Finite Group Databasebeta

← #14648238

Subgroups — #14648238

Order 2816.

476 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 155 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#13069419C211yesmaximal, characteristic
2#13069379C212yesmaximal
3C2×#10622184C211yesmaximal, characteristic
4#13066457C212yesmaximal
5C11×#2369C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2211yescharacteristic
7C11×#391—22no—
8C11×#389—22no—
9C4×C11×C4⋊C4—22no—
10C4×C11×C4⋊C4C2212yes—
11C2×#66899—22no—
12C2×#66872—22no—
13#10622548C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×C4×C11⋊C8C2211yescharacteristic
16#10622184C414yescomplemented
17#10622167—22no—
18C22×Q8×C11D412yes—
19C11×C4⋊Q8—22no—
20C11×C4⋊Q8C2×C412yes—
21C11×C4⋊Q8Q812yes—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4D412yes—
25C2×C11×C4⋊C4D412yes—
26C2×C42×C11—22no—
27C2×C42×C11—22no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—22no—
30C2×C4⋊Dic11—21no—
31C22×C11⋊C8—21no—
32C22×C11⋊C8—22no—
33C11×#95—24no—
34C11×#95—22no—
35#66899—44no—
36#66872—44no—
37C4⋊(C11⋊C8)—22no—
38C4⋊(C11⋊C8)C2×C414yes—
39C4×C11⋊C8—22no—
40#8928—111nomaximal, Sylow
41C2×Q8×C11—22no—
42C2×Q8×C11—42no—
43C2×Q8×C11—42no—
44C2×Q8×C11C4⋊C414yes—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11—22no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—41no—
51C11×C4⋊C4—24no—
52C11×C4⋊C4—24no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—82no—
57C11×C4⋊C4SD1614yes—
58C42×C11—42no—
59C42×C11—42no—
60C42×C11—82no—
61C42×C11C22×C411yescharacteristic
62C42×C11C2×Q811yescharacteristic
63C42×C11#4112yes—
64C4⋊Dic11—42no—
65C4⋊Dic11—42no—
66C4⋊Dic11—42no—
67C2×C11⋊C8—22no—
68C2×C11⋊C8—24no—
69C2×C11⋊C8—41no—
70C2×C11⋊C8—41no—
71C2×C11⋊C8—42no—
72C2×C11⋊C8—42no—
73#2369D1111yescharacteristic
74#1956—111no—
75#1948—112no—
76C2×#333—111no—
77#1279—112no—
78C23×C11#12011yescharacteristic
79Q8×C11—44no—
80Q8×C11—82no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—24no—
84C2×C4×C11—24no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11C2×C4⋊C411yescharacteristic
93C2×C4×C11C4×D412yes—
94C2×C4×C11C22⋊Q812yes—
95C2×C4×C11#12311yescharacteristic
96C2×C4×C11C2×SD1612yes—
97C2×C4×C11#13512yes—
98C2×C4×C11#13712yes—
99C2×C4×C11#13712yes—
100C2×Dic11—82no—
101C2×Dic11—81no—
102C11⋊C8—42no—
103C11⋊C8—44no—
104C2×C4⋊Q8C2×D1111yescharacteristic
105C2×#106—222no—
106C2×C4⋊C8—112no—
107C2×#103—222no—
108C2×C4×C8—111no—
109#391—22no—
110#389—22no—
111#384—111no—
112C4×C4⋊C4—22no—
113C4×C4⋊C4C2×D1112yes—
114#340—222no—
115#333—114no—
116C22×C11#38511yescharacteristic
117C22×C11#44812yes—
118C22×C11#45212yes—
119C22×C11#45311yescharacteristic
120C22×C11#45511yescharacteristic
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—44no—
124C4×C11—44no—
125C4×C11—82no—
126C4×C11C4×SD1612yes—
127C4×C11#44112yes—
128C4×C11#47512yes—
129C4×C11#47912yes—
130Dic11—161no—
131C22×Q8C22⋊D1112yes—
132C22×C8—222no—
133C22×C8—221no—
134C4⋊Q8—22no—
135C4⋊Q8Dic2212yes—
136C4⋊Q8C4×D1112yes—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—222no—
140C2×C4⋊C4—221no—
141C2×C4⋊C4C22⋊D1112yes—
142C2×C4⋊C4C22⋊D1112yes—
143C2×C42—22no—
144C2×C42—22no—
145C2×C42C22×D1111yescharacteristic
146#106—444no—
147C4⋊C8—114no—
148C4⋊C8—222no—
149#103—444no—
150C4×C8—222no—
151#95—24no—
152#95—22no—
153C2×C11#162311yescharacteristic
154C2×C11#163411yescharacteristic
155C2×C11#164312yes—
156C2×C11#185611yescharacteristic
157C2×C11#186512yes—
158C2×Q8—22no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8Dic11⋊C414yes—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—441no—
166C22×C4C2×C22⋊D1111yescharacteristic
167C22×C4C2×C22⋊D1112yes—
168C2×C8—222no—
169C2×C8—224no—
170C2×C8—441no—
171C2×C8—441no—
172C2×C8—442no—
173C2×C8—442no—
174C4⋊C4—24no—
175C4⋊C4—24no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—82no—
180C4⋊C4—442no—
181C4⋊C4—442no—
182C4⋊C4—442no—
183C4⋊C4#432514yes—
184C42—42no—
185C42—42no—
186C42—82no—
187C42C2×Dic2211yescharacteristic
188C42C2×C4×D1111yescharacteristic
189C42#433912yes—
190C11#892811yescharacteristic, complemented, Sylow
191C23#6700611yescharacteristic
192Q8—44no—
193Q8—82no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—882no—
206C2×C4—881no—
207C2×C4C2×Dic11⋊C411yescharacteristic
208C2×C4#6697712yes—
209C2×C4C4×C22⋊D1112yes—
210C2×C4#6698211yescharacteristic
211C2×C4C2×#432512yes—
212C2×C4#6699512yes—
213C2×C4#6700312yes—
214C2×C4#6700412yes—
215C8—442no—
216C8—444no—
217C22#1062282311yescharacteristic
218C22#1062284012yes—
219C22#1062285212yes—
220C22#1062285411yescharacteristic
221C22#1062285511yescharacteristic
222C4—21no—
223C4—21no—
224C4—44no—
225C4—44no—
226C4—82no—
227C4—1761no—
228C4#1062263312yes—
229C4#1062263512yes—
230C4C4×#432512yes—
231C4#1062264312yes—
232C2#1306769411yescharacteristic
233C2#1306776111yescharacteristic
234C2#1306782312yes—
235C2#1306882611yescharacteristic
236C2#1306888412yes—
subgroupG/H
centerC23#67006
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2369C2
socle, prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#2369D11
hypocenterC11#8928
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2369

Complements

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

NH ≅ G/Ntype
16. #10622184C4semidirect
190. C11#8928semidirect

Maximal subgroups

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

subgroupindex
#130694192
#130693792
C2×#106221842
#130664572
C11×#23692
#892811