Finite Group Databasebeta

← #7632693

Subgroups — #7632693

Order 512.

8119 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C211yesmaximal, characteristic
2C2×#3503C211yesmaximal, characteristic, complemented
3Q8×#124C212yesmaximal, complemented
4#36467C212yesmaximal, complemented
5#36303C216yesmaximal, complemented
6#36238C216yesmaximal, complemented
7#36042C216yesmaximal, complemented
8#35948C212yesmaximal, complemented
9#35939C216yesmaximal, complemented
10#35910C212yesmaximal, complemented
11#35644C213yesmaximal, complemented
12#35628C213yesmaximal, complemented
13#35592C213yesmaximal, complemented
14#35542C213yesmaximal, complemented
15#35312C213yesmaximal, complemented
16#35158C213yesmaximal, complemented
17#34813C213yesmaximal, complemented
18C2×#2492C213yesmaximal, complemented
19#34259C211yesmaximal, characteristic, complemented
20#34259C211yesmaximal, characteristic, complemented
21#34175C211yesmaximal, characteristic, complemented
22C22⋊C4×#41C211yesmaximal, characteristic, complemented
23C4×#520C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C23×#41C2211yescharacteristic
26#3503—216no—
27#3489—216no—
28C2×Q82C2212yescomplemented
29C2×#557C2212yescomplemented
30C2×#554C2216yescomplemented
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2216yescomplemented
33C2×#548C2212yes—
34C2×#547C2216yes—
35C2×#546C2216yes—
36C2×#544C2213yescomplemented
37C2×#544C2213yescomplemented
38C2×#537C2213yes—
39C2×#536C2213yes—
40C2×#533C2213yescomplemented
41C22×C4⋊Q8C2213yescomplemented
42C2×#525C2213yes—
43C22×C22⋊Q8C2213yes—
44C2×#520C2211yescharacteristic
45C2×#520C2211yescharacteristic
46C2×#520C2211yescharacteristic
47C2×C4×#41C2211yescharacteristic
48C2×C4×#41C2211yescharacteristic
49#2862C2216yescomplemented
50#2861C2216yescomplemented
51#2850C22112yescomplemented
52#2642C2216yescomplemented
53#2640C2216yescomplemented
54#2639C22112yescomplemented
55#2592C2216yescomplemented
56#2592C2216yescomplemented
57#2591C22112yescomplemented
58#2568C2216yescomplemented
59#2568C2216yescomplemented
60#2563C2216yes—
61#2562C2216yes—
62#2562C2216yescomplemented
63#2561C22112yes—
64#2547C2216yescomplemented
65#2503C22112yescomplemented
66#2492C2216yes—
67#2492C2216yes—
68#2492C2216yes—
69#2492C2216yes—
70#2492C2213yes—
71#2492C2216yescomplemented
72#2492C2216yescomplemented
73#2492C2216yescomplemented
74#2492C2216yescomplemented
75#2492C2213yescomplemented
76#2492C2216yescomplemented
77#2492C2216yescomplemented
78#2492C2216yescomplemented
79#2492C2216yescomplemented
80#2492C2216yescomplemented
81#2491C2211yescharacteristic
82#2491C2213yescomplemented
83#2491C2216yescomplemented
84#2491C2216yescomplemented
85#2491C2216yescomplemented
86#2491C2216yescomplemented
87#2490C2213yes—
88#2490C2213yescomplemented
89#2490C2216yescomplemented
90#2489C2213yes—
91#2489C2216yes—
92#2489C2216yescomplemented
93#2489C2216yescomplemented
