Finite Group Databasebeta

← #719512

Subgroups — #719512

Order 512.

4416 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2543C211yesmaximal, characteristic, complemented
2C2×#2424C212yesmaximal, complemented
3C2×#2617C211yesmaximal, characteristic, complemented
4C2×#2361C211yesmaximal, characteristic, complemented
5C2×#2321C211yesmaximal, characteristic, complemented
6#17069C211yesmaximal, characteristic, complemented
7#17068C211yesmaximal, characteristic, complemented
8#16821C211yesmaximal, characteristic, complemented
9#16819C211yesmaximal, characteristic, complemented
10#15780C212yesmaximal, complemented
11#15307C212yesmaximal, complemented
12#15303C212yesmaximal, complemented
13#15274C212yesmaximal, complemented
14#15147C211yesmaximal, characteristic, complemented
15#15123C211yesmaximal, characteristic, complemented
16#15081C211yesmaximal, characteristic, complemented
17#14806C211yesmaximal, characteristic, complemented
18#14747C212yesmaximal, complemented
19#14718C212yesmaximal, complemented
20#13965C211yesmaximal, characteristic, complemented
21#13899C212yesmaximal, complemented
22#13872C211yesmaximal, characteristic, complemented
23C2×#1439C211yesmaximal, characteristic, complemented
24C22×#121C2212yes—
25C22×#121C2211yescharacteristic
26C22×#121C2212yes—
27C22×#120C2212yes—
28C22×#120C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic, complemented
32C23×C4⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2212yes—
35#2617—28no—
36#2543—28no—
37#2424—216no—
38C2×#398C2211yescharacteristic, complemented
39C2×#397C2211yescharacteristic
40C2×#397C2211yescharacteristic
41C2×#397C2211yescharacteristic, complemented
42C2×#396C2212yes—
43C2×#394C2212yes—
44C2×#394C2212yes—
45C2×#394C2212yes—
46C2×#394C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2211yescharacteristic, complemented
50C2×#394C2212yescomplemented
51C2×#392C2211yescharacteristic
52C2×#392C2212yes—
53C2×#392C2211yescharacteristic
54C2×#392C2211yescharacteristic, complemented
55#2361—28no—
56#2321—28no—
57C2×#390C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2212yes—
60C2×#390C2211yescharacteristic, complemented
61C2×#389C2211yescharacteristic, complemented
62C2×#388C2211yescharacteristic
63C2×#388C2211yescharacteristic
64C2×#388C2211yescharacteristic
65C2×#388C2211yescharacteristic
66C2×#388C2212yes—
67C2×#388C2212yescomplemented
68C2×#388C2212yescomplemented
69C2×#386C2212yes—
70C2×#386C2211yescharacteristic
71C2×#386C2211yescharacteristic
72C2×#386C2211yescharacteristic
73C2×#386C2212yes—
74C2×#386C2212yes—
75C2×#386C2212yes—
76C2×#386C2212yes—
77C2×#386C2212yescomplemented
78C2×#385C2211yescharacteristic
79C2×#385C2212yes—
80C2×#385C2212yes—
81C2×#385C2212yescomplemented
82C2×#380C2211yescharacteristic
83C2×#380C2212yescomplemented
84C2×#380C2212yescomplemented
85C2×#379C2211yescharacteristic
86C2×C4×C4⋊C4C2211yescharacteristic, complemented
87C2×C4×C22⋊C4C2211yescharacteristic
88C22×#95C2211yescharacteristic
89C22×#95C2212yes—
90#1444C2212yescomplemented
91#1444C2212yescomplemented
92#1442C2212yescomplemented
93#1441C2211yescharacteristic, complemented
94#1441C2211yescharacteristic, complemented
95#1441C2212yescomplemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1440C2212yes—
99#1440C2212yes—
100#1440C2212yescomplemented
101#1440C2212yescomplemented
102#1439C2211yescharacteristic
103#1439C2211yescharacteristic
104#1439C2212yes—
105#1439C2211yescharacteristic
106#1439C2211yescharacteristic
107#1439C2212yes—
108#1439C2212yes—
109#1439C2212yes—
110#1439C2211yescharacteristic, complemented
111#1439C2211yescharacteristic, complemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1439C2212yescomplemented
115#1439C2212yescomplemented
116#1438C2212yes—
117#1438C2212yes—
