Finite Group Databasebeta

← #560992

Subgroups — #560992

Order 512.

1754 conjugacy classes of subgroups.

The subgroup lattice has 1217 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2655C211yesmaximal, characteristic
2#14611C211yesmaximal, characteristic
3#14607C211yesmaximal, characteristic
4#14607C211yesmaximal, characteristic
5#14593C211yesmaximal, characteristic
6#14555C211yesmaximal, characteristic
7#14548C211yesmaximal, characteristic
8#14532C211yesmaximal, characteristic
9#14532C211yesmaximal, characteristic
10#14499C211yesmaximal, characteristic
11#14482C211yesmaximal, characteristic
12#14480C211yesmaximal, characteristic
13#14480C211yesmaximal, characteristic
14#14266C211yesmaximal, characteristic
15#14251C211yesmaximal, characteristic
16#14247C211yesmaximal, characteristic
17#14245C211yesmaximal, characteristic
18#14235C211yesmaximal, characteristic
19#14234C211yesmaximal, characteristic
20#14234C211yesmaximal, characteristic
21#14212C211yesmaximal, characteristic
22#14192C211yesmaximal, characteristic
23#14147C211yesmaximal, characteristic
24#14094C211yesmaximal, characteristic
25#14069C211yesmaximal, characteristic
26#14062C211yesmaximal, characteristic
27#14055C211yesmaximal, characteristic
28#13928C211yesmaximal, characteristic
29#13833C211yesmaximal, characteristic
30#13815C211yesmaximal, characteristic
31#13792C211yesmaximal, characteristic
32#2655C4116yescomplemented
33C2×#401C2211yescharacteristic
34C2×#400C2211yescharacteristic
35C2×#400C2211yescharacteristic
36C2×#400C2211yescharacteristic
37C2×#400C2211yescharacteristic
38C2×#398C2211yescharacteristic
39C2×#398C2211yescharacteristic
40C2×#398C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#387C2211yescharacteristic
46C2×#387C2211yescharacteristic
47C2×#387C2211yescharacteristic
48C2×#387C2211yescharacteristic
49C2×#387C2211yescharacteristic
50C2×#387C2211yescharacteristic
51C2×#387C2211yescharacteristic
52C2×#387C2211yescharacteristic
53C2×#387C2211yescharacteristic
54C2×#387C2211yescharacteristic
55C2×#387C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×#376C2211yescharacteristic
60#1445C2211yescharacteristic
61#1445C2211yescharacteristic
62#1445C2211yescharacteristic
63#1445C2211yescharacteristic
64#1445C2211yescharacteristic
65#1445C2211yescharacteristic
66#1444C2211yescharacteristic
67#1443C2211yescharacteristic
68#1443C2211yescharacteristic
69#1443C2211yescharacteristic
70#1443C2211yescharacteristic
71#1443C2211yescharacteristic
72#1443C2211yescharacteristic
73#1443C2211yescharacteristic
74#1443C2211yescharacteristic
75#1443C2211yescharacteristic
76#1443C2211yescharacteristic
77#1442C2211yescharacteristic
78#1442C2211yescharacteristic
79#1442C2211yescharacteristic
80#1442C2211yescharacteristic
81#1442C2211yescharacteristic
82#1442C2211yescharacteristic
83#1442C2211yescharacteristic
84#1442C2211yescharacteristic
85#1442C2211yescharacteristic
86#1442C2211yescharacteristic
87#1442C2211yescharacteristic
88#1442C2211yescharacteristic
89#1442C2211yescharacteristic
90#1442C2211yescharacteristic
91#1442C2211yescharacteristic
92#1441C2211yescharacteristic
93#1441C2211yescharacteristic
94#1441C2211yescharacteristic
95#1441C2211yescharacteristic
96#1441C2211yescharacteristic
97#1441C2211yescharacteristic
98#1441C2211yescharacteristic
99#1441C2211yescharacteristic
100#1436C2211yescharacteristic
101#1436C2211yescharacteristic
