Finite Group Databasebeta

← #7626316

Subgroups — #7626316

Order 512.

7080 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3538C211yesmaximal, characteristic
2#34516C218yesmaximal, complemented
3#34432C214yesmaximal, complemented
4#34427C214yesmaximal, complemented
5#34421C212yesmaximal, complemented
6#34413C212yesmaximal, complemented
7#34380C212yesmaximal, complemented
8#34360C211yesmaximal, characteristic
9#34334C214yesmaximal, complemented
10#34314C214yesmaximal, complemented
11#34304C214yesmaximal, complemented
12#34296C218yesmaximal, complemented
13#34291C214yesmaximal, complemented
14#34281C212yesmaximal, complemented
15#34278C214yesmaximal, complemented
16#34271C214yesmaximal, complemented
17#34268C212yesmaximal, complemented
18C4×#525C211yesmaximal, characteristic
19C2×C4×C22⋊Q8C212yesmaximal, complemented
20#3538C4132yescomplemented
21C2×#563C2214yes—
22C2×#552C2214yes—
23C2×#551C2214yes—
24C2×D4×Q8C2214yes—
25C2×#544C2214yes—
26C2×#541C2212yes—
27C2×#539C2214yes—
28C2×#536C2212yes—
29C2×#525C2211yescharacteristic
30C22×C22⋊Q8C2212yes—
31C2×#519C2212yescomplemented
32C2×C4×#41C2211yescharacteristic
33C22×C4×Q8C2212yes—
34C23×C42C2211yescharacteristic
35#2382C2218yescomplemented
36#2381C2214yescomplemented
37#2378C2218yes—
38#2376C2214yes—
39#2376C2214yescomplemented
40#2374C2214yescomplemented
41#2373C2218yes—
42#2373C2218yes—
43#2373C2218yescomplemented
44#2373C2218yescomplemented
45#2371C2218yescomplemented
46#2370C2214yescomplemented
47#2370C2218yescomplemented
48#2370C2218yescomplemented
49#2370C2218yescomplemented
50#2370C2218yescomplemented
51#2369C2218yescomplemented
52#2369C2214yescomplemented
53#2368C2218yes—
54#2368C2218yescomplemented
55#2367C2218yes—
56#2365C2214yescomplemented
57#2365C2218yescomplemented
58#2365C2218yescomplemented
59#2362C2214yescomplemented
60#2362C2218yescomplemented
61#2360C2214yes—
62#2360C2214yes—
63#2360C2218yes—
64#2360C2214yescomplemented
65#2359C2218yes—
66#2359C2218yes—
67#2359C2218yes—
68#2359C2218yescomplemented
69#2358C2214yes—
70#2355C2214yescomplemented
71#2352C2214yes—
72#2352C2218yes—
73#2351C2214yescomplemented
74#2349C2218yes—
75D4×C4⋊C4C2214yes—
76#2347C2214yescomplemented
77#2344C2214yes—
78#2343C2218yes—
79#2343C2218yes—
80#2342C2218yes—
81Q8×C22⋊C4C2214yes—
82Q8×C22⋊C4C2214yescomplemented
83#2337C2218yes—
84#2336C2218yescomplemented
85#2336C2218yescomplemented
86#2335C2218yes—
87#2334C2218yes—
88#2334C2218yes—
89#2334C2218yescomplemented
90#2334C2218yescomplemented
91#2331C2218yescomplemented
92#2330C2212yescomplemented
93#2329C2218yes—
94#2329C2214yes—
95#2329C2214yes—
96#2329C2214yes—
97#2329C2218yescomplemented
98#2327C2218yescomplemented
99#2327C2212yescomplemented
100#2325C2214yes—
101#2323C2214yes—
102#2323C2214yes—
103#2323C2214yescomplemented
104#2323C2218yescomplemented
105#2322C2218yes—
106#2316C2214yes—
