Finite Group Databasebeta

← #14720782

Subgroups — #14720782

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077741C211yesmaximal, characteristic, complemented
2#13077260C211yesmaximal, characteristic, complemented
3#13067085C211yesmaximal, characteristic, complemented
4#13067081C211yesmaximal, characteristic, complemented
5#13067076C211yesmaximal, characteristic, complemented
6#13067059C211yesmaximal, characteristic, complemented
7#13067050C211yesmaximal, characteristic, complemented
8#13067041C211yesmaximal, characteristic, complemented
9#13067029C211yesmaximal, characteristic, complemented
10#13067024C211yesmaximal, characteristic, complemented
11#13067015C211yesmaximal, characteristic, complemented
12#13067007C211yesmaximal, characteristic, complemented
13#13067003C211yesmaximal, characteristic, complemented
14C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C11×#3481C211yesmaximal, characteristic
16C11×#559C411yescharacteristic
17C11×#554C411yescharacteristic
18C11×#554C411yescharacteristic
19C11×#553—21no—
20C11×#553C411yescharacteristic
21C11×#553C411yescharacteristic
22C11×#551—21no—
23C11×#551—21no—
24C11×#546—21no—
25C11×#546C411yescharacteristic
26C11×#546C411yescharacteristic
27D42×C11C411yescharacteristic
28C11×#532C2211yescharacteristic
29C11×#529—21no—
30C11×#529C2211yescharacteristic
31C11×#529C2211yescharacteristic
32C11×#525—21no—
33C11×#525—21no—
34C4×C11×#41C2211yescharacteristic
35C4×C11×#41C2211yescharacteristic
36C2×C4×D4×C11—21no—
37C2×C4×D4×C11C2211yescharacteristic
38C2×C4×D4×C11C2211yescharacteristic
39#10622847—21no—
40#10622637—21no—
41#10622624—21no—
42#10622624—21no—
43D4×C11⋊C8—21no—
44#10622613—21no—
45#10622613—21no—
46#10622612—21no—
47#10622539C2211yescharacteristic, complemented
48#10622539C2211yescharacteristic, complemented
49#10622538C2211yescharacteristic, complemented
50#10622538C2211yescharacteristic, complemented
51#10622538C2211yescharacteristic, complemented
52#10622538C2211yescharacteristic, complemented
53#10622538C2211yescharacteristic, complemented
54#10622537C2211yescharacteristic, complemented
55C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
56C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
57C4×#4318C2211yescharacteristic, complemented
58C2×C4×C11⋊C8C2211yescharacteristic, complemented
59Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
60Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
61Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
62Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
63D4⋊(C11⋊C8)C2211yescharacteristic
64D4⋊(C11⋊C8)C2211yescharacteristic
65D4⋊(C11⋊C8)C2211yescharacteristic
66D4⋊(C11⋊C8)C2211yescharacteristic
67D4⋊(C11⋊C8)C2211yescharacteristic, complemented
68D4⋊(C11⋊C8)C2211yescharacteristic, complemented
69D4⋊(C11⋊C8)C2211yescharacteristic, complemented
70D4⋊(C11⋊C8)C2211yescharacteristic, complemented
71D4⋊(C11⋊C8)C2211yescharacteristic, complemented
72D4⋊(C11⋊C8)C2211yescharacteristic, complemented
73D4⋊(C11⋊C8)C2211yescharacteristic, complemented
