Finite Group Databasebeta

← #754832

Subgroups — #754832

Order 512.

4396 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2561C211yesmaximal, characteristic, complemented
2C2×#2404C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic, complemented
4C2×#2638C211yesmaximal, characteristic, complemented
5C2×#2388C211yesmaximal, characteristic, complemented
6C2×#2321C211yesmaximal, characteristic, complemented
7#16812C211yesmaximal, characteristic, complemented
8#16810C211yesmaximal, characteristic, complemented
9#16511C211yesmaximal, characteristic, complemented
10#16509C211yesmaximal, characteristic, complemented
11#15561C212yesmaximal, complemented
12#15549C212yesmaximal, complemented
13#15283C212yesmaximal, complemented
14#15267C212yesmaximal, complemented
15#15167C211yesmaximal, characteristic, complemented
16#15144C211yesmaximal, characteristic, complemented
17#15007C211yesmaximal, characteristic, complemented
18#14985C212yesmaximal, complemented
19#14928C211yesmaximal, characteristic, complemented
20#14796C212yesmaximal, complemented
21#14189C212yesmaximal, complemented
22#14084C212yesmaximal, complemented
23#13807C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic, complemented
26C22×#124C2211yescharacteristic, complemented
27C22×C22⋊Q8C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×#120C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2212yescomplemented
32C23×C22⋊C4C2211yescharacteristic
33#2638—28no—
34#2561—28no—
35#2432—28no—
36#2404—28no—
37C2×#399C2212yes—
38C2×#398C2211yescharacteristic, complemented
39C2×#397C2212yes—
40C2×#397C2211yescharacteristic
41C2×#397C2211yescharacteristic
42C2×#397C2211yescharacteristic, complemented
43#2388—28no—
44C2×#395C2211yescharacteristic, complemented
45C2×#395C2211yescharacteristic, complemented
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2211yescharacteristic, complemented
51C2×#393C2211yescharacteristic
52C2×#393C2211yescharacteristic
53C2×#393C2211yescharacteristic
54C2×#393C2211yescharacteristic
55C2×#393C2211yescharacteristic, complemented
56C2×#393C2211yescharacteristic, complemented
57C2×#392C2211yescharacteristic
58C2×#392C2212yes—
59C2×#392C2211yescharacteristic
60C2×#392C2212yes—
61C2×#392C2212yes—
62C2×#392C2211yescharacteristic, complemented
63#2321—28no—
64C2×#391C2211yescharacteristic, complemented
65C2×#390C2212yes—
66C2×#390C2211yescharacteristic
67C2×#390C2211yescharacteristic
68C2×#390C2212yes—
69C2×#390C2212yes—
70C2×#390C2211yescharacteristic, complemented
71C2×#388C2211yescharacteristic
72C2×#388C2212yes—
73C2×#388C2211yescharacteristic
74C2×#388C2211yescharacteristic
75C2×#388C2211yescharacteristic
76C2×#388C2212yes—
77C2×#387C2212yescomplemented
78C2×#386C2212yes—
79C2×#386C2211yescharacteristic
80C2×#386C2211yescharacteristic
81C2×#386C2211yescharacteristic
82C2×#386C2212yes—
83C2×#386C2212yes—
84C2×#385C2211yescharacteristic
85C2×#385C2212yescomplemented
86C2×#385C2212yescomplemented
87C2×#385C2212yescomplemented
88C2×#381C2212yes—
89C2×#381C2211yescharacteristic
90C2×#379C2211yescharacteristic
91C2×#379C2212yes—
92C2×C4×C22⋊C4C2211yescharacteristic
93C2×C4×C22⋊C4C2211yescharacteristic
94C2×C4×C22⋊C4C2212yescomplemented
95#1445C2212yescomplemented
96#1445C2212yescomplemented
97#1445C2212yescomplemented
98#1445C2212yescomplemented
99#1444C2212yescomplemented
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1437C2212yes—
117#1437C2212yes—
118#1437C2212yes—
119#1437C2212yescomplemented
120#1437C2212yescomplemented
121#1437C2212yescomplemented
122C4⋊#95C2212yescomplemented
123#1434C2211yescharacteristic, complemented
124#1434C2211yescharacteristic, complemented
125#1434C2212yescomplemented
126C4×#95C2212yescomplemented
127C4×#95C2211yescharacteristic, complemented
128C4×#95C2211yescharacteristic, complemented
129C26C2311yescharacteristic
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—44no—
134C22×#41—44no—
135C23×Q8C2311yescharacteristic
136C23×Q8C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C23×D4C2312yes—
143C23×D4C2312yes—
144C23×D4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C2×C4⋊Q8—24no—
150C2×C4⋊Q8—44no—
151C2×#124—24no—
152C2×#124—44no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—24no—
156C2×#120—24no—
157C2×#120—24no—
158C2×#120—28no—
159C2×#120—24no—
160C2×#120—44no—
161C2×#120—44no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—28no—
166C2×C4×D4—44no—
167C2×C4×D4—44no—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224#399—44no—
225#398—24no—
226#397—28no—
227#397—24no—
228#397—24no—
229#397—24no—
230#395—24no—
231#395—24no—
232#394—28no—
233#394—28no—
234#394—28no—
235#394—28no—
236#394—24no—
237#393—24no—
238#393—24no—
239#393—24no—
240#393—24no—
241#393—24no—
242#393—24no—
243#392—28no—
244#392—28no—
245#392—24no—
246#392—24no—
247#392—24no—
248#392—44no—
249#391—24no—
250#390—28no—
251#390—24no—
