Finite Group Databasebeta

← C2×#40590 #7638995

Subgroups — C2×#40590 #7638995

Order 512.

12268 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#551C211yesmaximal, characteristic, complemented
2C22×D42C211yesmaximal, characteristic, complemented
3C2×#2714C212yesmaximal, complemented
4C2×#2678C212yesmaximal, complemented
5C2×#2676C212yesmaximal, complemented
6C2×#2670C212yesmaximal, complemented
7#40590C2132yesmaximal, direct product factor
8C2×#2818C211yesmaximal, characteristic, complemented
9C2×#2813C211yesmaximal, characteristic, complemented
10C2×#2598C211yesmaximal, characteristic, complemented
11C2×#2539C211yesmaximal, characteristic, complemented
12C2×#2411C212yesmaximal, complemented
13C2×#2435C211yesmaximal, characteristic, complemented
14C2×#2408C211yesmaximal, characteristic, complemented
15C2×#2405C212yesmaximal, complemented
16C2×#2410C212yesmaximal, complemented
17C2×#2403C212yesmaximal, complemented
18C2×#2619C211yesmaximal, characteristic, complemented
19C2×#2636C211yesmaximal, characteristic, complemented
20C2×#2639C211yesmaximal, characteristic, complemented
21C2×#2635C211yesmaximal, characteristic, complemented
22C2×#2613C211yesmaximal, characteristic, complemented
23C22×#392C211yesmaximal, characteristic, complemented
24C2×#2318C211yesmaximal, characteristic, complemented
25C24×D4C2212yes—
26C24×D4C2211yescharacteristic
27C24×D4C2211yescharacteristic, complemented
28C24×D4C2212yescomplemented
29C2×#551—216no—
30C2×#551C22116yescomplemented
31C2×D42—216no—
32C2×D42C22116yescomplemented
33C22×#127C2211yescharacteristic, complemented
34C22×#126C2211yescharacteristic, complemented
35C22×#126C2211yescharacteristic, complemented
36C22×#124C2211yescharacteristic, complemented
37C22×#124C2212yescomplemented
38C22×#123C2211yescharacteristic
39C22×#123C2211yescharacteristic, complemented
40C22×#123C2211yescharacteristic, complemented
41C22×#123C2212yescomplemented
42C22×C22⋊Q8C2211yescharacteristic, complemented
43C22×C22⋊Q8C2211yescharacteristic, complemented
44C22×#121C2211yescharacteristic
45C22×#121C2211yescharacteristic, complemented
46C22×#121C2212yescomplemented
47C22×#121C2212yescomplemented
48C22×#121C2212yescomplemented
49C22×#120C2211yescharacteristic
50C22×#120C2212yes—
51C22×#120C2212yescomplemented
52C22×#120C2212yescomplemented
53C22×#120C2212yescomplemented
54C22×#120C2212yescomplemented
55C22×C4×D4C2211yescharacteristic
56C22×C4×D4C2211yescharacteristic, complemented
57C22×C4×D4C2211yescharacteristic, complemented
58C22×#117C2211yescharacteristic, complemented
59C22×#117C2211yescharacteristic, complemented
60C23×C22⋊C4C2211yescharacteristic, complemented
61C23×C22⋊C4C2211yescharacteristic, complemented
62C23×C22⋊C4C2212yescomplemented
63#2818C22116yescomplemented
64#2813C22116yescomplemented
65#2714C22132yescomplemented
66#2678C22132yescomplemented
67#2676C22132yescomplemented
68#2670C22132yescomplemented
69#2639C22116yescomplemented
70#2636C22116yescomplemented
71#2635C22116yescomplemented
72#2619C22116yescomplemented
73#2613C22116yescomplemented
74#2598C22116yescomplemented
75#2539C22116yescomplemented
76#2435C22116yescomplemented
77#2411C22132yescomplemented
78#2410C22132yescomplemented
79#2408C22116yescomplemented
80#2405C22132yescomplemented
81#2403C22132yescomplemented
82C2×#400C2211yescharacteristic, complemented
83C2×#400C2211yescharacteristic, complemented
84C2×#399C2211yescharacteristic, complemented
85C2×#399C2211yescharacteristic, complemented
86C2×#397C2212yescomplemented
87C2×#396C2212yescomplemented
88C2×#396C2212yescomplemented
89C2×#394C2211yescharacteristic, complemented
90C2×#394C2212yescomplemented
91C2×#394C2211yescharacteristic, complemented
