Finite Group Databasebeta

← #545557

Subgroups — #545557

Order 512.

2418 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2438C211yesmaximal, characteristic
2#14640C211yesmaximal, characteristic, complemented
3#14638C211yesmaximal, characteristic, complemented
4#14472C211yesmaximal, characteristic, complemented
5#14472C211yesmaximal, characteristic, complemented
6#14471C211yesmaximal, characteristic, complemented
7#14464C211yesmaximal, characteristic, complemented
8#14463C211yesmaximal, characteristic, complemented
9#14458C211yesmaximal, characteristic, complemented
10#14446C211yesmaximal, characteristic, complemented
11#14430C211yesmaximal, characteristic, complemented
12#14330C211yesmaximal, characteristic, complemented
13#14329C211yesmaximal, characteristic, complemented
14#14329C211yesmaximal, characteristic, complemented
15#14327C211yesmaximal, characteristic, complemented
16#14263C211yesmaximal, characteristic
17#14254C211yesmaximal, characteristic, complemented
18#14237C211yesmaximal, characteristic, complemented
19#14159C211yesmaximal, characteristic
20#14149C211yesmaximal, characteristic
21#14131C211yesmaximal, characteristic
22#14131C211yesmaximal, characteristic
23#14052C211yesmaximal, characteristic
24#14047C211yesmaximal, characteristic
25#14044C211yesmaximal, characteristic
26#14040C211yesmaximal, characteristic
27#13962C211yesmaximal, characteristic
28C2×#1442C211yesmaximal, characteristic
29#13799C211yesmaximal, characteristic
30#13799C211yesmaximal, characteristic
31#13795C211yesmaximal, characteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#2438C4116yescomplemented
37C2×#400C2211yescharacteristic
38C2×#398C2211yescharacteristic
39C2×#398C2211yescharacteristic
40C2×#395C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#387C2211yescharacteristic
45C2×#387C2211yescharacteristic
46C2×#387C2211yescharacteristic
47C2×#387C2211yescharacteristic
48C2×#387C2211yescharacteristic
49C2×#385C2211yescharacteristic
50C2×#385C2211yescharacteristic
51C2×#385C2211yescharacteristic
52C2×#385C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#381C2211yescharacteristic
56C2×#381C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C22×#95C2211yescharacteristic
63C22×#95C2211yescharacteristic
64C22×#95C2211yescharacteristic
65C22×#95C2211yescharacteristic
66C22×#95C2211yescharacteristic
67C22×#95C2211yescharacteristic
68#1446C2211yescharacteristic
69#1446C2211yescharacteristic
70#1446C2211yescharacteristic
71#1445C2211yescharacteristic
72#1445C2211yescharacteristic
73#1445C2211yescharacteristic
74#1445C2211yescharacteristic
75#1445C2211yescharacteristic
76#1445C2211yescharacteristic
77#1445C2211yescharacteristic
78#1445C2211yescharacteristic
79#1444C2211yescharacteristic
80#1444C2211yescharacteristic
81#1444C2211yescharacteristic
82#1444C2211yescharacteristic
83#1443C2211yescharacteristic
84#1443C2211yescharacteristic
85#1443C2211yescharacteristic
86#1443C2211yescharacteristic
87#1443C2211yescharacteristic
88#1442C2211yescharacteristic
89#1442C2211yescharacteristic
90#1442C2211yescharacteristic
91#1442C2211yescharacteristic
