Finite Group Databasebeta

← #729349

Subgroups — #729349

Order 512.

3646 conjugacy classes of subgroups.

The subgroup lattice has 1333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×#2592C211yesmaximal, characteristic, complemented
3C2×#2544C211yesmaximal, characteristic, complemented
4C2×#2620C211yesmaximal, characteristic, complemented
5C2×#2396C211yesmaximal, characteristic, complemented
6C2×#2324C211yesmaximal, characteristic, complemented
7#17015C212yesmaximal, complemented
8#16801C212yesmaximal, complemented
9#15526C212yesmaximal, complemented
10#15493C212yesmaximal, complemented
11#15453C212yesmaximal, complemented
12#15325C212yesmaximal, complemented
13#15215C211yesmaximal, characteristic, complemented
14#15193C211yesmaximal, characteristic, complemented
15#15163C212yesmaximal, complemented
16#15148C211yesmaximal, characteristic, complemented
17#15124C211yesmaximal, characteristic
18#14815C212yesmaximal, complemented
19#14154C211yesmaximal, characteristic, complemented
20#14153C211yesmaximal, characteristic, complemented
21#13998C211yesmaximal, characteristic, complemented
22#13997C211yesmaximal, characteristic, complemented
23C4⋊C42C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2212yes—
29C22×#121C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×#117C2211yescharacteristic
34#2620—28no—
35#2592—28no—
36#2544—28no—
37#2538—28no—
38#2396—28no—
39C2×#400C2211yescharacteristic
40C2×#399C2211yescharacteristic
41C2×#399C2212yes—
42C2×#398C2211yescharacteristic
43C2×#398C2211yescharacteristic
44C2×#397C2212yes—
45C2×#396C2212yes—
46C2×#396C2212yes—
47C2×#396C2212yes—
48C2×#396C2212yes—
49C2×#396C2211yescharacteristic
50C2×#396C2211yescharacteristic
51C2×#395C2211yescharacteristic
52C2×#394C2212yes—
53C2×#394C2212yes—
54C2×#394C2212yes—
55C2×#394C2212yes—
56C2×#393C2212yes—
57C2×#393C2211yescharacteristic
58C2×#392C2212yes—
59C2×#392C2212yes—
60#2324—28no—
61C2×#391C2211yescharacteristic
62C2×#391C2211yescharacteristic
63C2×#391C2211yescharacteristic
64C2×#391C2211yescharacteristic
65C2×#390C2211yescharacteristic
66C2×#390C2212yes—
67C2×#390C2211yescharacteristic
68C2×#390C2211yescharacteristic
69C2×#390C2211yescharacteristic
70C2×#390C2211yescharacteristic
71C2×#390C2211yescharacteristic
72C2×#390C2211yescharacteristic
73C2×#390C2212yes—
74C2×#390C2212yes—
75C2×#390C2212yes—
76C2×#389C2211yescharacteristic
77C2×#389C2211yescharacteristic
78C2×#389C2211yescharacteristic
79C2×#388C2212yes—
80C2×#388C2212yes—
81C2×#388C2212yes—
82C2×#386C2212yes—
83C2×#386C2212yes—
84C2×#386C2212yes—
85C2×#385C2212yes—
86C2×#384C2211yescharacteristic
87C2×#380C2211yescharacteristic
88C2×#380C2212yes—
89C2×C4×C4⋊C4C2211yescharacteristic
90C2×C4×C4⋊C4C2211yescharacteristic
91C2×C4×C4⋊C4C2212yes—
92C2×C4×C4⋊C4C2211yescharacteristic
93C2×C4×C4⋊C4C2211yescharacteristic
94C2×C4×C4⋊C4C2211yescharacteristic
95C2×C4×C4⋊C4C2211yescharacteristic
96C2×C4×C22⋊C4C2211yescharacteristic
97C2×C4×C22⋊C4C2211yescharacteristic
98#1445C2212yes—
99#1445C2212yes—
100#1445C2212yes—
101#1445C2212yes—
102#1444C2212yes—
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yes—
109#1439C2212yes—
110#1439C2212yes—
111#1439C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yes—
117#1438C2212yes—
118#1438C2212yes—
119#1437C2212yes—
120#1437C2212yes—
121#1437C2212yes—
122#1437C2212yes—
123#1436C2212yes—
124#1436C2212yes—
125C4⋊#95C2211yescharacteristic
