Finite Group Databasebeta

← #4895652

Subgroups — #4895652

Order 512.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17266C211yesmaximal, characteristic, complemented
2#17154C211yesmaximal, characteristic, complemented
3#17143C211yesmaximal, characteristic, complemented
4#17132C211yesmaximal, characteristic, complemented
5#17072C211yesmaximal, characteristic, complemented
6#17033C211yesmaximal, characteristic, complemented
7#16996C211yesmaximal, characteristic, complemented
8#16942C211yesmaximal, characteristic, complemented
9#16906C211yesmaximal, characteristic, complemented
10#16905C211yesmaximal, characteristic, complemented
11#16827C211yesmaximal, characteristic, complemented
12#16827C211yesmaximal, characteristic, complemented
13#16630C211yesmaximal, characteristic, complemented
14#16610C211yesmaximal, characteristic, complemented
15#16481C211yesmaximal, characteristic
16#16400C211yesmaximal, characteristic
17#16318C211yesmaximal, characteristic
18#16299C211yesmaximal, characteristic
19#16299C211yesmaximal, characteristic
20#16264C211yesmaximal, characteristic
21#15992C211yesmaximal, characteristic
22#15770C211yesmaximal, characteristic
23#15426C211yesmaximal, characteristic
24#15279C211yesmaximal, characteristic
25#15168C211yesmaximal, characteristic, complemented
26#15011C211yesmaximal, characteristic, complemented
27#14766C211yesmaximal, characteristic
28#14758C211yesmaximal, characteristic
29#14343C211yesmaximal, characteristic
30#13962C211yesmaximal, characteristic
31#13943C211yesmaximal, characteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C2×#400C2211yescharacteristic
35C2×#398C2211yescharacteristic
36C2×#398C2211yescharacteristic
37C2×#398C2211yescharacteristic
38C2×#398C2211yescharacteristic
39C2×#395C2211yescharacteristic
40C2×#395C2211yescharacteristic
41C2×#395C2211yescharacteristic
42C2×#395C2211yescharacteristic
43C2×#395C2211yescharacteristic
44C2×#395C2211yescharacteristic
45C2×#395C2211yescharacteristic
46C2×#395C2211yescharacteristic
47C2×#395C2211yescharacteristic
48C2×#393C2211yescharacteristic
49C2×#393C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#388C2211yescharacteristic
53C2×#388C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#385C2211yescharacteristic
56C2×#385C2211yescharacteristic
57C2×#385C2211yescharacteristic
58C2×#381C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C22×#95C2211yescharacteristic
65#1446C2211yescharacteristic
66#1446C2211yescharacteristic
67#1446C2211yescharacteristic
68#1446C2211yescharacteristic
69#1446C2211yescharacteristic
70#1446C2211yescharacteristic
71#1446C2211yescharacteristic
72#1445C2211yescharacteristic
73#1445C2211yescharacteristic
74#1445C2211yescharacteristic
75#1445C2211yescharacteristic
76#1445C2211yescharacteristic
77#1445C2211yescharacteristic
78#1445C2211yescharacteristic
79#1445C2211yescharacteristic
80#1445C2211yescharacteristic
81#1445C2211yescharacteristic
82#1445C2211yescharacteristic
83#1445C2211yescharacteristic
84#1445C2211yescharacteristic
85#1444C2211yescharacteristic
86#1444C2211yescharacteristic
87#1444C2211yescharacteristic
88#1444C2211yescharacteristic
89#1444C2211yescharacteristic
90#1444C2211yescharacteristic
91#1444C2211yescharacteristic
92#1443C2211yescharacteristic
93#1443C2211yescharacteristic
94#1443C2211yescharacteristic
95#1443C2211yescharacteristic
96#1443C2211yescharacteristic
97#1443C2211yescharacteristic
98#1443C2211yescharacteristic
99#1443C2211yescharacteristic
100#1442C2211yescharacteristic
101#1442C2211yescharacteristic
102#1442C2211yescharacteristic
103#1442C2211yescharacteristic
