Finite Group Databasebeta

← #7628614

Subgroups — #7628614

Order 512.

8328 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#533C211yesmaximal, characteristic, complemented
2C22×C4×#41C211yesmaximal, characteristic
3#36625C214yesmaximal, complemented
4#35325C214yesmaximal, complemented
5#35316C212yesmaximal, complemented
6#35311C212yesmaximal, complemented
7#35305C212yesmaximal
8#35297C214yesmaximal, complemented
9#35279C212yesmaximal, complemented
10#35248C212yesmaximal, complemented
11#35240C212yesmaximal, complemented
12#35200C214yesmaximal, complemented
13#35138C214yesmaximal, complemented
14#35084C214yesmaximal, complemented
15#34979C214yesmaximal, complemented
16#34971C214yesmaximal, complemented
17#34953C212yesmaximal, complemented
18#34946C212yesmaximal, complemented
19#34809C214yesmaximal, complemented
20#34627C214yesmaximal, complemented
21C4×#536C214yesmaximal, complemented
22#34012C211yesmaximal, characteristic, complemented
23C23×#41C2211yescharacteristic
24C2×#536C2214yes—
25C2×#533—216no—
26C2×#533C2212yes—
27C2×#533C2212yes—
28C2×#533C2212yes—
29C2×#533C2212yes—
30C2×#533C2212yescomplemented
31C2×#533C2212yescomplemented
32C2×#533C2212yescomplemented
33C2×#533C2212yescomplemented
34C22×C4⋊Q8C2211yescharacteristic, complemented
35C22×C4⋊Q8C2211yescharacteristic, complemented
36C22×#125C2212yescomplemented
37C22×C22⋊Q8C2212yes—
38C22×C22⋊Q8C2212yes—
39C2×C4×#41—216no—
40C2×C4×#41C2212yes—
41C2×C4×#41C2212yes—
42C2×C4×#41C2212yes—
43C2×C4×#41C2212yes—
44C2×C4×#41C2212yes—
45C2×C4×#41C2212yes—
46C2×C4×#41C2212yes—
47C2×C4×#41C2212yes—
48C22×C4×Q8C2211yescharacteristic
49C22×C4×Q8C2211yescharacteristic
50C22×C4×Q8C2212yescomplemented
51C22×C4×Q8C2212yescomplemented
52C22×C4×D4C2212yes—
53C22×C4×D4C2211yescharacteristic
54C22×C4×D4C2211yescharacteristic
55C22×C4×D4C2212yes—
56C22×#117C2211yescharacteristic
57C22×#117C2212yes—
58C22×#117C2212yes—
59C23×C42C2212yes—
60C23×C42C2211yescharacteristic
61#2857C2218yescomplemented
62#2857C2218yescomplemented
63#2855C2218yes—
64#2855C2218yes—
65#2851C22116yescomplemented
66#2848C2218yes—
67#2848C2218yes—
68#2638C22116yescomplemented
69#2634C2218yescomplemented
70#2633C2218yescomplemented
71#2628C2218yescomplemented
72#2625C2218yescomplemented
73#2621C2218yescomplemented
74#2616C2218yes—
75#2611C22116yescomplemented
76#2599C22116yescomplemented
77#2584C2218yescomplemented
78#2583C2218yes—
79#2581C2218yescomplemented
80#2568C2214yescomplemented
81#2567C2214yescomplemented
82#2563C2214yescomplemented
83#2562C2218yescomplemented
84#2561C2218yes—
85#2547C2214yescomplemented
86#2547C2214yescomplemented
87#2546C2214yescomplemented
88#2546C2214yescomplemented
89#2542C2214yescomplemented
90#2536C2218yescomplemented
91#2503C2214yes—
92#2502C2214yes—
93#2499C2218yescomplemented
94#2487C2218yescomplemented
95#2486C2218yescomplemented
96#2486C2218yescomplemented
97#2485C22116yescomplemented
98#2484C2218yes—
99#2484C2218yescomplemented
100#2483C2218yes—
101#2482C2218yes—
102#2435C2214yes—
103#2434C2214yes—
104#2432C2218yes—
105#2415C22116yescomplemented
106#2409C2218yescomplemented
107#2406C2218yes—
108#2405C2218yes—
109#2399C2218yescomplemented
110#2398C2218yescomplemented
111#2395C22116yescomplemented
112#2327C2218yescomplemented
