Finite Group Databasebeta

← #949267

Subgroups — #949267

Order 512.

2214 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17306C211yesmaximal, characteristic, complemented
2#17269C211yesmaximal, characteristic, complemented
3#17269C211yesmaximal, characteristic, complemented
4#17143C211yesmaximal, characteristic, complemented
5#16998C211yesmaximal, characteristic, complemented
6#16996C211yesmaximal, characteristic, complemented
7#16996C211yesmaximal, characteristic, complemented
8#16981C211yesmaximal, characteristic, complemented
9#16898C211yesmaximal, characteristic, complemented
10#16630C211yesmaximal, characteristic, complemented
11#16475C211yesmaximal, characteristic, complemented
12#16332C211yesmaximal, characteristic, complemented
13#16103C211yesmaximal, characteristic, complemented
14#15963C211yesmaximal, characteristic, complemented
15#15863C211yesmaximal, characteristic, complemented
16#15592C211yesmaximal, characteristic, complemented
17#14920C211yesmaximal, characteristic
18#14920C211yesmaximal, characteristic
19#14914C211yesmaximal, characteristic
20#14766C211yesmaximal, characteristic
21#14766C211yesmaximal, characteristic
22#14720C211yesmaximal, characteristic
23#14281C211yesmaximal, characteristic
24#14281C211yesmaximal, characteristic
25#14052C211yesmaximal, characteristic
26#14052C211yesmaximal, characteristic
27#13908C211yesmaximal, characteristic
28#13907C211yesmaximal, characteristic
29#13882C211yesmaximal, characteristic
30#13882C211yesmaximal, characteristic
31C2×#1441C211yesmaximal, characteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C2×#398C2211yescharacteristic
37C2×#398C2211yescharacteristic
38C2×#395C2211yescharacteristic
39C2×#395C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#387C2211yescharacteristic
45C2×#387C2211yescharacteristic
46C2×#387C2211yescharacteristic
47C2×#387C2211yescharacteristic
48C2×#385C2211yescharacteristic
49C2×#385C2211yescharacteristic
50C2×#385C2211yescharacteristic
51C2×#385C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65#1446C2211yescharacteristic
66#1446C2211yescharacteristic
67#1446C2211yescharacteristic
68#1446C2211yescharacteristic
69#1446C2211yescharacteristic
70#1446C2211yescharacteristic
71#1446C2211yescharacteristic
72#1446C2211yescharacteristic
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#1445C2211yescharacteristic
86#1445C2211yescharacteristic
87#1445C2211yescharacteristic
88#1445C2211yescharacteristic
89#1444C2211yescharacteristic
90#1444C2211yescharacteristic
91#1444C2211yescharacteristic
92#1444C2211yescharacteristic
93#1444C2211yescharacteristic
94#1444C2211yescharacteristic
95#1444C2211yescharacteristic
96#1444C2211yescharacteristic
97#1444C2211yescharacteristic
98#1444C2211yescharacteristic
99#1442C2211yescharacteristic
100#1442C2211yescharacteristic
101#1442C2211yescharacteristic
102#1442C2211yescharacteristic
103#1442C2211yescharacteristic
104#1442C2211yescharacteristic
105#1442C2211yescharacteristic
106#1442C2211yescharacteristic
107#1442C2211yescharacteristic
108#1442C2211yescharacteristic
109#1441C2211yescharacteristic
110#1441C2211yescharacteristic
111#1441C2211yescharacteristic
112#1441C2211yescharacteristic
113#1441C2211yescharacteristic
114#1441C2211yescharacteristic
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#1441C2211yescharacteristic
150#1441C2211yescharacteristic
151#1441C2211yescharacteristic
152#1441C2211yescharacteristic
153#1441C2211yescharacteristic
154#1441C2211yescharacteristic
155#1441C2211yescharacteristic
156#1441C2211yescharacteristic
157#1436C2211yescharacteristic
158#1436C2211yescharacteristic
159#1436C2211yescharacteristic
160#1436C2211yescharacteristic
161#1436C2211yescharacteristic
162#1436C2211yescharacteristic
163#1436C2211yescharacteristic
164#1436C2211yescharacteristic
165#1436C2211yescharacteristic
166#1436C2211yescharacteristic
167#1436C2211yescharacteristic
168#1436C2211yescharacteristic
169C4⋊#95C2211yescharacteristic
170C4⋊#95C2211yescharacteristic
171C4⋊#95C2211yescharacteristic
172C4⋊#95C2211yescharacteristic
173C22⋊#95C2211yescharacteristic
174C22⋊#95C2211yescharacteristic
175C22⋊#95C2211yescharacteristic
176C22⋊#95C2211yescharacteristic
177C22⋊#95C2211yescharacteristic
178C22⋊#95C2211yescharacteristic
179C22⋊#95C2211yescharacteristic
180C22⋊#95C2211yescharacteristic
181C22⋊#95C2211yescharacteristic
182C22⋊#95C2211yescharacteristic
