Finite Group Databasebeta

← #28402045

Subgroups — #28402045

Order 14464.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299219C212yesmaximal, complemented
2#20298889C212yesmaximal, complemented
3#20298884C212yesmaximal, complemented
4#20298856C211yesmaximal, characteristic, complemented
5#20298851C211yesmaximal, characteristic
6#20298827C212yesmaximal, complemented
7#20298821C212yesmaximal, complemented
8#20298814C212yesmaximal, complemented
9#424×C113C211yesmaximal, characteristic, complemented
10C2×Dic452C2211yescharacteristic
11C2×#14268636C2212yes—
12C2×D904C2211yescharacteristic
13#16813622C2212yes—
14#16813617—22no—
15#16813610C2212yes—
16#16813608—22no—
17#16813604—22no—
18#16813601C2212yes—
19#16813600—22no—
20#16813596C2212yes—
21C4×Dic226C2212yes—
22C4×D452C2212yes—
23#16813554C2212yes—
24#16813554C2211yescharacteristic
25#16813554C2211yescharacteristic
26#16813547C2212yes—
27#16813547C2212yes—
28#16813544C2212yes—
29#16813544C2212yes—
30C2×M16×C113C2211yescharacteristic
31C22×C8×C113C2211yescharacteristic
32#117×C113C2211yescharacteristic
33C4⋊C8×C113C2212yes—
34C4⋊C8×C113C2212yes—
35C2×Dic226—22no—
36C2×Dic226C2312yes—
37C2×D452C2312yes—
38C2×C22⋊D113—22no—
39C2×C4×D113—22no—
40Dic452—41no—
41#14268636—42no—
42D904—41no—
43C4⋊Dic113—22no—
44C4⋊Dic113C2312yes—
45C4⋊Dic113C2312yes—
46#14268626—22no—
47#14268626—22no—
48C22⋊Dic113—22no—
49#14268624—22no—
50#14268624—22no—
51#14268624—22no—
52#14268624—22no—
53C4×Dic113—22no—
54C22×C4×C113C2311yescharacteristic
55M16×C113—41no—
56C2×C8×C113—41no—
57C2×C8×C113C2311yescharacteristic
58C2×C8×C113C2312yes—
59C2×C8×C113C2311yescharacteristic
60C4⋊C4×C113D412yes—
61C22⋊C4×C113D411yescharacteristic
62C22⋊C4×C113D411yescharacteristic
63C42×C113C2312yes—
64C23×C113C2×D411yescharacteristic
65C22×D113—22no—
66C2×C4×C113—21no—
67C2×C4×C113—21no—
68C2×C4×C113C2×D412yes—
69C2×C4×C113C2×D412yes—
70C2×C4×C113C2×D411yescharacteristic
71C2×C4×C113C2411yescharacteristic
72C22⋊D113—82no—
73C2×Dic113—22no—
74C2×Dic113—22no—
75C2×Dic113—22no—
76D452—22no—
77D452—22no—
78C4×D113—82no—
79Dic226—22no—
80Dic226—22no—
81Dic226—82no—
82C8×C113—22no—
83C8×C113—21no—
84C8×C113—21no—
85C22×C113—21no—
86C22×C113—22no—
87C22×C113C22×D411yescharacteristic
88C2×D113—42no—
89C2×D113—42no—
90C2×D113—42no—
91C4×C113—21no—
92C4×C113—22no—
93C4×C113—22no—
94C4×C113H(5,𝔽2)11yescharacteristic
95C4×C1132−1+411yescharacteristic
96Dic113—42no—
97Dic113—42no—
98Dic113—42no—
99C2×C113—41no—
100C2×C113#53711yescharacteristic
101C2×C113#57712yes—
102D113—82no—
103#3263—1131nomaximal, Sylow
104C113#326311yescharacteristic, complemented, Sylow
105#542—1132no—
106#476—1132no—
107#475—1132no—
108#470—1131no—
109#469—1131no—
110#465—1132no—
111#464—1132no—
112#463—1132no—
113#424D11311yescharacteristic, complemented
114C2×Q16—1131no—
115C2×SD16—1132no—
116C2×D8—1131no—
117C2×M16C2×D11311yescharacteristic
118C22×C8C2×D11311yescharacteristic
119C4⋊Q8—1132no—
120#126—2262no—
121#124—1132no—
122#124—2262no—
123#123—2262no—
124C22⋊Q8—1132no—
125C22⋊Q8—2262no—
126#121—1132no—
127C4×Q8—1132no—
128C4×D4—1132no—
129#117C2×D11311yescharacteristic
130#106—1132no—
131#106—1131no—
132#106—1131no—
133C4⋊C8C2×D11312yes—
134C4⋊C8C2×D11312yes—
135#103—1132no—
136#103—1132no—
137#102—1132no—
138#102—1132no—
139C2×Q8—1132no—
140C2×Q8—2262no—
141C2×D4—1132no—
142C2×D4—2262no—
143C22×C4—2262no—
144C22×C4C22×D11311yescharacteristic
145Q16—4521no—
146SD16—4522no—
147D8—4521no—
148M16—41no—
149C2×C8—41no—
150C2×C8C22×D11311yescharacteristic
151C2×C8C22×D11312yes—
152C2×C8C22×D11311yescharacteristic
153C4⋊C4—1132no—
154C4⋊C4—1132no—
155C4⋊C4—2262no—
156C4⋊C4—2262no—
157C4⋊C4—2262no—
158C4⋊C4D45212yes—
159C22⋊C4—2262no—
160C22⋊C4—2262no—
161C22⋊C4—2262no—
162C22⋊C4—2262no—
163C22⋊C4—2262no—
164C22⋊C4D45211yescharacteristic
165C22⋊C4D45211yescharacteristic
166C42—2262no—
167C42C22×D11312yes—
168C23—2262no—
169C23C2×D45211yescharacteristic
170Q8—9042no—
171Q8—2262no—
172Q8—2262no—
173D4—9042no—
174D4—2262no—
175D4—2262no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—9042no—
179C2×C4—2262no—
180C2×C4—2262no—
181C2×C4—2262no—
182C2×C4C2×D45212yes—
183C2×C4C2×D45212yes—
184C2×C4C2×D45211yescharacteristic
185C2×C4C23×D11311yescharacteristic
186C8—22no—
187C8—21no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—4522no—
192C22—4522no—
193C22—4522no—
194C22C22×D45211yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—4522no—
199C4—4522no—
200C4—4522no—
201C4#1681366711yescharacteristic
202C4#1681367011yescharacteristic
203C2—41no—
204C2—9042no—
205C2#2029917911yescharacteristic
206C2#2029941012yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#424×C113C2
socleC22×C113C22×D4
prime radical#20298851C2
hypercenter#424D113
hypocenterC113#3263
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #20299219C2semidirect
2. #20298889C2semidirect
3. #20298884C2semidirect
4. #20298856C2semidirect
6. #20298827C2semidirect
7. #20298821C2semidirect
8. #20298814C2semidirect
9. #424×C113C2semidirect
104. C113#3263semidirect
113. #424D113semidirect

Maximal subgroups

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

subgroupindex
#202992192
#202988892
#202988842
#202988562
#202988512
#202988272
#202988212
#202988142
#424×C1132
#3263113