Finite Group Databasebeta

← #719372

Subgroups — #719372

Order 512.

4886 conjugacy classes of subgroups.

The subgroup lattice has 1400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2534C211yesmaximal, characteristic, complemented
2C2×#2411C211yesmaximal, characteristic, complemented
3C2×#2410C211yesmaximal, characteristic
4C22×#394C211yesmaximal, characteristic, complemented
5C2×#2342C211yesmaximal, characteristic, complemented
6C2×#2321C211yesmaximal, characteristic, complemented
7#16819C212yesmaximal, complemented
8#16514C212yesmaximal, complemented
9#15780C212yesmaximal, complemented
10#15307C212yesmaximal, complemented
11#15303C212yesmaximal, complemented
12#15274C212yesmaximal, complemented
13#15130C212yesmaximal, complemented
14#14968C212yesmaximal, complemented
15#14918C211yesmaximal, characteristic, complemented
16#14912C211yesmaximal, characteristic, complemented
17#14724C211yesmaximal, characteristic, complemented
18#14718C211yesmaximal, characteristic, complemented
19#14338C211yesmaximal, characteristic, complemented
20#13962C211yesmaximal, characteristic, complemented
21#13880C211yesmaximal, characteristic, complemented
22#13877C211yesmaximal, characteristic, complemented
23#13872C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#121C2212yes—
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37#2534—28no—
38#2411—28no—
39#2410—28no—
40C2×#396C2211yescharacteristic, complemented
41C2×#396C2211yescharacteristic, complemented
42C2×#396C2212yescomplemented
43C2×#394—28no—
44C2×#394C2212yes—
45C2×#394C2212yes—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2212yes—
51C2×#394C2211yescharacteristic, complemented
52C2×#394C2211yescharacteristic, complemented
53C2×#394C2212yescomplemented
54C2×#394C2212yescomplemented
55C2×#392C2212yes—
56#2342—28no—
57#2321—28no—
58C2×#390C2212yescomplemented
59C2×#390C2212yescomplemented
60C2×#388C2211yescharacteristic, complemented
61C2×#388C2211yescharacteristic, complemented
62C2×#388C2212yescomplemented
63C2×#388C2212yescomplemented
64C2×#388C2212yescomplemented
65C2×#388C2212yescomplemented
66C2×#388C2212yescomplemented
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic
70C2×#386C2212yes—
71C2×#386C2211yescharacteristic, complemented
72C2×#386C2211yescharacteristic, complemented
73C2×#386C2212yescomplemented
74C2×#385C2211yescharacteristic
75C2×#385C2211yescharacteristic
76C2×#385C2211yescharacteristic
77C2×#385C2211yescharacteristic
78C2×#385C2211yescharacteristic
79C2×#385C2212yescomplemented
80C2×#384C2212yescomplemented
81C2×#381C2211yescharacteristic
82C2×#381C2211yescharacteristic
83C2×#380C2211yescharacteristic
84C2×#380C2211yescharacteristic
85C2×#380C2212yescomplemented
86C2×#380C2212yescomplemented
87C2×#379C2211yescharacteristic
88C2×#379C2211yescharacteristic
89C2×#379C2211yescharacteristic
90C2×#379C2211yescharacteristic
91C2×#379C2211yescharacteristic
92C2×C4×C22⋊C4C2211yescharacteristic
93C2×C4×C22⋊C4C2212yescomplemented
94C22×#95C2211yescharacteristic
95#1444C2212yescomplemented
96#1444C2212yescomplemented
97#1442C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1441C2212yescomplemented
101#1441C2212yescomplemented
102#1440C2212yescomplemented
103#1440C2212yescomplemented
104#1440C2212yescomplemented
105#1440C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1439C2212yescomplemented
115#1439C2212yescomplemented
116#1439C2212yescomplemented
117#1438C2212yes—
118#1438C2212yes—
119#1438C2212yescomplemented
120C4⋊#95C2212yescomplemented
121C4⋊#95C2212yescomplemented
122C4⋊#95C2212yescomplemented
123#1434C2212yescomplemented
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2211yescharacteristic
