Finite Group Databasebeta

← #7626962

Subgroups — #7626962

Order 512.

6786 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic
2#34485C212yesmaximal, complemented
3#34483C214yesmaximal, complemented
4#34474C218yesmaximal, complemented
5#34463C214yesmaximal, complemented
6#34448C218yesmaximal, complemented
7#34414C214yesmaximal, complemented
8#34403C212yesmaximal, complemented
9#34398C212yesmaximal, complemented
10#34367C211yesmaximal, characteristic, complemented
11#34365C211yesmaximal, characteristic, complemented
12#34321C212yesmaximal, complemented
13#34319C214yesmaximal, complemented
14#34317C212yesmaximal, complemented
15#34298C214yesmaximal, complemented
16#34252C214yesmaximal, complemented
17#34216C211yesmaximal, characteristic, complemented
18#34215C212yesmaximal, complemented
19#34191C211yesmaximal, characteristic, complemented
20C4×#554C212yesmaximal, complemented
21#34125C211yesmaximal, characteristic, complemented
22#34086C211yesmaximal, characteristic, complemented
23#34086C212yesmaximal, complemented
24#3511C4132yescomplemented
25C2×#556C2212yes—
26C2×#555C2212yes—
27C2×#554C2212yes—
28C2×#553C2214yes—
29C2×#548C2214yes—
30C2×#547C2212yes—
31C2×#542C2214yes—
32C2×#537C2212yes—
33C2×#533C2212yes—
34C2×#532C2211yescharacteristic
35C2×#532C2212yes—
36C22×C4⋊Q8C2211yescharacteristic
37C2×#520C2212yes—
38C2×C4×#41C2211yescharacteristic
39#2383C2218yes—
40#2381C2214yes—
41#2379C2218yes—
42#2379C2218yes—
43#2378C2218yes—
44#2377C2214yes—
45#2377C2218yes—
46#2374C2218yes—
47#2373C2218yes—
48#2370C2214yes—
49#2370C2214yes—
50#2369C2212yes—
51#2369C2212yes—
52#2369C2214yes—
53#2368C2218yes—
54#2368C2218yes—
55#2368C2218yes—
56#2367C2218yes—
57#2365C2214yes—
58#2363C2214yes—
59#2363C2218yes—
60#2363C2214yes—
61#2362C2214yes—
62#2362C2218yes—
63#2361C2214yes—
64#2361C2214yes—
65#2361C2214yes—
66#2360C2214yes—
67#2359C2218yes—
68#2357C2214yes—
69#2357C2218yes—
70#2357C2214yes—
71#2357C2212yes—
72#2356C2218yes—
73#2355C2212yes—
74#2355C2218yes—
75#2355C2218yes—
76#2354C2212yes—
77#2354C2218yes—
78#2352C2214yes—
79#2352C2214yes—
80#2351C2212yes—
81#2349C2214yes—
82D4×C4⋊C4C2212yes—
83D4×C4⋊C4C2212yes—
84#2347C2214yes—
85#2347C2214yes—
86#2347C2214yes—
87#2347C2212yes—
88#2346C2214yes—
89#2346C2212yes—
90#2346C2214yes—
91#2345C2214yes—
92#2345C2214yes—
93#2344C2214yes—
94#2344C2214yes—
95#2344C2214yes—
96#2343C2214yes—
97#2341C2212yes—
98Q8×C22⋊C4C2214yes—
99#2339C2218yes—
100#2339C2212yes—
101#2337C2218yes—
102#2337C2214yes—
103#2337C2218yes—
104#2337C2214yes—
105#2335C2218yes—
106#2334C2218yes—
107#2334C2218yes—
108#2333C2218yes—
109#2333C2218yes—
110#2333C2214yes—
111#2332C2218yes—
112#2332C2218yes—
113#2331C2212yes—
114#2331C2211yescharacteristic
115#2331C2211yescharacteristic
116#2331C2212yes—
117#2331C2212yes—
118#2331C2214yes—
119#2331C2212yes—
120#2331C2212yes—
121#2328C2211yescharacteristic
122#2328C2212yes—
123#2328C2211yescharacteristic
124#2326C2218yes—
125#2325C2218yes—
126#2324C2212yes—
127#2324C2214yes—
128#2324C2212yes—
129#2324C2214yes—
130#2324C2218yes—
131#2324C2214yes—
132#2323C2214yes—
133#2320C2218yes—
134#2320C2212yes—
135#2318C2218yes—
136#2318C2214yes—
137#2318C2218yes—
138#2317C2214yes—
139#2317C2214yes—
140#2316C2212yes—
141#2311C2214yes—
142#2310C2214yes—
143C4×C4⋊Q8C2212yes—
144C4×C4⋊Q8C2212yes—
145C4×#125C2214yes—
146C4×#125C2214yes—
147C4×C22⋊Q8C2214yes—
148C4×C22⋊Q8C2218yes—
149C4×#123C2218yes—
150C4×#121C2214yes—
151#2297C2214yes—
152#2297C2218yes—
153#2296C2214yes—
154#2293C2214yes—
155#2293C2212yes—
