Finite Group Databasebeta

← #611900

Subgroups — #611900

Order 512.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17003C211yesmaximal, characteristic
2#16997C211yesmaximal, characteristic
3#16995C211yesmaximal, characteristic
4#16995C211yesmaximal, characteristic
5#16994C211yesmaximal, characteristic
6#16990C211yesmaximal, characteristic
7#16981C211yesmaximal, characteristic
8#16959C211yesmaximal, characteristic
9#16900C211yesmaximal, characteristic
10#16827C211yesmaximal, characteristic
11#16713C211yesmaximal, characteristic
12#16598C211yesmaximal, characteristic
13#16553C211yesmaximal, characteristic
14#16482C211yesmaximal, characteristic
15#16412C211yesmaximal, characteristic
16#16325C211yesmaximal, characteristic
17C4×#398C211yesmaximal, characteristic
18C4×#398C211yesmaximal, characteristic
19C4×#398C211yesmaximal, characteristic
20C4×#395C211yesmaximal, characteristic
21C4×#395C211yesmaximal, characteristic
22C4×#395C211yesmaximal, characteristic
23#13856C211yesmaximal, characteristic
24#13848C211yesmaximal, characteristic
25#13848C211yesmaximal, characteristic
26#13846C211yesmaximal, characteristic
27#13846C211yesmaximal, characteristic
28#13846C211yesmaximal, characteristic
29C4×#389C211yesmaximal, characteristic
30C4×#389C211yesmaximal, characteristic
31C4×#387C211yesmaximal, characteristic
32C22×C4×Q8C2211yescharacteristic
33C2×#398C2211yescharacteristic
34C2×#398C2211yescharacteristic
35C2×#398C2211yescharacteristic
36C2×#395C2211yescharacteristic
37C2×#395C2211yescharacteristic
38C2×#395C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#387C2211yescharacteristic
44C2×#387C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×#376C2211yescharacteristic
63C2×#376C2211yescharacteristic
64C2×C43C2211yescharacteristic
65#1446C2211yescharacteristic
66#1446C2211yescharacteristic
67#1446C2211yescharacteristic
68#1445C2211yescharacteristic
69#1445C2211yescharacteristic
70#1445C2211yescharacteristic
71#1445C2211yescharacteristic
72#1445C2211yescharacteristic
73#1445C2211yescharacteristic
74#1445C2211yescharacteristic
75#1445C2211yescharacteristic
76#1445C2211yescharacteristic
77#1444C2211yescharacteristic
78#1444C2211yescharacteristic
79#1444C2211yescharacteristic
80#1444C2211yescharacteristic
81#1444C2211yescharacteristic
82#1444C2211yescharacteristic
83#1444C2211yescharacteristic
84#1444C2211yescharacteristic
85#1444C2211yescharacteristic
86#1444C2211yescharacteristic
87#1444C2211yescharacteristic
88#1444C2211yescharacteristic
89#1444C2211yescharacteristic
90#1444C2211yescharacteristic
91#1444C2211yescharacteristic
92#1444C2211yescharacteristic
93#1444C2211yescharacteristic
94#1444C2211yescharacteristic
95#1444C2211yescharacteristic
96#1444C2211yescharacteristic
97#1444C2211yescharacteristic
98#1444C2211yescharacteristic
99#1444C2211yescharacteristic
100#1444C2211yescharacteristic
101#1443C2211yescharacteristic
102#1443C2211yescharacteristic
103#1443C2211yescharacteristic
104#1443C2211yescharacteristic
105#1443C2211yescharacteristic
106#1443C2211yescharacteristic
107#1442C2211yescharacteristic
108#1442C2211yescharacteristic
109#1442C2211yescharacteristic
110#1442C2211yescharacteristic
111#1442C2211yescharacteristic
112#1442C2211yescharacteristic
113#1442C2211yescharacteristic
114#1442C2211yescharacteristic
