Finite Group Databasebeta

← #2142147

Subgroups — #2142147

Order 512.

2306 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17281C211yesmaximal, characteristic, complemented
2#16986C211yesmaximal, characteristic
3#16826C211yesmaximal, characteristic, complemented
4#16708C211yesmaximal, characteristic
5#16694C211yesmaximal, characteristic, complemented
6#16617C211yesmaximal, characteristic, complemented
7#16389C211yesmaximal, characteristic, complemented
8#16161C211yesmaximal, characteristic
9#16137C211yesmaximal, characteristic, complemented
10#16044C211yesmaximal, characteristic
11#16037C211yesmaximal, characteristic, complemented
12#15964C211yesmaximal, characteristic, complemented
13#15959C211yesmaximal, characteristic
14#15867C211yesmaximal, characteristic, complemented
15#15853C211yesmaximal, characteristic, complemented
16#15490C211yesmaximal, characteristic
17#15332C211yesmaximal, characteristic, complemented
18#15332C211yesmaximal, characteristic, complemented
19#15013C211yesmaximal, characteristic, complemented
20#14923C211yesmaximal, characteristic
21#14874C211yesmaximal, characteristic
22#14800C211yesmaximal, characteristic, complemented
23#14553C211yesmaximal, characteristic
24#14452C211yesmaximal, characteristic
25#14378C211yesmaximal, characteristic, complemented
26#14319C211yesmaximal, characteristic
27#14243C211yesmaximal, characteristic
28#14214C211yesmaximal, characteristic, complemented
29#14067C211yesmaximal, characteristic
30#13922C211yesmaximal, characteristic
31#13922C211yesmaximal, characteristic
32C24×Q8C2211yescharacteristic
33C2×#400C2211yescharacteristic
34C2×#395C2211yescharacteristic
35C2×#395C2211yescharacteristic
36C2×#395C2211yescharacteristic
37C2×#395C2211yescharacteristic
38C2×#393C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#387C2211yescharacteristic
51C2×#387C2211yescharacteristic
52C2×#387C2211yescharacteristic
53C2×#387C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#385C2211yescharacteristic
56C2×#385C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63#1446C2211yescharacteristic
64#1446C2211yescharacteristic
65#1446C2211yescharacteristic
66#1446C2211yescharacteristic
67#1446C2211yescharacteristic
68#1446C2211yescharacteristic
69#1446C2211yescharacteristic
70#1446C2211yescharacteristic
71#1446C2211yescharacteristic
72#1446C2211yescharacteristic
73#1446C2211yescharacteristic
74#1446C2211yescharacteristic
75#1446C2211yescharacteristic
76#1446C2211yescharacteristic
77#1446C2211yescharacteristic
78#1445C2211yescharacteristic
79#1445C2211yescharacteristic
80#1445C2211yescharacteristic
81#1444C2211yescharacteristic
82#1444C2211yescharacteristic
83#1444C2211yescharacteristic
84#1444C2211yescharacteristic
85#1444C2211yescharacteristic
86#1444C2211yescharacteristic
87#1443C2211yescharacteristic
88#1443C2211yescharacteristic
89#1443C2211yescharacteristic
90#1443C2211yescharacteristic
91#1443C2211yescharacteristic
92#1443C2211yescharacteristic
93#1443C2211yescharacteristic
94#1443C2211yescharacteristic
95#1443C2211yescharacteristic
96#1443C2211yescharacteristic
97#1442C2211yescharacteristic
98#1442C2211yescharacteristic
99#1442C2211yescharacteristic
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#1442C2211yescharacteristic
116#1442C2211yescharacteristic
117#1442C2211yescharacteristic
118#1442C2211yescharacteristic
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#1439C2211yescharacteristic
135#1439C2211yescharacteristic
