Finite Group Databasebeta

← C2×#35260 #7628524

Subgroups — C2×#35260 #7628524

Order 512.

9278 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#542C211yesmaximal, characteristic, complemented
2C23×#117C211yesmaximal, characteristic, complemented
3C2×#2857C211yesmaximal, characteristic, complemented
4C2×#2850C211yesmaximal, characteristic, complemented
5C2×#2848C211yesmaximal, characteristic, complemented
6C2×#2847C211yesmaximal, characteristic
7#35260C2132yesmaximal, direct product factor
8C2×#2479C212yesmaximal, complemented
9C2×#2470C212yesmaximal, complemented
10C2×#2477C212yesmaximal, complemented
11C2×#2474C212yesmaximal, complemented
12C2×#2481C212yesmaximal, complemented
13C2×#2472C212yesmaximal, complemented
14C2×#2449C212yesmaximal, complemented
15C2×#2418C212yesmaximal, complemented
16C2×#2625C211yesmaximal, characteristic, complemented
17C2×#2620C211yesmaximal, characteristic, complemented
18C2×#2624C211yesmaximal, characteristic, complemented
19C2×#2628C211yesmaximal, characteristic, complemented
20C2×#2324C211yesmaximal, characteristic, complemented
21C2×#2323C211yesmaximal, characteristic, complemented
22C2×#2314C211yesmaximal, characteristic, complemented
23C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
24C2×C4×#121C211yesmaximal, characteristic, complemented
25C25×C4C2211yescharacteristic
26C2×#542—216no—
27C2×#542C22116yescomplemented
28C22×C4⋊Q8C2211yescharacteristic, complemented
29C22×#126C2212yescomplemented
30C22×#124C2212yes—
31C22×#124C2211yescharacteristic, complemented
32C22×#123C2212yes—
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C22×C22⋊Q8C2212yes—
37C22×C22⋊Q8C2212yescomplemented
38C22×#121C2211yescharacteristic
39C22×#121C2211yescharacteristic
40C22×#121C2211yescharacteristic
41C22×#120C2212yes—
42C22×C4×Q8C2211yescharacteristic, complemented
43C22×C4×D4C2212yes—
44C22×C4×D4C2211yescharacteristic, complemented
45C22×#117—216no—
46C22×#117C2211yescharacteristic
47C22×#117C2211yescharacteristic
48C22×#117C2211yescharacteristic
49C22×#117C2211yescharacteristic
50C22×#117C2211yescharacteristic
51C22×#117C2211yescharacteristic
52C22×#117C2211yescharacteristic
53C22×#117C2211yescharacteristic
54C22×#117C22116yescomplemented
55C23×C4⋊C4C2211yescharacteristic
56C23×C4⋊C4C2211yescharacteristic
57C23×C22⋊C4C2211yescharacteristic
58C23×C22⋊C4C2211yescharacteristic
59C23×C42C2211yescharacteristic
60C23×C42C2211yescharacteristic
61#2857C22116yescomplemented
62#2850C22116yescomplemented
63#2848C22116yescomplemented
64#2847C22116yes—
65#2628C22116yescomplemented
66#2625C22116yescomplemented
67#2624C22116yescomplemented
68#2620C22116yescomplemented
69#2481C22132yescomplemented
70#2479C22132yescomplemented
71#2477C22132yescomplemented
72#2474C22132yescomplemented
73#2472C22132yescomplemented
74#2470C22132yescomplemented
75#2449C22132yescomplemented
76#2418C22132yescomplemented
77C2×#400C2212yescomplemented
78C2×#400C2212yescomplemented
79C2×#399C2212yes—
80C2×#399C2212yescomplemented
81C2×#398C2212yescomplemented
82C2×#397C2212yes—
83C2×#397C2212yes—
84C2×#397C2212yescomplemented
85C2×#396C2212yescomplemented
86C2×#396C2212yescomplemented
