Finite Group Databasebeta

← #28393905

Subgroups — #28393905

Order 14464.

864 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 185 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×#16813603C212yesmaximal, complemented
2C22×#14268626C211yesmaximal, characteristic, complemented
3#20298517C212yesmaximal, complemented
4#20298512C212yesmaximal, complemented
5#20298478C212yesmaximal, complemented
6#20298471C214yesmaximal, complemented
7#20298461C211yesmaximal, characteristic, complemented
8C22×#41×C113C211yesmaximal, characteristic
9C23×Dic113C2211yescharacteristic
10C23×Dic113C2211yescharacteristic
11#16813603—28no—
12C2×#14268626—24no—
13C2×#14268626C2212yes—
14C2×#14268626C2214yes—
15C2×#14268626C2212yes—
16C2×C22⋊Dic113C2214yes—
17C2×C22⋊Dic113C2214yes—
18C2×C22⋊Dic113C2212yes—
19#16813529C2212yes—
20#16813529C2214yes—
21#16813529C2212yes—
22C2×#41×C113—28no—
23C2×#41×C113—24no—
24C22×Q8×C113C2211yescharacteristic
25C22×D4×C113C2211yescharacteristic
26C22×D4×C113C2212yes—
27C23×C4×C113C2212yes—
28C23×C4×C113C2211yescharacteristic
29C22×Dic113—22no—
30C22×Dic113—24no—
31C22×Dic113—22no—
32C22×Dic113—24no—
33C22×Dic113C2314yes—
34C22×Dic113C2312yes—
35C22×Dic113C2312yes—
36#14268626—24no—
37#14268626—24no—
38#14268626—28no—
39C22⋊Dic113—24no—
40C22⋊Dic113—28no—
41C22⋊Dic113—28no—
42C24×C113C2312yes—
43C24×C113C2311yescharacteristic
44#41×C113—232no—
45C2×Q8×C113—24no—
46C2×Q8×C113—22no—
47C2×D4×C113—24no—
48C2×D4×C113—24no—
49C2×D4×C113—24no—
50C2×D4×C113—22no—
51C2×D4×C113D418yes—
52C22×C4×C113—24no—
53C22×C4×C113—24no—
54C22×C4×C113—24no—
55C22×C4×C113—24no—
56C22×C4×C113D414yes—
57C22×C4×C113C2311yescharacteristic
58C22×C4×C113C2312yes—
59C22×C4×C113C2311yescharacteristic
60C23×C113—22no—
61C23×C113—22no—
62C23×C113—22no—
63C23×C113—22no—
64C23×C113—24no—
65C23×C113—24no—
66C23×C113C2×D414yes—
67C23×C113C2×D414yes—
68C23×C113C2×D412yes—
69C23×C113C2411yescharacteristic
70Q8×C113—28no—
71D4×C113—28no—
72D4×C113—216no—
73C2×C4×C113—216no—
74C2×C4×C113—28no—
75C2×C4×C113—22no—
76C2×C4×C113—22no—
77C2×C4×C113—22no—
78C2×C4×C113—22no—
79C2×C4×C113C2×D412yes—
80C2×C4×C113C2×D414yes—
81C2×C4×C113C2×D412yes—
82C2×Dic113—28no—
83C2×Dic113—22no—
84C2×Dic113—22no—
85C2×Dic113—24no—
86C2×Dic113—24no—
87C2×Dic113—22no—
88C2×Dic113—24no—
89C2×Dic113—24no—
90C2×Dic113—44no—
91C2×Dic113#4114yescomplemented
92C22×C113—22no—
93C22×C113—22no—
94C22×C113—28no—
95C22×C113—24no—
96C22×C113—28no—
97C22×C113—42no—
98C22×C113—42no—
99C22×C113—44no—
100C22×C113#12014yes—
101C22×C113C22×D411yescharacteristic
102C22×C113C22×D412yes—
103C22×C113C2×#4112yes—
104C22×C1132−1+412yes—
105C4×C113—22no—
106C4×C113—24no—
107C4×C113—22no—
108Dic113—24no—
109Dic113—42no—
110Dic113—44no—
111C2×C113—24no—
112C2×C113—44no—
113C2×C113C2×#12011yescharacteristic
114C2×C113#52511yescharacteristic
115C2×C113#53611yescharacteristic
116C2×C113#54714yes—