136#1439C2211yescharacteristic
137#1439C2211yescharacteristic
138#1439C2211yescharacteristic
139#1439C2211yescharacteristic
140#1439C2211yescharacteristic
141#1439C2211yescharacteristic
142#1439C2211yescharacteristic
143#1439C2211yescharacteristic
144#1439C2211yescharacteristic
145#1437C2211yescharacteristic
146#1437C2211yescharacteristic
147#1437C2211yescharacteristic
148#1437C2211yescharacteristic
149#1436C2211yescharacteristic
150#1436C2211yescharacteristic
151#1436C2211yescharacteristic
152#1436C2211yescharacteristic
153#1436C2211yescharacteristic
154#1436C2211yescharacteristic
155#1436C2211yescharacteristic
156#1436C2211yescharacteristic
157#1436C2211yescharacteristic
158#1436C2211yescharacteristic
159#1436C2211yescharacteristic
160#1436C2211yescharacteristic
161#1436C2211yescharacteristic
162#1436C2211yescharacteristic
163C4⋊#95C2211yescharacteristic
164#1434C2211yescharacteristic
165#1434C2211yescharacteristic
166#1434C2211yescharacteristic
167#1434C2211yescharacteristic
168#1434C2211yescharacteristic
169#1434C2211yescharacteristic
170#1434C2211yescharacteristic
171#1434C2211yescharacteristic
172#1434C2211yescharacteristic
173#1434C2211yescharacteristic
174#1434C2211yescharacteristic
175C22⋊#95C2211yescharacteristic
176C22⋊#95C2211yescharacteristic
177C22⋊#95C2211yescharacteristic
178C22⋊#95C2211yescharacteristic
179C22⋊#95C2211yescharacteristic
180C22⋊#95C2211yescharacteristic
181C22⋊#95C2211yescharacteristic
182C22⋊#95C2211yescharacteristic
183C22⋊#95C2211yescharacteristic
184C22⋊#95C2211yescharacteristic
185C22⋊#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C23×Q8—24no—
188C23×Q8—24no—
189C23×Q8—42no—
190C23×Q8—42no—
191C23×Q8—42no—
192C23×Q8—42no—
193C23×Q8—42no—
194C23×Q8C2311yescharacteristic
195C23×Q8C2311yescharacteristic
196C23×Q8C2311yescharacteristic
197C23×Q8C2311yescharacteristic
198C23×Q8C2311yescharacteristic
199C24×C4C2311yescharacteristic
200C24×C4C2311yescharacteristic
201C24×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×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×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243#400—42no—
244#395—24no—
245#395—42no—
246#395—42no—
247#395—42no—
248#393Q818yescomplemented
249#391—24no—
250#391—42no—
251#391—42no—
252#391—42no—
253#391—42no—
254#391—42no—
255#391—42no—
256#391—42no—
257#391—42no—
258#391—42no—
259#391—42no—
260#387—42no—
261#387—42no—
262#387—42no—
263#387—42no—
264#385—24no—
265#385—42no—
266#385—42no—
267#382—42no—
268#380—24no—
269#380—42no—
270C4×C4⋊C4—42no—
271C4×C22⋊C4—42no—
272C4×C22⋊C4—42no—
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
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—22no—
384C22×Q8—22no—
385C22×Q8—22no—
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—22no—
393C22×Q8—22no—
394C22×Q8—22no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—41no—
398C22×Q8—41no—
399C22×Q8—41no—
400C22×Q8—41no—
401C22×Q8—41no—
402C22×Q8—41no—
403C22×Q8—41no—
404C22×Q8—41no—
405C22×Q8—41no—
406C22×Q8—41no—
407C22×Q8—41no—
408C22×Q8—41no—
409C22×Q8—41no—
410C22×Q8—41no—
411C22×Q8—41no—
412C22×Q8—41no—
413C22×Q8—416no—
414C22×Q8—416no—
415C22×Q8—416no—
416C22×Q8—416no—
417C22×Q8—416no—
418C22×Q8—416no—
419C22×Q8—416no—
420C22×Q8C2×Q814yescomplemented
421C22×Q8#4114yes—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—22no—
427C23×C4—22no—
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—41no—
433C23×C4—41no—
434C23×C4—41no—
435C23×C4—41no—
436C23×C4—41no—