92#1442C2211yescharacteristic
93#1442C2211yescharacteristic
94#1442C2211yescharacteristic
95#1442C2211yescharacteristic
96#1442C2211yescharacteristic
97#1442C2211yescharacteristic
98#1442C2211yescharacteristic
99#1442C2211yescharacteristic
100#1442C2211yescharacteristic
101#1442C2211yescharacteristic
102#1442C2211yescharacteristic
103#1442C2211yescharacteristic
104#1442C2211yescharacteristic
105#1441C2211yescharacteristic
106#1441C2211yescharacteristic
107#1441C2211yescharacteristic
108#1441C2211yescharacteristic
109#1441C2211yescharacteristic
110#1441C2211yescharacteristic
111#1441C2211yescharacteristic
112#1441C2211yescharacteristic
113#1441C2211yescharacteristic
114#1441C2211yescharacteristic
115#1441C2211yescharacteristic
116#1441C2211yescharacteristic
117#1441C2211yescharacteristic
118#1441C2211yescharacteristic
119#1441C2211yescharacteristic
120#1436C2211yescharacteristic
121#1436C2211yescharacteristic
122#1436C2211yescharacteristic
123#1436C2211yescharacteristic
124#1436C2211yescharacteristic
125#1436C2211yescharacteristic
126#1436C2211yescharacteristic
127#1436C2211yescharacteristic
128#1436C2211yescharacteristic
129#1436C2211yescharacteristic
130#1436C2211yescharacteristic
131#1436C2211yescharacteristic
132#1436C2211yescharacteristic
133#1436C2211yescharacteristic
134#1436C2211yescharacteristic
135#1436C2211yescharacteristic
136#1436C2211yescharacteristic
137#1436C2211yescharacteristic
138#1436C2211yescharacteristic
139#1436C2211yescharacteristic
140#1436C2211yescharacteristic
141#1436C2211yescharacteristic
142#1436C2211yescharacteristic
143#1436C2211yescharacteristic
144#1436C2211yescharacteristic
145#1436C2211yescharacteristic
146#1436C2211yescharacteristic
147#1436C2211yescharacteristic
148C4⋊#95C2211yescharacteristic
149C4⋊#95C2211yescharacteristic
150C4⋊#95C2211yescharacteristic
151C4⋊#95C2211yescharacteristic
152C4⋊#95C2211yescharacteristic
153C4⋊#95C2211yescharacteristic
154C4⋊#95C2211yescharacteristic
155C4⋊#95C2211yescharacteristic
156C4⋊#95C2211yescharacteristic
157C4⋊#95C2211yescharacteristic
158C4⋊#95C2211yescharacteristic
159C4⋊#95C2211yescharacteristic
160C4⋊#95C2211yescharacteristic
161#1434C2211yescharacteristic
162#1434C2211yescharacteristic
163#1434C2211yescharacteristic
164#1434C2211yescharacteristic
165#1434C2211yescharacteristic
166#1434C2211yescharacteristic
167#1434C2211yescharacteristic
168#1434C2211yescharacteristic
169#1434C2211yescharacteristic
170#1434C2211yescharacteristic
171#1434C2211yescharacteristic
172C22⋊#95C2211yescharacteristic
173C22⋊#95C2211yescharacteristic
174C22⋊#95C2211yescharacteristic
175C22⋊#95C2211yescharacteristic
176C22⋊#95C2211yescharacteristic
177C22⋊#95C2211yescharacteristic
178C22⋊#95C2211yescharacteristic
179C22⋊#95C2211yescharacteristic
180C22⋊#95C2211yescharacteristic
181C22⋊#95C2211yescharacteristic
182C22⋊#95C2211yescharacteristic
183C22⋊#95C2211yescharacteristic
184C4×#95C2211yescharacteristic
185C4×#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C4×#95C2211yescharacteristic
188C23×Q8C2311yescharacteristic
189C24×C4C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192C24×C4C2311yescharacteristic