94#2489C2216yescomplemented
95#2489C2216yescomplemented
96#2489C2213yescomplemented
97#2488C22112yescomplemented
98#2488C22112yescomplemented
99#2488C22112yescomplemented
100#2488C22112yescomplemented
101#2488C2216yescomplemented
102#2488C22112yescomplemented
103#2488C2216yescomplemented
104#2472C2216yes—
105#2472C22112yes—
106#2472C2216yes—
107#2436C22112yescomplemented
108#2398C2216yes—
109#2398C2216yescomplemented
110C2×#400C2216yescomplemented
111C2×#393C2216yes—
112#2341C2211yescharacteristic
113#2341C2211yescharacteristic
114#2341C2212yes—
115Q8×C22⋊C4C2211yescharacteristic
116Q8×C22⋊C4C2211yescharacteristic
117Q8×C22⋊C4C2212yes—
118Q8×C22⋊C4C2212yescomplemented
119Q8×C22⋊C4C2212yescomplemented
120Q8×C22⋊C4C2212yescomplemented
121Q8×C22⋊C4C2212yescomplemented
122#2339C2213yes—
123#2339C2213yes—
124#2339C2216yes—
125#2339C2216yescomplemented
126#2339C2216yescomplemented
127#2339C2216yescomplemented
128#2339C2216yescomplemented
129D4×C22⋊C4C2213yes—
130D4×C22⋊C4C2213yes—
131D4×C22⋊C4C2216yes—
132#2311C2213yes—
133#2311C2213yes—
134#2311C2213yescomplemented
135#2311C2213yescomplemented
136#2310C2213yescomplemented
137#2310C2213yescomplemented
138C4×#124C2216yes—
139C4×#124C2216yescomplemented
140#2297C2213yes—
141#2297C2213yes—
142#2297C2213yescomplemented
143#2297C2213yescomplemented
144C2×#391C2213yescomplemented
145C2×#391C2216yescomplemented
146C2×#391C2213yescomplemented
147C2×#388C2216yes—
148#2280C2213yes—
149#2280C2213yes—
150C2×#380C2213yes—
151#2276C2212yescomplemented
152#2275C2216yescomplemented
153#2274C2213yescomplemented
154#2274C2213yescomplemented
155C42×Q8C2212yescomplemented
156C42×D4C2216yescomplemented
157C4×#117C2213yescomplemented
158C2×C4×C4⋊C4C2213yescomplemented
159C2×C4×C22⋊C4C2213yes—
160C2×2−1+4—28no—
161C2×2−1+4—28no—
162C2×2−1+4—28no—
163C22×#41—28no—
164C22×#41—28no—
165C22×#41—28no—
166C22×#41C2313yes—
167C22×#41C2313yes—
168C22×#41C2311yescharacteristic
169C22×#41C2313yes—
170C22×#41C2316yes—
171C22×#41C2311yescharacteristic
172C23×Q8C2313yes—
173C23×Q8C2311yescharacteristic
174C23×Q8C2312yes—
175C23×Q8C2316yes—
176C23×D4C2313yes—
177C24×C4C2313yes—
178Q82—216no—
179#557—216no—
180#554—248no—
181D4×Q8—216no—
182D4×Q8—248no—
183#548—216no—
184#547—248no—
185#546—248no—
186#544—224no—
187#544—224no—
188#537—224no—
189#536—224no—
190#533—224no—
191C2×C4⋊Q8—224no—
192C2×C4⋊Q8C2316yes—
193C2×C4⋊Q8C2316yes—
194C2×C4⋊Q8C2313yes—
195C2×C4⋊Q8C2316yes—
196C2×C4⋊Q8C2316yes—
197C2×C4⋊Q8C2316yes—
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2316yes—
200C2×#125C2316yes—
201C2×#125C2313yes—
202C2×#125C2313yes—
203C2×#125C2316yes—
204C2×#124C2316yes—
205C2×#124C2312yes—
206C2×#124C2316yes—
207C2×#124C23112yes—
208#525—224no—
209C2×#123C2316yes—
210C2×#123C23112yes—
211C2×C22⋊Q8—224no—
212C2×C22⋊Q8C23112yes—
213C2×C22⋊Q8C2313yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2316yes—
