Finite Group Databasebeta

← #14653195

Subgroups — #14653195

Order 2816.

374 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079198C211yesmaximal, characteristic
2#13068368C211yesmaximal, characteristic
3#13067377C211yesmaximal, characteristic
4#13067232C211yesmaximal, characteristic
5#13067231C211yesmaximal, characteristic
6#13067127C211yesmaximal, characteristic
7C11×#1506C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622706C411yescharacteristic, complemented
13#10622705C411yescharacteristic, complemented
14#10622694C411yescharacteristic, complemented
15#10622691C411yescharacteristic, complemented
16#10622664—21no—
17#10622664—21no—
18C4×#4326—21no—
19C4×#4326—21no—
20#10622539C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#328—22no—
24#10622181—22no—
25#10622162—21no—
26#10622162—21no—
27#10622118—21no—
28#10622117—21no—
29#10622103—22no—
30#10622090—22no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#125—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C11×#117—21no—
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4326—21no—
42C2×#4326—21no—
43#66979—21no—
44#66977—21no—
45#66977—21no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8D411yescharacteristic
48C22×C11⋊C8D411yescharacteristic
49#66923—21no—
50#66922C2×C411yescharacteristic
51#66922C2×C411yescharacteristic
52C4×Dic22—21no—
53C4×Dic22—21no—
54C11×C4⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#97—21no—
57C11×#95—21no—
58C11×#95D412yes—
59#66899—21no—
60#66899—21no—
61C22⋊(C11⋊C8)—21no—
62#66874—21no—
63#66874—21no—
64#66871—21no—
65#66871—21no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68#66867—21no—
69#66867D412yes—
70C4×C11⋊C8C2×C411yescharacteristic
71C4×C11⋊C8C2×C411yescharacteristic
72C4×C11⋊C8D411yescharacteristic
73C4×C11⋊C8D411yescharacteristic
74#9765—111nomaximal, Sylow
75C2×Q8×C11—21no—
76C2×Q8×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C2×Dic22—21no—
82C2×Dic22—21no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11—41no—
92C42×C11—41no—
93C42×C11—41no—
94C42×C11C22×C411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11#4111yescharacteristic
98C22⋊Dic11—41no—
99#4326—42no—
100#4326—42no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—41no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8C22⋊C411yescharacteristic
115C2×C11⋊C8C22⋊C411yescharacteristic
116C2×C11⋊C8C22⋊C411yescharacteristic
117C2×C11⋊C8C22⋊C411yescharacteristic
118#3170—111no—
119#1746—111no—
120#1568—111no—
121#1531—111no—
122#1531—111no—
123#1506—111no—
124#1506D1111yescharacteristic
125C23×C11#12111yescharacteristic
126Q8×C11—41no—
127Q8×C11—41no—
128Q8×C11—81no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—42no—
138C2×C4×C11C2×C22⋊C411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12411yescharacteristic
143C2×C4×C11#12711yescharacteristic
144C2×Dic11—41no—
145C2×Dic11—41no—
146Dic22—41no—
147Dic22—41no—
148Dic22—81no—
149C8×C11—81no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153C11⋊C8—21no—
154C11⋊C8—42no—
155C11⋊C8—81no—
156#533—111no—
157#533C2×D1111yescharacteristic
158#500—111no—
159#494—111no—
160#487—111no—
161#487—111no—
162#467—221no—
163#467—221no—
164C4×Q16—221no—
165C4×Q16—221no—
166#432—111no—
167#432C2×D1111yescharacteristic
168C2×#97—111no—
169C2×C4×C8—111no—
170#376C2×D1111yescharacteristic
171#336—221no—
172#336—221no—
173#335—221no—
174#334—221no—
175#330—222no—
176#330—222no—
177#328—22no—
178#328—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39011yescharacteristic
182C22×C11#47312yes—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—82no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11#42111yescharacteristic
192C4×C11#42111yescharacteristic
193Dic11—81no—
194Dic11—81no—
195C2×Q16—221no—
196C2×Q16—221no—
197C22×C8—111no—
198C22×C8—111no—
199C22×C8—221no—
200C4⋊Q8—111no—
201C4⋊Q8—111no—
202C4⋊Q8C4×D1111yescharacteristic
203C4⋊Q8C4×D1111yescharacteristic
204#125—21no—
205#125—221no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C22⋊Q8—221no—
209C22⋊Q8—221no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—221no—
213C4×Q8—221no—
214#117—21no—
215#117—221no—
216C2×C42—21no—
217C2×C42C22×D1111yescharacteristic
218#107—221no—
219#107—221no—
220C4⋊C8—21no—
221C4⋊C8—221no—
222#103—221no—
223#103—221no—
224#103—221no—
225#103—221no—
226C22⋊C8—21no—
227C22⋊C8—221no—
228#97—21no—
229#97—112no—
230#97—221no—
231#97—221no—
232C4×C8—111no—
233C4×C8—111no—
234C4×C8—111no—
235C4×C8—111no—
236#95—21no—
237#95C22⋊D1112yes—
238C2×C11—22no—
239C2×C11#196311yescharacteristic
240C2×C11#197611yescharacteristic
241C2×C11#197911yescharacteristic
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—221no—
245C2×Q8—221no—
246C22×C4—22no—
247C22×C4D4×D1111yescharacteristic
248C22×C4#434111yescharacteristic
249C22×C4C2×C22⋊D1111yescharacteristic
250Q16—442no—
251Q16—442no—
252C2×C8—41no—
253C2×C8—111no—
254C2×C8—111no—
255C2×C8—111no—
256C2×C8—111no—
257C2×C8—222no—
258C2×C8—441no—
259C2×C8—441no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—441no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C22⋊C4—41no—
276C22⋊C4—441no—
277C42—41no—
278C42—41no—
279C42—41no—
280C42—441no—
281C42C2×C4×D1111yescharacteristic
282C42#433911yescharacteristic
283C42D4×D1111yescharacteristic
284C42D4×D1111yescharacteristic
285C11#976511yescharacteristic, complemented, Sylow
286C23#6699211yescharacteristic
287Q8—41no—
288Q8—41no—
289Q8—81no—
290Q8—441no—
291Q8—441no—
292Q8—881no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4C22⋊C4×D1111yescharacteristic
305C2×C4(C22⋊D11)⋊C411yescharacteristic
306C2×C4#6693711yescharacteristic
307C2×C4#6693811yescharacteristic
308C2×C4C4×C22⋊D1111yescharacteristic
309C2×C4#6699311yescharacteristic
310C8—81no—
311C8—221no—
312C8—221no—
313C8—221no—
314C8—221no—
315C8—442no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22#1062257011yescharacteristic
320C22#1062281712yes—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—81no—
329C4—881no—
330C4—881no—
331C4#1062243411yescharacteristic
332C4#1062243411yescharacteristic
333C2—22no—
334C2#1306944611yescharacteristic
335C2#1306951111yescharacteristic
336C2#1306953011yescharacteristic
subgroupG/H
centerC22#10622570
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1506C2
socleC22×C11#390
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1506D11
hypocenterC11#9765
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
12. #10622706C4semidirect
13. #10622705C4semidirect
14. #10622694C4semidirect
15. #10622691C4semidirect
285. C11#9765semidirect

Maximal subgroups

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

subgroupindex
#130791982
#130683682
#130673772
#130672322
#130672312
#130671272
C11×#15062
#976511