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C26C2311yescharacteristic
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—44no—
134C23×D4—42no—
135C23×D4—44no—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C23×D4C2311yescharacteristic
141C23×D4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—42no—
152C2×#121—28no—
153C2×#121—44no—
154C2×#121—44no—
155C2×#120—24no—
156C2×#120—24no—
157C2×#120—24no—
158C2×#120—24no—
159C2×#120—42no—
160C2×#120D418yes—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×#117—24no—
165C2×#117—24no—
166C2×#117—24no—
167C22×C4⋊C4—24no—
168C22×C4⋊C4—44no—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—24no—
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—24no—
194C22×C22⋊C4—44no—
195C22×C22⋊C4—42no—
196C22×C22⋊C4D418yescomplemented
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C42C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2312yes—
239#396—28no—
240#396—24no—
241#396—24no—
242#394—28no—
243#394—28no—
244#394—28no—
245#394—28no—
246#394—28no—
247#394—28no—
248#394—24no—
249#394—24no—
250#394—44no—
251#394—44no—
252#394—44no—
253#392—28no—
254#390—28no—
255#390—28no—
256#388—28no—
257#388—24no—
258#388—24no—
259#388—28no—
260#388—28no—
261#388—28no—
262#388—28no—
263#386—24no—
264#386—24no—
265#386—24no—
266#386—28no—
267#386—24no—
268#386—24no—
269#386—28no—
270#385—24no—
271#385—24no—
272#385—24no—
273#385—28no—
274#385—42no—
275#385—42no—
276#384—44no—
277#381—24no—
278#381—24no—
279#380—24no—
280#380—24no—
281#380—44no—
282#380—44no—
283#379—24no—
284#379—24no—
285#379—24no—
286#379—24no—
287#379—24no—
288C4×C22⋊C4—28no—
289C4×C22⋊C4D418yescomplemented
290C2×#95—24no—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C25—22no—
320C25—24no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—22no—
326C25—22no—
327C25—22no—
328C25—22no—
329C25—22no—
330C25—22no—
331C25—22no—
332C25—42no—
333C25—42no—
334C25—42no—
335C25—42no—
336C25—42no—
337C25—42no—
338C25—42no—
339C25C2×D414yes—
340C25C2×D414yes—
341C25C2411yescharacteristic
342C25C2412yes—
343C25C2411yescharacteristic
344C25C2411yescharacteristic
345C25C2411yescharacteristic
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—22no—
363C22×D4—24no—
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—416no—
374C22×D4—41no—
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—432no—
384C22×D4—416no—
385C22×D4—416no—
386C22×D4—432no—
387C22×D4C2×D414yes—
388C22×D4C2×D418yes—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4C2×D414yes—
425C23×C4C2×D414yes—
426C23×C4C2×D414yes—
427C23×C4#4114yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446#123—416no—
447#121—432no—
448#120—232no—
449#120—416no—
450C4×D4—416no—
451#117—416no—
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—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—416no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4—42no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—232no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
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—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
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—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
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—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
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—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
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—41no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—416no—
583C2×C22⋊C4—416no—
584C2×C22⋊C4—416no—
585C2×C22⋊C4—416no—
