Finite Group Databasebeta

← #14670614

Subgroups — #14670614

Order 2816.

460 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 103 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#13071706C211yesmaximal, characteristic
2#13069010C211yesmaximal, characteristic
3#13068833C212yesmaximal
4#13066742C212yesmaximal
5C2×C11×#356C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7#10623343C2211yescharacteristic
8C2×C11×#101C2212yes—
9#10622843—21no—
10#10622843C2212yes—
11C2×#66900C2211yescharacteristic
12#10622838—21no—
13#10622734—22no—
14#10622598—22no—
15C4⋊C4×Dic11—22no—
16C4×C4⋊Dic11—21no—
17C11×#356C414yescomplemented
18#10622193—22no—
19#10622161—21no—
20C22×Q8×C11D411yescharacteristic
21C22×Q8×C11C2311yescharacteristic
22C2×C11×M16—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8C2×C412yes—
25C11×C4⋊Q8Q812yes—
26C2×C11×C4⋊C4—22no—
27C2×C42×C11D411yescharacteristic
28Q8×Dic11—41no—
29Q8×Dic11—41no—
30#66979—22no—
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D412yes—
36C2×C4×Dic11—22no—
37C2×C4×Dic11—21no—
38C2×C4×Dic11D412yes—
39C2×#4318—21no—
40C11×#101—22no—
41C11×#101C2×C414yes—
42#66900—22no—
43#66899—41no—
44#66899—41no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48#66882—42no—
49#66881—42no—
50#12973—111nomaximal, Sylow
51C2×Q8×C11—21no—
52C2×Q8×C11—41no—
53C2×Q8×C11—41no—
54C2×Q8×C11—41no—
55C2×Q8×C11—41no—
56C2×Q8×C11C4⋊C412yes—
57C2×Q8×C11C22×C411yescharacteristic
58C2×Q8×C11C2×Q811yescharacteristic
59C2×Q8×C11#4112yes—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D412yes—
64C22×Dic11—22no—
65C22×Dic11—22no—
66C11×M16—24no—
67C11×M16—42no—
68C2×C8×C11—42no—
69C11×C4⋊C4—24no—
70C11×C4⋊C4—24no—
71C42×C11—21no—
72C42×C11C4⋊C412yes—
73C22⋊Dic11—41no—
74C4⋊Dic11—24no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11—42no—
80C4⋊Dic11—42no—
81C4⋊Dic11—81no—
82C4×Dic11—42no—
83C4×Dic11—44no—
84C4×Dic11—41no—
85C4×Dic11—42no—
86C4×Dic11—81no—
87#4318—41no—
88#4318—41no—
89C2×C11⋊C8—41no—
90#2369—111no—
91C2×#356D1111yescharacteristic
92#1886—111no—
93#1857—112no—
94#1394—112no—
95C23×C11#12011yescharacteristic
96Q8×C11—41no—
97Q8×C11—41no—
98Q8×C11—42no—
99Q8×C11—42no—
100Q8×C11—81no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11C2×C4⋊C411yescharacteristic
112C2×C4×C11C4×D412yes—
113C2×C4×C11C22⋊Q812yes—
114C2×C4×C11#12311yescharacteristic
115C2×Dic11—24no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—42no—
123C8×C11—44no—
124C11⋊C8—81no—
125C2×C4⋊Q8C2×D1111yescharacteristic
126#519—111no—
127#428—222no—
128#419—221no—
129C2×#101—111no—
130C2×#101C2×D1112yes—
131#391—112no—
132#391—221no—
133#389—222no—
134C4×C4⋊C4—222no—
135C4×C4⋊C4—221no—
136#356Dic1114yescomplemented
137#339—222no—
138#339—221no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11#38511yescharacteristic
142C22×C11B(4,𝔽2)11yescharacteristic
143C22×C11#45811yescharacteristic
144C4×C11—24no—
145C4×C11—21no—
146C4×C11—22no—
147C4×C11—22no—
148C4×C11—21no—
149C4×C11—42no—
150Dic11—44no—
151Dic11—81no—
152Dic11—82no—
153Dic11—81no—
154C22×Q8D4411yescharacteristic
155C22×Q8C22×D1111yescharacteristic
156C2×M16—22no—
157C2×M16—221no—
158C4⋊Q8—22no—
159C4⋊Q8Dic2212yes—
160C4⋊Q8C2×Dic1112yes—
161C4×Q8—441no—
162C4×Q8—441no—
163#117—221no—
164#117—222no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—112no—
167C2×C4⋊C4—221no—
168C2×C4⋊C4—221no—
169C2×C4⋊C4—221no—
170C2×C42—112no—
171C2×C42—222no—
172C2×C42—221no—
173C2×C42D4411yescharacteristic
174#107—442no—
175#106—442no—
176#103—441no—
177#103—441no—
178#101—22no—
179#101—222no—
180#101C2×Dic1114yes—
181#95—222no—
182#95—222no—
183#95—222no—
184C2×C11—21no—
185C2×C11—21no—
186C2×C11#186711yescharacteristic
187C2×C11#220411yescharacteristic
188C2×C11#220511yescharacteristic
189C2×Q8—21no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8C4⋊Dic1112yes—
195C2×Q8C2×Dic2211yescharacteristic
196C2×Q8#434112yes—
197C2×Q8C22×Dic1111yescharacteristic
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—222no—
201C22×C4—222no—
202C22×C4C2×D4411yescharacteristic
203C22×C4D4×D1112yes—
204M16—24no—
205M16—42no—
206M16—441no—
207M16—441no—
208C2×C8—42no—
209C2×C8—441no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—224no—
213C4⋊C4—221no—
214C4⋊C4—221no—
215C4⋊C4—222no—
216C4⋊C4—222no—
217C4⋊C4—442no—
218C4⋊C4—442no—
219C4⋊C4—881no—
220C22⋊C4—441no—
221C42—21no—
222C42—442no—
223C42—444no—
224C42—442no—
225C42—441no—
226C42—881no—
227C42C4⋊Dic1112yes—
228C11#1297311yescharacteristic, complemented, Sylow
229C23#6693511yescharacteristic
230Q8—41no—
231Q8—42no—
232Q8—41no—
233Q8—42no—
234Q8—81no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—224no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4—442no—
250C2×C4—441no—
251C2×C4—441no—
252C2×C4—442no—
253C2×C4#6693112yes—
254C2×C4#6693911yescharacteristic
255C2×C4C2×C4⋊Dic1111yescharacteristic
256C2×C4D4×Dic1112yes—
257C8—44no—
258C8—881no—
259C22—21no—
260C22—21no—
261C22#1062235411yescharacteristic
262C22#1062235511yescharacteristic
263C22#1062256311yescharacteristic
264C4—24no—
265C4—22no—
266C4—21no—
267C4—22no—
268C4—21no—
269C4—42no—
270C4—444no—
271C4—882no—
272C4—881no—
273C4—881no—
274C2—21no—
275C2—21no—
276C2#1306889911yescharacteristic
277C2#1307064411yescharacteristic
278C2#1307064711yescharacteristic
subgroupG/H
centerC22#10622354
commutatorC2×Q8×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC2×C11×#356C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
cosocleC22×Q8×C11C23
hypercenterC2×#356D11
hypocenterC11#12973
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
17. C11×#356C4semidirect
136. #356Dic11semidirect
228. C11#12973semidirect

Maximal subgroups

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

subgroupindex
#130717062
#130690102
#130688332
#130667422
C2×C11×#3562
#1297311