Finite Group Databasebeta

← #14656393

Subgroups — #14656393

Order 2816.

562 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#10622295C211yesmaximal, characteristic, complemented
2C2×#10622621C212yesmaximal
3C2×#10622119C212yesmaximal, complemented
4#13066451C211yesmaximal, characteristic, complemented
5C11×#1954C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66922C2212yes—
8C2×C11×C4⋊C8C2211yescharacteristic
9C2×C11×C22⋊C8—22no—
10C2×C4×C8×C11C2211yescharacteristic
11C2×#66896—22no—
12C2×#66882—22no—
13#10622621—24no—
14#10622621—24no—
15C2×#66872—22no—
16C2×C4⋊(C11⋊C8)C2212yes—
17#10622295—24no—
18#10622119—24no—
19C22×D4×C11D411yescharacteristic
20C23×C4×C11—21no—
21C22×Dic22—22no—
22C22×C8×C11—21no—
23C22×C8×C11D412yes—
24C4×D4×C11—22no—
25C4×D4×C11—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4—21no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—22no—
30C2×C4⋊Dic11—22no—
31C22×C11⋊C8—22no—
32#66922—22no—
33#66922—22no—
34#66922—22no—
35#66922D414yes—
36C11×C4⋊C8—22no—
37C11×C22⋊C8—44no—
38C4×C8×C11—22no—
39#66896—28no—
40#66882—28no—
41#66872—28no—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)D414yes—
44#10278—111nomaximal, Sylow
45C24×C11—21no—
46C2×D4×C11—22no—
47C2×D4×C11—21no—
48C2×D4×C11—22no—
49C2×D4×C11Q1612yes—
50C22×C4×C11—21no—
51C22×C4×C11—41no—
52C22×C4×C11—41no—
53C22×C4×C11—42no—
54C22×C4×C11—42no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C22×Dic11—42no—
59C2×Dic22—24no—
60C2×Dic22—42no—
61C2×Dic22—84no—
62C2×C8×C11—22no—
63C2×C8×C11—22no—
64C2×C8×C11—41no—
65C2×C8×C11—42no—
66C2×C8×C11SD1614yes—
67C11×C4⋊C4—22no—
68C11×C22⋊C4—42no—
69C42×C11C2×D412yes—
70C42×C11C2×D412yes—
71C4⋊Dic11—24no—
72C4⋊Dic11—24no—
73C4⋊Dic11—42no—
74C4⋊Dic11—42no—
75C2×C11⋊C8—24no—
76C2×C11⋊C8—42no—
77C2×C11⋊C8—42no—
78C2×#500—111no—
79C2×#476—112no—
80#1954D1111yescharacteristic
81C2×#333—112no—
82#1277—111no—
83C23×C11—22no—
84C23×C11—41no—
85C23×C11—42no—
86C23×C11—41no—
87C23×C11—42no—
88C23×C11#12111yescharacteristic
89D4×C11—24no—
90D4×C11—42no—
91C2×C4×C11—22no—
92C2×C4×C11—41no—
93C2×C4×C11—42no—
94C2×C4×C11—82no—
95C2×C4×C11—81no—
96C2×C4×C11—81no—
97C2×C4×C11#12012yes—
98C2×C4×C11#12011yescharacteristic
99C2×C4×C11#12112yes—
100C2×C4×C11#12711yescharacteristic
101C2×C4×C11C2×SD1612yes—
102C2×C4×C11C2×Q1611yescharacteristic
103C2×C4×C11#13511yescharacteristic
104C2×C4×C11#13712yes—
105C2×C4×C11#13712yes—
106C2×Dic11—44no—
107C2×Dic11—84no—
108Dic22—84no—
109Dic22—84no—
110C8×C11—24no—
111C8×C11—81no—
112C11⋊C8—44no—
113C2×C4⋊Q8—112no—
114C2×C4×D4C2×D1111yescharacteristic
115#500—224no—
116#476—224no—
117#476—224no—
118C2×#107—222no—
119C2×#106—222no—
120C2×C4⋊C8—112no—
121C2×C4⋊C8C2×D1111yescharacteristic
122C2×#102—222no—
123C2×C22⋊C8—22no—
124C2×C4×C8C2×D1111yescharacteristic
125#333—224no—
126C22×C11—44no—
127C22×C11—42no—
128C22×C11—82no—
129C22×C11—81no—
130C22×C11—81no—
131C22×C11#39211yescharacteristic
132C22×C11#46112yes—
133C22×C11#46711yescharacteristic
134C22×C11#47011yescharacteristic