216C2×C22⋊Q8C2316yes—
217C2×C22⋊Q8C2313yes—
218C2×C22⋊Q8C2316yes—
219C2×C22⋊Q8C2316yes—
220C2×C22⋊Q8C2316yes—
221C2×C22⋊Q8C23112yes—
222C2×#121C23112yes—
223C2×#121C2311yescharacteristic
224C2×#121C2313yes—
225C2×#121C2316yes—
226C2×#120C2316yes—
227#520—28no—
228#520—28no—
229#520D4116yes—
230C4×#41—28no—
231C4×#41—28no—
232C2×C4×Q8C2316yes—
233C2×C4×Q8C2316yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×D4C2316yes—
242C2×C4×D4C2316yes—
243C2×C4×D4C2313yes—
244C2×C4×D4C2313yes—
245C2×C4×D4C2313yes—
246C2×C4×D4C2313yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2316yes—
249C2×C4×D4C2316yes—
250C2×#117C2313yes—
251C2×#117C2313yes—
252C2×#117C2313yes—
253C2×#117C2313yes—
254C2×#117C2313yes—
255C22×C4⋊C4C2313yes—
256C22×C4⋊C4C2313yes—
257C22×C4⋊C4C2316yes—
258C22×C4⋊C4C2316yes—
259C22×C4⋊C4C2313yes—
260C22×C22⋊C4C2316yes—
261C22×C22⋊C4C2313yes—
262C22×C22⋊C4C2313yes—
263C22×C22⋊C4C2316yes—
264C22×C42C2313yes—
265C22×C42C2313yes—
266C22×C42C2316yes—
267#400C23112yes—
268#400C23112yes—
269#400C2316yes—
270#400C23112yes—
271#400C23112yes—
272#400C23112yes—
273#400C23112yes—
274#400C2316yes—
275#400C2316yes—
276#400C2316yes—
277#397C2316yes—
278#397C23112yes—
279#397C23112yes—
280#397C2316yes—
281#397C2316yes—
282#397C2316yes—
283#394C2316yes—
284#394C23112yes—
285#394C2316yes—
286#394C2316yes—
287#394C2312yes—
288#393C23112yes—
289#393C23112yes—
290#393C23112yes—
291#393C2316yes—
292#393C23112yes—
293#393C23112yes—
294#393C2316yes—
295#393C2316yes—
296#393C2312yes—
297#391C2313yes—
298#391C2313yes—
299#391C2316yes—
300#391C2316yes—
301#391C2316yes—
302#391C2316yes—
303#391C2316yes—
304#391C2316yes—
305#391C2316yes—
306#391C2316yes—
307#391C2313yes—
308#391C2313yes—
309#391C2316yes—
310#391C2316yes—
311#391C2316yes—
312#391C23112yes—
313#391C23112yes—
314#391C2313yes—
315#391C2313yes—
316#391C2316yes—
317#391C2316yes—
318#391C23112yes—
319#391C23112yes—
320#391C2316yes—
321#391C2313yes—
322#391C2313yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2313yes—
327#390C2313yes—
328#390C2313yes—
329#390C2313yes—
330#390C2313yes—
331#390C2313yes—
332#390C2316yes—
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#388C2316yes—
336#388C23112yes—
337#388C23112yes—
338#388C23112yes—
339#388C23112yes—
340#388C2316yes—
341#388C23112yes—
342#388C2316yes—
343#388C23112yes—
344#388C2316yes—
345#388C2316yes—
346#388C23112yes—
347#388C2316yes—
348#388C2316yes—
349#388C2312yes—
350#386C23112yes—
351#386C23112yes—
352#386C23112yes—
353#386C23112yes—
354#386C2316yes—
355#386C2316yes—
356#386C2316yes—
357#386C2316yes—
358#386C2316yes—
359#386C2316yes—
360#386C2316yes—
361#386C2316yes—
362#382C23112yes—
363#382C23112yes—
364#382C2316yes—
365#382C2316yes—
366#381C23112yes—
367#381C23112yes—
368#381C2316yes—
369#381C2316yes—
370#380C2313yes—
371#380C2316yes—
372#380C2316yes—
373#380C2316yes—
374#380C2313yes—
375#380C2316yes—
376#380C2316yes—
