Finite Group Databasebeta

← #14665133

Subgroups — #14665133

Order 2816.

306 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 111 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#13070419C211yesmaximal, characteristic
2C2×#10622096C211yesmaximal, characteristic
3#13066671C212yesmaximal, complemented
4#13066665C212yesmaximal, complemented
5C11×#3170C211yesmaximal, characteristic
6C11×#533—21no—
7C11×#500C2211yescharacteristic
8C11×#494C2211yescharacteristic
9C11×#487—21no—
10C11×#467—21no—
11C11×#467C412yes—
12C4×C11×Q16—21no—
13C4×C11×Q16C412yes—
14C2×C4×C8×C11C2211yescharacteristic
15C2×C4⋊(C11⋊C8)—21no—
16C22⋊(C11⋊C16)—21no—
17C4⋊(C11⋊C16)C2212yes—
18#10622099—21no—
19#10622096—21no—
20#10622096C2212yes—
21C2×C11×Q16—21no—
22C2×C11×Q16C2×C412yes—
23C22×C8×C11C2×C411yescharacteristic
24C22×C8×C11D411yescharacteristic
25C11×C4⋊Q8—21no—
26C11×C4⋊Q8—21no—
27C11×#125—41no—
28C11×C22⋊Q8—22no—
29C11×C22⋊Q8—41no—
30C4×Q8×C11—22no—
31C4×Q8×C11—41no—
32C11×#117—41no—
33C2×C42×C11D411yescharacteristic
34C22×C11⋊C8—41no—
35C11×#107—21no—
36C11×#107C2×C412yes—
37C11×#103—22no—
38C11×#103—22no—
39C4×C8×C11C2×C411yescharacteristic
40C4×C8×C11D411yescharacteristic
41C4×C8×C11D411yescharacteristic
42C4×C8×C11C2311yescharacteristic
43C2×C11⋊C16—22no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—41no—
46#11954—111nomaximal, Sylow
47C2×Q8×C11—22no—
48C2×Q8×C11—41no—
49C22×C4×C11C22⋊C411yescharacteristic
50C22×C4×C11D811yescharacteristic
51C22×C4×C11SD1611yescharacteristic
52C11×Q16—42no—
53C11×Q16—42no—
54C2×C8×C11—22no—
55C2×C8×C11—41no—
56C2×C8×C11C22⋊C411yescharacteristic
57C2×C8×C11C22⋊C411yescharacteristic
58C2×C8×C11C22×C411yescharacteristic
59C2×C8×C11C2×D411yescharacteristic
60C11×C4⋊C4—22no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C11×C22⋊C4—42no—
67C42×C11—42no—
68C42×C11C22⋊C411yescharacteristic
69C42×C11D811yescharacteristic
70C42×C11SD1611yescharacteristic
71C42×C11C2×D411yescharacteristic
72C2×C11⋊C8—42no—
73C2×C11⋊C8—82no—
74C11⋊C16—42no—
75#3170D1111yescharacteristic
76#2163—111no—
77C2×#335—111no—
78#1364—112no—
79#1362—112no—
80C23×C11#10211yescharacteristic
81Q8×C11—42no—
82Q8×C11—42no—
83Q8×C11—81no—
84Q8×C11—81no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11#10211yescharacteristic
93C2×C4×C11#10211yescharacteristic
94C2×C4×C11#10211yescharacteristic
95C2×C4×C11C2×C22⋊C411yescharacteristic
96C2×C4×C11C2×D811yescharacteristic
97C2×C4×C11C2×SD1611yescharacteristic
98C8×C11—21no—
99C8×C11—21no—
100C8×C11—21no—
101C8×C11#13512yes—
102C11⋊C8—82no—
103#533—21no—
104#500C2×D1111yescharacteristic
105#494C2×D1111yescharacteristic
106#487—21no—
107#467—21no—
108#467Dic1112yes—
109C4×Q16—21no—
110C4×Q16Dic1112yes—
111C2×C4⋊C8—221no—
112C2×C4×C8C2×D1111yescharacteristic
113C4⋊C16—112no—
114C22⋊C16—221no—
115#346—221no—
116#335—112no—
117#335—221no—
118C22×C11—21no—
119C22×C11—21no—
