Finite Group Databasebeta

← #7626936

Subgroups — #7626936

Order 512.

6358 conjugacy classes of subgroups.

The subgroup lattice has 989 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic
2#34507C218yesmaximal, complemented
3#34499C214yesmaximal, complemented
4#34488C212yesmaximal, complemented
5#34462C214yesmaximal, complemented
6#34445C218yesmaximal, complemented
7#34439C214yesmaximal
8#34403C212yesmaximal, complemented
9#34373C211yesmaximal, characteristic, complemented
10#34373C212yesmaximal, complemented
11#34371C211yesmaximal, characteristic, complemented
12#34337C212yesmaximal, complemented
13#34328C214yesmaximal, complemented
14#34324C212yesmaximal, complemented
15#34300C214yesmaximal, complemented
16#34262C214yesmaximal, complemented
17#34221C212yesmaximal, complemented
18#34216C211yesmaximal, characteristic, complemented
19#34193C211yesmaximal, characteristic
20C4×#556C212yesmaximal, complemented
21#34123C211yesmaximal, characteristic
22#34085C211yesmaximal, characteristic, complemented
23#34074C212yesmaximal, complemented
24#3509C4132yescomplemented
25C2×#557C2212yes—
26C2×#557C2212yes—
27C2×#556C2212yes—
28C2×#556C2212yes—
29C2×#552C2214yes—
30C2×#552C2214yes—
31C2×#541C2214yes—
32C2×#536C2212yes—
33C2×#533C2212yes—
34C2×#533C2211yescharacteristic
35C2×#533C2212yes—
36C22×C4⋊Q8C2211yescharacteristic
37C2×#519C2212yes—
38C2×C4×#41C2211yescharacteristic
39#2383C2218yes—
40#2382C2218yes—
41#2381C2214yes—
42#2378C2218yes—
43#2378C2214yes—
44#2378C2218yes—
45#2376C2218yes—
46#2374C2218yes—
47#2373C2218yes—
48#2373C2218yes—
49#2373C2218yes—
50#2371C2218yes—
51#2371C2218yes—
52#2370C2218yes—
53#2370C2214yes—
54#2370C2218yes—
55#2370C2214yes—
56#2369C2214yes—
57#2368C2218yes—
58#2367C2214yes—
59#2367C2214yes—
60#2365C2212yes—
61#2365C2214yes—
62#2365C2214yes—
63#2365C2214yes—
64#2365C2212yes—
65#2362C2214yes—
66#2362C2214yes—
67#2362C2214yes—
68#2356C2212yes—
69#2356C2218yes—
70#2356C2214yes—
71#2356C2218yes—
72#2355C2214yes—
73#2355C2214yes—
74#2355C2212yes—
75#2355C2218yes—
76#2355C2214yes—
77#2354C2212yes—
78#2354C2214yes—
79#2353C2214yes—
80#2351C2214yes—
81Q8×C4⋊C4C2212yes—
82Q8×C4⋊C4C2214yes—
83Q8×C4⋊C4C2212yes—
84Q8×C4⋊C4C2214yes—
85#2349C2212yes—
86#2347C2214yes—
87#2347C2214yes—
88#2347C2212yes—
89#2347C2218yes—
90#2346C2214yes—
91#2346C2212yes—
92#2346C2218yes—
93#2345C2214yes—
94#2345C2214yes—
95#2343C2214yes—
96#2343C2218yes—
97#2341C2212yes—
98Q8×C22⋊C4C2214yes—
99Q8×C22⋊C4C2214yes—
100#2339C2212yes—
101#2336C2218yes—
102#2336C2218yes—
103#2336C2214yes—
104#2336C2214yes—
105#2336C2218yes—
106#2335C2218yes—
107#2335C2218yes—
108#2334C2218yes—
109#2334C2218yes—
110#2334C2218yes—
111#2332C2214yes—
112#2332C2218yes—
113#2331C2211yescharacteristic
114#2331C2212yes—
115#2331C2212yes—
116#2331C2212yes—
117#2331C2211yescharacteristic
118#2331C2212yes—
119#2331C2212yes—
120#2330C2214yes—
121#2330C2214yes—
122#2330C2218yes—
123#2329C2218yes—
124#2329C2218yes—
125#2327C2214yes—
126#2327C2214yes—
127#2327C2211yescharacteristic
128#2327C2211yescharacteristic
129#2327C2212yes—
130#2326C2214yes—
131#2323C2212yes—
132#2323C2212yes—
133#2320C2218yes—
134#2320C2214yes—
135#2320C2214yes—
136#2319C2212yes—
137#2319C2214yes—
138#2316C2212yes—
139#2314C2214yes—
140#2314C2218yes—
141#2314C2218yes—
142#2313C2214yes—
143C4×C4⋊Q8C2212yes—
144C4×C4⋊Q8C2214yes—