117#2406—1131nomaximal, Sylow
118C113#240611yescharacteristic, complemented, Sylow
119C22×#41D11311yescharacteristic
120C2×#123—1132no—
121C22×C4⋊C4—1131no—
122#395—1132no—
123#394—1132no—
124#386—1132no—
125#385—1134no—
126#381—1131no—
127C2×#41—28no—
128C2×#41—24no—
129C22×Q8C2×D11311yescharacteristic
130C22×D4C2×D11311yescharacteristic
131C22×D4C2×D11312yes—
132C23×C4—1131no—
133C23×C4—1131no—
134C23×C4C2×D11312yes—
135C23×C4C2×D11311yescharacteristic
136#123—2268no—
137C2×C4⋊C4—1132no—
138C2×C4⋊C4—1132no—
139C2×C4⋊C4—1134no—
140C2×C4⋊C4—2264no—
141C2×C22⋊C4—1132no—
142C2×C22⋊C4—1134no—
143C2×C22⋊C4—1134no—
144#95—1132no—
145#95—1132no—
146#95—1134no—
147C24C22×D11312yes—
148C24C22×D11311yescharacteristic
149#41—232no—
150C2×Q8—24no—
151C2×Q8—22no—
152C2×D4—24no—
153C2×D4—24no—
154C2×D4—24no—
155C2×D4—22no—
156C2×D4C22⋊D11318yes—
157C22×C4—24no—
158C22×C4—24no—
159C22×C4—24no—
160C22×C4—24no—
161C22×C4—1132no—
162C22×C4—1134no—
163C22×C4—1132no—
164C22×C4—2264no—
165C22×C4—2262no—
166C22×C4—2264no—
167C22×C4—2262no—
168C22×C4C22⋊D11314yes—
169C22×C4C22×D11311yescharacteristic
170C22×C4C22×D11312yes—
171C22×C4C22×D11311yescharacteristic
172C4⋊C4—2264no—
173C4⋊C4—2264no—
174C4⋊C4—2268no—
175C22⋊C4—2268no—
176C22⋊C4—2264no—
177C22⋊C4—2268no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23—22no—
182C23—24no—
183C23—24no—
184C23C2×C22⋊D11314yes—
185C23C2×C22⋊D11314yes—
186C23C2×C22⋊D11312yes—
187C23C23×D11311yescharacteristic
188Q8—28no—
189D4—28no—
190D4—216no—
191C2×C4—216no—
192C2×C4—28no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—1134no—
198C2×C4—4524no—
199C2×C4—2264no—
200C2×C4—2264no—
201C2×C4—2262no—
202C2×C4—2264no—
203C2×C4—2264no—
204C2×C4—2268no—
205C2×C4—2262no—
206C2×C4—2262no—
207C2×C4C2×C22⋊D11312yes—
208C2×C4C2×C22⋊D11314yes—
209C2×C4C2×C22⋊D11312yes—
210C22—22no—
211C22—22no—
212C22—28no—
213C22—24no—
214C22—28no—
215C22—42no—
216C22—42no—
217C22—44no—
218C22#1681359114yes—
219C22C22×C22⋊D11311yescharacteristic
220C22C22×C22⋊D11312yes—
221C22#41×D11312yes—
222C22#1681366912yes—
223C4—22no—
224C4—24no—
225C4—22no—
226C4—4522no—
227C4—4524no—
228C4—2264no—
229C2—24no—
230C2—44no—
231C2C2×#1681359111yescharacteristic
232C2#2029910511yescharacteristic
233C2#2029916911yescharacteristic
234C2#2029924714yes—
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting, prime radicalC22×#41×C113C2
hypercenterC22×#41D113
hypocenterC113#2406
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16813603C2semidirect
2. C22×#14268626C2semidirect
3. #20298517C2semidirect
4. #20298512C2semidirect
5. #20298478C2semidirect
6. #20298471C2semidirect
7. #20298461C2semidirect
91. C2×Dic113#41semidirect
118. C113#2406semidirect

Maximal subgroups

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

subgroupindex
C2×#168136032
C22×#142686262
#202985172
#202985122
#202984782
#202984712
#202984612
C22×#41×C1132
#2406113