Finite Group Databasebeta

← #648377

Subgroups — #648377

Order 512.

5555 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C211yesmaximal, characteristic, complemented
2C2×#2411C211yesmaximal, characteristic, complemented
3C2×#2412C211yesmaximal, characteristic, complemented
4C2×#2342C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic, complemented
6C2×#2280C211yesmaximal, characteristic, complemented
7#15429C212yesmaximal, complemented
8#15376C212yesmaximal, complemented
9#15308C212yesmaximal, complemented
10#15307C212yesmaximal, complemented
11#14927C211yesmaximal, characteristic, complemented
12#14918C211yesmaximal, characteristic, complemented
13#14755C212yesmaximal, complemented
14#14754C212yesmaximal, complemented
15#14726C211yesmaximal, characteristic, complemented
16#14715C211yesmaximal, characteristic
17#14207C212yesmaximal, complemented
18#14135C211yesmaximal, characteristic, complemented
19#14128C211yesmaximal, characteristic, complemented
20#13995C211yesmaximal, characteristic, complemented
21#13988C212yesmaximal, complemented
22#13972C211yesmaximal, characteristic, complemented
23#13867C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2849—28no—
37#2412—28no—
38#2411—28no—
39C2×#397C2212yescomplemented
40C2×#396C2211yescharacteristic, complemented
41C2×#396C2211yescharacteristic, complemented
42C2×#396C2212yescomplemented
43C2×#394C2211yescharacteristic, complemented
44C2×#394C2212yescomplemented
45C2×#394C2211yescharacteristic, complemented
46C2×#392C2212yes—
47C2×#392C2212yes—
48#2342—28no—
49C2×#390C2211yescharacteristic, complemented
50C2×#390C2211yescharacteristic, complemented
51C2×#390C2212yescomplemented
52C2×#388C2212yescomplemented
53C2×#388C2212yescomplemented
54C2×#388C2211yescharacteristic, complemented
55C2×#388C2211yescharacteristic, complemented
56C2×#386—28no—
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2211yescharacteristic
66C2×#386C2212yescomplemented
67C2×#386C2212yescomplemented
68C2×#386C2212yescomplemented
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#385C2211yescharacteristic
72C2×#385C2212yescomplemented
73C2×#385C2212yescomplemented
74C2×#385C2212yescomplemented
75#2280—28no—
76C2×#381C2211yescharacteristic
77C2×#381C2211yescharacteristic
78C2×#381C2211yescharacteristic
79C2×#381C2211yescharacteristic
80C2×#380C2211yescharacteristic
81C2×#380C2212yescomplemented
82C2×#380C2212yescomplemented
83C2×#380C2212yescomplemented
84C2×#379C2211yescharacteristic
85C2×#379C2211yescharacteristic
86C2×#379C2211yescharacteristic
87C2×#379C2211yescharacteristic
88C2×#379C2211yescharacteristic
89C2×C4×C22⋊C4C2211yescharacteristic
90C2×C4×C22⋊C4C2212yescomplemented
91C2×C4×C22⋊C4C2212yescomplemented
92C2×C4×C22⋊C4C2212yescomplemented
93C22×#95C2211yescharacteristic
94C22×#95C2211yescharacteristic
95#1444C2212yescomplemented
96#1443C2212yescomplemented
97#1442C2212yescomplemented
98#1442C2212yescomplemented
99#1442C2212yescomplemented
100#1441C2212yescomplemented
101#1441C2212yescomplemented
102#1440C2212yescomplemented
103#1440C2212yescomplemented
104#1440C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yes—
117#1438C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1436C2212yescomplemented
121#1436C2212yescomplemented
122#1436C2212yescomplemented
123#1436C2212yescomplemented
124#1434C2212yescomplemented
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2211yescharacteristic
128C22⋊#95C2211yescharacteristic
129C26C2311yescharacteristic
130C26C2311yescharacteristic
131C23×D4—24no—
132C23×D4—28no—
133C23×D4—24no—
134C23×D4—42no—
135C23×D4—44no—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C24×C4—24no—
143C24×C4—24no—
144C24×C4—24no—
145C24×C4—24no—
146C24×C4—24no—
147C24×C4—42no—
148C24×C4—42no—
149C24×C4C2311yescharacteristic
150C24×C4C2312yes—
151C24×C4C2312yes—
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2312yes—
