Finite Group Databasebeta

← #7641865

Subgroups — #7641865

Order 512.

9206 conjugacy classes of subgroups.

The subgroup lattice has 1127 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic
2C23×C22⋊Q8C211yesmaximal, characteristic, complemented
3#37453C212yesmaximal, complemented
4#37451C212yesmaximal, complemented
5#37449C214yesmaximal, complemented
6#37447C214yesmaximal, complemented
7#37442C214yesmaximal, complemented
8#37441C214yesmaximal, complemented
9#37438C214yesmaximal, complemented
10#35311C212yesmaximal, complemented
11#35306C214yesmaximal, complemented
12#35305C212yesmaximal, complemented
13#35242C212yesmaximal, complemented
14#35227C212yesmaximal, complemented
15#35085C214yesmaximal, complemented
16#35084C214yesmaximal, complemented
17#35057C214yesmaximal, complemented
18#35019C212yesmaximal, complemented
19#35011C212yesmaximal, complemented
20#35010C214yesmaximal, complemented
21#34992C214yesmaximal, complemented
22C2×#2280C211yesmaximal, characteristic, complemented
23C23×#41C2211yescharacteristic
24C24×Q8C2211yescharacteristic, complemented
25C25×C4C2211yescharacteristic
26C2×#536C2214yescomplemented
27C2×#525—216no—
28C2×#525C2212yes—
29C2×#525C2212yes—
30C2×#525C2212yes—
31C2×#525C2212yes—
32C2×#525C2212yes—
33C2×#525C2212yes—
34C2×#525C2212yes—
35C2×#525C2212yes—
36C22×#123C2212yes—
37C22×C22⋊Q8—216no—
38C22×C22⋊Q8C2212yes—
39C22×C22⋊Q8C2212yes—
40C22×C22⋊Q8C2212yes—
41C22×C22⋊Q8C2211yescharacteristic
42C22×C22⋊Q8C2212yes—
43C22×C22⋊Q8C2212yes—
44C22×C22⋊Q8C2212yes—
45C22×C22⋊Q8C2211yescharacteristic
46C22×C22⋊Q8C2212yescomplemented
47C22×C22⋊Q8C2212yescomplemented
48C22×C22⋊Q8C2212yescomplemented
49C22×C22⋊Q8C2212yescomplemented
50C22×C22⋊Q8C2212yescomplemented
51C22×C22⋊Q8C2212yescomplemented
52C22×#121C2211yescharacteristic
53C22×#121C2211yescharacteristic
54C22×#120C2212yes—
55C22×C4×D4C2212yes—
56C22×C4×D4C2212yes—
57C22×#117C2211yescharacteristic
58C22×#117C2212yescomplemented
59C23×C4⋊C4C2211yescharacteristic, complemented
60C23×C4⋊C4C2212yescomplemented
61C23×C22⋊C4C2212yes—
62#2857C2218yescomplemented
63#2855C2218yescomplemented
64#2850C2218yescomplemented
65#2849C2218yescomplemented
66#2849C2218yescomplemented
67#2848C2218yescomplemented
68#2817C2218yescomplemented
69#2816C2218yescomplemented
70#2814C22116yescomplemented
71#2663C22116yescomplemented
72#2659C2218yescomplemented
73#2639C2218yescomplemented
74#2638C22116yescomplemented
75#2627C2218yescomplemented
76#2627C2218yescomplemented
77#2626C2218yescomplemented
78#2625C2218yescomplemented
79#2623C2218yescomplemented
80#2622C22116yescomplemented
81#2621C2218yescomplemented
82#2620C2218yescomplemented
83#2618C2218yescomplemented
84#2616C2218yescomplemented
85#2614C2218yescomplemented
86#2591C2218yescomplemented
87#2583C2218yescomplemented
88#2583C2218yescomplemented
89#2579C22116yescomplemented