92C2×#394C2211yescharacteristic, complemented
93C2×#394C2212yescomplemented
94C2×#394C2211yescharacteristic, complemented
95C2×#394C2211yescharacteristic, complemented
96C2×#394C2211yescharacteristic, complemented
97C2×#394C2212yescomplemented
98C2×#394C2212yescomplemented
99C2×#394C2212yescomplemented
100C2×#394C2212yescomplemented
101C2×#394C2212yescomplemented
102C2×#394C2212yescomplemented
103C2×#393C2212yescomplemented
104C2×#392C2211yescharacteristic
105C2×#392C2211yescharacteristic
106C2×#392C2211yescharacteristic, complemented
107C2×#392C2212yescomplemented
108C2×#392C2211yescharacteristic, complemented
109C2×#392C2211yescharacteristic, complemented
110C2×#392C2211yescharacteristic, complemented
111C2×#392C2212yescomplemented
112C2×#392C2212yescomplemented
113C2×#392C2212yescomplemented
114C2×#392C2212yescomplemented
115C2×#392C2212yescomplemented
116C2×#392C2212yescomplemented
117C2×#392C2212yescomplemented
118C2×#392C22116yescomplemented
119#2318C22116yescomplemented
120C2×#390C2212yescomplemented
121C2×#390C2212yescomplemented
122C2×#390C2212yescomplemented
123C2×#390C2212yescomplemented
124C2×#390C2212yescomplemented
125C2×#388C2212yescomplemented
126C2×#388C2212yescomplemented
127C2×#388C2212yescomplemented
128C2×#387C2212yescomplemented
129C2×#386C2212yes—
130C2×#386C2212yescomplemented
131C2×#386C2212yescomplemented
132C2×#386C2212yescomplemented
133C2×#386C2212yescomplemented
134C2×#386C2212yescomplemented
135C2×#386C2212yescomplemented
136C2×#385C2212yescomplemented
137C2×#385C2212yescomplemented
138C2×#385C2212yescomplemented
139C2×#383C2211yescharacteristic, complemented
140C2×#382C2211yescharacteristic, complemented
141C2×#381C2211yescharacteristic, complemented
142C2×#380C2211yescharacteristic, complemented
143C2×#379C2212yescomplemented
144C2×#379C2212yescomplemented
145C2×#379C2212yescomplemented
146C2×#379C2212yescomplemented
147C2×C4×C22⋊C4C2211yescharacteristic, complemented
148C22×#95C2211yescharacteristic, complemented
149C26C2312yes—
150C26C2311yescharacteristic
151C26C2312yes—
152C23×Q8C2311yescharacteristic
153C23×D4—216no—
154C23×D4—28no—
155C23×D4—28no—
156C23×D4—48no—
157C23×D4—48no—
158C23×D4—48no—
159C23×D4—48no—
160C23×D4—48no—
161C23×D4—48no—
162C23×D4—48no—
163C23×D4C2311yescharacteristic
164C23×D4C2312yes—
165C23×D4C2312yes—
166C23×D4C2312yes—
167C23×D4C2312yes—
168C23×D4C2311yescharacteristic
169C23×D4C2311yescharacteristic
170C23×D4C2312yes—
171C23×D4C2312yes—
172C23×D4C2311yescharacteristic
173C23×D4C2318yes—
174C23×D4C23116yes—
175C23×D4C2312yes—
176C23×D4C2312yes—
177C23×D4C2311yescharacteristic
178C23×D4C2311yescharacteristic
179C23×D4C2312yes—
180C23×D4C2312yes—
181C23×D4C2312yes—
182C23×D4C2312yes—
183C23×D4C2318yescomplemented
184C23×D4C23116yescomplemented
185C24×C4C2311yescharacteristic
186C24×C4C2311yescharacteristic
187C24×C4C2312yes—
188C24×C4C2312yes—
189C24×C4C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192#551—2128no—
193D42—2128no—
194C2×#127—28no—
195C2×#127C2318yescomplemented
196C2×#126—28no—
197C2×#126—28no—
198C2×#126C2318yescomplemented
199C2×#126C2318yescomplemented
200C2×#124—28no—
201C2×#124—48no—
202C2×#124C2318yescomplemented
203C2×#124C23116yescomplemented
204C2×#123—28no—
205C2×#123—28no—
206C2×#123—28no—
207C2×#123—48no—
208C2×#123C2318yes—
209C2×#123C2318yescomplemented
210C2×#123C2318yescomplemented
211C2×#123C23116yescomplemented
212C2×C22⋊Q8—28no—
213C2×C22⋊Q8—28no—
214C2×C22⋊Q8C2318yescomplemented
215C2×C22⋊Q8C2318yescomplemented
216C2×#121—28no—
217C2×#121—28no—
218C2×#121—216no—
219C2×#121—48no—
220C2×#121—48no—
221C2×#121C2318yes—
222C2×#121C2318yescomplemented
223C2×#121C23116yescomplemented