118#1438C2212yescomplemented
119C4⋊#95C2211yescharacteristic, complemented
120C4⋊#95C2212yescomplemented
121C4⋊#95C2211yescharacteristic, complemented
122C4⋊#95C2212yescomplemented
123C4⋊#95C2211yescharacteristic, complemented
124C4⋊#95C2211yescharacteristic, complemented
125#1434C2212yescomplemented
126C22⋊#95C2212yes—
127C22⋊#95C2212yescomplemented
128C26C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2312yes—
133C23×D4C2312yes—
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2312yes—
139C24×C4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C2×#121—24no—
144C2×#121—24no—
145C2×#121—28no—
146C2×#121—28no—
147C2×#121—28no—
148C2×#121—44no—
149C2×#121—44no—
150C2×#121—44no—
151C2×#121D418yescomplemented
152C2×#120—28no—
153C2×#120—28no—
154C2×#120—24no—
155C2×#120—24no—
156C2×#120—44no—
157C2×#120D418yescomplemented
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—28no—
162C2×C4×D4—28no—
163C2×C4×D4—28no—
164C2×C4×D4—24no—
165C2×C4×D4—44no—
166C22×C4⋊C4—24no—
167C22×C4⋊C4—44no—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C22⋊C4—28no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—24no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4—44no—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#398—24no—
228#397—24no—
229#397—24no—
230#397—24no—
231#396—28no—
232#394—28no—
233#394—24no—
234#394—28no—
235#394—28no—
236#394—28no—
237#394—44no—
238#394—44no—
239#394—44no—
240#392—24no—
241#392—24no—
242#392—28no—
243#392—24no—
244#390—28no—
245#390—24no—
246#390—24no—
247#390—24no—
248#389—24no—
249#388—28no—
250#388—28no—
251#388—24no—
252#388—24no—
253#388—24no—
254#388—24no—
255#388—28no—
256#386—28no—
257#386—28no—
258#386—28no—
259#386—24no—
260#386—28no—
261#386—28no—
262#386—28no—
263#386—24no—
264#386—24no—
265#385—24no—
266#385—28no—
267#385—28no—
268#385—44no—
269#380—24no—
270#380—44no—
271#380—44no—
272#379—24no—
273C4×C4⋊C4—24no—
274C4×C22⋊C4D418yescomplemented
275C2×#95—24no—
276C2×#95—44no—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25C2×D414yes—
319C25C2411yescharacteristic
320C25C2411yescharacteristic
321C25C2412yes—
322C25C2411yescharacteristic
323C25C2411yescharacteristic
324C22×D4—24no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—24no—
328C22×D4—22no—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—22no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—42no—
350C22×D4—42no—
351C22×D4—42no—
352C22×D4—42no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4C2×D418yes—
370C22×D4C2×D414yes—
371C22×D4C2×D414yes—
372C22×D4C2×D414yes—
373C22×D4C2×D414yes—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4C2×D414yes—
408C23×C4C2×D414yes—
409C23×C4#4114yes—
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428#121—232no—
429#121—432no—
430#121—432no—
431#120—232no—
432#120—432no—
433C4×D4—416no—
434C4×D4—416no—
435C4×D4—432no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—416no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4C2×D414yes—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
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—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—22no—
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—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—432no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—416no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4C2×D414yes—
571C2×C22⋊C4C2×D418yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D414yes—
574C2×C22⋊C4C2×D414yes—
575C2×C22⋊C4#4114yes—
576C2×C42—24no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—22no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42C2×D414yes—
585C2×C42C2×D414yes—
586#95—24no—
587#95—22no—
588#95—22no—
589#95—24no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95C2×D414yes—