87C2×#395C2212yescomplemented
88C2×#394C2212yes—
89C2×#394C2212yes—
90C2×#394C2212yes—
91C2×#394C2212yes—
92C2×#393C2212yes—
93#2324C22116yescomplemented
94#2323C22116yescomplemented
95#2314C22116yescomplemented
96C4×C22⋊Q8C22116yescomplemented
97C4×#121C22116yescomplemented
98C2×#391C2211yescharacteristic, complemented
99C2×#391C2212yescomplemented
100C2×#391C2211yescharacteristic, complemented
101C2×#390C2212yes—
102C2×#390C2211yescharacteristic, complemented
103C2×#390C2211yescharacteristic, complemented
104C2×#389C2211yescharacteristic, complemented
105C2×#389C2212yescomplemented
106C2×#389C2211yescharacteristic, complemented
107C2×#389C2212yescomplemented
108C2×#389C2211yescharacteristic, complemented
109C2×#389C2211yescharacteristic, complemented
110C2×#388C2212yes—
111C2×#388C2212yes—
112C2×#388C2212yes—
113C2×#388C2212yes—
114C2×#388C2212yescomplemented
115C2×#388C2212yescomplemented
116C2×#388C2212yescomplemented
117C2×#388C2212yescomplemented
118C2×#387C2212yescomplemented
119C2×#387C2212yescomplemented
120C2×#387C2212yescomplemented
121C2×#387C2212yescomplemented
122C2×#386C2212yes—
123C2×#386C2212yes—
124C2×#386C2212yes—
125C2×#386C2212yes—
126C2×#386C2212yes—
127C2×#386C2212yes—
128C2×#386C2212yes—
129C2×#385C2212yes—
130C2×#385C2212yes—
131C2×#385C2212yes—
132C2×#385C2212yes—
133C2×#385C2212yescomplemented
134C2×#384C2211yescharacteristic, complemented
135C2×#382C2211yescharacteristic, complemented
136C2×#380C2211yescharacteristic
137C2×#380C2211yescharacteristic
138C2×#380C2211yescharacteristic
139C2×#380C2211yescharacteristic
140C2×#380C2211yescharacteristic
141C2×#380C2211yescharacteristic
142C2×#380C2212yes—
143C2×#379C2212yes—
144C2×C4×C4⋊C4C2211yescharacteristic, complemented
145C2×C4×C4⋊C4C2211yescharacteristic, complemented
146C2×C4×C4⋊C4C2212yescomplemented
147C2×C4×C22⋊C4C2212yes—
148C2×C4×C22⋊C4C2212yescomplemented
149C26C2311yescharacteristic
150C23×Q8C2311yescharacteristic
151C23×Q8C2312yes—
152C23×D4C2312yes—
153C23×D4C2311yescharacteristic
154C23×D4C2312yes—
155C23×D4C2312yes—
156C24×C4—28no—
157C24×C4—28no—
158C24×C4—28no—
159C24×C4C2318yes—
160C24×C4C2311yescharacteristic
161C24×C4C2311yescharacteristic
162C24×C4C2311yescharacteristic
163C24×C4C2311yescharacteristic
164C24×C4C2311yescharacteristic
165C24×C4C2311yescharacteristic
166C24×C4C2311yescharacteristic
167C24×C4C2311yescharacteristic
168C24×C4C2311yescharacteristic
169C24×C4C2311yescharacteristic
170C24×C4C2312yes—
171#542—2128no—
172C2×C4⋊Q8—28no—
173C2×C4⋊Q8C2318yescomplemented
174C2×#126—216no—
175C2×#126C23116yescomplemented
176C2×#124—216no—
177C2×#124—28no—
178C2×#124C23116yes—
179C2×#124C2318yescomplemented
180C2×#123—216no—
181C2×#123C23116yes—
182C2×C22⋊Q8—28no—
183C2×C22⋊Q8—28no—
184C2×C22⋊Q8—28no—
185C2×C22⋊Q8—216no—
186C2×C22⋊Q8—48no—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C23116yes—
191C2×C22⋊Q8C23116yescomplemented
192C2×#121—28no—
193C2×#121—28no—
194C2×#121—28no—
195C2×#121C2318yes—
196C2×#121C2318yes—
197C2×#121C2318yes—
198C2×#120—48no—
199C2×#120C23116yes—
200C2×C4×Q8—28no—
201C2×C4×Q8C2318yescomplemented
202C2×C4×D4—28no—
203C2×C4×D4—48no—
204C2×C4×D4C23116yes—