102#1436C2211yescharacteristic
103#1436C2211yescharacteristic
104#1436C2211yescharacteristic
105#1436C2211yescharacteristic
106#1436C2211yescharacteristic
107#1436C2211yescharacteristic
108#1436C2211yescharacteristic
109#1436C2211yescharacteristic
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
146C4⋊#95C2211yescharacteristic
147C4⋊#95C2211yescharacteristic
148C4⋊#95C2211yescharacteristic
149C4⋊#95C2211yescharacteristic
150C4⋊#95C2211yescharacteristic
151C4⋊#95C2211yescharacteristic
152C4⋊#95C2211yescharacteristic
153C4⋊#95C2211yescharacteristic
154C4⋊#95C2211yescharacteristic
155#1434C2211yescharacteristic
156#1434C2211yescharacteristic
157#1434C2211yescharacteristic
158#1434C2211yescharacteristic
159#1434C2211yescharacteristic
160#1434C2211yescharacteristic
161#1434C2211yescharacteristic
162#1434C2211yescharacteristic
163#1434C2211yescharacteristic
164#1434C2211yescharacteristic
165#1434C2211yescharacteristic
166#1434C2211yescharacteristic
167#1434C2211yescharacteristic
168#1434C2211yescharacteristic
169#1434C2211yescharacteristic
170#1434C2211yescharacteristic
171#1434C2211yescharacteristic
172#1434C2211yescharacteristic
173#1434C2211yescharacteristic
174#1434C2211yescharacteristic
175#1434C2211yescharacteristic
176#1434C2211yescharacteristic
177#1434C2211yescharacteristic
178#1434C2211yescharacteristic
179C4×#95C2211yescharacteristic
180C4×#95C2211yescharacteristic
181C4×#95C2211yescharacteristic
182C4×#95C2211yescharacteristic
183C4×#95C2211yescharacteristic
184C4×#95C2211yescharacteristic
185C4×#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C4×#95C2211yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2311yescharacteristic
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
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×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231#401C2×C418yes—
232#400C2×C418yes—
233#400C2×C418yes—
234#400C2×C418yes—
235#400C2×C418yes—
236#398C2×C418yes—
237#398C2×C418yes—
238#398C2×C418yes—
239#389—24no—
240#389—42no—
241#389—42no—
242#389C2×C418yes—
243#387—24no—
244#387—24no—
245#387—24no—
246#387—24no—
247#387—24no—
248#387—42no—
249#387C2×C418yes—
250#387C2×C418yes—
251#387C2×C418yes—
252#387C2×C418yes—
253#387C2×C418yes—
254C4×C4⋊C4—42no—
255C4×C4⋊C4—42no—
256C4×C4⋊C4C2×C418yes—
257#376—42no—
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2311yescharacteristic
328C2×#95C2311yescharacteristic
329C2×#95C2311yescharacteristic
330C2×#95C2311yescharacteristic
331C2×#95C2311yescharacteristic
332C2×#95C2311yescharacteristic
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2311yescharacteristic
338C2×#95C2311yescharacteristic
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2311yescharacteristic
343C2×#95C2311yescharacteristic
344C2×#95C2311yescharacteristic
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C2×#95C2311yescharacteristic
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C2×#95C2311yescharacteristic
351C2×#95C2311yescharacteristic
352C2×#95C2311yescharacteristic
353C2×#95C2311yescharacteristic
354C2×#95C2311yescharacteristic
355C2×#95C2311yescharacteristic
356C2×#95C2311yescharacteristic
357C2×#95C2311yescharacteristic
358C2×#95C2311yescharacteristic
359C2×#95C2311yescharacteristic
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2311yescharacteristic
363C2×#95C2311yescharacteristic