156C24×C4C2311yescharacteristic
157C2×#123—24no—
158C2×#123—24no—
159C2×#123—24no—
160C2×#123—24no—
161C2×#123—24no—
162C2×#123—42no—
163C2×#120—24no—
164C2×#120—24no—
165C2×#120—24no—
166C2×#120—24no—
167C2×#120—42no—
168C2×#120—42no—
169C2×#117—24no—
170C2×#117—24no—
171C2×#117—24no—
172C2×#117—24no—
173C2×#117—42no—
174C2×#117—42no—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C22⋊C4—24no—
187C22×C22⋊C4—24no—
188C22×C22⋊C4—24no—
189C22×C22⋊C4—24no—
190C22×C22⋊C4—24no—
191C22×C22⋊C4—24no—
192C22×C22⋊C4—24no—
193C22×C22⋊C4—42no—
194C22×C22⋊C4—44no—
195C22×C22⋊C4—42no—
196C22×C22⋊C4D418yescomplemented
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2312yes—
238C22×C42C2312yes—
239#397—28no—
240#396—24no—
241#396—24no—
242#396—44no—
243#394—24no—
244#394—24no—
245#394—28no—
246#392—28no—
247#392—44no—
248#390—24no—
249#390—24no—
250#390—44no—
251#388—24no—
252#388—24no—
253#388—28no—
254#388—28no—
255#386—28no—
256#386—24no—
257#386—24no—
258#386—28no—
259#386—28no—
260#386—28no—
261#386—28no—
262#386—28no—
263#386—28no—
264#386—28no—
265#386—44no—
266#386—42no—
267#385—24no—
268#385—24no—
269#385—28no—
270#385—28no—
271#385—28no—
272#385—42no—
273#381—24no—
274#381—24no—
275#381D418yescomplemented
276#381D418yescomplemented
277#380—24no—
278#380—28no—
279#380—28no—
280#380—28no—
281#379—24no—
282#379—24no—
283#379—24no—
284#379—24no—
285#379—24no—
286C4×C22⋊C4—24no—
287C4×C22⋊C4—28no—
288C4×C22⋊C4—28no—
289C4×C22⋊C4—28no—
290C2×#95—24no—
291C2×#95—24no—
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
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×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2312yes—
322C25—22no—
323C25—24no—
324C25—24no—
325C25—22no—
326C25—22no—
327C25—22no—
328C25—22no—
329C25—24no—
330C25—22no—
331C25—22no—
332C25—22no—
333C25—22no—
334C25—22no—
335C25—22no—
336C25—22no—
337C25—42no—
338C25—42no—
339C25—42no—
340C25—42no—
341C25—42no—
342C25C2×D414yes—
343C25#4114yes—
344C25C2411yescharacteristic
345C25C2411yescharacteristic
346C25C2411yescharacteristic
347C25C2412yes—
348C25C2411yescharacteristic
349C22×D4—232no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—24no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—24no—
371C22×D4—24no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—24no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—41no—
381C22×D4—41no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—432no—
388C22×D4—416no—
389C22×D4—432no—
390C22×D4—416no—
391C22×D4#4118yes—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—232no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—24no—
412C23×C4—24no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—24no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4—416no—
431C23×C4—416no—
432C23×C4—42no—
433C23×C4—42no—
434C23×C4—42no—
435C23×C4—42no—
436C23×C4—42no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—416no—
441C23×C4—416no—
442C23×C4—416no—
443C23×C4—416no—
444C23×C4C2×D414yes—
445C23×C4C2×D414yes—
446C23×C4C2×D414yes—
447C23×C4C2×D414yes—
448C23×C4#4114yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2412yes—
458C23×C4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467#123—416no—
468#123—416no—
469#120—416no—
470#120—416no—
471#117—416no—
472#117—416no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4—41no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—42no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—42no—
503C2×C4⋊C4—42no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—232no—
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—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
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—22no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