90#2564C22116yescomplemented
91#2561C2218yescomplemented
92#2504C2214yescomplemented
93#2503C2214yescomplemented
94#2503C2214yescomplemented
95#2502C2214yescomplemented
96#2502C2214yescomplemented
97#2501C2214yescomplemented
98#2499C2218yescomplemented
99#2487C2218yescomplemented
100#2486C2218yescomplemented
101#2484C2218yescomplemented
102#2483C2218yes—
103#2483C2218yes—
104#2436C2214yescomplemented
105#2436C2214yescomplemented
106#2435C2214yescomplemented
107#2434C2214yescomplemented
108#2434C2214yescomplemented
109#2434C2214yescomplemented
110#2432C2218yescomplemented
111#2417C22116yescomplemented
112#2415C22116yescomplemented
113#2413C22116yescomplemented
114#2412C22116yescomplemented
115#2412C22116yescomplemented
116#2409C2218yescomplemented
117#2409C2218yescomplemented
118#2406C2218yescomplemented
119#2405C2218yes—
120#2405C2218yes—
121#2322C22116yescomplemented
122#2317C2214yescomplemented
123#2315C2218yes—
124#2311C2214yescomplemented
125#2310C2214yescomplemented
126#2308C2218yes—
127#2280C2212yes—
128#2280C2212yes—
129#2280C2212yes—
130#2280C2212yes—
131#2280C2212yescomplemented
132#2280C2212yescomplemented
133#2280C2212yescomplemented
134#2280C2212yescomplemented
135C2×#381C2212yescomplemented
136C2×#380C2212yes—
137C2×#380C2212yescomplemented
138C2×#379C2212yes—
139C2×C4×C22⋊C4C2212yes—
140C2×C4×C22⋊C4C2212yescomplemented
141C26C2311yescharacteristic
142C22×#41—28no—
143C22×#41—48no—
144C22×#41C2312yes—
145C22×#41C2312yes—
146C22×#41C2312yes—
147C22×#41C2312yes—
148C23×Q8—28no—
149C23×Q8—48no—
150C23×Q8C2312yes—
151C23×Q8C2312yes—
152C23×Q8C2312yes—
153C23×Q8C2312yes—
154C23×Q8C2312yes—
155C23×Q8C2312yes—
156C23×Q8C2311yescharacteristic
157C23×D4C2312yes—
158C23×D4C2312yes—
159C23×D4C2311yescharacteristic
160C23×D4C2312yes—
161C24×C4—48no—
162C24×C4D4116yes—
163C24×C4C2311yescharacteristic
164C24×C4C2311yescharacteristic
165C24×C4C2311yescharacteristic
166C24×C4C2312yes—
167C24×C4C2312yes—
168C24×C4C2312yes—
169C24×C4C2311yescharacteristic
170C24×C4C2311yescharacteristic
171C24×C4C2311yescharacteristic
172C24×C4C2311yescharacteristic
173C24×C4C2311yescharacteristic
174C24×C4C2311yescharacteristic
175C24×C4C2311yescharacteristic
176C24×C4C2311yescharacteristic
177C24×C4C2311yescharacteristic
178C24×C4C2311yescharacteristic
179C24×C4C2311yescharacteristic
180#536—416no—
181C2×C4⋊Q8C2318yescomplemented
182C2×#124C2318yescomplemented
183#525—216no—
184#525—216no—
185#525—216no—
186#525—216no—
187#525—216no—
188#525—216no—
189#525—216no—
190#525—216no—
191C2×#123—216no—
192C2×#123C2314yes—
193C2×#123C2314yes—
194C2×#123C2314yes—
195C2×#123C2314yes—
196C2×#123C23116yes—
197C2×#123C23116yes—
198C2×C22⋊Q8—216no—
199C2×C22⋊Q8—216no—
200C2×C22⋊Q8—216no—
201C2×C22⋊Q8—216no—
202C2×C22⋊Q8—216no—
203C2×C22⋊Q8—216no—
204C2×C22⋊Q8—216no—
205C2×C22⋊Q8—216no—
206C2×C22⋊Q8—216no—
207C2×C22⋊Q8—216no—
208C2×C22⋊Q8—216no—
