Finite Group Databasebeta

← C2×#35703 #7629164

Subgroups — C2×#35703 #7629164

Order 512.

10558 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#548C211yesmaximal, characteristic, complemented
2C22×#518C211yesmaximal, characteristic, complemented
3#35703C2132yesmaximal, direct product factor
4C2×#2610C211yesmaximal, characteristic, complemented
5C2×#2599C211yesmaximal, characteristic, complemented
6C2×#2561C211yesmaximal, characteristic, complemented
7C2×#2543C211yesmaximal, characteristic, complemented
8C2×#2404C211yesmaximal, characteristic, complemented
9C2×#2477C212yesmaximal, complemented
10C2×#2409C211yesmaximal, characteristic, complemented
11C2×#2444C212yesmaximal, complemented
12C2×#2459C212yesmaximal, complemented
13C2×#2472C212yesmaximal, complemented
14C2×#2463C212yesmaximal, complemented
15C2×#2410C212yesmaximal, complemented
16C2×#2631C211yesmaximal, characteristic, complemented
17C2×#2638C211yesmaximal, characteristic, complemented
18C2×#2617C211yesmaximal, characteristic, complemented
19C2×#2398C211yesmaximal, characteristic, complemented
20C2×#2388C211yesmaximal, characteristic, complemented
21C22×#393C211yesmaximal, characteristic, complemented
22C2×#2364C212yesmaximal, complemented
23C2×#2358C212yesmaximal, complemented
24C2×#2353C211yesmaximal, characteristic, complemented
25C23×#41C2211yescharacteristic, complemented
26C24×Q8C2211yescharacteristic, complemented
27C24×D4C2211yescharacteristic
28C2×#548—216no—
29C2×#548C22116yescomplemented
30C22×#124C2211yescharacteristic, complemented
31C22×#124C2212yescomplemented
32C22×C22⋊Q8C2211yescharacteristic, complemented
33C22×C22⋊Q8C2212yescomplemented
34C22×C22⋊Q8C2212yescomplemented
35C22×#121C2212yes—
36C22×#121C2212yes—
37C22×#121C2211yescharacteristic, complemented
38C22×#120C2212yes—
39C22×#120C2212yes—
40C2×#518—216no—
41C2×#518C22116yescomplemented
42C22×C4×Q8C2211yescharacteristic, complemented
43C22×C4×D4C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45C22×C4×D4C2211yescharacteristic
46C22×C4×D4C2211yescharacteristic
47C22×C4×D4C2211yescharacteristic
48C22×C4×D4C2211yescharacteristic
49C22×C4×D4C2211yescharacteristic
50C22×C4×D4C2211yescharacteristic
51C22×C4×D4C2212yescomplemented
52C22×C4×D4C2212yescomplemented
53C22×#117C2211yescharacteristic
54C22×#117C2211yescharacteristic
55C23×C22⋊C4C2211yescharacteristic
56C23×C22⋊C4C2211yescharacteristic
57C23×C22⋊C4C2211yescharacteristic
58C23×C22⋊C4C2211yescharacteristic
59C23×C22⋊C4C2212yes—
60#2638C22116yescomplemented
61#2631C22116yescomplemented
62#2617C22116yescomplemented
63#2610C22116yescomplemented
64#2599C22116yescomplemented
65#2561C22116yescomplemented
66#2543C22116yescomplemented
67#2477C22132yescomplemented
68#2472C22132yescomplemented
69#2463C22132yescomplemented
70#2459C22132yescomplemented
71#2444C22132yescomplemented
72#2410C22132yescomplemented
73#2409C22116yescomplemented
74#2404C22116yescomplemented
75#2398C22116yescomplemented
76C2×#400C2212yescomplemented
77C2×#398C2211yescharacteristic, complemented
78C2×#397C2211yescharacteristic
79C2×#397C2212yescomplemented
80C2×#397C2211yescharacteristic, complemented