377#380C2313yes—
378#380C2316yes—
379#380C2313yes—
380#380C2316yes—
381#380C2313yes—
382#380C2313yes—
383#380C2311yescharacteristic
384#380C2313yes—
385#379C2316yes—
386#379C2316yes—
387C4×C4⋊C4C2316yes—
388C4×C4⋊C4C2316yes—
389C4×C4⋊C4C2313yes—
390C4×C4⋊C4C2316yes—
391C4×C4⋊C4C2311yescharacteristic
392C4×C4⋊C4C2313yes—
393C4×C4⋊C4C2316yes—
394C4×C4⋊C4C2316yes—
395C4×C4⋊C4C2316yes—
396C4×C4⋊C4C2313yes—
397C4×C4⋊C4C2316yes—
398C4×C22⋊C4C23112yes—
399C4×C22⋊C4C2313yes—
400C4×C22⋊C4C2316yes—
401C4×C22⋊C4C2313yes—
402C4×C22⋊C4C2313yes—
403C4×C22⋊C4C2316yes—
404C4×C22⋊C4C2313yes—
405C4×C22⋊C4C2316yes—
406C4×C22⋊C4C2316yes—
407C4×C22⋊C4C2316yes—
408C4×C22⋊C4C2316yes—
409C4×C22⋊C4C2316yes—
410C4×C22⋊C4C2316yes—
411C4×C22⋊C4C23112yes—
412C4×C22⋊C4C2313yes—
413C4×C22⋊C4C2316yes—
414C4×C22⋊C4C2313yes—
415C4×C22⋊C4C2311yescharacteristic
416C4×C22⋊C4C2313yes—
417#376C2316yes—
418C2×#95C2313yes—
419C2×#95C2316yes—
420C2×#95C2313yes—
421C2×#95C2316yes—
422C2×#95C2316yes—
423C2×#95C2316yes—
424C2×#95C2316yes—
425C2×#95C2316yes—
426C43C2316yes—
427C25C2413yes—
4282−1+4—464no—
429C2×#41—24no—
430C2×#41—24no—
431C2×#41—24no—
432C2×#41—224no—
433C2×#41—212no—
434C2×#41—212no—
435C2×#41—212no—
436C2×#41—224no—
437C2×#41—224no—
438C2×#41—212no—
439C2×#41—212no—
440C2×#41—212no—
441C2×#41—212no—
442C2×#41—212no—
443C2×#41—212no—
444C2×#41—464no—
445C2×#41C2×D418yes—
446C2×#41#4118yes—
447C2×#41#4118yes—
448C22×Q8—28no—
449C22×Q8—24no—
450C22×Q8—24no—
451C22×Q8—24no—
452C22×Q8—28no—
453C22×Q8—28no—
454C22×Q8—212no—
455C22×Q8—224no—
456C22×Q8—212no—
457C22×Q8—212no—
458C22×Q8—412no—
459C22×Q8—86no—
460C22×Q8C2413yes—
461C22×Q8C2416yes—
462C22×Q8C2413yes—
463C22×Q8C2412yes—
464C22×Q8C2416yes—
465C22×Q8C24112yes—
466C22×Q8C2411yescharacteristic
467C22×D4—212no—
468C22×D4—212no—
469C22×D4—212no—
470C22×D4C2416yes—
471C22×D4C2411yescharacteristic
472C22×D4C2416yes—
473C22×D4C2413yes—
474C22×D4C2412yes—
475C22×D4C2416yes—
476C22×D4C2413yes—
477C23×C4—212no—
478C23×C4—212no—
479C23×C4—212no—
480C23×C4C2416yes—
481C23×C4C2413yes—
482C23×C4C2416yes—
483C23×C4C2413yes—
484C23×C4C2413yes—
485C23×C4C2411yescharacteristic
486C23×C4C2413yes—
487C23×C4C2413yes—
488C23×C4C2413yes—
489C23×C4C2413yes—
490C23×C4C2416yes—
491C23×C4C2416yes—
492C23×C4C2413yes—
493C23×C4C2416yes—
494C23×C4C2413yes—
495C4⋊Q8—212no—
496C4⋊Q8—224no—
497C4⋊Q8—224no—
498C4⋊Q8—224no—
499C4⋊Q8—24no—
500C4⋊Q8—224no—
501C4⋊Q8—224no—
502C4⋊Q8—224no—
503#125—212no—
504#125—212no—
505#125—224no—
506#125—224no—
507#124—28no—
508#124—224no—
509#124—412no—
510#124—812no—
511#123—224no—
512#123—248no—
513C22⋊Q8—248no—
514C22⋊Q8—212no—
515C22⋊Q8—224no—
516C22⋊Q8—224no—
517C22⋊Q8—224no—
518C22⋊Q8—212no—
519C22⋊Q8—224no—
520C22⋊Q8—224no—
521C22⋊Q8—224no—
522C22⋊Q8—248no—
523#121—248no—
524#121—24no—
525#121—212no—
526#121—224no—
527#120—224no—
528C4×Q8—24no—
529C4×Q8—24no—
530C4×Q8—28no—