209C2×C22⋊Q8—216no—
210C2×C22⋊Q8—28no—
211C2×C22⋊Q8—28no—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C23116yescomplemented
237C2×#121—28no—
238C2×#121—28no—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×#120—216no—
248C2×#120C2314yes—
249C2×#120C2314yes—
250C2×#120C2314yes—
251C2×#120C2314yes—
252C2×C4×D4—216no—
253C2×C4×D4—216no—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×#117—28no—
263C2×#117—48no—
264C2×#117C2312yes—
265C2×#117C2314yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C22×C4⋊C4—28no—
273C22×C4⋊C4—216no—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2314yes—
279C22×C4⋊C4C2314yes—
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2314yes—
283C22×C4⋊C4C2314yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2314yes—
291C22×C22⋊C4—216no—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2314yes—
294C22×C22⋊C4C2314yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2314yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2314yes—
299C22×C22⋊C4C2314yes—
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2314yes—
302C22×C22⋊C4C2312yes—
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2314yes—
306C22×C42C2312yes—
307C22×C42C2314yes—
308#400C23116yescomplemented
309#400C23116yescomplemented
310#399C23116yescomplemented
311#398C23116yescomplemented
312#398C23132yescomplemented
313#398C23116yescomplemented
314#397C23132yes—
315#397C23132yes—
316#397C23116yescomplemented
317#396C23132yescomplemented
318#395C23116yescomplemented
319#395C23116yescomplemented
320#395C23116yescomplemented
321#394C23132yes—
322#394C23132yes—
323#394C23116yescomplemented
324#393C23116yescomplemented
325#393C23116yescomplemented
326#391C2318yescomplemented
327#391C23116yescomplemented
328#391C2318yescomplemented
329#391C2318yescomplemented
330#390C2318yescomplemented
331#389C23116yescomplemented
332#389C23132yescomplemented
333#388C23132yescomplemented
334#387C23132yescomplemented
335#386C23132yes—
336#386C23116yes—
337#386C23116yes—
338#386C23116yes—
339#386C23116yes—
340#385C23116yes—
341#385C23116yes—
342#385C23116yes—
343#385C23116yes—
344#385C23116yes—
345#385C23116yes—
346#385C23132yescomplemented
347#384C2318yescomplemented
348#382C2318yescomplemented
349#381C2314yes—
350#381C23116yes—
351#381C23116yes—
352#381C23116yes—
353#381C2314yes—
354#381C2314yes—
355#381C2314yes—
356#380C23132yes—
357#380C2314yes—
358#380C2314yes—
359#380C2314yes—
360#380C2314yes—
361#380C2314yes—
362#380C2314yes—
363#380C2314yes—
364#380C2314yes—
365#380C23116yescomplemented
366#379C23116yes—
367#379C2314yes—
368#379C2314yes—
369#379C2314yes—
370#379C2314yes—
371C4×C22⋊C4C2314yes—
372C4×C22⋊C4C2314yes—
373C4×C22⋊C4C2314yes—
374C4×C22⋊C4C2314yes—
375C4×C22⋊C4C2314yes—
376C4×C22⋊C4C2314yes—
377C4×C22⋊C4C2314yes—
378C4×C22⋊C4C2314yes—
379C2×#95C2314yes—
380C2×#95C2314yes—
381C25—28no—
