Finite Group Databasebeta

← #7625619

Subgroups — #7625619

Order 512.

7488 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3480C211yesmaximal, characteristic
2#34336C212yesmaximal, complemented
3#34329C216yesmaximal, complemented
4#34319C216yesmaximal, complemented
5#34312C212yesmaximal, complemented
6#34307C216yesmaximal, complemented
7#34301C216yesmaximal, complemented
8#34295C212yesmaximal, complemented
9#34293C212yesmaximal, complemented
10#34155C213yesmaximal, complemented
11#34153C213yesmaximal, complemented
12#34151C213yesmaximal, complemented
13#34129C211yesmaximal, characteristic, complemented
14#34128C211yesmaximal, characteristic, complemented
15#34125C211yesmaximal, characteristic, complemented
16#34121C213yesmaximal, complemented
17#34086C213yesmaximal, complemented
18#34084C213yesmaximal, complemented
19C4×#529C213yesmaximal, complemented
20#34026C213yesmaximal, complemented
21C4×#519C211yesmaximal, characteristic, complemented
22C4×#520C211yesmaximal, characteristic, complemented
23C42×#41C211yesmaximal, characteristic, complemented
24#3480C4132yescomplemented
25C2×#559C2213yes—
26C2×#557C2211yescharacteristic
27C2×#556C2213yes—
28C2×#553C2213yes—
29C2×#553C2213yes—
30C2×#550C2211yescharacteristic
31C2×#548C2211yescharacteristic
32C2×#548C2211yescharacteristic
33C2×#532C2213yes—
34C2×#529C2213yes—
35C2×#529C2213yes—
36C2×#520C2212yes—
37C2×#519C2212yes—
38C2×C4×#41C2212yes—
39C2×C4×#41C2213yes—
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43#2374C22112yes—
44#2373C22112yes—
45#2373C22112yes—
46#2372C22112yes—
47#2370C2216yes—
48#2370C2216yes—
49#2369C2216yes—
50#2367C2216yes—
51#2367C2216yes—
52#2366C2216yes—
53#2363C2216yes—
54#2363C2216yes—
55#2363C22112yes—
56#2363C2216yes—
57#2362C2216yes—
58#2361C2216yes—
59#2360C2216yes—
60#2359C22112yes—
61#2357C2216yes—
62#2357C2216yes—
63#2356C2216yes—
64#2356C2216yes—
65#2355C2216yes—
66#2354C2216yes—
67#2354C2216yes—
68#2353C2216yes—
69#2353C2216yes—
70#2352C2216yes—
71#2352C2216yes—
72#2351C2212yes—
73#2351C2212yes—
74Q8×C4⋊C4C2212yes—
75#2347C2216yes—
76#2346C2216yes—
77#2344C2216yes—
78#2341C2212yes—
79#2341C2212yes—
80Q8×C22⋊C4C2212yes—
81#2337C22112yes—
82#2335C22112yes—
83#2334C22112yes—
84#2333C22112yes—
85#2331C2216yes—
86#2330C2216yes—
87#2328C2216yes—
88#2326C2216yes—
89#2324C2216yes—
90#2324C2216yes—
91#2324C2216yes—
92#2323C2216yes—
93C4×#125C2216yes—
94C4×#126C22112yes—
95C4×#124C2216yes—
96C4×C22⋊Q8C2216yes—
97C4×#123C22112yes—
98C4×#121C2216yes—