115#1442C2211yescharacteristic
116#1442C2211yescharacteristic
117#1442C2211yescharacteristic
118#1442C2211yescharacteristic
119#1442C2211yescharacteristic
120#1442C2211yescharacteristic
121#1442C2211yescharacteristic
122#1442C2211yescharacteristic
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#1436C2211yescharacteristic
156#1436C2211yescharacteristic
157#1436C2211yescharacteristic
158#1436C2211yescharacteristic
159#1436C2211yescharacteristic
160#1436C2211yescharacteristic
161#1436C2211yescharacteristic
162#1436C2211yescharacteristic
163#1436C2211yescharacteristic
164#1436C2211yescharacteristic
165#1436C2211yescharacteristic
166#1436C2211yescharacteristic
167C4⋊#95C2211yescharacteristic
168C4⋊#95C2211yescharacteristic
169C4⋊#95C2211yescharacteristic
170C4⋊#95C2211yescharacteristic
171#1434C2211yescharacteristic
172#1434C2211yescharacteristic
173C4×#95C2211yescharacteristic
174C4×#95C2211yescharacteristic
175C4×#95C2211yescharacteristic
176C4×#95C2211yescharacteristic
177C4×#95C2211yescharacteristic
178C4×#95C2211yescharacteristic
179C4×#95C2211yescharacteristic
180C4×#95C2211yescharacteristic
181C4×#95C2211yescharacteristic
182C4×#95C2211yescharacteristic
183C4×#95C2211yescharacteristic
184C4×#95C2211yescharacteristic
185C4×#95C2211yescharacteristic
186C4×#95C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C2×C4×Q8—42no—
189C2×C4×Q8—42no—
190C2×C4×Q8—42no—
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×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×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
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
247#398—24no—
248#398—24no—
249#398—24no—
250#395—24no—
251#395—24no—
252#395—24no—
253#389—24no—
254#389—24no—
255#389—24no—
256#389—24no—
257#387—24no—
258#387—24no—
259C4×C4⋊C4—24no—
260C4×C4⋊C4—24no—
261C4×C4⋊C4—42no—
262C4×C4⋊C4—42no—
263C4×C4⋊C4—42no—
264C4×C4⋊C4—42no—
265C4×C4⋊C4—42no—
266C4×C4⋊C4—42no—
267C4×C4⋊C4—42no—
268C4×C4⋊C4—42no—
269C4×C4⋊C4—42no—
270C4×C4⋊C4—42no—
271C4×C4⋊C4—42no—
272C4×C4⋊C4—42no—
273C4×C4⋊C4—42no—
274C4×C4⋊C4Q818yescomplemented
275C4×C4⋊C4Q818yescomplemented
276#376—24no—
277#376—42no—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2311yescharacteristic
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2311yescharacteristic
317C2×#95C2311yescharacteristic
318C2×#95C2311yescharacteristic
319C2×#95C2311yescharacteristic
320C2×#95C2311yescharacteristic
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C2×#95C2311yescharacteristic
326C2×#95C2311yescharacteristic
327C2×#95C2311yescharacteristic
328C2×#95C2311yescharacteristic
329C2×#95C2311yescharacteristic
330C2×#95C2311yescharacteristic
331C2×#95C2311yescharacteristic
332C2×#95C2311yescharacteristic
333C2×#95C2311yescharacteristic
334C2×#95C2311yescharacteristic
335C2×#95C2311yescharacteristic
336C2×#95C2311yescharacteristic
337C2×#95C2311yescharacteristic
338C2×#95C2311yescharacteristic
339C2×#95C2311yescharacteristic
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2311yescharacteristic
343C2×#95C2311yescharacteristic
344C2×#95C2311yescharacteristic
345C2×#95C2311yescharacteristic
346C2×#95C2311yescharacteristic
347C2×#95C2311yescharacteristic
348C2×#95C2311yescharacteristic
349C2×#95C2311yescharacteristic
350C2×#95C2311yescharacteristic
351C2×#95C2311yescharacteristic