81C2×#397C2211yescharacteristic, complemented
82C2×#397C2212yescomplemented
83#2388C22116yescomplemented
84C2×#395C2211yescharacteristic, complemented
85C2×#395C2211yescharacteristic, complemented
86C2×#394C2212yes—
87C2×#394C2212yes—
88C2×#394C2212yes—
89C2×#394C2211yescharacteristic, complemented
90C2×#394C2212yescomplemented
91C2×#394C2212yescomplemented
92C2×#393C2211yescharacteristic
93C2×#393C2211yescharacteristic
94C2×#393C2212yes—
95C2×#393C2211yescharacteristic, complemented
96C2×#393C2211yescharacteristic, complemented
97C2×#393C2212yescomplemented
98C2×#393C2211yescharacteristic, complemented
99C2×#393C2211yescharacteristic, complemented
100C2×#393C22116yescomplemented
101C2×#392C2212yes—
102C2×#392C2211yescharacteristic
103C2×#392C2212yes—
104C2×#392C2211yescharacteristic, complemented
105C2×#392C2211yescharacteristic, complemented
106#2364C22132yescomplemented
107#2358C22132yescomplemented
108#2353C22116yescomplemented
109C2×#391C2212yescomplemented
110C2×#390C2212yes—
111C2×#388C2212yes—
112C2×#388C2212yes—
113C2×#388C2212yescomplemented
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×#386C2212yescomplemented
127C2×#386C2212yescomplemented
128C2×#386C2212yescomplemented
129C2×#386C2212yescomplemented
130C2×#386C2212yescomplemented
131C2×#386C2212yescomplemented
132C2×#386C2212yescomplemented
133C2×#385C2212yes—
134C2×#385C2212yescomplemented
135C2×#385C2212yescomplemented
136C2×#383C2211yescharacteristic, complemented
137C2×#381C2211yescharacteristic, complemented
138C2×#381C2212yescomplemented
139C2×#380C2211yescharacteristic, complemented
140C2×#379C2212yes—
141C2×C4×C22⋊C4C2211yescharacteristic, complemented
142C2×C4×C22⋊C4C2212yescomplemented
143C2×C4×C22⋊C4C2212yescomplemented
144C2×C4×C22⋊C4C2212yescomplemented
145C2×C4×C22⋊C4C2212yescomplemented
146C2×#376C2211yescharacteristic, complemented
147C22×#95C2211yescharacteristic, complemented
148C22×#95C2212yescomplemented
149C26C2311yescharacteristic
150C26C2311yescharacteristic
151C22×#41—28no—
152C22×#41—48no—
153C22×#41C2318yescomplemented
154C23×Q8—28no—
155C23×Q8—48no—
156C23×Q8C2311yescharacteristic
157C23×Q8C2312yes—
158C23×Q8C2311yescharacteristic
159C23×Q8C2318yescomplemented
160C23×D4—28no—
161C23×D4—28no—
162C23×D4—28no—
163C23×D4C2311yescharacteristic
164C23×D4C2311yescharacteristic
165C23×D4C2318yes—
166C23×D4C2312yes—
167C23×D4C2312yes—
168C23×D4C2311yescharacteristic
169C23×D4C2311yescharacteristic
170C23×D4C2311yescharacteristic
171C23×D4C2312yes—
172C23×D4C2312yes—
173C23×D4C2312yes—
174C24×C4C2311yescharacteristic
175C24×C4C2312yes—
176C24×C4C2312yes—
177C24×C4C2311yescharacteristic
178C24×C4C2311yescharacteristic
179C24×C4C2311yescharacteristic
180C24×C4C2311yescharacteristic
181C24×C4C2311yescharacteristic
182C24×C4C2311yescharacteristic
183C24×C4C2312yes—
184C24×C4C2311yescharacteristic
185C24×C4C2311yescharacteristic
186#548—2128no—
187C2×#124—216no—
188C2×#124—28no—
189C2×#124C2318yescomplemented
190C2×#124C23116yescomplemented
191C2×C22⋊Q8—28no—
192C2×C22⋊Q8—216no—
193C2×C22⋊Q8—48no—
194C2×C22⋊Q8C2318yescomplemented
195C2×C22⋊Q8C23116yescomplemented
196C2×C22⋊Q8C23116yescomplemented
