Finite Group Databasebeta

← #13069714

Subgroups — #13069714

Order 1408.

370 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C22×C11×Q16C211yesmaximal, characteristic
2C2×#66997C211yesmaximal, characteristic
3C22×#4326C211yesmaximal, characteristic
4#10622843C211yesmaximal, characteristic
5C2×#66899C211yesmaximal, characteristic
6C2×#66880C211yesmaximal, characteristic
7#10622188C211yesmaximal, characteristic
8C22×Q8×C11C2211yescharacteristic
9C22×Q8×C11C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C2×C11×Q16—22no—
12C2×C11×Q16—22no—
13C2×C11×Q16—22no—
14C22×C8×C11C2211yescharacteristic
15#66997—22no—
16#66997—22no—
17C2×#4326—22no—
18C2×#4326—22no—
19C2×#4326—22no—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4—22no—
22C2×C4×Dic11C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66899—22no—
25C11⋊#95—22no—
26#66880—22no—
27C2×Q8×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11—21no—
30C2×Q8×C11—21no—
31C2×Q8×C11—21no—
32C2×Q8×C11—21no—
33C2×Q8×C11—21no—
34C2×Q8×C11—21no—
35C2×Q8×C11—21no—
36C2×Q8×C11—21no—
37C2×Q8×C11D412yes—
38C2×Q8×C11D412yes—
39C22×C4×C11—21no—
40C22×C4×C11—21no—
41C22×C4×C11C2311yescharacteristic
42C22×Dic11—21no—
43C22×Dic11—21no—
44C22×Dic11D412yes—
45C2×Dic22—21no—
46C2×Dic22—21no—
47C2×Dic22—21no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22D412yes—
51C11×Q16—28no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11D412yes—
55#4326—28no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58Dic11⋊C4—28no—
59C4×Dic11—21no—
60C4×Dic11—21no—
61C2×C11⋊C8—21no—
62C2×C11⋊C8—21no—
63C2×C11⋊C8D412yes—
64#2016—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66Q8×C11—22no—
67Q8×C11—22no—
68Q8×C11—22no—
69Q8×C11—22no—
70Q8×C11—41no—
71Q8×C11—41no—
72Q8×C11—41no—
73Q8×C11—41no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—41no—
77C2×C4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11#4111yescharacteristic
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—41no—
90C2×Dic11—41no—
91C2×Dic11—41no—
92C2×Dic11—42no—
93C2×Dic11Q1614yescomplemented
94Dic22—22no—
95Dic22—22no—
96Dic22—41no—
97Dic22—41no—
98C8×C11—22no—
99C11⋊C8—22no—
100C22×Q16—111no—
101C22×Q16D1111yescharacteristic
102C2×C4⋊Q8—111no—
103C2×#103—111no—
104C2×#103—111no—
105#391—111no—
106#336—111no—
107C22×C11#12011yescharacteristic
108C22×C11#12111yescharacteristic
109C22×C11#12711yescharacteristic
110C22×C11C2×Q1612yes—
111C22×C11#13712yes—
112C4×C11—42no—
113C4×C11—42no—
114C4×C11#12011yescharacteristic
115C4×C11#12011yescharacteristic
116C4×C11#12111yescharacteristic
117C4×C11#12111yescharacteristic
118Dic11—24no—
119Dic11—42no—
120Dic11—81no—
121C22×Q8—111no—
122C22×Q8C2×D1111yescharacteristic
123C22×Q8C2×D1111yescharacteristic
124C2×Q16—22no—
125C2×Q16—22no—
126C2×Q16—22no—
127C2×Q16—222no—
128C2×Q16—222no—
129C2×Q16—222no—
130C22×C8—111no—
131C22×C8C2×D1111yescharacteristic
132C4⋊Q8—222no—
133C4⋊Q8—222no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4—222no—
136C2×C42—111no—
137#103—222no—
138#103—222no—
139#95—222no—
140C2×C11#39211yescharacteristic
141C2×C11#45112yes—
142C2×C11#46212yes—
143C2×C11#49411yescharacteristic
144C2×C11#49711yescharacteristic
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—112no—
156C2×Q8—221no—
157C2×Q8—221no—
158C2×Q8—221no—
159C2×Q8—221no—
160C2×Q8—221no—
161C2×Q8C22⋊D1112yes—
162C2×Q8C22⋊D1112yes—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—112no—
166C22×C4—221no—
167C22×C4—221no—
168C22×C4C22×D1111yescharacteristic
169Q16—28no—
170Q16—228no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—112no—
174C2×C8—221no—
175C2×C8—221no—
176C2×C8C22⋊D1112yes—
177C4⋊C4—228no—
178C4⋊C4—221no—
179C4⋊C4—221no—
180C42—221no—
181C42—221no—
182C11#201611yescharacteristic, complemented, Sylow
183C23D4×D1111yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192Q8—222no—
193Q8—222no—
194Q8—441no—
195Q8—441no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—114no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—441no—
207C2×C4—441no—
208C2×C4—442no—
209C2×C4—441no—
210C2×C4D4×D1111yescharacteristic
211C2×C4D4×D1111yescharacteristic
212C2×C4#434111yescharacteristic
213C2×C4C2×C22⋊D1111yescharacteristic
214C2×C4C2×C22⋊D1111yescharacteristic
215C2×C4C2×C22⋊D1111yescharacteristic
216C8—22no—
217C8—222no—
218C22Q16×D1112yes—
219C22#6697112yes—
220C22#6699011yescharacteristic
221C22#6699211yescharacteristic
222C22#6699311yescharacteristic
223C4—42no—
224C4—42no—
225C4—224no—
226C4—442no—
227C4—881no—
228C4#6699011yescharacteristic
229C4#6699111yescharacteristic
230C4#6699211yescharacteristic
231C4#6700611yescharacteristic
232C2#1062279411yescharacteristic
233C2#1062279512yes—
234C2#1062279912yes—
235C2#1062280311yescharacteristic
236C2#1062283611yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC22×C11×Q16C2
socle, prime radicalC23×C11C2×D4
hypercenterC22×Q16D11
hypocenterC11#2016
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
93. C2×Dic11Q16semidirect
182. C11#2016semidirect

Maximal subgroups

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

subgroupindex
C22×C11×Q162
C2×#669972
C22×#43262
#106228432
C2×#668992
C2×#668802
#106221882
#201611