107#2314C2212yes—
108#2313C2214yes—
109#2311C2212yes—
110C4×C4⋊Q8C2212yescomplemented
111C4×#125C2212yescomplemented
112C4×C22⋊Q8C2214yes—
113C4×C22⋊Q8C2214yes—
114C4×C22⋊Q8C2214yes—
115C4×C22⋊Q8C2214yes—
116C4×C22⋊Q8C2212yes—
117C4×C22⋊Q8C2214yes—
118C4×C22⋊Q8C2214yes—
119C4×C22⋊Q8C2214yes—
120C4×C22⋊Q8C2212yes—
121C4×C22⋊Q8C2214yes—
122C4×C22⋊Q8C2218yes—
123C4×C22⋊Q8C2214yescomplemented
124C4×#123C2218yes—
125C4×#123C2214yes—
126C4×#121C2212yes—
127C4×#121C2212yes—
128C4×#120C2214yes—
129#2297C2211yescharacteristic
130#2296C2218yes—
131#2296C2211yescharacteristic
132#2296C2212yescomplemented
133#2295C2214yescomplemented
134C2×#391C2212yes—
135C2×#391C2212yescomplemented
136C2×#389C2212yes—
137#2290C2214yes—
138#2290C2218yes—
139C2×#387C2214yes—
140C2×#385C2214yes—
141#2280C2211yescharacteristic
142C2×#380C2212yes—
143#2276C2214yescomplemented
144#2275C2218yes—
145#2274C2218yes—
146#2274C2212yescomplemented
147C42×D4C2214yes—
148C4×#117C2211yescharacteristic
149C2×C4×C4⋊C4C2212yes—
150C2×C4×C4⋊C4C2214yes—
151C2×C4×C22⋊C4C2214yes—
152C22×#41C2311yescharacteristic
153C23×Q8C2312yes—
154C23×Q8C2312yes—
155C24×C4C2312yes—
156C24×C4C2311yescharacteristic
157#563C2×C4164yescomplemented
158#552C2×C4164yescomplemented
159#551C2×C4164yescomplemented
160D4×Q8C2×C4164yescomplemented
161#544C2×C4164yescomplemented
162#541C2×C4132yescomplemented
163#539C2×C4164yescomplemented
164#536C2×C4132yescomplemented
165C2×C4⋊Q8C2312yes—
166C2×C4⋊Q8C2318yes—
167C2×C4⋊Q8C2314yes—
168C2×#126C2318yes—
169C2×#126C2318yes—
170C2×#125C2312yes—
171C2×#125C2318yes—
172C2×#125C2318yes—
173C2×#124C2314yes—
174#525C2×C4116yes—
175C2×#123C2318yes—
176C2×#123C2314yes—
177C2×#123C2312yes—
178C2×#123C2314yes—
179C2×C22⋊Q8C2×C4132yescomplemented
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2312yes—
183C2×C22⋊Q8C2318yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2318yes—
187C2×C22⋊Q8C2314yes—
188C2×#121C2312yes—
189C2×#120C2312yes—
190#519—48no—
191C4×#41—44no—
192C2×C4×Q8—48no—
193C2×C4×Q8C2314yes—
194C2×C4×Q8C2314yes—
195C2×C4×Q8C2314yes—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2318yes—
198C2×C4×Q8C2314yes—
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2312yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2318yes—
209C2×#117C2312yes—
210C2×#117C2312yes—
211C2×#117C2318yes—
212C2×#117C2311yescharacteristic
213C2×#117C2311yescharacteristic
214C2×#117C2318yes—
215C2×#117C2311yescharacteristic
216C2×#117C2318yes—
217C2×#117C2312yes—
218C22×C4⋊C4C2314yes—
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2312yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2314yes—
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2312yes—
225C22×C22⋊C4C2314yes—
226C22×C22⋊C4C2314yes—
227C22×C42—44no—
228C22×C42C2312yes—
229C22×C42C2311yescharacteristic
230C22×C42C2312yes—
231C22×C42C2312yes—
