Finite Group Databasebeta

← #636034

Subgroups — #636034

Order 512.

4154 conjugacy classes of subgroups.

The subgroup lattice has 1340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2440C211yesmaximal, characteristic, complemented
2C2×#2628C211yesmaximal, characteristic, complemented
3C2×#2280C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic
5#16304C212yesmaximal, complemented
6#16303C212yesmaximal, complemented
7#16300C212yesmaximal, complemented
8#16299C212yesmaximal, complemented
9#15220C211yesmaximal, characteristic, complemented
10#15220C211yesmaximal, characteristic, complemented
11#15135C211yesmaximal, characteristic, complemented
12#15125C211yesmaximal, characteristic, complemented
13#14767C212yesmaximal, complemented
14#14758C212yesmaximal, complemented
15#14734C212yesmaximal
16#14717C212yesmaximal
17#14680C211yesmaximal, characteristic
18#14340C211yesmaximal, characteristic, complemented
19#14264C211yesmaximal, characteristic, complemented
20#14264C211yesmaximal, characteristic, complemented
21#14130C211yesmaximal, characteristic, complemented
22#13907C211yesmaximal, characteristic, complemented
23#13881C211yesmaximal, characteristic, complemented
24C25×C4C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic, complemented
26C22×C22⋊Q8C2212yes—
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32#2628—28no—
33#2440—28no—
34C2×#400C2212yescomplemented
35C2×#399C2212yes—
36C2×#399C2212yes—
37C2×#398C2212yescomplemented
38C2×#395C2212yescomplemented
39C2×#395C2212yescomplemented
40C2×#393C2212yes—
41C2×#393C2212yes—
42C2×#389C2211yescharacteristic, complemented
43C2×#389C2211yescharacteristic, complemented
44C2×#389C2211yescharacteristic, complemented
45C2×#389C2211yescharacteristic, complemented
46C2×#389C2211yescharacteristic, complemented
47C2×#389C2211yescharacteristic, complemented
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#384C2211yescharacteristic, complemented
51C2×#382C2211yescharacteristic, complemented
52C2×#382C2211yescharacteristic, complemented
53#2280—28no—
54C2×#381C2211yescharacteristic
55C2×#381C2211yescharacteristic
56C2×#380—28no—
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×#380C2212yes—
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#380C2212yes—
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2212yes—
72C2×#380C2211yescharacteristic
73C2×#380C2211yescharacteristic
74C2×#379C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×#379C2212yes—
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C22×#95C2212yes—
82#1446C2212yescomplemented
83#1445C2212yescomplemented
84#1444C2212yescomplemented
85#1444C2212yescomplemented
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1443C2212yescomplemented
89#1443C2212yescomplemented
90#1442C2212yescomplemented
91#1442C2212yescomplemented
92#1442C2212yescomplemented
93#1442C2212yescomplemented
94#1442C2212yescomplemented
95#1442C2212yescomplemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1441C2212yescomplemented
101#1441C2212yescomplemented
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yes—
109#1439C2212yes—
110#1439C2212yes—
111#1439C2212yes—
112#1439C2212yes—
113#1439C2212yes—
114C4⋊#95C2211yescharacteristic, complemented
115C4⋊#95C2211yescharacteristic, complemented
116C4⋊#95C2211yescharacteristic, complemented
117C4⋊#95C2211yescharacteristic, complemented
118C4⋊#95C2211yescharacteristic, complemented
119C4⋊#95C2211yescharacteristic, complemented
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C26C2311yescharacteristic
128C23×Q8C2312yes—
129C24×C4—24no—
130C24×C4—24no—