205C2×C4×D4C2318yescomplemented
206C2×#117—28no—
207C2×#117—2128no—
208C2×#117—28no—
209C2×#117—28no—
210C2×#117—28no—
211C2×#117—28no—
212C2×#117—28no—
213C2×#117—28no—
214C2×#117D4116yescomplemented
215C2×#117C2318yes—
216C2×#117C2318yes—
217C2×#117C2318yes—
218C2×#117C2318yes—
219C2×#117C2318yes—
220C2×#117C2318yes—
221C2×#117C2318yes—
222C2×#117C2318yes—
223C22×C4⋊C4—28no—
224C22×C4⋊C4—28no—
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2318yes—
235C22×C4⋊C4C2318yes—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—28no—
253C22×C22⋊C4—28no—
254C22×C22⋊C4C2311yescharacteristic
255C22×C22⋊C4C2311yescharacteristic
256C22×C22⋊C4C2311yescharacteristic
257C22×C22⋊C4C2311yescharacteristic
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2312yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2311yescharacteristic
265C22×C22⋊C4C2311yescharacteristic
266C22×C22⋊C4C2318yes—
267C22×C22⋊C4C2318yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C42—28no—
284C22×C42—28no—
285C22×C42C2318yes—
286C22×C42C2311yescharacteristic
287C22×C42C2311yescharacteristic
288C22×C42C2311yescharacteristic
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2311yescharacteristic
292C22×C42C2318yes—
293C22×C42C2312yes—
294C22×C42C2312yes—
295C22×C42C2312yes—
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298#400C23116yescomplemented
299#400C23116yescomplemented
300#399C23116yes—
301#399C23116yescomplemented
302#398C23116yescomplemented
303#397C23116yes—
304#397C23116yes—
305#397C23116yescomplemented
306#396C23116yescomplemented
307#396C23116yescomplemented
308#395C23116yescomplemented
309#394C23116yes—
310#394C23116yes—
311#394C23116yes—
312#394C23116yes—
313#393C23116yes—
314#391C2318yescomplemented
315#391C23116yescomplemented
316#391C2318yescomplemented
317#390C23116yes—
318#390C2318yescomplemented
319#390C2318yescomplemented
320#389C2318yescomplemented
321#389C23116yescomplemented
322#389C2318yescomplemented
323#389C23116yescomplemented
324#389C2318yescomplemented
325#389C2318yescomplemented
326#388C23116yes—
327#388C23116yes—
328#388C23116yes—
329#388C23116yes—
330#388C23116yescomplemented
331#388C23116yescomplemented
332#388C23116yescomplemented
333#388C23116yescomplemented
334#387C23116yescomplemented
335#387C23116yescomplemented
336#387C23116yescomplemented
337#387C23116yescomplemented
338#386C23116yes—
339#386C23116yes—
340#386C23116yes—
341#386C23116yes—
342#386C23116yes—
343#386C23116yes—
344#386C23116yes—
345#385C23116yes—
346#385C23116yes—
347#385C23116yes—
348#385C23116yes—
349#385C23116yescomplemented
350#384C2318yescomplemented
351#382C2318yescomplemented
352#380C2318yes—
353#380C2318yes—
354#380C2318yes—
355#380C2318yes—
356#380C2318yes—
357#380C2318yes—
358#380C23116yes—
359#379C23116yes—
360C4×C4⋊C4C2318yescomplemented
361C4×C4⋊C4C2318yescomplemented
362C4×C4⋊C4C23116yescomplemented
363C4×C22⋊C4C23116yes—
364C4×C22⋊C4C23116yescomplemented
365C2×#95C2312yes—
366C2×#95C2312yes—
367C2×#95C2312yes—
368C2×#95C2312yes—
369C2×#95C2312yes—
370C2×#95C2312yes—
371C2×#95C2312yes—
372C2×#95C2312yes—
373C2×#95C2312yes—
374C2×#95C2312yes—
375C2×#95C2312yes—
376C2×#95C2312yes—
