Finite Group Databasebeta

← #825292

Subgroups — #825292

Order 512.

4184 conjugacy classes of subgroups.

The subgroup lattice has 1319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2491C211yesmaximal, characteristic, complemented
2C2×#2459C212yesmaximal, complemented
3C2×#2472C212yesmaximal, complemented
4C2×#2358C211yesmaximal, characteristic, complemented
5#17068C211yesmaximal, characteristic, complemented
6#16807C211yesmaximal, characteristic, complemented
7#15833C212yesmaximal, complemented
8#15549C212yesmaximal, complemented
9#15453C212yesmaximal, complemented
10#15267C212yesmaximal, complemented
11#15178C211yesmaximal, characteristic, complemented
12#15144C211yesmaximal, characteristic, complemented
13#15079C211yesmaximal, characteristic, complemented
14#14900C211yesmaximal, characteristic, complemented
15#14811C211yesmaximal, characteristic, complemented
16#14762C211yesmaximal, characteristic, complemented
17#14716C211yesmaximal, characteristic, complemented
18#14228C212yesmaximal, complemented
19#14228C211yesmaximal, characteristic, complemented
20#14084C212yesmaximal, complemented
21#13903C211yesmaximal, characteristic, complemented
22#13847C211yesmaximal, characteristic, complemented
23#13816C211yesmaximal, characteristic, complemented
24C22×C4⋊Q8C2211yescharacteristic, complemented
25C22×#124C2212yes—
26C22×C22⋊Q8C2212yes—
27C22×#121C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×#120C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2491—28no—
35#2472—216no—
36#2459—216no—
37C2×#397C2212yes—
38C2×#394C2212yes—
39C2×#394C2212yes—
40C2×#394C2212yes—
41C2×#394C2212yes—
42C2×#394C2212yescomplemented
43C2×#393C2212yes—
44C2×#393C2212yescomplemented
45C2×#393C2212yescomplemented
46C2×#392C2212yes—
47C2×#392C2211yescharacteristic
48C2×#392C2212yes—
49C2×#392C2211yescharacteristic
50C2×#392C2212yes—
51C2×#392C2211yescharacteristic, complemented
52#2358—28no—
53C2×#391C2212yescomplemented
54C2×#390C2212yes—
55C2×#390C2211yescharacteristic
56C2×#390C2212yes—
57C2×#390C2212yes—
58C2×#390C2211yescharacteristic, complemented
59C2×#390C2211yescharacteristic, complemented
60C2×#390C2212yescomplemented
61C2×#388C2211yescharacteristic
62C2×#388C2211yescharacteristic
63C2×#388C2212yes—
64C2×#388C2212yes—
65C2×#388C2212yescomplemented
66C2×#388C2212yescomplemented
67C2×#388C2212yescomplemented
68C2×#387C2212yescomplemented
69C2×#386C2212yes—
70C2×#386C2211yescharacteristic
71C2×#386C2211yescharacteristic
72C2×#386C2211yescharacteristic
73C2×#386C2212yes—
74C2×#386C2212yes—
75C2×#386C2212yescomplemented
76C2×#385C2211yescharacteristic
77C2×#385C2211yescharacteristic
78C2×#381C2212yes—
79C2×#380C2211yescharacteristic
80C2×#379C2212yes—
81C2×C4×C4⋊C4C2211yescharacteristic, complemented
82C2×C4×C22⋊C4C2212yes—
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2212yescomplemented
87C2×#376C2211yescharacteristic, complemented
88#1445C2212yescomplemented
89#1445C2212yescomplemented
90#1445C2212yescomplemented
91#1444C2211yescharacteristic, complemented
92#1444C2212yescomplemented
93#1444C2211yescharacteristic, complemented
94#1444C2211yescharacteristic, complemented
95#1439C2212yes—
96#1439C2211yescharacteristic
97#1439C2211yescharacteristic
98#1439C2211yescharacteristic
99#1439C2211yescharacteristic
100#1439C2211yescharacteristic
101#1439C2211yescharacteristic
102#1439C2212yes—
103#1439C2212yescomplemented
104#1439C2211yescharacteristic, complemented
105#1439C2211yescharacteristic, complemented
106#1439C2211yescharacteristic, complemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yes—
114#1438C2211yescharacteristic, complemented
115#1437C2212yes—
116#1437C2212yes—
117#1437C2212yes—
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1436C2212yescomplemented
