Finite Group Databasebeta

← #7672209

Subgroups — #7672209

Order 512.

7056 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C22×#533C211yesmaximal, characteristic, complemented
3#59071C214yesmaximal, complemented
4#59067C214yesmaximal, complemented
5#59065C214yesmaximal, complemented
6#59055C214yesmaximal, complemented
7#38919C214yesmaximal, complemented
8#38917C214yesmaximal, complemented
9#37765C218yesmaximal, complemented
10#36625C211yesmaximal, characteristic, complemented
11#36427C214yesmaximal, complemented
12#36423C214yesmaximal, complemented
13#36151C214yesmaximal, complemented
14#36134C214yesmaximal, complemented
15#35672C212yesmaximal, complemented
16#35661C212yesmaximal
17#35281C211yesmaximal, characteristic, complemented
18#35279C211yesmaximal, characteristic, complemented
19#35182C212yesmaximal, complemented
20#34249C212yesmaximal, complemented
21#34209C211yesmaximal, characteristic, complemented
22C4×#525C211yesmaximal, characteristic
23#3509—216no—
24C2×#557C2212yescomplemented
25C2×#557C2212yescomplemented
26C2×#556C2212yescomplemented
27C2×#556C2212yescomplemented
28C2×#552C2214yes—
29C2×#552C2214yes—
30C2×#541C2214yescomplemented
31C2×#536C2212yes—
32C2×#533—216no—
33C2×#533C2211yescharacteristic
34C2×#533C2214yes—
35C2×#533C2214yes—
36C2×#533C2214yes—
37C2×#533C2214yes—
38C2×#533C2212yescomplemented
39C2×#533C2212yescomplemented
40C22×C4⋊Q8C2211yescharacteristic
41C22×C4⋊Q8C2211yescharacteristic
42C22×#125C2212yes—
43C2×#525C2211yescharacteristic
44C22×C22⋊Q8C2212yes—
45C22×C22⋊Q8C2212yes—
46C2×#519C2212yes—
47C2×#519C2212yes—
48C2×C4×#41C2211yescharacteristic
49C22×C4×Q8C2212yes—
50C22×C4×Q8C2212yes—
51C22×#117C2212yes—
52C23×C42C2211yescharacteristic
53#2868C2212yescomplemented
54#2862C2212yescomplemented
55#2857C2212yes—
56#2857C2212yes—
57#2857C2214yescomplemented
58#2855C2212yes—
59#2855C2212yes—
60#2853C2218yes—
61#2851C2214yes—
62#2848C2212yes—
63#2848C2212yes—
64#2723C22116yes—
65#2721C22116yescomplemented
66#2720C22116yes—
67#2719C22116yescomplemented
68#2660C2214yescomplemented
69#2628C2214yescomplemented
70#2623C2218yes—
71#2568C2212yescomplemented
72#2567C2214yescomplemented
73#2567C2212yescomplemented
74#2563C2212yescomplemented
75#2552C2218yescomplemented
76#2546C2214yescomplemented
77#2542C2218yes—
78#2542C2212yescomplemented
79#2538C2218yes—
80#2536C2218yes—
81#2502C2214yes—
82#2489C2218yes—
83#2489C2218yescomplemented
84#2487C2214yes—
85#2484C2218yes—
86#2482C2218yes—
87#2479C22116yes—
88#2475C22116yes—
89#2469C22116yescomplemented
90#2462C22116yescomplemented
91#2453C2218yescomplemented
92#2453C2218yescomplemented
93#2448C2218yescomplemented
94#2446C2218yescomplemented
95#2441C2218yes—
96#2441C2218yescomplemented
97#2434C2214yes—
98#2429C2218yes—
99#2429C2218yes—
100#2429C2218yescomplemented
101#2426C2218yes—
102#2423C2218yes—
103#2423C2218yes—
104#2423C2218yescomplemented
105#2421C2218yes—
106#2421C2218yes—
107#2421C2218yescomplemented
108#2415C2218yes—
109#2415C2218yes—
110#2413C2218yes—
111#2411C2218yes—
112#2409C2214yes—
113#2365C2218yescomplemented
114#2365C2214yescomplemented
