Finite Group Databasebeta

← #560586

Subgroups — #560586

Order 512.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2660C211yesmaximal, characteristic
2#14600C211yesmaximal, characteristic
3#14598C211yesmaximal, characteristic
4#14595C211yesmaximal, characteristic
5#14593C211yesmaximal, characteristic
6#14585C211yesmaximal, characteristic
7#14554C211yesmaximal, characteristic
8#14550C211yesmaximal, characteristic
9#14538C211yesmaximal, characteristic
10#14455C211yesmaximal, characteristic
11#14454C211yesmaximal, characteristic
12#14451C211yesmaximal, characteristic
13#14450C211yesmaximal, characteristic
14#14276C211yesmaximal, characteristic
15#14241C211yesmaximal, characteristic
16#14238C211yesmaximal, characteristic
17#14236C211yesmaximal, characteristic
18#14219C211yesmaximal, characteristic
19#14217C211yesmaximal, characteristic
20#14214C211yesmaximal, characteristic
21#14186C211yesmaximal, characteristic
22#14174C211yesmaximal, characteristic
23#14168C211yesmaximal, characteristic
24#14106C211yesmaximal, characteristic
25#14097C211yesmaximal, characteristic
26#14029C211yesmaximal, characteristic
27#14024C211yesmaximal, characteristic
28#13963C211yesmaximal, characteristic
29#13829C211yesmaximal, characteristic
30#13805C211yesmaximal, characteristic
31#13779C211yesmaximal, characteristic
32C22×C4⋊Q8C2211yescharacteristic
33C22×#125C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2660C4116yescomplemented
36C2×#398C2211yescharacteristic
37C2×#398C2211yescharacteristic
38C2×#398C2211yescharacteristic
39C2×#398C2211yescharacteristic
40C2×#395C2211yescharacteristic
41C2×#395C2211yescharacteristic
42C2×#395C2211yescharacteristic
43C2×#395C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#387C2211yescharacteristic
54C2×#387C2211yescharacteristic
55C2×#387C2211yescharacteristic
56C2×#387C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#382C2211yescharacteristic
62C2×#382C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×#376C2211yescharacteristic
68C2×#376C2211yescharacteristic
69C2×#376C2211yescharacteristic
70#1446C2211yescharacteristic
71#1446C2211yescharacteristic
72#1445C2211yescharacteristic
73#1445C2211yescharacteristic
74#1445C2211yescharacteristic
75#1445C2211yescharacteristic
76#1444C2211yescharacteristic
77#1444C2211yescharacteristic
78#1444C2211yescharacteristic
79#1443C2211yescharacteristic
80#1443C2211yescharacteristic
81#1442C2211yescharacteristic
82#1442C2211yescharacteristic
83#1442C2211yescharacteristic
84#1442C2211yescharacteristic
85#1442C2211yescharacteristic
86#1441C2211yescharacteristic
87#1441C2211yescharacteristic
88#1441C2211yescharacteristic
89#1441C2211yescharacteristic
90#1441C2211yescharacteristic
91#1441C2211yescharacteristic
92#1441C2211yescharacteristic
93#1441C2211yescharacteristic
94#1441C2211yescharacteristic
95#1441C2211yescharacteristic
96#1441C2211yescharacteristic
97#1441C2211yescharacteristic
98#1441C2211yescharacteristic
99#1441C2211yescharacteristic
100#1441C2211yescharacteristic
101#1441C2211yescharacteristic
102#1441C2211yescharacteristic
103#1441C2211yescharacteristic
104#1441C2211yescharacteristic
105#1441C2211yescharacteristic
106#1441C2211yescharacteristic
107#1441C2211yescharacteristic
108#1441C2211yescharacteristic
109#1441C2211yescharacteristic
110#1436C2211yescharacteristic
111#1436C2211yescharacteristic
112#1436C2211yescharacteristic
113#1436C2211yescharacteristic
114#1436C2211yescharacteristic
