Finite Group Databasebeta

← #648532

Subgroups — #648532

Order 512.

4955 conjugacy classes of subgroups.

The subgroup lattice has 1337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2539C211yesmaximal, characteristic
2C2×#2413C211yesmaximal, characteristic, complemented
3C2×#2411C211yesmaximal, characteristic, complemented
4C2×#2425C211yesmaximal, characteristic, complemented
5C2×C4×#120C211yesmaximal, characteristic, complemented
6C22×#380C211yesmaximal, characteristic, complemented
7#15479C212yesmaximal, complemented
8#15309C212yesmaximal, complemented
9#15307C212yesmaximal, complemented
10#15294C212yesmaximal, complemented
11#15069C211yesmaximal, characteristic, complemented
12#14918C211yesmaximal, characteristic, complemented
13#14911C211yesmaximal, characteristic, complemented
14#14771C212yesmaximal, complemented
15#14732C212yesmaximal, complemented
16#14719C211yesmaximal, characteristic, complemented
17#14694C211yesmaximal, characteristic, complemented
18#14043C211yesmaximal, characteristic, complemented
19#14012C212yesmaximal, complemented
20#13996C211yesmaximal, characteristic, complemented
21#13968C211yesmaximal, characteristic, complemented
22#13920C212yesmaximal, complemented
23#13799C211yesmaximal, characteristic, complemented
24C25×C4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#123C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C22×#120C2211yescharacteristic
32C22×C4×D4C2212yes—
33C22×C4×D4C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39#2539—28no—
40#2425—28no—
41#2413—28no—
42#2411—28no—
43C2×#399C2212yes—
44C2×#398C2211yescharacteristic, complemented
45C2×#398C2212yescomplemented
46C2×#397C2211yescharacteristic, complemented
47C2×#396C2212yes—
48C2×#396C2211yescharacteristic, complemented
49C2×#396C2212yescomplemented
50C2×#394C2212yes—
51C2×#394C2211yescharacteristic, complemented
52C2×#394C2212yescomplemented
53C2×#392C2212yes—
54C4×#120—28no—
55C2×#390C2212yes—
56C2×#390C2212yes—
57C2×#390C2212yes—
58C2×#389C2212yescomplemented
59C2×#389C2211yescharacteristic, complemented
60C2×#389C2212yescomplemented
61C2×#388C2212yes—
62C2×#388C2211yescharacteristic, complemented
63C2×#388C2212yescomplemented
64C2×#386C2211yescharacteristic
65C2×#386C2211yescharacteristic
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic
70C2×#386C2211yescharacteristic
71C2×#386C2212yes—
72C2×#386C2211yescharacteristic, complemented
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2212yes—
76C2×#385C2211yescharacteristic
77C2×#381C2211yescharacteristic
78C2×#381C2211yescharacteristic
79C2×#381C2211yescharacteristic
80C2×#380—28no—
81C2×#380C2212yes—
82C2×#380C2212yes—
83C2×#380C2212yes—
84C2×#380C2212yes—
85C2×#380C2211yescharacteristic, complemented
86C2×#379C2211yescharacteristic
87C2×#379C2211yescharacteristic
88C2×C4×C22⋊C4C2211yescharacteristic
89C2×C4×C22⋊C4C2211yescharacteristic
90C2×C4×C22⋊C4C2212yes—
91C22×#95C2211yescharacteristic
92C22×#95C2211yescharacteristic
93#1445C2212yescomplemented
94#1444C2212yescomplemented
95#1444C2212yescomplemented
96#1444C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1440C2212yes—
101#1440C2212yes—
102#1440C2212yescomplemented
103#1439C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1438C2212yes—
113#1438C2212yes—
114#1437C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119C4⋊#95C2212yescomplemented
120#1434C2212yescomplemented
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2212yescomplemented
128C4×#95C2212yescomplemented
129C26C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2312yes—
134C23×D4C2311yescharacteristic
135C24×C4—24no—
136C24×C4—28no—
137C24×C4—24no—
138C24×C4—44no—
139C24×C4—42no—
