Finite Group Databasebeta

← C2×#45097 #7669664

Subgroups — C2×#45097 #7669664

Order 512.

9510 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×#559C211yesmaximal, characteristic, complemented
2C22×#535C211yesmaximal, characteristic
3C2×#2701C212yesmaximal, complemented
4C2×#2697C212yesmaximal, complemented
5C2×#2686C212yesmaximal, complemented
6C2×#2684C212yesmaximal, complemented
7#45097C2132yesmaximal, direct product factor
8C2×#2547C211yesmaximal, characteristic, complemented
9C2×#2592C211yesmaximal, characteristic, complemented
10C2×#2545C211yesmaximal, characteristic, complemented
11C2×#2544C211yesmaximal, characteristic, complemented
12C2×#2534C212yesmaximal, complemented
13C2×#2432C211yesmaximal, characteristic, complemented
14C2×#2447C211yesmaximal, characteristic, complemented
15C2×#2435C211yesmaximal, characteristic, complemented
16C2×#2445C211yesmaximal, characteristic, complemented
17C2×#2444C212yesmaximal, complemented
18C2×#2425C212yesmaximal, complemented
19C2×#2418C212yesmaximal, complemented
20C2×#2396C211yesmaximal, characteristic, complemented
21C2×#2366C211yesmaximal, characteristic, complemented
22C2×#2339C211yesmaximal, characteristic, complemented
23C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
24C2×#2323C211yesmaximal, characteristic, complemented
25C23×#41C2211yescharacteristic
26C24×D4C2211yescharacteristic
27C2×#559—216no—
28C2×#559C22116yescomplemented
29C2×#535—216no—
30C2×#535C22116yes—
31C22×C4⋊Q8C2211yescharacteristic, complemented
32C22×#127C2211yescharacteristic
33C22×#127C2211yescharacteristic
34C22×#124C2211yescharacteristic
35C22×#124C2211yescharacteristic
36C22×#124C2211yescharacteristic
37C22×#124C2211yescharacteristic
38C22×#124C2211yescharacteristic, complemented
39C22×#124C2212yescomplemented
40C22×#123C2212yescomplemented
41C22×#123C2212yescomplemented
42C22×#123C2212yescomplemented
43C22×C22⋊Q8C2211yescharacteristic
44C22×#121C2212yes—
45C22×#121C2212yes—
46C22×#120C2212yes—
47C22×#120C2212yes—
48C22×C4×Q8C2211yescharacteristic, complemented
49C22×C4×Q8C2211yescharacteristic, complemented
50C22×C4×D4C2211yescharacteristic
51C22×C4×D4C2211yescharacteristic
52C22×C4×D4C2211yescharacteristic, complemented
53C22×C4×D4C2212yescomplemented
54C22×C4×D4C2212yescomplemented
55C22×C4×D4C2211yescharacteristic, complemented
56C22×#117C2211yescharacteristic
57C23×C22⋊C4C2212yes—
58#2701C22132yescomplemented
59#2697C22132yescomplemented
60#2686C22132yescomplemented
61#2684C22132yescomplemented
62#2592C22116yescomplemented
63#2547C22116yescomplemented
64#2545C22116yescomplemented
65#2544C22116yescomplemented
66#2534C22132yescomplemented
67#2447C22116yescomplemented
68#2445C22116yescomplemented
69#2444C22132yescomplemented
70#2435C22116yescomplemented
71#2432C22116yescomplemented
72#2425C22132yescomplemented
73#2418C22132yescomplemented
74#2396C22116yescomplemented
75C2×#400C2211yescharacteristic, complemented
76C2×#399C2211yescharacteristic
77C2×#398C2211yescharacteristic, complemented
78C2×#398C2211yescharacteristic, complemented
79C2×#397C2212yescomplemented