197C2×#121—216no—
198C2×#121—216no—
199C2×#121—28no—
200C2×#121C23116yes—
201C2×#121C23116yes—
202C2×#121C2318yescomplemented
203C2×#120—216no—
204C2×#120—48no—
205C2×#120C23116yes—
206C2×#120C23116yes—
207#518—2128no—
208C2×C4×Q8—28no—
209C2×C4×Q8C2318yescomplemented
210C2×C4×D4—28no—
211C2×C4×D4—28no—
212C2×C4×D4—28no—
213C2×C4×D4—28no—
214C2×C4×D4—28no—
215C2×C4×D4—28no—
216C2×C4×D4—216no—
217C2×C4×D4—28no—
218C2×C4×D4—48no—
219C2×C4×D4D4116yescomplemented
220C2×C4×D4C2318yes—
221C2×C4×D4C2318yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2318yes—
225C2×C4×D4C2318yes—
226C2×C4×D4C2318yes—
227C2×C4×D4C2318yes—
228C2×C4×D4C23116yescomplemented
229C2×C4×D4C23116yescomplemented
230C2×#117—28no—
231C2×#117—28no—
232C2×#117C2318yes—
233C2×#117C2318yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—28no—
246C22×C22⋊C4—28no—
247C22×C22⋊C4—28no—
248C22×C22⋊C4—28no—
249C22×C22⋊C4—48no—
250C22×C22⋊C4C2318yes—
251C22×C22⋊C4C2318yes—
252C22×C22⋊C4C2318yes—
253C22×C22⋊C4C2311yescharacteristic
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2312yes—
257C22×C22⋊C4C2311yescharacteristic
258C22×C22⋊C4C2311yescharacteristic
259C22×C22⋊C4C2311yescharacteristic
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2311yescharacteristic
262C22×C22⋊C4C2312yes—
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2312yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2311yescharacteristic
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2311yescharacteristic
272C22×C22⋊C4C2311yescharacteristic
273C22×C22⋊C4C2318yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C23116yes—
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2312yes—
280C22×C22⋊C4C2312yes—
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2311yescharacteristic
288C22×C42C2311yescharacteristic
289C22×C42C2311yescharacteristic
290C22×C42C2311yescharacteristic
291C22×C42C2312yes—
292C22×C42C2312yes—
293C22×C42C2312yes—
294C22×C42C2311yescharacteristic
295#400C23116yescomplemented
296#398C2318yescomplemented
297#397C2318yes—
298#397C2318yescomplemented
299#397C2318yescomplemented
300#397C23116yescomplemented
301#397C23116yescomplemented
302#395C2318yescomplemented
303#395C2318yescomplemented
304#394C23116yes—
305#394C23116yes—
306#394C23116yes—
307#394C2318yescomplemented
308#394C23116yescomplemented
309#394C23116yescomplemented
310#393C2318yes—
311#393C2318yes—
312#393C23116yes—
313#393C2318yescomplemented
314#393C2318yescomplemented
315#393C2318yescomplemented
316#393C23116yescomplemented
317#393C2318yescomplemented
318#392C2318yes—
319#392C23116yes—
320#392C23116yes—
321#392C2318yescomplemented
322#392C2318yescomplemented
323#391C23116yescomplemented
324#390C23116yes—
325#388C23116yes—
326#388C23116yes—
327#388C23116yescomplemented
328#388C23116yescomplemented
329#388C23116yescomplemented
330#388C23116yescomplemented
331#388C23116yescomplemented
332#387C23116yescomplemented
333#387C23116yescomplemented
334#387C23116yescomplemented
335#387C23116yescomplemented
336#386C23116yes—
337#386C23116yes—
338#386C23116yes—
339#386C23116yes—
340#386C23116yescomplemented
341#386C23116yescomplemented