224C2×#121C23116yescomplemented
225C2×#121C23116yescomplemented
226C2×#120—28no—
227C2×#120—216no—
228C2×#120—216no—
229C2×#120—48no—
230C2×#120—48no—
231C2×#120—48no—
232C2×#120C2318yes—
233C2×#120C23116yes—
234C2×#120C23116yescomplemented
235C2×#120C23116yescomplemented
236C2×#120C23116yescomplemented
237C2×#120C23116yescomplemented
238C2×C4×D4—28no—
239C2×C4×D4—28no—
240C2×C4×D4D4116yescomplemented
241C2×C4×D4C2318yes—
242C2×C4×D4C2318yescomplemented
243C2×C4×D4C2318yescomplemented
244C2×#117—28no—
245C2×#117—28no—
246C2×#117C2318yescomplemented
247C2×#117C2318yescomplemented
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—28no—
262C22×C22⋊C4—28no—
263C22×C22⋊C4—48no—
264C22×C22⋊C4C2311yescharacteristic
265C22×C22⋊C4C2311yescharacteristic
266C22×C22⋊C4C2311yescharacteristic
267C22×C22⋊C4C2311yescharacteristic
268C22×C22⋊C4C2311yescharacteristic
269C22×C22⋊C4C2311yescharacteristic
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2311yescharacteristic
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2311yescharacteristic
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C22⋊C4C2311yescharacteristic
277C22×C22⋊C4C2312yes—
278C22×C22⋊C4C2312yes—
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2312yes—
282C22×C22⋊C4C2312yes—
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2318yescomplemented
305C22×C22⋊C4C2318yescomplemented
306C22×C22⋊C4C23116yescomplemented
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2312yes—
310C22×C42C2311yescharacteristic
311#400C2318yescomplemented
312#400C2318yescomplemented
313#399C2318yescomplemented
314#399C2318yescomplemented
315#397C23116yescomplemented
316#396C23116yescomplemented
317#396C23116yescomplemented
318#394C2318yescomplemented
319#394C2318yescomplemented
320#394C23116yescomplemented
321#394C23116yescomplemented
322#394C2318yescomplemented
323#394C2318yescomplemented
324#394C23116yescomplemented
325#394C23116yescomplemented
326#394C2318yescomplemented
327#394C23116yescomplemented
328#394C2318yescomplemented
329#394C23116yescomplemented
330#394C23116yescomplemented
331#394C23116yescomplemented
332#393C23116yescomplemented
333#392C2318yes—
334#392C2318yes—
335#392C2318yescomplemented
336#392C2318yescomplemented
337#392C23116yescomplemented
338#392C23116yescomplemented
339#392C23116yescomplemented
340#392C2318yescomplemented
341#392C23116yescomplemented
342#392C2318yescomplemented
343#392C23116yescomplemented
344#392C23116yescomplemented
345#392C23116yescomplemented
346#392C23116yescomplemented
347#390C23116yescomplemented
348#390C23116yescomplemented
349#390C23116yescomplemented
350#390C23116yescomplemented
351#390C23116yescomplemented
352#388C23116yescomplemented
353#388C23116yescomplemented
354#388C23116yescomplemented
355#387C23116yescomplemented
356#386C23116yes—
357#386C23116yescomplemented
358#386C23116yescomplemented
359#386C23116yescomplemented
360#386C23116yescomplemented
361#386C23116yescomplemented
362#386C23116yescomplemented
363#385C23116yescomplemented
364#385C23116yescomplemented
365#385C23116yescomplemented
366#383C2318yescomplemented
367#382C2318yescomplemented
368#381C2318yescomplemented
369#380C2318yescomplemented
370#379C23116yescomplemented
371#379C23116yescomplemented
372#379C23116yescomplemented
373#379C23116yescomplemented
374C4×C22⋊C4C2318yescomplemented
375C2×#95C2311yescharacteristic
376C2×#95C2311yescharacteristic
377C2×#95C2312yes—
378C2×#95C2312yes—
379C2×#95C2311yescharacteristic
380C2×#95C2311yescharacteristic
381C2×#95C2312yes—
382C2×#95C2312yes—
383C2×#95C2312yes—
384C2×#95C2312yes—
385C2×#95C2312yes—
386C2×#95C2312yes—
387C2×#95C2312yes—
388C2×#95C2318yescomplemented
389C25—28no—
390C25—24no—
