Finite Group Databasebeta

← #836690

Subgroups — #836690

Order 512.

2248 conjugacy classes of subgroups.

The subgroup lattice has 1460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16944C211yesmaximal, characteristic, complemented
2#16717C211yesmaximal, characteristic, complemented
3#16201C211yesmaximal, characteristic, complemented
4#16158C211yesmaximal, characteristic, complemented
5#16019C211yesmaximal, characteristic, complemented
6#16014C211yesmaximal, characteristic
7#15954C211yesmaximal, characteristic
8#15787C211yesmaximal, characteristic, complemented
9#15477C211yesmaximal, characteristic, complemented
10#15385C211yesmaximal, characteristic, complemented
11#15248C211yesmaximal, characteristic, complemented
12#14975C211yesmaximal, characteristic, complemented
13#14923C211yesmaximal, characteristic, complemented
14#14897C211yesmaximal, characteristic, complemented
15#14812C211yesmaximal, characteristic
16#14767C211yesmaximal, characteristic, complemented
17#14752C211yesmaximal, characteristic, complemented
18#14235C211yesmaximal, characteristic, complemented
19#14222C211yesmaximal, characteristic, complemented
20#14218C211yesmaximal, characteristic, complemented
21#14080C211yesmaximal, characteristic, complemented
22#14072C211yesmaximal, characteristic, complemented
23#14064C211yesmaximal, characteristic
24#14050C211yesmaximal, characteristic, complemented
25#14047C211yesmaximal, characteristic, complemented
26#14044C211yesmaximal, characteristic, complemented
27#13988C211yesmaximal, characteristic
28#13899C211yesmaximal, characteristic
29#13842C211yesmaximal, characteristic, complemented
30#13813C211yesmaximal, characteristic
31#13799C211yesmaximal, characteristic, complemented
32C22×C4×D4C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C2×#400C2211yescharacteristic
35C2×#400C2211yescharacteristic
36C2×#396C2211yescharacteristic
37C2×#396C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#388C2211yescharacteristic
40C2×#387C2211yescharacteristic
41C2×#387C2211yescharacteristic
42C2×#387C2211yescharacteristic
43C2×#387C2211yescharacteristic
44C2×#387C2211yescharacteristic
45C2×#386C2211yescharacteristic
46C2×#386C2211yescharacteristic
47C2×#386C2211yescharacteristic
48C2×#386C2211yescharacteristic
49C2×#385C2211yescharacteristic
50C2×#385C2211yescharacteristic
51C2×#385C2211yescharacteristic
52C2×#385C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#385C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#381C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×#376C2211yescharacteristic
68C22×#95C2211yescharacteristic
69C22×#95C2211yescharacteristic
70#1445C2211yescharacteristic
71#1445C2211yescharacteristic
72#1445C2211yescharacteristic
73#1445C2211yescharacteristic
74#1445C2211yescharacteristic
75#1444C2211yescharacteristic
76#1444C2211yescharacteristic
77#1443C2211yescharacteristic
78#1443C2211yescharacteristic
79#1443C2211yescharacteristic
80#1443C2211yescharacteristic
81#1443C2211yescharacteristic
82#1443C2211yescharacteristic
83#1443C2211yescharacteristic
84#1443C2211yescharacteristic
85#1443C2211yescharacteristic
86#1443C2211yescharacteristic
87#1443C2211yescharacteristic
88#1443C2211yescharacteristic
89#1443C2211yescharacteristic
90#1443C2211yescharacteristic
91#1443C2211yescharacteristic