99#2298C2216yes—
100#2298C2213yes—
101#2298C2213yes—
102#2298C2211yescharacteristic
103#2298C2213yes—
104#2297C2213yes—
105#2297C2216yes—
106#2297C2213yes—
107#2296C2213yes—
108#2296C2213yes—
109#2295C2216yes—
110#2295C2216yes—
111#2295C2213yes—
112#2295C2213yes—
113#2293C2216yes—
114#2293C2213yes—
115#2293C2216yes—
116#2293C2213yes—
117#2293C2213yes—
118#2293C2213yes—
119#2293C2216yes—
120#2290C2216yes—
121#2290C2216yes—
122#2290C2216yes—
123#2290C2216yes—
124#2290C2216yes—
125#2290C2216yes—
126#2285C2213yes—
127#2283C2213yes—
128#2283C2213yes—
129#2276C2216yes—
130#2276C2212yes—
131#2276C2212yes—
132#2275C2216yes—
133#2274C2216yes—
134#2274C2216yes—
135C42×Q8C2212yes—
136C42×Q8C2213yes—
137C42×Q8C2211yescharacteristic
138C42×Q8C2211yescharacteristic
139C42×Q8C2211yescharacteristic
140C42×Q8C2213yes—
141C42×Q8C2211yescharacteristic
142C42×D4C2216yes—
143C42×D4C2213yes—
144C42×D4C2213yes—
145C42×D4C2213yes—
146C42×D4C2213yes—
147C42×D4C2216yes—
148C4×#117C2216yes—
149C4×#117C2213yes—
150C4×#117C2213yes—
151C4×#117C2213yes—
152C4×#117C2216yes—
153C4×#117C2213yes—
154C4×#117C2213yes—
155C4×#117C2213yes—
156C4×#117C2213yes—
157C2×C4×C4⋊C4C2213yes—
158C2×C43C2213yes—
159C22×#41C2311yescharacteristic
160C22×#41C2311yescharacteristic
161C22×#41C2313yes—
162C23×Q8C2311yescharacteristic
163#559C2×C4148yescomplemented
164#557C2×C4116yescomplemented
165#556C2×C4148yescomplemented
166#553C2×C4148yescomplemented
167#553C2×C4148yescomplemented
168#550C2×C4116yes—
169#548C2×C4116yescomplemented
170#548C2×C4116yescomplemented
171#532C2×C4148yescomplemented
172C2×C4⋊Q8C2313yes—
173C2×#127C2313yes—
174#529C2×C4148yescomplemented
175#529C2×C4148yescomplemented
176C2×#126C2316yes—
177C2×#126C2316yes—
178C2×#125C2313yes—
179C2×#125C2313yes—
180C2×#124C2313yes—
181C2×#124C2316yes—
182C2×#124C2313yes—
183C2×#123C2316yes—
184C2×#123C2316yes—
185C2×C22⋊Q8C2313yes—
186C2×C22⋊Q8C2313yes—
187C2×#121C2313yes—
188C2×#121C2313yes—
189C2×#121C2313yes—
190C2×#121C2316yes—
191C2×#121C2313yes—
192#520—216no—
193#519—216no—
194C4×#41—216no—
195C4×#41C2×C4148yescomplemented
196C4×#41C2×C4116yescomplemented
197C4×#41C2×C4116yescomplemented
198C2×C4×Q8C2×C4116yescomplemented
199C2×C4×Q8C2316yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2312yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2316yes—
204C2×C4×Q8C2311yescharacteristic
205C2×C4×Q8C2311yescharacteristic
206C2×C4×Q8C2311yescharacteristic
207C2×C4×Q8C2313yes—
208C2×C4×Q8C2313yes—
209C2×C4×Q8C2313yes—
