Finite Group Databasebeta

← #28401229

Subgroups — #28401229

Order 14464.

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

normal subgroups only

This group has 338 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#20299206C212yesmaximal
2#20298999C211yesmaximal, characteristic, complemented
3#20298976C211yesmaximal, characteristic, complemented
4#20298965C212yesmaximal, complemented
5#20298855C212yesmaximal
6#20298840C211yesmaximal, characteristic
7#20298836C211yesmaximal, characteristic
8#20298703C212yesmaximal, complemented
9C4×Dic452C211yesmaximal, characteristic, complemented
10#20298552C211yesmaximal, characteristic
11C4×Q16×C113C211yesmaximal, characteristic, complemented
12C2×Dic452C2211yescharacteristic
13C2×#14268637C2212yes—
14C2×#14268630C2211yescharacteristic
15C2×C8×D113C2211yescharacteristic
16#16813620C2212yes—
17#16813617—22no—
18#16813616—22no—
19#16813614—22no—
20#16813613C2212yes—
21#16813612—22no—
22#16813602C2212yes—
23#16813598C2212yes—
24C4×Dic226C2212yes—
25#16813579C2211yescharacteristic
26#16813556C2211yescharacteristic
27#16813553C2212yes—
28#16813547C2212yes—
29#16813546C2212yes—
30#16813545C2212yes—
31#16813533C2211yescharacteristic
32#16813532C2211yescharacteristic
33C8×Dic113C2211yescharacteristic
34C2×Q16×C113C2211yescharacteristic
35C4×Q8×C113C2212yes—
36#107×C113C2211yescharacteristic
37#103×C113C2212yes—
38C4×C8×C113C2211yescharacteristic
39C2×Dic226C2312yes—
40C2×C4×D113C2311yescharacteristic
41Dic452—22no—
42#14268637—24no—
43#14268630—22no—
44C2×#11744751C2311yescharacteristic
45C2×#11744751C2311yescharacteristic
46C8×D113—22no—
47C4⋊Dic113—22no—
48C4⋊Dic113—22no—
49C4⋊Dic113C2312yes—
50#14268626—22no—
51#14268626—22no—
52#14268626—22no—
53#14268626—22no—
54#14268626—22no—
55#14268626D411yescharacteristic
56#14268626D411yescharacteristic
57#14268624—22no—
58#14268624—22no—
59#14268624D411yescharacteristic
60#14268624D411yescharacteristic
61C4×Dic113—22no—
62C4×Dic113C2311yescharacteristic
63C2×Q8×C113C2312yes—
64Q16×C113—22no—
65C2×C8×C113C2311yescharacteristic
66C2×C8×C113C2311yescharacteristic
67C4⋊C4×C113—22no—
68C4⋊C4×C113C2312yes—
69C42×C113—22no—
70C42×C113C2311yescharacteristic
71C22×D113C2×D411yescharacteristic
72Q8×C113—22no—
73Q8×C113—22no—
74C2×C4×C113—22no—
75C2×C4×C113—22no—
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2411yescharacteristic
79C2×Dic113—22no—
80C2×Dic113—22no—
81C2×Dic113C2×D411yescharacteristic
82C2×Dic113C2×D411yescharacteristic
83C2×Dic113C2×D411yescharacteristic
84C4×D113—21no—
85C4×D113—21no—
86Dic226—22no—
87Dic226—22no—
88C8×C113—21no—
89C8×C113#4112yes—
90#11744751—21no—
91#11744751#4112yes—
92C22×C113C22×D411yescharacteristic
93C2×D113—21no—
94C2×D113—21no—
95C2×D113—21no—
96C4×C113—21no—
97C4×C113—21no—
98C4×C113—42no—
99C4×C113—42no—
100C4×C113C2×#4111yescharacteristic
101C4×C113C2×#4111yescharacteristic
102Dic113—21no—
103Dic113—21no—
104Dic113—21no—