74D4⋊(C11⋊C8)C2211yescharacteristic, complemented
75C2×C11×#41—21no—
76C2×C11×#41C2×C411yescharacteristic
77C2×C11×#41D411yescharacteristic
78C22×D4×C11—21no—
79C22×D4×C11C2×C411yescharacteristic
80C22×D4×C11C2×C411yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C11×C4⋊Q8C2×C411yescharacteristic
84C11×#127C2×C411yescharacteristic
85C11×#126—21no—
86C11×#126—21no—
87C11×#126—21no—
88C11×#126—21no—
89C11×#125—21no—
90C11×#125C2×C411yescharacteristic
91C11×#125C2×C411yescharacteristic
92C11×#124—21no—
93C11×#124—21no—
94C11×#124C2×C411yescharacteristic
95C11×#124C2×C411yescharacteristic
96C11×#123—21no—
97C11×#123—21no—
98C11×#123—21no—
99C11×#123—21no—
100C11×#123—21no—
101C11×#123—21no—
102C11×#123—21no—
103C11×#123—21no—
104C11×C22⋊Q8—21no—
105C11×C22⋊Q8—21no—
106C11×C22⋊Q8—21no—
107C11×C22⋊Q8—21no—
108C11×C22⋊Q8—21no—
109C11×C22⋊Q8C2×C411yescharacteristic
110C11×C22⋊Q8C2×C411yescharacteristic
111C11×#121—21no—
112C11×#121—21no—
113C11×#121—21no—
114C11×#121—21no—
115C11×#121—21no—
116C11×#121—21no—
117C11×#121C2×C411yescharacteristic
118C11×#121C2×C411yescharacteristic
119C11×#121C2×C411yescharacteristic
120C11×#121C2×C411yescharacteristic
121C11×#120—21no—
122C11×#120—21no—
123C11×#120—21no—
124C11×#120—21no—
125C4×Q8×C11C2×C411yescharacteristic
126C4×Q8×C11C2×C411yescharacteristic
127C4×Q8×C11D411yescharacteristic
128C4×Q8×C11C2311yescharacteristic
129C4×D4×C11—21no—
130C4×D4×C11—21no—
131C4×D4×C11—21no—
132C4×D4×C11—21no—
133C4×D4×C11—21no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11—21no—
142C4×D4×C11C2×C411yescharacteristic
143C4×D4×C11C2×C411yescharacteristic
144C4×D4×C11C2×C411yescharacteristic
145C4×D4×C11C2×C411yescharacteristic
146C4×D4×C11C2×C411yescharacteristic
147C4×D4×C11C2×C411yescharacteristic
148C4×D4×C11C2×C411yescharacteristic
149C4×D4×C11C2×C411yescharacteristic
150C4×D4×C11D411yescharacteristic
151C4×D4×C11D411yescharacteristic
152C4×D4×C11D411yescharacteristic
153C4×D4×C11C2311yescharacteristic
154C4×D4×C11C2311yescharacteristic
155C4×D4×C11C2311yescharacteristic
156C11×#117—21no—
157C11×#117—21no—
158C11×#117—21no—
159C11×#117C2×C411yescharacteristic
160C11×#117D411yescharacteristic
161C11×#117D411yescharacteristic
162C11×#117D411yescharacteristic
163C2×C11×C4⋊C4—21no—
164C2×C11×C4⋊C4C2×C411yescharacteristic
165C2×C11×C4⋊C4C2×C411yescharacteristic
166C2×C11×C22⋊C4—21no—
167C2×C11×C22⋊C4—21no—
168C2×C11×C22⋊C4—21no—
169C2×C11×C22⋊C4—21no—
170C2×C42×C11—21no—
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2311yescharacteristic
173C2×C42×C11C2311yescharacteristic
174C2×#4318—21no—
175C2×#4318—21no—
176C22×C11⋊C8—21no—
177C22×C11⋊C8—21no—
178C22×C11⋊C8—21no—
179C22⋊(C11⋊C8)—21no—
180C22⋊(C11⋊C8)—21no—
181C22⋊(C11⋊C8)—21no—
182C22⋊(C11⋊C8)—21no—
183C22⋊(C11⋊C8)—21no—
184C22⋊(C11⋊C8)—21no—
185C22⋊(C11⋊C8)—21no—
186C4⋊(C11⋊C8)—21no—
187C4⋊(C11⋊C8)—21no—
188C4⋊(C11⋊C8)—21no—
189C4⋊(C11⋊C8)—21no—
190C4⋊(C11⋊C8)—21no—
191C4⋊(C11⋊C8)—21no—
192C4⋊(C11⋊C8)—21no—
193C4⋊(C11⋊C8)C2311yescharacteristic