382C25—44no—
383C25—44no—
384C25C2×D418yes—
385C25C2411yescharacteristic
386C25C2411yescharacteristic
387C25C2411yescharacteristic
388C25C2411yescharacteristic
389C25C2411yescharacteristic
390C25C2412yes—
391C25C2411yescharacteristic
392C25C2411yescharacteristic
393C2×#41—28no—
394C2×#41—28no—
395C2×#41—28no—
396C2×#41—28no—
397C2×#41—216no—
398C2×#41—48no—
399C2×#41—48no—
400C2×#41—48no—
401C2×#41—464no—
402C22×Q8—28no—
403C22×Q8—28no—
404C22×Q8—28no—
405C22×Q8—28no—
406C22×Q8—28no—
407C22×Q8—28no—
408C22×Q8—24no—
409C22×Q8—216no—
410C22×Q8—48no—
411C22×Q8—48no—
412C22×Q8—48no—
413C22×Q8—48no—
414C22×Q8—48no—
415C22×Q8—44no—
416C22×Q8—464no—
417C22×Q8C2414yes—
418C22×Q8C2414yes—
419C22×Q8C2412yes—
420C22×Q8C2414yes—
421C22×Q8C2414yes—
422C22×Q8C2412yes—
423C22×D4—28no—
424C22×D4—28no—
425C22×D4—28no—
426C22×D4—216no—
427C22×D4—24no—
428C22×D4—44no—
429C22×D4—48no—
430C22×D4—48no—
431C22×D4C2414yes—
432C22×D4C2414yes—
433C22×D4C2414yes—
434C22×D4C2414yes—
435C22×D4C2412yes—
436C22×D4C2414yes—
437C22×D4C2414yes—
438C22×D4C2412yes—
439C23×C4—28no—
440C23×C4—28no—
441C23×C4—28no—
442C23×C4—28no—
443C23×C4—28no—
444C23×C4—28no—
445C23×C4—464no—
446C23×C4—44no—
447C23×C4—44no—
448C23×C4—44no—
449C23×C4—44no—
450C23×C4—44no—
451C23×C4—44no—
452C23×C4—44no—
453C23×C4—44no—
454C23×C4—48no—
455C23×C4—44no—
456C23×C4—44no—
457C23×C4—44no—
458C23×C4—48no—
459C23×C4—48no—
460C23×C4C2×D418yes—
461C23×C4C2×D418yes—
462C23×C4C2×D418yes—
463C23×C4C2×D418yes—
464C23×C4C2×D418yes—
465C23×C4C2×D418yes—
466C23×C4C2×D418yes—
467C23×C4C2×D418yes—
468C23×C4C2×D418yes—
469C23×C4C2×D418yes—
470C23×C4C2×D418yes—
471C23×C4C2×D418yes—
472C23×C4C2×D418yes—
473C23×C4C2×D418yes—
474C23×C4C2412yes—
475C23×C4C2414yes—
476C23×C4C2414yes—
477C23×C4C2414yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2411yescharacteristic
481C23×C4C2411yescharacteristic
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489C23×C4C2411yescharacteristic
490C23×C4C2411yescharacteristic
491C23×C4C2411yescharacteristic
492C23×C4C2411yescharacteristic
493C23×C4C2412yes—
494C23×C4C2418yes—
495C23×C4C2414yes—
496C23×C4C2414yes—
497C23×C4C2412yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2414yes—
501C23×C4C2411yescharacteristic
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C4⋊Q8—416no—
515#124—416no—
516#123—216no—
517#123—216no—
518#123—216no—
519#123—216no—
520#123—432no—
521#123—432no—
522C22⋊Q8—216no—
523C22⋊Q8—216no—
524C22⋊Q8—216no—
525C22⋊Q8—216no—
526C22⋊Q8—216no—
527C22⋊Q8—216no—
528C22⋊Q8—216no—
529C22⋊Q8—216no—
530C22⋊Q8—216no—
531C22⋊Q8—216no—
532C22⋊Q8—216no—
533C22⋊Q8—216no—
534C22⋊Q8—216no—
535C22⋊Q8—216no—
536C22⋊Q8—216no—
537C22⋊Q8—216no—
538C22⋊Q8—28no—
539C22⋊Q8—28no—
540C22⋊Q8—28no—
541C22⋊Q8—28no—
542C22⋊Q8—28no—
543C22⋊Q8—28no—
544C22⋊Q8—28no—
545C22⋊Q8—28no—
546C22⋊Q8—432no—
547#121—28no—
548#121—28no—