80C2×#397C2212yescomplemented
81C2×#397C2212yescomplemented
82C2×#397C2212yescomplemented
83C2×#397C2212yescomplemented
84C2×#396C2211yescharacteristic
85C2×#396C2211yescharacteristic
86C2×#396C2212yescomplemented
87C2×#396C2212yescomplemented
88C2×#395C2211yescharacteristic, complemented
89C2×#394C2212yes—
90C2×#394C2212yes—
91C2×#394C2212yes—
92C2×#394C2212yes—
93C2×#394C2212yescomplemented
94C2×#394C2212yescomplemented
95C2×#394C2212yescomplemented
96C2×#394C2212yescomplemented
97C2×#393C2211yescharacteristic
98C2×#393C2212yescomplemented
99#2366C22116yescomplemented
100#2339C22116yescomplemented
101D4×C22⋊C4C22116yescomplemented
102#2323C22116yescomplemented
103C2×#391C2211yescharacteristic, complemented
104C2×#391C2211yescharacteristic, complemented
105C2×#391C2211yescharacteristic, complemented
106C2×#391C2211yescharacteristic, complemented
107C2×#390C2211yescharacteristic
108C2×#390C2211yescharacteristic
109C2×#390C2211yescharacteristic
110C2×#390C2211yescharacteristic
111C2×#390C2211yescharacteristic, complemented
112C2×#390C2212yescomplemented
113C2×#389C2212yescomplemented
114C2×#389C2211yescharacteristic, complemented
115C2×#388C2212yes—
116C2×#388C2212yes—
117C2×#388C2212yescomplemented
118C2×#388C2212yescomplemented
119C2×#388C2212yescomplemented
120C2×#388C2212yescomplemented
121C2×#387C2212yescomplemented
122C2×#386C2212yes—
123C2×#386C2212yes—
124C2×#386C2212yes—
125C2×#386C2212yes—
126C2×#386C2212yescomplemented
127C2×#386C2212yescomplemented
128C2×#386C2212yescomplemented
129C2×#386C2212yescomplemented
130C2×#386C2212yescomplemented
131C2×#385C2212yescomplemented
132C2×#385C2212yescomplemented
133C2×#385C2212yescomplemented
134C2×#381C2212yescomplemented
135C2×#381C2212yescomplemented
136C2×#380C2211yescharacteristic
137C2×#380C2212yescomplemented
138C2×#380C2212yescomplemented
139C2×#379C2212yes—
140C2×#379C2212yes—
141C2×#379C2212yes—
142C2×C4×C4⋊C4C2211yescharacteristic, complemented
143C2×C4×C4⋊C4C2211yescharacteristic, complemented
144C2×C4×C4⋊C4C2211yescharacteristic, complemented
145C2×C4×C4⋊C4C2211yescharacteristic, complemented
146C2×C4×C22⋊C4C2211yescharacteristic
147C2×C4×C22⋊C4C2211yescharacteristic
148C22×#95C2212yescomplemented
149C26C2312yes—
150C22×#41—28no—
151C22×#41—28no—
152C22×#41—44no—
153C22×#41C2318yes—
154C23×Q8C2311yescharacteristic
155C23×Q8C2311yescharacteristic
156C23×Q8C2311yescharacteristic
157C23×D4—28no—
158C23×D4—28no—
159C23×D4—44no—
160C23×D4C2311yescharacteristic
161C23×D4C2318yes—
162C23×D4C2312yes—
163C23×D4C2312yes—
164C23×D4C2311yescharacteristic
165C23×D4C2311yescharacteristic
166C23×D4C2312yes—
167C23×D4C2312yes—
168C23×D4C2312yes—
169C23×D4C2312yes—
170C24×C4C2312yes—
171C24×C4C2311yescharacteristic
172C24×C4C2312yes—
173C24×C4C2312yes—
174C24×C4C2312yes—
175C24×C4C2312yes—
176#559—2128no—
177#535—2128no—
178C2×C4⋊Q8—44no—
179C2×C4⋊Q8C2318yescomplemented
180C2×#127—28no—
181C2×#127D4116yes—
182C2×#127C2318yes—
183C2×#127C2318yes—
184C2×#124—28no—
185C2×#124—28no—
186C2×#124—28no—
187C2×#124—216no—
188C2×#124—28no—
