Finite Group Databasebeta

← #648731

Subgroups — #648731

Order 512.

5918 conjugacy classes of subgroups.

The subgroup lattice has 1310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#123C211yesmaximal, characteristic
2C2×#2488C212yesmaximal, complemented
3C2×#2437C211yesmaximal, characteristic, complemented
4#15669C212yesmaximal, complemented
5#15668C212yesmaximal, complemented
6#15667C212yesmaximal, complemented
7#15667C212yesmaximal, complemented
8#14927C212yesmaximal, complemented
9#14912C212yesmaximal, complemented
10#14843C211yesmaximal, characteristic, complemented
11#14843C211yesmaximal, characteristic, complemented
12#14820C211yesmaximal, characteristic, complemented
13#14717C211yesmaximal, characteristic, complemented
14#14681C211yesmaximal, characteristic, complemented
15#14139C211yesmaximal, characteristic, complemented
16#13996C212yesmaximal, complemented
17#13971C211yesmaximal, characteristic, complemented
18#13971C211yesmaximal, characteristic, complemented
19#13881C211yesmaximal, characteristic, complemented
20#13867C211yesmaximal, characteristic
21#13867C211yesmaximal, characteristic
22C22⋊C42C211yesmaximal, characteristic, complemented
23C2×C22⋊#95C211yesmaximal, 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
34C23×C4⋊C4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40C23×C22⋊C4C2211yescharacteristic
41#2488—216no—
42#2437—28no—
43C2×#400C2212yescomplemented
44C2×#400C2212yescomplemented
45C2×#399C2211yescharacteristic, complemented
46C2×#397C2212yescomplemented
47C2×#396C2211yescharacteristic, complemented
48C2×#396C2211yescharacteristic, complemented
49C2×#393C2211yescharacteristic, complemented
50C2×#393C2212yescomplemented
51C2×#391C2212yescomplemented
52C2×#388C2212yescomplemented
53C2×#388C2212yescomplemented
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#385C2211yescharacteristic
59C2×#385C2211yescharacteristic
60C2×#385C2211yescharacteristic, complemented
61C2×#385C2211yescharacteristic, complemented
62C2×#382C2212yescomplemented
63C2×#381C2212yescomplemented
64C2×#381C2212yescomplemented
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic, complemented
67C2×#379C2211yescharacteristic
68C2×#379C2211yescharacteristic
69C2×#379C2211yescharacteristic
70C2×#379C2211yescharacteristic
71C2×#379C2211yescharacteristic
72C2×#379C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2212yescomplemented
76C22×#95C2212yescomplemented
77C22×#95C2212yescomplemented
78#1445C2212yescomplemented
79#1445C2212yescomplemented
80#1442C2212yescomplemented
81#1442C2212yescomplemented
82#1442C2212yescomplemented
83#1442C2212yescomplemented
84#1441C2212yescomplemented
85#1441C2212yescomplemented
86#1441C2212yescomplemented
87#1441C2212yescomplemented
88#1440C2212yescomplemented
89#1440C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1437C2212yescomplemented
103#1437C2212yescomplemented
104#1437C2212yescomplemented
105#1437C2212yescomplemented
106C4⋊#95C2212yescomplemented
107C4⋊#95C2212yescomplemented
108C22⋊#95C2211yescharacteristic
109C22⋊#95C2211yescharacteristic
110C22⋊#95C2211yescharacteristic
111C22⋊#95C2211yescharacteristic
112C22⋊#95C2211yescharacteristic
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—28no—
132C23×D4—24no—
133C23×D4—24no—
134C23×D4—44no—
135C23×D4C2312yes—
136C23×D4C2312yes—
137C24×C4—24no—
138C24×C4—28no—
139C24×C4—24no—
140C24×C4—24no—
141C24×C4—44no—
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C2×#123—2128no—
153C2×#123—28no—
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×#123D4116yes—
165C2×C22⋊Q8—24no—
166C2×C22⋊Q8—24no—
167C2×C22⋊Q8—28no—
168C2×C22⋊Q8—24no—
169C2×C22⋊Q8—42no—
170C22×C4⋊C4—24no—
171C22×C4⋊C4—24no—
172C22×C4⋊C4—28no—