549#121—28no—
550#121—28no—
551#121—28no—
552#121—28no—
553#121—28no—
554#121—28no—
555#120—216no—
556#120—216no—
557#120—216no—
558#120—216no—
559C4×D4—216no—
560C4×D4—216no—
561C4×D4—216no—
562C4×D4—216no—
563C4×D4—216no—
564C4×D4—216no—
565C4×D4—216no—
566C4×D4—216no—
567#117—28no—
568#117—28no—
569#117—28no—
570#117—28no—
571#117—216no—
572#117—48no—
573#117—48no—
574#117—48no—
575C2×C4⋊C4—28no—
576C2×C4⋊C4—28no—
577C2×C4⋊C4—28no—
578C2×C4⋊C4—28no—
579C2×C4⋊C4—28no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—216no—
582C2×C4⋊C4—216no—
583C2×C4⋊C4—216no—
584C2×C4⋊C4—216no—
585C2×C4⋊C4—216no—
586C2×C4⋊C4—216no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4—28no—
591C2×C4⋊C4—48no—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C24132yes—
611C2×C4⋊C4C24132yes—
612C2×C22⋊C4—216no—
613C2×C22⋊C4—216no—
614C2×C22⋊C4—216no—
615C2×C22⋊C4—216no—
616C2×C22⋊C4—216no—
617C2×C22⋊C4—216no—
618C2×C22⋊C4—28no—
619C2×C22⋊C4—28no—
620C2×C22⋊C4—28no—
621C2×C22⋊C4—216no—
622C2×C22⋊C4—28no—
623C2×C22⋊C4—28no—
624C2×C22⋊C4—48no—
625C2×C22⋊C4—48no—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C24132yes—
647C2×C22⋊C4C24132yes—
648C2×C42—28no—
649C2×C42—48no—
650C2×C42C2414yes—
651C2×C42C2414yes—
652C2×C42C2418yes—
653C2×C42C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C24132yes—
659#95C24132yes—
660#95C24132yes—
661#95C24132yes—
662C24—24no—
663C24—24no—
664C24—24no—
665C24—232no—
666C24—24no—
667C24—24no—
668C24—24no—
669C24—24no—
670C24—24no—
671C24—24no—
672C24—24no—
673C24—24no—
674C24—24no—
675C24—24no—
676C24—28no—
677C24—416no—
678C24—42no—
679C24—42no—
680C24—42no—
681C24—42no—
682C24—416no—
683C24—42no—
684C24—42no—
685C24—42no—
686C24—42no—
687C24—44no—
688C24—44no—
689C24—464no—
690C24C22×D414yes—
691C24C22×D414yes—
692C24C22×D414yes—
693C24C22×D414yes—
694C24C22×D414yes—
695C24C22×D414yes—
696C24C22×D414yes—
697C242−1+418yes—
698C24C2514yes—
699C24C2511yescharacteristic
700C24C2511yescharacteristic
701C24C2511yescharacteristic
702C24C2511yescharacteristic
703C24C2511yescharacteristic
704C24C2511yescharacteristic
705C24C2511yescharacteristic
706#41—432no—
707#41—432no—
708#41—432no—
709#41—432no—
710C2×Q8—28no—
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—28no—
714C2×Q8—24no—
715C2×Q8—24no—
716C2×Q8—216no—
717C2×Q8—216no—
718C2×Q8—28no—
719C2×Q8—48no—
720C2×Q8—48no—
721C2×Q8—44no—
722C2×Q8—432no—
723C2×Q8—432no—
724C2×Q8—432no—
725C2×Q8—432no—
726C2×Q8—432no—
727C2×Q8—416no—
728C2×Q8—432no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—216no—
736C2×D4—216no—
737C2×D4—216no—
738C2×D4—216no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—28no—
742C2×D4—48no—
743C2×D4—44no—
744C2×D4—48no—
745C2×D4—416no—
746C2×D4—432no—
747C2×D4—432no—
748C2×D4—432no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—232no—
753C22×C4—232no—