194C4⋊(C11⋊C8)C2311yescharacteristic
195C4⋊(C11⋊C8)C2311yescharacteristic
196C4⋊(C11⋊C8)C2311yescharacteristic
197#66867—21no—
198#66867—21no—
199#66867—21no—
200C4×C11⋊C8—21no—
201C4×C11⋊C8—21no—
202C4×C11⋊C8C2311yescharacteristic
203C4×C11⋊C8C2311yescharacteristic
204C4×C11⋊C8C2311yescharacteristic
205C4×C11⋊C8C2311yescharacteristic
206#17521—111nomaximal, Sylow
207C24×C11—21no—
208C24×C11—21no—
209C11×#41—22no—
210C11×#41—42no—
211C11×#41—41no—
212C11×#41—81no—
213C11×#41—81no—
214C2×Q8×C11—21no—
215C2×Q8×C11C22⋊C411yescharacteristic
216C2×Q8×C11C22×C411yescharacteristic
217C2×D4×C11—22no—
218C2×D4×C11—22no—
219C2×D4×C11—21no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—21no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11—41no—
229C2×D4×C11—41no—
230C2×D4×C11—44no—
231C2×D4×C11C22⋊C411yescharacteristic
232C2×D4×C11C22⋊C411yescharacteristic
233C2×D4×C11C22⋊C411yescharacteristic
234C2×D4×C11C22×C411yescharacteristic
235C2×D4×C11C22×C411yescharacteristic
236C2×D4×C11C22×C411yescharacteristic
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—81no—
249C22×C4×C11—81no—
250C22×C4×C11—81no—
251C22×C4×C11—81no—
252C22×C4×C11C22×C411yescharacteristic
253C22×C4×C11C22×C411yescharacteristic
254C22×C4×C11C22×C411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D411yescharacteristic
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4C22⋊C411yescharacteristic
273C11×C4⋊C4C22⋊C411yescharacteristic
274C11×C4⋊C4C22⋊C411yescharacteristic
275C11×C4⋊C4C22⋊C411yescharacteristic
276C11×C4⋊C4C22⋊C411yescharacteristic
277C11×C4⋊C4C22⋊C411yescharacteristic
278C11×C4⋊C4C22×C411yescharacteristic
279C11×C4⋊C4C22×C411yescharacteristic
280C11×C4⋊C4C22×C411yescharacteristic
281C11×C4⋊C4C22×C411yescharacteristic
282C11×C22⋊C4—21no—
283C11×C22⋊C4—21no—
284C11×C22⋊C4—21no—
285C11×C22⋊C4—21no—
286C11×C22⋊C4—21no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C11×C22⋊C4—21no—
290C11×C22⋊C4—21no—
291C11×C22⋊C4—21no—
292C11×C22⋊C4—21no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—21no—
295C11×C22⋊C4—21no—
296C11×C22⋊C4—21no—
297C11×C22⋊C4—21no—
298C11×C22⋊C4—21no—
299C11×C22⋊C4—21no—
300C11×C22⋊C4—21no—
301C11×C22⋊C4C22⋊C411yescharacteristic
302C11×C22⋊C4C22⋊C411yescharacteristic
303C11×C22⋊C4C22⋊C411yescharacteristic
304C11×C22⋊C4C22⋊C411yescharacteristic
305C11×C22⋊C4C22⋊C411yescharacteristic
306C11×C22⋊C4C22⋊C411yescharacteristic
307C42×C11—21no—
308C42×C11—21no—
309C42×C11—21no—
310C42×C11C22×C411yescharacteristic
311C42×C11C22×C411yescharacteristic
312C42×C11C22×C411yescharacteristic
313C42×C11C2×D411yescharacteristic
314C42×C11C2×D411yescharacteristic
315C42×C11C2×D411yescharacteristic
316C42×C11C2×D411yescharacteristic
317C42×C11C2×D411yescharacteristic
318C42×C11C2×D411yescharacteristic
319C42×C11C2411yescharacteristic
320#4318—42no—
321#4318—81no—
322C2×C11⋊C8—21no—
323C2×C11⋊C8—21no—
324C2×C11⋊C8—21no—
325C2×C11⋊C8—21no—
326C2×C11⋊C8—21no—
327C2×C11⋊C8—21no—
328C2×C11⋊C8—21no—
329C2×C11⋊C8—21no—
330C2×C11⋊C8—42no—
331C2×C11⋊C8—81no—
332C2×C11⋊C8—81no—
