Finite Group Databasebeta

← #7630381

Subgroups — #7630381

Order 512.

5294 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36640C211yesmaximal, characteristic, complemented
2#36635C212yesmaximal, complemented
3#36600C211yesmaximal, characteristic, complemented
4#36565C211yesmaximal, characteristic, complemented
5#36497C212yesmaximal, complemented
6#36479C214yesmaximal, complemented
7#36407C212yesmaximal, complemented
8#36363C214yesmaximal, complemented
9#36283C214yesmaximal, complemented
10#36281C218yesmaximal, complemented
11#36192C211yesmaximal, characteristic, complemented
12#36191C212yesmaximal, complemented
13#36132C211yesmaximal, characteristic, complemented
14#36131C212yesmaximal, complemented
15#34938C212yesmaximal, complemented
16#34912C214yesmaximal, complemented
17#34882C218yesmaximal, complemented
18#34745C214yesmaximal
19#34145C214yesmaximal, complemented
20#34121C212yesmaximal
21C4×#533C212yesmaximal, complemented
22C2×C4×#125C211yesmaximal, characteristic, complemented
23C42×#41C211yesmaximal, characteristic
24C2×#533C2212yes—
25C2×#533C2214yes—
26C22×#125C2211yescharacteristic
27C2×C4×#41C2212yes—
28C2×C4×#41C2211yescharacteristic
29#2864C2214yes—
30#2864C2214yes—
31#2863C2218yes—
32#2862C2212yes—
33#2859C2212yes—
34#2859C2211yescharacteristic
35#2859C2212yes—
36#2859C2211yescharacteristic
37#2857C2214yes—
38#2855C2218yes—
39#2851C2212yes—
40#2851C2212yes—
41#2851C2212yes—
42#2851C2212yes—
43#2851C2214yes—
44#2608C2218yes—
45#2607C2218yes—
46#2606C2218yes—
47#2605C2218yes—
48#2586C2218yes—
49#2586C2218yes—
50#2585C2218yes—
51#2585C2218yes—
52#2574C2218yes—
53#2574C2218yes—
54#2570C2214yes—
55#2570C2214yes—
56#2556C2218yes—
57#2556C2218yes—
58#2552C2212yes—
59#2552C2212yes—
60#2551C2212yes—
61#2551C2212yes—
62#2550C2214yes—
63#2550C2214yes—
64#2550C2214yes—
65#2550C2214yes—
66#2549C2218yes—
67#2522C2218yes—
68#2522C2218yes—
69#2520C2218yes—
70#2520C2218yes—
71#2465C2218yes—
72#2465C2218yes—
73#2462C2218yes—
74#2462C2218yes—
75#2454C2214yes—
76#2454C2214yes—
77#2453C2214yes—
78#2453C2214yes—
79#2452C2214yes—
80#2452C2214yes—
81#2451C2214yes—
82#2451C2214yes—
83#2450C2218yes—
84#2450C2218yes—
85#2449C2218yes—
86#2449C2218yes—
87#2441C2214yes—
88#2441C2214yes—
89#2440C2214yes—
90#2440C2214yes—
91#2439C2214yes—
92#2439C2214yes—
93#2399C2218yes—
94#2396C2218yes—
95#2396C2218yes—
96#2370C2214yes—
97#2370C2214yes—
98#2370C2214yes—
99#2370C2214yes—
100#2369C2214yes—
101#2369C2214yes—
102#2368C2218yes—
103#2368C2218yes—
104#2365C2214yes—
105#2365C2214yes—
106#2360C2218yes—
107#2360C2218yes—
108#2357C2214yes—
109#2356C2214yes—
110#2355C2212yes—
111#2355C2212yes—
112#2354C2212yes—
113#2354C2212yes—
114#2353C2218yes—
115#2352C2214yes—
116#2352C2214yes—
117C4×C4⋊Q8C2214yes—
118C4×C4⋊Q8C2214yes—
119C4×C4⋊Q8C2214yes—
120C4×#125C2211yescharacteristic
121C4×#125C2212yes—
122C4×#125C2214yes—
123C4×#125C2212yes—
124C4×#125C2212yes—
125C4×#125C2211yescharacteristic
126C4×#125C2212yes—
127C4×#125C2214yes—
128C4×#125C2212yes—
129C4×#125C2212yes—
130C4×#125C2211yescharacteristic
131C4×#125C2214yes—
132C4×#125C2211yescharacteristic
133C4×C22⋊Q8C2218yes—
134C4×C22⋊Q8C2218yes—
135C4×C22⋊Q8C2218yes—
136#2298C2218yes—