754C22×C4—232no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—24no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—216no—
777C22×C4—28no—
778C22×C4—216no—
779C22×C4—216no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—216no—
783C22×C4—416no—
784C22×C4—416no—
785C22×C4—416no—
786C22×C4—416no—
787C22×C4—416no—
788C22×C4—416no—
789C22×C4—416no—
790C22×C4—416no—
791C22×C4—416no—
792C22×C4—416no—
793C22×C4—416no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—42no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—44no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—432no—
816C22×C4—432no—
817C22×C4—432no—
818C22×C4C22×D414yes—
819C22×C4C22×D414yes—
820C22×C4C22×D414yes—
821C22×C4C22×D414yes—
822C22×C4C22×D414yes—
823C22×C4C22×D414yes—
824C22×C4C22×D414yes—
825C22×C4C22×D414yes—
826C22×C4C22×D414yes—
827C22×C4C22×D414yes—
828C22×C4C22×D414yes—
829C22×C4C22×D414yes—
830C22×C4C22×D414yes—
831C22×C4C22×D414yes—
832C22×C4C22×D414yes—
833C22×C4C22×D414yes—
834C22×C4C22×D414yes—
835C22×C4C22×D414yes—
836C22×C4C22×D414yes—
837C22×C4C22×D414yes—
838C22×C4C22×D414yes—
839C22×C4C22×D414yes—
840C22×C4C22×D414yes—
841C22×C4C22×D414yes—
842C22×C4C22×D414yes—
843C22×C4C22×D414yes—
844C22×C4C22×D414yes—
845C22×C4C22×D414yes—
846C22×C4H(5,𝔽2)18yes—
847C22×C4C2514yes—
848C22×C4C25116yes—
849C22×C4C2514yes—
850C22×C4C2518yes—
851C22×C4C2518yes—
852C22×C4C2514yes—
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—216no—
866C4⋊C4—216no—
867C4⋊C4—216no—
868C4⋊C4—216no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—216no—
878C4⋊C4—48no—
879C4⋊C4—432no—
880C4⋊C4—432no—
881C22⋊C4—216no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—216no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—216no—
892C22⋊C4—216no—
893C22⋊C4—216no—
894C22⋊C4—216no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—432no—
902C22⋊C4—432no—
903C42—28no—
904C42—28no—
905C42—216no—
906C42—48no—
907C23—232no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—28no—
919C23—28no—
920C23—28no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—28no—
928C23—28no—
929C23—28no—
930C23—28no—
931C23—28no—
932C23—28no—
933C23—28no—
934C23—28no—
935C23—28no—
936C23—24no—
937C23—28no—
938C23—28no—
939C23—28no—
940C23—44no—
941C23—44no—
942C23—44no—
943C23—44no—
944C23—44no—
945C23—44no—
946C23—44no—
947C23—44no—
948C23—416no—
949C23—416no—
950C23—416no—
951C23—416no—
952C23—416no—
953C23—4128no—
954C23—416no—
955C23—48no—
956C23—48no—
957C23—48no—
958C23—816no—
959C23#536116yescomplemented
960C23C23×D412yes—
961C23C23×D412yes—
962C23C23×D412yes—
963C23C23×D412yes—
964C23C23×D412yes—
965C23C23×D412yes—
966C23C23×D412yes—
967C23C2×H(5,𝔽2)14yes—
968C23C2×2−1+414yes—
969C23C2×2−1+414yes—
970C23C2×2−1+414yes—
971C23#58514yes—
972C23C2611yescharacteristic
973Q8—416no—
974Q8—416no—
975Q8—48no—
976Q8—416no—
977Q8—416no—
978Q8—48no—
979D4—48no—