377C2×#95C2312yes—
378C2×#95C2312yes—
379C2×#95C2312yes—
380C2×#95C2312yes—
381C2×#95C2312yes—
382C2×#95C2312yes—
383C25—24no—
384C25—24no—
385C25—24no—
386C25—24no—
387C25—24no—
388C25—42no—
389C25—42no—
390C25C2412yes—
391C25C2411yescharacteristic
392C25C2411yescharacteristic
393C25C2414yes—
394C25C2411yescharacteristic
395C22×Q8—24no—
396C22×Q8—28no—
397C22×Q8—24no—
398C22×Q8—24no—
399C22×Q8—44no—
400C22×Q8—44no—
401C22×Q8C2414yes—
402C22×Q8C2418yes—
403C22×D4—28no—
404C22×D4—28no—
405C22×D4—28no—
406C22×D4—28no—
407C22×D4—28no—
408C22×D4—24no—
409C22×D4—24no—
410C22×D4—24no—
411C22×D4—44no—
412C22×D4—44no—
413C22×D4—44no—
414C22×D4—44no—
415C22×D4C2418yes—
416C22×D4C2414yes—
417C22×D4C2418yes—
418C22×D4C2418yes—
419C23×C4—2128no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—232no—
426C23×C4—24no—
427C23×C4—24no—
428C23×C4—24no—
429C23×C4—24no—
430C23×C4—24no—
431C23×C4—24no—
432C23×C4—232no—
433C23×C4—232no—
434C23×C4—24no—
435C23×C4—24no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—24no—
441C23×C4—24no—
442C23×C4—24no—
443C23×C4—24no—
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—28no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4—42no—
451C23×C4—44no—
452C23×C4—44no—
453C23×C4C2×D418yes—
454C23×C4#4118yes—
455C23×C4#4118yes—
456C23×C4C2414yes—
457C23×C4C2414yes—
458C23×C4C2414yes—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2414yes—
471C23×C4C2414yes—
472C23×C4C2414yes—
473C23×C4C2414yes—
474C23×C4C2414yes—
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2411yescharacteristic
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2414yes—
481C23×C4C2414yes—
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2418yes—
485C23×C4C2411yescharacteristic
486C4⋊Q8—232no—
487#126—264no—
488#124—264no—
489#124—232no—
490#123—264no—
491C22⋊Q8—232no—
492C22⋊Q8—232no—
493C22⋊Q8—232no—
494C22⋊Q8—264no—
495C22⋊Q8—432no—
496#121—232no—
497#121—232no—
498#121—232no—
499#120—432no—
500C4×Q8—232no—
501C4×D4—232no—
502C4×D4—432no—
503#117—232no—
504#117—232no—
505#117—232no—
506#117—232no—
507#117—232no—
508#117—232no—
509#117—232no—
510#117C2×D4164yescomplemented
511C2×C4⋊C4—24no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—24no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—28no—
520C2×C4⋊C4—28no—
521C2×C4⋊C4—28no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—24no—
526C2×C4⋊C4—28no—
527C2×C4⋊C4—28no—
528C2×C4⋊C4—232no—
529C2×C4⋊C4—232no—
530C2×C4⋊C4—44no—
531C2×C4⋊C4—44no—
532C2×C4⋊C4—44no—
533C2×C4⋊C4—44no—
534C2×C4⋊C4—44no—
535C2×C4⋊C4—44no—
536C2×C4⋊C4C2×D418yes—
537C2×C4⋊C4C2×D418yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—28no—
566C2×C22⋊C4—28no—
567C2×C22⋊C4—28no—
568C2×C22⋊C4—28no—
569C2×C22⋊C4—28no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—28no—
577C2×C22⋊C4—28no—
578C2×C22⋊C4—28no—
579C2×C22⋊C4—28no—
580C2×C22⋊C4—232no—
581C2×C22⋊C4—232no—
582C2×C22⋊C4—44no—
583C2×C22⋊C4—44no—
584C2×C22⋊C4—44no—
585C2×C22⋊C4—44no—
586C2×C22⋊C4—44no—
587C2×C22⋊C4—44no—
588C2×C22⋊C4—44no—
589C2×C22⋊C4—44no—
590C2×C22⋊C4C2×D418yes—
591C2×C22⋊C4C2×D418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C42—24no—
