Finite Group Databasebeta

← #13069852

Subgroups — #13069852

Order 1408.

318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 87 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×C11×#124C211yesmaximal, characteristic
2C2×#66899C211yesmaximal, characteristic, complemented
3C2×#66899C211yesmaximal, characteristic, complemented
4C2×#66896C211yesmaximal, characteristic
5C2×#66896C211yesmaximal, characteristic
6#10622541C211yesmaximal, characteristic, complemented
7#10622162C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic
10C11×#124—22no—
11C11×#124—22no—
12C2×C11×C22⋊C4—21no—
13C2×C11×C22⋊C4—21no—
14C2×C42×C11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4—21no—
18C22×C11⋊C8C2211yescharacteristic
19C22×C11⋊C8C2211yescharacteristic
20#66899—22no—
21#66899—22no—
22#66896—22no—
23#66896—22no—
24C11⋊#95—21no—
25C24×C11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11—21no—
30C2×Q8×C11—21no—
31C2×Q8×C11D412yes—
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11—21no—
36C2×D4×C11—21no—
37C2×D4×C11D412yes—
38C22×C4×C11—21no—
39C22×C4×C11D411yescharacteristic
40C22×C4×C11D411yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×Dic11—21no—
43C22×Dic11—21no—
44C11×C22⋊C4—24no—
45C11×C22⋊C4—24no—
46C42×C11—21no—
47C42×C11—21no—
48C4⋊Dic11—21no—
49C4⋊Dic11—21no—
50C4⋊Dic11—21no—
51C4⋊Dic11D412yes—
52Dic11⋊C4—42no—
53C2×C11⋊C8—21no—
54C2×C11⋊C8—21no—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58C2×C11⋊C8—21no—
59#2042—111nomaximal, Sylow
60C23×C11—22no—
61C23×C11—41no—
62C23×C11—41no—
63C23×C11—41no—
64C23×C11—41no—
65C23×C11—41no—
66C23×C11—41no—
67C23×C11C2×D411yescharacteristic
68Q8×C11—22no—
69Q8×C11—22no—
70Q8×C11—41no—
71Q8×C11—41no—
72D4×C11—22no—
73D4×C11—22no—
74D4×C11—41no—
75D4×C11—41no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11#4111yescharacteristic
89C2×C4×C11#4111yescharacteristic
90C2×C4×C11#4111yescharacteristic
91C2×Dic11—22no—
92C2×Dic11—41no—
93C2×Dic11—41no—
94C2×Dic11—41no—
95C2×Dic11—41no—
96C2×Dic11—41no—
97C11⋊C8—41no—
98C11⋊C8—41no—
99C2×#124D1111yescharacteristic
100C2×#103—111no—
101C2×#103—111no—
102C2×#102—111no—
103C2×#102—111no—
104#389—111no—
105#336—111no—
106C22×C11—42no—
107C22×C11—42no—
108C22×C11—42no—
109C22×C11—81no—
110C22×C11—81no—
111C22×C11—81no—
112C22×C11—81no—
113C22×C11#12011yescharacteristic
114C22×C11#12111yescharacteristic
115C22×C11#12411yescharacteristic
116C22×C11#13511yescharacteristic
117C22×C11#13511yescharacteristic
118C22×C11AGL(1,ℤ/8)11yescharacteristic
119C22×C11#13711yescharacteristic
120C4×C11—42no—
121C4×C11—41no—
122C4×C11—41no—
123C4×C11#12111yescharacteristic
124C4×C11#12111yescharacteristic
125C4×C11#12311yescharacteristic
126C4×C11#12311yescharacteristic
127Dic11—42no—
128Dic11—81no—
129C22×Q8C2×D1111yescharacteristic
130C22×D4C2×D1111yescharacteristic
131C22×C8—111no—
132C22×C8—111no—
133#124—22no—
134#124—22no—
135C2×C4⋊C4—111no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4—221no—
138C2×C22⋊C4—21no—
139C2×C22⋊C4—21no—
140C2×C42C2×D1111yescharacteristic
141#103—222no—
142#103—222no—
143#102—222no—
144#102—222no—
145#95—221no—
146C2×C11—82no—
147C2×C11#39411yescharacteristic
148C2×C11#44911yescharacteristic
149C2×C11#45211yescharacteristic
150C2×C11#46311yescharacteristic
151C2×C11#46411yescharacteristic
152C2×C11#48811yescharacteristic
153C2×C11#48911yescharacteristic
154C24—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8C22⋊D1112yes—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4C22⋊D1112yes—
167C22×C4—21no—
168C22×C4—221no—
169C22×C4—221no—
170C22×C4C22⋊D1111yescharacteristic
171C22×C4C22⋊D1111yescharacteristic
172C22×C4C22×D1111yescharacteristic
173C2×C8—221no—
174C2×C8—221no—
175C2×C8—221no—
176C2×C8—221no—
177C2×C8—221no—
178C2×C8—221no—
179C4⋊C4—112no—
180C4⋊C4—221no—
181C4⋊C4—221no—
182C4⋊C4—221no—
183C4⋊C4—442no—
184C22⋊C4—24no—
185C22⋊C4—24no—
186C42—21no—
187C42—21no—
188C11#204211yescharacteristic, complemented, Sylow
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23C2×C22⋊D1111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—222no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4—441no—
218C2×C4—441no—
219C2×C4—441no—
220C2×C4D4×D1111yescharacteristic
221C2×C4#434111yescharacteristic
222C2×C4#434111yescharacteristic
223C2×C4#434111yescharacteristic
224C2×C4C2×C22⋊D1111yescharacteristic
225C2×C4C2×C22⋊D1111yescharacteristic
226C8—441no—
227C8—441no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22#6698911yescharacteristic
236C22#6699111yescharacteristic
237C22#6700211yescharacteristic
238C22#6700311yescharacteristic
239C22#6700311yescharacteristic
240C22#6700411yescharacteristic
241C22#6700611yescharacteristic
242C4—42no—
243C4—41no—
244C4—41no—
245C4—442no—
246C4—881no—
247C4#6698811yescharacteristic
248C4#6698811yescharacteristic
249C4#6699211yescharacteristic
250C4#6699211yescharacteristic
251C2—82no—
252C2#1062266711yescharacteristic
253C2#1062266811yescharacteristic
254C2#1062266911yescharacteristic
255C2#1062267011yescharacteristic
256C2#1062283511yescharacteristic
257C2#1062285111yescharacteristic
258C2#1062285211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#124C2
socleC23×C11C2×D4
prime radicalC22×D4×C11C22
hypercenterC2×#124D11
hypocenterC11#2042
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×#66899C2semidirect
3. C2×#66899C2semidirect
6. #10622541C2semidirect
7. #10622162C2semidirect
188. C11#2042semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×#668992
C2×#668962
#106225412
#106221622
#204211