Finite Group Databasebeta

← #7630376

Subgroups — #7630376

Order 512.

7836 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C212yesmaximal, complemented
2#36631C213yesmaximal, complemented
3#36576C211yesmaximal, characteristic, complemented
4Q8×#121C211yesmaximal, characteristic, complemented
5#36467C212yesmaximal, complemented
6#36466C211yesmaximal, characteristic, complemented
7#36465C211yesmaximal, characteristic, complemented
8#36434C212yesmaximal, complemented
9#36424C216yesmaximal, complemented
10#36271C213yesmaximal, complemented
11#36270C213yesmaximal, complemented
12#36268C216yesmaximal, complemented
13#36186C213yesmaximal, complemented
14#36126C213yesmaximal, complemented
15#34964C216yesmaximal, complemented
16#34934C213yesmaximal, complemented
17#34929C213yesmaximal, complemented
18#34919C216yesmaximal, complemented
19C4×D4×Q8C211yesmaximal, characteristic, complemented
20C4×#550C211yesmaximal, characteristic, complemented
21C4×#548C212yesmaximal, complemented
22C4×#532C213yesmaximal, complemented
23C2×C42×Q8C211yesmaximal, characteristic, complemented
24#3482—232no—
25C2×#557C2212yes—
26C2×#556C2216yes—
27C2×#552C2216yes—
28C2×#552C2216yes—
29C2×#550C2211yescharacteristic
30C2×D4×Q8C2212yes—
31C2×D4×Q8C2211yescharacteristic
32C2×#548C2212yes—
33C2×#548C2212yes—
34C2×#548C2212yes—
35C2×#547C2216yes—
36C2×#533C2216yes—
37C2×#532C2213yes—
38C2×#529C2216yes—
39C2×#529C2216yes—
40C2×C4×#41C2212yes—
41C2×C4×#41C2216yes—
42C22×C4×Q8C2211yescharacteristic
43C22×C4×Q8C2212yes—
44C22×C4×Q8C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46#2861C2216yes—
47#2860C2216yes—
48#2860C2216yes—
49#2859C2213yes—
50#2858C2213yes—
51#2857C2213yes—
52#2856C2213yes—
53#2854C2216yes—
54#2854C2216yes—
55#2850C2216yes—
56#2601C22112yes—
57#2601C22112yes—
58#2592C2216yes—
59#2584C2216yes—
60#2562C2216yes—
61#2560C22112yes—
62#2558C22112yes—
63#2556C22112yes—
64#2554C22112yes—
65#2552C2213yes—
66#2551C2213yes—
67#2550C2216yes—
68#2548C2213yes—
69#2546C2213yes—
70#2545C2216yes—
71#2542C2213yes—
72#2541C2213yes—
73#2540C2216yes—
74#2540C2216yes—
75#2538C2213yes—
76#2538C2213yes—
77#2536C2216yes—
78#2519C22112yes—
79#2512C2216yes—
80#2506C2216yes—
81#2498C22112yes—
82#2492C2216yes—
83#2491C2216yes—
84#2490C2216yes—
85#2489C2216yes—
86#2461C22112yes—
87#2452C2216yes—
88#2445C2216yes—
89#2430C22112yes—
90#2429C2216yes—
91#2429C2216yes—
92#2426C2216yes—
93#2426C2216yes—
94#2417C2216yes—
95#2417C2216yes—
96#2416C2216yes—
97#2416C2216yes—
98#2396C22112yes—
99#2392C22112yes—
100#2367C2216yes—
101#2366C2213yes—
102#2365C2213yes—
103#2363C2216yes—
104#2362C2216yes—
105#2361C2216yes—
106#2360C2216yes—
107#2354C2213yes—
108#2352C2216yes—
109#2351C2212yes—
110Q8×C4⋊C4C2211yescharacteristic
111Q8×C4⋊C4C2211yescharacteristic
112D4×C4⋊C4C2213yes—
113#2341C2212yes—
114#2341C2212yes—
115Q8×C22⋊C4C2212yes—
116Q8×C22⋊C4C2212yes—
117C4×C4⋊Q8C2213yes—
118C4×C4⋊Q8C2213yes—