189C2×#124—44no—
190C2×#124C2318yes—
191C2×#124C2318yes—
192C2×#124C2318yes—
193C2×#124C2318yes—
194C2×#124C23116yescomplemented
195C2×#124C2318yescomplemented
196C2×#123—216no—
197C2×#123—216no—
198C2×#123—48no—
199C2×#123C23116yescomplemented
200C2×#123C23116yescomplemented
201C2×#123C23116yescomplemented
202C2×C22⋊Q8—28no—
203C2×C22⋊Q8C2318yes—
204C2×#121—216no—
205C2×#121—216no—
206C2×#121C23116yes—
207C2×#121C23116yes—
208C2×#120—216no—
209C2×#120—216no—
210C2×#120C23116yes—
211C2×#120C23116yes—
212C2×C4×Q8—28no—
213C2×C4×Q8—28no—
214C2×C4×Q8C2318yescomplemented
215C2×C4×Q8C2318yescomplemented
216C2×C4×D4—28no—
217C2×C4×D4—28no—
218C2×C4×D4—216no—
219C2×C4×D4—44no—
220C2×C4×D4—44no—
221C2×C4×D4—48no—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2318yescomplemented
225C2×C4×D4C23116yescomplemented
226C2×C4×D4C2318yescomplemented
227C2×C4×D4C23116yescomplemented
228C2×#117—28no—
229C2×#117C2318yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—48no—
250C22×C22⋊C4C2311yescharacteristic
251C22×C22⋊C4C2312yes—
252C22×C22⋊C4C2311yescharacteristic
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2312yes—
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2311yescharacteristic
262C22×C22⋊C4C2312yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C23116yes—
267C22×C22⋊C4C2311yescharacteristic
268C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2312yes—
283C22×C42C2311yescharacteristic
284C22×C42C2311yescharacteristic
285C22×C42C2311yescharacteristic
286C22×C42C2311yescharacteristic
287C22×C42C2312yes—
288C22×C42C2311yescharacteristic
289C22×C42C2312yes—
290C22×C42C2311yescharacteristic
291#400C2318yescomplemented
292#399C2318yes—
293#398C2318yescomplemented
294#398C2318yescomplemented
295#397C23116yescomplemented
296#397C23116yescomplemented
297#397C23116yescomplemented
298#397C23116yescomplemented
299#397C23116yescomplemented
300#396C2318yes—
301#396C2318yes—
302#396C23116yescomplemented
303#396C23116yescomplemented
304#395C2318yescomplemented
305#394C23116yes—
306#394C23116yes—
307#394C23116yes—
308#394C23116yes—
309#394C23116yescomplemented
310#394C23116yescomplemented
311#394C23116yescomplemented
312#394C23116yescomplemented
313#393C2318yes—
314#393C23116yescomplemented
315#391C2318yescomplemented
316#391C2318yescomplemented
317#391C2318yescomplemented
318#391C2318yescomplemented
319#390C2318yes—
320#390C2318yes—
321#390C2318yes—
322#390C2318yes—
323#390C2318yescomplemented
324#390C23116yescomplemented
325#389C23116yescomplemented
326#389C2318yescomplemented
327#388C23116yes—
328#388C23116yes—
329#388C23116yescomplemented
330#388C23116yescomplemented
331#388C23116yescomplemented
332#388C23116yescomplemented
333#387C23116yescomplemented
334#386C23116yes—
335#386C23116yes—
336#386C23116yes—
337#386C23116yes—
338#386C23116yescomplemented
339#386C23116yescomplemented
340#386C23116yescomplemented
341#386C23116yescomplemented
342#386C23116yescomplemented
343#385C23116yescomplemented
344#385C23116yescomplemented
345#385C23116yescomplemented
346#381C23116yescomplemented
347#381C23116yescomplemented