115#2365C2214yescomplemented
116#2362C2218yes—
117#2362C2218yescomplemented
118#2354C2218yes—
119#2351C2218yescomplemented
120#2351C2218yescomplemented
121Q8×C4⋊C4C2218yescomplemented
122Q8×C4⋊C4C2218yescomplemented
123#2344C2214yes—
124#2344C2214yes—
125#2327C2214yescomplemented
126#2317C2218yes—
127#2317C2212yes—
128#2317C2212yes—
129#2317C2212yes—
130#2311C2212yes—
131#2310C2212yes—
132C4×C4⋊Q8C2214yescomplemented
133C4×C22⋊Q8C2214yes—
134C4×C22⋊Q8C2214yes—
135C4×C22⋊Q8C2212yes—
136C4×C22⋊Q8C2212yes—
137C4×#123C2212yes—
138C4×#123C2212yes—
139C4×#121C2212yes—
140C4×#121C2212yes—
141C4×#120C2212yes—
142C4×#120C2212yes—
143#2297C2211yescharacteristic
144#2296C2212yes—
145#2296C2218yes—
146#2296C2211yescharacteristic
147#2290C2214yes—
148#2285C2211yescharacteristic
149#2280C2212yes—
150#2280C2211yescharacteristic
151C42×D4C2214yes—
152C4×#117C2211yescharacteristic
153C22×#41C2311yescharacteristic
154C23×Q8C2312yes—
155C23×Q8C2312yes—
156C24×C4C2311yescharacteristic
157C24×C4C2311yescharacteristic
158C24×C4C2311yescharacteristic
159#557—216no—
160#557—216no—
161#556—216no—
162#556—216no—
163#552—232no—
164#552—232no—
165#541—232no—
166#536—216no—
167#533—232no—
168#533—232no—
169#533—232no—
170#533—232no—
171#533—216no—
172#533—216no—
173#533—28no—
174C2×C4⋊Q8—28no—
175C2×C4⋊Q8D4116yescomplemented
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2312yes—
178C2×C4⋊Q8C2311yescharacteristic
179C2×C4⋊Q8C2311yescharacteristic
180C2×C4⋊Q8C2312yes—
181C2×C4⋊Q8C2312yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2318yes—
184C2×C4⋊Q8C2312yes—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2312yes—
188C2×#126C2318yes—
189C2×#126C2318yes—
190C2×#125—216no—
191C2×#125C2312yes—
192C2×#125C2318yes—
193C2×#125C2318yes—
194C2×#125C2314yes—
195C2×#125C2314yes—
196C2×#125C2318yes—
197C2×#125C2318yes—
198C2×#124C2314yes—
199#525—28no—
200C2×#123C2318yes—
201C2×#123C2312yes—
202C2×C22⋊Q8—216no—
203C2×C22⋊Q8—216no—
204C2×C22⋊Q8C2312yes—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2318yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2318yes—
218C2×#121C2312yes—
219C2×#120C2312yes—
220#519—216no—
221#519—216no—
222C4×#41—28no—
223C2×C4×Q8—216no—
224C2×C4×Q8—216no—
225C2×C4×Q8C2318yes—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2318yes—
232C2×C4×Q8C2318yes—
233C2×C4×Q8C2318yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2318yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2318yes—
240C2×C4×Q8C2312yes—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×#117—216no—
249C2×#117C2311yescharacteristic
250C2×#117C2312yes—
251C2×#117C2311yescharacteristic
252C2×#117C2312yes—
253C2×#117C2318yes—
254C2×#117C2318yes—
255C2×#117C2314yes—
256C2×#117C2318yes—
257C2×#117C2314yes—
258C2×#117C2312yes—
259C2×#117C2318yes—
260C2×#117C2311yescharacteristic
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C22⋊C4C2314yes—
268C22×C42—28no—
269C22×C42C2312yes—
270C22×C42C2314yes—
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2312yes—
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2311yescharacteristic