115#1436C2211yescharacteristic
116#1436C2211yescharacteristic
117#1436C2211yescharacteristic
118#1436C2211yescharacteristic
119#1436C2211yescharacteristic
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
148#1436C2211yescharacteristic
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
163#1436C2211yescharacteristic
164C4⋊#95C2211yescharacteristic
165C4⋊#95C2211yescharacteristic
166C4⋊#95C2211yescharacteristic
167C4⋊#95C2211yescharacteristic
168C4⋊#95C2211yescharacteristic
169C4⋊#95C2211yescharacteristic
170C4⋊#95C2211yescharacteristic
171C4⋊#95C2211yescharacteristic
172C4⋊#95C2211yescharacteristic
173C4⋊#95C2211yescharacteristic
174#1434C2211yescharacteristic
175#1434C2211yescharacteristic
176#1434C2211yescharacteristic
177#1434C2211yescharacteristic
178#1434C2211yescharacteristic
179#1434C2211yescharacteristic
180#1434C2211yescharacteristic
181#1434C2211yescharacteristic
182#1434C2211yescharacteristic
183C4×#95C2211yescharacteristic
184C4×#95C2211yescharacteristic
185C4×#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C4×#95C2211yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C2×C4⋊Q8—42no—
191C2×C4⋊Q8—42no—
192C2×C4⋊Q8C2×C418yes—
193C2×#125—42no—
194C2×#125—42no—
195C2×#125C2×C418yes—
196C2×C4×Q8—42no—
197C2×C4×Q8—42no—
198C2×C4×Q8—42no—
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2311yescharacteristic
212C22×C4⋊C4C2311yescharacteristic
213C22×C4⋊C4C2311yescharacteristic
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2311yescharacteristic
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2311yescharacteristic
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2311yescharacteristic
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2311yescharacteristic
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252#398C2×C418yes—
253#398C2×C418yes—
254#398C2×C418yes—
255#398C2×C418yes—
256#395C2×C418yes—
257#395C2×C418yes—
258#395C2×C418yes—
259#395C2×C418yes—
260#391—42no—
261#391—42no—
262#391—42no—
263#391—42no—
264#391—42no—
265#389—42no—
266#389—42no—
267#389—42no—
268#389—42no—
269#387—42no—
270#387—42no—
271#387—42no—
272#387—42no—
273#384C2×C418yes—
274#384C2×C418yes—
275#382—24no—
276#382C2×C418yes—
277#382C2×C418yes—
278#382Q818yescomplemented
279C4×C4⋊C4—42no—
280C4×C4⋊C4—42no—
281C4×C4⋊C4—42no—
282C4×C4⋊C4—42no—
283#376—24no—
284#376—24no—
285#376C2×C418yes—
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
386C22×Q8—22no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—41no—
391C22×Q8—41no—
392C22×Q8—41no—
393C22×Q8—41no—
394C22×Q8—41no—
395C22×Q8—41no—
396C22×Q8—41no—
397C22×Q8—41no—
398C22×Q8C22×C414yes—
399C22×Q8C22×C414yes—
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C4⋊Q8—416no—
432#125—416no—
433C4×Q8—416no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—41no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—41no—
460C2×C4⋊C4—41no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—41no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4—41no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—41no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—41no—
473C2×C4⋊C4—41no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—41no—
476C2×C4⋊C4—41no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—41no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—41no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4—41no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—41no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4—41no—