92#1443C2211yescharacteristic
93#1442C2211yescharacteristic
94#1442C2211yescharacteristic
95#1442C2211yescharacteristic
96#1442C2211yescharacteristic
97#1442C2211yescharacteristic
98#1442C2211yescharacteristic
99#1442C2211yescharacteristic
100#1442C2211yescharacteristic
101#1442C2211yescharacteristic
102#1442C2211yescharacteristic
103#1442C2211yescharacteristic
104#1442C2211yescharacteristic
105#1441C2211yescharacteristic
106#1441C2211yescharacteristic
107#1441C2211yescharacteristic
108#1441C2211yescharacteristic
109#1441C2211yescharacteristic
110#1441C2211yescharacteristic
111#1441C2211yescharacteristic
112#1441C2211yescharacteristic
113#1441C2211yescharacteristic
114#1441C2211yescharacteristic
115#1441C2211yescharacteristic
116#1440C2211yescharacteristic
117#1440C2211yescharacteristic
118#1440C2211yescharacteristic
119#1440C2211yescharacteristic
120#1440C2211yescharacteristic
121#1440C2211yescharacteristic
122#1440C2211yescharacteristic
123#1439C2211yescharacteristic
124#1439C2211yescharacteristic
125#1439C2211yescharacteristic
126#1439C2211yescharacteristic
127#1439C2211yescharacteristic
128#1439C2211yescharacteristic
129#1439C2211yescharacteristic
130#1439C2211yescharacteristic
131#1439C2211yescharacteristic
132#1438C2211yescharacteristic
133#1438C2211yescharacteristic
134#1437C2211yescharacteristic
135#1437C2211yescharacteristic
136#1437C2211yescharacteristic
137#1437C2211yescharacteristic
138#1437C2211yescharacteristic
139#1436C2211yescharacteristic
140#1436C2211yescharacteristic
141#1436C2211yescharacteristic
142#1436C2211yescharacteristic
143#1436C2211yescharacteristic
144#1436C2211yescharacteristic
145#1436C2211yescharacteristic
146#1436C2211yescharacteristic
147#1436C2211yescharacteristic
148#1436C2211yescharacteristic
149#1436C2211yescharacteristic
150#1436C2211yescharacteristic
151#1436C2211yescharacteristic
152#1436C2211yescharacteristic
153#1436C2211yescharacteristic
154#1436C2211yescharacteristic
155#1436C2211yescharacteristic
156#1436C2211yescharacteristic
157#1436C2211yescharacteristic
158C4⋊#95C2211yescharacteristic
159C4⋊#95C2211yescharacteristic
160C4⋊#95C2211yescharacteristic
161C4⋊#95C2211yescharacteristic
162C4⋊#95C2211yescharacteristic
163#1434C2211yescharacteristic
164#1434C2211yescharacteristic
165#1434C2211yescharacteristic
166#1434C2211yescharacteristic
167#1434C2211yescharacteristic
168#1434C2211yescharacteristic
169#1434C2211yescharacteristic
170C22⋊#95C2211yescharacteristic
171C22⋊#95C2211yescharacteristic
172C22⋊#95C2211yescharacteristic
173C22⋊#95C2211yescharacteristic
174C22⋊#95C2211yescharacteristic
175C22⋊#95C2211yescharacteristic
176C22⋊#95C2211yescharacteristic
177C22⋊#95C2211yescharacteristic
178C22⋊#95C2211yescharacteristic
179C22⋊#95C2211yescharacteristic
180C22⋊#95C2211yescharacteristic
181C22⋊#95C2211yescharacteristic
182C22⋊#95C2211yescharacteristic
183C4×#95C2211yescharacteristic
184C4×#95C2211yescharacteristic
185C4×#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C23×D4C2311yescharacteristic
188C24×C4C2311yescharacteristic
189C24×C4C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192C24×C4C2311yescharacteristic
193C24×C4C2311yescharacteristic
194C2×C4×D4—24no—
195C2×C4×D4—24no—
196C2×C4×D4—42no—
197C2×#117—24no—
198C2×#117—42no—
199C2×#117—42no—
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252#400—24no—