126C4⋊#95C2211yescharacteristic
127C4⋊#95C2212yes—
128C4⋊#95C2212yes—
129C23×Q8C2311yescharacteristic
130C23×Q8C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139C2×#127—24no—
140C2×#127—24no—
141C2×#127—42no—
142C2×#124—24no—
143C2×#124—24no—
144C2×#124—24no—
145C2×#124—24no—
146C2×#124—24no—
147C2×#124—42no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—28no—
151C2×C22⋊Q8—44no—
152C2×C22⋊Q8—44no—
153C2×C22⋊Q8—42no—
154C2×#121—24no—
155C2×#121—24no—
156C2×#121—24no—
157C2×#121—24no—
158C2×#121—24no—
159C2×#121—42no—
160C2×C4×Q8—24no—
161C2×C4×Q8—24no—
162C2×C4×Q8—24no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—24no—
166C2×#117—24no—
167C2×#117—24no—
168C2×#117—24no—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2312yes—
226C22×C42C2312yes—
227C22×C42C2312yes—
228C22×C42C2311yescharacteristic
229#400—24no—
230#399—24no—
231#399—44no—
232#398—24no—
233#398—24no—
234#397—28no—
235#396—28no—
236#396—28no—
237#396—24no—
238#396—24no—
239#396—28no—
240#396—28no—
241#395—24no—
242#394—28no—
243#394—28no—
244#394—28no—
245#394—28no—
246#393—28no—
247#393—24no—
248#392—44no—
249#392—44no—
250#391—24no—
251#391—24no—
252#391—24no—
253#391—24no—
254#390—24no—
255#390—24no—
256#390—24no—
257#390—24no—
258#390—24no—
259#390—24no—
260#390—28no—
261#390—24no—
262#390—44no—
263#390—44no—
264#390—44no—
265#389—24no—
266#389—24no—
267#389—24no—
268#388—28no—
269#388—28no—
270#388—28no—
271#386—28no—
272#386—28no—
273#386—28no—
274#385—28no—
275#384D418yescomplemented
276#380—24no—
277#380—28no—
278C4×C4⋊C4—24no—
279C4×C4⋊C4—24no—
280C4×C4⋊C4—44no—
281C4×C4⋊C4—42no—
282C4×C4⋊C4—42no—
283C4×C4⋊C4D418yescomplemented
284C4×C4⋊C4D418yescomplemented
285C4×C22⋊C4—24no—
286C4×C22⋊C4—24no—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C25C2412yes—
317C25C2411yescharacteristic
318C25C2412yes—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—41no—
332C22×Q8—41no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4#4114yes—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4#4114yes—
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2412yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2412yes—
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409#127—416no—
410#124—416no—
411#124—416no—
412C22⋊Q8—416no—
413C22⋊Q8—432no—
414#121—232no—
415#121—416no—
416C4×Q8—416no—
417C4×D4—416no—
418#117—416no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
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—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
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—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4—41no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—41no—
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⋊C4C2×D414yes—
478C2×C4⋊C4C2×D414yes—
479C2×C4⋊C4C2×D414yes—
480C2×C4⋊C4C2×D414yes—
481C2×C4⋊C4C2×D414yes—
482C2×C4⋊C4C2×D418yes—
483C2×C4⋊C4C2×D414yes—
484C2×C4⋊C4C2×D418yes—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
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—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—41no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—24no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42—42no—
589C2×C42—42no—
590C2×C42—42no—
591C2×C42—42no—
592C2×C42—42no—
593C2×C42C2×D414yes—
594C2×C42C2×D414yes—
595C2×C42C2×D418yes—
596C2×C42C2×D414yes—
597C2×C42C2×D414yes—