348#380C2318yes—
349#380C23116yescomplemented
350#380C23116yescomplemented
351#379C23116yes—
352#379C23116yes—
353#379C23116yes—
354C4×C4⋊C4C2318yescomplemented
355C4×C4⋊C4C2318yescomplemented
356C4×C4⋊C4C2318yescomplemented
357C4×C4⋊C4C2318yescomplemented
358C4×C22⋊C4C2318yes—
359C4×C22⋊C4C2318yes—
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2311yescharacteristic
363C2×#95C2312yes—
364C2×#95C2312yes—
365C2×#95C2312yes—
366C2×#95C2311yescharacteristic
367C2×#95C2311yescharacteristic
368C2×#95C2312yes—
369C2×#95C2312yes—
370C2×#95C2312yes—
371C2×#95C2312yes—
372C2×#95C2311yescharacteristic
373C2×#95C2311yescharacteristic
374C2×#95C2311yescharacteristic
375C2×#95C2311yescharacteristic
376C2×#95C2312yes—
377C2×#95C2312yes—
378C2×#95C2312yes—
379C2×#95C2311yescharacteristic
380C2×#95C2312yes—
381C2×#95C23116yescomplemented
382C25—28no—
383C25—28no—
384C25—44no—
385C25—44no—
386C25—44no—
387C25—44no—
388C25—44no—
389C25C2412yes—
390C25C2412yes—
391C25C2412yes—
392C25C2411yescharacteristic
393C25C2418yes—
394C2×#41—232no—
395C2×#41—232no—
396C2×#41—416no—
397C2×#41—464no—
398C22×Q8—24no—
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8—24no—
402C22×Q8—24no—
403C22×Q8—24no—
404C22×Q8—24no—
405C22×Q8—42no—
406C22×Q8—42no—
407C22×Q8C2414yes—
408C22×Q8C2414yes—
409C22×Q8C2414yes—
410C22×D4—28no—
411C22×D4—28no—
412C22×D4—28no—
413C22×D4—28no—
414C22×D4—28no—
415C22×D4—232no—
416C22×D4—24no—
417C22×D4—24no—
418C22×D4—24no—
419C22×D4—28no—
420C22×D4—232no—
421C22×D4—24no—
422C22×D4—24no—
423C22×D4—24no—
424C22×D4—24no—
425C22×D4—416no—
426C22×D4—464no—
427C22×D4—44no—
428C22×D4—44no—
429C22×D4—44no—
430C22×D4—44no—
431C22×D4—44no—
432C22×D4—44no—
433C22×D4—44no—
434C22×D4—44no—
435C22×D4—44no—
436C22×D4—44no—
437C22×D4C2×D418yes—
438C22×D4C2×D418yes—
439C22×D4C2×D4116yes—
440C22×D4C2×D4116yes—
441C22×D4C2414yes—
442C22×D4C2418yes—
443C22×D4C2418yes—
444C22×D4C2414yes—
445C22×D4C2414yes—
446C22×D4C2418yes—
447C22×D4C2418yes—
448C22×D4C2418yes—
449C22×D4C2418yes—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—28no—
453C23×C4—28no—
454C23×C4—28no—
455C23×C4—28no—
456C23×C4—28no—
457C23×C4—44no—
458C23×C4—44no—
459C23×C4—44no—
460C23×C4—44no—
461C23×C4—44no—
462C23×C4—44no—
463C23×C4—44no—
464C23×C4—44no—
465C23×C4—44no—
466C23×C4—44no—
467C23×C4#4118yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2412yes—
476C23×C4C2411yescharacteristic
477C23×C4C2411yescharacteristic
478C23×C4C2412yes—
479C23×C4C2412yes—
480C23×C4C2411yescharacteristic
481C23×C4C2411yescharacteristic
482C23×C4C2418yes—
483C23×C4C2411yescharacteristic
484C23×C4C2411yescharacteristic
485C23×C4C2414yes—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2418yes—
489C23×C4C2418yes—
490C23×C4C2418yes—
491C23×C4C2418yes—
492C23×C4C2411yescharacteristic
493C4⋊Q8—416no—
494#127—232no—
495#127C2×D4164yes—
496#124—232no—
497#124—232no—
498#124—232no—
499#124—264no—
500#124—232no—
501#124—416no—
502#123—264no—
503#123—264no—
504#123—432no—
505C22⋊Q8—232no—
506#121—264no—
507#121—264no—
508#120—264no—
509#120—264no—