342#386C23116yescomplemented
343#386C23116yescomplemented
344#386C23116yescomplemented
345#386C23116yescomplemented
346#386C23116yescomplemented
347#385C23116yes—
348#385C23116yescomplemented
349#385C23116yescomplemented
350#383C2318yescomplemented
351#381C23116yescomplemented
352#381C2318yescomplemented
353#380C2318yescomplemented
354#379C23116yes—
355C4×C22⋊C4C2318yescomplemented
356C4×C22⋊C4C23116yescomplemented
357C4×C22⋊C4C23116yescomplemented
358C4×C22⋊C4C23116yescomplemented
359C4×C22⋊C4C23116yescomplemented
360#376C2318yescomplemented
361C2×#95C2311yescharacteristic
362C2×#95C2312yes—
363C2×#95C2312yes—
364C2×#95C2311yescharacteristic
365C2×#95C2311yescharacteristic
366C2×#95C2311yescharacteristic
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×#95C2318yescomplemented
383C2×#95C23116yescomplemented
384C25—24no—
385C25—24no—
386C25—24no—
387C25—24no—
388C25—24no—
389C25—44no—
390C25—44no—
391C25—44no—
392C25—44no—
393C25#4118yescomplemented
394C25C2412yes—
395C25C2411yescharacteristic
396C25C2411yescharacteristic
397C25C2411yescharacteristic
398C25C2411yescharacteristic
399C25C2411yescharacteristic
400C25C2414yes—
401C25C2414yes—
402C2×#41—232no—
403C2×#41—432no—
404C2×#41—464no—
405C22×Q8—24no—
406C22×Q8—28no—
407C22×Q8—24no—
408C22×Q8—232no—
409C22×Q8—28no—
410C22×Q8—28no—
411C22×Q8—44no—
412C22×Q8—44no—
413C22×Q8—432no—
414C22×Q8—464no—
415C22×Q8C2414yes—
416C22×Q8C2418yes—
417C22×Q8C2414yes—
418C22×D4—2128no—
419C22×D4—24no—
420C22×D4—24no—
421C22×D4—24no—
422C22×D4—24no—
423C22×D4—24no—
424C22×D4—24no—
425C22×D4—24no—
426C22×D4—24no—
427C22×D4—232no—
428C22×D4—232no—
429C22×D4—232no—
430C22×D4—28no—
431C22×D4—28no—
432C22×D4—28no—
433C22×D4—28no—
434C22×D4—28no—
435C22×D4—28no—
436C22×D4—28no—
437C22×D4—24no—
438C22×D4—24no—
439C22×D4—24no—
440C22×D4—28no—
441C22×D4—44no—
442C22×D4—44no—
443C22×D4—44no—
444C22×D4—44no—
445C22×D4—44no—
446C22×D4—44no—
447C22×D4—44no—
448C22×D4—44no—
449C22×D4C2×D418yes—
450C22×D4#4118yescomplemented
451C22×D4C2414yes—
452C22×D4C2414yes—
453C22×D4C2418yes—
454C22×D4C2418yes—
455C22×D4C2414yes—
456C22×D4C2414yes—
457C22×D4C2418yes—
458C22×D4C2418yes—
459C22×D4C2418yes—
460C22×D4C2414yes—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—28no—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—28no—
468C23×C4—28no—
469C23×C4—28no—
470C23×C4—28no—
471C23×C4—24no—
472C23×C4—24no—
473C23×C4—24no—
474C23×C4—24no—
475C23×C4—44no—
476C23×C4—44no—
477C23×C4—44no—
478C23×C4—44no—
479C23×C4—44no—
480C23×C4—44no—
481C23×C4—44no—
482C23×C4—44no—
483C23×C4—44no—
484C23×C4—44no—
485C23×C4—44no—
486C23×C4—44no—
487C23×C4C2×D418yes—
488C23×C4C2×D418yes—
489C23×C4C2414yes—
490C23×C4C2412yes—
491C23×C4C2412yes—
492C23×C4C2411yescharacteristic
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2412yes—
500C23×C4C2418yes—
501C23×C4C2418yes—
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2412yes—
509C23×C4C2414yes—
510C23×C4C2414yes—
511C23×C4C2414yes—
512C23×C4C2414yes—
513C23×C4C2414yes—
514C23×C4C2414yes—
515C23×C4C2418yes—
516C23×C4C2414yes—
517C23×C4C2414yes—
518#124—264no—
519#124—232no—
520C22⋊Q8—232no—