232C22×C42C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235C22×C42C2314yes—
236C22×C42C2312yes—
237C22×C42C2314yes—
238#391C2314yes—
239#391C2314yes—
240#391C2314yes—
241#391C2314yes—
242#391C2318yes—
243#391C2318yes—
244#391C2318yes—
245#391C2318yes—
246#391C2318yes—
247#391C2314yes—
248#391C2314yes—
249#391C2314yes—
250#391C2311yescharacteristic
251#391C2311yescharacteristic
252#390C2314yes—
253#390C2311yescharacteristic
254#390C2311yescharacteristic
255#389C2314yes—
256#389C2318yes—
257#389C2318yes—
258#389C2318yes—
259#389C2318yes—
260#389C2318yes—
261#389C2318yes—
262#389C2318yes—
263#389C2314yes—
264#389C2314yes—
265#389C2318yes—
266#389C2318yes—
267#389C2318yes—
268#389C2318yes—
269#389C2318yes—
270#389C2318yes—
271#389C2314yes—
272#389C2314yes—
273#389C2312yes—
274#389C2314yes—
275#389C2312yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#388C2318yes—
282#388C2318yes—
283#388C2314yes—
284#388C2318yes—
285#388C2318yes—
286#388C2318yes—
287#388C2318yes—
288#388C2318yes—
289#388C2314yes—
290#387C2318yes—
291#387C2318yes—
292#387C2318yes—
293#387C2318yes—
294#387C2318yes—
295#387C2318yes—
296#387C2318yes—
297#387C2318yes—
298#387C2318yes—
299#387C2318yes—
300#387C2314yes—
301#387C2318yes—
302#387C2318yes—
303#387C2318yes—
304#387C2318yes—
305#387C2318yes—
306#387C2318yes—
307#387C2318yes—
308#387C2318yes—
309#387C2318yes—
310#387C2318yes—
311#387C2318yes—
312#387C2318yes—
313#387C2318yes—
314#387C2318yes—
315#387C2318yes—
316#387C2318yes—
317#387C2318yes—
318#387C2314yes—
319#387C2318yes—
320#386C2314yes—
321#386C2314yes—
322#386C2318yes—
323#386C2314yes—
324#386C2314yes—
325#386C2314yes—
326#385C2318yes—
327#385C2318yes—
328#385C2318yes—
329#385C2318yes—
330#385C2318yes—
331#385C2318yes—
332#385C2318yes—
333#385C2314yes—
334#385C2318yes—
335#385C2314yes—
336#385C2318yes—
337#385C2318yes—
338#385C2318yes—
339#385C2314yes—
340#384C2312yes—
341#383C2318yes—
342#382C2312yes—
343#382C2318yes—
344#382C2318yes—
345#381C2318yes—
346#381C2312yes—
347#380C2314yes—
348#380C2314yes—
349#380C2312yes—
350#380C2314yes—
351#380C2312yes—
352#380C2318yes—
353#380C2318yes—
354#380C2314yes—
355#380C2314yes—
356#379C2312yes—
357C4×C4⋊C4C2314yes—
358C4×C4⋊C4C2318yes—
359C4×C4⋊C4C2318yes—
360C4×C4⋊C4C2314yes—
361C4×C4⋊C4C2314yes—
362C4×C4⋊C4C2314yes—
363C4×C4⋊C4C2318yes—
364C4×C4⋊C4C2314yes—
365C4×C4⋊C4C2318yes—
366C4×C4⋊C4C2318yes—
367C4×C4⋊C4C2318yes—
368C4×C4⋊C4C2318yes—
369C4×C4⋊C4C2314yes—
370C4×C4⋊C4C2318yes—
371C4×C4⋊C4C2318yes—
372C4×C4⋊C4C2318yes—
373C4×C4⋊C4C2318yes—
374C4×C4⋊C4C2318yes—
375C4×C4⋊C4C2318yes—
376C4×C4⋊C4C2318yes—
377C4×C4⋊C4C2318yes—
378C4×C4⋊C4C2314yes—
379C4×C4⋊C4C2314yes—
380C4×C4⋊C4C2318yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2318yes—
383C4×C4⋊C4C2314yes—
384C4×C4⋊C4C2318yes—
385C4×C4⋊C4C2312yes—
386C4×C4⋊C4C2314yes—
387C4×C4⋊C4C2312yes—
388C4×C22⋊C4C2318yes—