156#2293C2212yes—
157#2293C2211yescharacteristic
158#2293C2212yes—
159#2293C2211yescharacteristic
160#2290C2218yes—
161#2290C2218yes—
162#2290C2214yes—
163#2285C2211yescharacteristic
164#2283C2211yescharacteristic
165#2283C2212yes—
166#2283C2211yescharacteristic
167#2283C2212yes—
168C2×#382C2212yes—
169#2275C2212yes—
170#2274C2214yes—
171#2274C2212yes—
172#2274C2214yes—
173C42×Q8C2211yescharacteristic
174C42×Q8C2211yescharacteristic
175C42×D4C2214yes—
176C42×D4C2212yes—
177C4×#117C2212yes—
178C4×#117C2211yescharacteristic
179C2×C4×C4⋊C4C2214yes—
180C22×#41C2312yes—
181C22×#41C2311yescharacteristic
182C22×#41C2314yes—
183C23×Q8C2312yes—
184#556C2×C4132yescomplemented
185#555C2×C4132yescomplemented
186#554C2×C4132yescomplemented
187#553C2×C4164yescomplemented
188#548C2×C4164yescomplemented
189#547C2×C4132yescomplemented
190#542C2×C4164yescomplemented
191#537C2×C4132yescomplemented
192#533C2×C4132yescomplemented
193#532C2×C4116yescomplemented
194#532C2×C4132yescomplemented
195C2×C4⋊Q8C2×C4116yescomplemented
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×#127C2311yescharacteristic
202C2×#126C2318yes—
203C2×#125C2314yes—
204C2×#124C2318yes—
205C2×#124C2312yes—
206C2×#124C2314yes—
207C2×#123C2318yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2318yes—
211C2×C22⋊Q8C2314yes—
212C2×#121C2314yes—
213C2×#121C2312yes—
214C2×#121C2318yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2312yes—
218#520C2×C4132yescomplemented
219C4×#41C2×C4116yescomplemented
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4C2312yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2318yes—
233C2×C4×D4C2318yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2318yes—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2314yes—
246C2×#117C2311yescharacteristic
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2314yes—
250C2×#117C2318yes—
251C2×#117C2318yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2314yes—
261C22×C42C2314yes—
262C22×C42C2318yes—
263C22×C42C2311yescharacteristic
264C22×C42C2312yes—
265#391C2314yes—
266#391C2314yes—
267#391C2318yes—
268#391C2318yes—
269#391C2318yes—
270#391C2318yes—
271#391C2318yes—
272#391C2314yes—
273#391C2318yes—
274#391C2318yes—
275#391C2314yes—
276#391C2314yes—
277#390C2318yes—
278#390C2318yes—
279#390C2312yes—
280#390C2312yes—
281#390C2314yes—
282#390C2314yes—
283#390C2312yes—
284#390C2314yes—
285#390C2314yes—
286#390C2318yes—
287#390C2314yes—
288#390C2312yes—
289#389C2312yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#389C2312yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2314yes—
303#389C2314yes—
304#389C2312yes—
305#389C2314yes—
306#389C2314yes—
307#389C2312yes—
308#388C2318yes—
309#388C2314yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2314yes—
317#388C2318yes—
318#388C2318yes—
319#388C2314yes—
320#388C2318yes—
321#388C2314yes—
322#388C2314yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2314yes—
328#388C2318yes—
329#388C2314yes—
330#388C2314yes—
331#388C2314yes—
332#388C2314yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2314yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2314yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2314yes—
355#386C2314yes—
356#386C2318yes—
357#386C2318yes—
358#386C2314yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2314yes—
363#386C2314yes—
364#386C2314yes—
365#386C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2314yes—
374#385C2318yes—
375#385C2314yes—
376#385C2318yes—
377#385C2318yes—
378#384C2312yes—
379#384C2318yes—