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—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4—42no—
602C2×C22⋊C4C2×D414yes—
603C2×C22⋊C4C2×D414yes—
604C2×C22⋊C4C2×D414yes—
605C2×C22⋊C4C2×D414yes—
606C2×C22⋊C4C2×D418yes—
607C2×C22⋊C4C2×D414yes—
608C2×C22⋊C4C2×D414yes—
609C2×C22⋊C4C2×D414yes—
610C2×C22⋊C4#4114yes—
611C2×C42—24no—
612C2×C42—24no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—24no—
616C2×C42—22no—
617C2×C42—42no—
618C2×C42—42no—
619C2×C42C2×D418yescomplemented
620#95—24no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—22no—
625#95—22no—
626#95—24no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—24no—
632#95—24no—
633#95—24no—
634#95—24no—
635#95—24no—
636#95—24no—
637#95—24no—
638#95—42no—
639#95—42no—
640#95—42no—
641#95—42no—
642#95—42no—
643#95—42no—
644#95—42no—
645#95—42no—
646#95—42no—
647#95C2×D418yescomplemented
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—22no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—21no—
664C24—22no—
665C24—22no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—22no—
671C24—21no—
672C24—21no—
673C24—22no—
674C24—21no—
675C24—22no—
676C24—22no—
677C24—21no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—28no—
698C24—28no—
699C24—28no—
700C24—28no—
701C24—28no—
702C24—44no—
703C24—48no—
704C24—44no—
705C24—44no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—48no—
713C24—44no—
714C24—44no—
715C24—48no—
716C24—44no—
717C24—44no—
718C24—48no—
719C24—44no—
720C24—44no—
721C24—44no—
722C24—44no—
723C24—44no—
724C24—44no—
725C24—44no—
726C24—44no—
727C24—84no—
728C24—84no—
729C24—84no—
730C24—84no—
731C24—84no—
732C24—84no—
733C24—84no—
734C24—84no—
735C24—84no—
736C24—84no—
737C24—84no—
738C24—84no—
739C24—84no—
740C24—84no—
741C24C22×D414yes—
742C24C22×D412yes—
743C24C22×D412yes—
744C24C22×D412yes—
745C24C22×D412yes—
746C24C22×D412yes—
747C24C22×D412yes—
748C24C2×#4112yes—
749C24C2×#4112yes—
750C24H(5,𝔽2)14yes—
751C24H(5,𝔽2)12yes—
752C242−1+412yes—
753C24C2511yescharacteristic
754C2×D4—216no—
755C2×D4—28no—
756C2×D4—28no—
757C2×D4—28no—
758C2×D4—216no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—4128no—
773C2×D4—48no—
774C2×D4—44no—
775C2×D4—48no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—48no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—84no—
785C2×D4—84no—
786C2×D4—84no—
787C2×D4—84no—
788C2×D4—82no—
789C2×D4—84no—
790C2×D4—82no—
791C2×D4—84no—
792C2×D4—84no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—28no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—48no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—48no—
902C22×C4—48no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—48no—
916C22×C4—44no—
917C22×C4—82no—
918C22×C4—82no—
919C22×C4—84no—
920C22×C4—84no—
921C22×C4—84no—
922C22×C4—84no—
923C22×C4—84no—
924C22×C4—84no—
925C22×C4—84no—
926C22×C4—84no—
927C22×C4#121116yescomplemented
928C22×C4C22×D412yes—
929C22×C4C22×D412yes—
930C22×C4C22×D412yes—
931C22×C4C22×D414yes—
932C22×C4C22×D412yes—
933C22×C4C22×D414yes—
934C22×C4C22×D412yes—
935C22×C4C22×D414yes—
936C22×C4C22×D412yes—
937C22×C4C22×D412yes—
938C22×C4C2×#4112yes—
939C22×C4C2×#4114yes—
940C22×C4C2×#4112yes—
941C22×C4H(5,𝔽2)14yes—
942C4⋊C4—48no—
943C4⋊C4—48no—
944C4⋊C4—48no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—48no—
948C4⋊C4—44no—
949C4⋊C4—82no—
950C4⋊C4—84no—
951C4⋊C4—82no—
952C4⋊C4—84no—
953C4⋊C4—84no—
954C4⋊C4—84no—
955C4⋊C4—84no—
956C22⋊C4—28no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—28no—
960C22⋊C4—28no—
961C22⋊C4—216no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—48no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—48no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—48no—
