Finite Group Databasebeta

← #846401

Subgroups — #846401

Order 512.

5956 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#123C211yesmaximal, characteristic, complemented
2C2×#2696C212yesmaximal, complemented
3C2×#2417C211yesmaximal, characteristic, complemented
4#16359C212yesmaximal, complemented
5#16256C212yesmaximal, complemented
6#15668C212yesmaximal, complemented
7#15464C212yesmaximal, complemented
8#15368C212yesmaximal, complemented
9#15272C212yesmaximal, complemented
10#14822C211yesmaximal, characteristic, complemented
11#14820C211yesmaximal, characteristic, complemented
12#14725C211yesmaximal, characteristic, complemented
13#14717C211yesmaximal, characteristic, complemented
14#14717C211yesmaximal, characteristic, complemented
15#14715C211yesmaximal, characteristic
16#14694C211yesmaximal, characteristic, complemented
17#14680C211yesmaximal, characteristic, complemented
18#14360C212yesmaximal, complemented
19#14019C211yesmaximal, characteristic, complemented
20#13967C211yesmaximal, characteristic, complemented
21#13967C211yesmaximal, characteristic, complemented
22#13902C211yesmaximal, characteristic, complemented
23#13882C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123—216no—
27C22×#123—28no—
28C22×#123C2212yes—
29C22×#123C2212yes—
30C22×#123C2212yes—
31C22×#123C2212yes—
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic, complemented
34C22×#120C2211yescharacteristic
35C22×#120C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40C23×C22⋊C4C2211yescharacteristic
41C23×C22⋊C4C2211yescharacteristic
42#2696—216no—
43#2417—28no—
44C2×#400C2212yescomplemented
45C2×#398C2211yescharacteristic, complemented
46C2×#398C2211yescharacteristic, complemented
47C2×#397C2212yescomplemented
48C2×#396C2211yescharacteristic, complemented
49C2×#396C2211yescharacteristic, complemented
50C2×#394C2212yescomplemented
51C2×#393C2212yescomplemented
52C2×#393C2212yescomplemented
53C2×#392C2212yes—
54C2×#392C2212yes—
55C2×#391C2211yescharacteristic, complemented
56C2×#390C2212yes—
57C2×#390C2212yes—
58C2×#389C2211yescharacteristic, complemented
59C2×#388C2212yescomplemented
60C2×#387C2212yescomplemented
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#386C2212yescomplemented
66C2×#386C2212yescomplemented
67C2×#386C2212yescomplemented
68C2×#386C2212yescomplemented
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×#380C2211yescharacteristic, complemented
73C2×#380C2212yescomplemented
74C2×#380C2212yescomplemented
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic
82#1445C2212yescomplemented
83#1442C2212yescomplemented
84#1442C2212yescomplemented
85#1442C2212yescomplemented
86#1441C2212yescomplemented
87#1441C2212yescomplemented
88#1440C2212yescomplemented
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yescomplemented
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1436C2212yescomplemented
112#1436C2212yescomplemented
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—28no—
131C23×D4—24no—
132C23×D4—24no—
133C23×D4—42no—
134C23×D4—44no—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C24×C4—24no—
141C24×C4—28no—
142C24×C4—24no—
143C24×C4—44no—
144C24×C4—42no—
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2312yes—
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C2×#123—2128no—
154C2×#123—28no—
155C2×#123—28no—
156C2×#123—28no—
157C2×#123—28no—
158C2×#123—28no—
159C2×#123—28no—
160C2×#123—28no—
161C2×#123—28no—
162C2×#123—28no—
163C2×#123—28no—
164C2×#123—28no—
165C2×#123D4116yescomplemented
166C2×C22⋊Q8—24no—
167C2×C22⋊Q8—24no—
168C2×C22⋊Q8—28no—
169C2×C22⋊Q8—42no—
170C2×C22⋊Q8—42no—
171C2×#120—24no—
172C2×#120—24no—
173C2×#120—24no—
174C2×#120—42no—
175C2×#120—42no—
176C2×#120—42no—
177C2×C4×D4—24no—
178C2×C4×D4—42no—
179C2×C4×D4—42no—
180C22×C4⋊C4—24no—
181C22×C4⋊C4—28no—
182C22×C4⋊C4—28no—
183C22×C4⋊C4D418yescomplemented
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C22⋊C4—24no—