104#1442C2211yescharacteristic
105#1442C2211yescharacteristic
106#1442C2211yescharacteristic
107#1442C2211yescharacteristic
108#1442C2211yescharacteristic
109#1442C2211yescharacteristic
110#1442C2211yescharacteristic
111#1442C2211yescharacteristic
112#1442C2211yescharacteristic
113#1442C2211yescharacteristic
114#1442C2211yescharacteristic
115#1441C2211yescharacteristic
116#1441C2211yescharacteristic
117#1441C2211yescharacteristic
118#1441C2211yescharacteristic
119#1441C2211yescharacteristic
120#1441C2211yescharacteristic
121#1441C2211yescharacteristic
122#1441C2211yescharacteristic
123#1441C2211yescharacteristic
124#1441C2211yescharacteristic
125#1441C2211yescharacteristic
126#1441C2211yescharacteristic
127#1441C2211yescharacteristic
128#1441C2211yescharacteristic
129#1441C2211yescharacteristic
130#1441C2211yescharacteristic
131#1441C2211yescharacteristic
132#1441C2211yescharacteristic
133#1441C2211yescharacteristic
134#1441C2211yescharacteristic
135#1441C2211yescharacteristic
136#1441C2211yescharacteristic
137#1441C2211yescharacteristic
138#1441C2211yescharacteristic
139#1441C2211yescharacteristic
140#1441C2211yescharacteristic
141#1441C2211yescharacteristic
142#1441C2211yescharacteristic
143#1441C2211yescharacteristic
144#1441C2211yescharacteristic
145#1441C2211yescharacteristic
146#1441C2211yescharacteristic
147#1441C2211yescharacteristic
148#1441C2211yescharacteristic
149#1440C2211yescharacteristic
150#1440C2211yescharacteristic
151#1440C2211yescharacteristic
152#1440C2211yescharacteristic
153#1440C2211yescharacteristic
154#1440C2211yescharacteristic
155#1439C2211yescharacteristic
156#1439C2211yescharacteristic
157#1439C2211yescharacteristic
158#1439C2211yescharacteristic
159#1439C2211yescharacteristic
160#1439C2211yescharacteristic
161#1436C2211yescharacteristic
162#1436C2211yescharacteristic
163#1436C2211yescharacteristic
164#1436C2211yescharacteristic
165#1436C2211yescharacteristic
166#1436C2211yescharacteristic
167#1436C2211yescharacteristic
168#1436C2211yescharacteristic
169C4⋊#95C2211yescharacteristic
170C4⋊#95C2211yescharacteristic
171C4⋊#95C2211yescharacteristic
172C4⋊#95C2211yescharacteristic
173C4⋊#95C2211yescharacteristic
174C4⋊#95C2211yescharacteristic
175C4⋊#95C2211yescharacteristic
176#1434C2211yescharacteristic
177#1434C2211yescharacteristic
178#1434C2211yescharacteristic
179#1434C2211yescharacteristic
180C22⋊#95C2211yescharacteristic
181C22⋊#95C2211yescharacteristic
182C22⋊#95C2211yescharacteristic
183C22⋊#95C2211yescharacteristic
184C22⋊#95C2211yescharacteristic
185C22⋊#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192C24×C4C2311yescharacteristic
193C2×C22⋊Q8—42no—
194C2×C22⋊Q8—42no—
195C2×C22⋊Q8—42no—
196C2×#117—42no—
197C2×#117—42no—
198C2×#117Q818yescomplemented
199C22×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊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×C22⋊C4C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246#400—42no—
247#398—42no—
248#398—42no—
249#398—42no—
250#398—42no—
251#395—42no—
252#395—42no—
253#395—42no—
254#395—42no—
255#395—42no—
256#395—42no—
257#395—42no—
258#395—42no—
259#395—42no—
260#393—42no—
261#393—42no—
262#391—42no—
263#391—42no—
264#388—42no—
265#388—42no—
266#385—42no—
267#385—42no—
268#385—42no—
269#385—42no—
270#381—42no—
271#380—42no—
272#380—42no—
273#380—42no—
274#380—42no—
275#380—42no—
276C2×#95—42no—
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
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
379C25C2411yescharacteristic
380C22×Q8—22no—
381C22×Q8—22no—
382C22×Q8—22no—
383C22×Q8—41no—