352C2×#95C2311yescharacteristic
353C2×#95C2311yescharacteristic
354C2×#95C2311yescharacteristic
355C2×#95C2311yescharacteristic
356C2×#95C2311yescharacteristic
357C2×#95C2311yescharacteristic
358C2×#95C2311yescharacteristic
359C2×#95C2311yescharacteristic
360C2×#95C2311yescharacteristic
361C2×#95C2311yescharacteristic
362C2×#95C2311yescharacteristic
363C2×#95C2311yescharacteristic
364C2×#95C2311yescharacteristic
365C2×#95C2311yescharacteristic
366C2×#95C2311yescharacteristic
367C2×#95C2311yescharacteristic
368C2×#95C2311yescharacteristic
369C2×#95C2311yescharacteristic
370C2×#95C2311yescharacteristic
371C2×#95C2311yescharacteristic
372C2×#95C2311yescharacteristic
373C2×#95C2311yescharacteristic
374C2×#95C2311yescharacteristic
375C2×#95C2311yescharacteristic
376C43—42no—
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—41no—
381C22×Q8—41no—
382C22×Q8—41no—
383C22×Q8—41no—
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
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
415C4×Q8—416no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
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—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
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⋊C4—41no—
517C2×C4⋊C4—41no—
518C2×C4⋊C4—41no—
519C2×C4⋊C4—41no—
520C2×C4⋊C4—41no—
521C2×C4⋊C4C2×Q814yes—
522C2×C4⋊C4C2×Q814yes—
523C2×C4⋊C4C2×Q814yes—
524C2×C4⋊C4C2×Q814yes—
525C2×C4⋊C4#4114yes—
526C2×C4⋊C4#4114yes—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
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—22no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
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×C42C2×Q814yes—
577C2×C42C2×Q814yes—
578C2×C42C2×Q814yes—
579C2×C42C2×Q814yes—
580C2×C42C2×Q814yes—
581C2×C42C2×Q814yes—
582C2×C42#4114yes—
583C2×C42#4114yes—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
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—41no—
624#95—41no—
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#95C2×Q814yes—
678#95C2×Q814yes—
679#95C2×Q814yes—
680#95C2×Q814yes—
681#95#4114yes—
682C24C2511yescharacteristic
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
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×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×C4C22×Q812yes—
875C22×C4C22×Q812yes—
876C22×C4C22×Q812yes—
877C22×C4C22×Q812yes—
878C22×C4C22×Q812yes—
879C22×C4C22×Q812yes—
880C22×C4C22×Q812yes—
881C22×C4C22×Q812yes—
882C22×C4C22×Q812yes—
883C22×C4C22×Q812yes—
884C22×C4C22×Q812yes—
885C22×C4C22×Q812yes—
886C22×C4C22×Q812yes—
887C22×C4C22×Q812yes—
888C22×C4C2×#4112yes—
889C22×C4C2×#4112yes—
890C22×C4C2×#4112yes—
891C22×C4C2×#4112yes—
892C22×C4C2×#4112yes—
893C22×C4C2×#4112yes—
894C22×C4C2×#4112yes—
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4C2×#4112yes—
899C22×C4C2×#4112yes—
900C22×C4C2×#4112yes—
901C22×C4C2×#4112yes—
902C22×C4C2×#4112yes—
903C22×C4H(5,𝔽2)12yes—
904C22×C4H(5,𝔽2)12yes—
905C22×C4H(5,𝔽2)12yes—
906C22×C42−1+412yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
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—
944C42—28no—
945C42—28no—
946C42—28no—
947C42—28no—
948C42—28no—
949C42—28no—
950C42—28no—
951C42—44no—
952C42—44no—
953C42—44no—
954C42—44no—
955C42—44no—
956C42—44no—
957C42—44no—
958C42—44no—
959C42—44no—