120C22×C11#36212yes—
121C22×C11C2×#10211yescharacteristic
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—82no—
127C4×C11—82no—
128C4×C11#41311yescharacteristic
129C4×C11#41611yescharacteristic
130C4×C11#50911yescharacteristic
131C4×C11#51011yescharacteristic
132C2×Q16—21no—
133C2×Q16C2×Dic1112yes—
134C22×C8—441no—
135C22×C8C2×Dic1111yescharacteristic
136C22×C8C22⋊D1111yescharacteristic
137C4⋊Q8—21no—
138C4⋊Q8—21no—
139#125—41no—
140C22⋊Q8—22no—
141C22⋊Q8—41no—
142C4×Q8—22no—
143C4×Q8—41no—
144#117—41no—
145C2×C42C22⋊D1111yescharacteristic
146C2×C16—222no—
147#107—21no—
148#107C2×Dic1112yes—
149C4⋊C8—222no—
150C4⋊C8—441no—
151#103—22no—
152#103—22no—
153C4×C8C2×Dic1111yescharacteristic
154C4×C8C22⋊D1111yescharacteristic
155C4×C8C22⋊D1111yescharacteristic
156C4×C8C22×D1111yescharacteristic
157C2×C11—22no—
158C2×C11#154011yescharacteristic
159C2×C11#213911yescharacteristic
160C2×C11C2×#36211yescharacteristic
161C2×Q8—22no—
162C2×Q8—41no—
163C22×C4#432311yescharacteristic
164C22×C4#432411yescharacteristic
165C22×C4C22⋊Dic1111yescharacteristic
166Q16—42no—
167Q16—42no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—442no—
171C2×C8—882no—
172C2×C8C22⋊Dic1111yescharacteristic
173C2×C8C22⋊Dic1111yescharacteristic
174C2×C8C22×Dic1111yescharacteristic
175C2×C8C2×C22⋊D1111yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C22⋊C4—42no—
183C42—42no—
184C42#432311yescharacteristic
185C42#432411yescharacteristic
186C42C22⋊Dic1111yescharacteristic
187C42C2×C22⋊D1111yescharacteristic
188C16—442no—
189C11#1195411yescharacteristic, complemented, Sylow
190C23#6689611yescharacteristic
191Q8—42no—
192Q8—42no—
193Q8—81no—
194Q8—81no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4#6689611yescharacteristic
203C2×C4#6689611yescharacteristic
204C2×C4#6689611yescharacteristic
205C2×C4C2×#432311yescharacteristic
206C2×C4C2×#432411yescharacteristic
207C2×C4C2×C22⋊Dic1111yescharacteristic
208C8—21no—
209C8—21no—
210C8—21no—
211C8—882no—
212C8#6700312yes—
213C22—21no—
214C22—21no—
215C22#1062220312yes—
216C22C2×#6689611yescharacteristic
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—82no—
222C4—82no—
223C4#1062280611yescharacteristic
224C4#1062280811yescharacteristic
225C4#1062284611yescharacteristic
226C4#1062285011yescharacteristic
227C2—22no—
228C2#1306726511yescharacteristic
229C2#1307032811yescharacteristic
230C2C2×#1062220311yescharacteristic
subgroupG/H
centerC22C2×#66896
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#3170C2
socleC22×C11C2×#102
prime radicalC23×C11#102
cosocleC4×C8×C11C23
hypercenter#3170D11
hypocenterC11#11954
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13066671C2semidirect
4. #13066665C2semidirect
189. C11#11954semidirect

Maximal subgroups

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

subgroupindex
#130704192
C2×#106220962
#130666712
#130666652
C11×#31702
#1195411