137#2297C2214yes—
138#2296C2214yes—
139#2296C2214yes—
140#2296C2214yes—
141#2295C2218yes—
142#2295C2218yes—
143#2295C2218yes—
144#2295C2218yes—
145C2×#389C2212yes—
146C2×#387C2214yes—
147#2285C2212yes—
148#2285C2212yes—
149#2283C2214yes—
150C2×#382C2211yescharacteristic
151C42×Q8C2218yes—
152C42×Q8C2211yescharacteristic
153C42×Q8C2212yes—
154C42×Q8C2211yescharacteristic
155C42×D4C2212yes—
156C42×D4C2212yes—
157C42×D4C2211yescharacteristic
158C42×D4C2211yescharacteristic
159C42×D4C2212yes—
160C42×D4C2214yes—
161C4×#117C2214yes—
162C4×#117C2214yes—
163C4×#117C2214yes—
164C4×#117C2212yes—
165C4×#117C2212yes—
166C4×#117C2211yescharacteristic
167C2×C4×C4⋊C4C2212yes—
168C2×C4×C4⋊C4C2214yes—
169C2×C43C2212yes—
170C2×C43C2211yescharacteristic
171C22×#41C2311yescharacteristic
172#533—216no—
173#533—232no—
174C2×C4⋊Q8C2314yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×#125—28no—
179C2×#125C2311yescharacteristic
180C2×#125C2312yes—
181C2×#125C2312yes—
182C2×#125C2314yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#125C2312yes—
186C2×#125C2314yes—
187C2×#125C2311yescharacteristic
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2318yes—
192C4×#41—216no—
193C4×#41Q8116yescomplemented
194C2×C4×Q8C2318yes—
195C2×C4×Q8C2318yes—
196C2×C4×Q8C2318yes—
197C2×C4×Q8C2312yes—
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2318yes—
200C2×C4×Q8C2311yescharacteristic
201C2×C4×Q8C2311yescharacteristic
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2312yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2311yescharacteristic
209C2×C4×D4C2311yescharacteristic
210C2×#117C2314yes—
211C2×#117C2314yes—
212C2×#117C2314yes—
213C2×#117C2314yes—
214C2×#117C2311yescharacteristic
215C2×#117C2312yes—
216C2×#117C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2314yes—
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2314yes—
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223C22×C42C2312yes—
224C22×C42C2314yes—
225C22×C42C2314yes—
226C22×C42C2312yes—
227C22×C42C2311yescharacteristic
228C22×C42C2314yes—
229C22×C42C2312yes—
230C22×C42C2311yescharacteristic
231C22×C42C2312yes—
232#400C2318yes—
233#400C2318yes—
234#399C2318yes—
235#399C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#395C2318yes—
249#395C2318yes—
250#395C2318yes—
251#395C2318yes—
252#395C2318yes—
253#395C2318yes—
254#393C2318yes—
255#393C2318yes—
256#391C2318yes—
257#391C2318yes—
258#391C2318yes—
259#391C2318yes—
260#391C2318yes—
261#391C2318yes—
262#391C2318yes—
263#391C2318yes—
264#391C2318yes—
265#391C2318yes—
266#391C2314yes—
267#391C2314yes—
268#390C2314yes—
269#390C2314yes—
270#389C2312yes—
271#389C2312yes—
272#389C2314yes—
273#389C2314yes—
274#389C2312yes—
275#389C2312yes—
276#389C2314yes—
277#389C2314yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2318yes—
284#389C2314yes—
285#389C2318yes—
286#389C2318yes—
287#389C2318yes—
288#389C2318yes—
289#389C2318yes—
290#389C2318yes—
291#389C2318yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#389C2318yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#387C2314yes—
307#387C2314yes—
308#387C2314yes—
309#387C2314yes—
310#387C2314yes—
311#387C2314yes—
312#387C2314yes—