200C22×C22⋊C4—24no—
201C22×C22⋊C4—24no—
202C22×C22⋊C4—28no—
203C22×C22⋊C4—28no—
204C22×C22⋊C4—28no—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C42C2311yescharacteristic
240C22×C42C2312yes—
241#400—28no—
242#398—24no—
243#398—24no—
244#397—28no—
245#396—24no—
246#396—24no—
247#394—28no—
248#393—28no—
249#393—28no—
250#392—28no—
251#392—44no—
252#391—24no—
253#390—28no—
254#390—44no—
255#389—24no—
256#388—28no—
257#387—28no—
258#386—24no—
259#386—24no—
260#386—24no—
261#386—28no—
262#386—28no—
263#386—28no—
264#386—42no—
265#386—44no—
266#380—24no—
267#380—24no—
268#380—28no—
269#380—24no—
270#380—42no—
271#380—44no—
272#379—42no—
273#379—42no—
274#379—42no—
275#379—42no—
276#379—42no—
277#379—42no—
278C4×C22⋊C4—42no—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
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—
311C25—24no—
312C25—22no—
313C25—24no—
314C25—22no—
315C25—24no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—22no—
326C25—22no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25—42no—
331C25—42no—
332C25#4114yes—
333C25C2412yes—
334C25C2411yescharacteristic
335C25C2412yes—
336C25C2411yescharacteristic
337C22×Q8—22no—
338C22×Q8—24no—
339C22×Q8—41no—
340C22×Q8—41no—
341C22×Q8—42no—
342C22×D4—232no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—416no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—432no—
378C22×D4—416no—
379C22×D4—432no—
380C22×D4C2×D418yes—
381C22×D4#4114yes—
382C23×C4—232no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—24no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—24no—
411C23×C4—42no—
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—41no—
421C23×C4—41no—
422C23×C4—42no—
423C23×C4—432no—
424C23×C4—416no—
425C23×C4—416no—
426C23×C4—432no—
427C23×C4C2×D414yes—
428C23×C4C2×D414yes—
429C23×C4C2×D414yes—
430C23×C4C2×D418yes—
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2412yes—
438C23×C4C2411yescharacteristic
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450#123—264no—
451#123—264no—
452#123—264no—
453#123—264no—
454C22⋊Q8—416no—
455C22⋊Q8—416no—
456#120—416no—
457#120—416no—
458C4×D4—416no—
459C2×C4⋊C4—232no—
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—24no—
468C2×C4⋊C4—232no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—41no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4C2×D418yes—
493C2×C4⋊C4C2×D414yes—
494C2×C4⋊C4C2×D414yes—
495C2×C4⋊C4C2×D414yes—
496C2×C4⋊C4C2×D418yes—
497C2×C4⋊C4C2×D414yes—
498C2×C22⋊C4—232no—
499C2×C22⋊C4—232no—
500C2×C22⋊C4—232no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
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—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—24no—
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—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
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—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4C2×D418yes—
597C2×C22⋊C4C2×D418yes—
598C2×C22⋊C4C2×D418yes—
599C2×C42—22no—
600C2×C42—24no—
601C2×C42—41no—
602C2×C42—41no—
603C2×C42—42no—
604C2×C42—42no—
605#95—22no—
606#95—22no—
607#95—24no—
608#95—24no—
609#95—22no—
610#95—22no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—24no—
619#95—24no—
620#95—24no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95—42no—
632#95—42no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—28no—
642C24—28no—
643C24—216no—
644C24—216no—
645C24—28no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—28no—
659C24—28no—
660C24—28no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—21no—
672C24—22no—
673C24—21no—
674C24—21no—
675C24—22no—
676C24—22no—
677C24—21no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—48no—
700C24—44no—
701C24—44no—
702C24—48no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24—44no—
707C24—44no—
708C24—44no—
709C24—44no—
710C24—44no—
711C24—44no—
712C24—44no—