598C2×C42C2×D414yes—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95C2×D418yes—
626#95C2×D414yes—
627#95C2×D414yes—
628C24—21no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—22no—
637C24—21no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—21no—
643C24—22no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—21no—
649C24—22no—
650C24—22no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24C2×#4114yes—
672C24C2×#4112yes—
673C24C2511yescharacteristic
674C2×Q8—28no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×D4—216no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—84no—
712C2×D4—84no—
713C2×D4—84no—
714C2×D4—84no—
715C2×D4—84no—
716C2×D4—84no—
717C2×D4—84no—
718C2×D4—84no—
719C2×D4—84no—
720C2×D4—84no—
721C2×D4—84no—
722C2×D4—84no—
723C2×D4—84no—
724C2×D4—84no—
725C2×D4—84no—
726C2×D4—84no—
727C2×D4—84no—
728C2×D4—84no—
729C2×D4—84no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—22no—
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—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—22no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C22×D414yes—
861C22×C4C22×D414yes—
862C22×C4C22×D414yes—
863C22×C4C22×D412yes—
864C22×C4C22×D414yes—
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C22×D412yes—
875C22×C4C2×#4112yes—
876C22×C4C2×#4112yes—
877C22×C4C2×#4112yes—
878C22×C4H(5,𝔽2)12yes—
879C22×C4H(5,𝔽2)12yes—
880C22×C4H(5,𝔽2)12yes—
881C22×C4H(5,𝔽2)12yes—
882C22×C42−1+412yes—
883C22×C42−1+412yes—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—84no—
906C22⋊C4—216no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C42—28no—
936C42—28no—
937C42—48no—
938C42—44no—
939C42—44no—
940C42—44no—
941C42—84no—
942C42—84no—
943C42#127116yes—
944C23—24no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—22no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—41no—
959C23—42no—
960C23—41no—
961C23—41no—
962C23—42no—
963C23—42no—
964C23—41no—
965C23—42no—
966C23—41no—
967C23—42no—
968C23—41no—
969C23—42no—
970C23—42no—
971C23—41no—
972C23—42no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—41no—
982C23—42no—
983C23—42no—
984C23—41no—
985C23—41no—
986C23—42no—
987C23—41no—
988C23—41no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—42no—
1000C23—41no—
1001C23—42no—
1002C23—41no—
1003C23—42no—
1004C23—41no—
1005C23—41no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—42no—
1010C23—42no—
1011C23—41no—
1012C23—42no—
1013C23—41no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23C23×D411yescharacteristic
1050C23C23×D411yescharacteristic
1051C23C23×D411yescharacteristic
1052C23C22×#4111yescharacteristic
1053C23C22×#4111yescharacteristic
1054C23C2×H(5,𝔽2)11yescharacteristic
1055C23C2×H(5,𝔽2)11yescharacteristic
1056C23C2×H(5,𝔽2)11yescharacteristic
1057C23C2×H(5,𝔽2)11yescharacteristic
1058C23C2×2−1+411yescharacteristic
1059C23C2×2−1+411yescharacteristic
1060C23#58511yescharacteristic
1061C23#58511yescharacteristic
1062C23#58511yescharacteristic
1063C23#58511yescharacteristic
1064Q8—416no—
1065Q8—88no—
1066D4—416no—
1067D4—816no—
1068D4—816no—
1069D4—816no—
1070D4—816no—
1071D4—88no—
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—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—416no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—816no—
1204C2×C4#52514yes—
1205C2×C4C2×#12714yes—
1206C2×C4C2×#12714yes—
1207C2×C4C2×#12714yes—
1208C2×C4#53714yes—