313#387C2314yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#386C2318yes—
339#386C2318yes—
340#385C2318yes—
341#385C2318yes—
342#385C2318yes—
343#385C2318yes—
344#385C2318yes—
345#385C2318yes—
346#385C2318yes—
347#385C2318yes—
348#384C2314yes—
349#384C2314yes—
350#384C2312yes—
351#384C2312yes—
352#383C2318yes—
353#382C2311yescharacteristic
354#382C2312yes—
355#382C2314yes—
356#382C2312yes—
357#382C2311yescharacteristic
358#382C2312yes—
359#382C2314yes—
360#382C2314yes—
361#382C2314yes—
362#382C2314yes—
363#381C2318yes—
364#380C2318yes—
365#380C2318yes—
366#380C2314yes—
367#380C2314yes—
368#380C2314yes—
369#380C2314yes—
370C4×C4⋊C4C2312yes—
371C4×C4⋊C4C2312yes—
372C4×C4⋊C4C2314yes—
373C4×C4⋊C4C2312yes—
374C4×C4⋊C4C2312yes—
375C4×C4⋊C4C2314yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2314yes—
378C4×C4⋊C4C2314yes—
379C4×C4⋊C4C2314yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2314yes—
382C4×C4⋊C4C2318yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2314yes—
385C4×C4⋊C4C2314yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2318yes—
388C4×C4⋊C4C2314yes—
389C4×C4⋊C4C2314yes—
390C4×C4⋊C4C2318yes—
391C4×C4⋊C4C2318yes—
392C4×C4⋊C4C2318yes—
393C4×C4⋊C4C2318yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2312yes—
397C4×C4⋊C4C2318yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2312yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2312yes—
432#376C2318yes—
433#376C2312yes—
434#376C2314yes—
435#376C2318yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C43C2311yescharacteristic
440C43C2312yes—
441C43C2311yescharacteristic
442C43C2311yescharacteristic
443C43C2311yescharacteristic
444C43C2312yes—
445C43C2312yes—
446C43C2312yes—
447C43C2312yes—
448C43C2314yes—
449C43C2314yes—
450C43C2318yes—
451C2×#41—28no—
452C2×#41C2×Q818yes—
453C22×Q8C2418yes—
454C22×Q8C2411yescharacteristic
455C22×Q8C2418yes—
456C22×D4C2412yes—
457C22×D4C2411yescharacteristic
458C23×C4C2414yes—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2414yes—
462C23×C4C2414yes—
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2414yes—
467C23×C4C2411yescharacteristic
468C23×C4C2412yes—
469C23×C4C2411yescharacteristic
470C4⋊Q8—216no—
471C4⋊Q8—216no—
472C4⋊Q8—216no—
473C4⋊Q8—48no—
474#125—28no—
475#125—216no—
476#125—216no—
477#125—216no—
478#125—24no—
479#125—28no—
480#125—44no—
481#125—48no—
482#125#4118yescomplemented
483C22⋊Q8—232no—
484C22⋊Q8—232no—
485C22⋊Q8—232no—
486C22⋊Q8—416no—
487C4×Q8—28no—
488C4×Q8—28no—
489C4×Q8—232no—
490C4×Q8—232no—
491C4×Q8—232no—
492C4×Q8—416no—
493C4×Q8C2×Q818yes—
494C4×Q8C2×Q818yes—
495C4×D4—28no—
496C4×D4—28no—
497C4×D4—216no—
498C4×D4—216no—
499C4×D4C2×Q8116yes—
500C4×D4C2×Q818yes—
501C4×D4C2×Q8116yes—
502C4×D4C2×Q818yes—
503#117—216no—
504#117—216no—
505#117—216no—
506#117—48no—
507#117C2×Q8116yes—
508#117C2×Q818yes—
509#117#41116yes—
510C2×C4⋊C4—28no—
511C2×C4⋊C4—216no—
512C2×C4⋊C4—44no—
513C2×C4⋊C4—48no—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2414yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2411yescharacteristic
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2418yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2418yes—
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2412yes—