119C4×C4⋊Q8C2213yes—
120C4×#127C2213yes—
121C4×#127C2213yes—
122C4×#127C2213yes—
123C4×#124C2216yes—
124C4×#124C2216yes—
125C4×#124C2216yes—
126C4×C22⋊Q8C2216yes—
127C4×C22⋊Q8C2216yes—
128C4×#121C2213yes—
129C4×#121C2216yes—
130C4×#121C2213yes—
131C4×#121C2216yes—
132C4×#121C2213yes—
133C4×#121C2216yes—
134C4×#121C2216yes—
135C4×#121C2216yes—
136C4×#121C2211yescharacteristic
137#2297C2216yes—
138#2293C2216yes—
139#2293C2216yes—
140#2293C2216yes—
141#2293C2213yes—
142#2293C2213yes—
143#2285C2213yes—
144C42×Q8C2213yes—
145C42×Q8C2211yescharacteristic
146C42×Q8C2211yescharacteristic
147C42×Q8C2213yes—
148C42×Q8C2211yescharacteristic
149C42×Q8C2211yescharacteristic
150C42×Q8C2213yes—
151C42×Q8C2213yes—
152C42×D4C2216yes—
153C42×D4C2213yes—
154C42×D4C2213yes—
155C2×C4×C4⋊C4C2213yes—
156C2×C4×C4⋊C4C2213yes—
157C2×C4×C4⋊C4C2213yes—
158C2×C43C2213yes—
159C22×#41C2312yes—
160C22×#41C2316yes—
161C23×Q8C2312yes—
162C23×Q8C2311yescharacteristic
163#557—216no—
164#556—248no—
165#552—248no—
166#552—248no—
167#550—28no—
168D4×Q8—216no—
169D4×Q8—28no—
170#548—216no—
171#548—216no—
172#548—216no—
173#547—248no—
174#533—248no—
175#532—224no—
176C2×C4⋊Q8C2313yes—
177C2×C4⋊Q8C2313yes—
178C2×C4⋊Q8C2316yes—
179C2×C4⋊Q8C2316yes—
180C2×#127C2313yes—
181C2×#127C2313yes—
182#529—248no—
183#529—248no—
184C2×#126C23112yes—
185C2×#126C23112yes—
186C2×#125C2316yes—
187C2×#125C2316yes—
188C2×#125C23112yes—
189C2×#124C2316yes—
190C2×#124C2316yes—
191C2×#124C2316yes—
192C2×#124C2316yes—
193C2×#123C23112yes—
194C2×#123C23112yes—
195C2×C22⋊Q8C23112yes—
196C2×C22⋊Q8C2316yes—
197C2×C22⋊Q8C2316yes—
198C2×C22⋊Q8C2316yes—
199C2×C22⋊Q8C2316yes—
200C2×C22⋊Q8C2316yes—
201C2×C22⋊Q8C2316yes—
202C2×#121C2316yes—
203C2×#121C2313yes—
204C2×#121C2316yes—
205C2×#121C2316yes—
206C2×#121C2316yes—
207C2×#121C2316yes—
208C2×#121C2316yes—
209C2×#121C2311yescharacteristic
210C4×#41—216no—
211C4×#41—248no—
212C2×C4×Q8—216no—
213C2×C4×Q8—28no—
214C2×C4×Q8—28no—
215C2×C4×Q8D4116yescomplemented
216C2×C4×Q8C2316yes—
217C2×C4×Q8C2316yes—
218C2×C4×Q8C2316yes—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2316yes—
224C2×C4×Q8C2313yes—
225C2×C4×Q8C2313yes—
226C2×C4×Q8C2313yes—
227C2×C4×Q8C2313yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2313yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2313yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2313yes—
236C2×C4×D4C2316yes—
237C2×C4×D4C2313yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2313yes—
240C2×C4×D4C2316yes—
241C2×C4×D4C2316yes—
242C2×C4×D4C2313yes—
243C2×C4×D4C2316yes—
244C2×C4×D4C2316yes—
245C2×C4×D4C2313yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2316yes—
249C2×C4×D4C2316yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×#117C2316yes—
253C2×#117C2316yes—
254C2×#117C2316yes—
255C2×#117C23112yes—
256C2×#117C2316yes—
257C22×C4⋊C4C2316yes—
258C22×C4⋊C4C2313yes—
259C22×C4⋊C4C2313yes—
260C22×C4⋊C4C2313yes—