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2313yes—
212C2×C4×Q8C2312yes—
213C2×C4×D4C2316yes—
214C2×C4×D4C2316yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C2316yes—
217C2×C4×D4C23112yes—
218C2×C4×D4C2313yes—
219C2×C4×D4C2313yes—
220C2×C4×D4C2313yes—
221C2×C4×D4C2313yes—
222C2×C4×D4C2313yes—
223C2×C4×D4C2313yes—
224C2×C4×D4C2313yes—
225C2×C4×D4C2313yes—
226C2×C4×D4C2313yes—
227C2×C4×D4C2313yes—
228C2×C4×D4C2316yes—
229C2×#117C2316yes—
230C2×#117C2316yes—
231C2×#117C2316yes—
232C2×#117C2316yes—
233C2×#117C2316yes—
234C2×#117C2316yes—
235C2×#117C2316yes—
236C2×#117C2313yes—
237C2×#117C2313yes—
238C2×#117C2313yes—
239C2×#117C2313yes—
240C2×#117C2311yescharacteristic
241C2×#117C2313yes—
242C2×#117C2313yes—
243C22×C4⋊C4C2316yes—
244C22×C4⋊C4C2313yes—
245C22×C42C2316yes—
246C22×C42C2313yes—
247C22×C42C2313yes—
248C22×C42C2316yes—
249C22×C42C2316yes—
250C22×C42C2313yes—
251C22×C42C2313yes—
252C22×C42C2313yes—
253#391C2316yes—
254#391C2316yes—
255#391C23112yes—
256#391C2316yes—
257#391C2316yes—
258#390C2316yes—
259#390C2316yes—
260#390C2316yes—
261#390C2316yes—
262#390C23112yes—
263#390C23112yes—
264#390C2316yes—
265#390C2316yes—
266#389C2316yes—
267#389C2316yes—
268#389C2316yes—
269#389C2316yes—
270#389C2316yes—
271#389C2316yes—
272#389C2316yes—
273#389C2316yes—
274#389C23112yes—
275#389C2316yes—
276#389C2316yes—
277#388C2316yes—
278#388C23112yes—
279#388C23112yes—
280#388C23112yes—
281#388C23112yes—
282#388C23112yes—
283#388C23112yes—
284#388C23112yes—
285#388C23112yes—
286#388C23112yes—
287#388C23112yes—
288#388C2316yes—
289#388C2316yes—
290#388C2316yes—
291#388C2316yes—
292#388C2312yes—
293#388C2312yes—
294#388C2316yes—
295#387C2316yes—
296#387C23112yes—
297#387C23112yes—
298#387C2316yes—
299#387C23112yes—
300#387C23112yes—
301#387C23112yes—
302#387C23112yes—
303#387C2316yes—
304#387C2316yes—
305#387C2316yes—
306#387C2316yes—
307#387C2312yes—
308#387C2312yes—
309#386C2316yes—
310#386C23112yes—
311#386C23112yes—
312#386C2316yes—
313#386C23112yes—
314#386C23112yes—
315#386C2316yes—
316#386C2316yes—
317#385C2316yes—
318#385C23112yes—
319#385C23112yes—
320#385C2316yes—
321#385C2316yes—
322#385C2316yes—
323#384C2316yes—
324#383C2316yes—
325#383C2316yes—
326#382C2316yes—
327#382C2316yes—
328#382C2316yes—
329#381C2316yes—
330#381C2316yes—
331#380C2316yes—
332#380C2316yes—
333#380C2316yes—
334#380C2316yes—
335C4×C4⋊C4C23112yes—
336C4×C4⋊C4C23112yes—
337C4×C4⋊C4C23112yes—
338C4×C4⋊C4C2316yes—
339C4×C4⋊C4C2316yes—