616#95C2×D414yes—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—28no—
622C24—21no—
623C24—21no—
624C24—22no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—21no—
654C24—21no—
655C24—21no—
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—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—44no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—82no—
679C24—82no—
680C24—84no—
681C24—84no—
682C24—82no—
683C24—82no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24C22×D412yes—
689C24C22×D412yes—
690C24C22×D412yes—
691C24C22×D414yes—
692C24C22×D412yes—
693C24C22×D412yes—
694C24C22×D412yes—
695C24C2×#4112yes—
696C24C2×#4112yes—
697C24H(5,𝔽2)12yes—
698C242−1+412yes—
699C24C2511yescharacteristic
700C2×D4—28no—
701C2×D4—216no—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—216no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—48no—
710C2×D4—44no—
711C2×D4—48no—
712C2×D4—44no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—44no—
718C2×D4—48no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—48no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—82no—
731C2×D4—82no—
732C2×D4—82no—
733C2×D4—82no—
734C2×D4—84no—
735C2×D4—84no—
736C2×D4—84no—
737C2×D4—84no—
738C2×D4—84no—
739C2×D4—84no—
740C2×D4—84no—
741C2×D4—84no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C2×D4—84no—
747C2×D4—84no—
748C2×D4—84no—
749C2×D4—84no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
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—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—48no—
853C22×C4—44no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—44no—
858C22×C4—82no—
859C22×C4—84no—
860C22×C4—82no—
861C22×C4—84no—
862C22×C4—84no—
863C22×C4—84no—
864C22×C4—84no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—82no—
872C22×C4—82no—
873C22×C4#121116yescomplemented
874C22×C4C22×D414yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C2×#4112yes—
887C22×C4C2×#4112yes—
888C22×C4C2×#4112yes—
889C22×C4C2×#4112yes—
890C22×C4H(5,𝔽2)14yes—
891C22×C4H(5,𝔽2)14yes—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—44no—
900C4⋊C4—84no—
901C4⋊C4—84no—
902C4⋊C4—82no—
903C4⋊C4—82no—
904C4⋊C4—84no—
905C4⋊C4—84no—
906C22⋊C4—216no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—216no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—82no—
930C22⋊C4—82no—
931C22⋊C4—82no—
932C22⋊C4—84no—
933C22⋊C4—82no—
934C22⋊C4—82no—
935C22⋊C4—82no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4#121116yes—
941C42—44no—
942C42—44no—
943C42—48no—
944C42—44no—
945C23—24no—
946C23—22no—
947C23—24no—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—432no—
984C23—41no—
985C23—41no—
986C23—42no—
987C23—41no—
988C23—42no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—41no—
998C23—42no—
999C23—41no—
1000C23—41no—
1001C23—42no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—42no—
1006C23—41no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—41no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—416no—
1067C23—816no—
1068C23—88no—
1069C23—88no—
1070C23—88no—
1071C23—816no—
1072C23—816no—
1073C23—88no—
1074C23—88no—
1075C23—88no—
1076C23C2×#12114yes—
1077C23C2×#12114yes—
1078C23#53714yes—
1079C23D4214yes—
1080C23#54714yes—
1081C23#54714yes—
1082C23#55514yes—
1083C23C23×D411yescharacteristic
1084C23C23×D411yescharacteristic
1085C23C23×D411yescharacteristic
1086C23C22×#4111yescharacteristic
1087C23C22×#4111yescharacteristic
1088C23C2×H(5,𝔽2)11yescharacteristic
1089C23C2×H(5,𝔽2)12yes—
1090C23C2×H(5,𝔽2)12yes—
1091C23C2×2−1+411yescharacteristic
1092C23#58512yes—
1093C23#58512yes—
1094D4—416no—
1095D4—416no—
1096D4—432no—
1097D4—88no—
1098D4—88no—
1099D4—816no—
1100D4—816no—