261C22×C42C2313yes—
262C22×C42C2313yes—
263C22×C42C2313yes—
264C22×C42C2316yes—
265C22×C42C2316yes—
266C22×C42C2311yescharacteristic
267C22×C42C2313yes—
268C22×C42C2313yes—
269C22×C42C2313yes—
270#400C23112yes—
271#399C23112yes—
272#398C23112yes—
273#398C23112yes—
274#398C23112yes—
275#397C23112yes—
276#396C23112yes—
277#396C23112yes—
278#396C23112yes—
279#396C23112yes—
280#395C23112yes—
281#394C23112yes—
282#394C23112yes—
283#394C23112yes—
284#393C23112yes—
285#392C23112yes—
286#391C2316yes—
287#391C2316yes—
288#391C2316yes—
289#391C2316yes—
290#391C2316yes—
291#391C2316yes—
292#390C2316yes—
293#390C2311yescharacteristic
294#390C2316yes—
295#390C2316yes—
296#390C2316yes—
297#390C2316yes—
298#390C2313yes—
299#390C2316yes—
300#390C2313yes—
301#390C2316yes—
302#390C2313yes—
303#390C2316yes—
304#390C2316yes—
305#390C2316yes—
306#390C2316yes—
307#390C2316yes—
308#390C2316yes—
309#390C2316yes—
310#390C2316yes—
311#389C2311yescharacteristic
312#389C2316yes—
313#389C2316yes—
314#389C2316yes—
315#389C2313yes—
316#389C2316yes—
317#389C2313yes—
318#389C2313yes—
319#389C2316yes—
320#389C2316yes—
321#389C2316yes—
322#389C2316yes—
323#389C2316yes—
324#389C2316yes—
325#389C2316yes—
326#389C2316yes—
327#389C2316yes—
328#388C2316yes—
329#388C23112yes—
330#388C23112yes—
331#388C2316yes—
332#388C23112yes—
333#388C2316yes—
334#388C23112yes—
335#388C23112yes—
336#388C23112yes—
337#388C23112yes—
338#388C23112yes—
339#388C23112yes—
340#388C2316yes—
341#388C2316yes—
342#388C2316yes—
343#388C2316yes—
344#388C2312yes—
345#387C23112yes—
346#387C23112yes—
347#386C23112yes—
348#386C2316yes—
349#386C23112yes—
350#386C23112yes—
351#386C2316yes—
352#386C2316yes—
353#386C2312yes—
354#385C23112yes—
355#385C23112yes—
356#384C2313yes—
357#384C2313yes—
358#384C2313yes—
359#384C2313yes—
360#382C2316yes—
361#382C2316yes—
362#380C2316yes—
363#380C2316yes—
364#380C2316yes—
365#380C2316yes—
366#380C2313yes—
367#380C2316yes—
368#380C2316yes—
369#380C2311yescharacteristic
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2313yes—
372C4×C4⋊C4C2311yescharacteristic
373C4×C4⋊C4C2313yes—
374C4×C4⋊C4C2313yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2316yes—
377C4×C4⋊C4C2316yes—
378C4×C4⋊C4C2316yes—
379C4×C4⋊C4C2313yes—
380C4×C4⋊C4C2316yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2313yes—
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2313yes—
385C4×C4⋊C4C2313yes—
386C4×C4⋊C4C2316yes—
387C4×C4⋊C4C2313yes—
388C4×C4⋊C4C2316yes—
389C4×C4⋊C4C2316yes—
390C4×C4⋊C4C2316yes—
391C4×C4⋊C4C2313yes—
392C4×C4⋊C4C2313yes—
393C4×C4⋊C4C2313yes—
394C4×C4⋊C4C2313yes—
395C4×C4⋊C4C2316yes—
396C4×C4⋊C4C2313yes—
397C4×C4⋊C4C2313yes—
398C4×C22⋊C4C2316yes—
399C4×C22⋊C4C2316yes—
400C4×C22⋊C4C2316yes—
401C4×C22⋊C4C2316yes—
402C4×C22⋊C4C2316yes—
403C4×C22⋊C4C2316yes—
404C4×C22⋊C4C2316yes—
405C4×C22⋊C4C2316yes—
406C4×C22⋊C4C2316yes—
407C4×C22⋊C4C23112yes—
408C4×C22⋊C4C2316yes—