391C25—24no—
392C25—28no—
393C25—28no—
394C25—28no—
395C25—28no—
396C25—28no—
397C25—28no—
398C25—44no—
399C25—44no—
400C25—44no—
401C25—44no—
402C25—44no—
403C25—44no—
404C25—44no—
405C25—42no—
406C25—44no—
407C25—44no—
408C25C2411yescharacteristic
409C25C2412yes—
410C25C2412yes—
411C25C2411yescharacteristic
412C25C2412yes—
413C25C2411yescharacteristic
414C25C2414yes—
415C25C2418yes—
416C25C2411yescharacteristic
417C25C2418yes—
418C22×Q8—24no—
419C22×Q8—44no—
420C22×Q8C2414yes—
421C22×D4—28no—
422C22×D4—28no—
423C22×D4—24no—
424C22×D4—28no—
425C22×D4—28no—
426C22×D4—24no—
427C22×D4—28no—
428C22×D4—28no—
429C22×D4—28no—
430C22×D4—28no—
431C22×D4—28no—
432C22×D4—28no—
433C22×D4—28no—
434C22×D4—28no—
435C22×D4—24no—
436C22×D4—28no—
437C22×D4—264no—
438C22×D4—24no—
439C22×D4—28no—
440C22×D4—28no—
441C22×D4—24no—
442C22×D4—24no—
443C22×D4—28no—
444C22×D4—232no—
445C22×D4—28no—
446C22×D4—232no—
447C22×D4—44no—
448C22×D4—44no—
449C22×D4—44no—
450C22×D4—44no—
451C22×D4—44no—
452C22×D4—44no—
453C22×D4—44no—
454C22×D4—44no—
455C22×D4—44no—
456C22×D4—44no—
457C22×D4—44no—
458C22×D4—44no—
459C22×D4—44no—
460C22×D4—44no—
461C22×D4—44no—
462C22×D4—44no—
463C22×D4—432no—
464C22×D4—42no—
465C22×D4—44no—
466C22×D4—44no—
467C22×D4—44no—
468C22×D4—44no—
469C22×D4—44no—
470C22×D4—44no—
471C22×D4—44no—
472C22×D4—44no—
473C22×D4—432no—
474C22×D4—432no—
475C22×D4—432no—
476C22×D4—432no—
477C22×D4—432no—
478C22×D4—432no—
479C22×D4—464no—
480C22×D4—464no—
481C22×D4—4128no—
482C22×D4—4128no—
483C22×D4C2×D418yes—
484C22×D4C2414yes—
485C22×D4C2418yes—
486C22×D4C2414yes—
487C22×D4C2418yes—
488C22×D4C2418yes—
489C22×D4C2418yes—
490C22×D4C2414yes—
491C22×D4C2414yes—
492C22×D4C2418yes—
493C22×D4C2418yes—
494C22×D4C2418yes—
495C22×D4C2418yes—
496C22×D4C2414yes—
497C22×D4C2414yes—
498C22×D4C2418yes—
499C22×D4C2418yes—
500C22×D4C2418yes—
501C22×D4C2418yes—
502C23×C4—24no—
503C23×C4—28no—
504C23×C4—28no—
505C23×C4—24no—
506C23×C4—24no—
507C23×C4—28no—
508C23×C4—24no—
509C23×C4—42no—
510C23×C4—44no—
511C23×C4—44no—
512C23×C4—44no—
513C23×C4—44no—
514C23×C4—44no—
515C23×C4—44no—
516C23×C4—44no—
517C23×C4C2×D418yes—
518C23×C4C2×D418yescomplemented
519C23×C4C2414yes—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2412yes—
526C23×C4C2411yescharacteristic
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2414yes—
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2414yes—
538C23×C4C2418yes—
539C23×C4C2418yes—
540C23×C4C2414yes—
541C23×C4C2414yes—
542#127—232no—
543#126—232no—
544#126—232no—
545#124—232no—
546#124—432no—
547#123—232no—
548#123—232no—
549#123—232no—
550#123—432no—
551C22⋊Q8—232no—
552C22⋊Q8—232no—
553#121—232no—
554#121—232no—
555#121—264no—
556#121—432no—
557#121—432no—
558#120—232no—
559#120—264no—
560#120—264no—
561#120—432no—
562#120—432no—
563#120—432no—
564C4×D4—232no—
565C4×D4—232no—
566C4×D4C2×D4164yescomplemented
567#117—232no—
568#117—232no—
569C2×C4⋊C4—24no—
570C2×C4⋊C4—24no—
571C2×C4⋊C4—24no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4—44no—
578C2×C4⋊C4—44no—
579C2×C4⋊C4—44no—
580C2×C4⋊C4—44no—
581C2×C4⋊C4C2×D418yescomplemented
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2414yes—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—28no—
600C2×C22⋊C4—28no—
601C2×C22⋊C4—28no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—232no—
609C2×C22⋊C4—24no—
610C2×C22⋊C4—28no—
611C2×C22⋊C4—28no—
612C2×C22⋊C4—28no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—232no—
615C2×C22⋊C4—44no—
616C2×C22⋊C4—44no—
617C2×C22⋊C4—44no—
618C2×C22⋊C4—44no—
619C2×C22⋊C4—432no—
620C2×C22⋊C4—44no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4—44no—
623C2×C22⋊C4—44no—
624C2×C22⋊C4—44no—
625C2×C22⋊C4—44no—