1209C2×C4#53714yes—
1210C2×C4#54614yes—
1211C2×C4#54614yes—
1212C2×C4#54814yes—
1213C2×C4#54814yes—
1214C22—42no—
1215C22—42no—
1216C22—44no—
1217C22—42no—
1218C22—44no—
1219C22—42no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—42no—
1224C22—44no—
1225C22—42no—
1226C22—42no—
1227C22—44no—
1228C22—82no—
1229C22—82no—
1230C22—81no—
1231C22—82no—
1232C22—81no—
1233C22—82no—
1234C22—81no—
1235C22—81no—
1236C22—82no—
1237C22—81no—
1238C22—81no—
1239C22—82no—
1240C22—81no—
1241C22—82no—
1242C22—82no—
1243C22—81no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22C2×#52511yescharacteristic
1260C22C22×#12711yescharacteristic
1261C22C2×#53711yescharacteristic
1262C22C2×#53711yescharacteristic
1263C22#344911yescharacteristic
1264C22C2×#54611yescharacteristic
1265C22C2×#54611yescharacteristic
1266C22C2×#54811yescharacteristic
1267C22C2×#54811yescharacteristic
1268C22#348411yescharacteristic
1269C22#348711yescharacteristic
1270C22#348811yescharacteristic
1271C22#348811yescharacteristic
1272C22#348811yescharacteristic
1273C22#348811yescharacteristic
1274C22#349611yescharacteristic
1275C22#349611yescharacteristic
1276C22#349711yescharacteristic
1277C22#349711yescharacteristic
1278C22#350611yescharacteristic
1279C22#350711yescharacteristic
1280C22#350811yescharacteristic
1281C22#351011yescharacteristic
1282C22#351311yescharacteristic
1283C22#351411yescharacteristic
1284C22#352011yescharacteristic
1285C22#352111yescharacteristic
1286C22#354311yescharacteristic
1287C22#354611yescharacteristic
1288C22#355011yescharacteristic
1289C22#355411yescharacteristic
1290C22#355411yescharacteristic
1291C22#355711yescharacteristic
1292C22#356111yescharacteristic
1293C22#356211yescharacteristic
1294C4—24no—
1295C4—24no—
1296C4—24no—
1297C4—42no—
1298C4—44no—
1299C4—44no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—44no—
1304C4—44no—
1305C4—42no—
1306C4—42no—
1307C4—82no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—82no—
1313C4#254018yes—
1314C2—82no—
1315C2—84no—
1316C2—162no—
1317C2C2×#254011yescharacteristic
1318C2#3516611yescharacteristic
1319C2#3556511yescharacteristic
1320C2#3578711yescharacteristic
1321C2#3580811yescharacteristic
1322C2#3802411yescharacteristic
1323C2#3803411yescharacteristic
1324C2#3971811yescharacteristic
1325C2#3972611yescharacteristic
1326C2#4244411yescharacteristic
1327C2#4279911yescharacteristic
1328C2#4487611yescharacteristic
1329C2#4488311yescharacteristic
1330C2#4511111yescharacteristic
1331C2#4524011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#15124C2
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×#2538C2semidirect
2. C2×#2592C2semidirect
3. C2×#2544C2semidirect
4. C2×#2620C2semidirect
5. C2×#2396C2semidirect
6. C2×#2324C2semidirect
7. #17015C2semidirect
8. #16801C2semidirect
9. #15526C2semidirect
10. #15493C2semidirect
11. #15453C2semidirect
12. #15325C2semidirect
13. #15215C2semidirect
14. #15193C2semidirect
15. #15163C2semidirect
16. #15148C2semidirect
18. #14815C2semidirect
19. #14154C2semidirect
20. #14153C2semidirect
21. #13998C2semidirect
22. #13997C2semidirect
23. C4⋊C42C2semidirect
275. #384D4semidirect
283. C4×C4⋊C4D4semidirect
284. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#25922
C2×#25442
C2×#26202
C2×#23962
C2×#23242
#170152
#168012
#155262
#154932
#154532
#153252
#152152
#151932
#151632
#151482
#151242
#148152
#141542
#141532
#139982
#139972
C4⋊C422