982C22⋊C4—48no—
983C22⋊C4—48no—
984C22⋊C4—44no—
985C22⋊C4—84no—
986C22⋊C4—84no—
987C22⋊C4—84no—
988C22⋊C4—84no—
989C22⋊C4—84no—
990C22⋊C4—84no—
991C22⋊C4—82no—
992C22⋊C4—82no—
993C22⋊C4—84no—
994C22⋊C4#121116yes—
995C42—48no—
996C42—48no—
997C42—44no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—24no—
1002C23—22no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—24no—
1019C23—22no—
1020C23—22no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—22no—
1027C23—24no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—24no—
1033C23—22no—
1034C23—22no—
1035C23—24no—
1036C23—22no—
1037C23—24no—
1038C23—24no—
1039C23—22no—
1040C23—24no—
1041C23—24no—
1042C23—24no—
1043C23—24no—
1044C23—22no—
1045C23—416no—
1046C23—416no—
1047C23—416no—
1048C23—416no—
1049C23—416no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—41no—
1062C23—41no—
1063C23—42no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—42no—
1068C23—41no—
1069C23—42no—
1070C23—41no—
1071C23—41no—
1072C23—42no—
1073C23—41no—
1074C23—41no—
1075C23—42no—
1076C23—41no—
1077C23—42no—
1078C23—42no—
1079C23—41no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
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—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—416no—
1119C23—416no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23—42no—
1124C23—88no—
1125C23—88no—
1126C23—816no—
1127C23—88no—
1128C23—816no—
1129C23—816no—
1130C23—816no—
1131C23—816no—
1132C23—816no—
1133C23—88no—
1134C23—816no—
1135C23—88no—
1136C23—88no—
1137C23—816no—
1138C23—88no—
1139C23C2×#12114yes—
1140C23C2×#12114yes—
1141C23#53514yes—
1142C23#53714yes—
1143C23D4214yes—
1144C23#54714yes—
1145C23#54714yes—
1146C23#55514yes—
1147C23C23×D411yescharacteristic
1148C23C23×D411yescharacteristic
1149C23C23×D411yescharacteristic
1150C23C22×#4111yescharacteristic
1151C23C22×#4111yescharacteristic
1152C23C2×H(5,𝔽2)12yes—
1153C23C2×H(5,𝔽2)11yescharacteristic
1154C23C2×H(5,𝔽2)12yes—
1155C23C2×2−1+411yescharacteristic
1156C23#58512yes—
1157C23#58512yes—
1158D4—432no—
1159D4—432no—
1160D4—416no—
1161D4—816no—
1162D4—88no—
1163D4—88no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—24no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—416no—
1194C2×C4—416no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—416no—
1215C2×C4—42no—
1216C2×C4—41no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—41no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—42no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—42no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—41no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—41no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—41no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—41no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—42no—
1266C2×C4—42no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—42no—
1271C2×C4—42no—
1272C2×C4—42no—
1273C2×C4—42no—
1274C2×C4—816no—
1275C2×C4—88no—
1276C2×C4—88no—
1277C2×C4—88no—
1278C2×C4C2×#12114yes—
1279C2×C4C2×#12118yes—
1280C2×C4C2×#12114yes—
1281C22—24no—
1282C22—24no—
1283C22—24no—
1284C22—28no—
1285C22—28no—
1286C22—24no—
1287C22—24no—
1288C22—28no—
1289C22—28no—
1290C22—24no—
1291C22—24no—
1292C22—24no—
1293C22—24no—
1294C22—42no—
1295C22—42no—
1296C22—44no—
1297C22—44no—
1298C22—42no—
1299C22—42no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—44no—
1308C22—42no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—42no—
1313C22—42no—
1314C22—44no—
1315C22—42no—
1316C22—42no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—42no—