389C4×C22⋊C4C2318yes—
390C4×C22⋊C4C2314yes—
391C4×C22⋊C4C2318yes—
392C4×C22⋊C4C2318yes—
393C4×C22⋊C4C2318yes—
394C4×C22⋊C4C2314yes—
395C4×C22⋊C4C2318yes—
396C4×C22⋊C4C2318yes—
397C4×C22⋊C4C2318yes—
398C4×C22⋊C4C2318yes—
399C4×C22⋊C4C2318yes—
400C4×C22⋊C4C2314yes—
401C4×C22⋊C4C2314yes—
402C4×C22⋊C4C2314yes—
403C4×C22⋊C4C2318yes—
404C4×C22⋊C4C2318yes—
405C4×C22⋊C4C2314yes—
406C4×C22⋊C4C2314yes—
407#376C2312yes—
408#376C2318yes—
409#376C2318yes—
410C2×#95C2314yes—
411C2×#95C2314yes—
412C2×#95C2318yes—
413C2×#95C2314yes—
414C2×#95C2314yes—
415C2×#95C2314yes—
416C43C2312yes—
417C25C2411yescharacteristic
418C2×#41—42no—
419C2×#41—42no—
420C2×#41C22×C418yes—
421C22×Q8—44no—
422C22×Q8—44no—
423C22×Q8—44no—
424C22×Q8—44no—
425C22×Q8C22×C4116yes—
426C22×Q8C22×C4116yescomplemented
427C22×Q8C2414yes—
428C22×Q8C2414yes—
429C22×Q8C2414yes—
430C22×Q8C2411yescharacteristic
431C22×D4C2414yes—
432C22×D4C2412yes—
433C22×D4C2411yescharacteristic
434C23×C4—28no—
435C23×C4—42no—
436C23×C4—44no—
437C23×C4—42no—
438C23×C4—44no—
439C23×C4C22×C418yes—
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2414yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2411yescharacteristic
448C23×C4C2414yes—
449C23×C4C2414yes—
450C23×C4C2414yes—
451C23×C4C2412yes—
452C23×C4C2414yes—
453C23×C4C2414yes—
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2411yescharacteristic
457C23×C4C2412yes—
458C4⋊Q8C22×C4132yescomplemented
459C4⋊Q8C22×C4116yescomplemented
460C4⋊Q8C22×C4164yescomplemented
461#126C22×C4164yes—
462#126C22×C4164yescomplemented
463#125C22×C4164yescomplemented
464#125C22×C4116yescomplemented
465#125C22×C4164yescomplemented
466#124C22×C4132yes—
467#123C22×C4116yes—
468#123C22×C4132yes—
469#123C22×C4164yes—
470#123C22×C4132yescomplemented
471C22⋊Q8C22×C4132yes—
472C22⋊Q8C22×C4132yes—
473C22⋊Q8C22×C4132yes—
474C22⋊Q8C22×C4132yes—
475C22⋊Q8C22×C4116yes—
476C22⋊Q8C22×C4164yes—
477C22⋊Q8C22×C4132yescomplemented
478C22⋊Q8C22×C4164yescomplemented
479#121C22×C4116yes—
480#120C22×C4116yes—
481C4×Q8—216no—
482C4×Q8—48no—
483C4×Q8—48no—
484C4×Q8—44no—
485C4×Q8—416no—
486C4×Q8—48no—
487C4×Q8—48no—
488C4×Q8—48no—
489C4×Q8C22×C4132yescomplemented
490C4×D4—216no—
491C4×D4—44no—
492C4×D4—48no—
493C4×D4—416no—
494C4×D4—48no—
495C4×D4C22×C4132yes—
496C4×D4C22×C4164yes—
497#117—28no—
498#117—42no—
499#117—42no—
500#117—416no—
501#117—416no—
502#117—44no—
503#117C22×C418yes—
504#117C22×C4164yes—
505#117C22×C4116yescomplemented
506C2×C4⋊C4—216no—
507C2×C4⋊C4—44no—
508C2×C4⋊C4—44no—
509C2×C4⋊C4—44no—
510C2×C4⋊C4—48no—
511C2×C4⋊C4C22×C4132yes—
512C2×C4⋊C4C22×C4116yes—
513C2×C4⋊C4C2414yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2418yes—
516C2×C4⋊C4C2418yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2411yescharacteristic
527C2×C4⋊C4C2411yescharacteristic
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2418yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C22⋊C4—48no—