183C22⋊#95C2211yescharacteristic
184C22⋊#95C2211yescharacteristic
185C22⋊#95C2211yescharacteristic
186C22⋊#95C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C24×C4C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192C24×C4C2311yescharacteristic
193C24×C4C2311yescharacteristic
194C24×C4C2311yescharacteristic
195C24×C4C2311yescharacteristic
196C2×C22⋊Q8—24no—
197C2×C22⋊Q8—42no—
198C2×C22⋊Q8—42no—
199C2×C22⋊Q8—42no—
200C2×C22⋊Q8—42no—
201C2×C22⋊Q8Q818yescomplemented
202C22×C4⋊C4—24no—
203C22×C4⋊C4—42no—
204C22×C4⋊C4—42no—
205C22×C4⋊C4—42no—
206C22×C4⋊C4—42no—
207C22×C4⋊C4Q818yescomplemented
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×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4C2311yescharacteristic
243C22×C22⋊C4C2311yescharacteristic
244C22×C22⋊C4C2311yescharacteristic
245C22×C22⋊C4C2311yescharacteristic
246C22×C22⋊C4C2311yescharacteristic
247C22×C22⋊C4C2311yescharacteristic
248C22×C22⋊C4C2311yescharacteristic
249C22×C22⋊C4C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254#398—42no—
255#398—42no—
256#395—42no—
257#395—42no—
258#391—42no—
259#391—42no—
260#389—42no—
261#389—42no—
262#387—42no—
263#387—42no—
264#387—42no—
265#387—42no—
266#385—42no—
267#385—42no—
268#385—42no—
269#385—42no—
270#380—42no—
271#380—42no—
272#380—42no—
273#380—42no—
274#380—42no—
275#380—42no—
276C4×C22⋊C4—42no—
277C4×C22⋊C4—42no—
278C2×#95—24no—
279C2×#95—42no—
280C2×#95—42no—
281C2×#95—42no—
282C2×#95—42no—
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
379C2×#95C2311yescharacteristic
380C2×#95C2311yescharacteristic
381C2×#95C2311yescharacteristic
382C2×#95C2311yescharacteristic
383C25C2411yescharacteristic
384C22×Q8—22no—
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×Q8C2×Q814yes—
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—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
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×C4—41no—
436C23×C4—41no—
437C23×C4—41no—
438C23×C4—41no—
439C23×C4—41no—
440C23×C4—41no—
441C23×C4—41no—
442C23×C4C2×Q814yes—
443C23×C4C2×Q814yes—
444C23×C4C2×Q814yes—
445C23×C4C2×Q814yes—
446C23×C4#4114yes—
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
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C22⋊Q8—416no—
478C22⋊Q8—416no—
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—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—416no—
503C2×C4⋊C4—416no—
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⋊C4—41no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—41no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4C2×Q814yes—
577C2×C4⋊C4C2×Q814yes—
578C2×C4⋊C4C2×Q814yes—
579C2×C4⋊C4C2×Q814yes—
580C2×C4⋊C4C2×Q814yes—
581C2×C4⋊C4C2×Q814yes—
582C2×C4⋊C4C2×Q814yes—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4C2×Q814yes—
606C2×C22⋊C4C2×Q814yes—
607C2×C42—22no—
608C2×C42—22no—
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—
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—22no—
631#95—22no—
632#95—22no—
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#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—41no—
717#95—41no—
718#95—41no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24C22×Q812yes—
728C24C22×Q812yes—
729C24C2×#4112yes—
730C24H(5,𝔽2)12yes—
731C24H(5,𝔽2)12yes—
732C24H(5,𝔽2)12yes—
733C242−1+412yes—
734C24C2511yescharacteristic
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—82no—
740C2×Q8—82no—
741C2×Q8—82no—
742C2×Q8—82no—
743C2×Q8—82no—
744C2×Q8—82no—
745C2×Q8—82no—
746C2×Q8—82no—
747C2×Q8—82no—
748C2×Q8—82no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—28no—
754C22×C4—28no—
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—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—28no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—28no—
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—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—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
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×C4—82no—
984C22×C4—82no—
985C22×C4—82no—
986C22×C4—82no—
987C22×C4—82no—
988C22×C4—82no—
989C22×C4—82no—
990C22×C4C22×Q812yes—
991C22×C4C22×Q812yes—
992C22×C4C22×Q812yes—
993C22×C4C22×Q812yes—
994C22×C4C22×Q812yes—
995C22×C4C22×Q812yes—
996C22×C4C22×Q812yes—
997C22×C4C22×Q812yes—
998C22×C4C22×Q812yes—
999C22×C4C22×Q812yes—
1000C22×C4C22×Q812yes—
1001C22×C4C22×Q812yes—
1002C22×C4C2×#4112yes—