173C22×C4⋊C4—28no—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C22⋊C4—24no—
188C22×C22⋊C4—24no—
189C22×C22⋊C4—28no—
190C22×C22⋊C4—28no—
191C22×C22⋊C4—28no—
192C22×C22⋊C4—24no—
193C22×C22⋊C4—24no—
194C22×C22⋊C4—24no—
195C22×C22⋊C4—24no—
196C22×C22⋊C4—42no—
197C22×C22⋊C4—42no—
198C22×C22⋊C4D418yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C42C2312yes—
233C22×C42C2312yes—
234#400—28no—
235#400—28no—
236#399—24no—
237#397—28no—
238#396—24no—
239#396—24no—
240#393—24no—
241#393—28no—
242#391—28no—
243#388—28no—
244#388—28no—
245#386—28no—
246#386—28no—
247#386—44no—
248#386—44no—
249#385—24no—
250#385—24no—
251#385—24no—
252#385—24no—
253#382—28no—
254#381—28no—
255#381—44no—
256#380—24no—
257#380—24no—
258#379—24no—
259#379—24no—
260#379—24no—
261#379—24no—
262#379—42no—
263#379—42no—
264C4×C22⋊C4—28no—
265C4×C22⋊C4—24no—
266C4×C22⋊C4—42no—
267C2×#95—28no—
268C2×#95—44no—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C25—24no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—24no—
310C25—22no—
311C25—24no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25—42no—
324C25C2×D414yes—
325C25#4114yes—
326C25#4114yes—
327C25C2412yes—
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2411yescharacteristic
331C22×Q8—22no—
332C22×Q8—24no—
333C22×Q8—22no—
334C22×Q8—41no—
335C22×Q8—42no—
336C22×D4—232no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—432no—
351C22×D4—432no—
352C22×D4—416no—
353C22×D4—416no—
354C22×D4C2×D418yes—
355C23×C4—232no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—22no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—22no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—22no—
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—41no—
404C23×C4—41no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—432no—
410C23×C4—432no—
411C23×C4—416no—
412C23×C4—416no—
413C23×C4C2×D418yes—
414C23×C4C2×D414yes—
415C23×C4C2×D414yes—
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435#123—264no—
436#123—264no—
437#123—264no—
438#123—264no—
439C22⋊Q8—416no—
440C22⋊Q8—416no—
441C2×C4⋊C4—232no—
442C2×C4⋊C4—232no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—41no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4C2×D418yes—
475C2×C4⋊C4C2×D418yes—
476C2×C22⋊C4—232no—
477C2×C22⋊C4—232no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
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—232no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—416no—
539C2×C22⋊C4—416no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—41no—
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—42no—
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⋊C4C2×D418yes—
564C2×C22⋊C4C2×D418yes—
565C2×C22⋊C4C2×D414yes—
566C2×C22⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4C2×D418yes—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4#4114yes—
571C2×C22⋊C4#4114yes—
572C2×C42—24no—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42—42no—
578#95—24no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—21no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—28no—
625C24—28no—
626C24—28no—
627C24—28no—
628C24—28no—
629C24—216no—
630C24—216no—
631C24—28no—
632C24—28no—
633C24—28no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—22no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—28no—
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—44no—
658C24—44no—
659C24—48no—
660C24—48no—
661C24—48no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—44no—
676C24—44no—
677C24—44no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—44no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24#124116yes—
692C24C22×D414yes—
693C24C22×D412yes—
694C24C22×D412yes—
695C24C22×D414yes—
696C24C22×D412yes—
697C24C2×#4112yes—