409C4×C22⋊C4C2312yes—
410C4×C22⋊C4C2316yes—
411C2×#95C2316yes—
412C43C2313yes—
413C43C2313yes—
414C43C2313yes—
415C43C2313yes—
416C43C2313yes—
417C43C2313yes—
418C43C2313yes—
419C43C2313yes—
420C2×#41—28no—
421C2×#41—28no—
422C2×#41—28no—
423C2×#41—224no—
424C2×#41—224no—
425C2×#41—412no—
426C22×Q8—24no—
427C22×Q8—24no—
428C22×Q8—28no—
429C22×Q8—28no—
430C22×Q8—28no—
431C22×Q8C2×D418yes—
432C22×Q8C2416yes—
433C22×Q8C2416yes—
434C22×Q8C2413yes—
435C22×Q8C2411yescharacteristic
436C22×D4C2413yes—
437C22×D4C2416yes—
438C22×D4C2416yes—
439C22×D4C2416yes—
440C22×D4C2416yes—
441C22×D4C2411yescharacteristic
442C22×D4C2412yes—
443C22×D4C2416yes—
444C23×C4C2416yes—
445C23×C4C2416yes—
446C23×C4C2411yescharacteristic
447C23×C4C2416yes—
448C23×C4C2412yes—
449C23×C4C2416yes—
450C23×C4C2413yes—
451C23×C4C2413yes—
452C23×C4C2416yes—
453C23×C4C2413yes—
454C23×C4C2413yes—
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C4⋊Q8—224no—
458C4⋊Q8—224no—
459C4⋊Q8—212no—
460C4⋊Q8—212no—
461#127—212no—
462#127—212no—
463#126—248no—
464#126—248no—
465#125—224no—
466#125—248no—
467#125—224no—
468#124—224no—
469#124—224no—
470#124—224no—
471#124—224no—
472#123—248no—
473#123—248no—
474C22⋊Q8—224no—
475C22⋊Q8—224no—
476C22⋊Q8—224no—
477C22⋊Q8—248no—
478C22⋊Q8—224no—
479C22⋊Q8—224no—
480C22⋊Q8—224no—
481#121—224no—
482#121—224no—
483#121—212no—
484#121—224no—
485#121—224no—
486#121—224no—
487#121—412no—
488#121#4118yescomplemented
489C4×Q8—28no—
490C4×Q8—28no—
491C4×Q8—24no—
492C4×Q8—24no—
493C4×Q8—224no—
494C4×Q8—212no—
495C4×Q8—212no—
496C4×Q8—224no—
497C4×Q8—224no—
498C4×Q8—224no—
499C4×Q8—212no—
500C4×Q8—212no—
501C4×Q8C2×D418yes—
502C4×Q8C2×D4124yes—
503C4×Q8C2×D418yes—
504C4×Q8C2×D4124yes—
505C4×Q8#4118yescomplemented
506C4×Q8#4118yescomplemented
507C4×D4—212no—
508C4×D4—28no—
509C4×D4—224no—
510C4×D4—224no—
511C4×D4—224no—
512C4×D4—224no—
513C4×D4—212no—
514C4×D4—224no—
515C4×D4—224no—
516C4×D4—224no—
517C4×D4—224no—
518C4×D4—224no—
519C4×D4—212no—
520C4×D4—212no—
521C4×D4—24no—
522C4×D4—212no—
523C4×D4—412no—
524C4×D4—412no—
525#117—224no—
526#117—224no—
527#117—224no—
528#117—224no—
529#117—248no—
530C2×C4⋊C4—224no—
531C2×C4⋊C4—212no—
532C2×C4⋊C4—212no—
533C2×C4⋊C4C2×D4124yes—
534C2×C4⋊C4C2416yes—
535C2×C4⋊C4C24112yes—
536C2×C4⋊C4C2413yes—
537C2×C4⋊C4C2413yes—
538C2×C4⋊C4C2416yes—
539C2×C4⋊C4C2416yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2416yes—
542C2×C4⋊C4C2416yes—
543C2×C4⋊C4C2416yes—
544C2×C4⋊C4C2416yes—
545C2×C4⋊C4C2416yes—
546C2×C4⋊C4C2416yes—
547C2×C4⋊C4C24112yes—
548C2×C4⋊C4C24112yes—
549C2×C4⋊C4C2411yescharacteristic
550C2×C4⋊C4C2413yes—
551C2×C4⋊C4C2416yes—
552C2×C4⋊C4C2416yes—
553C2×C4⋊C4C2413yes—
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2413yes—
556C2×C4⋊C4C2416yes—
557C2×C4⋊C4C2416yes—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2413yes—
561C2×C4⋊C4C2413yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2413yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2411yescharacteristic
