C22semidirect
141. #2295C22semidirect
142. #2290C22semidirect
143. #2290C22semidirect
172. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#35092
#435282
#397462
#397442
#397412
#397402
#377742
#377732
#356772
#356672
#356172
#353292
#353272
#353172
#353162
C2×#26582
#342112
#342092
#340742
#340702