531C4×Q8—24no—
532C4×Q8—24no—
533C4×Q8—28no—
534C4×Q8—224no—
535C4×Q8—224no—
536C4×Q8C2×D4116yes—
537C4×D4—212no—
538C4×D4—212no—
539C4×D4—224no—
540C4×D4—212no—
541C4×D4—212no—
542C4×D4—224no—
543C4×D4—224no—
544C4×D4—224no—
545C4×D4C2×D4148yes—
546#117—212no—
547#117—212no—
548#117—212no—
549#117—212no—
550#117C2×D4124yes—
551C2×C4⋊C4—212no—
552C2×C4⋊C4—224no—
553C2×C4⋊C4—224no—
554C2×C4⋊C4—212no—
555C2×C4⋊C4C2×D4124yes—
556C2×C4⋊C4C2413yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C24112yes—
563C2×C4⋊C4C24112yes—
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2413yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2413yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2416yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2416yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2413yes—
577C2×C4⋊C4C2416yes—
578C2×C4⋊C4C2411yescharacteristic
579C2×C22⋊C4—224no—
580C2×C22⋊C4—212no—
581C2×C22⋊C4—46no—
582C2×C22⋊C4—86no—
583C2×C22⋊C4C2411yescharacteristic
584C2×C22⋊C4C2416yes—
585C2×C22⋊C4C24112yes—
586C2×C22⋊C4C2413yes—
587C2×C22⋊C4C2413yes—
588C2×C22⋊C4C2413yes—
589C2×C22⋊C4C2413yes—
590C2×C22⋊C4C2416yes—
591C2×C22⋊C4C2416yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2416yes—
602C2×C22⋊C4C24112yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2413yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2411yescharacteristic
616C2×C42—212no—
617C2×C42—212no—
618C2×C42—86no—
619C2×C42C2413yes—
620C2×C42C2413yes—
621C2×C42C2416yes—
622C2×C42C2416yes—
623C2×C42C2413yes—
624C2×C42C2413yes—
625C2×C42C2413yes—
626C2×C42C2413yes—
627C2×C42C2412yes—
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2416yes—
631C2×C42C24112yes—
632C2×C42C2416yes—
633C2×C42C2416yes—
634C2×C42C2416yes—
635#95C2411yescharacteristic
636#95C2411yescharacteristic
637#95C2416yes—
638#95C2416yes—
639#95C2416yes—
640#95C2416yes—
641#95C2416yes—
642#95C2416yes—
643#95C24112yes—
644#95C2413yes—
645#95C2413yes—
646#95C2413yes—
647#95C2413yes—
648#95C2413yes—
649#95C2413yes—
650#95C24112yes—
651#95C24112yes—
652#95C24112yes—
653#95C24112yes—
654#95C24112yes—
655#95C2412yes—
656#95C2416yes—
657#95C2416yes—
658#95C2412yes—
659#95C2416yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667C24—26no—
668C24—26no—
669C24—26no—
670C24—26no—
671C24—43no—
672C24—43no—
673C24—43no—
674C24C2513yes—
675C24C2512yes—
676C24C2511yescharacteristic
677C24C2513yes—
678#41—416no—
679#41—448no—
680#41—496no—
681#41—448no—
682#41—448no—
683#41#124164yescomplemented
684C2×Q8—24no—
685C2×Q8—212no—
686C2×Q8—26no—
687C2×Q8—212no—
688C2×Q8—26no—
689C2×Q8—224no—
690C2×Q8—26no—
691C2×Q8—212no—
692C2×Q8—212no—
693C2×Q8—26no—
694C2×Q8—26no—
695C2×Q8—26no—
696C2×Q8—24no—
697C2×Q8—212no—
698C2×Q8—46no—
699C2×Q8—42no—
700C2×Q8—412no—
701C2×Q8—412no—
702C2×Q8—416no—
703C2×Q8—432no—
704C2×Q8—448no—
705C2×Q8—848no—
706C2×Q8C22×D414yes—
707C2×Q8C2×#4114yes—