279#400C2318yes—
280#400C23116yes—
281#400C23116yes—
282#399C23116yes—
283#399C2318yes—
284#399C23116yes—
285#398C23116yes—
286#398C23116yes—
287#398C23116yes—
288#398C23116yes—
289#397C23116yes—
290#397C23116yes—
291#396C23116yes—
292#396C23116yes—
293#395C2318yes—
294#395C23116yes—
295#394C23116yes—
296#393C2318yes—
297#391C2318yes—
298#391C2318yes—
299#391C2314yes—
300#391C2318yes—
301#391C2318yes—
302#391C2314yes—
303#391C2314yes—
304#391C2318yes—
305#391C2312yes—
306#390C2314yes—
307#390C23116yes—
308#390C2312yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2318yes—
315#389C23116yes—
316#389C23116yes—
317#389C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2312yes—
322#389C23116yes—
323#389C2312yes—
324#389C23116yes—
325#389C23116yes—
326#388C23116yes—
327#388C23116yes—
328#388C23116yes—
329#388C23116yes—
330#388C23116yes—
331#388C23116yes—
332#388C2314yes—
333#388C2314yes—
334#387C23116yes—
335#387C23116yes—
336#387C2318yes—
337#387C2318yes—
338#387C23116yes—
339#387C23116yes—
340#387C23116yes—
341#387C23116yes—
342#387C2314yes—
343#387C2314yes—
344#386C2318yes—
345#386C2312yes—
346#386C2312yes—
347#386C2314yes—
348#386C2314yes—
349#385C2312yes—
350#385C2314yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2314yes—
357#385C2314yes—
358#385C2314yes—
359#385C2312yes—
360#384C2312yes—
361#384C2314yes—
362#384C2318yes—
363#384C2314yes—
364#384C23116yes—
365#384C2314yes—
366#382C2314yes—
367#382C2314yes—
368#382C2314yes—
369#382C23116yes—
370#382C2312yes—
371#381C2318yes—
372#381C2314yes—
373#381C2312yes—
374#380C2318yes—
375#380C2318yes—
376#380C2312yes—
377#380C2312yes—
378#380C2314yes—
379#380C2314yes—
380#380C2314yes—
381#380C2314yes—
382#380C2312yes—
383#380C2312yes—
384#379C2314yes—
385#379C2312yes—
386C4×C4⋊C4C2318yes—
387C4×C4⋊C4C2318yes—
388C4×C4⋊C4C2312yes—
389C4×C4⋊C4C2312yes—
390C4×C4⋊C4C2312yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C23116yes—
393C4×C4⋊C4C23116yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2314yes—
396C4×C4⋊C4C2312yes—
397C4×C4⋊C4C2314yes—
398C4×C22⋊C4C2312yes—
399C4×C22⋊C4C2312yes—
400C4×C22⋊C4C2314yes—
401C4×C22⋊C4C2314yes—
402C4×C22⋊C4C2314yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2314yes—
405C4×C22⋊C4C2314yes—
406C4×C22⋊C4C2314yes—
407#376C2312yes—
408C43C2312yes—
409C25C2411yescharacteristic
410C2×#41—24no—
411C2×#41—24no—
412C2×#41—24no—
413C22×Q8—28no—
414C22×Q8—28no—
415C22×Q8—28no—
416C22×Q8—48no—
417C22×Q8C2×D4116yes—
418C22×Q8C2412yes—
419C22×Q8C2412yes—
420C22×Q8C2414yes—
421C22×Q8C2411yescharacteristic
422C22×Q8C2414yes—
423C22×Q8C2414yes—
424C22×Q8C2414yes—
425C22×D4C2412yes—
426C22×D4C2411yescharacteristic
427C22×D4C2414yes—
428C23×C4—24no—
429C23×C4—28no—
430C23×C4—24no—
431C23×C4—24no—
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—44no—
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2414yes—
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2412yes—
448C23×C4C2414yes—
449C23×C4C2411yescharacteristic
450C23×C4C2412yes—
451C23×C4C2411yescharacteristic
452C4⋊Q8—216no—
453C4⋊Q8—28no—
454C4⋊Q8—28no—
455C4⋊Q8—28no—
456C4⋊Q8—28no—