565C2×C22⋊C4C2412yes—
566C2×C22⋊C4C2414yes—
567C2×C42—28no—
568C2×C42—216no—
569C2×C42—216no—
570C2×C42—24no—
571C2×C42—28no—
572C2×C42—48no—
573C2×C42—42no—
574C2×C42—44no—
575C2×C42—44no—
576C2×C42C2×Q8116yes—
577C2×C42C2×Q818yes—
578C2×C42C2418yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2414yes—
582C2×C42C2414yes—
583C2×C42C2414yes—
584C2×C42C2414yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2411yescharacteristic
588C2×C42C2411yescharacteristic
589C2×C42C2414yes—
590C2×C42C2412yes—
591C2×C42C2412yes—
592C2×C42C2414yes—
593C2×C42C2412yes—
594C2×C42C2411yescharacteristic
595C2×C42C2412yes—
596C2×C42C2418yes—
597C2×C42C2414yes—
598C2×C42C2414yes—
599C2×C42C2412yes—
600C2×C42C2418yes—
601C2×C42C2418yes—
602C2×C42C2418yes—
603C2×C42C2414yes—
604C2×C42C2414yes—
605C2×C42C2412yes—
606C2×C42C2412yes—
607C2×C42C2412yes—
608C2×C42C2414yes—
609C2×C42C2412yes—
610C2×C42C2411yescharacteristic
611C2×C42C2412yes—
612C2×C42C2411yescharacteristic
613C2×C42C2412yes—
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2412yes—
635#95C2414yes—
636#95C2412yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655C24C2512yes—
656C24C2511yescharacteristic
657#41—232no—
658C2×Q8—24no—
659C2×Q8—216no—
660C2×Q8—216no—
661C2×Q8—216no—
662C2×Q8—48no—
663C2×Q8—48no—
664C2×Q8—48no—
665C2×Q8C22×Q814yes—
666C2×D4—28no—
667C2×D4—24no—
668C2×D4C22×Q818yes—
669C2×D4C22×Q814yes—
670C22×C4—22no—
671C22×C4—24no—
672C22×C4—28no—
673C22×C4—22no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—24no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—28no—
684C22×C4—24no—
685C22×C4—28no—
686C22×C4—44no—
687C22×C4—42no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4C22×Q818yes—
696C22×C4C22×Q818yes—
697C22×C4C22×Q814yes—
698C22×C4C22×Q818yes—
699C22×C4C22×Q814yes—
700C22×C4C22×Q814yes—
701C22×C4C2×#4118yes—
702C22×C4C2514yes—
703C22×C4C2512yes—
704C22×C4C2512yes—
705C22×C4C2514yes—
706C22×C4C2518yes—
707C22×C4C2518yes—
708C22×C4C2514yes—
709C22×C4C2511yescharacteristic
710C22×C4C2512yes—
711C22×C4C2512yes—
712C22×C4C2512yes—
713C22×C4C2511yescharacteristic
714C22×C4C2511yescharacteristic
715C22×C4C2512yes—
716C22×C4C2514yes—
717C22×C4C2514yes—
718C22×C4C2514yes—
719C22×C4C2512yes—
720C22×C4C2511yescharacteristic
721C22×C4C2511yescharacteristic
722C22×C4C2511yescharacteristic
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—24no—
728C4⋊C4—28no—
729C4⋊C4—28no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—216no—
734C4⋊C4—216no—
735C4⋊C4—216no—
736C4⋊C4—216no—
737C4⋊C4—216no—
738C4⋊C4—216no—
739C4⋊C4—216no—
740C4⋊C4—216no—
741C4⋊C4—24no—
742C4⋊C4—28no—
743C4⋊C4—28no—
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—216no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C4⋊C4—44no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4C22×Q818yes—
758C4⋊C4C22×Q818yes—
759C4⋊C4C22×Q814yes—
760C4⋊C4C22×Q814yes—
761C4⋊C4C2×#4118yes—
762C4⋊C4C2×#41116yes—
763C4⋊C4C2×#4118yes—
764C4⋊C4C2×#4118yes—
765C22⋊C4—216no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—216no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—48no—
772C22⋊C4C22×Q818yes—
773C22⋊C4C22×Q818yes—
774C22⋊C4C22×Q818yes—
775C22⋊C4C2×#41116yes—