333#3481D1111yescharacteristic
334#2990—111no—
335#2922—111no—
336#1496—111no—
337#1495—111no—
338#1494—111no—
339#1490—111no—
340#1488—111no—
341#1486—111no—
342#1483—111no—
343#1482—111no—
344#1480—111no—
345#1478—111no—
346#1477—111no—
347C2×D4⋊C8—111no—
348C23×C11—21no—
349C23×C11—21no—
350C23×C11—21no—
351C23×C11—42no—
352C23×C11—42no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11—81no—
356C23×C11—81no—
357C23×C11C2×C22⋊C411yescharacteristic
358C23×C11C2×C22⋊C411yescharacteristic
359C23×C11C2×C22⋊C411yescharacteristic
360Q8×C11—21no—
361Q8×C11—21no—
362Q8×C11—41no—
363Q8×C11—81no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—21no—
367D4×C11—21no—
368D4×C11—21no—
369D4×C11—21no—
370D4×C11—21no—
371D4×C11—41no—
372D4×C11—42no—
373D4×C11—42no—
374D4×C11—42no—
375D4×C11—42no—
376D4×C11—42no—
377D4×C11—42no—
378D4×C11—81no—
379D4×C11—81no—
380D4×C11—81no—
381D4×C11#13112yes—
382C2×C4×C11—22no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—21no—
387C2×C4×C11—21no—
388C2×C4×C11—21no—
389C2×C4×C11—21no—
390C2×C4×C11—21no—
391C2×C4×C11—21no—
392C2×C4×C11—21no—
393C2×C4×C11—21no—
394C2×C4×C11—21no—
395C2×C4×C11—21no—
396C2×C4×C11—21no—
397C2×C4×C11—21no—
398C2×C4×C11—21no—
399C2×C4×C11—21no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—42no—
403C2×C4×C11—42no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11—81no—
411C2×C4×C11—81no—
412C2×C4×C11—81no—
413C2×C4×C11—81no—
414C2×C4×C11—81no—
415C2×C4×C11—81no—
416C2×C4×C11C2×C22⋊C411yescharacteristic
417C2×C4×C11C2×C22⋊C411yescharacteristic
418C2×C4×C11C2×C22⋊C411yescharacteristic
419C2×C4×C11C2×C22⋊C411yescharacteristic
420C2×C4×C11C2×C22⋊C411yescharacteristic
421C2×C4×C11C2×C22⋊C411yescharacteristic
422C2×C4×C11C2×C22⋊C411yescharacteristic
423C2×C4×C11C2×C22⋊C411yescharacteristic
424C2×C4×C11C2×C22⋊C411yescharacteristic
425C2×C4×C11C23×C411yescharacteristic
426C2×C4×C11C22×D411yescharacteristic
427C2×C4×C11C22×D411yescharacteristic
428C11⋊C8—41no—
429C11⋊C8—41no—
430C11⋊C8—41no—
431C11⋊C8—41no—
432C11⋊C8—41no—
433C11⋊C8—41no—
434C11⋊C8—41no—
435C11⋊C8—41no—
436#559Dic1111yescharacteristic
437#554Dic1111yescharacteristic
438#554Dic1111yescharacteristic
439#553—21no—
440#553Dic1111yescharacteristic
441#553Dic1111yescharacteristic
442#551—21no—
443#551—21no—
444#546—21no—
445#546Dic1111yescharacteristic
446#546Dic1111yescharacteristic
447D42Dic1111yescharacteristic
448#532C2×D1111yescharacteristic
449#529—21no—
450#529C2×D1111yescharacteristic
451#529C2×D1111yescharacteristic
452#525—21no—
453#525—21no—
454C4×#41C2×D1111yescharacteristic
455C4×#41C2×D1111yescharacteristic
456C2×C4×D4—21no—
457C2×C4×D4C2×D1111yescharacteristic
458C2×C4×D4C2×D1111yescharacteristic
459#446—221no—
460#435—221no—
461#435—221no—
462C8×D4—221no—
463#433—221no—
464#433—221no—
465#432—111no—
466#432—111no—
467#431—111no—
468#431—111no—
469#431—111no—
470#431—111no—
471#431—111no—
472#424—221no—
473#423—111no—
474C2×C4⋊C8—111no—
475C2×C4⋊C8—111no—
476#408—221no—
477C4×M16—111no—
478C2×C4×C8—111no—
479Q8⋊C8—111no—