252#390—24no—
253#390—24no—
254#390—44no—
255#390—44no—
256#388—28no—
257#388—28no—
258#388—24no—
259#388—24no—
260#388—24no—
261#388—24no—
262#387—28no—
263#386—24no—
264#386—28no—
265#386—24no—
266#386—24no—
267#386—28no—
268#386—28no—
269#385—24no—
270#385—28no—
271#385—28no—
272#385—28no—
273#381—28no—
274#381D418yescomplemented
275#379—28no—
276#379—24no—
277C4×C22⋊C4—28no—
278C4×C22⋊C4D418yescomplemented
279C4×C22⋊C4D418yescomplemented
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×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2312yes—
310C2×#95C2311yescharacteristic
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—41no—
317C25—41no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25C2411yescharacteristic
323C25C2411yescharacteristic
324C25C2411yescharacteristic
325C25C2412yes—
326C25C2411yescharacteristic
327C2×#41—432no—
328C2×#41—432no—
329C2×#41—416no—
330C2×#41—416no—
331C2×#41—416no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—24no—
339C22×Q8—42no—
340C22×Q8—42no—
341C22×Q8—42no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—24no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—41no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4#4114yescomplemented
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4C2×D414yes—
412C23×C4C2×D414yes—
413C23×C4C2×D414yes—
414C23×C4C2412yes—
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C4⋊Q8—416no—
433#124—416no—
434C22⋊Q8—416no—
435#120—232no—
436#120—432no—
437C4×D4—432no—
438C4×D4—416no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
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—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
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—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
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⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—416no—
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⋊C4C2×D414yes—
569C2×C22⋊C4C2×D418yes—
570C2×C22⋊C4C2×D418yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4#4114yescomplemented
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—24no—
577C2×C42—42no—
578C2×C42—42no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42C2×D418yes—
587C2×C42C2×D414yes—
588C2×C42C2×D414yes—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—22no—
596#95—22no—
597#95—24no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95—22no—
603#95—22no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95C2×D414yes—
614#95C2×D414yes—
615#95C2×D414yes—
616#95C2×D414yes—
617#95C2×D418yes—
618#95C2×D414yes—
619#95C2×D414yes—
620C24—21no—
621C24—21no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—21no—
628C24—28no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—21no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—21no—
660C24—21no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24—22no—
673C24—44no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—48no—
679C24—48no—
680C24—44no—
681C24—84no—
682C24—82no—
683C24—82no—
684C24—82no—
685C24—82no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24C22×D412yes—
696C24C22×D412yes—
697C24C22×D412yes—
698C24C2×#4112yes—
699C24C2×#4112yes—
700C24C2×#4112yes—
701C24H(5,𝔽2)14yes—
702C24C2511yescharacteristic
703#41—4128no—
704C2×Q8—28no—
705C2×Q8—48no—
706C2×Q8—48no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—44no—
711C2×Q8—44no—
712C2×Q8—84no—
713C2×Q8—84no—
714C2×D4—28no—
715C2×D4—216no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—48no—
720C2×D4—44no—
721C2×D4—48no—
722C2×D4—44no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—44no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—44no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—44no—
749C2×D4—82no—
750C2×D4—82no—
751C2×D4—84no—
752C2×D4—82no—
753C2×D4—84no—
754C2×D4—84no—
755C2×D4—82no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—216no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
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—21no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—48no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—82no—
868C22×C4—82no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—82no—
872C22×C4—82no—
873C22×C4#127116yes—
874C22×C4C22×D414yes—
875C22×C4C22×D414yes—
876C22×C4C22×D414yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D414yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C2×#4112yes—
889C22×C4C2×#4112yes—
890C22×C4C2×#4112yes—
891C22×C4H(5,𝔽2)14yes—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—82no—
900C4⋊C4—84no—
901C4⋊C4—82no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—82no—
929C22⋊C4—84no—
930C22⋊C4—82no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—82no—
934C22⋊C4—82no—
935C22⋊C4—82no—
936C22⋊C4—82no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C42—48no—
940C42—44no—