1321C22—832no—
1322C22—832no—
1323C22—81no—
1324C22—82no—
1325C22—82no—
1326C22—82no—
1327C22—82no—
1328C22—82no—
1329C22—82no—
1330C22—81no—
1331C22—82no—
1332C22—81no—
1333C22—82no—
1334C22—82no—
1335C22—82no—
1336C22—82no—
1337C22—82no—
1338C22—82no—
1339C22—81no—
1340C22—82no—
1341C22#253718yes—
1342C22C22×#12111yescharacteristic
1343C22C22×#12111yescharacteristic
1344C22C2×#53511yescharacteristic
1345C22C2×#53711yescharacteristic
1346C22#344911yescharacteristic
1347C22C2×D4211yescharacteristic
1348C22C2×#54711yescharacteristic
1349C22C2×#54711yescharacteristic
1350C22C2×#55511yescharacteristic
1351C22#348411yescharacteristic
1352C22#348412yes—
1353C22#348511yescharacteristic
1354C22#348512yes—
1355C22#348812yes—
1356C22#349412yes—
1357C22#349612yes—
1358C22#350512yes—
1359C22#351312yes—
1360C22#351412yes—
1361C22#353212yes—
1362C22#353312yes—
1363C22#353512yes—
1364C22#356112yes—
1365C4—24no—
1366C4—24no—
1367C4—28no—
1368C4—44no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—81no—
1374C4—82no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—82no—
1380C4—82no—
1381C4—81no—
1382C4—82no—
1383C2—28no—
1384C2—44no—
1385C2—82no—
1386C2—82no—
1387C2—84no—
1388C2C2×#253711yescharacteristic
1389C2#3525211yescharacteristic
1390C2#3535811yescharacteristic
1391C2#3576112yes—
1392C2#3764511yescharacteristic
1393C2#3765411yescharacteristic
1394C2#3803911yescharacteristic
1395C2#3804411yescharacteristic
1396C2#4051412yes—
1397C2#4305312yes—
1398C2#4393812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2410C2
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×#2534C2semidirect
2. C2×#2411C2semidirect
4. C22×#394C2semidirect
5. C2×#2342C2semidirect
6. C2×#2321C2semidirect
7. #16819C2semidirect
8. #16514C2semidirect
9. #15780C2semidirect
10. #15307C2semidirect
11. #15303C2semidirect
12. #15274C2semidirect
13. #15130C2semidirect
14. #14968C2semidirect
15. #14918C2semidirect
16. #14912C2semidirect
17. #14724C2semidirect
18. #14718C2semidirect
19. #14338C2semidirect
20. #13962C2semidirect
21. #13880C2semidirect
22. #13877C2semidirect
23. #13872C2semidirect
40. C2×#396C22semidirect
41. C2×#396C22semidirect
42. C2×#396C22semidirect
51. C2×#394C22semidirect
52. C2×#394C22semidirect
53. C2×#394C22semidirect
54. C2×#394C22semidirect
58. C2×#390C22semidirect
59. C2×#390C22semidirect
60. C2×#388C22semidirect
61. C2×#388C22semidirect
62. C2×#388C22semidirect
63. C2×#388C22semidirect
64. C2×#388C22semidirect
65. C2×#388C22semidirect
66. C2×#388C22semidirect
71. C2×#386C22semidirect
72. C2×#386C22semidirect
73. C2×#386C22semidirect
79. C2×#385C22semidirect
80. C2×#384C22semidirect
85. C2×#380C22semidirect
86. C2×#380C22semidirect
93. C2×C4×C22⋊C4C22semidirect
95. #1444C22semidirect
96. #1444C22semidirect
97. #1442C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
100. #1441C22semidirect
101. #1441C22semidirect
102. #1440C22semidirect
103. #1440C22semidirect
104. #1440C22semidirect
105. #1440C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
114. #1439C22semidirect
115. #1439C22semidirect
116. #1439C22semidirect
119. #1438C22semidirect
120. C4⋊#95C22semidirect
121. C4⋊#95C22semidirect
122. C4⋊#95C22semidirect
123. #1434C22semidirect
128. C22⋊#95C22semidirect
196. C22×C22⋊C4D4semidirect
289. C4×C22⋊C4D4semidirect
619. C2×C42C2×D4semidirect
647. #95C2×D4semidirect
927. C22×C4#121semidirect

Maximal subgroups

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

subgroupindex
C2×#25342
C2×#24112
C2×#24102
C22×#3942
C2×#23422
C2×#23212
#168192
#165142
#157802
#153072
#153032
#152742
#151302
#149682
#149182
#149122
#147242
#147182
#143382
#139622
#138802
#138772
#138722