113#2326C2218yescomplemented
114#2323C22116yescomplemented
115#2322C22116yescomplemented
116#2317C2214yescomplemented
117#2311C2214yes—
118#2310C2214yescomplemented
119C4×C4⋊Q8C2218yescomplemented
120C4×#124C2218yescomplemented
121C4×C22⋊Q8C22116yescomplemented
122C4×C22⋊Q8C22116yescomplemented
123C4×#123C22116yescomplemented
124#2296C2218yes—
125#2285C2212yes—
126#2285C2212yescomplemented
127#2285C2212yescomplemented
128#2283C2212yes—
129#2283C2212yes—
130#2283C2212yescomplemented
131#2283C2212yescomplemented
132#2283C2212yescomplemented
133#2283C2212yescomplemented
134#2280C2212yes—
135#2280C2218yes—
136#2280C2212yes—
137#2280C2212yes—
138C4×#117C2212yes—
139C4×#117C2212yescomplemented
140C4×#117C2212yescomplemented
141C22×#41—216no—
142C22×#41—28no—
143C22×#41C2312yes—
144C22×#41C2312yes—
145C22×#41C2312yes—
146C22×#41C2312yes—
147C23×Q8C2312yes—
148C23×Q8C2311yescharacteristic
149C23×Q8C2312yes—
150C23×D4C2312yes—
151C23×D4C2311yescharacteristic
152C24×C4C2312yes—
153C24×C4C2312yes—
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C24×C4C2312yes—
157C24×C4C2311yescharacteristic
158#536—232no—
159#533—216no—
160#533—216no—
161#533—216no—
162#533—216no—
163#533—216no—
164#533—216no—
165#533—216no—
166#533—216no—
167C2×C4⋊Q8—28no—
168C2×C4⋊Q8—28no—
169C2×C4⋊Q8C2318yes—
170C2×C4⋊Q8C2312yes—
171C2×C4⋊Q8C2312yes—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2312yes—
178C2×#125—216no—
179C2×#125C2314yes—
180C2×#125C2314yes—
181C2×#125C2314yes—
182C2×#125C2314yes—
183C2×#124C2318yes—
184C2×#123C23116yes—
185C2×C22⋊Q8—216no—
186C2×C22⋊Q8—216no—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C23116yes—
189C2×C22⋊Q8C2314yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C23116yes—
197C4×#41—216no—
198C4×#41—216no—
199C4×#41—216no—
200C4×#41—216no—
201C4×#41—216no—
202C4×#41—216no—
203C4×#41—216no—
204C4×#41—216no—
205C2×C4×Q8—28no—
206C2×C4×Q8—28no—
207C2×C4×Q8—216no—
208C2×C4×Q8—216no—
209C2×C4×Q8C2312yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2314yes—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2314yes—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2314yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×D4—216no—
226C2×C4×D4—216no—
227C2×C4×D4—28no—
228C2×C4×D4—28no—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×#117—28no—
246C2×#117—216no—
247C2×#117—216no—
248C2×#117C2312yes—
249C2×#117C2314yes—
250C2×#117C2314yes—
251C2×#117C2314yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2314yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C2×#117C2314yes—
261C2×#117C2314yes—
262C2×#117C2314yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2312yes—
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2314yes—
277C22×C42—216no—
278C22×C42D4116yes—
279C22×C42C2314yes—
280C22×C42C2312yes—
281C22×C42C2312yes—
282C22×C42C2314yes—
283C22×C42C2312yes—
284C22×C42C2314yes—
285C22×C42C2314yes—
286C22×C42C2314yes—
287C22×C42C2311yescharacteristic
288C22×C42C2311yescharacteristic
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299#400C23116yes—
300#400C23116yes—
301#399C23116yes—
302#398C23116yes—
303#398C23116yes—
304#398C23116yes—
305#397C23116yes—
306#397C23116yes—
307#397C23132yes—
308#395C23116yes—
309#395C23116yes—
310#394C23116yes—