492C2×C4⋊C4—41no—
493C2×C4⋊C4—41no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—41no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—41no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—41no—
504C2×C4⋊C4—41no—
505C2×C4⋊C4—41no—
506C2×C4⋊C4—41no—
507C2×C4⋊C4—41no—
508C2×C4⋊C4—41no—
509C2×C4⋊C4—41no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—41no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—41no—
514C2×C4⋊C4—41no—
515C2×C4⋊C4—41no—
516C2×C4⋊C4C22×C414yes—
517C2×C4⋊C4C22×C414yes—
518C2×C4⋊C4C22×C414yes—
519C2×C4⋊C4C22×C414yes—
520C2×C4⋊C4C22×C414yes—
521C2×C4⋊C4C22×C414yes—
522C2×C4⋊C4C22×C414yes—
523C2×C4⋊C4C22×C414yes—
524C2×C4⋊C4C22×C414yes—
525C2×C4⋊C4C22×C414yes—
526C2×C4⋊C4C22×C414yes—
527C2×C4⋊C4C22×C414yes—
528C2×C4⋊C4C22×C414yes—
529C2×C4⋊C4C22×C414yes—
530C2×C4⋊C4C22×C414yes—
531C2×C4⋊C4C22×C414yes—
532C2×C4⋊C4C22×C414yes—
533C2×C4⋊C4C22×C414yes—
534C2×C4⋊C4C2×Q814yes—
535C2×C4⋊C4C2×Q814yes—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—22no—
556C2×C42—41no—
557C2×C42—41no—
558C2×C42—41no—
559C2×C42—41no—
560C2×C42—41no—
561C2×C42—41no—
562C2×C42—41no—
563C2×C42—41no—
564C2×C42—41no—
565C2×C42—41no—
566C2×C42—41no—
567C2×C42—41no—
568C2×C42—41no—
569C2×C42—41no—
570C2×C42—41no—
571C2×C42—41no—
572C2×C42—41no—
573C2×C42—41no—
574C2×C42—41no—
575C2×C42—41no—
576C2×C42—41no—
577C2×C42—41no—
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×C42C22×C414yes—
589C2×C42C22×C414yes—
590C2×C42C22×C414yes—
591C2×C42C2×Q814yes—
592C2×C42#4114yes—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—41no—
626#95—41no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95—41no—
640#95—41no—
641#95—41no—
642#95—41no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95—41no—
650#95—41no—
651#95—41no—
652#95—41no—
653#95—41no—
654#95—41no—
655#95—41no—
656#95—41no—
657#95—41no—
658#95—41no—
659#95—41no—
660#95—41no—
661#95—41no—
662#95—41no—
663#95—41no—
664#95—41no—
665#95—41no—
666#95—41no—
667#95—41no—
668#95—41no—
669#95—41no—
670#95—41no—
671#95—41no—
672#95—41no—
673#95—41no—
674#95—41no—
675#95—41no—
676#95—41no—
677#95C22×C414yes—
678#95C22×C414yes—
679#95C22×C414yes—
680#95C22×C414yes—
681#95C22×C414yes—
682#95C22×C414yes—
683#95C22×C414yes—
684#95C22×C414yes—
685#95C22×C414yes—
686#95C22×C414yes—
687#95C22×C414yes—
688#95C22×C414yes—
689#95C2×Q814yes—
690#95C2×Q814yes—
691#95C2×Q814yes—
692#95C2×Q814yes—
693C24C2511yescharacteristic
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—44no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×Q8—44no—
704C2×Q8—82no—
705C2×Q8—82no—
706C2×Q8—82no—
707C2×Q8—82no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4C23×C412yes—
893C22×C4C23×C412yes—
894C22×C4C23×C412yes—
895C22×C4C23×C412yes—
896C22×C4C23×C412yes—
897C22×C4C23×C412yes—
898C22×C4C23×C412yes—
899C22×C4C23×C412yes—
900C22×C4C23×C412yes—
901C22×C4C23×C412yes—
902C22×C4C23×C412yes—
903C22×C4C23×C412yes—
904C22×C4C23×C412yes—
905C22×C4C23×C412yes—
906C22×C4C23×C412yes—
907C22×C4C22×Q812yes—
908C22×C4C22×Q812yes—
909C22×C4C22×Q812yes—
910C22×C4C22×Q812yes—
911C22×C4C22×Q812yes—
912C22×C4C22×Q812yes—
913C22×C4C22×Q812yes—
914C22×C4C2×#4112yes—
915C22×C4C2×#4112yes—
916C22×C4C2×#4112yes—
917C22×C4H(5,𝔽2)12yes—
918C22×C4H(5,𝔽2)12yes—
919C22×C4H(5,𝔽2)12yes—
920C22×C4H(5,𝔽2)12yes—
921C22×C42−1+412yes—
922C22×C42−1+412yes—
923C22×C42−1+412yes—