131C24×C4—24no—
132C24×C4—24no—
133C24×C4—42no—
134C24×C4—42no—
135C24×C4Q818yescomplemented
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2312yes—
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C2×C4⋊Q8—24no—
145C2×C4⋊Q8—24no—
146C2×C4⋊Q8—42no—
147C2×C22⋊Q8—28no—
148C2×C22⋊Q8—44no—
149C2×C22⋊Q8—44no—
150C2×#117—24no—
151C2×#117—24no—
152C2×#117—24no—
153C2×#117—24no—
154C2×#117—42no—
155C2×#117—42no—
156C22×C4⋊C4—24no—
157C22×C4⋊C4—24no—
158C22×C4⋊C4—24no—
159C22×C4⋊C4—24no—
160C22×C4⋊C4—42no—
161C22×C4⋊C4—42no—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C22⋊C4—28no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4—44no—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214#400—28no—
215#399—28no—
216#399—44no—
217#398—28no—
218#395—28no—
219#395—28no—
220#393—28no—
221#393—44no—
222#389—24no—
223#389—24no—
224#389—24no—
225#389—24no—
226#389—42no—
227#389—42no—
228#385—28no—
229#385—44no—
230#384—24no—
231#382—24no—
232#382—42no—
233#381—24no—
234#381—24no—
235#380—24no—
236#380—24no—
237#380—24no—
238#380—24no—
239#380—24no—
240#380—24no—
241#380—24no—
242#380—28no—
243#380—24no—
244#380—24no—
245#380—28no—
246#380—24no—
247#380—24no—
248#380—44no—
249#380—42no—
250#380—42no—
251#380D418yes—
252#379—24no—
253#379—24no—
254#379—44no—
255C4×C22⋊C4—24no—
256C4×C22⋊C4—24no—
257C4×C22⋊C4—24no—
258C4×C22⋊C4D418yes—
259C2×#95—28no—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2311yescharacteristic
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C25—22no—
301C25—22no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—41no—
311C25—41no—
312C25—41no—
313C25—41no—
314C25C2×Q814yes—
315C25C2411yescharacteristic
316C25C2411yescharacteristic
317C25C2411yescharacteristic
318C22×Q8—24no—
319C22×Q8—24no—
320C22×Q8—42no—
321C22×Q8—42no—
322C22×Q8—42no—
323C22×Q8—42no—
324C22×Q8—42no—
325C23×C4—22no—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—232no—
338C23×C4—232no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—416no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—41no—
366C23×C4—41no—
367C23×C4—41no—
368C23×C4—416no—
369C23×C4—416no—
370C23×C4—416no—
371C23×C4—416no—
372C23×C4—42no—
373C23×C4—42no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4C2×D414yes—
379C23×C4C2×D414yes—
380C23×C4C2×Q814yes—
381C23×C4C2×Q814yes—
382C23×C4C2×Q814yes—
383C23×C4C2×Q814yes—
384C23×C4C2×Q814yes—
385C23×C4C2×Q814yes—
386C23×C4#4114yes—
387C23×C4#4114yes—
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2412yes—
403C23×C4C2412yes—
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C4⋊Q8—416no—
409C22⋊Q8—432no—
410#117—416no—
411#117—416no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—416no—
455C2×C4⋊C4—416no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4C2×D414yes—
482C2×C4⋊C4C2×D414yes—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—41no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—41no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—432no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4C2×D414yes—
548C2×C22⋊C4C2×D414yes—
549C2×C22⋊C4C2×D418yes—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42C2×D414yes—
561C2×C42C2×D414yes—
562#95—24no—
563#95—24no—
564#95—24no—
565#95—22no—
566#95—22no—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—22no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95C2×D418yes—
600#95C2×D414yes—
601#95C2×D414yes—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—28no—
611C24—28no—
612C24—28no—
613C24—28no—
614C24—28no—
615C24—28no—
616C24—28no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—28no—
