Finite Group Databasebeta

← #28402035

Subgroups — #28402035

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#20298894C212yesmaximal, complemented
3#20298879C212yesmaximal, complemented
4#20298844C212yesmaximal, complemented
5#20298839C211yesmaximal, characteristic, complemented
6#20298834C211yesmaximal, characteristic
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#16813556C2211yescharacteristic
24#16813556C2211yescharacteristic
25#16813556C2212yes—
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×C113D411yescharacteristic
61C4⋊C4×C113D411yescharacteristic
62C22⋊C4×C113D412yes—
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—21no—
83C8×C113—21no—
84C8×C113—22no—
85C22×C113—21no—
86C22×C113—21no—
87C22×C113—21no—
88C22×C113C22×D411yescharacteristic
89C2×D113—42no—
90C2×D113—42no—
91C2×D113—42no—
92C4×C113—21no—
93C4×C113—22no—
94C4×C113—22no—
95C4×C113H(5,𝔽2)11yescharacteristic
96C4×C1132−1+411yescharacteristic
97Dic113—42no—
98Dic113—42no—
99Dic113—42no—
100C2×C113—41no—
101C2×C113#53711yescharacteristic
102C2×C113#57611yescharacteristic
103C2×C113#57811yescharacteristic
104D113—82no—
105#3262—1131nomaximal, Sylow
106C113#326211yescharacteristic, complemented, Sylow
107#542—1132no—
108#477—1132no—
109#474—1132no—
110#468—1132no—
111#467—1131no—
112#466—1131no—
113#464—1132no—
114#463—1132no—
115#424D11311yescharacteristic, complemented
116C2×Q16—1131no—
117C2×SD16—1132no—
118C2×D8—1131no—
119C2×M16C2×D11311yescharacteristic
120C22×C8C2×D11311yescharacteristic
121C4⋊Q8—1132no—
122#126—2262no—
123#124—1132no—
124#124—2262no—
125#123—2262no—
126C22⋊Q8—1132no—
127C22⋊Q8—2262no—
128#121—1132no—
129C4×Q8—1132no—
130C4×D4—1132no—
131#117C2×D11311yescharacteristic
132#107—1131no—
133#107—1131no—
134#107—1132no—
135C4⋊C8C2×D11312yes—
136C4⋊C8C2×D11312yes—
137#103—1132no—
138#103—1132no—
139#102—1132no—
140#102—1132no—
141C2×Q8—1132no—
142C2×Q8—2262no—
143C2×D4—1132no—
144C2×D4—2262no—
145C22×C4—2262no—
146C22×C4C22×D11311yescharacteristic
147Q16—4521no—
148SD16—4522no—
149D8—4521no—
150M16—41no—
151C2×C8—41no—
152C2×C8C22×D11311yescharacteristic
153C2×C8C22×D11312yes—
154C2×C8C22×D11311yescharacteristic
155C4⋊C4—1132no—
156C4⋊C4—1132no—
157C4⋊C4—2262no—
158C4⋊C4—2262no—
159C4⋊C4—2262no—
160C4⋊C4D45211yescharacteristic
161C4⋊C4D45211yescharacteristic
162C22⋊C4—2262no—
163C22⋊C4—2262no—
164C22⋊C4—2262no—
165C22⋊C4—2262no—
166C22⋊C4—2262no—
167C22⋊C4D45212yes—
168C42—2262no—
169C42C22×D11312yes—
170C23—2262no—
171C23C2×D45211yescharacteristic
172Q8—9042no—
173Q8—2262no—
174Q8—2262no—
175D4—9042no—
176D4—2262no—
177D4—2262no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—9042no—
181C2×C4—2262no—
182C2×C4—2262no—
183C2×C4—2262no—
184C2×C4C2×D45212yes—
185C2×C4C2×D45212yes—
186C2×C4C2×D45211yescharacteristic
187C2×C4C23×D11311yescharacteristic
188C8—21no—
189C8—21no—
190C8—22no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—4522no—
195C22—4522no—
196C22—4522no—
197C22C22×D45211yescharacteristic
198C4—22no—
199C4—22no—
200C4—21no—
201C4—4522no—
202C4—4522no—
203C4—4522no—
204C4#1681366711yescharacteristic
205C4#1681367011yescharacteristic
206C2—41no—
207C2—9042no—
208C2#2029917911yescharacteristic
209C2#2029940311yescharacteristic
210C2#2029941511yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#424×C113C2
socleC22×C113C22×D4
prime radical#20298834C2
hypercenter#424D113
hypocenterC113#3262
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. #20298894C2semidirect
3. #20298879C2semidirect
4. #20298844C2semidirect
5. #20298839C2semidirect
7. #20298821C2semidirect
8. #20298814C2semidirect
9. #424×C113C2semidirect
106. C113#3262semidirect
115. #424D113semidirect

Maximal subgroups

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

subgroupindex
#202992192
#202988942
#202988792
#202988442
#202988392
#202988342
#202988212
#202988142
#424×C1132
#3262113