698C24C2×#4112yes—
699C24C2×#4112yes—
700C24C2×#4112yes—
701C24C2×#4112yes—
702C24C2×#4112yes—
703C24C2×#4112yes—
704C24C2×#4112yes—
705C24H(5,𝔽2)14yes—
706C24H(5,𝔽2)12yes—
707C242−1+412yes—
708C24C2511yescharacteristic
709C2×Q8—44no—
710C2×Q8—48no—
711C2×Q8—44no—
712C2×Q8—82no—
713C2×Q8—84no—
714C2×D4—216no—
715C2×D4—216no—
716C2×D4—216no—
717C2×D4—216no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—4128no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—28no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—216no—
739C22×C4—216no—
740C22×C4—28no—
741C22×C4—216no—
742C22×C4—216no—
743C22×C4—28no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—22no—
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—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
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—44no—
838C22×C4—44no—
839C22×C4—48no—
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—44no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—48no—
863C22×C4—4128no—
864C22×C4—44no—
865C22×C4—48no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—44no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—48no—
876C22×C4—82no—
877C22×C4—82no—
878C22×C4—84no—
879C22×C4—84no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4C22×D414yes—
884C22×C4C22×D414yes—
885C22×C4C22×D414yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C22×D414yes—
889C22×C4C22×D414yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C2×#4114yes—
893C22×C4C2×#4112yes—
894C22×C4C2×#4112yes—
895C4⋊C4—216no—
896C4⋊C4—216no—
897C4⋊C4—216no—
898C4⋊C4—216no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—82no—
906C4⋊C4—82no—
907C4⋊C4—82no—
908C22⋊C4—216no—
909C22⋊C4—216no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—216no—
916C22⋊C4—216no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—82no—
934C22⋊C4—82no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4#120116yes—
941C42—48no—
942C42—84no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—24no—
949C23—22no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—232no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—24no—
991C23—24no—
992C23—232no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—416no—
1001C23—432no—
1002C23—432no—
1003C23—416no—
1004C23—416no—
1005C23—432no—
1006C23—432no—
1007C23—416no—
1008C23—416no—
1009C23—416no—
1010C23—416no—
1011C23—416no—
1012C23—42no—
1013C23—42no—
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—816no—
1049C23—816no—
1050C23—816no—
1051C23—816no—
1052C23—88no—
1053C23—88no—
1054C23—88no—
1055C23—88no—
1056C23C2×#12014yes—
1057C23C2×#12414yes—
1058C23C2×#12414yes—
1059C23C2×#12414yes—
1060C23#52914yes—
1061C23#53514yes—
1062C23#53914yes—
1063C23#54618yes—
1064C23#54618yes—
1065C23#54614yes—
1066C23#54714yes—
1067C23#55114yes—
1068C23#55214yes—
1069C23C23×D411yescharacteristic
1070C23C23×D412yes—
1071C23C22×#4111yescharacteristic
1072C23C22×#4111yescharacteristic
1073C23C22×#4111yescharacteristic
1074C23C22×#4111yescharacteristic
1075C23C2×H(5,𝔽2)12yes—
1076C23C2×H(5,𝔽2)11yescharacteristic
1077C23C2×2−1+411yescharacteristic
1078C23#58512yes—
1079C23#58512yes—
1080Q8—88no—
1081D4—432no—
1082D4—432no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—416no—
1114C2×C4—416no—
1115C2×C4—416no—
1116C2×C4—416no—
1117C2×C4—432no—
1118C2×C4—416no—
1119C2×C4—41no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—432no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
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—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
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—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