480Q8⋊C8—111no—
481Q8⋊C8—111no—
482Q8⋊C8—111no—
483D4⋊C8—111no—
484D4⋊C8—111no—
485D4⋊C8—111no—
486D4⋊C8—111no—
487D4⋊C8—111no—
488D4⋊C8—111no—
489D4⋊C8—111no—
490D4⋊C8—111no—
491D4⋊C8—111no—
492D4⋊C8—111no—
493D4⋊C8—111no—
494D4⋊C8—111no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—22no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—21no—
503C22×C11—21no—
504C22×C11—41no—
505C22×C11—41no—
506C22×C11—41no—
507C22×C11—41no—
508C22×C11—41no—
509C22×C11—41no—
510C22×C11—41no—
511C22×C11—41no—
512C22×C11—84no—
513C22×C11—84no—
514C22×C11#42112yes—
515C22×C11C22×C22⋊C411yescharacteristic
516C4×C11—21no—
517C4×C11—21no—
518C4×C11—21no—
519C4×C11—21no—
520C4×C11—21no—
521C4×C11—21no—
522C4×C11—21no—
523C4×C11—21no—
524C4×C11—21no—
525C4×C11—21no—
526C4×C11—41no—
527C4×C11—41no—
528C4×C11—41no—
529C4×C11—41no—
530C4×C11—41no—
531C4×C11C2×#13111yescharacteristic
532C4×C11#56811yescharacteristic
533C4×C11#57611yescharacteristic
534C4×C11#57711yescharacteristic
535C2×#41—21no—
536C2×#41C2×Dic1111yescharacteristic
537C2×#41C22⋊D1111yescharacteristic
538C22×D4—21no—
539C22×D4C2×Dic1111yescharacteristic
540C22×D4C2×Dic1111yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C2×M16—221no—
544C2×M16—221no—
545C22×C8—221no—
546C22×C8—221no—
547C22×C8—221no—
548C4⋊Q8C2×Dic1111yescharacteristic
549#127C2×Dic1111yescharacteristic
550#126—21no—
551#126—21no—
552#126—21no—
553#126—21no—
554#125—21no—
555#125C2×Dic1111yescharacteristic
556#125C2×Dic1111yescharacteristic
557#124—21no—
558#124—21no—
559#124C2×Dic1111yescharacteristic
560#124C2×Dic1111yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8C2×Dic1111yescharacteristic
575C22⋊Q8C2×Dic1111yescharacteristic
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121C2×Dic1111yescharacteristic
583#121C2×Dic1111yescharacteristic
584#121C2×Dic1111yescharacteristic
585#121C2×Dic1111yescharacteristic
586#120—21no—
587#120—21no—
588#120—21no—
589#120—21no—
590C4×Q8C2×Dic1111yescharacteristic
591C4×Q8C2×Dic1111yescharacteristic
592C4×Q8C22⋊D1111yescharacteristic
593C4×Q8C22×D1111yescharacteristic
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4C2×Dic1111yescharacteristic
608C4×D4C2×Dic1111yescharacteristic
609C4×D4C2×Dic1111yescharacteristic
610C4×D4C2×Dic1111yescharacteristic
611C4×D4C2×Dic1111yescharacteristic
612C4×D4C2×Dic1111yescharacteristic
613C4×D4C2×Dic1111yescharacteristic
614C4×D4C2×Dic1111yescharacteristic
615C4×D4C22⋊D1111yescharacteristic
616C4×D4C22⋊D1111yescharacteristic
617C4×D4C22⋊D1111yescharacteristic
618C4×D4C22×D1111yescharacteristic
619C4×D4C22×D1111yescharacteristic
620C4×D4C22×D1111yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624#117C2×Dic1111yescharacteristic
625#117C22⋊D1111yescharacteristic
626#117C22⋊D1111yescharacteristic
627#117C22⋊D1111yescharacteristic
628C2×C4⋊C4—21no—
629C2×C4⋊C4C2×Dic1111yescharacteristic
630C2×C4⋊C4C2×Dic1111yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C4⋊C8—111no—
640C4⋊C8—111no—
641C4⋊C8—111no—
642C4⋊C8—111no—
643C4⋊C8—221no—
644C4⋊C8—221no—