311#394C23132yes—
312#393C23116yes—
313#391C2318yes—
314#391C2318yes—
315#391C23116yes—
316#391C2318yes—
317#391C23116yes—
318#390C2318yes—
319#389C23132yes—
320#389C23116yes—
321#389C23116yes—
322#389C23116yes—
323#389C23116yes—
324#388C23132yes—
325#388C23132yes—
326#387C23132yes—
327#387C23132yes—
328#387C23132yes—
329#386C23116yes—
330#385C23116yes—
331#385C23132yes—
332#385C23116yes—
333#385C23116yes—
334#385C23132yes—
335#384C2318yes—
336#384C2314yes—
337#383C2314yes—
338#383C2314yes—
339#382C2318yes—
340#382C2314yes—
341#382C2314yes—
342#382C2314yes—
343#381C23116yes—
344#381C23116yes—
345#381C2314yes—
346#381C2314yes—
347#381C2314yes—
348#380C23116yes—
349#380C23116yes—
350#380C23116yes—
351#380C2314yes—
352#380C2314yes—
353#380C23116yes—
354#380C2314yes—
355#380C2314yes—
356#380C2314yes—
357#380C2314yes—
358#379C23116yes—
359#379C2314yes—
360C4×C4⋊C4C2314yes—
361C4×C4⋊C4C23132yes—
362C4×C4⋊C4C2314yes—
363C4×C4⋊C4C2314yes—
364C4×C4⋊C4C2314yes—
365C4×C4⋊C4C2314yes—
366C4×C4⋊C4C2314yes—
367C4×C22⋊C4C2314yes—
368C4×C22⋊C4C2314yes—
369C4×C22⋊C4C2314yes—
370C4×C22⋊C4C23132yes—
371C4×C22⋊C4C2314yes—
372C4×C22⋊C4C2314yes—
373C4×C22⋊C4C2314yes—
374#376C2314yes—
375#376C2314yes—
376#376C2314yes—
377C43C2314yes—
378C25C2412yes—
379C25C2411yescharacteristic
380C2×#41—2128no—
381C2×#41—28no—
382C2×#41—216no—
383C2×#41—28no—
384C2×#41—28no—
385C2×#41—28no—
386C2×#41—28no—
387C2×#41—28no—
388C2×#41—216no—
389C2×#41—28no—
390C2×#41#41116yes—
391C22×Q8—28no—
392C22×Q8—24no—
393C22×Q8—28no—
394C22×Q8—28no—
395C22×Q8—216no—
396C22×Q8—48no—
397C22×Q8C2412yes—
398C22×Q8C2414yes—
399C22×Q8C2414yes—
400C22×Q8C2414yes—
401C22×Q8C2412yes—
402C22×Q8C2414yes—
403C22×D4—28no—
404C22×D4—216no—
405C22×D4—28no—
406C22×D4—24no—
407C22×D4C2412yes—
408C22×D4C2414yes—
409C22×D4C2414yes—
410C22×D4C2412yes—
411C23×C4—28no—
412C23×C4—216no—
413C23×C4—28no—
414C23×C4—28no—
415C23×C4—28no—
416C23×C4—28no—
417C23×C4—216no—
418C23×C4—44no—
419C23×C4—48no—
420C23×C4C2×D418yes—
421C23×C4C2×D418yes—
422C23×C4C2×D418yes—
423C23×C4C2412yes—
424C23×C4C2414yes—
425C23×C4C2412yes—
426C23×C4C2414yes—
427C23×C4C2414yes—
428C23×C4C2414yes—
429C23×C4C2414yes—
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2414yes—
444C23×C4C2412yes—
445C23×C4C2414yes—
446C23×C4C2414yes—
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C4⋊Q8—232no—
453C4⋊Q8—28no—
454C4⋊Q8—28no—
455C4⋊Q8—28no—
456C4⋊Q8—28no—
457C4⋊Q8—28no—
458C4⋊Q8—28no—
459C4⋊Q8—28no—
460C4⋊Q8—28no—
461#125—216no—
462#125—216no—
463#125—216no—
464#125—216no—
465#124—232no—
466#123—264no—
467C22⋊Q8—216no—
468C22⋊Q8—216no—
469C22⋊Q8—216no—
470C22⋊Q8—216no—
471C22⋊Q8—216no—
472C22⋊Q8—216no—
473C22⋊Q8—216no—
474C22⋊Q8—216no—
475C22⋊Q8—264no—
476C22⋊Q8—432no—
477C4×Q8—28no—
478C4×Q8—28no—
479C4×Q8—28no—
480C4×Q8—28no—
481C4×Q8—28no—
482C4×Q8—28no—
483C4×Q8—28no—
484C4×Q8—28no—
485C4×Q8—216no—
486C4×Q8—216no—
487C4×Q8—216no—
488C4×Q8—216no—
489C4×Q8—216no—
490C4×Q8—216no—
491C4×Q8—216no—
492C4×Q8—216no—
493C4×D4—216no—
494C4×D4—216no—
495C4×D4—216no—
496C4×D4—216no—
497C4×D4—216no—
498C4×D4—216no—
499C4×D4—216no—
500C4×D4—216no—
501C4×D4—28no—
502C4×D4—28no—
503C4×D4—28no—
504C4×D4—28no—
505C4×D4—28no—
506C4×D4—28no—
507C4×D4—28no—
508C4×D4—28no—
509#117—28no—
510#117—28no—
