Finite Group Databasebeta

← #14760794

Subgroups — #14760794

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic
2C2×C4×#4318C211yesmaximal, characteristic, complemented
3#13069231C211yesmaximal, characteristic, complemented
4#13069224C211yesmaximal, characteristic, complemented
5#13069182C211yesmaximal, characteristic, complemented
6#13069175C211yesmaximal, characteristic, complemented
7#13068914C211yesmaximal, characteristic
8#13068801C211yesmaximal, characteristic, complemented
9#13068684C211yesmaximal, characteristic, complemented
10#13068491C211yesmaximal, characteristic, complemented
11C4⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
12#13068400C211yesmaximal, characteristic, complemented
13#13068400C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C4×C11×#123C211yesmaximal, characteristic
16C2×C11×#123C411yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C11×#388C411yescharacteristic
23C11×#388C411yescharacteristic
24C11×#387C411yescharacteristic
25C11×#387C411yescharacteristic
26C11×#386C411yescharacteristic
27C11×#385C411yescharacteristic
28C11×#381C411yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39#10622625—24no—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C4×#4318—24no—
44C2×#66867C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2×C411yescharacteristic
62C23×C4×C11C2×C411yescharacteristic
63C23×C4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C11×#123—24no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C11×C22⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C42×C11—22no—
83C2×C42×C11—22no—
84C2×C42×C11C2×C411yescharacteristic
85C2×C42×C11C2×C411yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—22no—
99C2×#4318D414yes—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C11×#95C2×C411yescharacteristic
109C11×#95C2×C411yescharacteristic
110C11×#95C2×C411yescharacteristic
111C11×#95C2×C411yescharacteristic
112C11×#95C2×C411yescharacteristic
113C11×#95C2×C411yescharacteristic
114C11×#95C2×C411yescharacteristic
115C11×#95C2×C411yescharacteristic
116C11×#95C2×C411yescharacteristic
117C11×#95C2×C411yescharacteristic
118C22⋊(C11⋊C8)—22no—
119C22⋊(C11⋊C8)—22no—
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)—22no—
122C22⋊(C11⋊C8)—22no—
123C4⋊(C11⋊C8)—22no—
124C4⋊(C11⋊C8)—22no—
125C4⋊(C11⋊C8)—22no—
126#66867—22no—
127#66867—22no—
128#66867—22no—
129C4×C11⋊C8—22no—
130C4×C11⋊C8—22no—
131C4×C11⋊C8—22no—
132C4×C11⋊C8—22no—
133#21565—111nomaximal, Sylow
134C24×C11C22×C411yescharacteristic
135C24×C11C22×C411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—41no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11C22×C411yescharacteristic
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11#4112yes—
169C22×C4×C11C2411yescharacteristic
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4M1614yescomplemented
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195#4318—28no—
196#4318—28no—
197#4318—44no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8C2×D412yes—
218C2×C11⋊C8#4112yes—
219C2×C11⋊C8#4112yes—
220C2×C11⋊C8#4112yes—
221C2×C11⋊C8#4112yes—
222C2×#436—111no—
223C2×C4×M16—111no—
224C4×#123D1111yescharacteristic
225#1924—111no—
226#1923—111no—
227#1917—111no—
228#1916—111no—
229#1870—111no—
230#1851—111no—
231#1817—111no—
232#1771—111no—
233C8×C4⋊C4—111no—
234#1753—111no—
235#1753—111no—
236#1753—111no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11C4×D412yes—
251C23×C11C23×C411yescharacteristic
252D4×C11—44no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—44no—
