Finite Group Databasebeta

← #14657686

Subgroups — #14657686

Order 2816.

366 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 85 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#13069606C211yesmaximal, characteristic, complemented
2#13067404C211yesmaximal, characteristic, complemented
3#13067351C211yesmaximal, characteristic
4#13067301C211yesmaximal, characteristic, complemented
5#13067033C211yesmaximal, characteristic
6#13066507C211yesmaximal, characteristic, complemented
7C11×#3226C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#500—21no—
11C11×#486—21no—
12C11×#480—22no—
13C11×#474—21no—
14C11×#474—21no—
15C11×#431C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19C4×#4318C2211yescharacteristic
20#10622185—22no—
21#10622184—21no—
22#10622182—21no—
23D4⋊(C11⋊C8)—22no—
24#10622168—22no—
25#10622118—21no—
26#10622117—21no—
27C2×C11×#41—21no—
28C22×Q8×C11—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×#127D411yescharacteristic
35C11×#124—21no—
36C11×#121—21no—
37C11×#121—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4D412yes—
42C2×C42×C11C2311yescharacteristic
43C2×#4318—21no—
44C2×#4318—21no—
45C2×#4318—21no—
46C11×#107—22no—
47C11×#107—22no—
48C11×C4⋊C8D411yescharacteristic
49C11×C4⋊C8D411yescharacteristic
50C11×#102—22no—
51C11×#102—22no—
52C11×C22⋊C8—21no—
53C4×C8×C11—21no—
54C22⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)D412yes—
60#66867—21no—
61C4×C11⋊C8—21no—
62C4×C11⋊C8—21no—
63#10490—111nomaximal, Sylow
64C11×#41—82no—
65C2×Q8×C11—21no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—82no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—41no—
73C22×C4×C11—22no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92#4318—22no—
93#4318—41no—
94#4318—42no—
95#4318—81no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100#3226D1111yescharacteristic
101#1997—111no—
102#1574—111no—
103#1560—111no—
104#1549—111no—
105#1484—111no—
106#1299—111no—
107C23×C11—41no—
108C23×C11#12311yescharacteristic
109Q8×C11—81no—
110Q8×C11—82no—
111Q8×C11—82no—
112D4×C11—41no—
113D4×C11—41no—
114D4×C11—41no—
115D4×C11—41no—
116D4×C11—81no—
117D4×C11—82no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—82no—
126C2×C4×C11—82no—
127C2×C4×C11#12011yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11#12111yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11#12411yescharacteristic
133C8×C11—41no—
134C8×C11—41no—
135C11⋊C8—42no—
136C11⋊C8—42no—
137C11⋊C8—81no—
138C11⋊C8—81no—
139#532C2×D1111yescharacteristic
140C2×C4⋊Q8C2×D1111yescharacteristic
141#500—21no—
142#486—21no—
143#480—22no—
144#474—21no—
145#474—21no—
146#431—111no—
147#431C2×D1111yescharacteristic
148#423—111no—
149#423—111no—
150C4×M16—111no—
151#343—222no—
152#335—221no—
153#334—221no—
154#333—221no—
155#332—222no—
156#331—221no—
157D4⋊C8—222no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—81no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11#39411yescharacteristic
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—81no—
169C4×C11—82no—
170C4×C11#45411yescharacteristic
171C4×C11#45611yescharacteristic
172C4×C11#47111yescharacteristic
173C4×C11#47212yes—
174C4×C11#47311yescharacteristic
175C2×#41—21no—
176C22×Q8—21no—
177C2×M16—221no—
178C2×M16—221no—
179C2×M16—221no—
180C4⋊Q8—21no—
181C4⋊Q8—21no—
182C4⋊Q8—21no—
183C4⋊Q8—21no—
184C4⋊Q8C22⋊D1111yescharacteristic
185#127C22⋊D1111yescharacteristic
186#124—21no—
187#121—21no—
188#121—21no—
189C4×D4—21no—
190C4×D4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C22⋊D1112yes—
193C2×C42C22×D1111yescharacteristic
194#107—22no—
195#107—22no—
196C4⋊C8—112no—
197C4⋊C8—221no—
198C4⋊C8—221no—
199C4⋊C8—221no—
200C4⋊C8—221no—
201C4⋊C8C22⋊D1111yescharacteristic
202C4⋊C8C22⋊D1111yescharacteristic
203#102—22no—
204#102—22no—
205C22⋊C8—21no—
206C22⋊C8—221no—
207#97—221no—
208C4×C8—21no—
209C4×C8—221no—
210C4×C8—221no—
211C2×C11—41no—
212C2×C11—161no—
213C2×C11#203811yescharacteristic
214C2×C11#204511yescharacteristic
215C2×C11#205211yescharacteristic
216#41—82no—
217C2×Q8—21no—
218C2×Q8—41no—
219C2×Q8—41no—
220C2×Q8—82no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4—21no—
224C2×D4—41no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4#434111yescharacteristic
228C22×C4#434111yescharacteristic
229C22×C4C2×C22⋊D1111yescharacteristic
230M16—222no—
231M16—441no—
232M16—442no—
233M16—881no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—222no—
237C2×C8—441no—
238C2×C8—441no—
239C2×C8—441no—
240C4⋊C4—22no—
241C4⋊C4—21no—
242C4⋊C4—22no—
243C4⋊C4—21no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C42D4×D1111yescharacteristic
249C42#434111yescharacteristic
250C42C2×C22⋊D1111yescharacteristic
251C42C2×C22⋊D1111yescharacteristic
252C11#1049011yescharacteristic, complemented, Sylow
253C23—41no—
254C23#6698811yescharacteristic
255Q8—81no—
256Q8—82no—
257Q8—82no—
258D4—41no—
259D4—41no—
260D4—41no—
261D4—41no—
262D4—81no—
263D4—82no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4#6698811yescharacteristic
274C2×C4#6698911yescharacteristic
275C2×C4#6699111yescharacteristic
276C2×C4#6699211yescharacteristic
277C2×C4#6699211yescharacteristic
278C2×C4#6700611yescharacteristic
279C8—41no—
280C8—41no—
281C8—442no—
282C8—442no—
283C8—881no—
284C8—881no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—81no—
289C22—81no—
290C22—81no—
291C22#1062283511yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—81no—
296C4—82no—
297C4#1062277312yes—
298C4#1062281611yescharacteristic
299C4#1062281711yescharacteristic
300C4#1062285811yescharacteristic
301C4#1062285911yescharacteristic
302C2—41no—
303C2—161no—
304C2#1306983011yescharacteristic
305C2#1306986911yescharacteristic
306C2#1306991211yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3226C2
socleC22×C11#394
prime radicalC11×#532C22
hypercenter#3226D11
hypocenterC11#10490
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
1. #13069606C2semidirect
2. #13067404C2semidirect
4. #13067301C2semidirect
6. #13066507C2semidirect
252. C11#10490semidirect

Maximal subgroups

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

subgroupindex
#130696062
#130674042
#130673512
#130673012
#130670332
#130665072
C11×#32262
#1049011