708C2×Q8C2×#4114yes—
709C2×D4—212no—
710C2×D4—212no—
711C2×D4—212no—
712C2×D4—212no—
713C2×D4—212no—
714C2×D4—212no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—22no—
718C2×D4—26no—
719C2×D4—212no—
720C2×D4—26no—
721C2×D4—26no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—42no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—448no—
728C2×D4C22×D4112yes—
729C2×D4C2×#41112yes—
730C2×D4C2×#41112yes—
731C22×C4—26no—
732C22×C4—26no—
733C22×C4—212no—
734C22×C4—26no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—26no—
738C22×C4—212no—
739C22×C4—212no—
740C22×C4—212no—
741C22×C4—26no—
742C22×C4—212no—
743C22×C4—212no—
744C22×C4—26no—
745C22×C4—26no—
746C22×C4—22no—
747C22×C4—26no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—26no—
751C22×C4—26no—
752C22×C4—26no—
753C22×C4—26no—
754C22×C4—26no—
755C22×C4—26no—
756C22×C4—212no—
757C22×C4—212no—
758C22×C4—26no—
759C22×C4—26no—
760C22×C4—26no—
761C22×C4—43no—
762C22×C4—46no—
763C22×C4—43no—
764C22×C4—46no—
765C22×C4—43no—
766C22×C4—46no—
767C22×C4—43no—
768C22×C4—46no—
769C22×C4—43no—
770C22×C4—46no—
771C22×C4—46no—
772C22×C4—448no—
773C22×C4C22×D4124yes—
774C22×C4C22×D4112yes—
775C22×C4C2×#41112yes—
776C22×C4C2×#41112yes—
777C22×C4C2511yescharacteristic
778C22×C4C2516yes—
779C22×C4C2511yescharacteristic
780C22×C4C2513yes—
781C22×C4C2512yes—
782C22×C4C2513yes—
783C22×C4C2513yes—
784C22×C4C2516yes—
785C22×C4C2512yes—
786C22×C4C2513yes—
787C22×C4C2513yes—
788C22×C4C2516yes—
789C22×C4C2512yes—
790C22×C4C2516yes—
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2513yes—
795C22×C4C2511yescharacteristic
796C4⋊C4—26no—
797C4⋊C4—212no—
798C4⋊C4—212no—
799C4⋊C4—212no—
800C4⋊C4—224no—
801C4⋊C4—224no—
802C4⋊C4—22no—
803C4⋊C4—26no—
804C4⋊C4—26no—
805C4⋊C4—212no—
806C4⋊C4—24no—
807C4⋊C4—212no—
808C4⋊C4—212no—
809C4⋊C4—212no—
810C4⋊C4—212no—
811C4⋊C4—26no—
812C4⋊C4—212no—
813C4⋊C4—22no—
814C4⋊C4—26no—
815C4⋊C4—26no—
816C4⋊C4C22×D4112yes—
817C4⋊C4C22×D4124yes—
818C4⋊C4C22×D414yes—
819C22⋊C4—212no—
820C22⋊C4—212no—
821C22⋊C4—212no—
822C22⋊C4—212no—
823C22⋊C4—26no—
824C22⋊C4—24no—
825C22⋊C4—212no—
826C22⋊C4—224no—
827C22⋊C4—24no—
828C22⋊C4—212no—
829C22⋊C4—212no—
830C22⋊C4—26no—
831C22⋊C4—26no—
832C22⋊C4—24no—
833C22⋊C4—24no—
834C22⋊C4—22no—
835C22⋊C4—26no—
836C22⋊C4—24no—
837C22⋊C4—43no—
838C22⋊C4—43no—
839C22⋊C4—46no—
840C22⋊C4—412no—
841C22⋊C4—46no—
842C22⋊C4—46no—
843C22⋊C4—46no—
844C22⋊C4—42no—
845C22⋊C4—46no—
846C22⋊C4—46no—
847C22⋊C4—46no—
848C22⋊C4—46no—
849C22⋊C4—46no—
850C22⋊C4C22×D4124yes—
851C22⋊C42−1+414yescomplemented
852C42—22no—
853C42—26no—
854C42—26no—
855C42—26no—
856C42—212no—
857C42—22no—
858C42—26no—
859C42—26no—
860C42—26no—
861C42—212no—
862C42—24no—
863C42—46no—
864C42—412no—
865C42—46no—
866C42—46no—
867C42C22×D4124yes—
868C23—23no—
869C23—23no—
870C23—23no—
871C23—23no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—21no—
877C23—21no—