289C2×C4×C11—44no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11C4×D412yes—
295C2×C4×C11C2×M1612yes—
296C2×C4×C11C2×M1612yes—
297C2×C4×C11C2×M1612yes—
298C2×C4×C11#13112yes—
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×C4×C11C2×#4111yescharacteristic
305C11⋊C8—22no—
306C11⋊C8—22no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C11⋊C8#12314yescomplemented
313C22×M16—111no—
314C22×M16—111no—
315C22×M16—111no—
316C2×#123Dic1111yescharacteristic
317C2×C4×D4C2×D1111yescharacteristic
318C22×C42C2×D1111yescharacteristic
319#436—224no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8—111no—
322C2×C4⋊C8—111no—
323C2×C22⋊C8—111no—
324C2×C22⋊C8—111no—
325C2×C22⋊C8—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
328C4×M16—224no—
329C2×#97—111no—
330C2×#97—111no—
331C2×#97—111no—
332C2×C4×C8—111no—
333C2×C4×C8—111no—
334C2×C4×C8—111no—
335C2×C4×C8—111no—
336#388Dic1111yescharacteristic
337#388Dic1111yescharacteristic
338#387Dic1111yescharacteristic
339#387Dic1111yescharacteristic
340#386Dic1111yescharacteristic
341#385Dic1111yescharacteristic
342#381Dic1111yescharacteristic
343C4×C4⋊C4C2×D1111yescharacteristic
344C4×C4⋊C4C2×D1111yescharacteristic
345C4×C22⋊C4C2×D1111yescharacteristic
346C4×C22⋊C4C2×D1111yescharacteristic
347C4×C22⋊C4C2×D1111yescharacteristic
348#336—111no—
349#336—111no—
350#336—111no—
351#336—111no—
352#336—111no—
353#336—111no—
354#336—111no—
355#336—111no—
356#336—111no—
357#336—111no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11C2×C4×D411yescharacteristic
373C22×C11C4×#4111yescharacteristic
374C22×C11C4×#4111yescharacteristic
375C22×C11C22×M1611yescharacteristic
376C22×C11C2×#13111yescharacteristic
377C22×C11#56811yescharacteristic
378C22×C11#56811yescharacteristic
379C4×C11—22no—
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11C2×#12311yescharacteristic
392C4×C11#52511yescharacteristic
393C4×C11#52911yescharacteristic
394C4×C11#52911yescharacteristic
395C22×D4C2×Dic1111yescharacteristic
396C23×C4C2×Dic1111yescharacteristic
397C23×C4C2×Dic1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C2×M16—114no—
401C2×M16—222no—
402C2×M16—222no—
403C2×M16—222no—
404C2×M16—222no—
405C2×M16—222no—
406C2×M16—222no—
407C2×M16—222no—
408C2×M16—222no—
409C22×C8—111no—
410C22×C8—111no—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8—111no—
416C22×C8—111no—
417#123—24no—
418C4×D4—22no—
419C4×D4—22no—
420C2×C4⋊C4C2×Dic1111yescharacteristic
421C2×C4⋊C4C2×Dic1111yescharacteristic
422C2×C4⋊C4C2×Dic1111yescharacteristic
423C2×C4⋊C4C2×Dic1111yescharacteristic
424C2×C4⋊C4C2×Dic1111yescharacteristic
425C2×C22⋊C4C2×Dic1111yescharacteristic
426C2×C22⋊C4C2×Dic1111yescharacteristic
427C2×C22⋊C4C2×Dic1111yescharacteristic
428C2×C22⋊C4C2×Dic1111yescharacteristic
429C2×C22⋊C4C2×Dic1111yescharacteristic
430C2×C22⋊C4C2×Dic1111yescharacteristic
431C2×C22⋊C4C2×Dic1111yescharacteristic
432C2×C22⋊C4C2×Dic1111yescharacteristic
433C2×C42—22no—
434C2×C42—22no—
435C2×C42C2×Dic1111yescharacteristic
436C2×C42C2×Dic1111yescharacteristic
437C2×C42C22×D1111yescharacteristic
438C2×C42C22×D1111yescharacteristic
439C2×C42C22×D1111yescharacteristic
440C2×C42C22×D1111yescharacteristic
441C2×C42C22×D1111yescharacteristic
442C4⋊C8—222no—
443C4⋊C8—222no—
444C4⋊C8—222no—
445C22⋊C8—222no—
446C22⋊C8—222no—
447C22⋊C8—222no—
448C22⋊C8—222no—
449C22⋊C8—222no—
450#97—222no—
451#97—222no—
452#97—222no—
453C4×C8—222no—
454C4×C8—222no—
455C4×C8—222no—
456C4×C8—222no—
457#95C2×Dic1111yescharacteristic
458#95C2×Dic1111yescharacteristic
459#95C2×Dic1111yescharacteristic
460#95C2×Dic1111yescharacteristic