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—24no—
152C2×#123—24no—
153C2×#123—24no—
154C2×#123—24no—
155C2×#123—24no—
156C2×#123—24no—
157C2×#123—24no—
158C2×#123—42no—
159C2×#123—42no—
160C2×#123—42no—
161C2×#121—24no—
162C2×#121—24no—
163C2×#121—42no—
164C2×#120—24no—
165C2×#120—24no—
166C2×#120—24no—
167C2×#120—24no—
168C2×#120—42no—
169C2×#120D418yes—
170C2×C4×D4—24no—
171C2×C4×D4—28no—
172C2×C4×D4—28no—
173C2×C4×D4—24no—
174C2×C4×D4—44no—
175C2×C4×D4—42no—
176C2×#117—24no—
177C2×#117—24no—
178C2×#117—24no—
179C22×C4⋊C4—24no—
180C22×C4⋊C4—24no—
181C22×C4⋊C4—24no—
182C22×C4⋊C4—44no—
183C22×C4⋊C4—42no—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2312yes—
197C22×C4⋊C4C2312yes—
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2311yescharacteristic
201C22×C22⋊C4—24no—
202C22×C22⋊C4—24no—
203C22×C22⋊C4—24no—
204C22×C22⋊C4—24no—
205C22×C22⋊C4—42no—
206C22×C22⋊C4—42no—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2311yescharacteristic
238C22×C42C2312yes—
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242#399—28no—
243#398—28no—
244#398—24no—
245#397—24no—
246#396—28no—
247#396—28no—
248#396—24no—
249#394—28no—
250#394—24no—
251#394—44no—
252#392—28no—
253#390—28no—
254#390—28no—
255#390—28no—
256#389—28no—
257#389—24no—
258#389—44no—
259#388—28no—
260#388—28no—
261#388—24no—
262#386—24no—
263#386—24no—
264#386—24no—
265#386—24no—
266#386—28no—
267#386—24no—
268#386—28no—
269#386—44no—
270#386—42no—
271#385—24no—
272#385—28no—
273#385—24no—
274#385D418yescomplemented
275#381—24no—
276#381—24no—
277#381—42no—
278#380—24no—
279#380—28no—
280#380—28no—
281#380—28no—
282#380—28no—
283#379—24no—
284#379—24no—
285C4×C22⋊C4—24no—
286C4×C22⋊C4—24no—
287C4×C22⋊C4—28no—
288C2×#95—24no—
289C2×#95D418yescomplemented
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2312yes—
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C25—22no—
323C25—24no—
324C25—22no—
325C25—24no—
326C25—22no—
327C25—22no—
328C25—22no—
329C25—22no—
330C25—42no—
331C25—42no—
332C25C2×D414yes—
333C25C2411yescharacteristic
334C25C2411yescharacteristic
335C25C2412yes—
336C25C2411yescharacteristic
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—41no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4C2×D414yes—
369C22×D4C2×D418yes—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—232no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—416no—
414C23×C4—432no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—41no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—416no—
422C23×C4—432no—
423C23×C4C2×D414yes—
424C23×C4C2×D414yes—
425C23×C4C2×D414yes—
426C23×C4C2×D414yes—
427C23×C4#4118yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2412yes—
447#123—416no—
448#123—416no—
449#123—416no—
450#123—416no—
451#121—416no—
452#120—232no—
453#120—416no—
454C4×D4—416no—
455C4×D4—432no—
456#117—416no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—416no—
503C2×C4⋊C4—416no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4C2×D418yes—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
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—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—416no—
586C2×C22⋊C4—416no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4C2×D414yes—
596C2×C22⋊C4C2×D418yes—
597C2×C22⋊C4C2×D414yes—
598C2×C22⋊C4C2×D414yes—
599C2×C22⋊C4#4114yes—
600C2×C22⋊C4#4114yes—
601C2×C42—24no—
602C2×C42—24no—
603C2×C42—22no—
604C2×C42—24no—
605C2×C42—22no—
606C2×C42—24no—
607C2×C42—24no—
608C2×C42—24no—
609C2×C42—42no—
610C2×C42—41no—
611C2×C42—42no—
612C2×C42—42no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—22no—
619#95—24no—
620#95—24no—
621#95—22no—
622#95—24no—
623#95—22no—
624#95—24no—
625#95—24no—