364C2×#95C2311yescharacteristic
365C2×#95C2311yescharacteristic
366C2×#95C2311yescharacteristic
367C2×#95C2311yescharacteristic
368C2×#95C2311yescharacteristic
369C2×#95C2311yescharacteristic
370C23×C4C2411yescharacteristic
371C23×C4C2411yescharacteristic
372C23×C4C2411yescharacteristic
373C23×C4C2411yescharacteristic
374C23×C4C2411yescharacteristic
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—41no—
436C2×C4⋊C4—41no—
437C2×C4⋊C4—41no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4—41no—
440C2×C4⋊C4—41no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4—41no—
447C2×C4⋊C4—41no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4—41no—
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⋊C4C22×C414yes—
462C2×C4⋊C4C22×C414yes—
463C2×C4⋊C4C22×C414yes—
464C2×C4⋊C4C22×C414yes—
465C2×C4⋊C4C22×C414yes—
466C2×C4⋊C4C22×C414yes—
467C2×C4⋊C4C22×C414yes—
468C2×C4⋊C4C22×C414yes—
469C2×C4⋊C4C22×C414yes—
470C2×C4⋊C4C22×C414yes—
471C2×C4⋊C4C22×C414yes—
472C2×C4⋊C4C22×C414yes—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—41no—
486C2×C42—41no—
487C2×C42—41no—
488C2×C42—41no—
489C2×C42—41no—
490C2×C42—41no—
491C2×C42—41no—
492C2×C42—41no—
493C2×C42—41no—
494C2×C42—41no—
495C2×C42—41no—
496C2×C42—41no—
497C2×C42—41no—
498C2×C42—41no—
499C2×C42—41no—
500C2×C42—41no—
501C2×C42—41no—
502C2×C42—41no—
503C2×C42—41no—
504C2×C42—41no—
505C2×C42—41no—
506C2×C42—41no—
507C2×C42—41no—
508C2×C42—41no—
509C2×C42—41no—
510C2×C42—41no—
511C2×C42—41no—
512C2×C42—41no—
513C2×C42—41no—
514C2×C42—41no—
515C2×C42—41no—
516C2×C42—41no—
517C2×C42—41no—
518C2×C42—41no—
519C2×C42—41no—
520C2×C42—41no—
521C2×C42—41no—
522C2×C42—41no—
523C2×C42—41no—
524C2×C42—41no—
525C2×C42—41no—
526C2×C42—41no—
527C2×C42C22×C414yes—
528C2×C42C22×C414yes—
529C2×C42C22×C414yes—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—41no—
559#95—41no—
560#95—41no—
561#95—41no—
562#95—41no—
563#95—41no—
564#95—41no—
565#95—41no—
566#95—41no—
567#95—41no—
568#95—41no—
569#95—41no—
570#95—41no—
571#95—41no—
572#95—41no—
573#95—41no—
574#95—41no—
575#95—41no—
576#95—41no—
577#95—41no—
578#95—41no—
579#95—41no—
580#95—41no—
581#95—41no—
582#95—41no—
583#95—41no—
584#95—41no—
585#95—41no—
586#95—41no—
587#95—41no—
588#95—41no—
589#95—41no—
590#95—41no—
591#95—41no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—41no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95—41no—
612#95—41no—
613#95—41no—
614#95—41no—
615#95—41no—
616#95—41no—
617#95—41no—
618#95—41no—
619#95—41no—
620#95C22×C414yes—
621#95C22×C414yes—
622#95C22×C414yes—
623#95C22×C414yes—
624#95C22×C414yes—
625#95C22×C414yes—
626#95C22×C414yes—
627#95C22×C414yes—
628#95C22×C414yes—
629#95C22×C414yes—
630#95C22×C414yes—
631#95C22×C414yes—
632#95C22×C414yes—
633#95C22×C414yes—
634#95C22×C414yes—
635#95C22×C414yes—
636#95C22×C414yes—
637#95C22×C414yes—
638#95C22×C414yes—
639#95C22×C414yes—
640#95#4114yes—
641#95#4114yes—
642C24C2511yescharacteristic
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
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×C4C23×C412yes—
836C22×C4C23×C412yes—
837C22×C4C23×C412yes—
838C22×C4C23×C412yes—
839C22×C4C23×C412yes—
840C22×C4C23×C412yes—
841C22×C4C23×C412yes—
842C22×C4C23×C412yes—
843C22×C4C23×C412yes—
844C22×C4C23×C412yes—
845C22×C4C23×C412yes—
846C22×C4C23×C412yes—
847C22×C4C23×C412yes—
848C22×C4C23×C412yes—
849C22×C4C23×C412yes—
850C22×C4C2×#4112yes—