121C4⋊#95C2212yescomplemented
122C4⋊#95C2211yescharacteristic, complemented
123#1434C2211yescharacteristic, complemented
124C22⋊#95C2211yescharacteristic
125C4×#95C2212yescomplemented
126C4×#95C2211yescharacteristic, complemented
127C26C2311yescharacteristic
128C23×Q8C2312yes—
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2312yes—
133C23×D4C2311yescharacteristic
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C2×C4⋊Q8—24no—
143C2×C4⋊Q8—44no—
144C2×#124—28no—
145C2×#124—28no—
146C2×#124—28no—
147C2×C22⋊Q8—28no—
148C2×C22⋊Q8—44no—
149C2×C22⋊Q8—44no—
150C2×#121—24no—
151C2×#121—44no—
152C2×#120—24no—
153C2×#120—24no—
154C2×#120—28no—
155C2×#120—24no—
156C2×#120—44no—
157C2×#120—44no—
158C2×C4×D4—24no—
159C2×C4×D4—28no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—42no—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2312yes—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—28no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—42no—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222#397—28no—
223#394—28no—
224#394—28no—
225#394—28no—
226#394—28no—
227#394—28no—
228#393—28no—
229#393—28no—
230#393—28no—
231#392—28no—
232#392—28no—
233#392—24no—
234#392—42no—
235#392—42no—
236#392—44no—
237#391—28no—
238#390—28no—
239#390—24no—
240#390—28no—
241#390—24no—
242#390—24no—
243#390—44no—
244#390—44no—
245#388—24no—
246#388—28no—
247#388—24no—
248#388—28no—
249#388—28no—
250#388—28no—
251#388D4116yescomplemented
252#387—28no—
253#386—24no—
254#386—28no—
255#386—24no—
256#386—24no—
257#386—28no—
258#386—28no—
259#386—28no—
260#385—24no—
261#385—24no—
262#381—28no—
263#380—24no—
264#379—28no—
265C4×C4⋊C4—24no—
266C4×C22⋊C4—24no—
267C4×C22⋊C4—28no—
268C4×C22⋊C4—28no—
269C4×C22⋊C4—42no—
270C4×C22⋊C4D418yescomplemented
271#376—42no—
272C2×#95C2311yescharacteristic
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2312yes—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—24no—
306C25—22no—
307C25—22no—
308C25—41no—
309C25—42no—
310C25—41no—
311C25—42no—
312C25—42no—
313C25C2412yes—
314C25C2411yescharacteristic
315C25C2411yescharacteristic
316C25C2411yescharacteristic
317C25C2411yescharacteristic
318C22×Q8—24no—
319C22×Q8—24no—
320C22×Q8—24no—
321C22×Q8—24no—
322C22×Q8—42no—
323C22×Q8—42no—
324C22×Q8—42no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—24no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—41no—
352C22×D4—41no—
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×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4#4114yes—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—24no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—24no—
389C23×C4—41no—
390C23×C4—41no—
391C23×C4—41no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—41no—
398C23×C4—42no—
399C23×C4C2×D414yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2412yes—
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C4⋊Q8—416no—
419#124—432no—
420C22⋊Q8—432no—
421#121—416no—
422#120—232no—
423#120—432no—
424C4×D4—416no—
425C4×D4—416no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4C2×D418yes—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
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—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—416no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—416no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
552C2×C22⋊C4C2×D418yes—
553C2×C22⋊C4C2×D418yes—
554C2×C22⋊C4C2×D414yes—
555C2×C22⋊C4C2×D418yes—
556C2×C22⋊C4#4114yes—
557C2×C22⋊C4#4114yes—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—24no—
562C2×C42—24no—
563C2×C42—24no—
564C2×C42—24no—
565C2×C42—24no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42—42no—