145C4×C4⋊Q8C2212yes—
146C4×#125C2218yes—
147C4×#126C2218yes—
148C4×#124C2214yes—
149C4×C22⋊Q8C2214yes—
150C4×C22⋊Q8C2214yes—
151#2298C2214yes—
152#2298C2218yes—
153#2296C2214yes—
154#2295C2212yes—
155#2295C2218yes—
156#2295C2214yes—
157#2295C2218yes—
158#2295C2211yescharacteristic
159#2295C2214yes—
160#2295C2211yescharacteristic
161#2290C2212yes—
162#2290C2212yes—
163#2285C2212yes—
164#2285C2211yescharacteristic
165#2283C2211yescharacteristic
166#2283C2211yescharacteristic
167#2283C2212yes—
168#2283C2212yes—
169#2276C2214yes—
170#2276C2212yes—
171#2276C2214yes—
172#2274C2212yes—
173C42×Q8C2214yes—
174C42×Q8C2212yes—
175C42×D4C2211yescharacteristic
176C42×D4C2211yescharacteristic
177C4×#117C2214yes—
178C4×#117C2211yescharacteristic
179C2×#376C2212yes—
180C22×#41C2311yescharacteristic
181C23×Q8C2312yes—
182#557C2×C4132yescomplemented
183#557C2×C4132yescomplemented
184#556C2×C4132yes—
185#556C2×C4132yes—
186#552C2×C4164yescomplemented
187#552C2×C4164yescomplemented
188#541C2×C4164yescomplemented
189#536C2×C4132yes—
190#533C2×C4116yescomplemented
191#533C2×C4132yescomplemented
192#533C2×C4132yescomplemented
193C2×C4⋊Q8C2×C4116yescomplemented
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2311yescharacteristic
200C2×C4⋊Q8C2312yes—
201C2×#126C2318yes—
202C2×#126C2318yes—
203C2×#125C2318yes—
204C2×#125C2314yes—
205C2×#125C2318yes—
206C2×#125C2312yes—
207C2×#125C2314yes—
208C2×#124C2314yes—
209C2×#123C2318yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216#519C2×C4132yescomplemented
217C4×#41C2×C4116yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2314yes—
246C2×#117C2314yes—
247C2×#117C2312yes—
248C2×#117C2318yes—
249C2×#117C2312yes—
250C2×#117C2311yescharacteristic
251C2×#117C2314yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C42C2312yes—
255C22×C42C2312yes—
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#391C2312yes—
259#391C2314yes—
260#391C2314yes—
261#391C2312yes—
262#391C2314yes—
263#391C2314yes—
264#391C2318yes—
265#391C2318yes—
266#391C2312yes—
267#391C2314yes—
268#391C2312yes—
269#391C2314yes—
270#391C2318yes—
271#391C2318yes—
272#391C2318yes—
273#391C2314yes—
274#390C2314yes—
275#390C2318yes—
276#389C2314yes—
277#389C2318yes—
278#389C2314yes—
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2318yes—
283#389C2318yes—
284#389C2314yes—
285#389C2318yes—
286#389C2312yes—
287#389C2318yes—
288#389C2314yes—
289#389C2318yes—
290#389C2312yes—
291#389C2312yes—
292#389C2314yes—
293#389C2318yes—
294#389C2318yes—
295#389C2318yes—
296#389C2314yes—
297#389C2314yes—
298#389C2318yes—
299#389C2318yes—
300#389C2312yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2314yes—
305#388C2314yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2314yes—
314#388C2314yes—
315#388C2314yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2314yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2314yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2314yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2314yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2314yes—
343#387C2314yes—
344#387C2318yes—
345#387C2318yes—
346#387C2314yes—
347#387C2318yes—
348#387C2314yes—
349#387C2314yes—
350#387C2314yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2314yes—
355#387C2318yes—
356#387C2314yes—
357#387C2314yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2314yes—