980D4—416no—
981D4—416no—
982D4—416no—
983D4—416no—
984D4—416no—
985D4—416no—
986D4—48no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—28no—
994C2×C4—28no—
995C2×C4—28no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—28no—
999C2×C4—28no—
1000C2×C4—28no—
1001C2×C4—28no—
1002C2×C4—28no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—28no—
1006C2×C4—28no—
1007C2×C4—28no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—28no—
1011C2×C4—24no—
1012C2×C4—28no—
1013C2×C4—216no—
1014C2×C4—216no—
1015C2×C4—28no—
1016C2×C4—216no—
1017C2×C4—28no—
1018C2×C4—216no—
1019C2×C4—216no—
1020C2×C4—28no—
1021C2×C4—44no—
1022C2×C4—44no—
1023C2×C4—44no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—44no—
1028C2×C4—44no—
1029C2×C4—44no—
1030C2×C4—44no—
1031C2×C4—44no—
1032C2×C4—44no—
1033C2×C4—416no—
1034C2×C4—416no—
1035C2×C4—416no—
1036C2×C4—48no—
1037C2×C4—416no—
1038C2×C4—416no—
1039C2×C4—48no—
1040C2×C4—416no—
1041C2×C4—48no—
1042C2×C4—416no—
1043C2×C4—416no—
1044C2×C4—816no—
1045C2×C4#534116yes—
1046C2×C4C23×D412yes—
1047C2×C4C23×D412yes—
1048C2×C4C23×D412yes—
1049C2×C4C23×D412yes—
1050C2×C4C23×D412yes—
1051C2×C4C23×D412yes—
1052C2×C4C23×D412yes—
1053C2×C4C23×D412yes—
1054C2×C4C2×H(5,𝔽2)14yes—
1055C2×C4C2×H(5,𝔽2)14yes—
1056C22—232no—
1057C22—28no—
1058C22—28no—
1059C22—28no—
1060C22—28no—
1061C22—28no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—22no—
1066C22—22no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—22no—
1075C22—22no—
1076C22—22no—
1077C22—22no—
1078C22—416no—
1079C22—416no—
1080C22—416no—
1081C22—416no—
1082C22—416no—
1083C22—416no—
1084C22—44no—
1085C22—44no—
1086C22—416no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—816no—
1091C22C2×#53414yes—
1092C22C2×#53614yes—
1093C22C2×#53614yes—
1094C22C2×#53614yes—
1095C22#344914yes—
1096C22C24×D411yescharacteristic
1097C22C22×H(5,𝔽2)12yes—
1098C22C22×2−1+412yes—
1099C22C2×#58512yes—
1100C4—22no—
1101C4—22no—
1102C4—22no—
1103C4—22no—
1104C4—22no—
1105C4—22no—
1106C4—416no—
1107C4—44no—
1108C4—48no—
1109C4—44no—
1110C4—48no—
1111C4—44no—
1112C4C2×#53414yes—
1113C4C2×#53414yes—
1114C2—24no—
1115C2—24no—
1116C2—24no—
1117C2—24no—
1118C2—24no—
1119C2—42no—
1120C2—42no—
1121C2—84no—
1122C2C22×#53411yescharacteristic
1123C2C22×#53611yescharacteristic
1124C2C2×#344911yescharacteristic
1125C2#6281914yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#525C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊Q8C2semidirect
3. #37453C2semidirect
4. #37451C2semidirect
5. #37449C2semidirect
6. #37447C2semidirect
7. #37442C2semidirect
8. #37441C2semidirect
9. #37438C2semidirect
10. #35311C2semidirect
11. #35306C2semidirect
12. #35305C2semidirect
13. #35242C2semidirect
14. #35227C2semidirect
15. #35085C2semidirect
16. #35084C2semidirect
17. #35057C2semidirect
18. #35019C2semidirect
19. #35011C2semidirect
20. #35010C2semidirect