620C2×C42—24no—
621C2×C42—24no—
622C2×C42—24no—
623C2×C42—24no—
624C2×C42—24no—
625C2×C42—28no—
626C2×C42—232no—
627C2×C42—232no—
628C2×C42—44no—
629C2×C42—44no—
630C2×C42C2×D418yes—
631C2×C42C2×D418yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2414yes—
637C2×C42C2414yes—
638C2×C42C2418yes—
639C2×C42C2418yes—
640C2×C42C2418yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—232no—
666C24—28no—
667C24—22no—
668C24—28no—
669C24—28no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—24no—
682C24—24no—
683C24—24no—
684C24—24no—
685C24—28no—
686C24—24no—
687C24—28no—
688C24—24no—
689C24—24no—
690C24—44no—
691C24—44no—
692C24—416no—
693C24—416no—
694C24—416no—
695C24—416no—
696C24—416no—
697C24—416no—
698C24C22×D414yes—
699C24C2×#4114yes—
700C24C2×#4114yes—
701C24H(5,𝔽2)14yes—
702C242−1+414yes—
703C24C2514yes—
704C24C2512yes—
705C24C2512yes—
706C24C2512yes—
707C24C2511yescharacteristic
708C2×Q8—28no—
709C2×Q8—216no—
710C2×Q8—28no—
711C2×Q8—28no—
712C2×Q8—48no—
713C2×Q8—48no—
714C2×Q8—416no—
715C2×Q8—816no—
716C2×D4—216no—
717C2×D4—216no—
718C2×D4—216no—
719C2×D4—216no—
720C2×D4—216no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—432no—
729C2×D4—416no—
730C2×D4—816no—
731C2×D4—816no—
732C22×C4—232no—
733C22×C4—232no—
734C22×C4—232no—
735C22×C4—2256no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—232no—
754C22×C4—232no—
755C22×C4—232no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—24no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—216no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—416no—
817C22×C4—416no—
818C22×C4—416no—
819C22×C4—416no—
820C22×C4—816no—
821C22×C4C22×D414yes—
822C22×C4C22×D414yes—
823C22×C4C22×D414yes—
824C22×C4C22×D414yes—
825C22×C4C22×D414yes—
826C22×C4C22×D4116yes—
827C22×C4C22×D414yes—
828C22×C4C2×#4114yes—
829C22×C4C2×#4114yes—
830C22×C4C2×#41116yes—
831C22×C4C2×#41116yes—
832C22×C4C2×#4114yes—
833C22×C4C2×#4114yes—
834C22×C4C2514yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—216no—
862C4⋊C4—216no—
863C4⋊C4—216no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—216no—
869C4⋊C4—216no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4C22×D4116yes—
877C4⋊C4C22×D4116yes—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—216no—
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—216no—
890C22⋊C4—216no—
891C22⋊C4—216no—
892C22⋊C4—216no—
893C22⋊C4—216no—
894C22⋊C4—216no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4C22×D4116yes—
904C22⋊C4C22×D4116yes—
905C42—28no—
906C42—28no—
907C42—28no—
908C42—28no—
909C42—28no—
910C42—28no—
911C42—216no—
912C42—48no—
913C42—48no—
914C42C22×D4116yes—
915C42C22×D4116yes—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—28no—
921C23—28no—
922C23—28no—
923C23—28no—
924C23—28no—
925C23—28no—
926C23—232no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—28no—
940C23—28no—
941C23—28no—
942C23—28no—
943C23—28no—
944C23—28no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—416no—
953C23—416no—
954C23—416no—
955C23—416no—
956C23—4128no—
957C23—416no—
958C23—44no—
959C23—44no—
960C23—416no—
961C23—44no—
962C23—44no—
963C23—44no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—48no—
