Finite Group Databasebeta

← #28402008

Subgroups — #28402008

Order 14464.

370 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299201C212yesmaximal, complemented
2#20298901C212yesmaximal, complemented
3#20298896C212yesmaximal, complemented
4#20298849C212yesmaximal, complemented
5#20298834C211yesmaximal, characteristic, complemented
6#20298792C212yesmaximal, complemented
7#20298791C212yesmaximal, complemented
8#20298624C211yesmaximal, characteristic, complemented
9#466×C113C211yesmaximal, characteristic, complemented
10C2×D904C2211yescharacteristic
11C2×#14268632C2212yes—
12C2×#14268631C2211yescharacteristic
13#16813618C2212yes—
14#16813613C2212yes—
15#16813606—22no—
16#16813604—22no—
17#16813596C2212yes—
18#16813594—22no—
19#16813593—22no—
20D4×Dic113C2212yes—
21#16813584C2212yes—
22#16813581C2211yescharacteristic
23#16813556C2211yescharacteristic
24#16813553C2212yes—
25#16813551C2212yes—
26#16813551C2212yes—
27#16813544C2212yes—
28#16813543C2212yes—
29#16813542C2212yes—
30C2×D8×C113C2211yescharacteristic
31C22×C8×C113C2211yescharacteristic
32#121×C113C2212yes—
33#107×C113C2211yescharacteristic
34#102×C113C2212yes—
35C2×D452C2312yes—
36C2×C22⋊D113—22no—
37C2×C22⋊D113—22no—
38C2×C22⋊D113—22no—
39C22×Dic113—22no—
40C2×C4×D113—22no—
41D904—41no—
42#14268632—42no—
43#14268631—41no—
44C2×#11744751C2312yes—
45C4⋊Dic113—22no—
46C4⋊Dic113D411yescharacteristic
47C4⋊Dic113D411yescharacteristic
48C4⋊Dic113C2312yes—
49#14268626—22no—
50C22⋊Dic113—22no—
51C22⋊Dic113D412yes—
52#14268624—22no—
53#14268624—22no—
54C4×Dic113C2312yes—
55C2×D4×C113—22no—
56C2×D4×C113C2312yes—
57C22×C4×C113C2311yescharacteristic
58D8×C113—41no—
59C2×C8×C113—41no—
60C2×C8×C113C2311yescharacteristic
61C2×C8×C113C2311yescharacteristic
62C4⋊C4×C113C2312yes—
63C22⋊C4×C113—22no—
64C23×C113—22no—
65C23×C113C2×D411yescharacteristic
66C22×D113—22no—
67D4×C113—22no—
68D4×C113—22no—
69D4×C113—82no—
70C2×C4×C113—21no—
71C2×C4×C113—21no—
72C2×C4×C113—22no—
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113C2411yescharacteristic
75C22⋊D113—82no—
76C22⋊D113—82no—
77C22⋊D113—82no—
78C2×Dic113—22no—
79C2×Dic113—82no—
80C2×Dic113C2×D412yes—
81C2×Dic113C2×D412yes—
82D452—22no—
83D452—22no—
84C4×D113—82no—
85C8×C113—21no—
86C8×C113—21no—
87#11744751—22no—
88C22×C113—21no—
89C22×C113—21no—
90C22×C113—21no—
91C22×C113—42no—
92C22×C113—42no—
93C22×C113—42no—
94C22×C113C22×D411yescharacteristic
95C2×D113—42no—
96C2×D113—42no—
97C2×D113—42no—
98C4×C113—21no—
99C4×C113—42no—
100C4×C113H(5,𝔽2)11yescharacteristic
101C4×C1132−1+411yescharacteristic
102Dic113—22no—
103Dic113—22no—
104Dic113—42no—
105C2×C113—41no—
106C2×C113—82no—
107C2×C113#53711yescharacteristic
108C2×C113#57611yescharacteristic
109C2×C113#57611yescharacteristic
110D113—82no—
111#3259—1131nomaximal, Sylow
112C113#325911yescharacteristic, complemented, Sylow
113#540—1132no—
114#478—1132no—
115#478—1132no—
116#469—1132no—
117#466—1131no—
118#466D11311yescharacteristic, complemented
119#459—1132no—
120#459—1132no—
121#424—1131no—
122C2×D8—1132no—
123C2×D8—1131no—
124C2×D8C2×D11311yescharacteristic
125C2×M16—1131no—
126C22×C8C2×D11311yescharacteristic
127#127—1132no—
128#125—1132no—
129#123—2262no—
130#123—2262no—
131#121—1132no—
132#121—2262no—
133#121—2262no—
134#121C2×D11312yes—
135C4×D4—1132no—
136C4×D4—1132no—
137#117—1131no—
138#107—1131no—
139#107C2×D11311yescharacteristic
140#106—1132no—
141C4⋊C8—1132no—
142C4⋊C8—1132no—
143#102—1132no—
144#102—1132no—
145#102—1132no—
146#102C2×D11312yes—
147C2×D4—22no—
148C2×D4—1132no—
149C2×D4—2262no—
150C2×D4—2262no—
151C2×D4—2262no—
152C2×D4C22×D11312yes—
153C22×C4—2262no—
154C22×C4—2262no—
155C22×C4C22×D11311yescharacteristic
156D8—41no—
157D8—4521no—
158D8—4522no—
159M16—4521no—
160C2×C8—41no—
161C2×C8—1132no—
162C2×C8C22×D11311yescharacteristic
163C2×C8C22×D11311yescharacteristic
164C4⋊C4—1131no—
165C4⋊C4—1131no—
166C4⋊C4—1132no—
167C4⋊C4—2262no—
168C4⋊C4—2262no—
169C4⋊C4C22×D11312yes—
170C22⋊C4—22no—
171C22⋊C4—1132no—
172C22⋊C4—2262no—
173C22⋊C4—2262no—
174C22⋊C4—2262no—
175C42—1132no—
176C23—22no—
177C23—2262no—
178C23D4×D11311yescharacteristic
179D4—22no—
180D4—22no—
181D4—82no—
182D4—9042no—
183D4—9042no—
184D4—9042no—
185D4—2262no—
186D4—2262no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—1132no—
191C2×C4—1132no—
192C2×C4—9042no—
193C2×C4—9042no—
194C2×C4—2262no—
195C2×C4D4×D11311yescharacteristic
196C2×C4C23×D11311yescharacteristic
197C8—21no—
198C8—21no—
199C8—2262no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—4522no—
207C22—4522no—
208C22—4522no—
209C22C2×D4×D11311yescharacteristic
210C4—21no—
211C4—42no—
212C4—4522no—
213C4—2262no—
214C4—2262no—
215C4#1681366711yescharacteristic
216C4#1681366911yescharacteristic
217C2—41no—
218C2—82no—
219C2—9042no—
220C2#2029917511yescharacteristic
221C2#2029939911yescharacteristic
222C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#466×C113C2
socleC22×C113C22×D4
hypercenter#466D113
hypocenterC113#3259
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #20299201C2semidirect
2. #20298901C2semidirect
3. #20298896C2semidirect
4. #20298849C2semidirect
5. #20298834C2semidirect
6. #20298792C2semidirect
7. #20298791C2semidirect
8. #20298624C2semidirect
9. #466×C113C2semidirect
112. C113#3259semidirect
118. #466D113semidirect

Maximal subgroups

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

subgroupindex
#202992012
#202989012
#202988962
#202988492
#202988342
#202987922
#202987912
#202986242
#466×C1132
#3259113