941C42—44no—
942C42—44no—
943C42—84no—
944C42—84no—
945C23—22no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—416no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—41no—
998C23—42no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—41no—
1007C23—41no—
1008C23—42no—
1009C23—42no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—41no—
1019C23—41no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—41no—
1034C23—42no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—42no—
1039C23—41no—
1040C23—42no—
1041C23—41no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—88no—
1073C23—88no—
1074C23—88no—
1075C23—88no—
1076C23—816no—
1077C23—816no—
1078C23—816no—
1079C23—816no—
1080C23—88no—
1081C23—88no—
1082C23C2×#12714yes—
1083C23C23×D411yescharacteristic
1084C23C23×D411yescharacteristic
1085C23C23×D411yescharacteristic
1086C23C22×#4111yescharacteristic
1087C23C22×#4111yescharacteristic
1088C23C2×H(5,𝔽2)12yes—
1089C23C2×H(5,𝔽2)12yes—
1090C23#58511yescharacteristic
1091C23#58511yescharacteristic
1092C23#58512yes—
1093C23#58512yes—
1094Q8—416no—
1095Q8—88no—
1096D4—416no—
1097D4—416no—
1098D4—432no—
1099D4—432no—
1100D4—88no—
1101D4—88no—
1102D4—816no—
1103D4—816no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—416no—
1144C2×C4—432no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—88no—
1210C2×C4—88no—
1211C2×C4#52514yes—
1212C2×C4C2×#12714yes—
1213C2×C4C2×#12714yes—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—44no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—44no—
1222C22—42no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—44no—
1237C22—44no—
1238C22—42no—
1239C22—42no—
1240C22—44no—
1241C22—42no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—832no—
1248C22—82no—
1249C22—82no—
1250C22—81no—
1251C22—82no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—82no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22C2×#52511yescharacteristic
1275C22C22×#12711yescharacteristic
1276C22#344912yes—
1277C22#344911yescharacteristic
1278C22D4×#4111yescharacteristic
1279C22D4×#4111yescharacteristic
1280C22D4×#4111yescharacteristic
1281C22D4×#4111yescharacteristic
1282C22#348412yes—
1283C22#348411yescharacteristic
1284C22#348411yescharacteristic
1285C22#348412yes—
1286C22#349412yes—
1287C22#350012yes—
1288C22#350011yescharacteristic
1289C22#350011yescharacteristic
1290C22#350512yes—
1291C22#351312yes—
1292C22#351412yes—
1293C22#353312yes—
1294C22#354012yes—
1295C22#356012yes—
1296C22#356212yes—
1297C4—24no—
1298C4—24no—
1299C4—24no—
1300C4—44no—
1301C4—42no—
1302C4—42no—
1303C4—44no—
1304C4—42no—
1305C4—44no—
1306C4—42no—
1307C4—44no—
1308C4—44no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—82no—
1314C4—82no—
1315C2—44no—
1316C2—84no—
1317C2—82no—
1318C2—82no—
1319C2—82no—
1320C2#3493611yescharacteristic
1321C2#3532911yescharacteristic
1322C2#3539011yescharacteristic
1323C2#3570311yescharacteristic
1324C2#3573011yescharacteristic
1325C2#3837212yes—
1326C2#3986912yes—
1327C2#4050011yescharacteristic
1328C2#4050711yescharacteristic
1329C2#4300812yes—
1330C2#4389812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2561C2semidirect
2. C2×#2404C2semidirect
3. C2×#2432C2semidirect
4. C2×#2638C2semidirect
5. C2×#2388C2semidirect
6. C2×#2321C2semidirect
7. #16812C2semidirect
8. #16810C2semidirect
9. #16511C2semidirect
10. #16509C2semidirect
11. #15561C2semidirect
12. #15549C2semidirect
13. #15283C2semidirect
14. #15267C2semidirect
15. #15167C2semidirect
16. #15144C2semidirect
17. #15007C2semidirect
18. #14985C2semidirect
19. #14928C2semidirect
20. #14796C2semidirect
21. #14189C2semidirect
22. #14084C2semidirect
23. #13807C2semidirect
25. C22×C4⋊Q8C22semidirect
26. C22×#124C22semidirect
31. C22×C4×D4C22semidirect
38. C2×#398C22semidirect
42. C2×#397C22semidirect
44. C2×#395C22semidirect
45. C2×#395C22semidirect
50. C2×#394C22semidirect
55. C2×#393C22semidirect
56. C2×#393C22semidirect
62. C2×#392C22semidirect
64. C2×#391C22semidirect
70. C2×#390C22semidirect
77. C2×#387C22semidirect
85. C2×#385C22semidirect
86. C2×#385C22semidirect
87. C2×#385C22semidirect
94. C2×C4×C22⋊C4C22semidirect
95. #1445C22semidirect
96. #1445C22semidirect
97. #1445C22semidirect
98. #1445C22semidirect
99. #1444C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
119. #1437C22semidirect
120. #1437C22semidirect
121. #1437C22semidirect
122. C4⋊#95C22semidirect
123. #1434C22semidirect
124. #1434C22semidirect
125. #1434C22semidirect
126. C4×#95C22semidirect
127. C4×#95C22semidirect
128. C4×#95C22semidirect
274. #381D4semidirect
278. C4×C22⋊C4D4semidirect
279. C4×C22⋊C4D4semidirect
391. C22×D4#41semidirect
572. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25612
C2×#24042
C2×#24322
C2×#26382
C2×#23882
C2×#23212
#168122
#168102
#165112
#165092
#155612
#155492
#152832
#152672
#151672
#151442
#150072
#149852
#149282
#147962
#141892
#140842
#138072