340C4×C4⋊C4C23112yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2316yes—
343C4×C4⋊C4C2316yes—
344C4×C4⋊C4C2316yes—
345C4×C4⋊C4C2316yes—
346C4×C4⋊C4C2316yes—
347C4×C4⋊C4C2316yes—
348C4×C4⋊C4C2316yes—
349C4×C4⋊C4C2316yes—
350C4×C4⋊C4C2316yes—
351C4×C4⋊C4C2316yes—
352C4×C4⋊C4C2316yes—
353C4×C4⋊C4C2316yes—
354C4×C4⋊C4C2316yes—
355C4×C4⋊C4C23112yes—
356C4×C4⋊C4C2316yes—
357C4×C4⋊C4C2316yes—
358C4×C4⋊C4C2316yes—
359C4×C4⋊C4C2313yes—
360C4×C4⋊C4C2313yes—
361C4×C4⋊C4C2313yes—
362C4×C4⋊C4C2311yescharacteristic
363C4×C4⋊C4C2311yescharacteristic
364C4×C4⋊C4C2313yes—
365C4×C4⋊C4C2316yes—
366C4×C4⋊C4C2313yes—
367C4×C4⋊C4C2313yes—
368C4×C4⋊C4C2313yes—
369C4×C4⋊C4C2313yes—
370C4×C4⋊C4C2313yes—
371C4×C4⋊C4C2313yes—
372C4×C22⋊C4C23112yes—
373C4×C22⋊C4C23112yes—
374C4×C22⋊C4C23112yes—
375C4×C22⋊C4C2316yes—
376C4×C22⋊C4C23112yes—
377C4×C22⋊C4C2316yes—
378C4×C22⋊C4C2316yes—
379C4×C22⋊C4C2316yes—
380C4×C22⋊C4C2316yes—
381C4×C22⋊C4C23112yes—
382C4×C22⋊C4C2316yes—
383C4×C22⋊C4C2316yes—
384C4×C22⋊C4C2316yes—
385C4×C22⋊C4C23112yes—
386C4×C22⋊C4C23112yes—
387C4×C22⋊C4C23112yes—
388C4×C22⋊C4C2311yescharacteristic
389C4×C22⋊C4C2313yes—
390C4×C22⋊C4C2311yescharacteristic
391C4×C22⋊C4C2313yes—
392C4×C22⋊C4C2316yes—
393C4×C22⋊C4C2313yes—
394C4×C22⋊C4C2313yes—
395C4×C22⋊C4C2313yes—
396C4×C22⋊C4C2313yes—
397C4×C22⋊C4C2316yes—
398#376C2316yes—
399#376C2316yes—
400#376C2316yes—
401#376C2316yes—
402#376C2316yes—
403#376C2316yes—
404#376C2313yes—
405#376C2311yescharacteristic
406#376C2316yes—
407C2×#95C2316yes—
408C43C2316yes—
409C43C2316yes—
410C43C2311yescharacteristic
411C43C2313yes—
412C43C2313yes—
413C43C2313yes—
414C43C2313yes—
415C43C2313yes—
416C43C2316yes—
417C2×#41—28no—
418C2×#41—28no—
419C2×#41—46no—
420C2×#41—46no—
421C2×#41C22×C418yes—
422C2×#41C22×C418yes—
423C2×#41C22×C4124yes—
424C22×Q8—28no—
425C22×Q8C22×C418yes—
426C22×Q8C2413yes—
427C22×Q8C2413yes—
428C22×Q8C2411yescharacteristic
429C22×D4C2413yes—
430C22×D4C2413yes—
431C22×D4C2416yes—
432C22×D4C2413yes—
433C22×D4C2413yes—
434C22×D4C2413yes—
435C23×C4C2416yes—
436C23×C4C2413yes—
437C23×C4C2413yes—
438C23×C4C2413yes—
439C23×C4C2413yes—
440C23×C4C2413yes—
441C23×C4C2411yescharacteristic
442C23×C4C24112yes—
443C23×C4C2416yes—
444C23×C4C2413yes—
445C23×C4C2413yes—
446C23×C4C2413yes—
447C4⋊Q8C22×C4124yes—
448#127C22×C4124yes—
449#126C22×C4148yes—
450#126C22×C4148yes—
451#125C22×C4124yes—
452#125C22×C4124yes—
453#124C22×C4124yes—
454#124C22×C4124yes—
455#124C22×C4148yes—
456#123C22×C4148yes—
457#123C22×C4148yes—
458C22⋊Q8C22×C4124yes—