521C22⋊Q8—264no—
522C22⋊Q8—432no—
523#121—264no—
524#121—264no—
525#121—232no—
526#120—264no—
527#120—432no—
528C4×Q8—232no—
529C4×D4—232no—
530C4×D4—232no—
531C4×D4—232no—
532C4×D4—232no—
533C4×D4—232no—
534C4×D4—232no—
535C4×D4—264no—
536C4×D4—232no—
537C4×D4—432no—
538C4×D4C2×D4164yescomplemented
539#117—232no—
540#117—232no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—24no—
544C2×C4⋊C4—28no—
545C2×C4⋊C4—28no—
546C2×C4⋊C4—24no—
547C2×C4⋊C4—28no—
548C2×C4⋊C4—28no—
549C2×C4⋊C4—44no—
550C2×C4⋊C4—44no—
551C2×C4⋊C4C2×D418yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
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—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—232no—
579C2×C22⋊C4—232no—
580C2×C22⋊C4—28no—
581C2×C22⋊C4—28no—
582C2×C22⋊C4—28no—
583C2×C22⋊C4—28no—
584C2×C22⋊C4—28no—
585C2×C22⋊C4—28no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—232no—
588C2×C22⋊C4—232no—
589C2×C22⋊C4—432no—
590C2×C22⋊C4—44no—
591C2×C22⋊C4—44no—
592C2×C22⋊C4—44no—
593C2×C22⋊C4—44no—
594C2×C22⋊C4—44no—
595C2×C22⋊C4—44no—
596C2×C22⋊C4—44no—
597C2×C22⋊C4—44no—
598C2×C22⋊C4—44no—
599C2×C22⋊C4C2×D418yes—
600C2×C22⋊C4C2×D418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C42—24no—
635C2×C42—24no—
636C2×C42—24no—
637C2×C42—28no—
638C2×C42—44no—
639C2×C42—44no—
640C2×C42C2×D418yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2418yes—
645C2×C42C2418yes—
646C2×C42C2418yes—
647C2×C42C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2414yes—
656#95C2418yes—
657#95C2414yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669C24—24no—
670C24—24no—
671C24—232no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—24no—
681C24—24no—
682C24—24no—
683C24—24no—
684C24—24no—
685C24—24no—
686C24—24no—
687C24—24no—
688C24—232no—
689C24—28no—
690C24—28no—
691C24—28no—
692C24—28no—
693C24—28no—
694C24—24no—
695C24—24no—
696C24—24no—
697C24—24no—
698C24—24no—
699C24—24no—
700C24—24no—
701C24—48no—
702C24—432no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—88no—
707C24—88no—
708C24—816no—
709C24—88no—
710C24—88no—
711C24—816no—
712C24—816no—
713C24C22×D414yes—
714C24C22×D414yes—
715C24C2×#4114yes—
716C24C2×#4114yes—
717C24C2×#4114yes—
718C24C2×#4114yes—
719C24C2×#4114yes—
720C24C2×#41116yescomplemented
721C24C2514yes—
722C24C2512yes—
723C24C2512yes—
724C24C2512yes—
725C24C2512yes—
726C24C2512yes—
727C24C2511yescharacteristic
728#41—4128no—
729C2×Q8—232no—
730C2×Q8—28no—
731C2×Q8—216no—
732C2×Q8—28no—
733C2×Q8—216no—
734C2×Q8—216no—
735C2×Q8—48no—
736C2×Q8—48no—
737C2×Q8—432no—
738C2×Q8—416no—
739C2×Q8—4128no—
740C2×D4—2256no—
741C2×D4—232no—
742C2×D4—232no—
743C2×D4—232no—
744C2×D4—232no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—216no—
754C2×D4—216no—
755C2×D4—216no—
756C2×D4—216no—
757C2×D4—216no—
758C2×D4—216no—
759C2×D4—216no—
760C2×D4—28no—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—216no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—432no—
769C2×D4—416no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—432no—
775C2×D4—432no—
776C2×D4—816no—
777C2×D4—816no—
778C2×D4C22×D4116yes—
779C2×D4C2×#41116yescomplemented