544C2×C22⋊C4C22×C4132yes—
545C2×C22⋊C4C2418yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2414yes—
548C2×C22⋊C4C2414yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2418yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2418yes—
563C2×C42—28no—
564C2×C42—24no—
565C2×C42—48no—
566C2×C42—44no—
567C2×C42—44no—
568C2×C42—44no—
569C2×C42—44no—
570C2×C42—42no—
571C2×C42—44no—
572C2×C42—48no—
573C2×C42C2412yes—
574C2×C42C2418yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2414yes—
578C2×C42C2412yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2411yescharacteristic
582C2×C42C2418yes—
583C2×C42C2414yes—
584C2×C42C2418yes—
585C2×C42C2418yes—
586C2×C42C2414yes—
587C2×C42C2414yes—
588C2×C42C2418yes—
589C2×C42C2418yes—
590C2×C42C2418yes—
591C2×C42C2418yes—
592C2×C42C2418yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2411yescharacteristic
596C2×C42C2411yescharacteristic
597C2×C42C2414yes—
598C2×C42C2412yes—
599C2×C42C2418yes—
600C2×C42C2411yescharacteristic
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2418yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2414yes—
614#95C2418yes—
615#95C2418yes—
616#95C2414yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630C24—24no—
631C24—24no—
632C24—41no—
633C24—41no—
634C24C23×C414yes—
635C24C2511yescharacteristic
636C24C2512yes—
637C24C2512yes—
638#41—416no—
639C2×Q8—28no—
640C2×Q8—28no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—41no—
644C2×Q8—44no—
645C2×Q8—44no—
646C2×Q8—41no—
647C2×Q8—432no—
648C2×Q8—432no—
649C2×Q8C23×C4116yes—
650C2×Q8C23×C4116yes—
651C2×Q8C23×C4116yes—
652C2×Q8C23×C414yes—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4—41no—
656C2×D4—42no—
657C2×D4—41no—
658C2×D4—42no—
659C2×D4C23×C4116yes—
660C2×D4C23×C418yes—
661C2×D4C23×C414yes—
662C22×C4—28no—
663C22×C4—24no—
664C22×C4—28no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—22no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—22no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—28no—
683C22×C4—416no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—41no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—41no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—48no—
707C22×C4—432no—
708C22×C4C23×C4116yes—
709C22×C4C23×C418yes—
710C22×C4C23×C414yes—
711C22×C4C23×C418yes—
712C22×C4C23×C4116yes—
713C22×C4C23×C418yes—
714C22×C4C23×C4116yes—
715C22×C4C23×C414yes—
716C22×C42−1+418yes—
717C22×C4C2512yes—
718C22×C4C2512yes—
719C22×C4C2518yes—
720C22×C4C2514yes—
721C22×C4C2518yes—
722C22×C4C2512yes—
723C22×C4C2514yes—
724C22×C4C2518yes—
725C22×C4C2512yes—
726C22×C4C2518yes—
727C22×C4C2512yes—
728C22×C4C2511yescharacteristic
729C22×C4C2512yes—
730C22×C4C2512yes—
731C22×C4C2512yes—
732C22×C4C2511yescharacteristic
733C4⋊C4—216no—
734C4⋊C4—28no—
735C4⋊C4—28no—