362#387C2314yes—
363#386C2314yes—
364#386C2314yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2314yes—
370#385C2318yes—
371#384C2312yes—
372#384C2314yes—
373#384C2318yes—
374#384C2314yes—
375#383C2318yes—
376#383C2318yes—
377#383C2314yes—
378#383C2312yes—
379#383C2312yes—
380#383C2314yes—
381#382C2318yes—
382#382C2318yes—
383#382C2318yes—
384#382C2314yes—
385#382C2314yes—
386#382C2312yes—
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#382C2312yes—
390#381C2312yes—
391#381C2312yes—
392#381C2314yes—
393#381C2314yes—
394#380C2318yes—
395#380C2314yes—
396#380C2312yes—
397#380C2312yes—
398#380C2314yes—
399#380C2318yes—
400#380C2312yes—
401#380C2312yes—
402#380C2314yes—
403#380C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2318yes—
422C4×C4⋊C4C2318yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2318yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2312yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2312yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466#376C2312yes—
467#376C2314yes—
468#376C2312yes—
469#376C2314yes—
470#376C2318yes—
471#376C2311yescharacteristic
472#376C2312yes—
473#376C2311yescharacteristic
474#376C2312yes—
475#376C2318yes—
476#376C2314yes—
477#376C2318yes—
478#376C2314yes—
479C2×#95C2314yes—
480C2×#95C2314yes—
481C43C2318yes—
482C43C2311yescharacteristic
483C43C2311yescharacteristic
484C43C2314yes—
485C2×#41—44no—
486C2×#41C22×C418yes—
487C22×Q8—48no—
488C22×Q8C22×C4116yes—
489C22×Q8C2412yes—
490C22×Q8C2414yes—
491C22×Q8C2411yescharacteristic
492C22×Q8C2412yes—
493C22×Q8C2414yes—
494C22×D4C2411yescharacteristic
495C22×D4C2412yes—
496C23×C4C2411yescharacteristic
497C23×C4C2412yes—
498C23×C4C2411yescharacteristic
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C2411yescharacteristic
503C23×C4C2412yes—
504C23×C4C2412yes—
505C4⋊Q8C22×C4116yes—
506C4⋊Q8C22×C4116yes—
507C4⋊Q8C22×C4116yes—
508C4⋊Q8C22×C4116yes—
509C4⋊Q8C22×C418yes—
510C4⋊Q8C22×C418yes—
511C4⋊Q8C22×C4132yes—
512#126C22×C4164yes—
513#126C22×C4164yes—
514#125C22×C4116yes—
515#125C22×C4132yes—
516#125C22×C4132yes—
517#125C22×C4164yes—
518#125C22×C4164yes—
519#124C22×C4132yes—
520#123C22×C4164yes—
521C22⋊Q8C22×C4132yes—
522C22⋊Q8C22×C4132yes—
523C22⋊Q8C22×C4116yes—
524C22⋊Q8C22×C4116yes—
525C22⋊Q8C22×C4132yes—
526C22⋊Q8C22×C4132yes—
527C4×Q8—28no—
528C4×Q8—48no—
529C4×Q8—44no—
530C4×Q8—48no—
531C4×Q8—48no—
532C4×Q8—48no—
533C4×Q8—48no—
534C4×Q8—48no—
535C4×Q8C22×C418yes—
536C4×Q8C22×C418yes—
537C4×Q8C22×C4132yes—
538C4×Q8C22×C4132yes—
539C4×Q8C22×C4132yes—
540C4×Q8C22×C4132yes—
541C4×Q8C22×C4132yes—
542C4×Q8C22×C4132yes—
543C4×Q8C22×C4116yes—
544C4×Q8C22×C4116yes—
545C4×D4—44no—
546C4×D4—44no—
547C4×D4C22×C4116yes—
548C4×D4C22×C4116yes—
549C4×D4C22×C418yes—
550C4×D4C22×C418yes—
551#117—24no—
552#117—42no—
553#117—48no—
554#117—44no—
555#117C22×C418yes—
556#117C22×C4116yes—
557#117C22×C4116yes—
558#117C22×C4164yes—
559#117C22×C4132yes—
560#117C22×C4132yes—
561C2×C4⋊C4C22×C4116yes—
562C2×C4⋊C4C22×C4116yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C42—28no—
620C2×C42—44no—
621C2×C42C22×C418yes—
622C2×C42C22×C4116yes—
623C2×C42C2411yescharacteristic
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2414yes—
629C2×C42C2412yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2412yes—
633C2×C42C2418yes—
634C2×C42C2414yes—