437C23×C4—41no—
438C23×C4—41no—
439C23×C4—41no—
440C23×C4—41no—
441C23×C4—41no—
442C23×C4#4114yes—
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
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
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—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×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—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—41no—
552C2×C22⋊C4—41no—
553C2×C22⋊C4—41no—
554C2×C22⋊C4—41no—
555C2×C22⋊C4—41no—
556C2×C22⋊C4—41no—
557C2×C22⋊C4—41no—
558C2×C22⋊C4—41no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
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⋊C4C2×Q814yes—
570C2×C22⋊C4C2×Q814yes—
571C2×C22⋊C4C2×Q814yes—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—41no—
582C2×C42—41no—
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×C42—41no—
594C2×C42—41no—
595C2×C42—41no—
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—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
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—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—
697#95—41no—
698#95—41no—
699#95C2×Q814yescomplemented
700#95C2×Q814yescomplemented
701#95C2×Q814yescomplemented
702C24—21no—
703C24—21no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—21no—
708C24—21no—
709C24—21no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24C22×Q812yes—
715C24C2×#4112yes—
716C242−1+412yes—
717C24C2511yescharacteristic
718C2×Q8—28no—
719C2×Q8—28no—
720C2×Q8—28no—
721C2×Q8—28no—
722C2×Q8—44no—
723C2×Q8—44no—
724C2×Q8—44no—
725C2×Q8—44no—
726C2×Q8—44no—
727C2×Q8—44no—
728C2×Q8—44no—
729C2×Q8—44no—
730C2×Q8—44no—
731C2×Q8—44no—
732C2×Q8—44no—
733C2×Q8—44no—
734C2×Q8—44no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—44no—
741C2×Q8—44no—
742C2×Q8—44no—
743C2×Q8—44no—
744C2×Q8—44no—
745C2×Q8—44no—
746C2×Q8—4128no—
747C2×Q8—44no—
748C2×Q8—44no—
749C2×Q8—44no—
750C2×Q8—82no—
751C2×Q8—82no—
752C2×Q8—82no—
753C2×Q8—82no—
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—28no—
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—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—28no—
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—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
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—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4C22×Q812yes—
968C22×C4C22×Q812yes—
969C22×C4C22×Q812yes—
970C22×C4C22×Q812yes—
971C22×C4C22×Q812yes—
972C22×C4C22×Q812yes—
973C22×C4C2×#4112yes—
974C22×C4C2×#4112yes—
975C22×C4C2×#4112yes—
976C22×C4C2×#4112yes—
977C22×C4C2×#4112yes—
978C22×C4H(5,𝔽2)12yes—
979C22×C4H(5,𝔽2)12yes—
980C22×C4H(5,𝔽2)12yes—
981C22×C4H(5,𝔽2)12yes—
982C22×C4H(5,𝔽2)12yes—
983C22×C42−1+412yes—
984C22×C42−1+412yes—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C4⋊C4—44no—
990C4⋊C4—44no—
991C4⋊C4—82no—
992C4⋊C4—82no—
993C4⋊C4—82no—
994C4⋊C4—82no—
995C4⋊C4—82no—
996C4⋊C4—82no—
997C4⋊C4—82no—
998C4⋊C4—82no—
999C4⋊C4—82no—
1000C4⋊C4—82no—
1001C4⋊C4—82no—
1002C4⋊C4—82no—
1003C4⋊C4—82no—
1004C4⋊C4—82no—
1005C4⋊C4—82no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—82no—
1014C22⋊C4—82no—
1015C22⋊C4—82no—
1016C22⋊C4—82no—
1017C22⋊C4—82no—
1018C42—44no—
1019C42—44no—
1020C42—82no—
1021C42—82no—
1022C42—82no—
1023C42—82no—
1024C42—82no—
1025C42—82no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23#55714yes—
1061C23C23×Q811yescharacteristic
1062C23C22×#4111yescharacteristic
1063C23C22×#4111yescharacteristic