253#400—42no—
254#396—24no—
255#396—24no—
256#389—42no—
257#388—24no—
258#387—42no—
259#387—42no—
260#387—42no—
261#387—42no—
262#387—42no—
263#386—24no—
264#386—24no—
265#386—24no—
266#386—24no—
267#385—24no—
268#385—24no—
269#385—42no—
270#385—42no—
271#385—42no—
272#385—42no—
273#385—42no—
274#382—24no—
275#381—24no—
276#380—24no—
277#380—42no—
278C4×C4⋊C4—42no—
279C4×C22⋊C4—24no—
280C4×C22⋊C4—42no—
281C4×C22⋊C4—42no—
282C4×C22⋊C4—42no—
283C4×C22⋊C4—42no—
284C4×C22⋊C4—42no—
285#376—42no—
286C2×#95—24no—
287C2×#95—42no—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2311yescharacteristic
328C2×#95C2311yescharacteristic
329C2×#95C2311yescharacteristic
330C2×#95C2311yescharacteristic
331C2×#95C2311yescharacteristic
332C2×#95C2311yescharacteristic
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2311yescharacteristic
338C2×#95C2311yescharacteristic
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2311yescharacteristic
343C2×#95C2311yescharacteristic
344C2×#95C2311yescharacteristic
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C2×#95C2311yescharacteristic
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C2×#95C2311yescharacteristic
351C2×#95C2311yescharacteristic
352C2×#95C2311yescharacteristic
353C2×#95C2311yescharacteristic
354C2×#95C2311yescharacteristic
355C2×#95C2311yescharacteristic
356C2×#95C2311yescharacteristic
357C2×#95C2311yescharacteristic
358C2×#95C2311yescharacteristic
359C2×#95C2311yescharacteristic
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2311yescharacteristic
363C2×#95C2311yescharacteristic
364C2×#95C2311yescharacteristic
365C2×#95C2311yescharacteristic
366C2×#95C2311yescharacteristic
367C2×#95C2311yescharacteristic
368C2×#95C2311yescharacteristic
369C2×#95C2311yescharacteristic
370C2×#95C2311yescharacteristic
371C2×#95C2311yescharacteristic
372C2×#95C2311yescharacteristic
373C2×#95C2311yescharacteristic
374C2×#95C2311yescharacteristic
375C2×#95C2311yescharacteristic
376C2×#95C2311yescharacteristic
377C2×#95C2311yescharacteristic
378C2×#95C2311yescharacteristic
379C2×#95C2311yescharacteristic
380C2×#95C2311yescharacteristic
381C2×#95C2311yescharacteristic
382C2×#95C2311yescharacteristic
383C2×#95C2311yescharacteristic
384C25C2411yescharacteristic
385C25C2411yescharacteristic
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—22no—
390C22×D4—41no—
391C22×D4—41no—
392C22×D4#4114yes—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—41no—
414C23×C4—41no—
415C23×C4—41no—
416C23×C4—41no—
417C23×C4—41no—
418C23×C4—41no—
419C23×C4—41no—
420C23×C4—41no—
421C23×C4—41no—
422C23×C4—41no—
423C23×C4—41no—
424C23×C4—41no—
425C23×C4—41no—
426C23×C4—41no—
427C23×C4—41no—
428C23×C4—41no—
429C23×C4—41no—
430C23×C4—41no—
431C23×C4—41no—
432C23×C4—41no—
433C23×C4—41no—
434C23×C4—41no—
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C4×D4—416no—
465#117—416no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—41no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4—41no—
508C2×C4⋊C4—41no—
509C2×C4⋊C4—41no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4—41no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—41no—
523C2×C22⋊C4—22no—
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—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4—41no—