635C2×C42C2418yes—
636C2×C42C2418yes—
637C2×C42C2414yes—
638C2×C42C2418yes—
639C2×C42C2418yes—
640C2×C42C2418yes—
641C2×C42C2418yes—
642C2×C42C2414yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2418yes—
646C2×C42C2414yes—
647C2×C42C2414yes—
648C2×C42C2412yes—
649C2×C42C2418yes—
650C2×C42C2418yes—
651C2×C42C2411yescharacteristic
652C2×C42C2414yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659#95C2412yes—
660#95C2412yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2412yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2414yes—
672#95C2418yes—
673#95C2412yes—
674#95C2418yes—
675#95C2412yes—
676#95C2418yes—
677#95C2412yes—
678#95C2414yes—
679#95C2418yes—
680#95C2414yes—
681#95C2418yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2418yes—
686#95C2412yes—
687#95C2414yes—
688#95C2412yes—
689#95C2412yes—
690#95C2414yes—
691#95C2418yes—
692#95C2414yes—
693#95C2412yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2414yes—
698#95C2418yes—
699#95C2418yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2414yes—
705#95C2414yes—
706C24C2511yescharacteristic
707C24C2512yes—
708#41—416no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—24no—
714C2×Q8—48no—
715C2×Q8—44no—
716C2×Q8—432no—
717C2×Q8C23×C418yes—
718C2×Q8C23×C4116yes—
719C2×Q8C23×C414yes—
720C2×Q8C23×C418yes—
721C2×Q8C23×C4116yes—
722C2×D4—24no—
723C2×D4—44no—
724C2×D4C23×C414yes—
725C2×D4C23×C418yes—
726C22×C4—24no—
727C22×C4—22no—
728C22×C4—24no—
729C22×C4—22no—
730C22×C4—24no—
731C22×C4—28no—
732C22×C4—42no—
733C22×C4—44no—
734C22×C4—48no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4C23×C414yes—
742C22×C4C23×C414yes—
743C22×C4C23×C418yes—
744C22×C4C23×C414yes—
745C22×C4C23×C418yes—
746C22×C4C23×C418yes—
747C22×C4C23×C4116yes—
748C22×C4C2514yes—
749C22×C4C2512yes—
750C22×C4C2514yes—
751C22×C4C2512yes—
752C22×C4C2514yes—
753C22×C4C2512yes—
754C22×C4C2514yes—
755C22×C4C2518yes—
756C22×C4C2511yescharacteristic
757C22×C4C2511yescharacteristic
758C22×C4C2512yes—
759C22×C4C2514yes—
760C22×C4C2514yes—
761C22×C4C2511yescharacteristic
762C22×C4C2511yescharacteristic
763C22×C4C2512yes—
764C22×C4C2518yes—
765C22×C4C2512yes—
766C22×C4C2512yes—
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C4⋊C4—24no—
770C4⋊C4—28no—
771C4⋊C4—24no—
772C4⋊C4—28no—
773C4⋊C4—24no—
774C4⋊C4—24no—
775C4⋊C4—24no—
776C4⋊C4—28no—
777C4⋊C4—44no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—48no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—48no—
784C4⋊C4—42no—
785C4⋊C4—48no—
786C4⋊C4—44no—
787C4⋊C4—48no—
788C4⋊C4—48no—
789C4⋊C4—48no—
790C4⋊C4—48no—
791C4⋊C4—48no—
792C4⋊C4C23×C4116yes—
793C4⋊C4C23×C4116yes—
794C4⋊C4C23×C4116yes—
795C4⋊C4C23×C4116yes—
796C4⋊C4C23×C418yes—
797C4⋊C4C23×C418yes—
798C4⋊C4C23×C414yes—
799C4⋊C4C23×C414yes—
800C4⋊C4C23×C418yes—
801C4⋊C4C23×C418yes—
802C4⋊C4C23×C418yes—
803C4⋊C4C23×C418yes—
804C4⋊C4C23×C4132yes—
805C4⋊C4C23×C4132yes—
806C4⋊C4C23×C4132yes—
807C4⋊C4C23×C4132yes—
808C4⋊C4C23×C4116yes—
809C4⋊C4C23×C4116yes—
810C22⋊C4—24no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—48no—
814C22⋊C4—42no—
815C22⋊C4—44no—
816C22⋊C4—48no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4C23×C418yes—
820C22⋊C4C23×C4116yes—
821C22⋊C4C23×C418yes—
822C22⋊C4C23×C418yes—
823C22⋊C4C23×C4132yes—
824C22⋊C4C23×C4132yes—
825C42—28no—
826C42—24no—
827C42—22no—