645C4⋊C8—221no—
646C4⋊C8—221no—
647C4⋊C8—221no—
648C4⋊C8—221no—
649C4⋊C8—221no—
650C22⋊C8—221no—
651C22⋊C8—221no—
652C22⋊C8—221no—
653C22⋊C8—221no—
654C22⋊C8—221no—
655C22⋊C8—221no—
656C22⋊C8—221no—
657#97—221no—
658#97—221no—
659#97—221no—
660C4×C8—111no—
661C4×C8—111no—
662C4×C8—111no—
663C4×C8—111no—
664C4×C8—221no—
665C4×C8—221no—
666C2×C11—22no—
667C2×C11—41no—
668C2×C11—41no—
669C2×C11—42no—
670C2×C11—81no—
671C2×C11—81no—
672C2×C11#288011yescharacteristic
673C2×C11#289711yescharacteristic
674C2×C11C2×#42111yescharacteristic
675C24—21no—
676C24—21no—
677#41—22no—
678#41—42no—
679#41—41no—
680#41—81no—
681#41—81no—
682C2×Q8—21no—
683C2×Q8C22⋊Dic1111yescharacteristic
684C2×Q8C22×Dic1111yescharacteristic
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4—44no—
699C2×D4C22⋊Dic1111yescharacteristic
700C2×D4C22⋊Dic1111yescharacteristic
701C2×D4C22⋊Dic1111yescharacteristic
702C2×D4C22×Dic1111yescharacteristic
703C2×D4C22×Dic1111yescharacteristic
704C2×D4C22×Dic1111yescharacteristic
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—81no—
717C22×C4—81no—
718C22×C4—81no—
719C22×C4—81no—
720C22×C4C22×Dic1111yescharacteristic
721C22×C4C22×Dic1111yescharacteristic
722C22×C4C22×Dic1111yescharacteristic
723C22×C4C2×C22⋊D1111yescharacteristic
724C22×C4C2×C22⋊D1111yescharacteristic
725C22×C4C2×C22⋊D1111yescharacteristic
726C22×C4C2×C22⋊D1111yescharacteristic
727C22×C4C2×C22⋊D1111yescharacteristic
728C22×C4C2×C22⋊D1111yescharacteristic
729M16—442no—
730M16—881no—
731C2×C8—221no—
732C2×C8—221no—
733C2×C8—221no—
734C2×C8—221no—
735C2×C8—221no—
736C2×C8—221no—
737C2×C8—221no—
738C2×C8—221no—
739C2×C8—442no—
740C2×C8—881no—
741C2×C8—881no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4C22⋊Dic1111yescharacteristic
754C4⋊C4C22⋊Dic1111yescharacteristic
755C4⋊C4C22⋊Dic1111yescharacteristic
756C4⋊C4C22⋊Dic1111yescharacteristic
757C4⋊C4C22⋊Dic1111yescharacteristic
758C4⋊C4C22⋊Dic1111yescharacteristic
759C4⋊C4C22×Dic1111yescharacteristic
760C4⋊C4C22×Dic1111yescharacteristic
761C4⋊C4C22×Dic1111yescharacteristic
762C4⋊C4C22×Dic1111yescharacteristic
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⋊C4C22⋊Dic1111yescharacteristic
783C22⋊C4C22⋊Dic1111yescharacteristic
784C22⋊C4C22⋊Dic1111yescharacteristic
785C22⋊C4C22⋊Dic1111yescharacteristic
786C22⋊C4C22⋊Dic1111yescharacteristic
787C22⋊C4C22⋊Dic1111yescharacteristic
788C42—21no—
789C42—21no—
790C42—21no—
791C42C22×Dic1111yescharacteristic
792C42C22×Dic1111yescharacteristic
793C42C22×Dic1111yescharacteristic
794C42C2×C22⋊D1111yescharacteristic
795C42C2×C22⋊D1111yescharacteristic
796C42C2×C22⋊D1111yescharacteristic
797C42C2×C22⋊D1111yescharacteristic
798C42C2×C22⋊D1111yescharacteristic
799C42C2×C22⋊D1111yescharacteristic
800C42C23×D1111yescharacteristic
801C11#1752111yescharacteristic, complemented, Sylow
802C23—21no—
803C23—21no—
804C23—21no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—81no—
810C23—81no—
811C23C2×C22⋊Dic1111yescharacteristic
812C23C2×C22⋊Dic1111yescharacteristic