780C22×C4—232no—
781C22×C4—22no—
782C22×C4—24no—
783C22×C4—28no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—216no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—216no—
824C22×C4—216no—
825C22×C4—216no—
826C22×C4—216no—
827C22×C4—28no—
828C22×C4—28no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—416no—
832C22×C4—416no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—432no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—432no—
847C22×C4—88no—
848C22×C4—88no—
849C22×C4—88no—
850C22×C4—88no—
851C22×C4—88no—
852C22×C4—88no—
853C22×C4—816no—
854C22×C4C22×D414yes—
855C22×C4C22×D414yes—
856C22×C4C22×D414yes—
857C22×C4C22×D414yes—
858C22×C4C22×D414yes—
859C22×C4C22×D4116yes—
860C22×C4C22×D4116yes—
861C22×C4C2×#4114yes—
862C22×C4H(5,𝔽2)18yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2514yes—
871C22×C4C2514yes—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2514yes—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—216no—
884C4⋊C4—216no—
885C4⋊C4—28no—
886C4⋊C4—216no—
887C4⋊C4—216no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4C22×D4116yes—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—216no—
894C22⋊C4—216no—
895C22⋊C4—216no—
896C22⋊C4—216no—
897C22⋊C4—216no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—216no—
907C22⋊C4—216no—
908C22⋊C4—216no—
909C22⋊C4—216no—
910C22⋊C4—216no—
911C22⋊C4—216no—
912C22⋊C4—216no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4C22×D4116yes—
923C22⋊C4C22×D4116yes—
924C42—28no—
925C42—28no—
926C42—28no—
927C42—216no—
928C42—48no—
929C42—48no—
930C42C22×D4116yes—
931C23—24no—
932C23—24no—
933C23—28no—
934C23—28no—
935C23—216no—
936C23—216no—
937C23—232no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—28no—
955C23—28no—
956C23—28no—
957C23—28no—
958C23—28no—
959C23—28no—
960C23—216no—
961C23—216no—
962C23—216no—
963C23—232no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—432no—
972C23—44no—
973C23—44no—
974C23—44no—
975C23—44no—
976C23—44no—
977C23—44no—
978C23—48no—
979C23—48no—
980C23—48no—
981C23—48no—
982C23—48no—
983C23—48no—
984C23—48no—
985C23—48no—
986C23—48no—
987C23—48no—
988C23—48no—
989C23—48no—
990C23—88no—
991C23—816no—
992C23—88no—
993C23—864no—
994C23—88no—
995C23—816no—
996C23—816no—
997C23—88no—
998C23—864no—
999C23#525116yes—
1000C23C23×D414yes—
1001C23C23×D414yes—
1002C23C23×D412yes—
1003C23C22×#4114yes—
1004C23C22×#4114yes—
1005C23C22×#4114yes—
1006C23C22×#4114yes—
1007C23C22×#4114yes—
1008C23C22×#4112yes—
1009C23C22×#4112yes—
1010C23C2×H(5,𝔽2)14yes—
1011C23#58514yes—
1012C23C2611yescharacteristic
1013Q8—232no—
1014Q8—432no—
1015Q8—416no—
1016D4—232no—
1017D4—232no—
1018D4—232no—
1019D4—232no—
1020D4—432no—
1021D4—416no—
1022D4—432no—
1023D4—432no—
1024D4—816no—
1025D4—816no—
1026C2×C4—232no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—28no—
1038C2×C4—28no—
1039C2×C4—28no—
1040C2×C4—28no—
1041C2×C4—216no—
1042C2×C4—28no—
1043C2×C4—28no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—416no—
1071C2×C4—416no—
1072C2×C4—432no—
1073C2×C4—432no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—44no—
1077C2×C4—44no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—48no—