776C42—24no—
777C42—24no—
778C42—28no—
779C42—28no—
780C42—24no—
781C42—24no—
782C42—28no—
783C42—28no—
784C42—28no—
785C42—24no—
786C42—28no—
787C42—22no—
788C42—24no—
789C42—28no—
790C42—216no—
791C42—216no—
792C42—24no—
793C42—22no—
794C42—28no—
795C42—24no—
796C42—22no—
797C42—24no—
798C42—44no—
799C42—42no—
800C42—44no—
801C42—44no—
802C42—42no—
803C42—42no—
804C42—48no—
805C42—48no—
806C42—48no—
807C42C22×Q814yes—
808C42C22×Q818yes—
809C42C22×Q814yes—
810C42C22×Q818yes—
811C42C22×Q814yes—
812C42C22×Q818yes—
813C42C22×Q814yes—
814C42C2×#4114yes—
815C42C2×#41116yes—
816C23—21no—
817C23—22no—
818C23—21no—
819C23—22no—
820C23—24no—
821C23—24no—
822C23—22no—
823C23C23×Q814yes—
824C23C23×Q812yes—
825C23C22×#4114yes—
826C23C2611yescharacteristic
827Q8—28no—
828Q8—432no—
829Q8—816no—
830D4—216no—
831D4—28no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—21no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—21no—
849C2×C4—24no—
850C2×C4—216no—
851C2×C4—28no—
852C2×C4—216no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—24no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—44no—
875C2×C4—48no—
876C2×C4—416no—
877C2×C4—416no—
878C2×C4—48no—
879C2×C4—48no—
880C2×C4—416no—
881C2×C4—88no—
882C2×C4#533116yescomplemented
883C2×C4C23×Q812yes—
884C2×C4C23×Q814yes—
885C2×C4C23×Q812yes—
886C2×C4C23×Q814yes—
887C2×C4C23×Q812yes—
888C2×C4C23×Q814yes—
889C2×C4C23×Q812yes—
890C2×C4C23×Q812yes—
891C2×C4C23×Q812yes—
892C2×C4C22×#4114yes—
893C2×C4C22×#4118yes—
894C2×C4C22×#4118yes—
895C2×C4C22×#4118yes—
896C2×C4C22×#4114yes—
897C2×C4C22×#4114yes—
898C2×C4C22×#4112yes—
899C2×C4#58514yes—
900C2×C4#58512yes—
901C22—22no—
902C22—24no—
903C22—22no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—44no—
909C22—44no—
910C22C2×#53314yes—
911C22C24×Q811yescharacteristic
912C22C23×#4112yes—
913C22C23×#4111yescharacteristic
914C22C2×#58512yes—
915C22C2×#58511yescharacteristic
916C4—22no—
917C4—24no—
918C4—22no—
919C4—24no—
920C4—28no—
921C4—24no—
922C4—24no—
923C4—22no—
924C4—24no—
925C4—28no—
926C4—28no—
927C4—42no—
928C4—44no—
929C4—44no—
930C4—48no—
931C4—42no—
932C4—44no—
933C4—48no—
934C4C2×#53314yes—
935C4C2×#53314yes—
936C4Q8×#4114yes—
937C2—24no—
938C2—44no—
939C2C22×#53311yescharacteristic
940C2C2×Q8×#4111yescharacteristic
941C2#41212yes—
942C2#6281311yescharacteristic
943C2#6281612yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #36640C2semidirect
2. #36635C2semidirect
3. #36600C2semidirect
4. #36565C2semidirect
5. #36497C2semidirect
6. #36479C2semidirect
7. #36407C2semidirect
8. #36363C2semidirect
9. #36283C2semidirect
10. #36281C2semidirect
11. #36192C2semidirect
12. #36191C2semidirect
13. #36132C2semidirect
14. #36131C2semidirect
15. #34938C2semidirect
16. #34912C2semidirect
17. #34882C2semidirect
19. #34145C2semidirect
21. C4×#533C2semidirect
22. C2×C4×#125C2semidirect
193. C4×#41Q8semidirect
482. #125#41semidirect
882. C2×C4#533semidirect

Maximal subgroups

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

subgroupindex
#366402
#366352
#366002
#365652
#364972
#364792
#364072
#363632
#362832
#362812
#361922
#361912
#361322
#361312
#349382
#349122
#348822
#347452
#341452
#341212
C4×#5332
C2×C4×#1252
C42×#412