878C23—23no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—23no—
883C23—23no—
884C23—22no—
885C23—23no—
886C23—22no—
887C23—23no—
888C23—22no—
889C23—23no—
890C23—22no—
891C23—23no—
892C23—412no—
893C23—412no—
894C23—412no—
895C23—412no—
896C23—86no—
897C23—86no—
898C23—86no—
899C23C23×D416yes—
900C23C22×#4116yes—
901C23C22×#4116yes—
902C23C2×2−1+412yes—
903C23C2611yescharacteristic
904Q8—48no—
905Q8—424no—
906Q8—412no—
907Q8—424no—
908Q8—412no—
909Q8—824no—
910Q8C2×#124116yes—
911D4—48no—
912D4—424no—
913D4—424no—
914D4—412no—
915D4—44no—
916D4—812no—
917D4C2×#124148yes—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—22no—
922C2×C4—26no—
923C2×C4—21no—
924C2×C4—26no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—23no—
930C2×C4—23no—
931C2×C4—26no—
932C2×C4—26no—
933C2×C4—21no—
934C2×C4—23no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—23no—
938C2×C4—23no—
939C2×C4—26no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—23no—
943C2×C4—23no—
944C2×C4—26no—
945C2×C4—26no—
946C2×C4—22no—
947C2×C4—23no—
948C2×C4—23no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—23no—
952C2×C4—21no—
953C2×C4—23no—
954C2×C4—26no—
955C2×C4—23no—
956C2×C4—26no—
957C2×C4—26no—
958C2×C4—23no—
959C2×C4—23no—
960C2×C4—26no—
961C2×C4—23no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—424no—
965C2×C4—412no—
966C2×C4—412no—
967C2×C4—412no—
968C2×C4—412no—
969C2×C4—424no—
970C2×C4—44no—
971C2×C4—412no—
972C2×C4—412no—
973C2×C4—412no—
974C2×C4—424no—
975C2×C4—86no—
976C2×C4—812no—
977C2×C4—812no—
978C2×C4C2×#124148yes—
979C2×C4C23×D414yes—
980C2×C4C23×D4112yes—
981C2×C4C23×D416yes—
982C2×C4C23×D412yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4116yes—
985C2×C4C22×#4116yes—
986C2×C4C22×#4112yes—
987C2×C4C2×2−1+412yes—
988C2×C4C2×2−1+412yes—
989C2×C4#58512yes—
990C22—26no—
991C22—26no—
992C22—26no—
993C22—26no—
994C22—26no—
995C22—26no—
996C22—22no—
997C22—22no—
998C22—22no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—42no—
1004C22—43no—
1005C22—42no—
1006C22—43no—
1007C22—42no—
1008C22—43no—
1009C22—42no—
1010C22—43no—
1011C22—42no—
1012C22—43no—
1013C22—42no—
1014C22—43no—
1015C22—42no—
1016C22—43no—
1017C22—824no—
1018C22C22×#124112yes—
1019C22C24×D411yescharacteristic
1020C22C23×#4111yescharacteristic
1021C22C23×#4111yescharacteristic
1022C22C22×2−1+411yescharacteristic
1023C22C2×#58511yescharacteristic
1024C22H(7,𝔽2)11yescharacteristic
1025C222−1+611yescharacteristic
1026C4—22no—
1027C4—212no—
1028C4—22no—
1029C4—24no—
1030C4—22no—
1031C4—43no—
1032C4—46no—
1033C4—43no—
1034C4—42no—
1035C4—43no—
1036C4—43no—
1037C4—41no—
1038C4—42no—
1039C4—46no—
1040C4—41no—
1041C4—43no—
1042C4—46no—
1043C4C22×#12414yes—
1044C4C22×#124112yes—
1045C2—212no—
1046C2—42no—
1047C2—82no—
1048C2—83no—
1049C2C23×#12411yescharacteristic
1050C2#6280511yescharacteristic
1051C2#6285711yescharacteristic
1052C2#6298711yescharacteristic