626C2×C22⋊C4—44no—
627C2×C22⋊C4—44no—
628C2×C22⋊C4—44no—
629C2×C22⋊C4—44no—
630C2×C22⋊C4—44no—
631C2×C22⋊C4—44no—
632C2×C22⋊C4—44no—
633C2×C22⋊C4—44no—
634C2×C22⋊C4—44no—
635C2×C22⋊C4—44no—
636C2×C22⋊C4C2×D418yes—
637C2×C22⋊C4C2×D418yescomplemented
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C42—24no—
679C2×C42—24no—
680C2×C42—44no—
681C2×C42C2×D418yescomplemented
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2418yes—
685C2×C42C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2418yes—
689#95C2414yes—
690#95C2414yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699C24—24no—
700C24—22no—
701C24—22no—
702C24—22no—
703C24—24no—
704C24—24no—
705C24—22no—
706C24—24no—
707C24—24no—
708C24—24no—
709C24—24no—
710C24—24no—
711C24—24no—
712C24—24no—
713C24—24no—
714C24—22no—
715C24—22no—
716C24—22no—
717C24—24no—
718C24—24no—
719C24—24no—
720C24—24no—
721C24—24no—
722C24—24no—
723C24—24no—
724C24—24no—
725C24—24no—
726C24—24no—
727C24—24no—
728C24—24no—
729C24—216no—
730C24—28no—
731C24—24no—
732C24—24no—
733C24—22no—
734C24—24no—
735C24—24no—
736C24—22no—
737C24—28no—
738C24—216no—
739C24—216no—
740C24—216no—
741C24—216no—
742C24—216no—
743C24—216no—
744C24—48no—
745C24—48no—
746C24—48no—
747C24—48no—
748C24—48no—
749C24—48no—
750C24—48no—
751C24—44no—
752C24—48no—
753C24—48no—
754C24—432no—
755C24—432no—
756C24—432no—
757C24—432no—
758C24—416no—
759C24—432no—
760C24—432no—
761C24—432no—
762C24—416no—
763C24—88no—
764C24—816no—
765C24—816no—
766C24—816no—
767C24—816no—
768C24—816no—
769C24—816no—
770C24—816no—
771C24—816no—
772C24—816no—
773C24C22×D414yes—
774C24C22×D414yes—
775C24H(5,𝔽2)18yes—
776C24H(5,𝔽2)14yes—
777C24H(5,𝔽2)18yes—
778C24C2512yes—
779C24C2514yes—
780C24C2514yes—
781C24C2512yes—
782C24C2514yes—
783C24C2512yes—
784C24C2512yes—
785C24C2511yescharacteristic
786C2×Q8—28no—
787C2×Q8—48no—
788C2×Q8—88no—
789C2×D4—232no—
790C2×D4—232no—
791C2×D4—216no—
792C2×D4—216no—
793C2×D4—28no—
794C2×D4—216no—
795C2×D4—216no—
796C2×D4—28no—
797C2×D4—216no—
798C2×D4—216no—
799C2×D4—216no—
800C2×D4—216no—
801C2×D4—216no—
802C2×D4—216no—
803C2×D4—216no—
804C2×D4—216no—
805C2×D4—28no—
806C2×D4—216no—
807C2×D4—28no—
808C2×D4—216no—
809C2×D4—216no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—216no—
813C2×D4—216no—
814C2×D4—48no—
815C2×D4—48no—
816C2×D4—48no—
817C2×D4—48no—
818C2×D4—48no—
819C2×D4—48no—
820C2×D4—48no—
821C2×D4—48no—
822C2×D4—48no—
823C2×D4—48no—
824C2×D4—48no—
825C2×D4—48no—
826C2×D4—48no—
827C2×D4—48no—
828C2×D4—48no—
829C2×D4—48no—
830C2×D4—44no—
831C2×D4—432no—
832C2×D4—432no—
833C2×D4—432no—
834C2×D4—416no—
835C2×D4—416no—
836C2×D4—48no—
837C2×D4—48no—
838C2×D4—48no—
839C2×D4—48no—
840C2×D4—48no—
841C2×D4—48no—
842C2×D4—48no—
843C2×D4—48no—
844C2×D4—4128no—
845C2×D4—4128no—
846C2×D4—4256no—
847C2×D4—416no—
848C2×D4—432no—
849C2×D4—432no—
850C2×D4—432no—
851C2×D4—432no—
852C2×D4—4256no—
853C2×D4—432no—
854C2×D4—432no—
855C2×D4—816no—
856C2×D4—88no—
857C2×D4—816no—
858C2×D4—816no—
859C2×D4C22×D4116yes—
860C22×C4—24no—
861C22×C4—22no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—24no—
873C22×C4—28no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—216no—
886C22×C4—216no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—24no—
894C22×C4—24no—
895C22×C4—28no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—24no—
899C22×C4—28no—
900C22×C4—216no—
901C22×C4—28no—
902C22×C4—416no—
903C22×C4—416no—
904C22×C4—44no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—48no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4—48no—
912C22×C4—416no—
913C22×C4—432no—
914C22×C4—432no—
915C22×C4—416no—
916C22×C4—88no—
917C22×C4C22×D414yes—
918C22×C4C22×D414yes—