384C22×Q8—41no—
385C22×Q8—41no—
386C22×Q8—41no—
387C22×Q8—41no—
388C22×Q8—41no—
389C22×Q8—41no—
390C22×Q8—41no—
391C22×Q8—41no—
392C22×Q8—41no—
393C22×Q8—41no—
394C22×Q8—41no—
395C22×Q8—41no—
396C22×Q8—41no—
397C22×Q8—41no—
398C22×Q8—41no—
399C22×Q8—41no—
400C22×Q8—41no—
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—41no—
412C23×C4—41no—
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×C4C2×Q814yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
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
452C22⋊Q8—416no—
453#117—416no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
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—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—41no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—41no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4—41no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—41no—
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×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—41no—
530C2×C4⋊C4—41no—
531C2×C4⋊C4—41no—
532C2×C4⋊C4—41no—
533C2×C4⋊C4—41no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4C2×Q814yes—
546C2×C4⋊C4C2×Q814yes—
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—22no—
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⋊C4C2×Q814yes—
582C2×C22⋊C4C2×Q814yes—
583C2×C42—41no—
584C2×C42—41no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42—41no—
589C2×C42—41no—
590C2×C42—41no—
591C2×C42—41no—
592C2×C42—41no—
593C2×C42C2×Q814yes—
594C2×C42C2×Q814yes—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95—41no—
640#95—41no—
641#95—41no—
642#95—41no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95—41no—
654#95—41no—
655#95—41no—
656#95—41no—
657#95—41no—
658#95—41no—
659#95—41no—
660#95—41no—
661#95—41no—
662#95—41no—
663#95—41no—
664#95—41no—
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—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24C22×Q812yes—
710C24H(5,𝔽2)12yes—
711C24H(5,𝔽2)12yes—
712C24C2511yescharacteristic
713C2×Q8—44no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—82no—
717C2×Q8—82no—
718C2×Q8—82no—
719C2×Q8—82no—
720C2×Q8—82no—
721C2×Q8—82no—
722C2×Q8—82no—
723C2×Q8—82no—
724C2×Q8—82no—
725C2×Q8—82no—
726C2×Q8—82no—
727C2×Q8—82no—
728C2×Q8—82no—
729C2×Q8—82no—
730C2×Q8—82no—
731C2×Q8—82no—
732C2×Q8—82no—
733C2×Q8—82no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—28no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
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—21no—
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—28no—
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—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—82no—
944C22×C4—82no—
945C22×C4—82no—
946C22×C4—82no—
947C22×C4—82no—
948C22×C4—82no—
949C22×C4—82no—
950C22×C4—82no—
951C22×C4C22×Q812yes—
952C22×C4C22×Q812yes—
953C22×C4C22×Q812yes—
954C22×C4C22×Q812yes—
955C22×C4C22×Q812yes—
956C22×C4C22×Q812yes—
957C22×C4H(5,𝔽2)12yes—
958C22×C4H(5,𝔽2)12yes—
959C22×C4H(5,𝔽2)12yes—
960C22×C4H(5,𝔽2)12yes—
961C22×C42−1+412yes—
962C22×C42−1+412yes—
963C22×C42−1+412yes—
964C22×C42−1+412yes—
965C4⋊C4—44no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—44no—
969C4⋊C4—44no—
970C4⋊C4—82no—
971C4⋊C4—82no—
972C4⋊C4—82no—
973C4⋊C4—82no—
974C4⋊C4—82no—
975C4⋊C4—82no—
976C4⋊C4—82no—
977C4⋊C4—82no—
978C4⋊C4—82no—
979C4⋊C4—82no—
980C4⋊C4—82no—
981C4⋊C4—82no—
982C4⋊C4—82no—
983C4⋊C4—82no—
984C4⋊C4—82no—
985C4⋊C4—82no—
986C4⋊C4—82no—
987C4⋊C4—82no—
988C4⋊C4—82no—
989C4⋊C4—82no—
990C4⋊C4—82no—
991C4⋊C4—82no—
992C4⋊C4—82no—
993C4⋊C4—82no—
994C4⋊C4—82no—