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—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—416no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
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—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—416no—
597C2×C22⋊C4—416no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4—42no—
602C2×C22⋊C4—42no—
603C2×C22⋊C4—42no—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—42no—
606C2×C22⋊C4—42no—
607C2×C22⋊C4—42no—
608C2×C22⋊C4C2×D414yes—
609C2×C22⋊C4C2×D414yes—
610C2×C22⋊C4C2×D414yes—
611C2×C22⋊C4C2×D414yes—
612C2×C22⋊C4C2×D414yes—
613C2×C22⋊C4C2×D414yes—
614C2×C22⋊C4C2×D414yes—
615C2×C22⋊C4C2×D414yes—
616C2×C42—22no—
617C2×C42—24no—
618C2×C42—22no—
619C2×C42—24no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—24no—
623C2×C42—42no—
624C2×C42—41no—
625C2×C42—41no—
626C2×C42—42no—
627C2×C42—42no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—24no—
632#95—24no—
633#95—24no—
634#95—24no—
635#95—24no—
636#95—24no—
637#95—24no—
638#95—24no—
639#95—24no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—24no—
645#95—24no—
646#95—24no—
647#95—42no—
648#95—42no—
649#95—42no—
650#95—42no—
651#95—42no—
652#95—42no—
653#95—42no—
654#95C2×D418yescomplemented
655#95C2×D418yescomplemented
656#95C2×D418yescomplemented
657#95C2×D418yescomplemented
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—28no—
663C24—28no—
664C24—216no—
665C24—28no—
666C24—216no—
667C24—21no—
668C24—22no—
669C24—21no—
670C24—22no—
671C24—22no—
672C24—21no—
673C24—22no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—21no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—28no—
689C24—28no—
690C24—28no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—22no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—28no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—22no—
709C24—21no—
710C24—21no—
711C24—22no—
712C24—21no—
713C24—22no—
714C24—22no—
715C24—48no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—48no—
730C24—48no—
731C24—48no—
732C24—48no—
733C24—44no—
734C24—44no—
735C24—48no—
736C24—44no—
737C24—44no—
738C24—44no—
739C24—44no—
740C24—44no—
741C24—44no—
742C24—44no—
743C24—44no—
744C24—84no—
745C24—84no—
746C24—84no—
747C24—84no—
748C24—84no—
749C24—84no—
750C24C22×D412yes—
751C24C22×D412yes—
752C24C22×D412yes—
753C24C22×D412yes—
754C24C22×D412yes—
755C24C2×#4114yes—
756C24C2×#4114yes—
757C24C2×#4114yes—
758C24C2×#4112yes—
759C24C2×#4112yes—
760C24H(5,𝔽2)14yes—
761C24H(5,𝔽2)12yes—
762C24H(5,𝔽2)12yes—
763C24C2511yescharacteristic
764C2×D4—216no—
765C2×D4—216no—
766C2×D4—216no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—4128no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—48no—
795C2×D4—84no—
796C2×D4—82no—
797C2×D4—82no—
798C2×D4—84no—
799C2×D4—84no—
800C2×D4—84no—
801C2×D4—84no—
802C2×D4—84no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—28no—
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—216no—
818C22×C4—216no—
819C22×C4—28no—
820C22×C4—28no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—21no—
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—21no—
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—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—28no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—22no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—22no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—21no—
901C22×C4—22no—
902C22×C4—21no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—48no—
912C22×C4—48no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—48no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—48no—
923C22×C4—48no—
924C22×C4—4128no—
925C22×C4—48no—
926C22×C4—48no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—48no—
936C22×C4—48no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—84no—
941C22×C4—84no—
942C22×C4—84no—
943C22×C4—84no—
944C22×C4—84no—
945C22×C4—84no—
946C22×C4—84no—