851C22×C4C2×#4112yes—
852C22×C4C2×#4112yes—
853C22×C4C2×#4112yes—
854C22×C4C2×#4112yes—
855C22×C4C2×#4112yes—
856C22×C4H(5,𝔽2)12yes—
857C22×C42−1+412yes—
858C22×C42−1+412yes—
859C22×C42−1+412yes—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—82no—
876C4⋊C4—82no—
877C4⋊C4—82no—
878C4⋊C4—82no—
879C4⋊C4—82no—
880C4⋊C4—82no—
881C4⋊C4—82no—
882C4⋊C4—82no—
883C4⋊C4—82no—
884C42—44no—
885C42—44no—
886C42—44no—
887C42—44no—
888C42—44no—
889C42—44no—
890C42—82no—
891C42—82no—
892C42—82no—
893C42—82no—
894C42—82no—
895C42—82no—
896C42—82no—
897C42—82no—
898C42—82no—
899C42—82no—
900C42—82no—
901C42—82no—
902C42—82no—
903C23C24×C411yescharacteristic
904C23C22×#4111yescharacteristic
905C23C22×#4111yescharacteristic
906C23C2×H(5,𝔽2)11yescharacteristic
907C23C2×2−1+411yescharacteristic
908C23C2×2−1+411yescharacteristic
909C23C2×2−1+411yescharacteristic
910C23#58511yescharacteristic
911C23#58511yescharacteristic
912C23#58511yescharacteristic
913C23#58511yescharacteristic
914C23#58511yescharacteristic
915C23#58511yescharacteristic
916C23#58511yescharacteristic
917C23#58511yescharacteristic
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
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×C4C4×#4114yes—
1135C22C2×C4×#4111yescharacteristic
1136C22#342811yescharacteristic
1137C22#342811yescharacteristic
1138C22C4×H(5,𝔽2)11yescharacteristic
1139C22C4×2−1+411yescharacteristic
1140C22C4×2−1+411yescharacteristic
1141C22C4×2−1+411yescharacteristic
1142C22#351011yescharacteristic
1143C22#351011yescharacteristic
1144C22#351211yescharacteristic
1145C22#351211yescharacteristic
1146C22#351311yescharacteristic
1147C22#351511yescharacteristic
1148C22#351511yescharacteristic
1149C22#351611yescharacteristic
1150C22#352011yescharacteristic
1151C22#352111yescharacteristic
1152C22#352111yescharacteristic
1153C22#352311yescharacteristic
1154C22#353311yescharacteristic
1155C22#354111yescharacteristic
1156C22#355711yescharacteristic
1157C22#356011yescharacteristic
1158C22#356111yescharacteristic
1159C22#356311yescharacteristic
1160C22#356311yescharacteristic
1161C22#356411yescharacteristic
1162C22#356411yescharacteristic
1163C22#356511yescharacteristic
1164C22#356511yescharacteristic
1165C22#356511yescharacteristic
1166C22#356611yescharacteristic
1167C22#356611yescharacteristic
1168C22#356611yescharacteristic
1169C22#356711yescharacteristic
1170C4—24no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—42no—
1179C4—42no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C2#3422711yescharacteristic
1202C2#3428211yescharacteristic
1203C2#3428611yescharacteristic
1204C2#3444911yescharacteristic
1205C2#3445311yescharacteristic
1206C2#3445511yescharacteristic
1207C2#3445511yescharacteristic
1208C2#4832011yescharacteristic
1209C2#4832111yescharacteristic
1210C2#4854411yescharacteristic
1211C2#4854511yescharacteristic
1212C2#5041111yescharacteristic
1213C2#5041211yescharacteristic
1214C2#5043111yescharacteristic
1215C2#5043211yescharacteristic
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
32. #2655C4semidirect

Maximal subgroups

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

subgroupindex
C2×#26552
#146112
#146072
#145932
#145552
#145482
#145322
#144992
#144822
#144802
#142662
#142512
#142472
#142452
#142352
#142342
#142122
#141922
#141472
#140942
#140692
#140622
#140552
#139282
#138332
#138152
#137922