569C2×C42—42no—
570C2×C42—42no—
571C2×C42—42no—
572C2×C42—42no—
573C2×C42—42no—
574C2×C42C2×D414yes—
575C2×C42C2×D414yes—
576C2×C42C2×D418yes—
577#95—24no—
578#95—22no—
579#95—22no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—22no—
589#95—22no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95C2×D414yes—
604#95C2×D414yes—
605#95C2×D418yes—
606#95C2×D418yes—
607C24—21no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—21no—
623C24—21no—
624C24—28no—
625C24—21no—
626C24—22no—
627C24—22no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
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—22no—
659C24—22no—
660C24—44no—
661C24—48no—
662C24—48no—
663C24—44no—
664C24—44no—
665C24—44no—
666C24—48no—
667C24—48no—
668C24—44no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—82no—
673C24—84no—
674C24—84no—
675C24—82no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24C22×D414yes—
683C24C22×D412yes—
684C24C2×#4112yes—
685C24C2×#4112yes—
686C24C2×#4112yes—
687C24C2×#4112yes—
688C24H(5,𝔽2)12yes—
689C24C2511yescharacteristic
690C2×Q8—48no—
691C2×Q8—48no—
692C2×Q8—48no—
693C2×Q8—48no—
694C2×Q8—84no—
695C2×Q8—84no—
696C2×Q8—84no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—44no—
701C2×D4—48no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—48no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—82no—
727C2×D4—82no—
728C2×D4—84no—
729C2×D4—84no—
730C2×D4—84no—
731C2×D4—84no—
732C2×D4—84no—
733C2×D4—84no—
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—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—28no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—44no—
844C22×C4—48no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—82no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—82no—
854C22×C4—82no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4—82no—
859C22×C4C22×D412yes—
860C22×C4C22×D414yes—
861C22×C4C22×D414yes—
862C22×C4C22×D412yes—
863C22×C4C22×D414yes—
864C22×C4C22×D414yes—
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D414yes—
868C22×C4C22×D412yes—
869C22×C4C22×D414yes—
870C22×C4C22×D412yes—
871C22×C4C2×#4112yes—
872C22×C4C2×#4112yes—
873C22×C4C2×#4112yes—
874C22×C4C2×#4112yes—
875C22×C4C2×#4112yes—
876C22×C4H(5,𝔽2)14yes—
877C22×C4H(5,𝔽2)12yes—
878C4⋊C4—28no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—44no—
887C4⋊C4—44no—
888C4⋊C4—82no—
889C22⋊C4—28no—
890C22⋊C4—216no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—44no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—82no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4#127116yes—
925C42—28no—
926C42—48no—
927C42—44no—
928C42—44no—
929C42—48no—
930C42—84no—
931C42—84no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—22no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—24no—
954C23—22no—
955C23—24no—
956C23—22no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—22no—
965C23—22no—
966C23—416no—
967C23—416no—
968C23—41no—
969C23—41no—
970C23—42no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—42no—
975C23—42no—
976C23—41no—
977C23—42no—
978C23—42no—
979C23—41no—
980C23—42no—
981C23—42no—
982C23—41no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—41no—
999C23—41no—
1000C23—42no—
1001C23—42no—
1002C23—41no—
1003C23—41no—
1004C23—42no—
1005C23—42no—
1006C23—41no—
1007C23—41no—
1008C23—42no—
1009C23—42no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—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—816no—
1060C23—88no—
1061C23—88no—
1062C23—88no—
1063C23—816no—
1064C23—816no—
1065C23—816no—
1066C23—88no—
1067C23—88no—
1068C23C2×#12714yes—
1069C23#55514yes—
1070C23C23×D411yescharacteristic
1071C23C23×D412yes—
1072C23C22×#4111yescharacteristic
1073C23C22×#4111yescharacteristic