736C4⋊C4—216no—
737C4⋊C4—216no—
738C4⋊C4—28no—
739C4⋊C4—28no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C4⋊C4—44no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—48no—
746C4⋊C4—41no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4C23×C4116yes—
754C4⋊C4C23×C4132yes—
755C4⋊C4C23×C4132yes—
756C4⋊C4C23×C4116yes—
757C4⋊C4C23×C418yes—
758C4⋊C4C23×C4132yes—
759C4⋊C4C23×C4132yes—
760C4⋊C4C23×C4132yes—
761C4⋊C4C23×C4116yes—
762C4⋊C4C23×C4132yes—
763C22⋊C4—28no—
764C22⋊C4—216no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—48no—
769C22⋊C4—42no—
770C22⋊C4—44no—
771C22⋊C4—42no—
772C22⋊C4—44no—
773C22⋊C4—48no—
774C22⋊C4C23×C4132yes—
775C22⋊C4C23×C4132yes—
776C22⋊C4C23×C4116yes—
777C22⋊C4C23×C418yes—
778C22⋊C4C23×C4116yes—
779C22⋊C4C23×C4116yes—
780C22⋊C4C23×C4132yes—
781C42—22no—
782C42—24no—
783C42—24no—
784C42—24no—
785C42—24no—
786C42—24no—
787C42—216no—
788C42—28no—
789C42—24no—
790C42—41no—
791C42—42no—
792C42—42no—
793C42—41no—
794C42—48no—
795C42—48no—
796C42—44no—
797C42—48no—
798C42—48no—
799C42—48no—
800C42—48no—
801C42—44no—
802C42—44no—
803C42—48no—
804C42—48no—
805C42C23×C4116yes—
806C42C23×C418yes—
807C42C23×C4132yes—
808C42H(5,𝔽2)14yes—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—21no—
815C23—24no—
816C23—22no—
817C23—22no—
818C23—24no—
819C23—21no—
820C23—22no—
821C23—216no—
822C23—44no—
823C23—48no—
824C23—44no—
825C23—44no—
826C23C24×C412yes—
827C23C24×C414yes—
828C23C24×C414yes—
829C23C2×2−1+414yes—
830C23#58514yes—
831C23C2611yescharacteristic
832Q8—232no—
833Q8—416no—
834Q8—416no—
835Q8—44no—
836D4—232no—
837D4—44no—
838D4—48no—
839C2×C4—216no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—28no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—28no—
848C2×C4—22no—
849C2×C4—28no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—22no—
854C2×C4—28no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—232no—
859C2×C4—216no—
860C2×C4—28no—
861C2×C4—216no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—28no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—24no—
872C2×C4—28no—
873C2×C4—28no—
874C2×C4—24no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—22no—
878C2×C4—48no—
879C2×C4—44no—
880C2×C4—48no—
881C2×C4—416no—
882C2×C4—416no—
883C2×C4—48no—
884C2×C4—48no—
885C2×C4—48no—
886C2×C4—48no—
887C2×C4—88no—
888C2×C4—88no—
889C2×C4—88no—
890C2×C4—164no—
891C2×C4C24×C418yes—
892C2×C4C24×C4116yes—
893C2×C4C24×C414yes—
894C2×C4C24×C4116yes—
895C2×C4C24×C414yes—
896C2×C4C24×C412yes—
897C2×C4C24×C412yes—
898C2×C4C2×H(5,𝔽2)14yes—
899C2×C4C2×H(5,𝔽2)12yes—
900C2×C4C2×2−1+414yes—
901C2×C4C2×2−1+414yes—
902C2×C4#58512yes—
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—24no—
910C22—22no—
911C22—28no—
912C22—24no—
913C22—416no—
914C22—42no—
915C22—44no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22C4×2−1+418yes—
921C22C25×C411yescharacteristic