919C22×C4C22×D414yes—
920C22×C4C22×D414yes—
921C22×C4C22×D414yes—
922C22×C4C22×D4116yes—
923C22×C4C22×D4116yescomplemented
924C22×C4C2514yes—
925C22×C4C2514yes—
926C22×C4C2514yes—
927C22×C4C2514yes—
928C22×C4C2512yes—
929C22×C4C2514yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2512yes—
934C22×C4C2512yes—
935C22×C4C2512yes—
936C22×C4C2512yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C4⋊C4—28no—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—48no—
949C4⋊C4—48no—
950C4⋊C4—48no—
951C4⋊C4—48no—
952C4⋊C4C22×D4116yescomplemented
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—216no—
958C22⋊C4—216no—
959C22⋊C4—216no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—216no—
968C22⋊C4—216no—
969C22⋊C4—216no—
970C22⋊C4—28no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—48no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—48no—
980C22⋊C4—48no—
981C22⋊C4—48no—
982C22⋊C4—48no—
983C22⋊C4—48no—
984C22⋊C4—48no—
985C22⋊C4—48no—
986C22⋊C4—48no—
987C22⋊C4—48no—
988C22⋊C4—48no—
989C22⋊C4—48no—
990C22⋊C4—48no—
991C22⋊C4C22×D4116yes—
992C22⋊C4C22×D4116yescomplemented
993C42—28no—
994C42—28no—
995C42—48no—
996C42C22×D4116yescomplemented
997C23—24no—
998C23—22no—
999C23—22no—
1000C23—28no—
1001C23—28no—
1002C23—216no—
1003C23—216no—
1004C23—22no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—22no—
1017C23—22no—
1018C23—28no—
1019C23—28no—
1020C23—216no—
1021C23—28no—
1022C23—28no—
1023C23—216no—
1024C23—216no—
1025C23—216no—
1026C23—22no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—22no—
1042C23—24no—
1043C23—22no—
1044C23—24no—
1045C23—432no—
1046C23—432no—
1047C23—432no—
1048C23—432no—
1049C23—432no—
1050C23—416no—
1051C23—432no—
1052C23—48no—
1053C23—44no—
1054C23—44no—
1055C23—48no—
1056C23—48no—
1057C23—48no—
1058C23—48no—
1059C23—48no—
1060C23—48no—
1061C23—432no—
1062C23—48no—
1063C23—48no—
1064C23—416no—
1065C23—44no—
1066C23—48no—
1067C23—48no—
1068C23—44no—
1069C23—48no—
1070C23—48no—
1071C23—44no—
1072C23—48no—
1073C23—48no—
1074C23—48no—
1075C23—48no—
1076C23—48no—
1077C23—48no—
1078C23—48no—
1079C23—48no—
1080C23—48no—
1081C23—48no—
1082C23—816no—
1083C23—816no—
1084C23—88no—
1085C23—816no—
1086C23—816no—
1087C23—816no—
1088C23—816no—
1089C23—816no—
1090C23—864no—
1091C23—8128no—
1092C23—816no—
1093C23—816no—
1094C23—8128no—
1095C23#535116yes—
1096C23C23×D414yes—
1097C23C23×D414yes—
1098C23C23×D412yes—
1099C23C2×H(5,𝔽2)18yes—
1100C23C2×H(5,𝔽2)14yes—
1101C23C2×H(5,𝔽2)18yes—
1102C23C2×H(5,𝔽2)14yes—
1103C23C2×H(5,𝔽2)14yes—
1104C23C2×H(5,𝔽2)12yes—
1105C23#58512yes—
1106C23C2611yescharacteristic
1107Q8—88no—
1108D4—232no—
1109D4—232no—
1110D4—432no—
1111D4—432no—
1112D4—416no—
1113D4—416no—
1114D4—432no—
1115D4—416no—
1116D4—432no—
1117D4—432no—
1118D4—432no—
1119D4—432no—
1120D4—432no—
1121D4—432no—
1122D4—816no—
1123D4—88no—
1124D4—816no—
1125D4—816no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—28no—
1133C2×C4—28no—
1134C2×C4—28no—
1135C2×C4—28no—
1136C2×C4—28no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—416no—
1167C2×C4—416no—
1168C2×C4—416no—
1169C2×C4—432no—
1170C2×C4—432no—
1171C2×C4—416no—
1172C2×C4—44no—
1173C2×C4—44no—
1174C2×C4—48no—
1175C2×C4—44no—
1176C2×C4—44no—
1177C2×C4—44no—
1178C2×C4—44no—
1179C2×C4—48no—
1180C2×C4—48no—
1181C2×C4—48no—
1182C2×C4—48no—
1183C2×C4—88no—
1184C2×C4C23×D414yes—
1185C2×C4C23×D414yes—
1186C2×C4C23×D414yes—
1187C2×C4C23×D414yes—
1188C2×C4C23×D414yes—
1189C22—28no—
1190C22—24no—
1191C22—24no—
1192C22—232no—
1193C22—28no—
1194C22—28no—
1195C22—24no—
1196C22—28no—
1197C22—24no—
1198C22—24no—
1199C22—24no—
1200C22—28no—
1201C22—28no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—42no—