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2416yes—
569C2×C22⋊C4C2416yes—
570C2×C22⋊C4C24112yes—
571C2×C22⋊C4C2416yes—
572C2×C22⋊C4C2416yes—
573C2×C22⋊C4C24112yes—
574C2×C22⋊C4C24112yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2416yes—
577C2×C22⋊C4C2416yes—
578C2×C22⋊C4C2416yes—
579C2×C22⋊C4C2416yes—
580C2×C22⋊C4C2416yes—
581C2×C22⋊C4C2416yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2416yes—
584C2×C22⋊C4C24112yes—
585C2×C22⋊C4C2416yes—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C24112yes—
588C2×C22⋊C4C24112yes—
589C2×C22⋊C4C2412yes—
590C2×C42—212no—
591C2×C42—224no—
592C2×C42—224no—
593C2×C42—212no—
594C2×C42—212no—
595C2×C42—24no—
596C2×C42—46no—
597C2×C42—46no—
598C2×C42C2×D4124yes—
599C2×C42C2416yes—
600C2×C42C2416yes—
601C2×C42C2416yes—
602C2×C42C2413yes—
603C2×C42C2413yes—
604C2×C42C2416yes—
605C2×C42C2413yes—
606C2×C42C2413yes—
607C2×C42C2413yes—
608C2×C42C2413yes—
609C2×C42C2413yes—
610C2×C42C2413yes—
611C2×C42C2413yes—
612C2×C42C2413yes—
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2416yes—
616C2×C42C2413yes—
617C2×C42C2413yes—
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620C2×C42C2413yes—
621C2×C42C2413yes—
622C2×C42C2413yes—
623C2×C42C2413yes—
624C2×C42C2413yes—
625C2×C42C2413yes—
626C2×C42C2413yes—
627C2×C42C2413yes—
628C2×C42C2413yes—
629C2×C42C2413yes—
630C2×C42C2413yes—
631C2×C42C2413yes—
632C2×C42C2411yescharacteristic
633#95C2416yes—
634#95C2416yes—
635#95C2416yes—
636#95C2416yes—
637#95C2412yes—
638#95C2412yes—
639#95C2412yes—
640#95C2416yes—
641#95C2416yes—
642#95C2416yes—
643#95C2416yes—
644#95C2416yes—
645#95C2416yes—
646#95C2416yes—
647#95C2416yes—
648#95C2416yes—
649#95C24112yes—
650#95C24112yes—
651#95C24112yes—
652C24C2516yes—
653C24C2512yes—
654C24C2511yescharacteristic
655#41—496no—
656#41—432no—
657C2×Q8—232no—
658C2×Q8—212no—
659C2×Q8—212no—
660C2×Q8—26no—
661C2×Q8—26no—
662C2×Q8—212no—
663C2×Q8—212no—
664C2×Q8—212no—
665C2×Q8—46no—
666C2×Q8—432no—
667C2×Q8C22×D4112yes—
668C2×Q8C22×D414yes—
669C2×Q8C2×#4114yes—
670C2×Q8C2×#4114yes—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—212no—
674C2×D4—212no—
675C2×D4—212no—
676C2×D4—212no—
677C2×D4—212no—
678C2×D4—212no—
679C2×D4—212no—
680C2×D4—22no—
681C2×D4—212no—
682C2×D4—26no—
683C2×D4—26no—
684C2×D4—212no—
685C2×D4—212no—
686C2×D4—212no—
687C2×D4—22no—
688C2×D4—26no—
689C2×D4—46no—
690C2×D4—46no—
691C2×D4—46no—
692C2×D4—46no—
693C2×D4C2×#4114yes—
694C2×D4C2×#4118yes—
695C22×C4—26no—
696C22×C4—22no—
697C22×C4—26no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—26no—
701C22×C4—26no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—26no—
707C22×C4—212no—
708C22×C4—26no—
709C22×C4—24no—
710C22×C4—212no—
711C22×C4—212no—
712C22×C4—212no—
713C22×C4—212no—
714C22×C4—212no—
715C22×C4—26no—
716C22×C4—26no—
717C22×C4—212no—
718C22×C4—212no—
