Finite Group Databasebeta

← #28389170

Subgroups — #28389170

Order 14464.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D113C211yesmaximal, characteristic
2#20298653C211yesmaximal, characteristic, complemented
3#20298550C211yesmaximal, characteristic, complemented
4#20298338C211yesmaximal, characteristic, complemented
5#20298337C211yesmaximal, characteristic, complemented
6#20298337C211yesmaximal, characteristic, complemented
7#329×C113C211yesmaximal, characteristic, complemented
8C2×Q8×D113C411yescharacteristic
9C2×D4×D113C411yescharacteristic
10C2×#14268630—21no—
11#16813611C411yescharacteristic
12#16813610C2211yescharacteristic
13#16813609C411yescharacteristic
14#16813608—21no—
15#16813608—21no—
16C22⋊C4×D113—21no—
17C22⋊C4×D113—21no—
18C42×D113C2211yescharacteristic
19#16813551—21no—
20#16813534—21no—
21#16813533C2211yescharacteristic, complemented
22#16813533C2211yescharacteristic, complemented
23C8×Dic113—21no—
24#124×C113C2211yescharacteristic
25#97×C113C2211yescharacteristic, complemented
26#97×C113C2211yescharacteristic, complemented
27C23×D113—21no—
28C2×Dic226—21no—
29C2×Dic226C2×C411yescharacteristic
30Q8×D113—42no—
31C2×D452C2×C411yescharacteristic
32C2×C22⋊D113—21no—
33D4×D113—42no—
34C2×C4×D113—21no—
35C2×C4×D113C2×C411yescharacteristic
36C2×C4×D113D411yescharacteristic
37C2×C4×D113D411yescharacteristic
38#14268630—24no—
39C2×#11744751—21no—
40C2×#11744751—21no—
41C22⋊Dic113—21no—
42C22⋊Dic113—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—21no—
46#14268624—21no—
47C4×Dic113C2×C411yescharacteristic
48C4×Dic113D411yescharacteristic
49C4×Dic113D411yescharacteristic
50C2×Q8×C113C2×C411yescharacteristic
51C2×D4×C113C2×C411yescharacteristic
52C2×C8×C113—21no—
53C2×C8×C113—21no—
54C22⋊C4×C113—21no—
55C22⋊C4×C113—21no—
56C42×C113C2311yescharacteristic
57C23×C113—21no—
58C22×D113—21no—
59C22×D113—42no—
60C22×D113—42no—
61C22×D113—42no—
62C22×D113C22⋊C411yescharacteristic
63Q8×C113—41no—
64D4×C113—41no—
65C2×C4×C113—21no—
66C2×C4×C113C22×C411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C2×C4×C113C2×D411yescharacteristic
69C22⋊D113—42no—
70C2×Dic113—21no—
71C2×Dic113C22⋊C411yescharacteristic
72C2×Dic113C22⋊C411yescharacteristic
73C2×Dic113C22⋊C411yescharacteristic
74D452—41no—
75C4×D113—22no—
76C4×D113—22no—
77C4×D113—41no—
78C4×D113—42no—
79Dic226—42no—
80Dic226—41no—
81C8×C113—22no—
82C8×C113—41no—
83#11744751—22no—
84#11744751—41no—
85C22×C113—41no—
86C22×C113—41no—
87C22×C113—41no—
88C22×C113C2×C22⋊C411yescharacteristic
89C2×D113—21no—
90C2×D113—21no—
91C2×D113—41no—
92C2×D113—41no—
93C2×D113—41no—
94C2×D113—84no—
95C2×D113#10412yes—
96C4×C113—21no—
97C4×C113—21no—
98C4×C113—21no—
99C4×C113—41no—
100Dic113—21no—
101Dic113—21no—
102Dic113—41no—
103Dic113#10012yes—
104C2×C113—81no—
105C2×C113C2×#10011yescharacteristic
106C2×C113C2×#10411yescharacteristic
107C2×C113#42111yescharacteristic
108D113—22no—
109D113—81no—
110#1527—1131nomaximal, Sylow
111C113#152711yescharacteristic, complemented, Sylow
112C2×#124—1131no—
113#432—1131no—
114C4×M16—1131no—
115#329—1131no—
116#329—1131no—
117#329—1131no—
118#329D11311yescharacteristic, complemented
119C22×Q8—1131no—
120C22×D4—1131no—
121C2×M16—2261no—
122#124—1131no—
123#124—1131no—
124#124—1131no—
125#124—2261no—
126#124—2261no—
127#124C2×D11311yescharacteristic
128C2×C22⋊C4—2261no—
129C2×C22⋊C4—2261no—
130C2×C42—1131no—
131C4⋊C8—2261no—
132C22⋊C8—2261no—
133#97—1131no—
134#97—1131no—
135#97C2×D11311yescharacteristic, complemented
136#97C2×D11311yescharacteristic, complemented
137C4×C8—2261no—
138C24—2261no—
139C2×Q8—1131no—
140C2×Q8—4522no—
141C2×Q8—2261no—
142C2×Q8C4×D11311yescharacteristic
143C2×D4—1131no—
144C2×D4—4522no—
145C2×D4—2261no—
146C2×D4C4×D11311yescharacteristic
147C22×C4—1131no—
148C22×C4—1131no—
149C22×C4—1131no—
150C22×C4—2261no—
151M16—2264no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—2261no—
155C2×C8—2261no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—2261no—
159C22⋊C4—2261no—
160C22⋊C4—2261no—
161C22⋊C4—2261no—
162C22⋊C4—2261no—
163C22⋊C4—2261no—
164C42—1131no—
165C42—1131no—
166C42—1131no—
167C42C22×D11311yescharacteristic
168C23—21no—
169C23—1131no—
170C23—4522no—
171C23—4522no—
172C23—4522no—
173C23—2261no—
174Q8—41no—
175Q8—4521no—
176Q8—4522no—
177D4—41no—
178D4—4521no—
179D4—4522no—
180C2×C4—21no—
181C2×C4—1131no—
182C2×C4—1131no—
183C2×C4—1131no—
184C2×C4—4521no—
185C2×C4—4522no—
186C2×C4—2262no—
187C2×C4—2262no—
188C2×C4—2261no—
189C2×C4C2×C4×D11311yescharacteristic
190C2×C4D4×D11311yescharacteristic
191C2×C4D4×D11311yescharacteristic
192C8—22no—
193C8—41no—
194C8—4521no—
195C8—2262no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—1132no—
200C22—9044no—
201C22—4521no—
202C22—4521no—
203C22—4521no—
204C22—2261no—
205C22—2261no—
206C22C22⋊C4×D11311yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—1132no—
212C4—4521no—
213C4—2261no—
214C4—2261no—
215C2—81no—
216C2—9041no—
217C2—2262no—
218C2#100×D11311yescharacteristic
219C2#104×D11311yescharacteristic
220C2#2029861311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#329×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC2×D4×D113C4
cosocleC42×C113C23
hypercenter#329D113
hypocenterC113#1527
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20298653C2semidirect
3. #20298550C2semidirect
4. #20298338C2semidirect
5. #20298337C2semidirect
6. #20298337C2semidirect
7. #329×C113C2semidirect
21. #16813533C22semidirect
22. #16813533C22semidirect
25. #97×C113C22semidirect
26. #97×C113C22semidirect
111. C113#1527semidirect
118. #329D113semidirect
135. #97C2×D113semidirect
136. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#124×D1132
#202986532
#202985502
#202983382
#202983372
#329×C1132
#1527113