380#383C2314yes—
381#383C2314yes—
382#383C2318yes—
383#383C2312yes—
384#383C2312yes—
385#382C2314yes—
386#382C2318yes—
387#382C2318yes—
388#382C2314yes—
389#382C2314yes—
390#382C2314yes—
391#382C2311yescharacteristic
392#382C2312yes—
393#382C2311yescharacteristic
394#382C2312yes—
395#381C2312yes—
396#381C2312yes—
397#381C2318yes—
398#381C2318yes—
399#381C2314yes—
400#381C2314yes—
401#380C2312yes—
402#380C2312yes—
403#380C2314yes—
404#380C2314yes—
405#380C2318yes—
406#380C2312yes—
407#380C2318yes—
408#380C2312yes—
409#380C2314yes—
410#380C2314yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2318yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2318yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2318yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2318yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2318yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2318yes—
432C4×C4⋊C4C2318yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2312yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2312yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2318yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2314yes—
472#376C2318yes—
473#376C2312yes—
474#376C2311yescharacteristic
475#376C2312yes—
476#376C2311yescharacteristic
477#376C2314yes—
478C2×#95C2318yes—
479C2×#95C2314yes—
480C2×#95C2314yes—
481C43C2312yes—
482C43C2312yes—
483C43C2311yescharacteristic
484C43C2311yescharacteristic
485C2×#41—48no—
486C2×#41—44no—
487C2×#41—88no—
488C2×#41C22×C418yes—
489C2×#41C22×C4116yes—
490C2×#41C22×C4132yes—
491C22×Q8—84no—
492C22×Q8C22×C4116yes—
493C22×Q8C2411yescharacteristic
494C22×Q8C2414yes—
495C22×Q8C2412yes—
496C22×Q8C2414yes—
497C22×D4C2412yes—
498C22×D4C2411yescharacteristic
499C22×D4C2418yes—
500C22×D4C2412yes—
501C22×D4C2414yes—
502C22×D4C2412yes—
503C22×D4C2412yes—
504C23×C4C2412yes—
505C23×C4C2411yescharacteristic
506C23×C4C2414yes—
507C23×C4C2411yescharacteristic
508C23×C4C2414yes—
509C23×C4C2418yes—
510C23×C4C2418yes—
511C23×C4C2414yes—
512C23×C4C2414yes—
513C23×C4C2418yes—
514C23×C4C2412yes—
515C23×C4C2411yescharacteristic
516C23×C4C2412yes—
517C4⋊Q8C22×C4116yes—
518C4⋊Q8C22×C4116yes—
519C4⋊Q8C22×C4116yes—
520C4⋊Q8C22×C4116yes—
521C4⋊Q8C22×C418yes—
522#127C22×C418yes—
523#126C22×C4164yes—
524#125C22×C4132yes—
525#124C22×C4116yes—
526#124C22×C4132yes—
527#124C22×C4164yes—
528#123C22×C4164yes—
529C22⋊Q8C22×C4132yes—
530C22⋊Q8C22×C4132yes—
531C22⋊Q8C22×C4132yes—
532C22⋊Q8C22×C4164yes—
533#121C22×C4132yes—
534#121C22×C4116yes—
535#121C22×C4116yes—
536#121C22×C4132yes—
537#121C22×C4132yes—
538#121C22×C4164yes—
539C4×Q8—44no—
540C4×Q8—44no—
541C4×Q8—84no—
542C4×Q8—84no—
543C4×Q8C22×C418yes—
544C4×Q8C22×C418yes—
545C4×Q8C22×C4132yes—
546C4×Q8C22×C4132yes—
547C4×D4—28no—
548C4×D4—48no—
549C4×D4—44no—
550C4×D4—48no—
551C4×D4—88no—
552C4×D4—88no—
553C4×D4C22×C418yes—
554C4×D4C22×C4116yes—
555C4×D4C22×C4116yes—
556C4×D4C22×C418yes—
557C4×D4C22×C4132yes—
558C4×D4C22×C4164yes—
559C4×D4C22×C4116yes—
560C4×D4C22×C4132yes—
561C4×D4C22×C4116yes—
562#117—24no—
563#117—28no—
564#117—48no—
565#117—44no—
566#117—42no—
567#117—44no—
568#117—48no—
569#117—88no—
570#117—88no—
571#117C22×C418yes—
572#117C22×C4116yes—
573#117C22×C4132yes—
574#117C22×C4132yes—
575C2×C4⋊C4—48no—
576C2×C4⋊C4—48no—
577C2×C4⋊C4C22×C4116yes—
578C2×C4⋊C4C22×C4132yes—
579C2×C4⋊C4C22×C4116yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2418yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C42—48no—
641C2×C42—88no—
642C2×C42C22×C418yes—
643C2×C42C22×C4116yes—