193C24×C4C2311yescharacteristic
194C24×C4C2311yescharacteristic
195C24×C4C2311yescharacteristic
196C2×C22⋊Q8—42no—
197C2×C22⋊Q8—42no—
198C2×C22⋊Q8C2×C418yes—
199C2×#117—42no—
200C2×#117—42no—
201C2×#117—42no—
202C2×#117—42no—
203C2×#117C2×C418yes—
204C2×#117Q818yescomplemented
205C22×C4⋊C4—24no—
206C22×C4⋊C4—42no—
207C22×C4⋊C4—42no—
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×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253#400C2×C418yescomplemented
254#398C2×C418yescomplemented
255#398C2×C418yescomplemented
256#395C2×C418yescomplemented
257#391—42no—
258#391C2×C418yescomplemented
259#389C2×C418yescomplemented
260#387—42no—
261#387—42no—
262#387—42no—
263#387C2×C418yescomplemented
264#387C2×C418yescomplemented
265#385—42no—
266#385—42no—
267#385—42no—
268#385—42no—
269#385C2×C418yes—
270#385C2×C418yes—
271#381—24no—
272#381C2×C418yes—
273#380C2×C418yes—
274C4×C22⋊C4—42no—
275C4×C22⋊C4—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×#95C2×C418yes—
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
383C2×#95C2311yescharacteristic
384C2×#95C2311yescharacteristic
385C2×#95C2311yescharacteristic
386C25C2411yescharacteristic
387C22×Q8—41no—
388C22×Q8—41no—
389C22×Q8—41no—
390C22×Q8—41no—
391C22×Q8—41no—
392C22×Q8—41no—
393C22×Q8C22×C414yes—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—41no—
417C23×C4—41no—
418C23×C4—41no—
419C23×C4—41no—
420C23×C4—41no—
421C23×C4—41no—
422C23×C4—41no—
423C23×C4—41no—
424C23×C4—41no—
425C23×C4—41no—
426C23×C4—41no—
427C23×C4—41no—
428C23×C4—41no—
429C23×C4—41no—
430C23×C4—41no—
431C23×C4—41no—
432C23×C4—41no—
433C23×C4—41no—
434C23×C4—41no—
435C23×C4—41no—
436C23×C4—41no—
437C23×C4—41no—
438C23×C4C22×C414yes—
439C23×C4C22×C414yes—
440C23×C4C22×C414yes—
441C23×C4C2×Q814yes—
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
473C22⋊Q8—416no—
474#117—416no—
475#117—416no—
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—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—416no—
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⋊C4C22×C414yes—
540C2×C4⋊C4C22×C414yes—
541C2×C4⋊C4C22×C414yes—
542C2×C4⋊C4C22×C414yes—
543C2×C4⋊C4C22×C414yes—
544C2×C4⋊C4C22×C414yes—
545C2×C4⋊C4C22×C414yes—
546C2×C4⋊C4C22×C414yes—
547C2×C4⋊C4C22×C414yes—
548C2×C4⋊C4C22×C414yes—
549C2×C4⋊C4C22×C414yes—
550C2×C4⋊C4C2×Q814yes—
551C2×C4⋊C4C2×Q814yes—
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—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4C22×C414yes—
571C2×C22⋊C4C22×C414yes—
572C2×C22⋊C4C22×C414yes—
573C2×C22⋊C4C22×C414yes—
574C2×C22⋊C4C2×Q814yes—
575C2×C22⋊C4C2×Q814yes—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—41no—
579C2×C42—41no—
580C2×C42—41no—
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—
596C2×C42—41no—
597C2×C42—41no—
598C2×C42—41no—
599C2×C42—41no—
600C2×C42—41no—
601C2×C42—41no—
602C2×C42—41no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—41no—
606C2×C42—41no—
607C2×C42—41no—
608C2×C42C22×C414yes—
609C2×C42C22×C414yes—
610C2×C42C2×Q814yes—
611C2×C42C2×Q814yes—
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—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—