578C2×C22⋊C4—41no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4#4114yes—
587C2×C22⋊C4#4114yes—
588C2×C22⋊C4#4114yes—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—41no—
608C2×C42—41no—
609C2×C42—41no—
610C2×C42—41no—
611C2×C42—41no—
612C2×C42—41no—
613C2×C42—41no—
614C2×C42—41no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42—41no—
621C2×C42—41no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—41no—
666#95—41no—
667#95—41no—
668#95—41no—
669#95—41no—
670#95—41no—
671#95—41no—
672#95—41no—
673#95—41no—
674#95—41no—
675#95—41no—
676#95—41no—
677#95—41no—
678#95—41no—
679#95—41no—
680#95—41no—
681#95—41no—
682#95—41no—
683#95—41no—
684#95—41no—
685#95—41no—
686#95—41no—
687#95—41no—
688#95—41no—
689#95—41no—
690#95—41no—
691#95—41no—
692#95—41no—
693#95—41no—
694#95—41no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95—41no—
715#95—41no—
716#95#4114yes—
717#95#4114yes—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24C2×#4112yes—
743C24C2×#4112yes—
744C24C2×#4112yes—
745C24C2×#4112yes—
746C24C2×#4112yes—
747C242−1+412yes—
748C24C2511yescharacteristic
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—28no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
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—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—82no—
964C22×C4—82no—
965C22×C4—82no—
966C22×C4—82no—
967C22×C4—82no—
968C22×C4—82no—
969C22×C4—82no—
970C22×C4—82no—
971C22×C4—82no—
972C22×C4—82no—
973C22×C4—82no—
974C22×C4—82no—
975C22×C4—82no—
976C22×C4—82no—
977C22×C4—82no—
978C22×C4—82no—
979C22×C4—82no—
980C22×C4—82no—
981C22×C4—82no—
982C22×C4—82no—
983C22×C4C2×#4112yes—
984C22×C4C2×#4112yes—
985C22×C4C2×#4112yes—
986C22×C4C2×#4112yes—
987C22×C4C2×#4112yes—
988C22×C4C2×#4112yes—
989C22×C4C2×#4112yes—
990C22×C4C2×#4112yes—
991C22×C4C2×#4112yes—
992C22×C4C2×#4112yes—
993C22×C4C2×#4112yes—
994C22×C4C2×#4112yes—
995C22×C4C2×#4112yes—
996C22×C4H(5,𝔽2)12yes—
997C22×C4H(5,𝔽2)12yes—
998C22×C4H(5,𝔽2)12yes—
999C22×C4H(5,𝔽2)12yes—
1000C22×C42−1+412yes—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—82no—
1013C4⋊C4—82no—
1014C4⋊C4—82no—
1015C4⋊C4—82no—
1016C4⋊C4—82no—
1017C4⋊C4—82no—
1018C4⋊C4—82no—
1019C4⋊C4—82no—
1020C22⋊C4—28no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—82no—
1037C22⋊C4—82no—
1038C22⋊C4—82no—
1039C22⋊C4—82no—
1040C22⋊C4—82no—
1041C22⋊C4—82no—
1042C42—44no—
1043C42—44no—
1044C42—44no—
1045C42—44no—
1046C42—44no—
1047C42—44no—
1048C42—44no—
1049C42—44no—
1050C42—82no—
1051C42—82no—
1052C42—82no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23#52914yes—
1122C23#55214yes—
1123C23C22×#4111yescharacteristic
1124C23C22×#4111yescharacteristic
1125C23C22×#4111yescharacteristic
1126C23C22×#4111yescharacteristic
1127C23C22×#4111yescharacteristic
1128C23C22×#4111yescharacteristic
1129C23C2×H(5,𝔽2)11yescharacteristic
1130C23C2×H(5,𝔽2)11yescharacteristic
1131C23C2×H(5,𝔽2)11yescharacteristic
1132C23C2×H(5,𝔽2)11yescharacteristic
1133C23C2×2−1+411yescharacteristic
1134C23C2×2−1+411yescharacteristic
1135C23#58511yescharacteristic
1136C23#58511yescharacteristic
1137C23#58511yescharacteristic
1138D4—416no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—416no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
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—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—41no—
