Finite Group Databasebeta

← #13081430

Subgroups — #13081430

Order 1408.

350 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q82×C11C211yesmaximal, characteristic, complemented
2#10623116C211yesmaximal, characteristic
3#10622704C211yesmaximal, characteristic, complemented
4#10622702C212yesmaximal, complemented
5#10622701C211yesmaximal, characteristic
6#10622700C212yesmaximal, complemented
7C4×#4326C211yesmaximal, characteristic, complemented
8#10622641C212yesmaximal, complemented
9#10622640C211yesmaximal, characteristic
10#10622639C212yesmaximal, complemented
11#10622637C211yesmaximal, characteristic, complemented
12C11×C4⋊Q8—21no—
13C11×C4⋊Q8—22no—
14C11×C4⋊Q8C2212yes—
15C11×C4⋊Q8C2211yescharacteristic
16C4×Q8×C11—21no—
17C4×Q8×C11C2212yes—
18C4×Q8×C11C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20#67000—21no—
21C2×#4326C2211yescharacteristic
22C2×#4325C2212yes—
23#66947—22no—
24#66946—21no—
25#66928C2212yes—
26#66927C2211yescharacteristic
27C4×D44C2212yes—
28C4×Dic22C2211yescharacteristic
29#66899C2211yescharacteristic
30#66874C2212yes—
31#66874C2211yescharacteristic
32#66873C2212yes—
33#66873C2212yes—
34#66873C2212yes—
35#66871C2212yes—
36#66871C2211yescharacteristic
37C4⋊(C11⋊C8)C2211yescharacteristic
38C4⋊(C11⋊C8)C2212yes—
39#66867C2212yes—
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11—22no—
43C2×Q8×C11D411yescharacteristic
44C2×Q8×C11C2311yescharacteristic
45C2×D44—21no—
46C2×D44—21no—
47C2×D44C2312yes—
48C2×C4×D11—22no—
49C2×Dic22C2311yescharacteristic
50C11×C4⋊C4—22no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4—21no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4D411yescharacteristic
55C11×C4⋊C4D412yes—
56C11×C4⋊C4C2312yes—
57C11×C4⋊C4C2311yescharacteristic
58C42×C11—22no—
59C42×C11—21no—
60C42×C11C2311yescharacteristic
61C42×C11C2312yes—
62#4326—22no—
63#4325—24no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—22no—
67C4⋊Dic11C2311yescharacteristic
68Dic11⋊C4—21no—
69C4×Dic11—21no—
70C2×C11⋊C8C2311yescharacteristic
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2312yes—
73#3375—111nomaximal, Sylow
74C22×D11—22no—
75Q8×C11—22no—
76Q8×C11—21no—
77Q8×C11—82no—
78Q8×C11—81no—
79Q8×C11#4112yes—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D412yes—
85C2×C4×C11C2×D412yes—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2411yescharacteristic
88C2×Dic11—21no—
89C2×Dic11—21no—
90D44—22no—
91D44—22no—
92D44—42no—
93D44—81no—
94C4×D11—82no—
95Dic22—21no—
96Dic22—21no—
97C11⋊C8—22no—
98C11⋊C8—21no—
99C11⋊C8—21no—
100#559—111no—
101Q82D1111yescharacteristic, complemented
102#489—112no—
103#486—111no—
104#477—111no—
105#474—112no—
106#464—112no—
107#460—111no—
108#446—111no—
109#440—112no—
110C4×Q16—111no—
111C22×C11C22×D411yescharacteristic
112C2×D11—42no—
113C2×D11—42no—
114C2×D11—42no—
115C4×C11—22no—
116C4×C11—22no—
117C4×C11—22no—
118C4×C11—21no—
119C4×C11—41no—
120C4×C11—42no—
121C4×C11#13712yes—