1081C2×C4—48no—
1082C2×C4—48no—
1083C2×C4—48no—
1084C2×C4—88no—
1085C2×C4—88no—
1086C2×C4—88no—
1087C2×C4—88no—
1088C2×C4—816no—
1089C2×C4—88no—
1090C2×C4—88no—
1091C2×C4C23×D414yes—
1092C2×C4C23×D414yes—
1093C2×C4C23×D414yes—
1094C2×C4C23×D414yes—
1095C2×C4C23×D414yes—
1096C2×C4C22×#4114yes—
1097C2×C4C2×H(5,𝔽2)18yes—
1098C22—24no—
1099C22—28no—
1100C22—28no—
1101C22—24no—
1102C22—232no—
1103C22—24no—
1104C22—28no—
1105C22—28no—
1106C22—28no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—44no—
1116C22—44no—
1117C22—44no—
1118C22—44no—
1119C22—44no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—416no—
1124C22—416no—
1125C22—416no—
1126C22—416no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—44no—
1132C22—44no—
1133C22—44no—
1134C22—832no—
1135C22—832no—
1136C22—816no—
1137C22C2×#52518yes—
1138C22C2×#52514yes—
1139C22#348414yes—
1140C22#350014yes—
1141C22#350518yes—
1142C22#351418yes—
1143C22C24×D411yescharacteristic
1144C22C23×#4111yescharacteristic
1145C22C23×#4111yescharacteristic
1146C22C22×H(5,𝔽2)12yes—
1147C22C2×#58512yes—
1148C4—24no—
1149C4—24no—
1150C4—28no—
1151C4—24no—
1152C4—24no—
1153C4—24no—
1154C4—24no—
1155C4—44no—
1156C4—42no—
1157C4—44no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—44no—
1165C2—28no—
1166C2—44no—
1167C2—44no—
1168C2—44no—
1169C2—44no—
1170C2—84no—
1171C2#3570318yesdirect product factor
1172C2C22×#52511yescharacteristic
1173C2C2×#348411yescharacteristic
1174C2C2×#350512yes—
1175C2C2×#351412yes—
1176C2C2×#350011yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
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×#548C2semidirect
2. C22×#518C2semidirect
3. #35703C2direct (N × H)
4. C2×#2610C2semidirect
5. C2×#2599C2semidirect
6. C2×#2561C2semidirect
7. C2×#2543C2semidirect
8. C2×#2404C2semidirect
9. C2×#2477C2semidirect
10. C2×#2409C2semidirect
11. C2×#2444C2semidirect
12. C2×#2459C2semidirect
13. C2×#2472C2semidirect
14. C2×#2463C2semidirect
15. C2×#2410C2semidirect
16. C2×#2631C2semidirect
17. C2×#2638C2semidirect
18. C2×#2617C2semidirect
19. C2×#2398C2semidirect
20. C2×#2388C2semidirect
21. C22×#393C2semidirect
22. C2×#2364C2semidirect
23. C2×#2358C2semidirect
24. C2×#2353C2semidirect
25. C23×#41C22semidirect
26. C24×Q8C22semidirect
29. C2×#548C22semidirect
30. C22×#124C22semidirect
31. C22×#124C22semidirect
32. C22×C22⋊Q8C22semidirect
33. C22×C22⋊Q8C22semidirect
34. C22×C22⋊Q8C22semidirect
37. C22×#121C22semidirect
41. C2×#518C22semidirect
42. C22×C4×Q8C22semidirect
51. C22×C4×D4C22semidirect
52. C22×C4×D4C22semidirect
60. #2638C22semidirect
61. #2631C22semidirect
62. #2617C22semidirect
63. #2610C22semidirect
64. #2599C22semidirect
65. #2561C22semidirect
66. #2543C22semidirect
67. #2477C22semidirect
68. #2472C22semidirect
69. #2463C22semidirect
70. #2459C22semidirect
71. #2444C22semidirect
72. #2410C22semidirect
73. #2409C22semidirect
74. #2404C22semidirect
75. #2398C22semidirect
76. C2×#400C22semidirect
77. C2×#398C22semidirect
79. C2×#397C22semidirect
80. C2×#397C22semidirect
81. C2×#397C22semidirect
82. C2×#397C22semidirect
83. #2388C22semidirect
84. C2×#395C22semidirect
