Finite Group Databasebeta

← #13069920

Subgroups — #13069920

Order 1408.

264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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#10623353C211yesmaximal, characteristic
2C11×#416C211yesmaximal, characteristic, complemented
3#10622853C211yesmaximal, characteristic, complemented
4#10622726C211yesmaximal, characteristic, complemented
5#10622715C211yesmaximal, characteristic, complemented
6#10622619C211yesmaximal, characteristic, complemented
7#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C11×#117C2211yescharacteristic
12#67004—21no—
13#67003—22no—
14#67002—21no—
15#66995—21no—
16#66985—21no—
17#66979C2211yescharacteristic
18#66979C2211yescharacteristic
19C2×#4318C2211yescharacteristic
20C11×#103—21no—
21C11×#102—21no—
22#66898—22no—
23#66885—21no—
24#66880—21no—
25Dic11⋊C8—22no—
26#66870—22no—
27C11×#41—21no—
28C11×#41—21no—
29C11×#41—21no—
30C11×#41—21no—
31C2×Q8×C11D411yescharacteristic
32C2×D4×C11—21no—
33C2×D4×C11D411yescharacteristic
34C22×C4×C11—21no—
35C22×C4×C11C2311yescharacteristic
36C2×C22⋊D11—21no—
37#4339—21no—
38#4339—21no—
39#4339—21no—
40#4339—21no—
41C2×D44D411yescharacteristic
42C2×C4×D11—21no—
43C2×Dic22D411yescharacteristic
44C2×C8×C11—21no—
45C2×C8×C11—21no—
46C2×C8×C11—21no—
47C11×C4⋊C4—21no—
48C11×C22⋊C4—21no—
49C42×C11—21no—
50C22⋊Dic11—21no—
51C22⋊Dic11D412yes—
52#4326—22no—
53#4325—22no—
54#4324—22no—
55#4323—22no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4×Dic11—21no—
59C4×Dic11—21no—
60#4318—21no—
61#4318—21no—
62C2×C11⋊C8D412yes—
63#2053—111nomaximal, Sylow
64C23×C11—21no—
65C23×C11C2×D411yescharacteristic
66C22×D11—21no—
67Q8×C11—21no—
68Q8×C11—21no—
69D4×C11—21no—
70D4×C11—21no—
71D4×C11—41no—
72D4×C11—41no—
73C2×C4×C11—21no—
74C2×C4×C11—41no—
75C2×C4×C11—41no—
76C2×C4×C11—41no—
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11#4111yescharacteristic
81C2×C4×C11#4111yescharacteristic
82C2×C4×C11#4111yescharacteristic
83C22⋊D11—41no—
84C22⋊D11—41no—
85C2×Dic11—22no—
86C2×Dic11—21no—
87C2×Dic11—41no—
88D44—21no—
89D44—21no—
90C4×D11—41no—
91C4×D11—41no—
92Dic22—21no—
93Dic22—21no—
94C8×C11—41no—
95C11⋊C8—22no—
96#575—111no—
97#424—111no—
98#416—111no—
99#416D1111yescharacteristic, complemented
100#410—111no—
101#410—111no—
102H(3,ℤ/4)—111no—
103C22×C11—41no—
104C22×C11—41no—
105C22×C11—81no—
106C22×C11#12111yescharacteristic
107C22×C11#12111yescharacteristic
108C22×C11#12111yescharacteristic
109C2×D11—41no—
110C2×D11—81no—
111C4×C11—41no—
112C4×C11—81no—
113C4×C11#12011yescharacteristic
114C4×C11#12311yescharacteristic
115C4×C11#12311yescharacteristic
116C4×C11#12411yescharacteristic
117Dic11—42no—
118Dic11—41no—
119Dic11—81no—
120C2×#41—111no—
121C2×#41C2×D1111yescharacteristic
122#137—221no—
123#137—221no—
124AGL(1,ℤ/8)—221no—
125AGL(1,ℤ/8)—221no—
126#135—222no—
127C2×M16—111no—
128C22×C8C2×D1111yescharacteristic
129#117—111no—
130#117—111no—
131#117C2×D1111yescharacteristic
132C4⋊C8—222no—
133#103—21no—
134#103—221no—
135#102—21no—
136#102—221no—
137#99—222no—
138#99—222no—
139C2×C11—21no—
140C2×C11—21no—
141C2×C11—21no—
142C2×C11—81no—
143C2×C11#39411yescharacteristic
144D11—81no—
145#41—21no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—221no—
150#41—221no—
151#41—221no—
152#41—221no—
153C2×Q8—111no—
154C2×Q8C22⋊D1111yescharacteristic
155C2×D4—21no—
156C2×D4—111no—
157C2×D4—221no—
158C2×D4C22⋊D1111yescharacteristic
159C22×C4—21no—
160C22×C4—221no—
161C22×C4C22×D1111yescharacteristic
162Q16—222no—
163SD16—222no—
164SD16—222no—
165D8—222no—
166M16—221no—
167M16—221no—
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8—112no—
172C4⋊C4—21no—
173C4⋊C4—221no—
174C4⋊C4—221no—
175C22⋊C4—21no—
176C22⋊C4—112no—
177C22⋊C4—221no—
178C42—21no—
179C42—221no—
180C42—221no—
181C11#205311yescharacteristic, complemented, Sylow
182C23—21no—
183C23—221no—
184C23D4×D1111yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—221no—
188Q8—221no—
189D4—21no—
190D4—21no—
191D4—41no—
192D4—41no—
193D4—221no—
194D4—221no—
195D4—441no—
196D4—441no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—222no—
202C2×C4—221no—
203C2×C4—441no—
204C2×C4—441no—
205C2×C4—441no—
206C2×C4#433911yescharacteristic
207C2×C4#433911yescharacteristic
208C2×C4D4×D1111yescharacteristic
209C2×C4D4×D1111yescharacteristic
210C2×C4#434111yescharacteristic
211C2×C4C2×C22⋊D1111yescharacteristic
212C8—41no—
213C8—222no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—441no—
218C22—881no—
219C22#6693711yescharacteristic
220C22#6693711yescharacteristic
221C22#6699211yescharacteristic
222C4—41no—
223C4—81no—
224C4—442no—
225C4—441no—
226C4—881no—
227C4#6693611yescharacteristic
228C4#6693811yescharacteristic
229C4#6698211yescharacteristic
230C4#6699011yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—881no—
236C2#1062257211yescharacteristic
subgroupG/H
centerC4#66938
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#416C2
socleC2×C11#394
prime radical#10623353C2
hypercenter#416D11
hypocenterC11#2053
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C11×#416C2semidirect
3. #10622853C2semidirect
4. #10622726C2semidirect
5. #10622715C2semidirect
6. #10622619C2semidirect
7. #10622169C2semidirect
99. #416D11semidirect
181. C11#2053semidirect

Maximal subgroups

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

subgroupindex
#106233532
C11×#4162
#106228532
#106227262
#106227152
#106226192
#106221692
#205311