Finite Group Databasebeta

← #13069113

Subgroups — #13069113

Order 1408.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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×#67004C211yesmaximal, characteristic
2#10623047C211yesmaximal, characteristic, complemented
3C11×#410C211yesmaximal, characteristic
4#10622849C211yesmaximal, characteristic
5#10622617C211yesmaximal, characteristic, complemented
6#10622171C211yesmaximal, characteristic, complemented
7#10622169C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×Dic22C2211yescharacteristic
10C11×#117C2211yescharacteristic
11C11×#117C2211yescharacteristic
12#67004—22no—
13#67004—22no—
14C2×#4326C412yescomplemented
15C2×#4324C412yescomplemented
16#66979C2211yescharacteristic
17C2×#4318C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19#66940—22no—
20#66930—22no—
21C4×Dic22—22no—
22C11×#99—22no—
23#66901—22no—
24#66874—22no—
25C11×#41—21no—
26C11×#41—21no—
27C11×#41—21no—
28C11×#41—21no—
29C2×Q8×C11C2×C411yescharacteristic
30C2×D4×C11—21no—
31C2×D4×C11C2×C411yescharacteristic
32C22×C4×C11—21no—
33C22×C4×C11C2311yescharacteristic
34C22×Dic11—21no—
35C2×Dic22—21no—
36C2×Dic22—21no—
37C2×Dic22—21no—
38C2×Dic22C2×C412yes—
39C2×Dic22D412yes—
40C2×Dic22D412yes—
41C11×C4⋊C4—21no—
42C11×C4⋊C4—21no—
43C11×C22⋊C4—21no—
44C11×C22⋊C4D412yes—
45C42×C11—21no—
46C42×C11—21no—
47C22⋊Dic11—21no—
48#4326—24no—
49#4324—24no—
50C4⋊Dic11—21no—
51Dic11⋊C4—24no—
52C4×Dic11—24no—
53C4×Dic11D412yes—
54#4318—21no—
55#4318—21no—
56#4318—21no—
57#4318—21no—
58C2×C11⋊C8—21no—
59C2×C11⋊C8C2×C412yes—
60#1905—111nomaximal, Sylow
61C23×C11—21no—
62C23×C11C2×D411yescharacteristic
63Q8×C11—21no—
64Q8×C11—21no—
65D4×C11—21no—
66D4×C11—21no—
67D4×C11—41no—
68D4×C11—41no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—41no—
72C2×C4×C11—41no—
73C2×C4×C11—41no—
74C2×C4×C11C22×C411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11#4111yescharacteristic
79C2×C4×C11#4111yescharacteristic
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84Dic22—22no—
85Dic22—22no—
86Dic22—22no—
87Dic22C22⋊C414yes—
88C11⋊C8—22no—
89C11⋊C8—41no—
90C2×#137—111no—
91#519—111no—
92#421—111no—
93#419—111no—
94#410D1111yescharacteristic
95#344—111no—
96H(3,ℤ/4)—111no—
97C22×C11—41no—
98C22×C11—41no—
99C22×C11—81no—
100C22×C11C4×D411yescharacteristic
101C22×C11#12011yescharacteristic
102C22×C11#12111yescharacteristic
103C4×C11—42no—
104C4×C11—41no—
105C4×C11—81no—
106C4×C11C2×C22⋊C411yescharacteristic
107C4×C11C4×D411yescharacteristic
108C4×C11#12111yescharacteristic
109C4×C11#12311yescharacteristic
110Dic11—24no—
111Dic11—42no—
112C2×#41C2×D1111yescharacteristic
113C22×Q8—111no—
114#137—222no—
115#137—222no—
116C2×Q16—112no—
117C2×SD16—112no—
118C2×M16—111no—
119C2×M16—111no—
120C4×Q8—222no—
121C4×Q8—222no—
122#117—111no—
123#117—222no—
124#117C2×D1111yescharacteristic
125#117C2×D1111yescharacteristic
126#104—222no—
127#103—222no—
128#99—22no—
129C2×C11—21no—
130C2×C11—21no—
131C2×C11—21no—
132C2×C11—81no—
133C2×C11#38611yescharacteristic
134#41—21no—
135#41—21no—
136#41—21no—
137#41—21no—
138C2×Q8—112no—
139C2×Q8—112no—
140C2×Q8—112no—
141C2×Q8—221no—
142C2×Q8—221no—
143C2×Q8—221no—
144C2×Q8C4×D1111yescharacteristic
145C2×D4—21no—
146C2×D4C4×D1111yescharacteristic
147C22×C4—21no—
148C22×C4—221no—
149C22×C4C22×D1111yescharacteristic
150Q16—224no—
151SD16—224no—
152M16—221no—
153M16—221no—
154M16—221no—
155M16—221no—
156C2×C8—112no—
157C2×C8—221no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—224no—
161C4⋊C4—221no—
162C22⋊C4—21no—
163C22⋊C4—221no—
164C22⋊C4C22⋊D1112yes—
165C42—21no—
166C42—21no—
167C42—112no—
168C42—224no—
169C11#190511yescharacteristic, complemented, Sylow
170C23—21no—
171C23C2×C22⋊D1111yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—114no—
175Q8—222no—
176Q8—222no—
177Q8—222no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4C2×C4×D1111yescharacteristic
192C2×C4#433911yescharacteristic
193C2×C4D4×D1111yescharacteristic
194C2×C4D4×D1111yescharacteristic
195C2×C4D4×D1111yescharacteristic
196C2×C4#434111yescharacteristic
197C8—222no—
198C8—441no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22C4×C22⋊D1111yescharacteristic
203C22#6699011yescharacteristic
204C22#6699111yescharacteristic
205C4—42no—
206C4—41no—
207C4—81no—
208C4—224no—
209C4—442no—
210C4C22⋊C4×D1111yescharacteristic
211C4(C22⋊D11)⋊C411yescharacteristic
212C4#6693611yescharacteristic
213C4#6693711yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#1062256911yescharacteristic
subgroupG/H
centerC2#10622569
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#410C2
socleC2×C11#386
prime radicalC2×C11×#41C22
cosocleC22×C4×C11C23
hypercenter#410D11
hypocenterC11#1905
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #10623047C2semidirect
5. #10622617C2semidirect
6. #10622171C2semidirect
7. #10622169C2semidirect
14. C2×#4326C4semidirect
15. C2×#4324C4semidirect
169. C11#1905semidirect

Maximal subgroups

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

subgroupindex
C2×#670042
#106230472
C11×#4102
#106228492
#106226172
#106221712
#106221692
#190511