85. C2×#395C22semidirect
89. C2×#394C22semidirect
90. C2×#394C22semidirect
91. C2×#394C22semidirect
95. C2×#393C22semidirect
96. C2×#393C22semidirect
97. C2×#393C22semidirect
98. C2×#393C22semidirect
99. C2×#393C22semidirect
100. C2×#393C22semidirect
104. C2×#392C22semidirect
105. C2×#392C22semidirect
106. #2364C22semidirect
107. #2358C22semidirect
108. #2353C22semidirect
109. C2×#391C22semidirect
113. C2×#388C22semidirect
114. C2×#388C22semidirect
115. C2×#388C22semidirect
116. C2×#388C22semidirect
117. C2×#388C22semidirect
118. C2×#387C22semidirect
119. C2×#387C22semidirect
120. C2×#387C22semidirect
121. C2×#387C22semidirect
126. C2×#386C22semidirect
127. C2×#386C22semidirect
128. C2×#386C22semidirect
129. C2×#386C22semidirect
130. C2×#386C22semidirect
131. C2×#386C22semidirect
132. C2×#386C22semidirect
134. C2×#385C22semidirect
135. C2×#385C22semidirect
136. C2×#383C22semidirect
137. C2×#381C22semidirect
138. C2×#381C22semidirect
139. C2×#380C22semidirect
141. C2×C4×C22⋊C4C22semidirect
142. C2×C4×C22⋊C4C22semidirect
143. C2×C4×C22⋊C4C22semidirect
144. C2×C4×C22⋊C4C22semidirect
145. C2×C4×C22⋊C4C22semidirect
146. C2×#376C22semidirect
147. C22×#95C22semidirect
148. C22×#95C22semidirect
153. C22×#41C23semidirect
159. C23×Q8C23semidirect
189. C2×#124C23semidirect
190. C2×#124C23semidirect
194. C2×C22⋊Q8C23semidirect
195. C2×C22⋊Q8C23semidirect
196. C2×C22⋊Q8C23semidirect
202. C2×#121C23semidirect
209. C2×C4×Q8C23semidirect
219. C2×C4×D4D4semidirect
228. C2×C4×D4C23semidirect
229. C2×C4×D4C23semidirect
295. #400C23semidirect
296. #398C23semidirect
298. #397C23semidirect
299. #397C23semidirect
300. #397C23semidirect
301. #397C23semidirect
302. #395C23semidirect
303. #395C23semidirect
307. #394C23semidirect
308. #394C23semidirect
309. #394C23semidirect
313. #393C23semidirect
314. #393C23semidirect
315. #393C23semidirect
316. #393C23semidirect
317. #393C23semidirect
321. #392C23semidirect
322. #392C23semidirect
323. #391C23semidirect
327. #388C23semidirect
328. #388C23semidirect
329. #388C23semidirect
330. #388C23semidirect
331. #388C23semidirect
332. #387C23semidirect
333. #387C23semidirect
334. #387C23semidirect
335. #387C23semidirect
340. #386C23semidirect
341. #386C23semidirect
342. #386C23semidirect
343. #386C23semidirect
344. #386C23semidirect
345. #386C23semidirect
346. #386C23semidirect
348. #385C23semidirect
349. #385C23semidirect
350. #383C23semidirect
351. #381C23semidirect
352. #381C23semidirect
353. #380C23semidirect
355. C4×C22⋊C4C23semidirect
356. C4×C22⋊C4C23semidirect
357. C4×C22⋊C4C23semidirect
358. C4×C22⋊C4C23semidirect
359. C4×C22⋊C4C23semidirect
360. #376C23semidirect
382. C2×#95C23semidirect
383. C2×#95C23semidirect
393. C25#41semidirect
450. C22×D4#41semidirect
538. C4×D4C2×D4semidirect
720. C24C2×#41semidirect
779. C2×D4C2×#41semidirect
1171. C2#35703direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5482
C22×#5182
#357032
C2×#26102
C2×#25992
C2×#25612
C2×#25432
C2×#24042
C2×#24772
C2×#24092
C2×#24442
C2×#24592
C2×#24722
C2×#24632
C2×#24102
C2×#26312
C2×#26382
C2×#26172
C2×#23982
C2×#23882
C22×#3932
C2×#23642
C2×#23582
C2×#23532