1074C23C22×#4111yescharacteristic
1075C23C2×H(5,𝔽2)11yescharacteristic
1076C23C2×H(5,𝔽2)11yescharacteristic
1077C23C2×H(5,𝔽2)12yes—
1078C23#58512yes—
1079C23#58512yes—
1080C23#58511yescharacteristic
1081Q8—816no—
1082D4—416no—
1083D4—416no—
1084D4—88no—
1085D4—88no—
1086D4—816no—
1087D4—816no—
1088D4—816no—
1089D4—816no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—88no—
1193C2×C4—88no—
1194C2×C4—88no—
1195C2×C4—88no—
1196C2×C4—88no—
1197C2×C4#52514yes—
1198C2×C4C2×#12714yes—
1199C2×C4C2×#12714yes—
1200C2×C4#54614yes—
1201C22—28no—
1202C22—24no—
1203C22—24no—
1204C22—24no—
1205C22—24no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—832no—
1234C22—82no—
1235C22—82no—
1236C22—82no—
1237C22—82no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—82no—
1252C22—82no—
1253C22—82no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22C2×#52511yescharacteristic
1262C22C22×#12711yescharacteristic
1263C22#344911yescharacteristic
1264C22C2×#54611yescharacteristic
1265C22D4×#4112yes—
1266C22D4×#4112yes—
1267C22D4×#4112yes—
1268C22C2×#55511yescharacteristic
1269C22#347511yescharacteristic
1270C22#348412yes—
1271C22#348411yescharacteristic
1272C22#348812yes—
1273C22#348811yescharacteristic
1274C22#349612yes—
1275C22#350011yescharacteristic
1276C22#350512yes—
1277C22#350611yescharacteristic
1278C22#351412yes—
1279C22#351412yes—
1280C22#351911yescharacteristic
1281C22#354512yes—
1282C22#355812yes—
1283C22#356612yes—
1284C4—24no—
1285C4—24no—
1286C4—24no—
1287C4—24no—
1288C4—44no—
1289C4—44no—
1290C4—44no—
1291C4—44no—
1292C4—42no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—81no—
1298C4—82no—
1299C4—82no—
1300C4—81no—
1301C4—81no—
1302C2—44no—
1303C2—44no—
1304C2—82no—
1305C2—82no—
1306C2—162no—
1307C2#3493611yescharacteristic
1308C2#3570311yescharacteristic
1309C2#3592111yescharacteristic
1310C2#3616011yescharacteristic
1311C2#3626011yescharacteristic
1312C2#3802811yescharacteristic
1313C2#4239011yescharacteristic
1314C2#4303512yes—
1315C2#4303812yes—
1316C2#5916012yes—
1317C2#5916412yes—
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×#2491C2semidirect
2. C2×#2459C2semidirect
3. C2×#2472C2semidirect
4. C2×#2358C2semidirect
5. #17068C2semidirect
6. #16807C2semidirect
7. #15833C2semidirect
8. #15549C2semidirect
9. #15453C2semidirect
10. #15267C2semidirect
11. #15178C2semidirect
12. #15144C2semidirect
13. #15079C2semidirect
14. #14900C2semidirect
15. #14811C2semidirect
16. #14762C2semidirect
17. #14716C2semidirect
18. #14228C2semidirect
19. #14228C2semidirect
20. #14084C2semidirect
21. #13903C2semidirect
22. #13847C2semidirect
23. #13816C2semidirect
24. C22×C4⋊Q8C22semidirect
42. C2×#394C22semidirect
44. C2×#393C22semidirect
45. C2×#393C22semidirect
51. C2×#392C22semidirect
53. C2×#391C22semidirect
58. C2×#390C22semidirect
59. C2×#390C22semidirect
60. C2×#390C22semidirect
65. C2×#388C22semidirect
66. C2×#388C22semidirect
67. C2×#388C22semidirect
68. C2×#387C22semidirect
75. C2×#386C22semidirect
81. C2×C4×C4⋊C4C22semidirect
86. C2×C4×C22⋊C4C22semidirect
87. C2×#376C22semidirect
88. #1445C22semidirect
89. #1445C22semidirect
90. #1445C22semidirect
91. #1444C22semidirect
92. #1444C22semidirect
93. #1444C22semidirect
94. #1444C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
114. #1438C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1436C22semidirect
121. C4⋊#95C22semidirect
122. C4⋊#95C22semidirect
123. #1434C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
251. #388D4semidirect
270. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24912
C2×#24592
C2×#24722
C2×#23582
#170682
#168072
#158332
#155492
#154532
#152672
#151782
#151442
#150792
#149002
#148112
#147622
#147162
#142282
#140842
#139032
#138472
#138162