511#117—28no—
512#117—28no—
513#117—216no—
514#117—216no—
515#117—216no—
516#117—216no—
517#117—216no—
518#117—216no—
519#117—216no—
520#117—216no—
521#117—216no—
522#117—216no—
523#117—48no—
524C2×C4⋊C4—28no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—28no—
529C2×C4⋊C4—28no—
530C2×C4⋊C4—216no—
531C2×C4⋊C4—216no—
532C2×C4⋊C4—28no—
533C2×C4⋊C4—28no—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C24132yes—
558C2×C4⋊C4C24132yes—
559C2×C22⋊C4—28no—
560C2×C22⋊C4—216no—
561C2×C22⋊C4—28no—
562C2×C22⋊C4—28no—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C24132yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C24132yes—
576C2×C42—28no—
577C2×C42—216no—
578C2×C42—28no—
579C2×C42—28no—
580C2×C42—216no—
581C2×C42—216no—
582C2×C42—216no—
583C2×C42—216no—
584C2×C42C2×D418yes—
585C2×C42C2×D418yes—
586C2×C42C2×D418yes—
587C2×C42C2×D418yes—
588C2×C42C2×D418yes—
589C2×C42C2×D418yes—
590C2×C42C2×D418yes—
591C2×C42C2×D418yes—
592C2×C42C2×D418yes—
593C2×C42C2×D418yes—
594C2×C42C2×D418yes—
595C2×C42C2×D418yes—
596C2×C42C2414yes—
597C2×C42C2414yes—
598C2×C42C2418yes—
599C2×C42C2418yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603C2×C42C2418yes—
604C2×C42C2418yes—
605C2×C42C2414yes—
606C2×C42C2418yes—
607C2×C42C2411yescharacteristic
608C2×C42C2411yescharacteristic
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2411yescharacteristic
613C2×C42C2411yescharacteristic
614C2×C42C2411yescharacteristic
615C2×C42C2411yescharacteristic
616C2×C42C2411yescharacteristic
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2411yescharacteristic
621C2×C42C2411yescharacteristic
622C2×C42C2411yescharacteristic
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C24132yes—
630#95C24132yes—
631#95C24132yes—
632#95C24132yes—
633C24—24no—
634C24—28no—
635C24—24no—
636C24—24no—
637C24—28no—
638C24—42no—
639C24—44no—
640C24C22×D414yes—
641C24C2511yescharacteristic
642C24C2514yes—
643C24C2511yescharacteristic
644C24C2511yescharacteristic
645#41—264no—
646#41—264no—
647#41—264no—
648#41—264no—
649C2×Q8—232no—
650C2×Q8—24no—
651C2×Q8—24no—
652C2×Q8—28no—
653C2×Q8—28no—
654C2×Q8—28no—
655C2×Q8—28no—
656C2×Q8—28no—
657C2×Q8—24no—
658C2×Q8—216no—
659C2×Q8—216no—
660C2×Q8—216no—
661C2×Q8—48no—
662C2×Q8—432no—
663C2×Q8—432no—
664C2×Q8C2×#4118yes—
665C2×D4—264no—
666C2×D4—232no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—28no—
675C2×D4—24no—
676C2×D4C2×#41116yes—
677C2×D4C2×#4118yes—
678C22×C4—264no—
679C22×C4—24no—
680C22×C4—28no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—232no—
684C22×C4—232no—
685C22×C4—28no—
686C22×C4—28no—
687C22×C4—24no—
688C22×C4—28no—
689C22×C4—24no—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—28no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—216no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—28no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—216no—
712C22×C4—216no—
713C22×C4—216no—
714C22×C4—416no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—48no—
719C22×C4—44no—
720C22×C4—48no—
721C22×C4—432no—
722C22×C4—432no—
723C22×C4C22×D414yes—
724C22×C4C22×D414yes—
725C22×C4C22×D414yes—
726C22×C4C22×D414yes—
727C22×C4C22×D414yes—
728C22×C4C22×D414yes—
729C22×C4C22×D414yes—
730C22×C4C22×D414yes—
731C22×C4C22×D414yes—