105Dic113—42no—
106Dic113—42no—
107C2×C113#53211yescharacteristic
108C2×C113#57811yescharacteristic
109C2×C113#57811yescharacteristic
110D113—41no—
111#3177—1131nomaximal, Sylow
112C113#317711yescharacteristic, complemented, Sylow
113#541—1132no—
114#499—1131no—
115#494—1131no—
116#491—1132no—
117#470—1132no—
118#467—1131no—
119#467—1131no—
120#441—1132no—
121C4×Q16—1131no—
122C4×Q16D11311yescharacteristic, complemented
123#405—1131no—
124C2×Q16—1132no—
125C2×Q16—1131no—
126C2×Q16C2×D11311yescharacteristic
127C2×M16—1131no—
128C22×C8—1131no—
129C4⋊Q8—1132no—
130#126—2262no—
131#126—2262no—
132#125—1132no—
133#125—2262no—
134#125—2262no—
135C22⋊Q8—1132no—
136C22⋊Q8—1132no—
137C4×Q8—1132no—
138C4×Q8C2×D11312yes—
139#117—1131no—
140#107—1131no—
141#107C2×D11311yescharacteristic
142#106—1132no—
143#103—1132no—
144#103—1132no—
145#103—1132no—
146#103C2×D11312yes—
147#97—1131no—
148#97—1131no—
149C4×C8—1131no—
150C4×C8C2×D11311yescharacteristic
151C2×Q8—1132no—
152C2×Q8C22×D11312yes—
153C22×C4—1131no—
154Q16—22no—
155Q16—2264no—
156Q16—2262no—
157M16—2262no—
158C2×C8—1131no—
159C2×C8—1131no—
160C2×C8—2262no—
161C2×C8C22×D11311yescharacteristic
162C2×C8C22×D11311yescharacteristic
163C4⋊C4—22no—
164C4⋊C4—1131no—
165C4⋊C4—1131no—
166C4⋊C4—1132no—
167C4⋊C4—2262no—
168C4⋊C4—2262no—
169C4⋊C4—2262no—
170C4⋊C4—2262no—
171C4⋊C4—2262no—
172C4⋊C4—2262no—
173C4⋊C4—2262no—
174C4⋊C4C22×D11312yes—
175C22⋊C4—1131no—
176C22⋊C4—1131no—
177C22⋊C4—2262no—
178C22⋊C4—2262no—
179C42—22no—
180C42—1131no—
181C42—2262no—
182C42C22×D11311yescharacteristic
183C23—1131no—
184Q8—22no—
185Q8—22no—
186Q8—2262no—
187Q8—2262no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—1131no—
191C2×C4—1131no—
192C2×C4—1131no—
193C2×C4—2262no—
194C2×C4—2262no—
195C2×C4—2261no—
196C2×C4—2261no—
197C2×C4D4×D11311yescharacteristic
198C2×C4D4×D11311yescharacteristic
199C2×C4C23×D11311yescharacteristic
200C8—21no—
201C8—1132no—
202C8—2261no—
203C8#1426864712yes—
204C22—2261no—
205C22—2261no—
206C22—2261no—
207C22C2×D4×D11311yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—4522no—
213C4—4522no—
214C4—2261no—
215C4—2261no—
216C4—2261no—
217C4#41×D11311yescharacteristic
218C4C2×#1426864711yescharacteristic
219C2—4521no—
220C2#2029914511yescharacteristic
221C2#2029941111yescharacteristic
222C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×Q16×C113C2
socleC22×C113C22×D4
prime radicalC22×D113C2×D4
hypercenterC4×Q16D113
hypocenterC113#3177
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #20298999C2semidirect
3. #20298976C2semidirect
4. #20298965C2semidirect
8. #20298703C2semidirect
9. C4×Dic452C2semidirect
11. C4×Q16×C113C2semidirect
112. C113#3177semidirect
122. C4×Q16D113semidirect

Maximal subgroups

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

subgroupindex
#202992062
#202989992
#202989762
#202989652
#202988552
#202988402
#202988362
#202987032
C4×Dic4522
#202985522
C4×Q16×C1132
#3177113