1206C22—44no—
1207C22—416no—
1208C22—416no—
1209C22—432no—
1210C22—44no—
1211C22—42no—
1212C22—44no—
1213C22—44no—
1214C22—44no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—42no—
1222C22—44no—
1223C22—44no—
1224C22—42no—
1225C22—44no—
1226C22—44no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—832no—
1234C22—864no—
1235C22—864no—
1236C22—816no—
1237C22—816no—
1238C22—88no—
1239C22C2×#53518yes—
1240C22C2×#53514yes—
1241C22#348414yes—
1242C22#348814yes—
1243C22#353218yes—
1244C22#353418yes—
1245C22C24×D411yescharacteristic
1246C22C22×H(5,𝔽2)12yes—
1247C22C22×H(5,𝔽2)12yes—
1248C22C22×H(5,𝔽2)11yescharacteristic
1249C22C2×#58511yescharacteristic
1250C4—24no—
1251C4—24no—
1252C4—24no—
1253C4—24no—
1254C4—24no—
1255C4—44no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—44no—
1263C4—44no—
1264C4—44no—
1265C4—44no—
1266C2—28no—
1267C2—44no—
1268C2—48no—
1269C2—44no—
1270C2—82no—
1271C2—84no—
1272C2—84no—
1273C2#4059018yesdirect product factor
1274C2C22×#53511yescharacteristic
1275C2C2×#353212yes—
1276C2C2×#353412yes—
1277C2C2×#348411yescharacteristic
1278C2C2×#348811yescharacteristic
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×#551C2semidirect
2. C22×D42C2semidirect
3. C2×#2714C2semidirect
4. C2×#2678C2semidirect
5. C2×#2676C2semidirect
6. C2×#2670C2semidirect
7. #40590C2direct (N × H)
8. C2×#2818C2semidirect
9. C2×#2813C2semidirect
10. C2×#2598C2semidirect
11. C2×#2539C2semidirect
12. C2×#2411C2semidirect
13. C2×#2435C2semidirect
14. C2×#2408C2semidirect
15. C2×#2405C2semidirect
16. C2×#2410C2semidirect
17. C2×#2403C2semidirect
18. C2×#2619C2semidirect
19. C2×#2636C2semidirect
20. C2×#2639C2semidirect
21. C2×#2635C2semidirect
22. C2×#2613C2semidirect
23. C22×#392C2semidirect
24. C2×#2318C2semidirect
27. C24×D4C22semidirect
28. C24×D4C22semidirect
30. C2×#551C22semidirect
32. C2×D42C22semidirect
33. C22×#127C22semidirect
34. C22×#126C22semidirect
35. C22×#126C22semidirect
36. C22×#124C22semidirect
37. C22×#124C22semidirect
39. C22×#123C22semidirect
40. C22×#123C22semidirect
41. C22×#123C22semidirect
42. C22×C22⋊Q8C22semidirect
43. C22×C22⋊Q8C22semidirect
45. C22×#121C22semidirect
46. C22×#121C22semidirect
47. C22×#121C22semidirect
48. C22×#121C22semidirect
51. C22×#120C22semidirect
52. C22×#120C22semidirect
53. C22×#120C22semidirect
54. C22×#120C22semidirect
56. C22×C4×D4C22semidirect
57. C22×C4×D4C22semidirect
58. C22×#117C22semidirect
59. C22×#117C22semidirect
60. C23×C22⋊C4C22semidirect
61. C23×C22⋊C4C22semidirect
62. C23×C22⋊C4C22semidirect
63. #2818C22semidirect
64. #2813C22semidirect
65. #2714C22semidirect
66. #2678C22semidirect
67. #2676C22semidirect
68. #2670C22semidirect
69. #2639C22semidirect
70. #2636C22semidirect
71. #2635C22semidirect
72. #2619C22semidirect
73. #2613C22semidirect
74. #2598C22semidirect
75. #2539C22semidirect
76. #2435C22semidirect
77. #2411C22semidirect
78. #2410C22semidirect
79. #2408C22semidirect
80. #2405C22semidirect
81. #2403C22semidirect
82. C2×#400C22semidirect
83. C2×#400C22semidirect
84. C2×#399C22semidirect
85. C2×#399C22semidirect
86. C2×#397C22semidirect
87. C2×#396C22semidirect
88. C2×#396C22semidirect
89. C2×#394C22semidirect
90. C2×#394C22semidirect
91. C2×#394C22semidirect
92. C2×#394C22semidirect
93. C2×#394C22semidirect
94. C2×#394C22semidirect
95. C2×#394C22semidirect
96. C2×#394C22semidirect
97. C2×#394C22semidirect
98. C2×#394C22semidirect
99. C2×#394C22semidirect
100. C2×#394C22semidirect
101. C2×#394C22semidirect
102. C2×#394C22semidirect
103. C2×#393C22semidirect
106. C2×#392C22semidirect
107. C2×#392C22semidirect
108. C2×#392C22semidirect
109. C2×#392C22semidirect
110. C2×#392C22semidirect
111. C2×#392C22semidirect