719C22×C4—212no—
720C22×C4—212no—
721C22×C4—212no—
722C22×C4—24no—
723C22×C4—212no—
724C22×C4—24no—
725C22×C4—212no—
726C22×C4—43no—
727C22×C4—43no—
728C22×C4—46no—
729C22×C4—46no—
730C22×C4C22×D414yes—
731C22×C4C22×D4112yes—
732C22×C4C22×D4112yes—
733C22×C4C2×#4114yes—
734C22×C4C2513yes—
735C22×C4C2513yes—
736C22×C4C2512yes—
737C22×C4C2512yes—
738C22×C4C2516yes—
739C22×C4C2516yes—
740C22×C4C2516yes—
741C22×C4C2513yes—
742C22×C4C2513yes—
743C22×C4C2511yescharacteristic
744C22×C4C2513yes—
745C22×C4C2511yescharacteristic
746C22×C4C2511yescharacteristic
747C22×C4C2513yes—
748C22×C4C2513yes—
749C22×C4C2512yes—
750C22×C4C2511yescharacteristic
751C22×C4C2513yes—
752C22×C4C2511yescharacteristic
753C22×C4C2511yescharacteristic
754C4⋊C4—212no—
755C4⋊C4—224no—
756C4⋊C4—24no—
757C4⋊C4—212no—
758C4⋊C4—212no—
759C4⋊C4—212no—
760C4⋊C4—212no—
761C4⋊C4—212no—
762C4⋊C4—212no—
763C4⋊C4—224no—
764C4⋊C4—224no—
765C4⋊C4—212no—
766C4⋊C4—212no—
767C4⋊C4—26no—
768C4⋊C4—26no—
769C4⋊C4—22no—
770C4⋊C4—212no—
771C4⋊C4—26no—
772C4⋊C4—212no—
773C4⋊C4—26no—
774C4⋊C4—212no—
775C4⋊C4—22no—
776C4⋊C4—26no—
777C4⋊C4—46no—
778C4⋊C4—46no—
779C4⋊C4—46no—
780C4⋊C4C22×D4112yes—
781C4⋊C4C22×D4112yes—
782C4⋊C4C22×D4124yes—
783C4⋊C4C2×#41112yes—
784C4⋊C4C2×#41112yes—
785C4⋊C4C2×#4114yes—
786C22⋊C4—24no—
787C22⋊C4—212no—
788C22⋊C4—212no—
789C22⋊C4—24no—
790C22⋊C4—212no—
791C22⋊C4—224no—
792C22⋊C4—212no—
793C22⋊C4—212no—
794C22⋊C4—224no—
795C22⋊C4—224no—
796C22⋊C4—24no—
797C22⋊C4—212no—
798C22⋊C4—212no—
799C22⋊C4—212no—
800C22⋊C4—212no—
801C22⋊C4—212no—
802C22⋊C4—224no—
803C22⋊C4—24no—
804C22⋊C4—212no—
805C22⋊C4—46no—
806C22⋊C4—46no—
807C22⋊C4—412no—
808C22⋊C4—412no—
809C22⋊C4C2×#4118yes—
810C42—24no—
811C42—212no—
812C42—212no—
813C42—212no—
814C42—212no—
815C42—212no—
816C42—26no—
817C42—26no—
818C42—26no—
819C42—26no—
820C42—26no—
821C42—26no—
822C42—26no—
823C42—26no—
824C42—26no—
825C42—26no—
826C42—22no—
827C42—22no—
828C42—22no—
829C42—26no—
830C42—26no—
831C42—43no—
832C42—43no—
833C42—43no—
834C42—43no—
835C42—43no—
836C42—43no—
837C42C22×D4112yes—
838C42C22×D4112yes—
839C42C22×D4112yes—
840C42C22×D4112yes—
841C42C2×#41112yes—
842C42C2×#41112yes—
843C422−1+414yes—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—26no—
855C23—26no—
856C23—26no—
857C23—26no—
858C23—26no—
859C23—26no—
860C23—26no—
861C23C23×D412yes—
862C23C22×#4114yes—
863C23C22×#4112yes—
864C23#58512yes—
865C23C2611yescharacteristic
866Q8—224no—
867Q8—424no—
868Q8—424no—
869Q8#532116yescomplemented
870D4—216no—
871D4—28no—
872D4—424no—
873D4—424no—
874D4—424no—
875D4—424no—
876D4—412no—
877D4—812no—
878C2×C4—28no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—23no—
883C2×C4—23no—
884C2×C4—23no—
885C2×C4—23no—
886C2×C4—23no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—23no—
891C2×C4—23no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—23no—
896C2×C4—23no—
897C2×C4—23no—
898C2×C4—22no—