828C42—28no—
829C42—22no—
830C42—24no—
831C42—22no—
832C42—24no—
833C42—24no—
834C42—28no—
835C42—44no—
836C42—44no—
837C42—48no—
838C42—42no—
839C42—44no—
840C42—42no—
841C42—48no—
842C42—44no—
843C42—48no—
844C42—48no—
845C42—44no—
846C42—48no—
847C42—48no—
848C42—48no—
849C42—48no—
850C42C23×C414yes—
851C42C23×C418yes—
852C42C23×C414yes—
853C42C23×C418yes—
854C42C23×C418yes—
855C42C23×C414yes—
856C42C23×C414yes—
857C42C23×C4132yes—
858C42C23×C4132yes—
859C42C23×C4116yes—
860C422−1+414yes—
861C23—21no—
862C23—22no—
863C23—21no—
864C23—22no—
865C23—24no—
866C23—22no—
867C23—22no—
868C23—24no—
869C23C24×C414yes—
870C23C24×C412yes—
871C23C2611yescharacteristic
872Q8—232no—
873Q8—28no—
874Q8—216no—
875Q8—416no—
876Q8—48no—
877D4—28no—
878D4—48no—
879C2×C4—22no—
880C2×C4—24no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—21no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—22no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—22no—
896C2×C4—28no—
897C2×C4—216no—
898C2×C4—28no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—28no—
912C2×C4—28no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—28no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—44no—
924C2×C4—48no—
925C2×C4—416no—
926C2×C4—48no—
927C2×C4—88no—
928C2×C4—88no—
929C2×C4C24×C414yes—
930C2×C4C24×C414yes—
931C2×C4C24×C412yes—
932C2×C4C24×C412yes—
933C2×C4C24×C418yes—
934C2×C4C24×C418yes—
935C2×C4C24×C412yes—
936C2×C4C24×C412yes—
937C2×C4C24×C4116yes—
938C2×C4C24×C414yes—
939C2×C4C24×C412yes—
940C2×C4C24×C412yes—
941C2×C4C2×2−1+414yes—
942C2×C4C2×2−1+412yes—
943C2×C4#58514yes—
944C2×C4#58512yes—
945C22—22no—
946C22—24no—
947C22—22no—
948C22—24no—
949C22—22no—
950C22—24no—
951C22—44no—
952C22—42no—
953C22—44no—
954C22—42no—
955C22C25×C411yescharacteristic
956C22C22×2−1+411yescharacteristic
957C22C2×#58512yes—
958C22C2×#58511yescharacteristic
959C222−1+612yes—
960C4—22no—
961C4—24no—
962C4—216no—
963C4—24no—
964C4—22no—
965C4—28no—
966C4—22no—
967C4—22no—
968C4—24no—
969C4—28no—
970C4—24no—
971C4—42no—
972C4—44no—
973C4—44no—
974C4—42no—
975C4—44no—
976C4—48no—
977C4—44no—
978C4—42no—
979C4#342814yes—
980C4C4×2−1+414yes—
981C2—42no—
982C2—44no—
983C2C2×#342811yescharacteristic
984C2C2×C4×2−1+411yescharacteristic
985C2#6265311yescharacteristic
986C2#6295912yes—
987C2#6296712yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC22×#41C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34507C2semidirect
3. #34499C2semidirect
4. #34488C2semidirect
5. #34462C2semidirect
6. #34445C2semidirect
8. #34403C2semidirect
9. #34373C2semidirect
10. #34373C2semidirect
11. #34371C2semidirect
12. #34337C2semidirect
13. #34328C2semidirect
14. #34324C2semidirect
15. #34300C2semidirect
16. #34262C2semidirect
17. #34221C2semidirect
18. #34216C2semidirect
20. C4×#556C2semidirect
22. #34085C2semidirect
23. #34074C2semidirect
24. #3509C4semidirect
182. #557C2×C4semidirect
183. #557C2×C4semidirect
186. #552C2×C4semidirect
187. #552C2×C4semidirect
188. #541C2×C4semidirect
190. #533C2×C4semidirect
191. #533C2×C4semidirect
192. #533C2×C4semidirect
193. C2×C4⋊Q8C2×C4semidirect
216. #519C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
#345072
#344992
#344882
#344622
#344452
#344392
#344032
#343732
#343712
#343372
#343282
#343242
#343002
#342622
#342212
#342162
#341932
C4×#5562
#341232
#340852
#340742