510C4×Q8—232no—
511C4×Q8—232no—
512C4×D4—232no—
513C4×D4—232no—
514C4×D4—264no—
515C4×D4—416no—
516C4×D4—416no—
517C4×D4—432no—
518#117—232no—
519C2×C4⋊C4—24no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—24no—
527C2×C4⋊C4—28no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—24no—
531C2×C4⋊C4—42no—
532C2×C4⋊C4—42no—
533C2×C4⋊C4—42no—
534C2×C4⋊C4—42no—
535C2×C4⋊C4—44no—
536C2×C4⋊C4—44no—
537C2×C4⋊C4—44no—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C22⋊C4—28no—
558C2×C22⋊C4—28no—
559C2×C22⋊C4—28no—
560C2×C22⋊C4—28no—
561C2×C22⋊C4—28no—
562C2×C22⋊C4—28no—
563C2×C22⋊C4—28no—
564C2×C22⋊C4—28no—
565C2×C22⋊C4—28no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—28no—
569C2×C22⋊C4—28no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—28no—
572C2×C22⋊C4—28no—
573C2×C22⋊C4—432no—
574C2×C22⋊C4—44no—
575C2×C22⋊C4—44no—
576C2×C22⋊C4—44no—
577C2×C22⋊C4—44no—
578C2×C22⋊C4—44no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—44no—
581C2×C22⋊C4—44no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
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⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
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⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C42—24no—
623C2×C42—28no—
624C2×C42—24no—
625C2×C42—24no—
626C2×C42—24no—
627C2×C42—24no—
628C2×C42—44no—
629C2×C42C2×D418yes—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2418yes—
635C2×C42C2414yes—
636C2×C42C2418yes—
637C2×C42C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2418yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659C24—22no—
660C24—24no—
661C24—24no—
662C24—22no—
663C24—24no—
664C24—24no—
665C24—24no—
666C24—24no—
667C24—22no—
668C24—24no—
669C24—24no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—24no—
674C24—24no—
675C24—24no—
676C24—24no—
677C24—24no—
678C24—24no—
679C24—24no—
680C24—24no—
681C24—24no—
682C24—24no—
683C24—24no—
684C24—216no—
685C24—216no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—432no—
692C24—432no—
693C24—816no—
694C24—816no—
695C24—816no—
696C24—816no—
697C24—816no—
698C24C22×D418yes—
699C24C22×D418yes—
700C24C2×#4114yes—
701C24C2514yes—
702C24C2514yes—
703C24C2514yes—
704C24C2512yes—
705C24C2511yescharacteristic
706#41—4128no—
707C2×Q8—28no—
708C2×Q8—28no—
709C2×Q8—28no—
710C2×Q8—28no—
711C2×Q8—28no—
712C2×Q8—28no—
713C2×Q8—28no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—416no—
717C2×Q8—416no—
718C2×Q8—416no—
719C2×D4—216no—
720C2×D4—216no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—216no—
724C2×D4—232no—
725C2×D4—232no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—216no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—4128no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—432no—
738C2×D4—432no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—432no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—432no—
749C2×D4—416no—
750C2×D4—816no—
751C2×D4—816no—
752C2×D4C22×D4116yes—
753C2×D4C22×D4116yes—
754C2×D4C22×D4132yes—