457C4⋊Q8—24no—
458C4⋊Q8—24no—
459C4⋊Q8—416no—
460C4⋊Q8C2×D4116yes—
461C4⋊Q8C2×D4116yes—
462C4⋊Q8C2×D4116yes—
463C4⋊Q8C2×D4116yes—
464#126—232no—
465#126—232no—
466#125—232no—
467#125—232no—
468#125—216no—
469#125—216no—
470#125—232no—
471#125—232no—
472#125—28no—
473#124—216no—
474#123—232no—
475#123—28no—
476C22⋊Q8—232no—
477C22⋊Q8—232no—
478C22⋊Q8—216no—
479C22⋊Q8—216no—
480C22⋊Q8—28no—
481C22⋊Q8—28no—
482C22⋊Q8—216no—
483C22⋊Q8—232no—
484C22⋊Q8—232no—
485C22⋊Q8—216no—
486C22⋊Q8—216no—
487C22⋊Q8—28no—
488C22⋊Q8—416no—
489C22⋊Q8—48no—
490#121—28no—
491#120—28no—
492C4×Q8—232no—
493C4×Q8—232no—
494C4×Q8—216no—
495C4×Q8—216no—
496C4×Q8—216no—
497C4×Q8—216no—
498C4×Q8—232no—
499C4×Q8—232no—
500C4×Q8—216no—
501C4×Q8—216no—
502C4×Q8—232no—
503C4×Q8—24no—
504C4×Q8—24no—
505C4×Q8—28no—
506C4×Q8—28no—
507C4×Q8—232no—
508C4×D4—28no—
509C4×D4—28no—
510C4×D4—216no—
511C4×D4—24no—
512C4×D4—24no—
513C4×D4—216no—
514C4×D4—48no—
515#117—24no—
516#117—28no—
517#117—232no—
518#117—28no—
519#117—24no—
520#117—232no—
521#117—232no—
522#117—216no—
523#117—216no—
524#117—232no—
525#117—28no—
526#117#4118yes—
527C2×C4⋊C4—28no—
528C2×C4⋊C4—216no—
529C2×C4⋊C4—216no—
530C2×C4⋊C4—28no—
531C2×C4⋊C4C2×D4116yes—
532C2×C4⋊C4C2×D4116yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C24116yes—
536C2×C4⋊C4C24116yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2411yescharacteristic
542C2×C4⋊C4C2411yescharacteristic
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C24116yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C24116yes—
564C2×C4⋊C4C24116yes—
565C2×C4⋊C4C24116yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2412yes—
571C2×C22⋊C4—216no—
572C2×C22⋊C4C24116yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C24116yes—
590C2×C22⋊C4C2412yes—
591C2×C42—216no—
592C2×C42—24no—
593C2×C42—24no—
594C2×C42—24no—
595C2×C42—28no—
596C2×C42—28no—
597C2×C42—28no—
598C2×C42—28no—
599C2×C42—28no—
600C2×C42C2×D418yes—
601C2×C42C2412yes—
602C2×C42C24116yes—
603C2×C42C2418yes—
604C2×C42C2418yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C24116yes—
608C2×C42C2412yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2414yes—
612C2×C42C2414yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623C2×C42C2412yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2418yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C24116yes—
637#95C2414yes—
638#95C2414yes—
639#95C24116yes—
640#95C24116yes—
641#95C24116yes—
642#95C24116yes—
643#95C24116yes—
644C24—22no—
645C24—24no—
646C24—22no—
647C24—22no—
648C24—42no—
649C24C2512yes—
650C24C2512yes—
651C24C2511yescharacteristic
652#41—416no—
653C2×Q8—264no—
654C2×Q8—24no—
655C2×Q8—24no—
656C2×Q8—28no—
657C2×Q8—28no—
658C2×Q8—22no—
659C2×Q8—28no—
660C2×Q8—28no—
661C2×Q8—22no—
662C2×Q8—28no—
663C2×Q8—28no—
664C2×Q8—28no—
665C2×Q8—22no—
666C2×Q8—28no—
667C2×Q8—216no—
668C2×Q8—48no—
669C2×Q8—432no—
670C2×Q8C22×D4116yes—
671C2×Q8C22×D4116yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—28no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—28no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—44no—