459C22⋊Q8C22×C4124yes—
460#121C22×C4124yes—
461#121C22×C4124yes—
462#121C22×C4124yes—
463#121C22×C4124yes—
464#121C22×C4148yes—
465C4×Q8—28no—
466C4×Q8—28no—
467C4×Q8—28no—
468C4×Q8—224no—
469C4×Q8—224no—
470C4×Q8C22×C418yes—
471C4×Q8C22×C4124yes—
472C4×Q8C22×C418yes—
473C4×Q8C22×C4124yes—
474C4×Q8C22×C418yes—
475C4×Q8C22×C418yes—
476C4×Q8C22×C4124yes—
477C4×Q8C22×C4124yes—
478C4×Q8#41116yescomplemented
479C4×D4—224no—
480C4×D4—224no—
481C4×D4—224no—
482C4×D4—224no—
483C4×D4—424no—
484C4×D4C22×C4124yes—
485C4×D4C22×C4124yes—
486C4×D4C22×C4124yes—
487C4×D4C22×C4124yes—
488C4×D4C22×C4124yes—
489C4×D4C22×C4124yes—
490C4×D4C22×C4124yes—
491C4×D4C22×C4124yes—
492C4×D4C22×C4124yes—
493C4×D4C22×C4124yes—
494C4×D4C22×C4148yes—
495#117—224no—
496#117—224no—
497#117—224no—
498#117—224no—
499#117—46no—
500#117—412no—
501#117—46no—
502#117—412no—
503#117—412no—
504#117C22×C418yes—
505#117C22×C4124yes—
506#117C22×C4124yes—
507#117C22×C4124yes—
508#117C22×C4124yes—
509C2×C4⋊C4—224no—
510C2×C4⋊C4C22×C4124yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C2416yes—
517C2×C4⋊C4C2416yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2416yes—
520C2×C4⋊C4C2416yes—
521C2×C4⋊C4C24112yes—
522C2×C4⋊C4C2416yes—
523C2×C4⋊C4C2416yes—
524C2×C4⋊C4C2416yes—
525C2×C4⋊C4C2413yes—
526C2×C4⋊C4C2413yes—
527C2×C4⋊C4C2416yes—
528C2×C4⋊C4C2411yescharacteristic
529C2×C4⋊C4C2411yescharacteristic
530C2×C4⋊C4C2413yes—
531C2×C4⋊C4C2413yes—
532C2×C4⋊C4C2413yes—
533C2×C4⋊C4C2413yes—
534C2×C4⋊C4C2413yes—
535C2×C4⋊C4C2413yes—
536C2×C4⋊C4C2416yes—
537C2×C4⋊C4C2416yes—
538C2×C22⋊C4C2412yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2412yes—
541C2×C22⋊C4C2416yes—
542C2×C22⋊C4C24112yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C24112yes—
547C2×C22⋊C4C2416yes—
548C2×C22⋊C4C2416yes—
549C2×C22⋊C4C2416yes—
550C2×C22⋊C4C24112yes—
551C2×C22⋊C4C2411yescharacteristic
552C2×C22⋊C4C2411yescharacteristic
553C2×C22⋊C4C2413yes—
554C2×C22⋊C4C2413yes—
555C2×C22⋊C4C2416yes—
556C2×C22⋊C4C2416yes—
557C2×C22⋊C4C2413yes—
558C2×C22⋊C4C2413yes—
559C2×C22⋊C4C2416yes—
560C2×C22⋊C4C2416yes—
561C2×C42—224no—
562C2×C42—46no—
563C2×C42—412no—
564C2×C42—46no—
565C2×C42—412no—
566C2×C42C22×C4124yes—
567C2×C42C22×C4124yes—
568C2×C42C22×C4124yes—
569C2×C42C2416yes—
570C2×C42C2416yes—
571C2×C42C2416yes—
572C2×C42C24112yes—
573C2×C42C2416yes—
574C2×C42C2416yes—
575C2×C42C2412yes—
576C2×C42C2412yes—
577C2×C42C2413yes—
578C2×C42C2411yescharacteristic
579C2×C42C2411yescharacteristic
580C2×C42C2413yes—