697#95—41no—
698#95—41no—
699#95—41no—
700#95C22×C414yes—
701#95C22×C414yes—
702#95C22×C414yes—
703#95C22×C414yes—
704#95C22×C414yes—
705#95C22×C414yes—
706#95C22×C414yes—
707#95C22×C414yes—
708#95C22×C414yes—
709#95C22×C414yes—
710#95C22×C414yes—
711#95C22×C414yes—
712#95C22×C414yes—
713#95C22×C414yes—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24C23×C412yes—
723C24C22×Q812yes—
724C24C2×#4112yes—
725C24H(5,𝔽2)12yes—
726C24H(5,𝔽2)12yes—
727C24H(5,𝔽2)12yes—
728C242−1+412yes—
729C24C2511yescharacteristic
730C2×Q8—44no—
731C2×Q8—44no—
732C2×Q8—44no—
733C2×Q8—82no—
734C2×Q8—82no—
735C2×Q8—82no—
736C2×Q8—82no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
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—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—28no—
860C22×C4—28no—
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—44no—
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—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—82no—
950C22×C4—82no—
951C22×C4—82no—
952C22×C4—82no—
953C22×C4—82no—
954C22×C4—82no—
955C22×C4—82no—
956C22×C4—82no—
957C22×C4—82no—
958C22×C4—82no—
959C22×C4—82no—
960C22×C4—82no—
961C22×C4—82no—
962C22×C4—82no—
963C22×C4—82no—
964C22×C4—82no—
965C22×C4—82no—
966C22×C4—82no—
967C22×C4—82no—
968C22×C4—82no—
969C22×C4—82no—
970C22×C4—82no—
971C22×C4C4×Q8116yes—
972C22×C4C23×C412yes—
973C22×C4C23×C412yes—
974C22×C4C23×C412yes—
975C22×C4C23×C412yes—
976C22×C4C23×C412yes—
977C22×C4C23×C412yes—
978C22×C4C23×C412yes—
979C22×C4C23×C412yes—
980C22×C4C23×C412yes—
981C22×C4C23×C412yes—
982C22×C4C23×C412yes—
983C22×C4C23×C412yes—
984C22×C4C23×C412yes—
985C22×C4C23×C412yes—
986C22×C4C22×Q812yes—
987C22×C4C22×Q812yes—
988C22×C4C22×Q812yes—
989C22×C4C22×Q812yes—
990C22×C4C22×Q812yes—
991C22×C4C22×Q812yes—
992C22×C4C2×#4112yes—
993C22×C4C2×#4112yes—
994C22×C4H(5,𝔽2)12yes—
995C22×C42−1+412yes—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—44no—
1002C4⋊C4—44no—
1003C4⋊C4—44no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—82no—
1014C4⋊C4—82no—
1015C4⋊C4—82no—
1016C4⋊C4—82no—
1017C4⋊C4—82no—
1018C4⋊C4—82no—
1019C4⋊C4—82no—
1020C4⋊C4—82no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C42—44no—
1030C42—44no—
1031C42—44no—
1032C42—44no—
1033C42—82no—
1034C42—82no—
1035C42—82no—
1036C42—82no—
1037C42—82no—
1038C42—82no—
1039C42—82no—
1040C42—82no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23C2×C4×Q814yes—
1070C23#51814yes—
1071C23#52014yes—
1072C23#53814yes—
1073C23#53914yes—
1074C23#54314yes—
1075C23#54414yes—
1076C23C24×C411yescharacteristic
1077C23C23×Q811yescharacteristic
1078C23C22×#4111yescharacteristic
1079C23C2×H(5,𝔽2)11yescharacteristic
1080C23C2×H(5,𝔽2)11yescharacteristic
1081C23C2×H(5,𝔽2)11yescharacteristic
1082C23C2×H(5,𝔽2)11yescharacteristic
1083C23C2×2−1+411yescharacteristic
1084C23C2×2−1+411yescharacteristic
1085C23#58511yescharacteristic
1086C23#58511yescharacteristic
1087C23#58511yescharacteristic
1088C23#58511yescharacteristic
1089C23#58511yescharacteristic
1090C23#58511yescharacteristic
1091Q8—88no—
1092C2×C4—232no—