681C22×C4—232no—
682C22×C4—22no—
683C22×C4—28no—
684C22×C4—24no—
685C22×C4—28no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—28no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—28no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—48no—
719C22×C4—416no—
720C22×C4—416no—
721C22×C4C22×D414yes—
722C22×C4C22×D414yes—
723C22×C4C22×D4116yes—
724C22×C4C22×D414yes—
725C22×C4C2×#4114yes—
726C22×C42−1+418yes—
727C22×C42−1+414yes—
728C22×C4C2514yes—
729C22×C4C2518yes—
730C22×C4C2512yes—
731C22×C4C2512yes—
732C22×C4C2514yes—
733C22×C4C2512yes—
734C22×C4C2512yes—
735C22×C4C2518yes—
736C22×C4C2512yes—
737C22×C4C2514yes—
738C22×C4C2511yescharacteristic
739C22×C4C2511yescharacteristic
740C22×C4C2518yes—
741C22×C4C2514yes—
742C22×C4C2512yes—
743C22×C4C2511yescharacteristic
744C22×C4C2511yescharacteristic
745C22×C4C2511yescharacteristic
746C22×C4C2511yescharacteristic
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—232no—
750C4⋊C4—232no—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—24no—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—24no—
758C4⋊C4—24no—
759C4⋊C4—24no—
760C4⋊C4—24no—
761C4⋊C4—216no—
762C4⋊C4—216no—
763C4⋊C4—216no—
764C4⋊C4—216no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—232no—
768C4⋊C4—28no—
769C4⋊C4—28no—
770C4⋊C4—24no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—216no—
774C4⋊C4—28no—
775C4⋊C4—44no—
776C4⋊C4—416no—
777C4⋊C4—48no—
778C4⋊C4—416no—
779C4⋊C4—416no—
780C4⋊C4C22×D4116yes—
781C4⋊C4C22×D4116yes—
782C4⋊C4C22×D4116yes—
783C4⋊C4C22×D4116yes—
784C4⋊C4C2×#4118yes—
785C22⋊C4—24no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—24no—
789C22⋊C4—28no—
790C22⋊C4—216no—
791C22⋊C4—232no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—216no—
795C22⋊C4—216no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—416no—
803C22⋊C4C2×#4118yes—
804C42—24no—
805C42—24no—
806C42—24no—
807C42—24no—
808C42—24no—
809C42—24no—
810C42—232no—
811C42—24no—
812C42—24no—
813C42—24no—
814C42—216no—
815C42—216no—
816C42—28no—
817C42—232no—
818C42—28no—
819C42—24no—
820C42—28no—
821C42—28no—
822C42C22×D414yes—
823C42C22×D414yes—
824C42C22×D414yes—
825C42C22×D414yes—
826C42C2×#4118yes—
827C23—22no—
828C23—22no—
829C23—28no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—24no—
839C23—22no—
840C23—24no—
841C23—48no—
842C23—48no—
843C23—44no—
844C23—44no—
845C23C23×D412yes—
846C23C22×#4112yes—
847C23C2×2−1+414yes—
848C23C2×2−1+412yes—
849C23C2611yescharacteristic
850Q8—232no—
851Q8—232no—
852Q8—416no—
853Q8—44no—
854Q8—48no—
855Q8—48no—
856Q8—416no—
857D4—416no—
858D4—48no—
859D4—44no—
860C2×C4—216no—
861C2×C4—28no—
862C2×C4—22no—
863C2×C4—28no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—28no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—232no—
871C2×C4—28no—
872C2×C4—216no—
873C2×C4—28no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—28no—
881C2×C4—22no—
882C2×C4—28no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—28no—
888C2×C4—24no—
889C2×C4—28no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—28no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—28no—