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—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—88no—
1198C2×C4—816no—
1199C2×C4—88no—
1200C2×C4C2×#12014yes—
1201C2×C4C2×#12014yes—
1202C22—28no—
1203C22—28no—
1204C22—28no—
1205C22—28no—
1206C22—24no—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—24no—
1211C22—24no—
1212C22—28no—
1213C22—28no—
1214C22—24no—
1215C22—28no—
1216C22—28no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—24no—
1225C22—464no—
1226C22—44no—
1227C22—44no—
1228C22—42no—
1229C22—42no—
1230C22—44no—
1231C22—44no—
1232C22—42no—
1233C22—42no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—832no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22#243518yes—
1251C22#248818yescomplemented
1252C22C22×#12011yescharacteristic
1253C22C22×#12411yescharacteristic
1254C22C2×#52911yescharacteristic
1255C22C2×#53511yescharacteristic
1256C22C2×#53911yescharacteristic
1257C22C2×#54612yes—
1258C22C2×#54611yescharacteristic
1259C22C2×#54612yes—
1260C22C2×#54711yescharacteristic
1261C22D4×#4112yes—
1262C22D4×#4112yes—
1263C22C2×#55111yescharacteristic
1264C22C2×#55211yescharacteristic
1265C22#348511yescharacteristic
1266C22#348511yescharacteristic
1267C22#348812yes—
1268C22#348912yes—
1269C22#349112yes—
1270C22#349112yes—
1271C22#351312yes—
1272C22#351312yes—
1273C22#353412yes—
1274C22#353512yes—
1275C4—24no—
1276C4—24no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—44no—
1281C4—44no—
1282C4—44no—
1283C4—44no—
1284C4—42no—
1285C4—82no—
1286C4—82no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—82no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C2—28no—
1295C2—28no—
1296C2—44no—
1297C2—84no—
1298C2C2×#243511yescharacteristic
1299C2C2×#248811yescharacteristic
1300C2#3545511yescharacteristic
1301C2#3610912yes—
1302C2#3621211yescharacteristic
1303C2#3621311yescharacteristic
1304C2#3766112yes—
1305C2#3802311yescharacteristic
1306C2#3803911yescharacteristic
1307C2#5901112yes—
1308C2#5901212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2488C2semidirect
3. C2×#2437C2semidirect
4. #15669C2semidirect
5. #15668C2semidirect
6. #15667C2semidirect
7. #15667C2semidirect
8. #14927C2semidirect
9. #14912C2semidirect
10. #14843C2semidirect
11. #14843C2semidirect
12. #14820C2semidirect
13. #14717C2semidirect
14. #14681C2semidirect
15. #14139C2semidirect
16. #13996C2semidirect
17. #13971C2semidirect
18. #13971C2semidirect
19. #13881C2semidirect
22. C22⋊C42C2semidirect
23. C2×C22⋊#95C2semidirect
33. C22×C22⋊Q8C22semidirect
43. C2×#400C22semidirect
44. C2×#400C22semidirect
45. C2×#399C22semidirect
46. C2×#397C22semidirect
47. C2×#396C22semidirect
48. C2×#396C22semidirect
49. C2×#393C22semidirect
50. C2×#393C22semidirect
51. C2×#391C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
60. C2×#385C22semidirect
61. C2×#385C22semidirect
62. C2×#382C22semidirect
63. C2×#381C22semidirect
64. C2×#381C22semidirect
66. C2×#380C22semidirect
75. C2×C4×C22⋊C4C22semidirect
76. C22×#95C22semidirect
77. C22×#95C22semidirect
78. #1445C22semidirect
79. #1445C22semidirect
80. #1442C22semidirect
81. #1442C22semidirect
82. #1442C22semidirect
83. #1442C22semidirect
84. #1441C22semidirect
85. #1441C22semidirect
86. #1441C22semidirect
87. #1441C22semidirect
88. #1440C22semidirect
89. #1440C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
102. #1437C22semidirect
103. #1437C22semidirect
104. #1437C22semidirect
105. #1437C22semidirect
106. C4⋊#95C22semidirect
107. C4⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
1251. C22#2488semidirect

Maximal subgroups

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

subgroupindex
C23×#1232
C2×#24882
C2×#24372
#156692
#156682
#156672
#149272
#149122
#148432
#148202
#147172
#146812
#141392
#139962
#139712
#138812
#138672
C22⋊C422
C2×C22⋊#952