626#95—22no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—24no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95—42no—
640#95C2×D414yes—
641#95C2×D414yes—
642#95C2×D414yes—
643#95C2×D414yes—
644#95C2×D418yes—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—28no—
650C24—28no—
651C24—216no—
652C24—28no—
653C24—216no—
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—28no—
667C24—28no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24—21no—
673C24—22no—
674C24—21no—
675C24—21no—
676C24—22no—
677C24—22no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—44no—
699C24—44no—
700C24—48no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24C22×D412yes—
706C24C22×D414yes—
707C24C22×D412yes—
708C24C22×D412yes—
709C24C22×D412yes—
710C24C2×#4114yes—
711C24C2×#4112yes—
712C24C2×#4112yes—
713C24H(5,𝔽2)12yes—
714C24H(5,𝔽2)12yes—
715C242−1+414yes—
716C24C2511yescharacteristic
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—216no—
721C2×D4—216no—
722C2×D4—48no—
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—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—48no—
743C2×D4—44no—
744C2×D4—82no—
745C2×D4—84no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—84no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—216no—
753C22×C4—28no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—216no—
766C22×C4—216no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—216no—
818C22×C4—216no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—48no—
876C22×C4—48no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—4128no—
881C22×C4—48no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—82no—
899C22×C4—84no—
900C22×C4—84no—
901C22×C4—84no—
902C22×C4—84no—
903C22×C4—84no—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C22×D412yes—
910C22×C4C22×D412yes—
911C22×C4C22×D412yes—
912C22×C4C22×D414yes—
913C22×C4C22×D414yes—
914C22×C4C22×D412yes—
915C22×C4C22×D414yes—
916C22×C4C2×#4114yes—
917C22×C4C2×#4114yes—
918C22×C4C2×#4114yes—
919C22×C4C2×#4114yes—
920C22×C4H(5,𝔽2)14yes—
921C4⋊C4—216no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C4⋊C4—48no—
935C4⋊C4—48no—
936C4⋊C4—84no—
937C4⋊C4—82no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—216no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—82no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C22⋊C4—84no—
968C22⋊C4#121116yes—
969C42—44no—
970C42—48no—
971C42—48no—
972C42—84no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—232no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—24no—
1012C23—24no—
1013C23—432no—
1014C23—432no—
1015C23—416no—
1016C23—416no—
1017C23—432no—
1018C23—416no—
1019C23—416no—
1020C23—432no—
1021C23—416no—
1022C23—42no—
1023C23—42no—
1024C23—416no—
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—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—42no—
1045C23—41no—
1046C23—42no—
1047C23—42no—
1048C23—41no—
1049C23—41no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—42no—
1065C23—41no—
1066C23—42no—
1067C23—41no—
1068C23—42no—
1069C23—42no—
1070C23—41no—
1071C23—41no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23C2×#12114yes—
1081C23#53214yes—
1082C23#54014yes—
1083C23D4214yes—
1084C23D4214yes—
1085C23#54614yes—
1086C23#54718yes—
1087C23#55014yes—
1088C23C23×D411yescharacteristic
1089C23C23×D411yescharacteristic
1090C23C23×D411yescharacteristic
1091C23C22×#4111yescharacteristic
1092C23C22×#4112yes—
1093C23C22×#4111yescharacteristic
1094C23C2×H(5,𝔽2)11yescharacteristic
1095C23C2×H(5,𝔽2)11yescharacteristic
1096C23C2×H(5,𝔽2)12yes—
1097C23C2×2−1+412yes—
1098C23#58512yes—
1099D4—432no—
1100D4—416no—
1101D4—816no—
1102D4—88no—
1103D4—88no—
1104C2×C4—232no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—432no—