947C22×C4—84no—
948C22×C4#121116yes—
949C22×C4C22×D412yes—
950C22×C4C22×D412yes—
951C22×C4C22×D414yes—
952C22×C4C22×D412yes—
953C22×C4C22×D414yes—
954C22×C4C22×D414yes—
955C22×C4C22×D414yes—
956C22×C4C22×D412yes—
957C22×C4C22×D412yes—
958C22×C4C22×D412yes—
959C22×C4C22×D412yes—
960C22×C4C22×D412yes—
961C22×C4C2×#4114yes—
962C22×C4C2×#4112yes—
963C22×C4C2×#4112yes—
964C4⋊C4—48no—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—48no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—82no—
971C4⋊C4—82no—
972C4⋊C4—84no—
973C4⋊C4—84no—
974C4⋊C4—84no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—28no—
978C22⋊C4—28no—
979C22⋊C4—28no—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—48no—
984C22⋊C4—48no—
985C22⋊C4—48no—
986C22⋊C4—48no—
987C22⋊C4—48no—
988C22⋊C4—48no—
989C22⋊C4—48no—
990C22⋊C4—48no—
991C22⋊C4—48no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—82no—
1007C22⋊C4—82no—
1008C22⋊C4—84no—
1009C22⋊C4—84no—
1010C22⋊C4—84no—
1011C22⋊C4—82no—
1012C22⋊C4—82no—
1013C42—48no—
1014C42—44no—
1015C42—44no—
1016C42—84no—
1017C23—22no—
1018C23—22no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—22no—
1024C23—22no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—232no—
1034C23—22no—
1035C23—24no—
1036C23—24no—
1037C23—22no—
1038C23—22no—
1039C23—24no—
1040C23—24no—
1041C23—22no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—22no—
1052C23—22no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—24no—
1058C23—24no—
1059C23—24no—
1060C23—24no—
1061C23—24no—
1062C23—24no—
1063C23—24no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—432no—
1072C23—432no—
1073C23—416no—
1074C23—416no—
1075C23—416no—
1076C23—416no—
1077C23—416no—
1078C23—432no—
1079C23—416no—
1080C23—416no—
1081C23—416no—
1082C23—432no—
1083C23—42no—
1084C23—41no—
1085C23—416no—
1086C23—42no—
1087C23—42no—
1088C23—41no—
1089C23—42no—
1090C23—42no—
1091C23—41no—
1092C23—41no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—41no—
1111C23—416no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—42no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23—42no—
1124C23—42no—
1125C23—42no—
1126C23—42no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—42no—
1137C23—42no—
1138C23—42no—
1139C23—42no—
1140C23—41no—
1141C23—41no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—42no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—88no—
1151C23—88no—
1152C23—88no—
1153C23—816no—
1154C23—816no—
1155C23—816no—
1156C23—816no—
1157C23C2×#12114yes—
1158C23#52514yes—
1159C23#52514yes—
1160C23#53814yes—
1161C23D4214yes—
1162C23D4214yes—
1163C23#54614yes—
1164C23#54614yes—
1165C23#55118yes—
1166C23C23×D411yescharacteristic
1167C23C23×D411yescharacteristic
1168C23C23×D411yescharacteristic
1169C23C22×#4111yescharacteristic
1170C23C22×#4111yescharacteristic
1171C23C22×#4112yes—
1172C23C2×H(5,𝔽2)11yescharacteristic
1173C23C2×H(5,𝔽2)11yescharacteristic
1174C23C2×H(5,𝔽2)12yes—
1175C23#58512yes—
1176C23#58512yes—
1177D4—432no—
1178D4—432no—
1179D4—88no—
1180D4—816no—
1181D4—88no—
1182D4—88no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—232no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—432no—
1222C2×C4—432no—
1223C2×C4—416no—
1224C2×C4—42no—
1225C2×C4—41no—
1226C2×C4—416no—
1227C2×C4—41no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—41no—
1237C2×C4—42no—
1238C2×C4—41no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—42no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—42no—
1274C2×C4—42no—
1275C2×C4—42no—
1276C2×C4—42no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—42no—
1289C2×C4—42no—
1290C2×C4—42no—
1291C2×C4—42no—
1292C2×C4—42no—
1293C2×C4—42no—
1294C2×C4—42no—
1295C2×C4—42no—
1296C2×C4—88no—
1297C2×C4—816no—
1298C2×C4—88no—
1299C2×C4C2×#12114yes—
1300C2×C4C2×#12114yes—
1301C22—24no—
1302C22—24no—
1303C22—24no—
1304C22—28no—
1305C22—28no—