924C22×C42−1+412yes—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—44no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—82no—
951C4⋊C4—82no—
952C4⋊C4—82no—
953C4⋊C4—82no—
954C4⋊C4—82no—
955C4⋊C4—82no—
956C4⋊C4—82no—
957C4⋊C4—82no—
958C4⋊C4—82no—
959C42—28no—
960C42—28no—
961C42—28no—
962C42—44no—
963C42—44no—
964C42—44no—
965C42—44no—
966C42—44no—
967C42—44no—
968C42—44no—
969C42—44no—
970C42—82no—
971C42—82no—
972C42—82no—
973C42—82no—
974C42—82no—
975C42—82no—
976C42—82no—
977C42C4×Q8116yescomplemented
978C23C24×C411yescharacteristic
979C23C23×Q811yescharacteristic
980C23C22×#4111yescharacteristic
981C23C2×H(5,𝔽2)11yescharacteristic
982C23C2×H(5,𝔽2)11yescharacteristic
983C23C2×H(5,𝔽2)11yescharacteristic
984C23C2×H(5,𝔽2)11yescharacteristic
985C23C2×2−1+411yescharacteristic
986C23C2×2−1+411yescharacteristic
987C23C2×2−1+411yescharacteristic
988C23C2×2−1+411yescharacteristic
989C23#58511yescharacteristic
990C23#58511yescharacteristic
991C23#58511yescharacteristic
992C23#58511yescharacteristic
993Q8—416no—
994Q8—88no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4C2×C4×Q814yes—
1208C2×C4C2×C4×Q814yes—
1209C2×C4C2×C4×Q814yes—
1210C2×C4#51814yes—
1211C2×C4#51914yes—
1212C22C22×C4×Q811yescharacteristic
1213C22C2×#51811yescharacteristic
1214C22C2×#51911yescharacteristic
1215C22C4×H(5,𝔽2)11yescharacteristic
1216C22C4×H(5,𝔽2)11yescharacteristic
1217C22C4×2−1+411yescharacteristic
1218C22C4×2−1+411yescharacteristic
1219C22#349211yescharacteristic
1220C22#349311yescharacteristic
1221C22#349411yescharacteristic
1222C22#349511yescharacteristic
1223C22#350111yescharacteristic
1224C22#350211yescharacteristic
1225C22#350311yescharacteristic
1226C22#350311yescharacteristic
1227C22#350311yescharacteristic
1228C22#350411yescharacteristic
1229C22#351111yescharacteristic
1230C22#351111yescharacteristic
1231C22#353211yescharacteristic
1232C22#353311yescharacteristic
1233C22#353511yescharacteristic
1234C22#353811yescharacteristic
1235C22#353811yescharacteristic
1236C22#354011yescharacteristic
1237C22#354211yescharacteristic
1238C22#354211yescharacteristic
1239C22#354411yescharacteristic
1240C22#354711yescharacteristic
1241C22#354711yescharacteristic
1242C22#354711yescharacteristic
1243C22#356311yescharacteristic
1244C22#356311yescharacteristic
1245C22#356411yescharacteristic
1246C22#356511yescharacteristic
1247C4—24no—
1248C4—24no—
1249C4—24no—
1250C4—24no—
1251C4—24no—
1252C4—42no—
1253C4—42no—
1254C4—42no—
1255C4—42no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—42no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C2#3421611yescharacteristic
1279C2#3427111yescharacteristic
1280C2#3427211yescharacteristic
1281C2#3440611yescharacteristic
1282C2#3441211yescharacteristic
1283C2#3443211yescharacteristic
1284C2#3443511yescharacteristic
1285C2#5155911yescharacteristic
1286C2#5156211yescharacteristic
1287C2#5157311yescharacteristic
1288C2#5157511yescharacteristic
1289C2#5160011yescharacteristic
1290C2#5160211yescharacteristic
1291C2#5160311yescharacteristic
1292C2#5160511yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC24C25
commutatorC23C24×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
35. #2660C4semidirect
278. #382Q8semidirect
977. C42C4×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#26602
#146002
#145982
#145952
#145932
#145852
#145542
#145502
#145382
#144552
#144542
#144512
#144502
#142762
#142412
#142382
#142362
#142192
#142172
#142142
#141862
#141742
#141682
#141062
#140972
#140292
#140242
#139632
#138292
#138052
#137792