1334C2×C4—41no—
1335C2×C4—41no—
1336C2×C4—41no—
1337C2×C4—41no—
1338C2×C4—41no—
1339C2×C4—41no—
1340C2×C4—41no—
1341C2×C4—88no—
1342C2×C4—88no—
1343C2×C4—88no—
1344C2×C4—88no—
1345C2×C4—88no—
1346C2×C4#53814yes—
1347C2×C4#55114yes—
1348C22—24no—
1349C22—24no—
1350C22—24no—
1351C22—24no—
1352C22—24no—
1353C22—24no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22C2×#52911yescharacteristic
1379C22#344411yescharacteristic
1380C22C2×#53811yescharacteristic
1381C22C2×#55111yescharacteristic
1382C22C2×#55211yescharacteristic
1383C22#347511yescharacteristic
1384C22#347511yescharacteristic
1385C22#348111yescharacteristic
1386C22#348111yescharacteristic
1387C22#348111yescharacteristic
1388C22#348111yescharacteristic
1389C22#348211yescharacteristic
1390C22#349211yescharacteristic
1391C22#349411yescharacteristic
1392C22#349511yescharacteristic
1393C22#349511yescharacteristic
1394C22#350511yescharacteristic
1395C22#351311yescharacteristic
1396C22#351311yescharacteristic
1397C22#351411yescharacteristic
1398C22#351511yescharacteristic
1399C22#351511yescharacteristic
1400C22#351611yescharacteristic
1401C22#351911yescharacteristic
1402C22#351911yescharacteristic
1403C22#352011yescharacteristic
1404C22#352011yescharacteristic
1405C22#352111yescharacteristic
1406C22#352111yescharacteristic
1407C22#353611yescharacteristic
1408C22#354111yescharacteristic
1409C22#354211yescharacteristic
1410C22#354611yescharacteristic
1411C22#355211yescharacteristic
1412C22#356011yescharacteristic
1413C4—24no—
1414C4—24no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—42no—
1423C4—42no—
1424C4—42no—
1425C4—42no—
1426C4—42no—
1427C4—81no—
1428C4—81no—
1429C4—81no—
1430C4—81no—
1431C4—81no—
1432C4—81no—
1433C4—81no—
1434C4—81no—
1435C4—81no—
1436C4—81no—
1437C4—81no—
1438C4—81no—
1439C4—81no—
1440C4—81no—
1441C4—81no—
1442C2—44no—
1443C2—44no—
1444C2#3495911yescharacteristic
1445C2#3588911yescharacteristic
1446C2#3590811yescharacteristic
1447C2#3616711yescharacteristic
1448C2#3634611yescharacteristic
1449C2#3813211yescharacteristic
1450C2#4255211yescharacteristic
1451C2#4383511yescharacteristic
1452C2#4421611yescharacteristic
1453C2#4438011yescharacteristic
1454C2#4471411yescharacteristic
1455C2#5946911yescharacteristic
1456C2#5956211yescharacteristic
1457C2#5995411yescharacteristic
1458C2#5995811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #16944C2semidirect
2. #16717C2semidirect
3. #16201C2semidirect
4. #16158C2semidirect
5. #16019C2semidirect
8. #15787C2semidirect
9. #15477C2semidirect
10. #15385C2semidirect
11. #15248C2semidirect
12. #14975C2semidirect
13. #14923C2semidirect
14. #14897C2semidirect
16. #14767C2semidirect
17. #14752C2semidirect
18. #14235C2semidirect
19. #14222C2semidirect
20. #14218C2semidirect
21. #14080C2semidirect
22. #14072C2semidirect
24. #14050C2semidirect
25. #14047C2semidirect
26. #14044C2semidirect
29. #13842C2semidirect
31. #13799C2semidirect

Maximal subgroups

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

subgroupindex
#169442
#167172
#162012
#161582
#160192
#160142
#159542
#157872
#154772
#153852
#152482
#149752
#149232
#148972
#148122
#147672
#147522
#142352
#142222
#142182
#140802
#140722
#140642
#140502
#140472
#140442
#139882
#138992
#138422
#138132
#137992