713C24—44no—
714C24—44no—
715C24—44no—
716C24—44no—
717C24—84no—
718C24—84no—
719C24—84no—
720C24—84no—
721C24—84no—
722C24—84no—
723C24C22×D414yes—
724C24C22×D414yes—
725C24C22×D412yes—
726C24C2×#4112yes—
727C24C2×#4114yes—
728C24C2×#4112yes—
729C24C2×#4112yes—
730C24H(5,𝔽2)14yes—
731C24H(5,𝔽2)12yes—
732C24H(5,𝔽2)12yes—
733C24H(5,𝔽2)12yes—
734C242−1+412yes—
735C24C2511yescharacteristic
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—84no—
740C2×Q8—84no—
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—216no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—216no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—4128no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—48no—
762C2×D4—44no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—216no—
789C22×C4—28no—
790C22×C4—216no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—28no—
826C22×C4—216no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
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—22no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
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—48no—
904C22×C4—48no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—4128no—
911C22×C4—44no—
912C22×C4—48no—
913C22×C4—48no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—84no—
918C22×C4—84no—
919C22×C4C22×D414yes—
920C22×C4C22×D412yes—
921C22×C4C22×D414yes—
922C22×C4C22×D412yes—
923C22×C4C22×D412yes—
924C22×C4C22×D414yes—
925C22×C4C22×D414yes—
926C22×C4C22×D412yes—
927C22×C4C22×D414yes—
928C22×C4C22×D412yes—
929C22×C4C22×D412yes—
930C22×C4C2×#4112yes—
931C4⋊C4—216no—
932C4⋊C4—216no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—84no—
943C4⋊C4—82no—
944C4⋊C4—82no—
945C4⋊C4#120116yescomplemented
946C22⋊C4—216no—
947C22⋊C4—216no—
948C22⋊C4—216no—
949C22⋊C4—216no—
950C22⋊C4—216no—
951C22⋊C4—216no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—84no—
966C22⋊C4—82no—
967C22⋊C4—82no—
968C22⋊C4—84no—
969C22⋊C4—84no—
970C22⋊C4—84no—
971C22⋊C4—84no—
972C22⋊C4—84no—
973C22⋊C4—84no—
974C22⋊C4—84no—
975C22⋊C4—84no—
976C22⋊C4—84no—
977C22⋊C4—84no—
978C22⋊C4—84no—
979C22⋊C4—84no—
980C42—44no—
981C42—84no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—22no—
987C23—24no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—232no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—22no—
1019C23—24no—
1020C23—22no—
1021C23—24no—
1022C23—24no—
1023C23—22no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—432no—
1030C23—432no—
1031C23—416no—
1032C23—432no—
1033C23—416no—
1034C23—432no—
1035C23—416no—
1036C23—416no—
1037C23—416no—
1038C23—416no—
1039C23—416no—
1040C23—416no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—416no—
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—41no—
1059C23—41no—
1060C23—42no—
1061C23—41no—
1062C23—42no—
1063C23—42no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—41no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—41no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—41no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—41no—
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—816no—
1105C23—816no—
1106C23—816no—
1107C23—816no—
1108C23—88no—
1109C23—88no—
1110C23—88no—
1111C23—88no—
1112C23#53514yes—
1113C23#53814yes—
1114C23#53914yes—
1115C23#54618yes—
1116C23#54614yes—
1117C23#54814yes—
1118C23#55114yes—
1119C23#56214yes—
1120C23C23×D411yescharacteristic
1121C23C23×D412yes—
1122C23C22×#4111yescharacteristic
1123C23C22×#4111yescharacteristic
1124C23C2×H(5,𝔽2)11yescharacteristic
1125C23C2×H(5,𝔽2)11yescharacteristic
1126C23C2×H(5,𝔽2)11yescharacteristic
1127C23C2×H(5,𝔽2)12yes—
1128C23C2×2−1+411yescharacteristic
1129C23#58512yes—
1130C23#58512yes—
1131Q8—88no—
1132D4—432no—
1133D4—432no—
1134D4—416no—
1135D4—816no—
1136D4—816no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—416no—
1168C2×C4—416no—
1169C2×C4—432no—
1170C2×C4—416no—
1171C2×C4—416no—