112. C2×#392C22semidirect
113. C2×#392C22semidirect
114. C2×#392C22semidirect
115. C2×#392C22semidirect
116. C2×#392C22semidirect
117. C2×#392C22semidirect
118. C2×#392C22semidirect
119. #2318C22semidirect
120. C2×#390C22semidirect
121. C2×#390C22semidirect
122. C2×#390C22semidirect
123. C2×#390C22semidirect
124. C2×#390C22semidirect
125. C2×#388C22semidirect
126. C2×#388C22semidirect
127. C2×#388C22semidirect
128. C2×#387C22semidirect
130. C2×#386C22semidirect
131. C2×#386C22semidirect
132. C2×#386C22semidirect
133. C2×#386C22semidirect
134. C2×#386C22semidirect
135. C2×#386C22semidirect
136. C2×#385C22semidirect
137. C2×#385C22semidirect
138. C2×#385C22semidirect
139. C2×#383C22semidirect
140. C2×#382C22semidirect
141. C2×#381C22semidirect
142. C2×#380C22semidirect
143. C2×#379C22semidirect
144. C2×#379C22semidirect
145. C2×#379C22semidirect
146. C2×#379C22semidirect
147. C2×C4×C22⋊C4C22semidirect
148. C22×#95C22semidirect
183. C23×D4C23semidirect
184. C23×D4C23semidirect
195. C2×#127C23semidirect
198. C2×#126C23semidirect
199. C2×#126C23semidirect
202. C2×#124C23semidirect
203. C2×#124C23semidirect
209. C2×#123C23semidirect
210. C2×#123C23semidirect
211. C2×#123C23semidirect
214. C2×C22⋊Q8C23semidirect
215. C2×C22⋊Q8C23semidirect
222. C2×#121C23semidirect
223. C2×#121C23semidirect
224. C2×#121C23semidirect
225. C2×#121C23semidirect
234. C2×#120C23semidirect
235. C2×#120C23semidirect
236. C2×#120C23semidirect
237. C2×#120C23semidirect
240. C2×C4×D4D4semidirect
242. C2×C4×D4C23semidirect
243. C2×C4×D4C23semidirect
246. C2×#117C23semidirect
247. C2×#117C23semidirect
304. C22×C22⋊C4C23semidirect
305. C22×C22⋊C4C23semidirect
306. C22×C22⋊C4C23semidirect
311. #400C23semidirect
312. #400C23semidirect
313. #399C23semidirect
314. #399C23semidirect
315. #397C23semidirect
316. #396C23semidirect
317. #396C23semidirect
318. #394C23semidirect
319. #394C23semidirect
320. #394C23semidirect
321. #394C23semidirect
322. #394C23semidirect
323. #394C23semidirect
324. #394C23semidirect
325. #394C23semidirect
326. #394C23semidirect
327. #394C23semidirect
328. #394C23semidirect
329. #394C23semidirect
330. #394C23semidirect
331. #394C23semidirect
332. #393C23semidirect
335. #392C23semidirect
336. #392C23semidirect
337. #392C23semidirect
338. #392C23semidirect
339. #392C23semidirect
340. #392C23semidirect
341. #392C23semidirect
342. #392C23semidirect
343. #392C23semidirect
344. #392C23semidirect
345. #392C23semidirect
346. #392C23semidirect
347. #390C23semidirect
348. #390C23semidirect
349. #390C23semidirect
350. #390C23semidirect
351. #390C23semidirect
352. #388C23semidirect
353. #388C23semidirect
354. #388C23semidirect
355. #387C23semidirect
357. #386C23semidirect
358. #386C23semidirect
359. #386C23semidirect
360. #386C23semidirect
361. #386C23semidirect
362. #386C23semidirect
363. #385C23semidirect
364. #385C23semidirect
365. #385C23semidirect
366. #383C23semidirect
367. #382C23semidirect
368. #381C23semidirect
369. #380C23semidirect
370. #379C23semidirect
371. #379C23semidirect
372. #379C23semidirect
373. #379C23semidirect
374. C4×C22⋊C4C23semidirect
388. C2×#95C23semidirect
518. C23×C4C2×D4semidirect
566. C4×D4C2×D4semidirect
581. C2×C4⋊C4C2×D4semidirect
637. C2×C22⋊C4C2×D4semidirect
681. C2×C42C2×D4semidirect
923. C22×C4C22×D4semidirect
952. C4⋊C4C22×D4semidirect
992. C22⋊C4C22×D4semidirect
996. C42C22×D4semidirect
1273. C2#40590direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5512
C22×D422
C2×#27142
C2×#26782
C2×#26762
C2×#26702
#405902
C2×#28182
C2×#28132
C2×#25982
C2×#25392
C2×#24112
C2×#24352
C2×#24082
C2×#24052
C2×#24102
C2×#24032
C2×#26192
C2×#26362
C2×#26392
C2×#26352
C2×#26132
C22×#3922
C2×#23182