1053C2D4×2−1+411yescharacteristic
1054C2#6300011yescharacteristic
1055C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3489C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3503C2semidirect
3. Q8×#124C2semidirect
4. #36467C2semidirect
5. #36303C2semidirect
6. #36238C2semidirect
7. #36042C2semidirect
8. #35948C2semidirect
9. #35939C2semidirect
10. #35910C2semidirect
11. #35644C2semidirect
12. #35628C2semidirect
13. #35592C2semidirect
14. #35542C2semidirect
15. #35312C2semidirect
16. #35158C2semidirect
17. #34813C2semidirect
18. C2×#2492C2semidirect
19. #34259C2semidirect
20. #34259C2semidirect
21. #34175C2semidirect
22. C22⋊C4×#41C2semidirect
23. C4×#520C2semidirect
28. C2×Q82C22semidirect
29. C2×#557C22semidirect
30. C2×#554C22semidirect
32. C2×D4×Q8C22semidirect
36. C2×#544C22semidirect
37. C2×#544C22semidirect
40. C2×#533C22semidirect
41. C22×C4⋊Q8C22semidirect
49. #2862C22semidirect
50. #2861C22semidirect
51. #2850C22semidirect
52. #2642C22semidirect
53. #2640C22semidirect
54. #2639C22semidirect
55. #2592C22semidirect
56. #2592C22semidirect
57. #2591C22semidirect
58. #2568C22semidirect
59. #2568C22semidirect
62. #2562C22semidirect
64. #2547C22semidirect
65. #2503C22semidirect
71. #2492C22semidirect
72. #2492C22semidirect
73. #2492C22semidirect
74. #2492C22semidirect
75. #2492C22semidirect
76. #2492C22semidirect
77. #2492C22semidirect
78. #2492C22semidirect
79. #2492C22semidirect
80. #2492C22semidirect
82. #2491C22semidirect
83. #2491C22semidirect
84. #2491C22semidirect
85. #2491C22semidirect
86. #2491C22semidirect
88. #2490C22semidirect
89. #2490C22semidirect
92. #2489C22semidirect
93. #2489C22semidirect
94. #2489C22semidirect
95. #2489C22semidirect
96. #2489C22semidirect
97. #2488C22semidirect
98. #2488C22semidirect
99. #2488C22semidirect
100. #2488C22semidirect
101. #2488C22semidirect
102. #2488C22semidirect
103. #2488C22semidirect
107. #2436C22semidirect
109. #2398C22semidirect
110. C2×#400C22semidirect
118. Q8×C22⋊C4C22semidirect
119. Q8×C22⋊C4C22semidirect
120. Q8×C22⋊C4C22semidirect
121. Q8×C22⋊C4C22semidirect
125. #2339C22semidirect
126. #2339C22semidirect
127. #2339C22semidirect
128. #2339C22semidirect
134. #2311C22semidirect
135. #2311C22semidirect
136. #2310C22semidirect
137. #2310C22semidirect
139. C4×#124C22semidirect
142. #2297C22semidirect
143. #2297C22semidirect
144. C2×#391C22semidirect
145. C2×#391C22semidirect
146. C2×#391C22semidirect
151. #2276C22semidirect
152. #2275C22semidirect
153. #2274C22semidirect
154. #2274C22semidirect
155. C42×Q8C22semidirect
156. C42×D4C22semidirect
157. C4×#117C22semidirect
158. C2×C4×C4⋊C4C22semidirect
683. #41#124semidirect
851. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×#35032
Q8×#1242
#364672
#363032
#362382
#360422
#359482
#359392
#359102
#356442
#356282
#355922
#355422
#353122
#351582
#348132
C2×#24922
#342592
#341752
C22⋊C4×#412
C4×#5202