732C22×C4C22×D414yes—
733C22×C4C22×D414yes—
734C22×C4C22×D414yes—
735C22×C4C22×D414yes—
736C22×C4C22×D414yes—
737C22×C4C22×D414yes—
738C22×C4C22×D414yes—
739C22×C4C22×D414yes—
740C22×C4C22×D414yes—
741C22×C4C2×#41116yes—
742C22×C4C2×#4118yes—
743C22×C42−1+418yes—
744C22×C4C2514yes—
745C22×C4C25116yes—
746C22×C4C2514yes—
747C22×C4C2518yes—
748C22×C4C2518yes—
749C22×C4C2511yescharacteristic
750C22×C4C2511yescharacteristic
751C22×C4C2511yescharacteristic
752C22×C4C2511yescharacteristic
753C22×C4C2511yescharacteristic
754C22×C4C2511yescharacteristic
755C22×C4C2511yescharacteristic
756C22×C4C2514yes—
757C22×C4C2511yescharacteristic
758C22×C4C2511yescharacteristic
759C22×C4C2511yescharacteristic
760C22×C4C2511yescharacteristic
761C22×C4C2511yescharacteristic
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—24no—
767C4⋊C4—24no—
768C4⋊C4—24no—
769C4⋊C4—24no—
770C4⋊C4—28no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—216no—
775C4⋊C4—216no—
776C4⋊C4—216no—
777C4⋊C4—216no—
778C4⋊C4—28no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—216no—
783C4⋊C4—264no—
784C4⋊C4—216no—
785C4⋊C4—216no—
786C4⋊C4—432no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—216no—
790C22⋊C4—216no—
791C22⋊C4—216no—
792C22⋊C4—264no—
793C22⋊C4—216no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—48no—
799C22⋊C4—432no—
800C42—28no—
801C42—28no—
802C42—28no—
803C42—28no—
804C42—28no—
805C42—28no—
806C42—216no—
807C42—216no—
808C42—216no—
809C42—216no—
810C42—48no—
811C42C22×D414yes—
812C42C22×D414yes—
813C42C22×D414yes—
814C42C22×D414yes—
815C42C22×D414yes—
816C42C22×D414yes—
817C42C22×D414yes—
818C42C22×D414yes—
819C42C22×D414yes—
820C42C22×D414yes—
821C42C22×D414yes—
822C42C22×D414yes—
823C42C22×D414yes—
824C42C22×D414yes—
825C42C22×D414yes—
826C42C22×D414yes—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—216no—
832C23—24no—
833C23—22no—
834C23—24no—
835C23—28no—
836C23—22no—
837C23—28no—
838C23—22no—
839C23—28no—
840C23—28no—
841C23—44no—
842C23—416no—
843C23—432no—
844C23—48no—
845C23—48no—
846C23C23×D412yes—
847C23C23×D412yes—
848C23C23×D412yes—
849C23C22×#4118yes—
850C23C22×#4114yes—
851C23C2×2−1+414yes—
852C23C2611yescharacteristic
853Q8—216no—
854Q8—216no—
855Q8—416no—
856Q8—416no—
857Q8—416no—
858Q8—416no—
859D4—216no—
860D4—232no—
861D4—232no—
862D4—216no—
863C2×C4—216no—
864C2×C4—232no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—28no—
875C2×C4—28no—
876C2×C4—28no—
877C2×C4—28no—
878C2×C4—28no—
879C2×C4—28no—
880C2×C4—232no—
881C2×C4—28no—
882C2×C4—28no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—28no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—28no—
891C2×C4—28no—
892C2×C4—216no—
893C2×C4—216no—
894C2×C4—216no—
895C2×C4—28no—
896C2×C4—216no—
897C2×C4—216no—
898C2×C4—28no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—416no—
903C2×C4—48no—
904C2×C4—416no—
905C2×C4—416no—
906C2×C4—48no—
907C2×C4—416no—
908C2×C4—416no—
909C2×C4—416no—
910C2×C4#525116yes—
911C2×C4#536116yescomplemented
912C2×C4C23×D412yes—
913C2×C4C23×D412yes—
914C2×C4C23×D412yes—
915C2×C4C23×D412yes—
916C2×C4C23×D412yes—
917C2×C4C23×D412yes—
918C2×C4C23×D412yes—
919C2×C4C23×D412yes—
920C2×C4C23×D412yes—
921C2×C4C23×D412yes—
922C2×C4C23×D412yes—
923C2×C4C23×D412yes—
924C2×C4C22×#4118yes—