755C2×D4C22×D4132yes—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—232no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—24no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—24no—
774C22×C4—22no—
775C22×C4—24no—
776C22×C4—216no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—22no—
786C22×C4—24no—
787C22×C4—22no—
788C22×C4—24no—
789C22×C4—22no—
790C22×C4—24no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—24no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—24no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—216no—
811C22×C4—216no—
812C22×C4—216no—
813C22×C4—216no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—432no—
825C22×C4—816no—
826C22×C4—816no—
827C22×C4—816no—
828C22×C4—816no—
829C22×C4C22×D414yes—
830C22×C4C22×D414yes—
831C22×C4C22×D414yes—
832C22×C4C2×#4114yes—
833C22×C4C2×#41116yes—
834C22×C4C2×#4114yes—
835C22×C4H(5,𝔽2)14yes—
836C22×C4H(5,𝔽2)14yes—
837C22×C4C2512yes—
838C22×C4C2514yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—216no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—216no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C22⋊C4—216no—
876C22⋊C4—216no—
877C22⋊C4—216no—
878C22⋊C4—216no—
879C22⋊C4—216no—
880C22⋊C4—216no—
881C22⋊C4—216no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—216no—
887C22⋊C4—216no—
888C22⋊C4—28no—
889C22⋊C4—216no—
890C22⋊C4—216no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—44no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C42—28no—
908C42—216no—
909C42—28no—
910C42—28no—
911C42—28no—
912C42—28no—
913C42—48no—
914C42C22×D4116yes—
915C23—22no—
916C23—24no—
917C23—24no—
918C23—22no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—22no—
924C23—24no—
925C23—24no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—28no—
934C23—216no—
935C23—216no—
936C23—216no—
937C23—216no—
938C23—216no—
939C23—216no—
940C23—28no—
941C23—28no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—432no—
950C23—432no—
951C23—44no—
952C23—44no—
953C23—48no—
954C23—48no—
955C23—48no—
956C23—48no—
957C23—48no—
958C23—48no—
959C23—44no—
960C23—48no—
961C23—48no—
962C23—44no—
963C23—48no—
964C23—48no—
965C23—48no—
966C23—48no—
967C23—48no—
968C23—48no—
969C23—48no—
970C23—816no—
971C23—816no—
972C23—816no—
973C23—816no—
974C23—816no—
975C23—8128no—
976C23C23×D418yes—
977C23C23×D418yes—
978C23C23×D412yes—
979C23C22×#4114yes—
980C23C22×#4112yes—
981C23C2×H(5,𝔽2)12yes—
982C23C2×H(5,𝔽2)12yes—
983C23#58512yes—
984C23#58512yes—
985C23#58512yes—
986C23C2611yescharacteristic
987Q8—416no—
988Q8—416no—
989Q8—416no—
990D4—232no—
991D4—232no—
992D4—432no—
993D4—432no—
994D4—432no—
995D4—432no—
996D4—416no—
997D4—816no—
998D4—816no—
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—28no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—28no—
1011C2×C4—232no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—432no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—44no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—48no—
1062C2×C4—44no—
1063C2×C4—44no—
1064C2×C4—48no—
1065C2×C4—44no—
1066C2×C4—48no—
1067C2×C4—44no—
1068C2×C4—44no—
