Finite Group Databasebeta

← #14670609

Subgroups — #14670609

Order 2816.

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

normal subgroups only

This group has 492 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#13071728C211yesmaximal, characteristic
2#13069020C211yesmaximal, characteristic
3#13068833C212yesmaximal, complemented
4#13066742C212yesmaximal, complemented
5C2×C11×#355C211yesmaximal, characteristic
6C2×C11×#124C2211yescharacteristic
7#10623343C2211yescharacteristic
8C2×C11×#101C2212yes—
9#10622843C2212yes—
10C2×#66900C2211yescharacteristic
11#10622833—21no—
12#10622828—21no—
13#10622734—22no—
14#10622564—22no—
15C22⋊C4×Dic11—22no—
16#10622545—21no—
17C11×#355C414yescomplemented
18#10622193—22no—
19#10622161—21no—
20C22×Q8×C11C2311yescharacteristic
21C22×D4×C11D411yescharacteristic
22C23×Dic11—21no—
23C2×C11×M16—22no—
24C11×#124—22no—
25C11×#124C2×C412yes—
26C11×#124Q812yes—
27C2×C11×C22⋊C4—22no—
28C2×C42×C11D411yescharacteristic
29C2×C22⋊Dic11—22no—
30C2×C22⋊Dic11—21no—
31Q8×Dic11—42no—
32#66979—22no—
33#66979—21no—
34C2×C4⋊Dic11D412yes—
35C2×C4×Dic11—22no—
36C2×C4×Dic11D412yes—
37C2×#4318—21no—
38C11×#101—22no—
39C11×#101C2×C414yescomplemented
40#66900—22no—
41#66896—42no—
42C11⋊#95—21no—
43C11⋊#95—21no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46#66882—42no—
47#66881—42no—
48#12972—111nomaximal, Sylow
49C24×C11—21no—
50C2×Q8×C11—41no—
51C2×Q8×C11—41no—
52C2×Q8×C11C22×C411yescharacteristic
53C2×Q8×C11C2×Q811yescharacteristic
54C2×Q8×C11#4112yes—
55C2×D4×C11—21no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11C4⋊C412yes—
59C22×C4×C11—21no—
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D412yes—
62C22×Dic11—22no—
63C22×Dic11—22no—
64C22×Dic11—44no—
65C22×Dic11—81no—
66C11×M16—24no—
67C11×M16—42no—
68C2×C8×C11—42no—
69C11×C22⋊C4—24no—
70C11×C22⋊C4—24no—
71C42×C11—21no—
72C42×C11C4⋊C412yes—
73C22⋊Dic11—44no—
74C22⋊Dic11—41no—
75C22⋊Dic11—81no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79C4⋊Dic11—42no—
80C4×Dic11—42no—
81C4×Dic11—41no—
82C4×Dic11—42no—
83C4×Dic11—44no—
84#4318—41no—
85#4318—41no—
86C2×C11⋊C8—41no—
87#2372—111no—
88C2×#355D1111yescharacteristic
89#1888—111no—
90#1857—112no—
91#1394—112no—
92C23×C11—22no—
93C23×C11—42no—
94C23×C11—42no—
95C23×C11—41no—
96C23×C11—41no—
97C23×C11#12011yescharacteristic
98Q8×C11—41no—
99Q8×C11—41no—
100Q8×C11—42no—
101D4×C11—42no—
102D4×C11—81no—
103C2×C4×C11—21no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—42no—
109C2×C4×C11C2×C4⋊C411yescharacteristic
110C2×C4×C11C4×D412yes—
111C2×C4×C11C22⋊Q812yes—
112C2×C4×C11#12311yescharacteristic
113C2×Dic11—24no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—84no—
121C8×C11—44no—
122C11⋊C8—81no—
123C2×#124C2×D1111yescharacteristic
124#519—111no—
125#428—222no—
126#418—221no—
127C2×#101—111no—
128C2×#101C2×D1112yes—
129#391—112no—
130#388—222no—
131#386—221no—
132C4×C22⋊C4—222no—
133#376—221no—
134#355Dic1114yescomplemented
135#339—222no—
136#339—221no—
137C22×C11—22no—
138C22×C11—44no—
139C22×C11—42no—
140C22×C11—81no—
141C22×C11—81no—
142C22×C11—82no—