925C2×C4C22×#4114yes—
926C2×C4C22×#4114yes—
927C2×C4C2×2−1+414yes—
928C2×C4C2×2−1+414yes—
929C2×C4#58514yes—
930C22—28no—
931C22—28no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—216no—
937C22—22no—
938C22—28no—
939C22—22no—
940C22—22no—
941C22—416no—
942C22—432no—
943C22—48no—
944C22—44no—
945C22—44no—
946C22—44no—
947C22C2×#52514yes—
948C22C2×#53614yes—
949C22C24×D411yescharacteristic
950C22C23×#4112yes—
951C22C22×2−1+412yes—
952C22C2×#58512yes—
953C4—22no—
954C4—22no—
955C4—28no—
956C4—22no—
957C4—22no—
958C4—22no—
959C4—22no—
960C4—22no—
961C4—416no—
962C4—48no—
963C4—44no—
964C4—44no—
965C4—48no—
966C4C2×#52514yes—
967C4C2×#52514yes—
968C4C2×#53614yes—
969C4C2×#53614yes—
970C4#344914yes—
971C2—24no—
972C2—24no—
973C2—48no—
974C2—42no—
975C2C22×#52511yescharacteristic
976C2C22×#53611yescharacteristic
977C2C2×#344911yescharacteristic
978C2#6280514yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC23×#41C22
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. C22×#533C2semidirect
3. #36625C2semidirect
4. #35325C2semidirect
5. #35316C2semidirect
6. #35311C2semidirect
8. #35297C2semidirect
9. #35279C2semidirect
10. #35248C2semidirect
11. #35240C2semidirect
12. #35200C2semidirect
13. #35138C2semidirect
14. #35084C2semidirect
15. #34979C2semidirect
16. #34971C2semidirect
17. #34953C2semidirect
18. #34946C2semidirect
19. #34809C2semidirect
20. #34627C2semidirect
21. C4×#536C2semidirect
22. #34012C2semidirect
30. C2×#533C22semidirect
31. C2×#533C22semidirect
32. C2×#533C22semidirect
33. C2×#533C22semidirect
34. C22×C4⋊Q8C22semidirect
35. C22×C4⋊Q8C22semidirect
36. C22×#125C22semidirect
50. C22×C4×Q8C22semidirect
51. C22×C4×Q8C22semidirect
61. #2857C22semidirect
62. #2857C22semidirect
65. #2851C22semidirect
68. #2638C22semidirect
69. #2634C22semidirect
70. #2633C22semidirect
71. #2628C22semidirect
72. #2625C22semidirect
73. #2621C22semidirect
75. #2611C22semidirect
76. #2599C22semidirect
77. #2584C22semidirect
79. #2581C22semidirect
80. #2568C22semidirect
81. #2567C22semidirect
82. #2563C22semidirect
83. #2562C22semidirect
85. #2547C22semidirect
86. #2547C22semidirect
87. #2546C22semidirect
88. #2546C22semidirect
89. #2542C22semidirect
90. #2536C22semidirect
93. #2499C22semidirect
94. #2487C22semidirect
95. #2486C22semidirect
96. #2486C22semidirect
97. #2485C22semidirect
99. #2484C22semidirect
105. #2415C22semidirect
106. #2409C22semidirect
109. #2399C22semidirect
110. #2398C22semidirect
111. #2395C22semidirect
112. #2327C22semidirect
113. #2326C22semidirect
114. #2323C22semidirect
115. #2322C22semidirect
116. #2317C22semidirect
118. #2310C22semidirect
119. C4×C4⋊Q8C22semidirect
120. C4×#124C22semidirect
121. C4×C22⋊Q8C22semidirect
122. C4×C22⋊Q8C22semidirect
123. C4×#123C22semidirect
126. #2285C22semidirect
127. #2285C22semidirect
130. #2283C22semidirect
131. #2283C22semidirect
132. #2283C22semidirect
133. #2283C22semidirect
139. C4×#117C22semidirect
140. C4×#117C22semidirect
911. C2×C4#536semidirect

Maximal subgroups

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

subgroupindex
C22×#5332
C22×C4×#412
#366252
#353252
#353162
#353112
#353052
#352972
#352792
#352482
#352402
#352002
#351382
#350842
#349792
#349712
#349532
#349462
#348092
#346272
C4×#5362
#340122