995C4⋊C4—82no—
996C22⋊C4—28no—
997C22⋊C4—28no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—82no—
1003C22⋊C4—82no—
1004C22⋊C4—82no—
1005C22⋊C4—82no—
1006C22⋊C4—82no—
1007C22⋊C4—82no—
1008C42—44no—
1009C42—44no—
1010C42—82no—
1011C42—82no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23#54314yes—
1047C23C23×Q811yescharacteristic
1048C23C2×H(5,𝔽2)11yescharacteristic
1049C23C2×H(5,𝔽2)11yescharacteristic
1050C23C2×H(5,𝔽2)11yescharacteristic
1051C23C2×H(5,𝔽2)11yescharacteristic
1052C23C2×H(5,𝔽2)11yescharacteristic
1053C23C2×H(5,𝔽2)11yescharacteristic
1054C23C2×2−1+411yescharacteristic
1055C23C2×2−1+411yescharacteristic
1056C23C2×2−1+411yescharacteristic
1057C23C2×2−1+411yescharacteristic
1058C23#58511yescharacteristic
1059C23#58511yescharacteristic
1060C23#58511yescharacteristic
1061C23#58511yescharacteristic
1062Q8—88no—
1063Q8—88no—
1064Q8—88no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—416no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
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—88no—
1276C2×C4—88no—
1277C2×C4#54414yes—
1278C22—24no—
1279C22—24no—
1280C22—24no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22C2×#54311yescharacteristic
1294C22C2×#54411yescharacteristic
1295C22#345811yescharacteristic
1296C22#350311yescharacteristic
1297C22#350311yescharacteristic
1298C22#350311yescharacteristic
1299C22#350411yescharacteristic
1300C22#353211yescharacteristic
1301C22#353411yescharacteristic
1302C22#353411yescharacteristic
1303C22#353411yescharacteristic
1304C22#353411yescharacteristic
1305C22#353511yescharacteristic
1306C22#353511yescharacteristic
1307C22#353511yescharacteristic
1308C22#353611yescharacteristic
1309C22#353611yescharacteristic
1310C22#353711yescharacteristic
1311C22#353811yescharacteristic
1312C22#354111yescharacteristic
1313C22#354211yescharacteristic
1314C22#354411yescharacteristic
1315C22#354511yescharacteristic
1316C22#354711yescharacteristic
1317C22#355011yescharacteristic
1318C22#355011yescharacteristic
1319C22#355111yescharacteristic
1320C22#355511yescharacteristic
1321C22#355511yescharacteristic
1322C22#355811yescharacteristic
1323C22#355911yescharacteristic
1324C22#356111yescharacteristic
1325C22#356111yescharacteristic
1326C22#356411yescharacteristic
1327C22#356511yescharacteristic
1328C4—24no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C2—44no—
1359C2#3730811yescharacteristic
1360C2#3731411yescharacteristic
1361C2#3747811yescharacteristic
1362C2#4199711yescharacteristic
1363C2#4199811yescharacteristic
1364C2#4200811yescharacteristic
1365C2#4218711yescharacteristic
1366C2#5396211yescharacteristic
1367C2#5397811yescharacteristic
1368C2#5422811yescharacteristic
1369C2#5486511yescharacteristic
1370C2#5507711yescharacteristic
1371C2#5548811yescharacteristic
1372C2#5718811yescharacteristic
1373C2#5820211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17266C2semidirect
2. #17154C2semidirect
3. #17143C2semidirect
4. #17132C2semidirect
5. #17072C2semidirect
6. #17033C2semidirect
7. #16996C2semidirect
8. #16942C2semidirect
9. #16906C2semidirect
10. #16905C2semidirect
11. #16827C2semidirect
12. #16827C2semidirect
13. #16630C2semidirect
14. #16610C2semidirect
25. #15168C2semidirect
26. #15011C2semidirect
198. C2×#117Q8semidirect

Maximal subgroups

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

subgroupindex
#172662
#171542
#171432
#171322
#170722
#170332
#169962
#169422
#169062
#169052
#168272
#166302
#166102
#164812
#164002
#163182
#162992
#162642
#159922
#157702
#154262
#152792
#151682
#150112
#147662
#147582
#143432
#139622
#139432