21. #34992C2semidirect
22. C2×#2280C2semidirect
24. C24×Q8C22semidirect
26. C2×#536C22semidirect
46. C22×C22⋊Q8C22semidirect
47. C22×C22⋊Q8C22semidirect
48. C22×C22⋊Q8C22semidirect
49. C22×C22⋊Q8C22semidirect
50. C22×C22⋊Q8C22semidirect
51. C22×C22⋊Q8C22semidirect
58. C22×#117C22semidirect
59. C23×C4⋊C4C22semidirect
60. C23×C4⋊C4C22semidirect
62. #2857C22semidirect
63. #2855C22semidirect
64. #2850C22semidirect
65. #2849C22semidirect
66. #2849C22semidirect
67. #2848C22semidirect
68. #2817C22semidirect
69. #2816C22semidirect
70. #2814C22semidirect
71. #2663C22semidirect
72. #2659C22semidirect
73. #2639C22semidirect
74. #2638C22semidirect
75. #2627C22semidirect
76. #2627C22semidirect
77. #2626C22semidirect
78. #2625C22semidirect
79. #2623C22semidirect
80. #2622C22semidirect
81. #2621C22semidirect
82. #2620C22semidirect
83. #2618C22semidirect
84. #2616C22semidirect
85. #2614C22semidirect
86. #2591C22semidirect
87. #2583C22semidirect
88. #2583C22semidirect
89. #2579C22semidirect
90. #2564C22semidirect
91. #2561C22semidirect
92. #2504C22semidirect
93. #2503C22semidirect
94. #2503C22semidirect
95. #2502C22semidirect
96. #2502C22semidirect
97. #2501C22semidirect
98. #2499C22semidirect
99. #2487C22semidirect
100. #2486C22semidirect
101. #2484C22semidirect
104. #2436C22semidirect
105. #2436C22semidirect
106. #2435C22semidirect
107. #2434C22semidirect
108. #2434C22semidirect
109. #2434C22semidirect
110. #2432C22semidirect
111. #2417C22semidirect
112. #2415C22semidirect
113. #2413C22semidirect
114. #2412C22semidirect
115. #2412C22semidirect
116. #2409C22semidirect
117. #2409C22semidirect
118. #2406C22semidirect
121. #2322C22semidirect
122. #2317C22semidirect
124. #2311C22semidirect
125. #2310C22semidirect
131. #2280C22semidirect
132. #2280C22semidirect
133. #2280C22semidirect
134. #2280C22semidirect
135. C2×#381C22semidirect
137. C2×#380C22semidirect
140. C2×C4×C22⋊C4C22semidirect
181. C2×C4⋊Q8C23semidirect
182. C2×#124C23semidirect
236. C2×C22⋊Q8C23semidirect
308. #400C23semidirect
309. #400C23semidirect
310. #399C23semidirect
311. #398C23semidirect
312. #398C23semidirect
313. #398C23semidirect
316. #397C23semidirect
317. #396C23semidirect
318. #395C23semidirect
319. #395C23semidirect
320. #395C23semidirect
323. #394C23semidirect
324. #393C23semidirect
325. #393C23semidirect
326. #391C23semidirect
327. #391C23semidirect
328. #391C23semidirect
329. #391C23semidirect
330. #390C23semidirect
331. #389C23semidirect
332. #389C23semidirect
333. #388C23semidirect
334. #387C23semidirect
346. #385C23semidirect
347. #384C23semidirect
348. #382C23semidirect
365. #380C23semidirect
959. C23#536semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C23×C22⋊Q82
#374532
#374512
#374492
#374472
#374422
#374412
#374382
#353112
#353062
#353052
#352422
#352272
#350852
#350842
#350572
#350192
#350112
#350102
#349922
C2×#22802