581C2×C42C2413yes—
582C2×C42C2411yescharacteristic
583C2×C42C2413yes—
584C2×C42C2411yescharacteristic
585C2×C42C2416yes—
586C2×C42C2416yes—
587C2×C42C24112yes—
588C2×C42C2416yes—
589C2×C42C2416yes—
590C2×C42C2416yes—
591C2×C42C2416yes—
592C2×C42C24112yes—
593C2×C42C2413yes—
594C2×C42C2413yes—
595C2×C42C2413yes—
596C2×C42C2413yes—
597C2×C42C2413yes—
598C2×C42C2413yes—
599C2×C42C2411yescharacteristic
600C2×C42C2411yescharacteristic
601C2×C42C2413yes—
602C2×C42C2413yes—
603C2×C42C2416yes—
604#95C2416yes—
605#95C2416yes—
606#95C2416yes—
607#95C2412yes—
608#95C2412yes—
609#95C2412yes—
610#95C2416yes—
611#95C2412yes—
612#95C2416yes—
613#95C2416yes—
614#95C2416yes—
615#95C2416yes—
616#95C2416yes—
617#95C24112yes—
618#95C2416yes—
619#95C2416yes—
620#95C2412yes—
621#95C2412yes—
622#95C2416yes—
623#95C2416yes—
624#95C2416yes—
625#95C2416yes—
626#95C24112yes—
627#95C24112yes—
628#95C2416yes—
629#95C2416yes—
630#95C2416yes—
631#95C24112yes—
632C24C2511yescharacteristic
633C24C2513yes—
634C24C2513yes—
635#41—232no—
636#41—232no—
637#41—448no—
638C2×Q8—232no—
639C2×Q8—212no—
640C2×Q8—43no—
641C2×Q8—43no—
642C2×Q8C23×C4112yes—
643C2×Q8C23×C4112yes—
644C2×Q8C23×C414yes—
645C2×Q8C2×#4118yes—
646C2×D4—212no—
647C2×D4—212no—
648C2×D4—412no—
649C2×D4—43no—
650C2×D4—43no—
651C2×D4—43no—
652C2×D4—43no—
653C2×D4—43no—
654C2×D4—43no—
655C2×D4C23×C4112yes—
656C2×D4C23×C4112yes—
657C2×D4C23×C4112yes—
658C2×D4C23×C4112yes—
659C2×D4C23×C4112yes—
660C2×D4C23×C4124yes—
661C22×C4—212no—
662C22×C4—212no—
663C22×C4—212no—
664C22×C4—26no—
665C22×C4—26no—
666C22×C4—26no—
667C22×C4—26no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—212no—
673C22×C4—224no—
674C22×C4—46no—
675C22×C4—46no—
676C22×C4—46no—
677C22×C4—46no—
678C22×C4—46no—
679C22×C4—46no—
680C22×C4—412no—
681C22×C4—412no—
682C22×C4C23×C414yes—
683C22×C4C23×C4112yes—
684C22×C4C23×C4112yes—
685C22×C4C23×C4112yes—
686C22×C4C23×C4112yes—
687C22×C4C23×C4112yes—
688C22×C4C23×C4112yes—
689C22×C4C23×C4112yes—
690C22×C4C23×C4112yes—
691C22×C4C2516yes—
692C22×C4C2516yes—
693C22×C4C2512yes—
694C22×C4C2516yes—
695C22×C4C2512yes—
696C22×C4C2511yescharacteristic
697C22×C4C2511yescharacteristic
698C22×C4C2513yes—
699C22×C4C2511yescharacteristic
700C22×C4C2513yes—
701C22×C4C2513yes—
702C22×C4C2513yes—
703C22×C4C2513yes—
704C22×C4C2511yescharacteristic
705C22×C4C2511yescharacteristic
706C22×C4C2512yes—
707C22×C4C2516yes—
708C22×C4C2512yes—
709C22×C4C2513yes—
710C22×C4C2511yescharacteristic
711C4⋊C4—212no—
712C4⋊C4—212no—