1147C2×C4—416no—
1148C2×C4—432no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—416no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
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—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—88no—
1224C2×C4—88no—
1225C2×C4—88no—
1226C2×C4—88no—
1227C2×C4C2×#12118yes—
1228C2×C4#52514yes—
1229C2×C4#54618yes—
1230C22—24no—
1231C22—24no—
1232C22—24no—
1233C22—28no—
1234C22—28no—
1235C22—24no—
1236C22—24no—
1237C22—28no—
1238C22—24no—
1239C22—28no—
1240C22—28no—
1241C22—28no—
1242C22—28no—
1243C22—464no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—42no—
1257C22—44no—
1258C22—42no—
1259C22—42no—
1260C22—44no—
1261C22—81no—
1262C22—81no—
1263C22—82no—
1264C22—81no—
1265C22—81no—
1266C22—82no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—82no—
1271C22—82no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—82no—
1276C22—81no—
1277C22—82no—
1278C22#242818yes—
1279C22C22×#12111yescharacteristic
1280C22C2×#52511yescharacteristic
1281C22C2×#53211yescharacteristic
1282C22#344911yescharacteristic
1283C22C2×#54011yescharacteristic
1284C22C2×D4211yescharacteristic
1285C22C2×D4211yescharacteristic
1286C22C2×#54612yes—
1287C22C2×#54611yescharacteristic
1288C22C2×#54712yes—
1289C22C2×#55011yescharacteristic
1290C22#347512yes—
1291C22#347512yes—
1292C22#348411yescharacteristic
1293C22#348611yescharacteristic
1294C22#348912yes—
1295C22#349012yes—
1296C22#349212yes—
1297C22#349612yes—
1298C22#352012yes—
1299C22#352012yes—
1300C22#353512yes—
1301C22#354212yes—
1302C4—28no—
1303C4—24no—
1304C4—28no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—81no—
1315C4—82no—
1316C4—82no—
1317C4—81no—
1318C4—82no—
1319C4—81no—
1320C4—82no—
1321C2—28no—
1322C2—48no—
1323C2—82no—
1324C2—161no—
1325C2C2×#242811yescharacteristic
1326C2#3487711yescharacteristic
1327C2#3539711yescharacteristic
1328C2#3609811yescharacteristic
1329C2#3610311yescharacteristic
1330C2#3615312yes—
1331C2#3765311yescharacteristic
1332C2#3791112yes—
1333C2#3933211yescharacteristic
1334C2#5902212yes—
1335C2#5931112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2539C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2413C2semidirect
3. C2×#2411C2semidirect
4. C2×#2425C2semidirect
5. C2×C4×#120C2semidirect
6. C22×#380C2semidirect
7. #15479C2semidirect
8. #15309C2semidirect
9. #15307C2semidirect
10. #15294C2semidirect
11. #15069C2semidirect
12. #14918C2semidirect
13. #14911C2semidirect
14. #14771C2semidirect
15. #14732C2semidirect
16. #14719C2semidirect
17. #14694C2semidirect
18. #14043C2semidirect
19. #14012C2semidirect
20. #13996C2semidirect
21. #13968C2semidirect
22. #13920C2semidirect
23. #13799C2semidirect
44. C2×#398C22semidirect
45. C2×#398C22semidirect
46. C2×#397C22semidirect
48. C2×#396C22semidirect
49. C2×#396C22semidirect
51. C2×#394C22semidirect
52. C2×#394C22semidirect
58. C2×#389C22semidirect
59. C2×#389C22semidirect
60. C2×#389C22semidirect
62. C2×#388C22semidirect
63. C2×#388C22semidirect
72. C2×#386C22semidirect
85. C2×#380C22semidirect
93. #1445C22semidirect
94. #1444C22semidirect
95. #1444C22semidirect
96. #1444C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
102. #1440C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
114. #1437C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. C4⋊#95C22semidirect
120. #1434C22semidirect
127. C22⋊#95C22semidirect
128. C4×#95C22semidirect
274. #385D4semidirect
289. C2×#95D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25392
C2×#24132
C2×#24112
C2×#24252
C2×C4×#1202
C22×#3802
#154792
#153092
#153072
#152942
#150692
#149182
#149112
#147712
#147322
#147192
#146942
#140432
#140122
#139962
#139682
#139202
#137992