968C23—48no—
969C23—48no—
970C23—48no—
971C23—48no—
972C23—48no—
973C23—48no—
974C23#542116yescomplemented
975C23C23×D414yes—
976C23C23×D412yes—
977C23C22×#4114yes—
978C23C22×#4114yes—
979C23C22×#4112yes—
980C23C22×#4112yes—
981C23C2×H(5,𝔽2)14yes—
982C23C2×H(5,𝔽2)12yes—
983C23C2×2−1+414yes—
984C23C2×2−1+412yes—
985C23#58512yes—
986C23#58512yes—
987C23C2611yescharacteristic
988Q8—416no—
989Q8—816no—
990D4—432no—
991D4—416no—
992D4—816no—
993D4—816no—
994C2×C4—232no—
995C2×C4—232no—
996C2×C4—232no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—28no—
1012C2×C4—28no—
1013C2×C4—28no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—28no—
1017C2×C4—28no—
1018C2×C4—232no—
1019C2×C4—232no—
1020C2×C4—232no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—416no—
1055C2×C4—416no—
1056C2×C4—416no—
1057C2×C4—416no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—44no—
1062C2×C4—44no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—44no—
1066C2×C4—44no—
1067C2×C4—48no—
1068C2×C4—48no—
1069C2×C4—816no—
1070C2×C4#525116yes—
1071C2×C4C23×D414yes—
1072C2×C4C23×D414yes—
1073C2×C4C23×D414yes—
1074C2×C4C23×D414yes—
1075C2×C4C23×D414yes—
1076C2×C4C23×D414yes—
1077C2×C4C22×#4114yes—
1078C2×C4C22×#4114yes—
1079C2×C4C22×#4114yes—
1080C2×C4C22×#4114yes—
1081C22—24no—
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—232no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—24no—
1094C22—464no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—416no—
1100C22—416no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—44no—
1106C22—44no—
1107C22—44no—
1108C22—44no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—816no—
1113C22C2×#52514yes—
1114C22C2×#54214yes—
1115C22C2×#54218yescomplemented
1116C22#345514yes—
1117C22#348814yes—
1118C22#348914yes—
1119C22#349414yes—
1120C22#349514yes—
1121C22C24×D411yescharacteristic
1122C22C23×#4111yescharacteristic
1123C22C23×#4111yescharacteristic
1124C22C22×H(5,𝔽2)11yescharacteristic
1125C22C22×2−1+411yescharacteristic
1126C22C2×#58511yescharacteristic
1127C22C2×#58511yescharacteristic
1128C4—24no—
1129C4—24no—
1130C4—24no—
1131C4—24no—
1132C4—24no—
1133C4—24no—
1134C4—24no—
1135C4—42no—
1136C4—42no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—44no—
1141C4—42no—
1142C4—42no—
1143C4—44no—
1144C4—44no—
1145C4—44no—
1146C4C2×#52518yes—
1147C2—28no—
1148C2—44no—
1149C2—44no—
1150C2—84no—
1151C2#3526018yesdirect product factor
1152C2C22×#52511yescharacteristic
1153C2C22×#54211yescharacteristic
1154C2C2×#345511yescharacteristic
1155C2C2×#348811yescharacteristic
1156C2C2×#349411yescharacteristic
1157C2C2×#348911yescharacteristic
1158C2C2×#349511yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC2×#2847C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#542C2semidirect
2. C23×#117C2semidirect
3. C2×#2857C2semidirect
4. C2×#2850C2semidirect
5. C2×#2848C2semidirect
7. #35260C2direct (N × H)
8. C2×#2479C2semidirect
9. C2×#2470C2semidirect
10. C2×#2477C2semidirect
11. C2×#2474C2semidirect
12. C2×#2481C2semidirect
13. C2×#2472C2semidirect
14. C2×#2449C2semidirect
15. C2×#2418C2semidirect
16. C2×#2625C2semidirect