642C24—28no—
643C24—44no—
644C24—44no—
645C24—44no—
646C24—44no—
647C24—44no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—44no—
652C24—44no—
653C24—44no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24C22×D412yes—
670C24C22×D412yes—
671C24C22×Q812yes—
672C24C22×Q812yes—
673C24C22×Q812yes—
674C24C2×#4112yes—
675C24C2×#4112yes—
676C24H(5,𝔽2)12yes—
677C24H(5,𝔽2)12yes—
678C24H(5,𝔽2)12yes—
679C242−1+412yes—
680C242−1+412yes—
681C242−1+412yes—
682C24C2511yescharacteristic
683C2×Q8—48no—
684C2×Q8—48no—
685C2×Q8—84no—
686C2×Q8—84no—
687C2×Q8—84no—
688C2×Q8—84no—
689C2×Q8—84no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—28no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
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—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—4128no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—84no—
860C22×C4—84no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4C22⋊Q8116yes—
866C22×C4C22⋊Q8116yescomplemented
867C22×C4C22×D414yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D414yes—
871C22×C4C22×D412yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×Q812yes—
878C22×C4C22×Q812yes—
879C22×C4C22×Q812yes—
880C22×C4C22×Q812yes—
881C22×C4C2×#4112yes—
882C22×C4C2×#4112yes—
883C22×C4C2×#4112yes—
884C22×C4C2×#4112yes—
885C22×C4H(5,𝔽2)12yes—
886C22×C4H(5,𝔽2)12yes—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—84no—
906C4⋊C4—84no—
907C4⋊C4—84no—
908C4⋊C4—84no—
909C4⋊C4—84no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—44no—
927C22⋊C4—48no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C42—28no—
933C42—28no—
934C42—44no—
935C42—44no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—232no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—416no—
1002C23—416no—
1003C23—416no—
1004C23—416no—
1005C23—416no—
1006C23—416no—
1007C23—416no—
1008C23—416no—
1009C23—416no—
1010C23—416no—
1011C23—416no—
1012C23—416no—
1013C23—416no—
1014C23—416no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23C2×C22⋊Q814yes—
1048C23C2×C22⋊Q814yes—
1049C23#53514yes—
1050C23#53614yes—
1051C23#54214yes—
1052C23#54214yes—
1053C23#54414yes—
1054C23#54414yes—
1055C23#54414yes—
1056C23C23×D411yescharacteristic
1057C23C23×D411yescharacteristic
1058C23C23×Q811yescharacteristic
1059C23C22×#4111yescharacteristic
1060C23C22×#4111yescharacteristic
1061C23C2×H(5,𝔽2)11yescharacteristic
1062C23C2×H(5,𝔽2)11yescharacteristic
1063C23C2×H(5,𝔽2)11yescharacteristic
1064C23C2×H(5,𝔽2)11yescharacteristic
1065C23C2×H(5,𝔽2)11yescharacteristic
1066C23C2×2−1+411yescharacteristic
1067C23C2×2−1+411yescharacteristic
1068C23C2×2−1+411yescharacteristic
1069C23#58511yescharacteristic
1070C23#58511yescharacteristic
1071Q8—816no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—232no—
1085C2×C4—232no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—416no—
1108C2×C4—416no—
1109C2×C4—416no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—42no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—416no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—816no—
1210C2×C4—816no—
1211C2×C4C2×C22⋊Q814yes—
1212C2×C4C2×C22⋊Q814yes—
1213C2×C4C2×C22⋊Q814yes—
1214C2×C4C2×C22⋊Q814yes—
1215C2×C4#54314yes—
1216C2×C4D4214yes—
1217C2×C4#54614yes—
1218C2×C4#54614yes—
1219C2×C4#55114yes—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—24no—
1229C22—24no—
1230C22—24no—
1231C22—24no—
1232C22—24no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—464no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22#262818yescomplemented
1266C22C22×C22⋊Q811yescharacteristic