813C23C2×C22⋊Dic1111yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—41no—
817Q8—81no—
818D4—22no—
819D4—22no—
820D4—21no—
821D4—21no—
822D4—21no—
823D4—21no—
824D4—21no—
825D4—41no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—42no—
831D4—42no—
832D4—81no—
833D4—81no—
834D4—81no—
835D4#6700112yes—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4C2×C22⋊Dic1111yescharacteristic
871C2×C4C2×C22⋊Dic1111yescharacteristic
872C2×C4C2×C22⋊Dic1111yescharacteristic
873C2×C4C2×C22⋊Dic1111yescharacteristic
874C2×C4C2×C22⋊Dic1111yescharacteristic
875C2×C4C2×C22⋊Dic1111yescharacteristic
876C2×C4C2×C22⋊Dic1111yescharacteristic
877C2×C4C2×C22⋊Dic1111yescharacteristic
878C2×C4C2×C22⋊Dic1111yescharacteristic
879C2×C4C23×Dic1111yescharacteristic
880C2×C4C22×C22⋊D1111yescharacteristic
881C2×C4C22×C22⋊D1111yescharacteristic
882C8—441no—
883C8—441no—
884C8—441no—
885C8—441no—
886C8—441no—
887C8—441no—
888C8—441no—
889C8—441no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—22no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—84no—
908C22—84no—
909C22#1062284912yes—
910C22C22×C22⋊Dic1111yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—41no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—41no—
926C4C2×#6700111yescharacteristic
927C4#1062335011yescharacteristic
928C4#1062336611yescharacteristic
929C4#1062336711yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—42no—
934C2—81no—
935C2—81no—
936C2#1307706511yescharacteristic
937C2#1307714211yescharacteristic
938C2C2×#1062284911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3481C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3481D11
hypocenterC11#17521
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #13077741C2semidirect
2. #13077260C2semidirect
3. #13067085C2semidirect
4. #13067081C2semidirect
5. #13067076C2semidirect
6. #13067059C2semidirect
7. #13067050C2semidirect
8. #13067041C2semidirect
9. #13067029C2semidirect
10. #13067024C2semidirect
11. #13067015C2semidirect
12. #13067007C2semidirect
13. #13067003C2semidirect
14. C2×D4⋊(C11⋊C8)C2semidirect
47. #10622539C22semidirect
48. #10622539C22semidirect
49. #10622538C22semidirect
50. #10622538C22semidirect
51. #10622538C22semidirect
52. #10622538C22semidirect
53. #10622538C22semidirect
54. #10622537C22semidirect
55. C2×C4⋊(C11⋊C8)C22semidirect
56. C2×C4⋊(C11⋊C8)C22semidirect
57. C4×#4318C22semidirect
58. C2×C4×C11⋊C8C22semidirect
59. Q8⋊(C11⋊C8)C22semidirect
60. Q8⋊(C11⋊C8)C22semidirect
61. Q8⋊(C11⋊C8)C22semidirect
62. Q8⋊(C11⋊C8)C22semidirect
67. D4⋊(C11⋊C8)C22semidirect
68. D4⋊(C11⋊C8)C22semidirect
69. D4⋊(C11⋊C8)C22semidirect
70. D4⋊(C11⋊C8)C22semidirect
71. D4⋊(C11⋊C8)C22semidirect
72. D4⋊(C11⋊C8)C22semidirect
73. D4⋊(C11⋊C8)C22semidirect
74. D4⋊(C11⋊C8)C22semidirect
801. C11#17521semidirect

Maximal subgroups

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

subgroupindex
#130777412
#130772602
#130670852
#130670812
#130670762
#130670592
#130670502
#130670412
#130670292
#130670242
#130670152
#130670072
#130670032
C2×D4⋊(C11⋊C8)2
C11×#34812
#1752111