1069C2×C4—816no—
1070C2×C4—816no—
1071C2×C4—816no—
1072C2×C4—816no—
1073C2×C4#546116yes—
1074C2×C4C23×D414yes—
1075C2×C4C23×D414yes—
1076C2×C4C23×D414yes—
1077C2×C4C22×#4114yes—
1078C2×C4C22×#4114yes—
1079C2×C4C2×H(5,𝔽2)14yes—
1080C2×C4C2×H(5,𝔽2)14yes—
1081C22—28no—
1082C22—28no—
1083C22—24no—
1084C22—28no—
1085C22—28no—
1086C22—24no—
1087C22—24no—
1088C22—28no—
1089C22—28no—
1090C22—44no—
1091C22—44no—
1092C22—42no—
1093C22—44no—
1094C22—44no—
1095C22—42no—
1096C22—432no—
1097C22—432no—
1098C22—416no—
1099C22—42no—
1100C22—44no—
1101C22—44no—
1102C22—42no—
1103C22—44no—
1104C22—44no—
1105C22—44no—
1106C22—44no—
1107C22—44no—
1108C22—44no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—864no—
1113C22—816no—
1114C22C2×#54614yes—
1115C22#348514yes—
1116C22#349614yes—
1117C22#350614yes—
1118C22#351014yes—
1119C22#355814yes—
1120C22#356214yes—
1121C22C24×D411yescharacteristic
1122C22C23×#4111yescharacteristic
1123C22C22×H(5,𝔽2)11yescharacteristic
1124C22C22×H(5,𝔽2)11yescharacteristic
1125C22C2×#58511yescharacteristic
1126C22C2×#58511yescharacteristic
1127C22C2×#58511yescharacteristic
1128C4—24no—
1129C4—24no—
1130C4—24no—
1131C4—24no—
1132C4—42no—
1133C4—44no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—44no—
1138C4—42no—
1139C4—42no—
1140C4—44no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—44no—
1145C4—44no—
1146C4C2×#54618yes—
1147C2—48no—
1148C2—48no—
1149C2—44no—
1150C2—84no—
1151C2#4509718yesdirect product factor
1152C2C22×#54611yescharacteristic
1153C2C2×#355811yescharacteristic
1154C2C2×#356211yescharacteristic
1155C2C2×#349611yescharacteristic
1156C2C2×#350611yescharacteristic
1157C2C2×#348511yescharacteristic
1158C2C2×#351011yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC22×#535C2
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×#559C2semidirect
3. C2×#2701C2semidirect
4. C2×#2697C2semidirect
5. C2×#2686C2semidirect
6. C2×#2684C2semidirect
7. #45097C2direct (N × H)
8. C2×#2547C2semidirect
9. C2×#2592C2semidirect
10. C2×#2545C2semidirect
11. C2×#2544C2semidirect
12. C2×#2534C2semidirect
13. C2×#2432C2semidirect
14. C2×#2447C2semidirect
15. C2×#2435C2semidirect
16. C2×#2445C2semidirect
17. C2×#2444C2semidirect
18. C2×#2425C2semidirect
19. C2×#2418C2semidirect
20. C2×#2396C2semidirect
21. C2×#2366C2semidirect
22. C2×#2339C2semidirect
23. C2×D4×C22⋊C4C2semidirect
24. C2×#2323C2semidirect
28. C2×#559C22semidirect
31. C22×C4⋊Q8C22semidirect
38. C22×#124C22semidirect
39. C22×#124C22semidirect
40. C22×#123C22semidirect
41. C22×#123C22semidirect
42. C22×#123C22semidirect
48. C22×C4×Q8C22semidirect
49. C22×C4×Q8C22semidirect
52. C22×C4×D4C22semidirect
53. C22×C4×D4C22semidirect
54. C22×C4×D4C22semidirect
55. C22×C4×D4C22semidirect
58. #2701C22semidirect
59. #2697C22semidirect
60. #2686C22semidirect
61. #2684C22semidirect
62. #2592C22semidirect
63. #2547C22semidirect
64. #2545C22semidirect
65. #2544C22semidirect
66. #2534C22semidirect
67. #2447C22semidirect
68. #2445C22semidirect
69. #2444C22semidirect
70. #2435C22semidirect
71. #2432C22semidirect
72. #2425C22semidirect