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—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—22no—
1158C2×C4—22no—
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—88no—
1302C2×C4—88no—
1303C2×C4—88no—
1304C2×C4—88no—
1305C2×C4—88no—
1306C2×C4—88no—
1307C2×C4C2×C4×Q814yes—
1308C2×C4C2×C4×Q814yes—
1309C22—24no—
1310C22—24no—
1311C22—24no—
1312C22—24no—
1313C22—24no—
1314C22—24no—
1315C22—24no—
1316C22—24no—
1317C22—24no—
1318C22—24no—
1319C22—24no—
1320C22—24no—
1321C22—24no—
1322C22—24no—
1323C22#232918yes—
1324C22C22×C4×Q811yescharacteristic
1325C22C2×#51811yescharacteristic
1326C22C2×#52011yescharacteristic
1327C22#342811yescharacteristic
1328C22#342811yescharacteristic
1329C22C4×H(5,𝔽2)11yescharacteristic
1330C22C4×2−1+411yescharacteristic
1331C22C2×#53811yescharacteristic
1332C22C2×#53911yescharacteristic
1333C22C2×#54311yescharacteristic
1334C22C2×#54411yescharacteristic
1335C22#349411yescharacteristic
1336C22#349511yescharacteristic
1337C22#350311yescharacteristic
1338C22#350411yescharacteristic
1339C22#350411yescharacteristic
1340C22#350411yescharacteristic
1341C22#351011yescharacteristic
1342C22#351011yescharacteristic
1343C22#353311yescharacteristic
1344C22#353311yescharacteristic
1345C22#353411yescharacteristic
1346C22#353511yescharacteristic
1347C22#353511yescharacteristic
1348C22#353511yescharacteristic
1349C22#354211yescharacteristic
1350C22#354211yescharacteristic
1351C22#354511yescharacteristic
1352C22#354511yescharacteristic
1353C22#355911yescharacteristic
1354C22#356011yescharacteristic
1355C22#356011yescharacteristic
1356C22#356311yescharacteristic
1357C22#356411yescharacteristic
1358C22#356411yescharacteristic
1359C4—24no—
1360C4—24no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C2—28no—
1390C2C2×#232911yescharacteristic
1391C2#3421511yescharacteristic
1392C2#3427211yescharacteristic
1393C2#3445911yescharacteristic
1394C2#3446911yescharacteristic
1395C2#3447911yescharacteristic
1396C2#3449211yescharacteristic
1397C2#4196311yescharacteristic
1398C2#4196411yescharacteristic
1399C2#4199811yescharacteristic
1400C2#4200011yescharacteristic
1401C2#4215911yescharacteristic
1402C2#4218011yescharacteristic
1403C2#4218111yescharacteristic
1404C2#4231811yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14640C2semidirect
3. #14638C2semidirect
4. #14472C2semidirect
5. #14472C2semidirect
6. #14471C2semidirect
7. #14464C2semidirect
8. #14463C2semidirect
9. #14458C2semidirect
10. #14446C2semidirect
11. #14430C2semidirect
12. #14330C2semidirect
13. #14329C2semidirect
14. #14329C2semidirect
15. #14327C2semidirect
17. #14254C2semidirect
18. #14237C2semidirect
36. #2438C4semidirect
204. C2×#117Q8semidirect
253. #400C2×C4semidirect
254. #398C2×C4semidirect
255. #398C2×C4semidirect
256. #395C2×C4semidirect
258. #391C2×C4semidirect
259. #389C2×C4semidirect
263. #387C2×C4semidirect
264. #387C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24382
#146402
#146382
#144722
#144712
#144642
#144632
#144582
#144462
#144302
#143302
#143292
#143272
#142632
#142542
#142372
#141592
#141492
#141312
#140522
#140472
#140442
#140402
#139622
C2×#14422
#137992
#137952