713C4⋊C4—24no—
714C4⋊C4—212no—
715C4⋊C4—212no—
716C4⋊C4—212no—
717C4⋊C4—212no—
718C4⋊C4—24no—
719C4⋊C4—212no—
720C4⋊C4—46no—
721C4⋊C4—46no—
722C4⋊C4—46no—
723C4⋊C4—46no—
724C4⋊C4—412no—
725C4⋊C4C23×C4112yes—
726C4⋊C4C23×C4112yes—
727C4⋊C4C23×C4124yes—
728C4⋊C4C23×C414yes—
729C4⋊C4C23×C414yes—
730C4⋊C4C23×C4112yes—
731C4⋊C4C23×C4112yes—
732C4⋊C4C23×C4112yes—
733C4⋊C4C23×C4112yes—
734C4⋊C4C23×C4112yes—
735C4⋊C4C23×C4112yes—
736C4⋊C4C23×C4124yes—
737C4⋊C4C2×#41124yes—
738C22⋊C4—212no—
739C22⋊C4—24no—
740C22⋊C4—212no—
741C22⋊C4—224no—
742C22⋊C4—212no—
743C22⋊C4—24no—
744C22⋊C4—212no—
745C22⋊C4—46no—
746C22⋊C4—412no—
747C22⋊C4—46no—
748C22⋊C4—46no—
749C22⋊C4—46no—
750C22⋊C4—412no—
751C22⋊C4C23×C414yes—
752C22⋊C4C23×C414yes—
753C22⋊C4C23×C4112yes—
754C22⋊C4C23×C4112yes—
755C22⋊C4C23×C4124yes—
756C22⋊C4C23×C4124yes—
757C22⋊C4C23×C4112yes—
758C22⋊C4C23×C4112yes—
759C22⋊C4C23×C4124yes—
760C22⋊C4C23×C4124yes—
761C42—24no—
762C42—212no—
763C42—212no—
764C42—212no—
765C42—224no—
766C42—212no—
767C42—24no—
768C42—22no—
769C42—22no—
770C42—26no—
771C42—26no—
772C42—212no—
773C42—26no—
774C42—26no—
775C42—22no—
776C42—22no—
777C42—46no—
778C42—46no—
779C42—46no—
780C42—412no—
781C42—46no—
782C42—46no—
783C42—46no—
784C42—412no—
785C42C23×C414yes—
786C42C23×C414yes—
787C42C23×C4112yes—
788C42C23×C4112yes—
789C42C23×C4112yes—
790C42C23×C4112yes—
791C42C23×C4112yes—
792C42C23×C4112yes—
793C42C23×C4112yes—
794C42C23×C4112yes—
795C42C2×#41124yes—
796C23—22no—
797C23—26no—
798C23—26no—
799C23—22no—
800C23—26no—
801C23—23no—
802C23—23no—
803C23—23no—
804C23—26no—
805C23—23no—
806C23—21no—
807C23—21no—
808C23C24×C416yes—
809C23C24×C416yes—
810C23C24×C412yes—
811C23C2611yescharacteristic
812Q8—224no—
813Q8—412no—
814Q8C4×#41116yes—
815D4—224no—
816D4—224no—
817D4—424no—
818D4—412no—
819D4—412no—
820D4—412no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—26no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—26no—
829C2×C4—22no—
830C2×C4—26no—
831C2×C4—26no—
832C2×C4—23no—
833C2×C4—26no—
834C2×C4—23no—
835C2×C4—23no—
836C2×C4—22no—
837C2×C4—23no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—224no—
841C2×C4—224no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—224no—
845C2×C4—28no—
846C2×C4—22no—
847C2×C4—26no—
848C2×C4—22no—
849C2×C4—26no—
850C2×C4—26no—
851C2×C4—26no—
852C2×C4—26no—
853C2×C4—26no—
854C2×C4—22no—
855C2×C4—26no—
856C2×C4—22no—
857C2×C4—26no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—26no—
861C2×C4—412no—
862C2×C4—412no—