922C22C22×H(5,𝔽2)11yescharacteristic
923C22C22×2−1+412yes—
924C22C2×#58512yes—
925C22C2×#58511yescharacteristic
926C4—24no—
927C4—24no—
928C4—24no—
929C4—22no—
930C4—24no—
931C4—24no—
932C4—216no—
933C4—216no—
934C4—28no—
935C4—42no—
936C4—44no—
937C4—48no—
938C4—42no—
939C4—48no—
940C4—42no—
941C4C4×H(5,𝔽2)14yes—
942C2—28no—
943C2—44no—
944C2—42no—
945C2C2×C4×H(5,𝔽2)11yescharacteristic
946C2C2×C4×2−1+412yes—
947C2#6281912yes—
948C2#6282911yescharacteristic
949C2#6283711yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#525C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34516C2semidirect
3. #34432C2semidirect
4. #34427C2semidirect
5. #34421C2semidirect
6. #34413C2semidirect
7. #34380C2semidirect
9. #34334C2semidirect
10. #34314C2semidirect
11. #34304C2semidirect
12. #34296C2semidirect
13. #34291C2semidirect
14. #34281C2semidirect
15. #34278C2semidirect
16. #34271C2semidirect
17. #34268C2semidirect
19. C2×C4×C22⋊Q8C2semidirect
20. #3538C4semidirect
31. C2×#519C22semidirect
35. #2382C22semidirect
36. #2381C22semidirect
39. #2376C22semidirect
40. #2374C22semidirect
43. #2373C22semidirect
44. #2373C22semidirect
45. #2371C22semidirect
46. #2370C22semidirect
47. #2370C22semidirect
48. #2370C22semidirect
49. #2370C22semidirect
50. #2370C22semidirect
51. #2369C22semidirect
52. #2369C22semidirect
54. #2368C22semidirect
56. #2365C22semidirect
57. #2365C22semidirect
58. #2365C22semidirect
59. #2362C22semidirect
60. #2362C22semidirect
64. #2360C22semidirect
68. #2359C22semidirect
70. #2355C22semidirect
73. #2351C22semidirect
76. #2347C22semidirect
82. Q8×C22⋊C4C22semidirect
84. #2336C22semidirect
85. #2336C22semidirect
89. #2334C22semidirect
90. #2334C22semidirect
91. #2331C22semidirect
92. #2330C22semidirect
97. #2329C22semidirect
98. #2327C22semidirect
99. #2327C22semidirect
103. #2323C22semidirect
104. #2323C22semidirect
110. C4×C4⋊Q8C22semidirect
111. C4×#125C22semidirect
123. C4×C22⋊Q8C22semidirect
132. #2296C22semidirect
133. #2295C22semidirect
135. C2×#391C22semidirect
143. #2276C22semidirect
146. #2274C22semidirect
157. #563C2×C4semidirect
158. #552C2×C4semidirect
159. #551C2×C4semidirect
160. D4×Q8C2×C4semidirect
161. #544C2×C4semidirect
162. #541C2×C4semidirect
163. #539C2×C4semidirect
164. #536C2×C4semidirect
179. C2×C22⋊Q8C2×C4semidirect
426. C22×Q8C22×C4semidirect
458. C4⋊Q8C22×C4semidirect
459. C4⋊Q8C22×C4semidirect
460. C4⋊Q8C22×C4semidirect
462. #126C22×C4semidirect
463. #125C22×C4semidirect
464. #125C22×C4semidirect
465. #125C22×C4semidirect
470. #123C22×C4semidirect
477. C22⋊Q8C22×C4semidirect
478. C22⋊Q8C22×C4semidirect
489. C4×Q8C22×C4semidirect
505. #117C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35382
#345162
#344322
#344272
#344212
#344132
#343802
#343602
#343342
#343142
#343042
#342962
#342912
#342812
#342782
#342712
#342682
C4×#5252
C2×C4×C22⋊Q82