Finite Group Databasebeta

← #28403376

Subgroups — #28403376

Order 14464.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#20299326C211yesmaximal, characteristic
2#20299323C211yesmaximal, characteristic
3#20298965C212yesmaximal
4#20298950C211yesmaximal, characteristic
5#20298908C212yesmaximal
6#20298809C211yesmaximal, characteristic
7#20298807C212yesmaximal
8#20298725C211yesmaximal, characteristic
9#20298704C212yesmaximal
10C4×#14268637C211yesmaximal, characteristic
11#475×C113C211yesmaximal, characteristic
12C2×Dic452C2212yes—
13C2×#14268637C2211yescharacteristic
14#16813622C2211yescharacteristic
15#16813620—21no—
16#16813620C2212yes—
17#16813614—21no—
18#16813613C2212yes—
19#16813612—22no—
20#16813612—22no—
21Q8×Dic113—21no—
22C4×Dic226—21no—
23C4×Dic226C2211yescharacteristic
24C4×Dic226C2211yescharacteristic
25#16813587C2212yes—
26#16813587C2212yes—
27#16813555C2211yescharacteristic
28#16813551C2212yes—
29#16813547C2212yes—
30#16813546C2211yescharacteristic
31#16813545C2212yes—
32#16813545C2211yescharacteristic
33#16813545C2212yes—
34#16813532C2212yes—
35C4×#11744751C2211yescharacteristic
36C4⋊Q8×C113C2211yescharacteristic
37C4×Q8×C113C2211yescharacteristic
38#106×C113C2212yes—
39C4⋊C8×C113C2211yescharacteristic
40#103×C113C2212yes—
41C2×Dic226D411yescharacteristic
42C2×Dic226C2312yes—
43C2×Dic226C2311yescharacteristic
44Dic452—24no—
45#14268637—22no—
46C2×#11744751C2311yescharacteristic
47C2×#11744751C2311yescharacteristic
48C4⋊Dic113—21no—
49C4⋊Dic113—21no—
50C4⋊Dic113—22no—
51C4⋊Dic113D411yescharacteristic
52C4⋊Dic113C2311yescharacteristic
53#14268626—21no—
54#14268626—22no—
55#14268626—22no—
56#14268626—22no—
57#14268626—22no—
58#14268626—22no—
59#14268626D412yes—
60C4×Dic113—21no—
61C4×Dic113—22no—
62C4×Dic113—22no—
63C4×Dic113C2312yes—
64C2×Q8×C113—21no—
65C2×Q8×C113C2311yescharacteristic
66C2×C8×C113C2312yes—
67C4⋊C4×C113—21no—
68C4⋊C4×C113—21no—
69C4⋊C4×C113C2311yescharacteristic
70C4⋊C4×C113C2312yes—
71C42×C113—21no—
72C42×C113C2311yescharacteristic
73Q8×C113—21no—
74Q8×C113—21no—
75Q8×C113—42no—
76C2×C4×C113—21no—
77C2×C4×C113—21no—
78C2×C4×C113—22no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2411yescharacteristic
82C2×Dic113—21no—
83C2×Dic113—21no—
84C2×Dic113—22no—
85C2×Dic113C2×D412yes—
86C2×Dic113C2×D412yes—
87Dic226—22no—
88Dic226—21no—
89Dic226—22no—
90Dic226—22no—
91Dic226#4112yes—
92C8×C113—22no—
93#11744751—21no—
94#11744751—21no—
95C22×C113C22×D411yescharacteristic
96C4×C113—21no—
97C4×C113—41no—
98C4×C113—42no—
99C4×C113—41no—
100C4×C113#13712yes—
101C4×C113C2×#4111yescharacteristic
102C4×C1132−1+411yescharacteristic
103Dic113—22no—
104Dic113—22no—
105Dic113—22no—
106Dic113—42no—
107Dic113—41no—
108C2×C113#54811yescharacteristic
109C2×C113C2×#13711yescharacteristic
110C2×C113#57811yescharacteristic
111#3374—1131nomaximal, Sylow
112C113#337411yescharacteristic, complemented, Sylow
113#557—1131no—
114#557—1131no—
115#491—1132no—
116#487—1131no—
117#479—1132no—
118#475D11311yescharacteristic
119#462—1131no—
120#462—1132no—
121#446—1131no—
122#441—1132no—
123C4×Q16—1131no—
124C2×Q16—1131no—
125C2×Q16—1132no—
126C4⋊Q8—1132no—
127C4⋊Q8—1131no—
128C4⋊Q8—2261no—
129C4⋊Q8C2×D11311yescharacteristic
130#125—1132no—
131#125—2261no—
132#125—2262no—
133#125—2262no—
134C4×Q8—1131no—
135C4×Q8—1132no—
136C4×Q8—1132no—
137C4×Q8—1131no—
138C4×Q8—2261no—
139C4×Q8—2261no—
140C4×Q8C2×D11311yescharacteristic
141#107—1131no—
142#106C2×D11312yes—
143C4⋊C8—1132no—
144C4⋊C8C2×D11311yescharacteristic
145#103—1131no—
146#103—1132no—
147#103—1131no—
148#103—1132no—
149#103—1132no—
150#103C2×D11312yes—
151#97—1132no—
152C4×C8—1131no—
153C2×Q8—21no—
154C2×Q8—1131no—
155C2×Q8—1131no—
156C2×Q8—1132no—
157C2×Q8C22×D11311yescharacteristic
158Q16—2264no—
159Q16—2262no—
160C2×C8—1131no—
161C2×C8—1131no—
162C2×C8C22×D11312yes—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—1131no—
166C4⋊C4—1132no—
167C4⋊C4—1131no—
168C4⋊C4—2262no—
169C4⋊C4—2262no—
170C4⋊C4—2262no—
171C4⋊C4—2262no—
172C4⋊C4—2262no—
173C4⋊C4—2262no—
174C4⋊C4—2261no—
175C4⋊C4—2261no—
176C4⋊C4—2261no—
177C4⋊C4C22×D11312yes—
178C4⋊C4C22×D11311yescharacteristic
179C42—21no—
180C42—1132no—
181C42—2262no—
182C42—2262no—
183C42—2261no—
184C42C22×D11311yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—42no—
188Q8—1132no—
189Q8—2262no—
190Q8—2262no—
191Q8—2262no—
192Q8—2261no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—1132no—
197C2×C4—1132no—
198C2×C4—2261no—
199C2×C4—2262no—
200C2×C4—2261no—
201C2×C4D4×D11311yescharacteristic
202C2×C4D4×D11311yescharacteristic
203C2×C4C23×D11311yescharacteristic
204C8—22no—
205C8—2261no—
206C8—2261no—
207C22C2×D4×D11311yescharacteristic
208C4—21no—
209C4—42no—
210C4—41no—
211C4—41no—
212C4—4521no—
213C4—4522no—
214C4—2262no—
215C4—2262no—
216C4—2262no—
217C4#1681365112yes—
218C4#41×D11311yescharacteristic
219C4#1681367011yescharacteristic
220C2#2029925811yescharacteristic
221C2C2×#1681365111yescharacteristic
222C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#475×C113C2
socle, prime radicalC22×C113C22×D4
hypercenter#475D113
hypocenterC113#3374
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
112. C113#3374semidirect

Maximal subgroups

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

subgroupindex
#202993262
#202993232
#202989652
#202989502
#202989082
#202988092
#202988072
#202987252
#202987042
C4×#142686372
#475×C1132
#3374113