Finite Group Databasebeta

← #14664152

Subgroups — #14664152

Order 2816.

402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#66900C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic
3#13066646C212yesmaximal
4#13066622C212yesmaximal
5C11×#2399C211yesmaximal, characteristic
6C2×C4×Q8×C11C411yescharacteristic
7C2×C4×Q8×C11C2211yescharacteristic
8C11×#398—21no—
9C11×#398C411yescharacteristic
10C11×#398C2211yescharacteristic
11C11×#395—21no—
12C11×#395C411yescharacteristic
13C11×#395C2211yescharacteristic
14C4×C11×C4⋊C4—21no—
15C4×C11×C4⋊C4—21no—
16C11×#376C411yescharacteristic
17C2×#66900—21no—
18#10622538—21no—
19C4×#4318—21no—
20#10622168C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11C2×C411yescharacteristic
24C22×Q8×C11D411yescharacteristic
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C4×Q8×C11—41no—
28C4×Q8×C11—41no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4C2311yescharacteristic
38C2×C42×C11—21no—
39C2×C42×C11—21no—
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×#4318—22no—
44C11×#95—21no—
45C11×#95—21no—
46C11×#95—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95C2×C411yescharacteristic
50C11×#95C2×C411yescharacteristic
51#66900—24no—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—41no—
54#66867—41no—
55C4×C11⋊C8—41no—
56C4×C11⋊C8—41no—
57#11736—111nomaximal, Sylow
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—41no—
61C2×Q8×C11—42no—
62C2×Q8×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—42no—
78C11×C4⋊C4—42no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—42no—
83C42×C11—24no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—41no—
91C42×C11—41no—
92#4318—24no—
93#4318—42no—
94C2×C11⋊C8—42no—
95C2×C11⋊C8—42no—
96#2399D1111yescharacteristic
97C4×#101—111no—
98#1461—111no—
99#1354—112no—
100#1346—112no—
101C23×C11C2×C22⋊C411yescharacteristic
102Q8×C11—44no—
103Q8×C11—42no—
104Q8×C11—42no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11#9911yescharacteristic
133C2×C4×C11#10412yes—
134C2×C4×C11#13512yes—
135C11⋊C8—44no—
136C11⋊C8—82no—
137C2×C4×Q8Dic1111yescharacteristic
138C2×C4×Q8C2×D1111yescharacteristic
139#431—221no—
140C2×#101—221no—
141C4×M16—221no—
142#398—21no—
143#398Dic1111yescharacteristic
144#398C2×D1111yescharacteristic
145#395—21no—
146#395Dic1111yescharacteristic
147#395C2×D1111yescharacteristic
148C4×C4⋊C4—21no—
149C4×C4⋊C4—21no—
150#376Dic1111yescharacteristic
151#343—112no—
152#324—112no—
153#324—221no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11C2×#9911yescharacteristic
157C22×C11#41611yescharacteristic
158C22×C11C2×#10411yescharacteristic
159C4×C11—21no—
160C4×C11—22no—
161C4×C11—22no—
162C4×C11—42no—
163C4×C11—42no—
164C4×C11—41no—
165C4×C11—42no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—81no—
170C4×C11#35612yes—
171C22×Q8C2×Dic1111yescharacteristic
172C22×Q8C22⋊D1111yescharacteristic
173C2×M16—222no—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×Q8—41no—
177C4×Q8—41no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×Dic1111yescharacteristic
184C2×C4⋊C4C2×Dic1111yescharacteristic
185C2×C4⋊C4C22⋊D1111yescharacteristic
186C2×C4⋊C4C22×D1111yescharacteristic
187C2×C42—21no—
188C2×C42—21no—
189C2×C42C2×Dic1111yescharacteristic
190C2×C42C22⋊D1111yescharacteristic
191C2×C42C22⋊D1111yescharacteristic
192C4⋊C8—441no—
193#101—224no—
194C22⋊C8—222no—
195#97—441no—
196C4×C8—441no—
197C4×C8—441no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95C2×Dic1111yescharacteristic
204#95C2×Dic1111yescharacteristic
205C2×C11—21no—
206C2×C11—21no—
207C2×C11#150111yescharacteristic
208C2×C11#212011yescharacteristic
209C2×C11C2×#35611yescharacteristic
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8—41no—
213C2×Q8—42no—
214C2×Q8—41no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4C22⋊Dic1111yescharacteristic
220C22×C4C22⋊Dic1111yescharacteristic
221C22×C4C22⋊Dic1111yescharacteristic
222C22×C4C22⋊Dic1111yescharacteristic
223C22×C4C22×Dic1111yescharacteristic
224C22×C4C2×C22⋊D1111yescharacteristic
225C22×C4C2×C22⋊D1111yescharacteristic
226M16—224no—
227M16—442no—
228C2×C8—442no—
229C2×C8—442no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C42—24no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—41no—
247C42—41no—
248C11#1173611yescharacteristic, complemented, Sylow
249C23C2×C22⋊Dic1111yescharacteristic
250Q8—44no—
251Q8—42no—
252Q8—42no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4#6689811yescharacteristic
280C2×C4#6689811yescharacteristic
281C2×C4#6690112yes—
282C2×C4#6700312yes—
283C8—444no—
284C8—882no—
285C22—21no—
286C22—21no—
287C22C2×#6689811yescharacteristic
288C22#1062284611yescharacteristic
289C22C2×#6690111yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—42no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—42no—
298C4—41no—
299C4—41no—
300C4—81no—
301C4#1062218612yes—
302C2—21no—
303C2—21no—
304C2#1306710711yescharacteristic
305C2#1307025711yescharacteristic
306C2C2×#1062218611yescharacteristic
subgroupG/H
centerC2×C4#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2399C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#2399D11
hypocenterC11#11736
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2399

Complements

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

NH ≅ G/Ntype
248. C11#11736semidirect

Maximal subgroups

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

subgroupindex
C4×#669002
#130669402
#130666462
#130666222
C11×#23992
#1173611