73. #2418C22semidirect
74. #2396C22semidirect
75. C2×#400C22semidirect
77. C2×#398C22semidirect
78. C2×#398C22semidirect
79. C2×#397C22semidirect
80. C2×#397C22semidirect
81. C2×#397C22semidirect
82. C2×#397C22semidirect
83. C2×#397C22semidirect
86. C2×#396C22semidirect
87. C2×#396C22semidirect
88. C2×#395C22semidirect
93. C2×#394C22semidirect
94. C2×#394C22semidirect
95. C2×#394C22semidirect
96. C2×#394C22semidirect
98. C2×#393C22semidirect
99. #2366C22semidirect
100. #2339C22semidirect
101. D4×C22⋊C4C22semidirect
102. #2323C22semidirect
103. C2×#391C22semidirect
104. C2×#391C22semidirect
105. C2×#391C22semidirect
106. C2×#391C22semidirect
111. C2×#390C22semidirect
112. C2×#390C22semidirect
113. C2×#389C22semidirect
114. C2×#389C22semidirect
117. C2×#388C22semidirect
118. C2×#388C22semidirect
119. C2×#388C22semidirect
120. C2×#388C22semidirect
121. C2×#387C22semidirect
126. C2×#386C22semidirect
127. C2×#386C22semidirect
128. C2×#386C22semidirect
129. C2×#386C22semidirect
130. C2×#386C22semidirect
131. C2×#385C22semidirect
132. C2×#385C22semidirect
133. C2×#385C22semidirect
134. C2×#381C22semidirect
135. C2×#381C22semidirect
137. C2×#380C22semidirect
138. C2×#380C22semidirect
142. C2×C4×C4⋊C4C22semidirect
143. C2×C4×C4⋊C4C22semidirect
144. C2×C4×C4⋊C4C22semidirect
145. C2×C4×C4⋊C4C22semidirect
148. C22×#95C22semidirect
179. C2×C4⋊Q8C23semidirect
194. C2×#124C23semidirect
195. C2×#124C23semidirect
199. C2×#123C23semidirect
200. C2×#123C23semidirect
201. C2×#123C23semidirect
214. C2×C4×Q8C23semidirect
215. C2×C4×Q8C23semidirect
224. C2×C4×D4C23semidirect
225. C2×C4×D4C23semidirect
226. C2×C4×D4C23semidirect
227. C2×C4×D4C23semidirect
291. #400C23semidirect
293. #398C23semidirect
294. #398C23semidirect
295. #397C23semidirect
296. #397C23semidirect
297. #397C23semidirect
298. #397C23semidirect
299. #397C23semidirect
302. #396C23semidirect
303. #396C23semidirect
304. #395C23semidirect
309. #394C23semidirect
310. #394C23semidirect
311. #394C23semidirect
312. #394C23semidirect
314. #393C23semidirect
315. #391C23semidirect
316. #391C23semidirect
317. #391C23semidirect
318. #391C23semidirect
323. #390C23semidirect
324. #390C23semidirect
325. #389C23semidirect
326. #389C23semidirect
329. #388C23semidirect
330. #388C23semidirect
331. #388C23semidirect
332. #388C23semidirect
333. #387C23semidirect
338. #386C23semidirect
339. #386C23semidirect
340. #386C23semidirect
341. #386C23semidirect
342. #386C23semidirect
343. #385C23semidirect
344. #385C23semidirect
345. #385C23semidirect
346. #381C23semidirect
347. #381C23semidirect
349. #380C23semidirect
350. #380C23semidirect
354. C4×C4⋊C4C23semidirect
355. C4×C4⋊C4C23semidirect
356. C4×C4⋊C4C23semidirect
357. C4×C4⋊C4C23semidirect
381. C2×#95C23semidirect
1151. C2#45097direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5592
C22×#5352
C2×#27012
C2×#26972
C2×#26862
C2×#26842
#450972
C2×#25472
C2×#25922
C2×#25452
C2×#25442
C2×#25342
C2×#24322
C2×#24472
C2×#24352
C2×#24452
C2×#24442
C2×#24252
C2×#24182
C2×#23962
C2×#23662
C2×#23392
C2×D4×C22⋊C42
C2×#23232