899C2×C4—224no—
900C2×C4—224no—
901C2×C4—28no—
902C2×C4—28no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—26no—
906C2×C4—26no—
907C2×C4—26no—
908C2×C4—23no—
909C2×C4—23no—
910C2×C4—23no—
911C2×C4—22no—
912C2×C4—26no—
913C2×C4—26no—
914C2×C4—22no—
915C2×C4—26no—
916C2×C4—22no—
917C2×C4—26no—
918C2×C4—23no—
919C2×C4—23no—
920C2×C4—23no—
921C2×C4—22no—
922C2×C4—26no—
923C2×C4—26no—
924C2×C4—424no—
925C2×C4—412no—
926C2×C4—412no—
927C2×C4—424no—
928C2×C4—424no—
929C2×C4—424no—
930C2×C4—48no—
931C2×C4—424no—
932C2×C4C23×D416yes—
933C2×C4C23×D412yes—
934C2×C4C23×D416yes—
935C2×C4C23×D416yes—
936C2×C4C23×D416yes—
937C2×C4C23×D412yes—
938C2×C4C22×#4112yes—
939C2×C4C22×#4112yes—
940C2×C4C22×#4116yes—
941C2×C4C22×#4116yes—
942C2×C4C22×#4114yes—
943C2×C4C22×#4116yes—
944C2×C4C22×#4116yes—
945C2×C4C22×#4112yes—
946C2×C4C22×#4112yes—
947C2×C4C2×2−1+412yes—
948C2×C4C2×2−1+412yes—
949C2×C4C2×2−1+412yes—
950C2×C4#58512yes—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—46no—
965C22—46no—
966C22—46no—
967C22—46no—
968C22—46no—
969C22—46no—
970C22—46no—
971C22D4×#4114yes—
972C22C24×D411yescharacteristic
973C22C23×#4111yescharacteristic
974C22C23×#4111yescharacteristic
975C22C23×#4111yescharacteristic
976C22C22×2−1+411yescharacteristic
977C22C2×#58511yescharacteristic
978C22C2×#58511yescharacteristic
979C4—22no—
980C4—22no—
981C4—22no—
982C4—26no—
983C4—26no—
984C4—26no—
985C4—26no—
986C4—24no—
987C4—22no—
988C4—26no—
989C4—42no—
990C4—46no—
991C4—43no—
992C4—42no—
993C4—46no—
994C4—46no—
995C4—43no—
996C4C2×#532112yes—
997C4#348214yescomplemented
998C4#349714yes—
999C2—24no—
1000C2—44no—
1001C2—86no—
1002C2C22×#53211yescharacteristic
1003C2C2×D4×#4111yescharacteristic
1004C2C2×#348211yescharacteristic
1005C2#41211yescharacteristic
1006C2C2×#349711yescharacteristic
1007C2#6278811yescharacteristic
1008C2#6281011yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
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. C2×#3482C2semidirect
2. #36631C2semidirect
3. #36576C2semidirect
4. Q8×#121C2semidirect
5. #36467C2semidirect
6. #36466C2semidirect
7. #36465C2semidirect
8. #36434C2semidirect
9. #36424C2semidirect
10. #36271C2semidirect
11. #36270C2semidirect
12. #36268C2semidirect
13. #36186C2semidirect
14. #36126C2semidirect
15. #34964C2semidirect
16. #34934C2semidirect
17. #34929C2semidirect
18. #34919C2semidirect
19. C4×D4×Q8C2semidirect
20. C4×#550C2semidirect
21. C4×#548C2semidirect
22. C4×#532C2semidirect
23. C2×C42×Q8C2semidirect
215. C2×C4×Q8D4semidirect
488. #121#41semidirect
505. C4×Q8#41semidirect
506. C4×Q8#41semidirect
869. Q8#532semidirect
997. C4#3482semidirect

Maximal subgroups

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

subgroupindex
C2×#34822
#366312
#365762
Q8×#1212
#364672
#364662
#364652
#364342
#364242
#362712
#362702
#362682
#361862
#361262
#349642
#349342
#349292
#349192
C4×D4×Q82
C4×#5502
C4×#5482
C4×#5322
C2×C42×Q82