863C2×C4—412no—
864C2×C4—424no—
865C2×C4—424no—
866C2×C4—824no—
867C2×C4C24×C412yes—
868C2×C4C24×C412yes—
869C2×C4C24×C412yes—
870C2×C4C24×C412yes—
871C2×C4C24×C412yes—
872C2×C4C24×C416yes—
873C2×C4C24×C416yes—
874C2×C4C24×C416yes—
875C2×C4C24×C416yes—
876C2×C4C24×C416yes—
877C2×C4C24×C416yes—
878C2×C4C24×C412yes—
879C2×C4C22×#41112yes—
880C2×C4C22×#4114yes—
881C2×C4C22×#41112yes—
882C2×C4#58514yes—
883C2×C4#58512yes—
884C2×C4#58512yes—
885C22—22no—
886C22—26no—
887C22—26no—
888C22—22no—
889C22—26no—
890C22—26no—
891C22—22no—
892C22—26no—
893C22—26no—
894C22—46no—
895C22—42no—
896C22—46no—
897C22—46no—
898C22—46no—
899C22—42no—
900C22C25×C411yescharacteristic
901C22C23×#4112yes—
902C22C2×#58511yescharacteristic
903C22C2×#58512yes—
904C22C2×#58511yescharacteristic
905C4—24no—
906C4—24no—
907C4—212no—
908C4—22no—
909C4—22no—
910C4—26no—
911C4—22no—
912C4—26no—
913C4—26no—
914C4—22no—
915C4—26no—
916C4—22no—
917C4—26no—
918C4—42no—
919C4—46no—
920C4—46no—
921C4—42no—
922C4—46no—
923C4C2×C4×#41112yes—
924C4#342814yes—
925C2—42no—
926C2—46no—
927C2—46no—
928C2C22×C4×#4111yescharacteristic
929C2C2×#342811yescharacteristic
930C2C4×#58511yescharacteristic
931C2#6279312yes—
932C2#6281012yes—
subgroupG/H
centerC22×C4C25
commutatorC22C25×C4
Frattini, socle, cosocleC23C26
prime radicalC2×#3480C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34336C2semidirect
3. #34329C2semidirect
4. #34319C2semidirect
5. #34312C2semidirect
6. #34307C2semidirect
7. #34301C2semidirect
8. #34295C2semidirect
9. #34293C2semidirect
10. #34155C2semidirect
11. #34153C2semidirect
12. #34151C2semidirect
13. #34129C2semidirect
14. #34128C2semidirect
15. #34125C2semidirect
16. #34121C2semidirect
17. #34086C2semidirect
18. #34084C2semidirect
19. C4×#529C2semidirect
20. #34026C2semidirect
21. C4×#519C2semidirect
22. C4×#520C2semidirect
23. C42×#41C2semidirect
24. #3480C4semidirect
163. #559C2×C4semidirect
164. #557C2×C4semidirect
165. #556C2×C4semidirect
166. #553C2×C4semidirect
167. #553C2×C4semidirect
169. #548C2×C4semidirect
170. #548C2×C4semidirect
171. #532C2×C4semidirect
174. #529C2×C4semidirect
175. #529C2×C4semidirect
195. C4×#41C2×C4semidirect
196. C4×#41C2×C4semidirect
197. C4×#41C2×C4semidirect
198. C2×C4×Q8C2×C4semidirect
478. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34802
#343362
#343292
#343192
#343122
#343072
#343012
#342952
#342932
#341552
#341532
#341512
#341292
#341282
#341252
#341212
#340862
#340842
C4×#5292
#340262
C4×#5192
C4×#5202
C42×#412