Finite Group Databasebeta

← #28401196

Subgroups — #28401196

Order 14464.

362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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#20299210C211yesmaximal, characteristic, complemented
2#20298997C211yesmaximal, characteristic, complemented
3#20298970C211yesmaximal, characteristic, complemented
4#20298968C211yesmaximal, characteristic, complemented
5#20298962C211yesmaximal, characteristic, complemented
6#20298842C212yesmaximal, complemented
7#20298825C212yesmaximal, complemented
8#20298698C212yesmaximal, complemented
9C4×#14268635C212yesmaximal, complemented
10#20298554C211yesmaximal, characteristic, complemented
11#540×C113C211yesmaximal, characteristic
12C2×#14268635C2212yes—
13C2×#14268635C2212yes—
14C2×#14268631C2211yescharacteristic
15C22×#11744751C2211yescharacteristic
16#16813622C2211yescharacteristic
17#16813615—22no—
18#16813614C2211yescharacteristic
19#16813612—22no—
20#16813601C2212yes—
21C4×Dic226C2212yes—
22#16813555C2212yes—
23#16813553C2212yes—
24#16813545C2212yes—
25#16813545C2212yes—
26#16813543C2212yes—
27#16813543C2212yes—
28#16813533C2211yescharacteristic
29#16813533C2211yescharacteristic
30C4×#11744751C2211yescharacteristic
31C4×#11744751C2211yescharacteristic
32#127×C113C2211yescharacteristic
33#125×C113C2211yescharacteristic
34#123×C113—22no—
35#121×C113—22no—
36#121×C113C2212yes—
37C4×D4×C113C2212yes—
38#117×C113C2211yescharacteristic
39C2×Dic226C2312yes—
40#14268635—24no—
41#14268635—24no—
42#14268631—22no—
43C2×#11744751—22no—
44C2×#11744751C2311yescharacteristic
45C2×#11744751C2311yescharacteristic
46C2×#11744751C2311yescharacteristic
47C2×#11744751C2311yescharacteristic
48C4⋊Dic113—22no—
49C4⋊Dic113C2312yes—
50#14268626—22no—
51#14268626—22no—
52#14268626—22no—
53C22⋊Dic113—22no—
54C4×Dic113—22no—
55C2×D4×C113—22no—
56C2×D4×C113—22no—
57C2×D4×C113C2312yes—
58C22×C4×C113—22no—
59C22×C4×C113C2311yescharacteristic
60C4⋊C4×C113—22no—
61C4⋊C4×C113D412yes—
62C4⋊C4×C113C2312yes—
63C22⋊C4×C113—22no—
64C22⋊C4×C113—22no—
65C22⋊C4×C113D412yes—
66C42×C113C2311yescharacteristic
67C42×C113C2311yescharacteristic
68C23×C113—22no—
69C23×C113C2×D411yescharacteristic
70D4×C113—22no—
71D4×C113—22no—
72D4×C113—82no—
73D4×C113—82no—
74C2×C4×C113—21no—
75C2×C4×C113—21no—
76C2×C4×C113—22no—
77C2×C4×C113—82no—
78C2×C4×C113C2×D412yes—
79C2×C4×C113C2×D412yes—
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2411yescharacteristic
82C2×Dic113—22no—
83C2×Dic113—22no—
84Dic226—22no—
85Dic226—22no—
86#11744751—21no—
87#11744751—21no—
88#11744751#4112yes—
89#11744751#4112yes—
90C22×C113—21no—
91C22×C113—22no—
92C22×C113—42no—
93C22×C113—42no—
94C22×C113—42no—
95C22×C113C22×D411yescharacteristic
96C4×C113—21no—
97C4×C113—22no—
98C4×C113—22no—
99C4×C113—42no—
100C4×C113C2×#4111yescharacteristic
101C4×C113C2×#4111yescharacteristic
102Dic113—42no—
103Dic113—42no—
104C2×C113—41no—
105C2×C113—82no—
106C2×C113#53211yescharacteristic
107C2×C113#57712yes—
108#3174—1131nomaximal, Sylow
109C113#317411yescharacteristic, complemented, Sylow
110#541—1131no—
111#540D11311yescharacteristic
112#499—1131no—
113#492—1131no—
114#491—1131no—
115#490—1131no—
116#468—1132no—
117#465—1132no—
118#440—1132no—
119C4×SD16—1132no—
120#405—1131no—
121C2×SD16—1132no—
122C2×SD16—1132no—
123C2×M16—1131no—
124C22×C8—1131no—
125C4⋊Q8—1131no—
126#127C2×D11311yescharacteristic
127#126—2262no—
128#125—1131no—
129#125—2262no—
130#125C2×D11311yescharacteristic
131#123—22no—
132C22⋊Q8—1132no—
133#121—22no—
134#121C2×D11312yes—
135C4×Q8—1132no—
136C4×D4C2×D11312yes—
137#117C2×D11311yescharacteristic
138#107—1132no—
139#106—1132no—
140#103—1132no—
141#103—1132no—
142#102—1132no—
143#102—1132no—
144#97—1131no—
145#97—1131no—
146C4×C8—1131no—
147C4×C8—1131no—
148C2×Q8—1132no—
149C2×D4—22no—
150C2×D4—22no—
151C2×D4C22×D11312yes—
152C22×C4—22no—
153C22×C4C22×D11311yescharacteristic
154SD16—2264no—
155SD16—2264no—
156M16—2262no—
157C2×C8—1131no—
158C2×C8—1131no—
159C2×C8—1131no—
160C2×C8—1131no—
161C2×C8—2262no—
162C4⋊C4—22no—
163C4⋊C4—1132no—
164C4⋊C4—2262no—
165C4⋊C4—2262no—
166C4⋊C4—2262no—
167C4⋊C4—2262no—
168C4⋊C4C22⋊D11312yes—
169C4⋊C4C22×D11312yes—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—2262no—
173C22⋊C4C22⋊D11312yes—
174C42—2262no—
175C42C22×D11311yescharacteristic
176C42C22×D11311yescharacteristic
177C23—22no—
178C23C2×C22⋊D11311yescharacteristic
179Q8—2262no—
180Q8—2262no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—82no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—2262no—
190C2×C4—2262no—
191C2×C4C2×C22⋊D11312yes—
192C2×C4C2×C22⋊D11312yes—
193C2×C4C2×C22⋊D11311yescharacteristic
194C2×C4C23×D11311yescharacteristic
195C8—1132no—
196C8—1132no—
197C8—2261no—
198C8—2261no—
199C22—21no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22C22×C22⋊D11311yescharacteristic
205C4—21no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—4522no—
210C4—4522no—
211C4#41×D11311yescharacteristic
212C4#41×D11311yescharacteristic
213C2—41no—
214C2—82no—
215C2#2029914411yescharacteristic
216C2#2029940912yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#540×C113C2
socleC22×C113C22×D4
hypercenter#540D113
hypocenterC113#3174
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20299210C2semidirect
2. #20298997C2semidirect
3. #20298970C2semidirect
4. #20298968C2semidirect
5. #20298962C2semidirect
6. #20298842C2semidirect
7. #20298825C2semidirect
8. #20298698C2semidirect
9. C4×#14268635C2semidirect
10. #20298554C2semidirect
109. C113#3174semidirect

Maximal subgroups

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

subgroupindex
#202992102
#202989972
#202989702
#202989682
#202989622
#202988422
#202988252
#202986982
C4×#142686352
#202985542
#540×C1132
#3174113