644C2×C42C2411yescharacteristic
645C2×C42C2412yes—
646C2×C42C2411yescharacteristic
647C2×C42C2412yes—
648C2×C42C2414yes—
649C2×C42C2412yes—
650C2×C42C2411yescharacteristic
651C2×C42C2412yes—
652C2×C42C2414yes—
653C2×C42C2418yes—
654C2×C42C2418yes—
655C2×C42C2418yes—
656C2×C42C2414yes—
657C2×C42C2418yes—
658C2×C42C2418yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2414yes—
662C2×C42C2414yes—
663C2×C42C2418yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2412yes—
668C2×C42C2418yes—
669C2×C42C2411yescharacteristic
670C2×C42C2412yes—
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2412yes—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#95C2412yes—
677#95C2418yes—
678#95C2412yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2412yes—
686#95C2414yes—
687#95C2414yes—
688#95C2418yes—
689#95C2412yes—
690#95C2412yes—
691#95C2414yes—
692#95C2412yes—
693#95C2414yes—
694#95C2412yes—
695#95C2418yes—
696#95C2412yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2414yes—
701#95C2414yes—
702#95C2418yes—
703#95C2414yes—
704#95C2418yes—
705#95C2414yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2414yes—
712#95C2414yes—
713#95C2412yes—
714#95C2412yes—
715C24C2511yescharacteristic
716C24C2512yes—
717C24C2514yes—
718#41—432no—
719#41—416no—
720#41—832no—
721C2×Q8—24no—
722C2×Q8—44no—
723C2×Q8—44no—
724C2×Q8—48no—
725C2×Q8—44no—
726C2×Q8—816no—
727C2×Q8C23×C414yes—
728C2×Q8C23×C418yes—
729C2×Q8C23×C4116yes—
730C2×Q8C23×C4116yes—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4C23×C418yes—
742C2×D4C23×C414yes—
743C2×D4C23×C418yes—
744C2×D4C23×C4116yes—
745C2×D4C23×C418yes—
746C2×D4C23×C418yes—
747C2×D4C23×C4132yes—
748C22×C4—24no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—24no—
752C22×C4—28no—
753C22×C4—22no—
754C22×C4—24no—
755C22×C4—28no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—42no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—48no—
766C22×C4—48no—
767C22×C4—48no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4C23×C414yes—
774C22×C4C23×C414yes—
775C22×C4C23×C418yes—
776C22×C4C23×C4116yes—
777C22×C4C23×C418yes—
778C22×C4C23×C414yes—
779C22×C4C23×C418yes—
780C22×C4C23×C4116yes—
781C22×C4C23×C4132yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2518yes—
789C22×C4C2512yes—
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C22×C4C2512yes—
793C22×C4C2511yescharacteristic
794C22×C4C2512yes—
795C22×C4C2511yescharacteristic
796C22×C4C2514yes—
797C22×C4C2512yes—
798C22×C4C2518yes—
799C22×C4C2512yes—
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C4⋊C4—28no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—42no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—48no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—44no—
821C4⋊C4—44no—
822C4⋊C4—44no—
823C4⋊C4C23×C414yes—
824C4⋊C4C23×C4116yes—
825C4⋊C4C23×C4116yes—
826C4⋊C4C23×C4116yes—
827C4⋊C4C23×C4132yes—
828C4⋊C4C23×C4116yes—
829C4⋊C4C23×C414yes—
830C4⋊C4C23×C418yes—
831C4⋊C4C23×C418yes—
832C4⋊C4C23×C418yes—
833C4⋊C4C23×C418yes—
834C4⋊C4C23×C4132yes—
835C22⋊C4—24no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—42no—
841C22⋊C4—44no—
842C22⋊C4—48no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4C23×C418yes—
855C22⋊C4C23×C4132yes—
856C22⋊C4C23×C418yes—
857C22⋊C4C23×C418yes—
858C22⋊C4C23×C4132yes—
859C22⋊C4C23×C4132yes—
860C22⋊C4C23×C4116yes—
861C22⋊C4C23×C4116yes—
862C42—24no—
863C42—22no—
864C42—24no—
865C42—28no—
866C42—22no—
867C42—24no—
868C42—22no—
869C42—24no—
870C42—44no—
871C42—44no—
872C42—44no—
