Finite Group Databasebeta

← #14664888

Subgroups — #14664888

Order 2816.

390 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 107 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#13070227C211yesmaximal, characteristic
2#13068654C211yesmaximal, characteristic
3#13066634C214yesmaximal, complemented
4C2×C11×#467C211yesmaximal, characteristic
5C22×C11×Q16C411yescharacteristic
6C23×C8×C11C2211yescharacteristic
7C2×C11×C22⋊Q8—21no—
8C11×#467—21no—
9C11×#467—21no—
10C11×#467C412yes—
11C11×#467C2212yes—
12C2×C11×#107C411yescharacteristic
13C2×C11×#103—21no—
14#10622820—21no—
15C2×#66883—21no—
16C2×#66876—21no—
17#10622190C2212yes—
18C22⋊(C11⋊C16)—21no—
19C22⋊(C11⋊C16)C2212yes—
20C22×Q8×C11—21no—
21C23×C4×C11D411yescharacteristic
22C2×C11×Q16—21no—
23C2×C11×Q16—42no—
24C2×C11×Q16C2×C412yes—
25C22×C8×C11—42no—
26C22×C8×C11C2×C411yescharacteristic
27C22×C8×C11C2×C411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C22×C8×C11D411yescharacteristic
31C22×C8×C11C2311yescharacteristic
32C11×C22⋊Q8—22no—
33C11×C22⋊Q8—22no—
34C11×C22⋊Q8—41no—
35C11×C22⋊Q8—41no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—41no—
38C2×C11×C22⋊C4—41no—
39C2×#4318—22no—
40C11×#107—21no—
41C11×#107C2×C412yes—
42C11×#103—22no—
43C11×#103—22no—
44C22⋊(C11⋊C8)—41no—
45C22⋊(C11⋊C8)—41no—
46#66883—42no—
47#66876—42no—
48C2×C11⋊C16—22no—
49#11896—111nomaximal, Sylow
50C24×C11SD1611yescharacteristic
51C2×Q8×C11—22no—
52C2×Q8×C11—42no—
53C2×Q8×C11—42no—
54C2×Q8×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11D811yescharacteristic
62C22×C4×C11D811yescharacteristic
63C22×C4×C11SD1611yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C11×Q16—42no—
66C11×Q16—42no—
67C2×C8×C11—22no—
68C2×C8×C11—22no—
69C2×C8×C11—22no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11C22⋊C411yescharacteristic
74C2×C8×C11C22⋊C411yescharacteristic
75C2×C8×C11C22×C411yescharacteristic
76C2×C8×C11C2×D411yescharacteristic
77C11×C4⋊C4—22no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—42no—
80C11×C4⋊C4—42no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—42no—
83#4318—42no—
84#4318—42no—
85C2×C11⋊C8—42no—
86C11⋊C16—42no—
87C2×#467D1111yescharacteristic
88#2112—111no—
89#1810—111no—
90#1350—114no—
91C23×C11—22no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11#10211yescharacteristic
95C23×C11#10211yescharacteristic
96C23×C11C2×SD1611yescharacteristic
97Q8×C11—42no—
98Q8×C11—42no—
99Q8×C11—82no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—82no—
112C2×C4×C11—82no—
113C2×C4×C11#10211yescharacteristic
114C2×C4×C11#10211yescharacteristic
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11C2×D811yescharacteristic
117C8×C11—21no—
118C8×C11—21no—
119C8×C11—21no—
120C8×C11#9912yes—
121C11⋊C8—82no—
122C22×Q16Dic1111yescharacteristic
123C23×C8C2×D1111yescharacteristic
124C2×C22⋊Q8—21no—
125C2×M32—221no—
126#467—21no—
127#467—21no—
128#467Dic1112yes—
129#467C2×D1112yes—
130C2×#108—221no—
131C2×#107Dic1111yescharacteristic
132C2×#103—21no—
133#407—221no—
134C22⋊C16—112no—
135C22⋊C16—221no—
136#341—112no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—44no—
146C22×C11#36212yes—
147C22×C11C2×#10211yescharacteristic
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—82no—
152C4×C11—82no—
153C4×C11C2×#9911yescharacteristic
154C4×C11#42111yescharacteristic
155C22×Q8—21no—
156C23×C4C22⋊D1111yescharacteristic
157C2×Q16—21no—
158C2×Q16—42no—
159C2×Q16C2×Dic1112yes—
160C2×M16—222no—
161C22×C8—42no—
162C22×C8C2×Dic1111yescharacteristic
163C22×C8C2×Dic1111yescharacteristic
164C22×C8C22⋊D1111yescharacteristic
165C22×C8C22⋊D1111yescharacteristic
166C22×C8C22⋊D1111yescharacteristic
167C22×C8C22×D1111yescharacteristic
168C22⋊Q8—22no—
169C22⋊Q8—22no—
170C22⋊Q8—41no—
171C22⋊Q8—41no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—41no—
174C2×C22⋊C4—41no—
175M32—442no—
176C2×C16—222no—
177#108—442no—
178#107—21no—
179#107C2×Dic1112yes—
180#103—22no—
181#103—22no—
182C22⋊C8—441no—
183C22⋊C8—441no—
184C2×C11—22no—
185C2×C11—41no—
186C2×C11—41no—
187C2×C11#151911yescharacteristic
188C2×C11#214311yescharacteristic
189C2×C11C2×#36211yescharacteristic
190C24#432411yescharacteristic
191C2×Q8—22no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4#432311yescharacteristic
200C22×C4#432311yescharacteristic
201C22×C4#432411yescharacteristic
202C22×C4C22⋊Dic1111yescharacteristic
203C22×C4C22⋊Dic1111yescharacteristic
204C22×C4C2×C22⋊D1111yescharacteristic
205Q16—42no—
206Q16—42no—
207M16—442no—
208M16—442no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—442no—
216C2×C8C22⋊Dic1111yescharacteristic
217C2×C8C22⋊Dic1111yescharacteristic
218C2×C8C22×Dic1111yescharacteristic
219C2×C8C2×C22⋊D1111yescharacteristic
220C4⋊C4—22no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C22⋊C4—42no—
225C22⋊C4—42no—
226C16—442no—
227C11#1189611yescharacteristic, complemented, Sylow
228C23—22no—
229C23—41no—
230C23—41no—
231C23#6689611yescharacteristic
232C23#6689611yescharacteristic
233C23C2×#432411yescharacteristic
234Q8—42no—
235Q8—42no—
236Q8—82no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4#6689611yescharacteristic
251C2×C4#6689611yescharacteristic
252C2×C4C2×#432311yescharacteristic
253C2×C4C2×C22⋊Dic1111yescharacteristic
254C8—21no—
255C8—21no—
256C8—21no—
257C8—882no—
258C8#6689812yes—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—44no—
268C22#1062220312yes—
269C22C2×#6689611yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—82no—
274C4—82no—
275C4C2×#6689811yescharacteristic
276C4#1062284911yescharacteristic
277C2—22no—
278C2—41no—
279C2—41no—
280C2#1306718411yescharacteristic
281C2#1307034411yescharacteristic
282C2C2×#1062220311yescharacteristic
subgroupG/H
centerC22C2×#66896
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#467C2
socleC22×C11C2×#102
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenterC2×#467D11
hypocenterC11#11896
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #13066634C2semidirect
227. C11#11896semidirect

Maximal subgroups

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

subgroupindex
#130702272
#130686542
#130666342
C2×C11×#4672
#1189611