1003C22×C4C2×#4112yes—
1004C22×C4H(5,𝔽2)12yes—
1005C22×C4H(5,𝔽2)12yes—
1006C22×C4H(5,𝔽2)12yes—
1007C22×C42−1+412yes—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—82no—
1023C4⋊C4—82no—
1024C4⋊C4—82no—
1025C4⋊C4—82no—
1026C4⋊C4—82no—
1027C4⋊C4—82no—
1028C4⋊C4—82no—
1029C4⋊C4—82no—
1030C4⋊C4—82no—
1031C4⋊C4—82no—
1032C4⋊C4—82no—
1033C4⋊C4—82no—
1034C4⋊C4—82no—
1035C4⋊C4—82no—
1036C4⋊C4—82no—
1037C4⋊C4—82no—
1038C4⋊C4—82no—
1039C4⋊C4—82no—
1040C4⋊C4—82no—
1041C4⋊C4—82no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—44no—
1045C22⋊C4—44no—
1046C22⋊C4—44no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C42—82no—
1051C42—82no—
1052C42—82no—
1053C42—82no—
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#53814yes—
1083C23#54314yes—
1084C23#54414yes—
1085C23#55414yes—
1086C23#55714yes—
1087C23Q8214yes—
1088C23#56214yes—
1089C23C23×Q811yescharacteristic
1090C23C23×Q811yescharacteristic
1091C23C22×#4111yescharacteristic
1092C23C2×H(5,𝔽2)11yescharacteristic
1093C23C2×H(5,𝔽2)11yescharacteristic
1094C23C2×H(5,𝔽2)11yescharacteristic
1095C23C2×H(5,𝔽2)11yescharacteristic
1096C23C2×H(5,𝔽2)11yescharacteristic
1097C23C2×H(5,𝔽2)11yescharacteristic
1098C23C2×2−1+411yescharacteristic
1099C23C2×2−1+411yescharacteristic
1100C23#58511yescharacteristic
1101C23#58511yescharacteristic
1102C23#58511yescharacteristic
1103C23#58511yescharacteristic
1104Q8—88no—
1105Q8—88no—
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—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
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—416no—
1158C2×C4—416no—
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—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—88no—
1318C2×C4—88no—
1319C2×C4—88no—
1320C2×C4—88no—
1321C2×C4—88no—
1322C2×C4#54314yes—
1323C22—24no—
1324C22—24no—
1325C22—24no—
1326C22—24no—
1327C22—24no—
1328C22—24no—
1329C22—24no—
1330C22—24no—
1331C22—24no—
1332C22—24no—
1333C22—24no—
1334C22—24no—
1335C22—24no—
1336C22—24no—
1337C22#280618yes—
1338C22C2×#53811yescharacteristic
1339C22C2×#54311yescharacteristic
1340C22C2×#54311yescharacteristic
1341C22C2×#54411yescharacteristic
1342C22#345811yescharacteristic
1343C22C2×#55411yescharacteristic
1344C22C2×#55711yescharacteristic
1345C22C2×Q8211yescharacteristic
1346C22#349011yescharacteristic
1347C22#349111yescharacteristic
1348C22#349411yescharacteristic
1349C22#349511yescharacteristic
1350C22#350111yescharacteristic
1351C22#350111yescharacteristic
1352C22#350111yescharacteristic
1353C22#350211yescharacteristic
1354C22#350311yescharacteristic
1355C22#350411yescharacteristic
1356C22C2×#56211yescharacteristic
1357C22#353411yescharacteristic
1358C22#353411yescharacteristic
1359C22#353411yescharacteristic
1360C22#353511yescharacteristic
1361C22#353611yescharacteristic
1362C22#353711yescharacteristic
1363C22#354111yescharacteristic
1364C22#354111yescharacteristic
1365C22#354211yescharacteristic
1366C22#354211yescharacteristic
1367C22#355211yescharacteristic
1368C22#355311yescharacteristic
1369C22#355811yescharacteristic
1370C22#355911yescharacteristic
1371C22#356011yescharacteristic
1372C22#356011yescharacteristic
1373C4—24no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C2—28no—
1404C2#3713511yescharacteristic
1405C2#3747611yescharacteristic
1406C2#3787211yescharacteristic
1407C2#3787711yescharacteristic
1408C2#3962011yescharacteristic
1409C2#3962411yescharacteristic
1410C2#4060911yescharacteristic
1411C2#4064111yescharacteristic
1412C2#4199811yescharacteristic
1413C2#4201211yescharacteristic
1414C2#4312511yescharacteristic
1415C2#4355211yescharacteristic
1416C2C2×#280611yescharacteristic
1417C2#5242711yescharacteristic
1418C2#5245111yescharacteristic
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. #17306C2semidirect
2. #17269C2semidirect
3. #17269C2semidirect
4. #17143C2semidirect
5. #16998C2semidirect
6. #16996C2semidirect
7. #16996C2semidirect
8. #16981C2semidirect
9. #16898C2semidirect
10. #16630C2semidirect
11. #16475C2semidirect
12. #16332C2semidirect
13. #16103C2semidirect
14. #15963C2semidirect
15. #15863C2semidirect
16. #15592C2semidirect
201. C2×C22⋊Q8Q8semidirect
207. C22×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
#173062
#172692
#171432
#169982
#169962
#169812
#168982
#166302
#164752
#163322
#161032
#159632
#158632
#155922
#149202
#149142
#147662
#147202
#142812
#140522
#139082
#139072
#138822
C2×#14412