122C4×C11C2×#4111yescharacteristic
123C4×C112−1+411yescharacteristic
124Dic11—41no—
125Dic11—41no—
126C2×Q16—111no—
127C2×SD16—112no—
128C4⋊Q8—21no—
129C4⋊Q8—22no—
130C4⋊Q8C2×D1112yes—
131C4⋊Q8C2×D1111yescharacteristic
132#127—111no—
133#124—112no—
134#124—221no—
135#123—222no—
136C4×Q8—21no—
137C4×Q8—111no—
138C4×Q8C2×D1111yescharacteristic
139C4×Q8C2×D1112yes—
140C4×Q8C2×D1111yescharacteristic
141C4×D4—112no—
142C4×D4—221no—
143#107—111no—
144#107—112no—
145C4⋊C8—111no—
146C4⋊C8—112no—
147#103—111no—
148#103—111no—
149#103—112no—
150#102—112no—
151#102—112no—
152#102—112no—
153#97—112no—
154C4×C8—111no—
155C2×C11#54811yescharacteristic
156C2×C11C2×#13711yescharacteristic
157C2×C11#57611yescharacteristic
158D11—82no—
159C2×Q8—22no—
160C2×Q8—21no—
161C2×Q8—111no—
162C2×Q8C22⋊D1111yescharacteristic
163C2×Q8C22×D1111yescharacteristic
164C2×D4—112no—
165C2×D4—221no—
166C2×D4—221no—
167C22×C4—222no—
168Q16—222no—
169SD16—224no—
170C2×C8—111no—
171C2×C8—111no—
172C2×C8—112no—
173C4⋊C4—22no—
174C4⋊C4—21no—
175C4⋊C4—22no—
176C4⋊C4—21no—
177C4⋊C4—111no—
178C4⋊C4—221no—
179C4⋊C4C22⋊D1111yescharacteristic
180C4⋊C4C22⋊D1112yes—
181C4⋊C4C22×D1112yes—
182C4⋊C4C22×D1111yescharacteristic
183C22⋊C4—222no—
184C22⋊C4—222no—
185C22⋊C4—222no—
186C42—22no—
187C42—21no—
188C42—221no—
189C42C22×D1111yescharacteristic
190C42C22×D1112yes—
191C11#337511yescharacteristic, complemented, Sylow
192C23—222no—
193Q8—22no—
194Q8—21no—
195Q8—82no—
196Q8—81no—
197Q8—221no—
198Q8—221no—
199Q8#434312yes—
200D4—222no—
201D4—222no—
202D4—442no—
203D4—881no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—221no—
208C2×C4—221no—
209C2×C4—882no—
210C2×C4C2×C22⋊D1112yes—
211C2×C4C2×C22⋊D1112yes—
212C2×C4C2×C22⋊D1111yescharacteristic
213C2×C4C2×C22⋊D1111yescharacteristic
214C2×C4C23×D1111yescharacteristic
215C8—222no—
216C8—221no—
217C8—221no—
218C22—442no—
219C22—442no—
220C22—442no—
221C22C22×C22⋊D1111yescharacteristic
222C4—22no—
223C4—22no—
224C4—22no—
225C4—21no—
226C4—41no—
227C4—42no—
228C4—441no—
229C4—441no—
230C4#6699512yes—
231C4C2×#434311yescharacteristic
232C4#6704011yescharacteristic
233C2—882no—
234C2C2×#6699511yescharacteristic
235C2#1062334811yescharacteristic
236C2#1062336611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingQ82×C11C2
socleC22×C11C22×D4
prime radical#66927C22
hypercenterQ82D11
hypocenterC11#3375
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ Q82

Complements

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

NH ≅ G/Ntype
1. Q82×C11C2semidirect
3. #10622704C2semidirect
4. #10622702C2semidirect
6. #10622700C2semidirect
7. C4×#4326C2semidirect
8. #10622641C2semidirect
10. #10622639C2semidirect
11. #10622637C2semidirect
101. Q82D11semidirect
191. C11#3375semidirect

Maximal subgroups

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

subgroupindex
Q82×C112
#106231162
#106227042
#106227022
#106227012
#106227002
C4×#43262
#106226412
#106226402
#106226392
#106226372
#337511