1101D4—816no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—416no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—816no—
1206C2×C4—88no—
1207C2×C4—816no—
1208C2×C4—816no—
1209C2×C4—88no—
1210C2×C4C2×#12114yes—
1211C2×C4C2×#12114yes—
1212C2×C4C2×#12114yes—
1213C2×C4C2×#12114yes—
1214C22—28no—
1215C22—24no—
1216C22—24no—
1217C22—28no—
1218C22—28no—
1219C22—24no—
1220C22—28no—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—44no—
1246C22—832no—
1247C22—82no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—81no—
1261C22—82no—
1262C22—81no—
1263C22—81no—
1264C22—82no—
1265C22—82no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—82no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22#253718yes—
1274C22C22×#12111yescharacteristic
1275C22C22×#12111yescharacteristic
1276C22C2×#53711yescharacteristic
1277C22#345912yes—
1278C22C2×D4211yescharacteristic
1279C22C2×#54711yescharacteristic
1280C22C2×#54711yescharacteristic
1281C22C2×#55511yescharacteristic
1282C22#348412yes—
1283C22#348411yescharacteristic
1284C22#348512yes—
1285C22#348511yescharacteristic
1286C22#348812yes—
1287C22#349612yes—
1288C22#349811yescharacteristic
1289C22#350011yescharacteristic
1290C22#350612yes—
1291C22#351912yes—
1292C22#352112yes—
1293C22#353412yes—
1294C22#354112yes—
1295C22#354112yes—
1296C22#355812yes—
1297C4—24no—
1298C4—24no—
1299C4—24no—
1300C4—24no—
1301C4—44no—
1302C4—42no—
1303C4—42no—
1304C4—44no—
1305C4—44no—
1306C4—42no—
1307C4—82no—
1308C4—82no—
1309C4—82no—
1310C4—82no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C2—28no—
1316C2—84no—
1317C2—82no—
1318C2—82no—
1319C2—82no—
1320C2C2×#253711yescharacteristic
1321C2#3498411yescharacteristic
1322C2#3553311yescharacteristic
1323C2#3569111yescharacteristic
1324C2#3600911yescharacteristic
1325C2#3778812yes—
1326C2#3828012yes—
1327C2#4048911yescharacteristic
1328C2#4136811yescharacteristic
1329C2#4302312yes—
1330C2#4391112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2543C2semidirect
2. C2×#2424C2semidirect
3. C2×#2617C2semidirect
4. C2×#2361C2semidirect
5. C2×#2321C2semidirect
6. #17069C2semidirect
7. #17068C2semidirect
8. #16821C2semidirect
9. #16819C2semidirect
10. #15780C2semidirect
11. #15307C2semidirect
12. #15303C2semidirect
13. #15274C2semidirect
14. #15147C2semidirect
15. #15123C2semidirect
16. #15081C2semidirect
17. #14806C2semidirect
18. #14747C2semidirect
19. #14718C2semidirect
20. #13965C2semidirect
21. #13899C2semidirect
22. #13872C2semidirect
23. C2×#1439C2semidirect
31. C22×C4×D4C22semidirect
38. C2×#398C22semidirect
41. C2×#397C22semidirect
49. C2×#394C22semidirect
50. C2×#394C22semidirect
54. C2×#392C22semidirect
60. C2×#390C22semidirect
61. C2×#389C22semidirect
67. C2×#388C22semidirect
68. C2×#388C22semidirect
77. C2×#386C22semidirect
81. C2×#385C22semidirect
83. C2×#380C22semidirect
84. C2×#380C22semidirect
86. C2×C4×C4⋊C4C22semidirect
90. #1444C22semidirect
91. #1444C22semidirect
92. #1442C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
95. #1441C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
100. #1440C22semidirect
101. #1440C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
114. #1439C22semidirect
115. #1439C22semidirect
118. #1438C22semidirect
119. C4⋊#95C22semidirect
120. C4⋊#95C22semidirect
121. C4⋊#95C22semidirect
122. C4⋊#95C22semidirect
123. C4⋊#95C22semidirect
124. C4⋊#95C22semidirect
125. #1434C22semidirect
127. C22⋊#95C22semidirect
151. C2×#121D4semidirect
157. C2×#120D4semidirect
274. C4×C22⋊C4D4semidirect
873. C22×C4#121semidirect

Maximal subgroups

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

subgroupindex
C2×#25432
C2×#24242
C2×#26172
C2×#23612
C2×#23212
#170692
#170682
#168212
#168192
#157802
#153072
#153032
#152742
#151472
#151232
#150812
#148062
#147472
#147182
#139652
#138992
#138722
C2×#14392