135C22×C11#47212yes—
136C4×C11—22no—
137C4×C11—81no—
138C4×C11#44812yes—
139C4×C11#45112yes—
140C4×C11#45212yes—
141C4×C11#49211yescharacteristic
142C4×C11#49711yescharacteristic
143Dic11—84no—
144C22×Q8—222no—
145C22×D4D4411yescharacteristic
146C23×C4—21no—
147C22×C8—21no—
148C22×C8—222no—
149C22×C8C22⋊D1112yes—
150C4⋊Q8—114no—
151C4⋊Q8—222no—
152C4⋊Q8—222no—
153C4⋊Q8—222no—
154C4×D4—22no—
155C4×D4—22no—
156C2×C4⋊C4—222no—
157C2×C4⋊C4—222no—
158C2×C4⋊C4D4411yescharacteristic
159C2×C22⋊C4—21no—
160C2×C42C22×D1111yescharacteristic
161#107—228no—
162#106—228no—
163C4⋊C8—22no—
164C4⋊C8—114no—
165C4⋊C8—222no—
166#102—228no—
167C22⋊C8—44no—
168C4×C8—22no—
169C2×C11—82no—
170C2×C11#167512yes—
171C2×C11#169512yes—
172C2×C11#200111yescharacteristic
173C2×C11#201311yescharacteristic
174C2×C11#201811yescharacteristic
175C24—21no—
176C2×Q8—224no—
177C2×Q8—442no—
178C2×Q8—884no—
179C2×D4—22no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4Dic4412yes—
183C22×C4—21no—
184C22×C4—42no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—42no—
188C22×C4—442no—
189C22×C4C2×D4411yescharacteristic
190C22×C4#433911yescharacteristic
191C22×C4C2×C22⋊D1111yescharacteristic
192C2×C8—22no—
193C2×C8—22no—
194C2×C8—42no—
195C2×C8—41no—
196C2×C8—224no—
197C2×C8—442no—
198C2×C8—442no—
199C2×C8#432414yes—
200C4⋊C4—22no—
201C4⋊C4—224no—
202C4⋊C4—224no—
203C4⋊C4—442no—
204C4⋊C4—442no—
205C22⋊C4—42no—
206C42D4×D1112yes—
207C42D4×D1112yes—
208C11#1027811yescharacteristic, complemented, Sylow
209C23—22no—
210C23—41no—
211C23—42no—
212C23—41no—
213C23—42no—
214C23#6698311yescharacteristic
215Q8—884no—
216Q8—884no—
217D4—24no—
218D4—42no—
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—82no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—444no—
226C2×C4—884no—
227C2×C4#6693512yes—
228C2×C4#6693712yes—
229C2×C4#6695711yescharacteristic
230C2×C4C2×Dic4411yescharacteristic
231C2×C4#6696212yes—
232C2×C4C2×#432412yes—
233C2×C4#6699011yescharacteristic
234C2×C4#6699311yescharacteristic
235C2×C4#6700412yes—
236C8—24no—
237C8—81no—
238C8—444no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1062257311yescharacteristic
245C22#1062263212yes—
246C22#1062272911yescharacteristic
247C22#1062275011yescharacteristic
248C22#1062275512yes—
249C4—22no—
250C4—81no—
251C4—884no—
252C4#1062234612yes—
253C4#1062235212yes—
254C4#1062265312yes—
255C4#1062267311yescharacteristic
256C4#1062268911yescharacteristic
257C2—82no—
258C2#1306801512yes—
259C2#1306813912yes—
260C2#1306962611yescharacteristic
261C2#1306969811yescharacteristic
262C2#1306972511yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1954C2
socleC23×C11#121
prime radicalC22×D4×C11D4
hypercenter#1954D11
hypocenterC11#10278
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10622295C2semidirect
3. C2×#10622119C2semidirect
4. #13066451C2semidirect
208. C11#10278semidirect

Maximal subgroups

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

subgroupindex
C2×#106222952
C2×#106226212
C2×#106221192
#130664512
C11×#19542
#1027811