1172C2×C4—416no—
1173C2×C4—432no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
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—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
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—42no—
1237C2×C4—42no—
1238C2×C4—42no—
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—88no—
1251C2×C4C2×#12014yes—
1252C2×C4C2×#12014yes—
1253C2×C4C2×#12014yes—
1254C22—28no—
1255C22—24no—
1256C22—24no—
1257C22—28no—
1258C22—24no—
1259C22—28no—
1260C22—28no—
1261C22—24no—
1262C22—24no—
1263C22—24no—
1264C22—28no—
1265C22—28no—
1266C22—28no—
1267C22—464no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—42no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—42no—
1290C22—44no—
1291C22—42no—
1292C22—832no—
1293C22—82no—
1294C22—82no—
1295C22—81no—
1296C22—82no—
1297C22—81no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—82no—
1303C22—81no—
1304C22—82no—
1305C22—81no—
1306C22—82no—
1307C22#269618yescomplemented
1308C22C22×#12011yescharacteristic
1309C22C2×#53511yescharacteristic
1310C22#344911yescharacteristic
1311C22C2×#53811yescharacteristic
1312C22C2×#53911yescharacteristic
1313C22C2×#54612yes—
1314C22C2×#54611yescharacteristic
1315C22C2×#54811yescharacteristic
1316C22D4×#4112yes—
1317C22C2×#55111yescharacteristic
1318C22#348412yes—
1319C22#348411yescharacteristic
1320C22#348711yescharacteristic
1321C22#348812yes—
1322C22#348812yes—
1323C22#348912yes—
1324C22#349112yes—
1325C22#351312yes—
1326C22C2×#56211yescharacteristic
1327C22#353312yes—
1328C22#353412yes—
1329C22#353412yes—
1330C22#353512yes—
1331C4—24no—
1332C4—24no—
1333C4—24no—
1334C4—42no—
1335C4—44no—
1336C4—42no—
1337C4—44no—
1338C4—42no—
1339C4—42no—
1340C4—82no—
1341C4—82no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—82no—
1346C4—82no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C2—28no—
1351C2—48no—
1352C2—82no—
1353C2—84no—
1354C2#3525011yescharacteristic
1355C2#3615211yescharacteristic
1356C2#3642811yescharacteristic
1357C2#3671011yescharacteristic
1358C2#3766112yes—
1359C2#3771312yes—
1360C2#3784311yescharacteristic
1361C2#3911611yescharacteristic
1362C2#4545412yes—
1363C2C2×#269611yescharacteristic
1364C2#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. C23×#123C2semidirect
2. C2×#2696C2semidirect
3. C2×#2417C2semidirect
4. #16359C2semidirect
5. #16256C2semidirect
6. #15668C2semidirect
7. #15464C2semidirect
8. #15368C2semidirect
9. #15272C2semidirect
10. #14822C2semidirect
11. #14820C2semidirect
12. #14725C2semidirect
13. #14717C2semidirect
14. #14717C2semidirect
16. #14694C2semidirect
17. #14680C2semidirect
18. #14360C2semidirect
19. #14019C2semidirect
20. #13967C2semidirect
21. #13967C2semidirect
22. #13902C2semidirect
23. #13882C2semidirect
33. C22×C22⋊Q8C22semidirect
44. C2×#400C22semidirect
45. C2×#398C22semidirect
46. C2×#398C22semidirect
47. C2×#397C22semidirect
48. C2×#396C22semidirect
49. C2×#396C22semidirect
50. C2×#394C22semidirect
51. C2×#393C22semidirect
52. C2×#393C22semidirect
55. C2×#391C22semidirect
58. C2×#389C22semidirect
59. C2×#388C22semidirect
60. C2×#387C22semidirect
65. C2×#386C22semidirect
66. C2×#386C22semidirect
67. C2×#386C22semidirect
68. C2×#386C22semidirect
72. C2×#380C22semidirect
73. C2×#380C22semidirect
74. C2×#380C22semidirect
82. #1445C22semidirect
83. #1442C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1441C22semidirect
87. #1441C22semidirect
88. #1440C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
106. #1438C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
165. C2×#123D4semidirect
183. C22×C4⋊C4D4semidirect
945. C4⋊C4#120semidirect
1307. C22#2696semidirect

Maximal subgroups

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

subgroupindex
C23×#1232
C2×#26962
C2×#24172
#163592
#162562
#156682
#154642
#153682
#152722
#148222
#148202
#147252
#147172
#147152
#146942
#146802
#143602
#140192
#139672
#139022
#138822