1064C23C2×H(5,𝔽2)11yescharacteristic
1065C23C2×H(5,𝔽2)11yescharacteristic
1066C23C2×H(5,𝔽2)11yescharacteristic
1067C23C2×H(5,𝔽2)11yescharacteristic
1068C23C2×H(5,𝔽2)11yescharacteristic
1069C23C2×2−1+411yescharacteristic
1070C23C2×2−1+411yescharacteristic
1071C23C2×2−1+411yescharacteristic
1072C23#58511yescharacteristic
1073C23#58511yescharacteristic
1074C23#58511yescharacteristic
1075C23#58511yescharacteristic
1076Q8—416no—
1077Q8—416no—
1078Q8—416no—
1079Q8—416no—
1080Q8—88no—
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—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—416no—
1130C2×C4—416no—
1131C2×C4—416no—
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—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#53814yes—
1293C2×C4#55114yes—
1294C22—24no—
1295C22—24no—
1296C22—24no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22C2×#53811yescharacteristic
1310C22#346111yescharacteristic
1311C22C2×#55111yescharacteristic
1312C22C2×#55711yescharacteristic
1313C22Q8×#4111yescharacteristic
1314C22#349011yescharacteristic
1315C22#349011yescharacteristic
1316C22#349011yescharacteristic
1317C22#349511yescharacteristic
1318C22#350111yescharacteristic
1319C22#350111yescharacteristic
1320C22#350111yescharacteristic
1321C22#350311yescharacteristic
1322C22#350311yescharacteristic
1323C22#351011yescharacteristic
1324C22#351611yescharacteristic
1325C22#351611yescharacteristic
1326C22#351811yescharacteristic
1327C22#353211yescharacteristic
1328C22#353211yescharacteristic
1329C22#353811yescharacteristic
1330C22#353811yescharacteristic
1331C22#354011yescharacteristic
1332C22#354011yescharacteristic
1333C22#354011yescharacteristic
1334C22#354011yescharacteristic
1335C22#354111yescharacteristic
1336C22#354111yescharacteristic
1337C22#354711yescharacteristic
1338C22#354711yescharacteristic
1339C22#354711yescharacteristic
1340C22#355211yescharacteristic
1341C22#356111yescharacteristic
1342C22#356111yescharacteristic
1343C22#356211yescharacteristic
1344C4—24no—
1345C4—24no—
1346C4—42no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C4—42no—
1357C4—42no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C2—44no—
1375C2#3784811yescharacteristic
1376C2#3904311yescharacteristic
1377C2#3965411yescharacteristic
1378C2#3967611yescharacteristic
1379C2#4105911yescharacteristic
1380C2#4286711yescharacteristic
1381C2#4312511yescharacteristic
1382C2#4423311yescharacteristic
1383C2#4701811yescharacteristic
1384C2#5010211yescharacteristic
1385C2#5147311yescharacteristic
1386C2#5160511yescharacteristic
1387C2#5798611yescharacteristic
1388C2#5892611yescharacteristic
1389C2#5986711yescharacteristic
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. #17281C2semidirect
3. #16826C2semidirect
5. #16694C2semidirect
6. #16617C2semidirect
7. #16389C2semidirect
9. #16137C2semidirect
11. #16037C2semidirect
12. #15964C2semidirect
14. #15867C2semidirect
15. #15853C2semidirect
17. #15332C2semidirect
18. #15332C2semidirect
19. #15013C2semidirect
22. #14800C2semidirect
25. #14378C2semidirect
28. #14214C2semidirect
248. #393Q8semidirect
420. C22×Q8C2×Q8semidirect
699. #95C2×Q8semidirect
700. #95C2×Q8semidirect
701. #95C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#172812
#169862
#168262
#167082
#166942
#166172
#163892
#161612
#161372
#160442
#160372
#159642
#159592
#158672
#158532
#154902
#153322
#150132
#149232
#148742
#148002
#145532
#144522
#143782
#143192
#142432
#142142
#140672
#139222