873C42—48no—
874C42—48no—
875C42—48no—
876C42—44no—
877C42—48no—
878C42—44no—
879C42—48no—
880C42—48no—
881C42—44no—
882C42—44no—
883C42—42no—
884C42—42no—
885C42C23×C414yes—
886C42C23×C418yes—
887C42C23×C414yes—
888C42C23×C418yes—
889C42C23×C414yes—
890C42C23×C414yes—
891C42C23×C418yes—
892C42C23×C4132yes—
893C422−1+414yes—
894C23—21no—
895C23—22no—
896C23—24no—
897C23—21no—
898C23—24no—
899C23—22no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—22no—
904C23—22no—
905C23—24no—
906C23—24no—
907C23—24no—
908C23C24×C418yes—
909C23C24×C414yes—
910C23C24×C412yes—
911C23C2611yescharacteristic
912Q8—28no—
913Q8—416no—
914Q8—416no—
915Q8—48no—
916D4—28no—
917D4—216no—
918D4—48no—
919D4—416no—
920D4—48no—
921D4—432no—
922D4—48no—
923C2×C4—21no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—28no—
935C2×C4—22no—
936C2×C4—28no—
937C2×C4—22no—
938C2×C4—232no—
939C2×C4—28no—
940C2×C4—216no—
941C2×C4—28no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—28no—
955C2×C4—28no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—416no—
967C2×C4—44no—
968C2×C4—48no—
969C2×C4—432no—
970C2×C4—48no—
971C2×C4—416no—
972C2×C4—816no—
973C2×C4—88no—
974C2×C4—168no—
975C2×C4C24×C414yes—
976C2×C4C24×C412yes—
977C2×C4C24×C412yes—
978C2×C4C24×C412yes—
979C2×C4C24×C412yes—
980C2×C4C24×C418yes—
981C2×C4C24×C414yes—
982C2×C4C24×C414yes—
983C2×C4C24×C4116yes—
984C2×C4C24×C412yes—
985C2×C4C24×C412yes—
986C2×C4C2×2−1+414yes—
987C2×C4C2×2−1+412yes—
988C2×C4#58514yes—
989C2×C4#58512yes—
990C22—22no—
991C22—28no—
992C22—24no—
993C22—22no—
994C22—24no—
995C22—28no—
996C22—22no—
997C22—28no—
998C22—24no—
999C22—44no—
1000C22—44no—
1001C22—42no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—44no—
1006C22—42no—
1007C22C25×C411yescharacteristic
1008C22C22×2−1+411yescharacteristic
1009C22C2×#58512yes—
1010C22C2×#58511yescharacteristic
1011C22H(7,𝔽2)12yes—
1012C4—22no—
1013C4—28no—
1014C4—24no—
1015C4—22no—
1016C4—24no—
1017C4—24no—
1018C4—22no—
1019C4—216no—
1020C4—22no—
1021C4—24no—
1022C4—42no—
1023C4—44no—
1024C4—44no—
1025C4—42no—
1026C4—42no—
1027C4—44no—
1028C4—48no—
1029C4—44no—
1030C4#342814yes—
1031C4C4×2−1+414yes—
1032C2—42no—
1033C2—48no—
1034C2—44no—
1035C2C2×#342811yescharacteristic
1036C2C2×C4×2−1+411yescharacteristic
1037C2#6265211yescharacteristic
1038C2#6292612yes—
1039C2#6293812yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3511C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34485C2semidirect
3. #34483C2semidirect
4. #34474C2semidirect
5. #34463C2semidirect
6. #34448C2semidirect
7. #34414C2semidirect
8. #34403C2semidirect
9. #34398C2semidirect
10. #34367C2semidirect
11. #34365C2semidirect
12. #34321C2semidirect
13. #34319C2semidirect
14. #34317C2semidirect
15. #34298C2semidirect
16. #34252C2semidirect
17. #34216C2semidirect
18. #34215C2semidirect
19. #34191C2semidirect
20. C4×#554C2semidirect
21. #34125C2semidirect
22. #34086C2semidirect
23. #34086C2semidirect
24. #3511C4semidirect
184. #556C2×C4semidirect
185. #555C2×C4semidirect
186. #554C2×C4semidirect
187. #553C2×C4semidirect
188. #548C2×C4semidirect
189. #547C2×C4semidirect
190. #542C2×C4semidirect
191. #537C2×C4semidirect
192. #533C2×C4semidirect
193. #532C2×C4semidirect
194. #532C2×C4semidirect
195. C2×C4⋊Q8C2×C4semidirect
218. #520C2×C4semidirect
219. C4×#41C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
#344852
#344832
#344742
#344632
#344482
#344142
#344032
#343982
#343672
#343652
#343212
#343192
#343172
#342982
#342522
#342162
#342152
#341912
C4×#5542
#341252
#340862