960C42—44no—
961C42—44no—
962C42—44no—
963C23C23×Q811yescharacteristic
964C23C23×Q811yescharacteristic
965C23C22×#4111yescharacteristic
966C23C22×#4111yescharacteristic
967C23C22×#4111yescharacteristic
968C23C22×#4111yescharacteristic
969C23C22×#4111yescharacteristic
970C23C2×H(5,𝔽2)11yescharacteristic
971C23C2×H(5,𝔽2)11yescharacteristic
972C23C2×H(5,𝔽2)11yescharacteristic
973C23C2×2−1+411yescharacteristic
974C23#58511yescharacteristic
975C23#58511yescharacteristic
976C23#58511yescharacteristic
977C23#58511yescharacteristic
978Q8—416no—
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—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
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—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×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#53314yes—
1188C2×C4#53314yes—
1189C2×C4#53914yes—
1190C2×C4#54414yes—
1191C2×C4#54414yes—
1192C2×C4#55414yes—
1193C2×C4#55414yes—
1194C2×C4Q8214yes—
1195C2×C4#56014yes—
1196C22C2×#53311yescharacteristic
1197C22C2×#53311yescharacteristic
1198C22#344411yescharacteristic
1199C22C2×#53911yescharacteristic
1200C22#345511yescharacteristic
1201C22C2×#54411yescharacteristic
1202C22C2×#54411yescharacteristic
1203C22#345811yescharacteristic
1204C22#345811yescharacteristic
1205C22#345911yescharacteristic
1206C22#345911yescharacteristic
1207C22#345911yescharacteristic
1208C22#346011yescharacteristic
1209C22#346011yescharacteristic
1210C22#346011yescharacteristic
1211C22#346111yescharacteristic
1212C22#346111yescharacteristic
1213C22#346111yescharacteristic
1214C22#346111yescharacteristic
1215C22C2×#55411yescharacteristic
1216C22C2×#55411yescharacteristic
1217C22#347511yescharacteristic
1218C22C2×Q8211yescharacteristic
1219C22Q8×#4111yescharacteristic
1220C22Q8×#4111yescharacteristic
1221C22Q8×#4111yescharacteristic
1222C22Q8×#4111yescharacteristic
1223C22#348011yescharacteristic
1224C22#348111yescharacteristic
1225C22#348111yescharacteristic
1226C22#348111yescharacteristic
1227C22C2×#56011yescharacteristic
1228C22#352911yescharacteristic
1229C22#352911yescharacteristic
1230C22#352911yescharacteristic
1231C4—24no—
1232C4—24no—
1233C4—42no—
1234C4—42no—
1235C4—42no—
1236C4—42no—
1237C4—42no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—42no—
1242C4—42no—
1243C4—42no—
1244C4—42no—
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—42no—
1249C4—42no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4#279218yes—
1262C2#3459211yescharacteristic
1263C2#3459511yescharacteristic
1264C2#3462511yescharacteristic
1265C2#3484011yescharacteristic
1266C2#3489311yescharacteristic
1267C2#3495011yescharacteristic
1268C2#3667711yescharacteristic
1269C2C2×#279211yescharacteristic
1270C2#5223711yescharacteristic
1271C2#5226711yescharacteristic
1272C2#5227611yescharacteristic
1273C2#5228711yescharacteristic
1274C2#5228911yescharacteristic
1275C2#5228911yescharacteristic
1276C2#5229211yescharacteristic
subgroupG/H
centerC23×C4C24
commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
274. C4×C4⋊C4Q8semidirect
275. C4×C4⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
#170032
#169972
#169952
#169942
#169902
#169812
#169592
#169002
#168272
#167132
#165982
#165532
#164822
#164122
#163252
C4×#3982
C4×#3952
#138562
#138482
#138462
C4×#3892
C4×#3872