461#95C2×Dic1111yescharacteristic
462#95C2×Dic1111yescharacteristic
463#95C2×Dic1111yescharacteristic
464#95C2×Dic1111yescharacteristic
465#95C2×Dic1111yescharacteristic
466#95C2×Dic1111yescharacteristic
467C2×C11—42no—
468C2×C11—81no—
469C2×C11C4×#12311yescharacteristic
470C2×C11#293311yescharacteristic
471C2×C11D4×M1611yescharacteristic
472C2×C11#296511yescharacteristic
473C2×C11#296711yescharacteristic
474C2×C11#296911yescharacteristic
475C2×C11#297111yescharacteristic
476C24C22×Dic1111yescharacteristic
477C24C22×Dic1111yescharacteristic
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—41no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4D4×D1112yes—
498C22×C4#434112yes—
499C22×C4C22×Dic1111yescharacteristic
500C22×C4C22×Dic1111yescharacteristic
501C22×C4C22×Dic1111yescharacteristic
502C22×C4C22×Dic1111yescharacteristic
503C22×C4C22×Dic1111yescharacteristic
504C22×C4C22×Dic1111yescharacteristic
505C22×C4C22×Dic1111yescharacteristic
506C22×C4C22×Dic1111yescharacteristic
507C22×C4C22×Dic1111yescharacteristic
508C22×C4C22×Dic1111yescharacteristic
509C22×C4C22×Dic1111yescharacteristic
510C22×C4C22×Dic1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512M16—228no—
513M16—228no—
514M16—444no—
515C2×C8—112no—
516C2×C8—112no—
517C2×C8—112no—
518C2×C8—112no—
519C2×C8—112no—
520C2×C8—112no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—41no—
543C4⋊C4#431814yescomplemented
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C42—22no—
553C42—22no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C11#2156511yescharacteristic, complemented, Sylow
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23D4×Dic1112yes—
579C23C23×Dic1111yescharacteristic
580D4—44no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4C2×#431812yes—
623C2×C4C2×#431812yes—
624C2×C4C2×#431812yes—
625C2×C4D4×Dic1112yes—
626C2×C4#6700112yes—
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#41×D1111yescharacteristic
633C8—114no—
634C8—222no—
635C8—222no—
636C8—222no—
637C8—441no—
638C8—441no—
639C8—441no—
640C8—441no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22C22×#431811yescharacteristic
656C22C2×D4×Dic1111yescharacteristic
657C22C2×#6700111yescharacteristic
658C22#1062335011yescharacteristic
659C22#1062335011yescharacteristic
660C22#41×Dic1111yescharacteristic
661C22#41×Dic1111yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4#1062318011yescharacteristic
675C4#1062318011yescharacteristic
676C4D11×#12311yescharacteristic
677C4#1062318711yescharacteristic
678C2—42no—
679C2—81no—
680C2#123×Dic1111yescharacteristic
681C2#1307734311yescharacteristic
682C2D4×#431811yescharacteristic
683C2#1307758311yescharacteristic
684C2#1307760311yescharacteristic
685C2#1307762111yescharacteristic
686C2#1307763611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×#123C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC4×#123D11
hypocenterC11#21565
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4318C2semidirect
3. #13069231C2semidirect
4. #13069224C2semidirect
5. #13069182C2semidirect
6. #13069175C2semidirect
8. #13068801C2semidirect
9. #13068684C2semidirect
10. #13068491C2semidirect
11. C4⋊C4×C11⋊C8C2semidirect
12. #13068400C2semidirect
13. #13068400C2semidirect
14. #13068400C2semidirect
174. C11×C4⋊C4M16semidirect
312. C11⋊C8#123semidirect
543. C4⋊C4#4318semidirect
564. C11#21565semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×C4×#43182
#130692312
#130692242
#130691822
#130691752
#130689142
#130688012
#130686842
#130684912
C4⋊C4×C11⋊C82
#130684002
C4×C11×#1232
#2156511