17. C2×#2620C2semidirect
18. C2×#2624C2semidirect
19. C2×#2628C2semidirect
20. C2×#2324C2semidirect
21. C2×#2323C2semidirect
22. C2×#2314C2semidirect
23. C2×C4×C22⋊Q8C2semidirect
24. C2×C4×#121C2semidirect
27. C2×#542C22semidirect
28. C22×C4⋊Q8C22semidirect
29. C22×#126C22semidirect
31. C22×#124C22semidirect
37. C22×C22⋊Q8C22semidirect
42. C22×C4×Q8C22semidirect
44. C22×C4×D4C22semidirect
54. C22×#117C22semidirect
61. #2857C22semidirect
62. #2850C22semidirect
63. #2848C22semidirect
65. #2628C22semidirect
66. #2625C22semidirect
67. #2624C22semidirect
68. #2620C22semidirect
69. #2481C22semidirect
70. #2479C22semidirect
71. #2477C22semidirect
72. #2474C22semidirect
73. #2472C22semidirect
74. #2470C22semidirect
75. #2449C22semidirect
76. #2418C22semidirect
77. C2×#400C22semidirect
78. C2×#400C22semidirect
80. C2×#399C22semidirect
81. C2×#398C22semidirect
84. C2×#397C22semidirect
85. C2×#396C22semidirect
86. C2×#396C22semidirect
87. C2×#395C22semidirect
93. #2324C22semidirect
94. #2323C22semidirect
95. #2314C22semidirect
96. C4×C22⋊Q8C22semidirect
97. C4×#121C22semidirect
98. C2×#391C22semidirect
99. C2×#391C22semidirect
100. C2×#391C22semidirect
102. C2×#390C22semidirect
103. C2×#390C22semidirect
104. C2×#389C22semidirect
105. C2×#389C22semidirect
106. C2×#389C22semidirect
107. C2×#389C22semidirect
108. C2×#389C22semidirect
109. C2×#389C22semidirect
114. C2×#388C22semidirect
115. C2×#388C22semidirect
116. C2×#388C22semidirect
117. C2×#388C22semidirect
118. C2×#387C22semidirect
119. C2×#387C22semidirect
120. C2×#387C22semidirect
121. C2×#387C22semidirect
133. C2×#385C22semidirect
134. C2×#384C22semidirect
135. C2×#382C22semidirect
144. C2×C4×C4⋊C4C22semidirect
145. C2×C4×C4⋊C4C22semidirect
146. C2×C4×C4⋊C4C22semidirect
148. C2×C4×C22⋊C4C22semidirect
173. C2×C4⋊Q8C23semidirect
175. C2×#126C23semidirect
179. C2×#124C23semidirect
191. C2×C22⋊Q8C23semidirect
201. C2×C4×Q8C23semidirect
205. C2×C4×D4C23semidirect
214. C2×#117D4semidirect
298. #400C23semidirect
299. #400C23semidirect
301. #399C23semidirect
302. #398C23semidirect
305. #397C23semidirect
306. #396C23semidirect
307. #396C23semidirect
308. #395C23semidirect
314. #391C23semidirect
315. #391C23semidirect
316. #391C23semidirect
318. #390C23semidirect
319. #390C23semidirect
320. #389C23semidirect
321. #389C23semidirect
322. #389C23semidirect
323. #389C23semidirect
324. #389C23semidirect
325. #389C23semidirect
330. #388C23semidirect
331. #388C23semidirect
332. #388C23semidirect
333. #388C23semidirect
334. #387C23semidirect
335. #387C23semidirect
336. #387C23semidirect
337. #387C23semidirect
349. #385C23semidirect
350. #384C23semidirect
351. #382C23semidirect
360. C4×C4⋊C4C23semidirect
361. C4×C4⋊C4C23semidirect
362. C4×C4⋊C4C23semidirect
364. C4×C22⋊C4C23semidirect
510. #117C2×D4semidirect
974. C23#542semidirect
1115. C22C2×#542semidirect
1151. C2#35260direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5422
C23×#1172
C2×#28572
C2×#28502
C2×#28482
C2×#28472
#352602
C2×#24792
C2×#24702
C2×#24772
C2×#24742
C2×#24812
C2×#24722
C2×#24492
C2×#24182
C2×#26252
C2×#26202
C2×#26242
C2×#26282
C2×#23242
C2×#23232
C2×#23142
C2×C4×C22⋊Q82
C2×C4×#1212