Finite Group Databasebeta

← #28402036

Subgroups — #28402036

Order 14464.

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

normal subgroups only

This group has 346 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#20299221C212yesmaximal, complemented
2#20298891C212yesmaximal, complemented
3#20298877C212yesmaximal, complemented
4#20298846C212yesmaximal, complemented
5#20298834C211yesmaximal, characteristic
6#20298822C212yesmaximal, complemented
7#20298816C212yesmaximal, complemented
8#20298624C211yesmaximal, characteristic, complemented
9#467×C113C211yesmaximal, characteristic, complemented
10C2×#14268634C2212yes—
11C2×D904C2211yescharacteristic
12C2×#14268631C2211yescharacteristic
13#16813621C2212yes—
14#16813617—22no—
15#16813611C2212yes—
16#16813608—22no—
17#16813604—22no—
18#16813602—22no—
19#16813596C2212yes—
20Q8×Dic113C2212yes—
21#16813584C2212yes—
22#16813581C2211yescharacteristic
23#16813556C2211yescharacteristic
24#16813555C2212yes—
25#16813551C2212yes—
26#16813551C2212yes—
27#16813546C2212yes—
28#16813544C2212yes—
29#16813542C2212yes—
30C2×Q16×C113C2211yescharacteristic
31C22×C8×C113C2211yescharacteristic
32C22⋊Q8×C113C2212yes—
33#107×C113C2211yescharacteristic
34#103×C113C2212yes—
35C2×Dic226—22no—
36C2×D452C2312yes—
37C2×C22⋊D113—22no—
38C2×C4×D113—22no—
39#14268634—42no—
40D904—41no—
41#14268631—41no—
42C2×#11744751C2312yes—
43C4⋊Dic113—22no—
44C4⋊Dic113D411yescharacteristic
45C4⋊Dic113D411yescharacteristic
46C4⋊Dic113C2312yes—
47#14268626—22no—
48C22⋊Dic113D412yes—
49#14268624—22no—
50#14268624—22no—
51#14268624—22no—
52#14268624—22no—
53C4×Dic113—22no—
54C4×Dic113C2312yes—
55C2×Q8×C113C2312yes—
56C22×C4×C113C2311yescharacteristic
57Q16×C113—41no—
58C2×C8×C113—41no—
59C2×C8×C113C2311yescharacteristic
60C2×C8×C113C2311yescharacteristic
61C4⋊C4×C113—22no—
62C4⋊C4×C113C2312yes—
63C22⋊C4×C113—22no—
64C23×C113C2×D411yescharacteristic
65C22×D113—22no—
66Q8×C113—22no—
67Q8×C113—22no—
68C2×C4×C113—21no—
69C2×C4×C113—21no—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2411yescharacteristic
74C22⋊D113—82no—
75C2×Dic113—22no—
76C2×Dic113C2×D412yes—
77C2×Dic113C2×D412yes—
78D452—22no—
79D452—22no—
80C4×D113—82no—
81Dic226—82no—
82C8×C113—21no—
83C8×C113—21no—
84#11744751—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—42no—
94C4×C113—42no—
95C4×C113H(5,𝔽2)11yescharacteristic
96C4×C1132−1+411yescharacteristic
97Dic113—22no—
98Dic113—22no—
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#467D11311yescharacteristic, complemented
112#466—1131no—
113#464—1132no—
114#463—1132no—
115#424—1131no—
116C2×Q16C2×D11311yescharacteristic
117C2×SD16—1132no—
118C2×D8—1131no—
119C2×M16—1131no—
120C22×C8C2×D11311yescharacteristic
121C4⋊Q8—1132no—
122#126—2262no—
123#124—1132no—
124#124—2262no—
125#123—2262no—
126C22⋊Q8—2262no—
127C22⋊Q8C2×D11312yes—
128#121—1132no—
129C4×Q8—1132no—
130C4×D4—1132no—
131#117—1131no—
132#107—1131no—
133#107—1132no—
134#107C2×D11311yescharacteristic
135C4⋊C8—1132no—
136C4⋊C8—1132no—
137#103—1132no—
138#103C2×D11312yes—
139#102—1132no—
140#102—1132no—
141C2×Q8—2262no—
142C2×Q8C22×D11312yes—
143C2×D4—1132no—
144C2×D4—2262no—
145C22×C4—2262no—
146C22×C4C22×D11311yescharacteristic
147Q16—41no—
148SD16—4522no—
149D8—4521no—
150M16—4521no—
151C2×C8—41no—
152C2×C8—1132no—
153C2×C8C22×D11311yescharacteristic
154C2×C8C22×D11311yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—1131no—
157C4⋊C4—1131no—
158C4⋊C4—1132no—
159C4⋊C4—2262no—
160C4⋊C4—2262no—
161C4⋊C4C22×D11312yes—
162C22⋊C4—22no—
163C22⋊C4—1132no—
164C22⋊C4—2262no—
165C22⋊C4—2262no—
166C22⋊C4—2262no—
167C22⋊C4—2262no—
168C42—1132no—
169C42—2262no—
170C23—2262no—
171C23D4×D11311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—9042no—
175D4—9042no—
176D4—2262no—
177D4—2262no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—1132no—
183C2×C4—1132no—
184C2×C4—9042no—
185C2×C4—2262no—
186C2×C4D4×D11311yescharacteristic
187C2×C4C23×D11311yescharacteristic
188C8—21no—
189C8—21no—
190C8—2262no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—4522no—
195C22—4522no—
196C22—4522no—
197C22C2×D4×D11311yescharacteristic
198C4—21no—
199C4—42no—
200C4—42no—
201C4—4522no—
202C4—2262no—
203C4—2262no—
204C4#1681366711yescharacteristic
205C4#1681366911yescharacteristic
206C2—41no—
207C2—9042no—
208C2#2029917511yescharacteristic
209C2#2029940011yescharacteristic
210C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#467×C113C2
socleC22×C113C22×D4
prime radical#20298834C2
hypercenter#467D113
hypocenterC113#3262
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #20299221C2semidirect
2. #20298891C2semidirect
3. #20298877C2semidirect
4. #20298846C2semidirect
6. #20298822C2semidirect
7. #20298816C2semidirect
8. #20298624C2semidirect
9. #467×C113C2semidirect
106. C113#3262semidirect
111. #467D113semidirect

Maximal subgroups

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

subgroupindex
#202992212
#202988912
#202988772
#202988462
#202988342
#202988222
#202988162
#202986242
#467×C1132
#3262113