1306C22—28no—
1307C22—24no—
1308C22—24no—
1309C22—24no—
1310C22—28no—
1311C22—24no—
1312C22—28no—
1313C22—24no—
1314C22—28no—
1315C22—28no—
1316C22—24no—
1317C22—464no—
1318C22—44no—
1319C22—44no—
1320C22—42no—
1321C22—44no—
1322C22—42no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—44no—
1331C22—44no—
1332C22—42no—
1333C22—44no—
1334C22—42no—
1335C22—44no—
1336C22—44no—
1337C22—44no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—832no—
1346C22—82no—
1347C22—82no—
1348C22—82no—
1349C22—82no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—82no—
1355C22—82no—
1356C22—82no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—82no—
1361C22#242418yes—
1362C22C22×#12111yescharacteristic
1363C22C2×#52511yescharacteristic
1364C22C2×#52511yescharacteristic
1365C22#344911yescharacteristic
1366C22C2×#53811yescharacteristic
1367C22C2×D4211yescharacteristic
1368C22C2×D4211yescharacteristic
1369C22C2×#54611yescharacteristic
1370C22C2×#54611yescharacteristic
1371C22D4×#4112yes—
1372C22D4×#4112yes—
1373C22C2×#55112yes—
1374C22#347512yes—
1375C22#348411yescharacteristic
1376C22#348511yescharacteristic
1377C22#348812yes—
1378C22#348812yes—
1379C22#349012yes—
1380C22#349112yes—
1381C22#349412yes—
1382C22#351312yes—
1383C22#353312yes—
1384C22#353412yes—
1385C4—24no—
1386C4—24no—
1387C4—42no—
1388C4—42no—
1389C4—44no—
1390C4—44no—
1391C4—44no—
1392C4—44no—
1393C4—44no—
1394C4—42no—
1395C4—42no—
1396C4—81no—
1397C4—81no—
1398C4—82no—
1399C4—81no—
1400C4—82no—
1401C4—81no—
1402C4—81no—
1403C2—28no—
1404C2—48no—
1405C2—44no—
1406C2—82no—
1407C2—161no—
1408C2C2×#242411yescharacteristic
1409C2#3473711yescharacteristic
1410C2#3551411yescharacteristic
1411C2#3609911yescharacteristic
1412C2#3615811yescharacteristic
1413C2#3622212yes—
1414C2#3765211yescharacteristic
1415C2#3784211yescharacteristic
1416C2#3839612yes—
1417C2#5899212yes—
1418C2#5901112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#2849C2semidirect
2. C2×#2411C2semidirect
3. C2×#2412C2semidirect
4. C2×#2342C2semidirect
5. C22×#386C2semidirect
6. C2×#2280C2semidirect
7. #15429C2semidirect
8. #15376C2semidirect
9. #15308C2semidirect
10. #15307C2semidirect
11. #14927C2semidirect
12. #14918C2semidirect
13. #14755C2semidirect
14. #14754C2semidirect
15. #14726C2semidirect
17. #14207C2semidirect
18. #14135C2semidirect
19. #14128C2semidirect
20. #13995C2semidirect
21. #13988C2semidirect
22. #13972C2semidirect
23. #13867C2semidirect
39. C2×#397C22semidirect
40. C2×#396C22semidirect
41. C2×#396C22semidirect
42. C2×#396C22semidirect
43. C2×#394C22semidirect
44. C2×#394C22semidirect
45. C2×#394C22semidirect
49. C2×#390C22semidirect
50. C2×#390C22semidirect
51. C2×#390C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
55. C2×#388C22semidirect
66. C2×#386C22semidirect
67. C2×#386C22semidirect
68. C2×#386C22semidirect
72. C2×#385C22semidirect
73. C2×#385C22semidirect
74. C2×#385C22semidirect
81. C2×#380C22semidirect
82. C2×#380C22semidirect
83. C2×#380C22semidirect
90. C2×C4×C22⋊C4C22semidirect
91. C2×C4×C22⋊C4C22semidirect
92. C2×C4×C22⋊C4C22semidirect
95. #1444C22semidirect
96. #1443C22semidirect
97. #1442C22semidirect
98. #1442C22semidirect
99. #1442C22semidirect
100. #1441C22semidirect
101. #1441C22semidirect
102. #1440C22semidirect
103. #1440C22semidirect
104. #1440C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
117. #1438C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. #1436C22semidirect
123. #1436C22semidirect
124. #1434C22semidirect
196. C22×C22⋊C4D4semidirect
275. #381D4semidirect
276. #381D4semidirect
654. #95C2×D4semidirect
655. #95C2×D4semidirect
656. #95C2×D4semidirect
657. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#24112
C2×#24122
C2×#23422
C22×#3862
C2×#22802
#154292
#153762
#153082
#153072
#149272
#149182
#147552
#147542
#147262
#147152
#142072
#141352
#141282
#139952
#139882
#139722
#138672