143C22×C11#38511yescharacteristic
144C22×C11B(4,𝔽2)11yescharacteristic
145C22×C11#45811yescharacteristic
146C4×C11—21no—
147C4×C11—22no—
148C4×C11—22no—
149C4×C11—21no—
150C4×C11—42no—
151Dic11—44no—
152Dic11—82no—
153Dic11—82no—
154C22×Q8C22×D1111yescharacteristic
155C22×D4D4411yescharacteristic
156C23×C4—221no—
157C2×M16—22no—
158C2×M16—221no—
159#124—22no—
160#124Dic2212yes—
161#124C2×Dic1112yes—
162C4×Q8—442no—
163#117—221no—
164#117—222no—
165C2×C4⋊C4—112no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—222no—
168C2×C22⋊C4—221no—
169C2×C42—112no—
170C2×C42—222no—
171C2×C42D4411yescharacteristic
172#107—442no—
173#106—442no—
174#102—442no—
175#101—22no—
176#101—222no—
177#101C2×Dic1114yescomplemented
178#95—221no—
179#95—221no—
180#95—222no—
181#95—222no—
182C2×C11—21no—
183C2×C11—21no—
184C2×C11—82no—
185C2×C11#186711yescharacteristic
186C2×C11#220412yes—
187C24—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8C2×Dic2211yescharacteristic
191C2×Q8#434112yes—
192C2×Q8C22×Dic1111yescharacteristic
193C2×D4—21no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4C4⋊Dic1112yes—
197C22×C4—21no—
198C22×C4—222no—
199C22×C4—222no—
200C22×C4—444no—
201C22×C4—881no—
202C22×C4C2×D4411yescharacteristic
203C22×C4D4×D1112yes—
204M16—24no—
205M16—42no—
206M16—441no—
207M16—441no—
208C2×C8—42no—
209C2×C8—441no—
210C4⋊C4—222no—
211C4⋊C4—222no—
212C4⋊C4—222no—
213C4⋊C4—442no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—444no—
217C22⋊C4—441no—
218C22⋊C4—881no—
219C42—21no—
220C42—442no—
221C42—442no—
222C42—441no—
223C42—444no—
224C42C4⋊Dic1112yes—
225C11#1297211yescharacteristic, complemented, Sylow
226C23—22no—
227C23—42no—
228C23—42no—
229C23—41no—
230C23—41no—
231C23#6693511yescharacteristic
232Q8—41no—
233Q8—42no—
234Q8—41no—
235D4—42no—
236D4—81no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—224no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4—442no—
250C2×C4—884no—
251C2×C4#6693112yes—
252C2×C4#6693911yescharacteristic
253C2×C4C2×C4⋊Dic1111yescharacteristic
254C2×C4D4×Dic1112yes—
255C8—44no—
256C8—881no—
257C22—22no—
258C22—44no—
259C22—42no—
260C22—81no—
261C22—81no—
262C22—82no—
263C22#1062235411yescharacteristic
264C22#1062235511yescharacteristic
265C22#1062256311yescharacteristic
266C4—22no—
267C4—21no—
268C4—22no—
269C4—21no—
270C4—42no—
271C4—444no—
272C4—882no—
273C4—882no—
274C2—21no—
275C2—21no—
276C2—82no—
277C2#1306889911yescharacteristic
278C2#1307064312yes—
subgroupG/H
centerC22#10622354
commutatorC2×Q8×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC2×C11×#355C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D4×C11D4
cosocleC22×Q8×C11C23
hypercenterC2×#355D11
hypocenterC11#12972
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
3. #13068833C2semidirect
4. #13066742C2semidirect
17. C11×#355C4semidirect
39. C11×#101C2×C4semidirect
134. #355Dic11semidirect
177. #101C2×Dic11semidirect
225. C11#12972semidirect

Maximal subgroups

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

subgroupindex
#130717282
#130690202
#130688332
#130667422
C2×C11×#3552
#1297211