897C2×C4—216no—
898C2×C4—22no—
899C2×C4—48no—
900C2×C4—44no—
901C2×C4—416no—
902C2×C4—44no—
903C2×C4—48no—
904C2×C4—48no—
905C2×C4—48no—
906C2×C4—48no—
907C2×C4—48no—
908C2×C4—48no—
909C2×C4#547116yes—
910C2×C4C23×D4116yes—
911C2×C4C23×D412yes—
912C2×C4C23×D412yes—
913C2×C4C23×D412yes—
914C2×C4C23×D412yes—
915C2×C4C23×D412yes—
916C2×C4C23×D412yes—
917C2×C4C22×#4118yes—
918C2×C4C22×#4112yes—
919C2×C4C22×#4112yes—
920C2×C4C2×2−1+414yes—
921C2×C4C2×2−1+412yes—
922C2×C4C2×2−1+412yes—
923C2×C4C2×2−1+414yes—
924C2×C4#58514yes—
925C22—22no—
926C22—22no—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—416no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—44no—
940C22—44no—
941C22—42no—
942C22C2×#54714yes—
943C22C24×D411yescharacteristic
944C22C23×#4111yescharacteristic
945C22C22×2−1+412yes—
946C22C22×2−1+411yescharacteristic
947C22C2×#58512yes—
948C4—22no—
949C4—24no—
950C4—22no—
951C4—28no—
952C4—216no—
953C4—42no—
954C4—44no—
955C4—42no—
956C4—42no—
957C4—48no—
958C4—44no—
959C4—48no—
960C4—44no—
961C4—42no—
962C4—42no—
963C4C2×#54714yes—
964C4C2×#54714yes—
965C4#348614yes—
966C4#348714yes—
967C2—24no—
968C2—44no—
969C2—82no—
970C2C22×#54711yescharacteristic
971C2C2×#348611yescharacteristic
972C2C2×#348711yescharacteristic
973C2#6280512yes—
974C2#6283712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
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×#3509C2semidirect
2. C22×#533C2semidirect
3. #59071C2semidirect
4. #59067C2semidirect
5. #59065C2semidirect
6. #59055C2semidirect
7. #38919C2semidirect
8. #38917C2semidirect
9. #37765C2semidirect
10. #36625C2semidirect
11. #36427C2semidirect
12. #36423C2semidirect
13. #36151C2semidirect
14. #36134C2semidirect
15. #35672C2semidirect
17. #35281C2semidirect
18. #35279C2semidirect
19. #35182C2semidirect
20. #34249C2semidirect
21. #34209C2semidirect
24. C2×#557C22semidirect
25. C2×#557C22semidirect
26. C2×#556C22semidirect
27. C2×#556C22semidirect
30. C2×#541C22semidirect
38. C2×#533C22semidirect
39. C2×#533C22semidirect
53. #2868C22semidirect
54. #2862C22semidirect
57. #2857C22semidirect
65. #2721C22semidirect
67. #2719C22semidirect
68. #2660C22semidirect
69. #2628C22semidirect
71. #2568C22semidirect
72. #2567C22semidirect
73. #2567C22semidirect
74. #2563C22semidirect
75. #2552C22semidirect
76. #2546C22semidirect
78. #2542C22semidirect
83. #2489C22semidirect
89. #2469C22semidirect
90. #2462C22semidirect
91. #2453C22semidirect
92. #2453C22semidirect
93. #2448C22semidirect
94. #2446C22semidirect
96. #2441C22semidirect
100. #2429C22semidirect
104. #2423C22semidirect
107. #2421C22semidirect
113. #2365C22semidirect
114. #2365C22semidirect
115. #2365C22semidirect
117. #2362C22semidirect
119. #2351C22semidirect
120. #2351C22semidirect
121. Q8×C4⋊C4C22semidirect
122. Q8×C4⋊C4C22semidirect
125. #2327C22semidirect
132. C4×C4⋊Q8C22semidirect
175. C2×C4⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C22×#5332
#590712
#590672
#590652
#590552
#389192
#389172
#377652
#366252
#364272
#364232
#361512
#361342
#356722
#356612
#352812
#352792
#351822
#342492
#342092
C4×#5252