1267C22C22×C22⋊Q811yescharacteristic
1268C22C2×#53511yescharacteristic
1269C22C2×#53611yescharacteristic
1270C22C2×#54211yescharacteristic
1271C22C2×#54211yescharacteristic
1272C22C2×#54311yescharacteristic
1273C22C2×#54411yescharacteristic
1274C22C2×#54411yescharacteristic
1275C22C2×#54411yescharacteristic
1276C22#345811yescharacteristic
1277C22C2×D4211yescharacteristic
1278C22C2×#54611yescharacteristic
1279C22C2×#54611yescharacteristic
1280C22C2×#55111yescharacteristic
1281C22#348411yescharacteristic
1282C22#348611yescharacteristic
1283C22#348811yescharacteristic
1284C22#348811yescharacteristic
1285C22#348911yescharacteristic
1286C22#348911yescharacteristic
1287C22#349211yescharacteristic
1288C22#349211yescharacteristic
1289C22#349411yescharacteristic
1290C22#349411yescharacteristic
1291C22#349511yescharacteristic
1292C22#349511yescharacteristic
1293C22#353611yescharacteristic
1294C22#353611yescharacteristic
1295C22#353711yescharacteristic
1296C22#353811yescharacteristic
1297C22#354111yescharacteristic
1298C22#354111yescharacteristic
1299C22#354211yescharacteristic
1300C22#354211yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—44no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—81no—
1311C4—82no—
1312C4—82no—
1313C4—81no—
1314C4—82no—
1315C4—82no—
1316C4—81no—
1317C4—82no—
1318C4—81no—
1319C4—82no—
1320C4#243718yes—
1321C2—28no—
1322C2—44no—
1323C2—44no—
1324C2C2×#262811yescharacteristic
1325C2C2×#243711yescharacteristic
1326C2#3522411yescharacteristic
1327C2#3525311yescharacteristic
1328C2#3525311yescharacteristic
1329C2#3747611yescharacteristic
1330C2#3747711yescharacteristic
1331C2#3765011yescharacteristic
1332C2#3765111yescharacteristic
1333C2#3766411yescharacteristic
1334C2#3766511yescharacteristic
1335C2#3783811yescharacteristic
1336C2#3783911yescharacteristic
1337C2#3785211yescharacteristic
1338C2#3785311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2440C2semidirect
2. C2×#2628C2semidirect
5. #16304C2semidirect
6. #16303C2semidirect
7. #16300C2semidirect
8. #16299C2semidirect
9. #15220C2semidirect
10. #15220C2semidirect
11. #15135C2semidirect
12. #15125C2semidirect
13. #14767C2semidirect
14. #14758C2semidirect
18. #14340C2semidirect
19. #14264C2semidirect
20. #14264C2semidirect
21. #14130C2semidirect
22. #13907C2semidirect
23. #13881C2semidirect
25. C22×C4⋊Q8C22semidirect
34. C2×#400C22semidirect
37. C2×#398C22semidirect
38. C2×#395C22semidirect
39. C2×#395C22semidirect
42. C2×#389C22semidirect
43. C2×#389C22semidirect
44. C2×#389C22semidirect
45. C2×#389C22semidirect
46. C2×#389C22semidirect
47. C2×#389C22semidirect
50. C2×#384C22semidirect
51. C2×#382C22semidirect
52. C2×#382C22semidirect
82. #1446C22semidirect
83. #1445C22semidirect
84. #1444C22semidirect
85. #1444C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1443C22semidirect
89. #1443C22semidirect
90. #1442C22semidirect
91. #1442C22semidirect
92. #1442C22semidirect
93. #1442C22semidirect
94. #1442C22semidirect
95. #1442C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
100. #1441C22semidirect
101. #1441C22semidirect
114. C4⋊#95C22semidirect
115. C4⋊#95C22semidirect
116. C4⋊#95C22semidirect
117. C4⋊#95C22semidirect
118. C4⋊#95C22semidirect
119. C4⋊#95C22semidirect
135. C24×C4Q8semidirect
866. C22×C4C22⋊Q8semidirect
1265. C22#2628semidirect

Maximal subgroups

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

subgroupindex
C2×#24402
C2×#26282
C2×#22802
C22×#3802
#163042
#163032
#163002
#162992
#152202
#151352
#151252
#147672
#147582
#147342
#147172
#146802
#143402
#142642
#141302
#139072
#138812