Finite Group Databasebeta

← #28402029

Subgroups — #28402029

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#20299215C212yesmaximal, complemented
2#20298892C212yesmaximal, complemented
3#20298876C212yesmaximal, complemented
4#20298842C212yesmaximal, complemented
5#20298839C211yesmaximal, characteristic, complemented
6#20298819C212yesmaximal, complemented
7#20298811C212yesmaximal, complemented
8#20298624C211yesmaximal, characteristic, complemented
9#466×C113C211yesmaximal, characteristic
10C2×Dic452C2211yescharacteristic
11C2×#14268635C2212yes—
12C2×#14268631C2211yescharacteristic
13#16813621C2212yes—
14#16813615—22no—
15#16813609—22no—
16#16813609C2212yes—
17#16813603—22no—
18#16813601C2212yes—
19#16813599—22no—
20#16813587C2212yes—
21D4×Dic113C2212yes—
22#16813581C2211yescharacteristic
23#16813556C2211yescharacteristic
24#16813555C2212yes—
25#16813551C2212yes—
26#16813551C2212yes—
27#16813547C2212yes—
28#16813545C2212yes—
29#16813543C2212yes—
30C2×D8×C113C2211yescharacteristic
31C22×C8×C113C2211yescharacteristic
32#121×C113C2212yes—
33#107×C113C2211yescharacteristic
34#102×C113C2212yes—
35C2×Dic226—22no—
36C2×Dic226C2312yes—
37C22×Dic113—22no—
38Dic452—41no—
39#14268635—42no—
40#14268631—41no—
41C2×#11744751C2312yes—
42C4⋊Dic113D411yescharacteristic
43C4⋊Dic113D411yescharacteristic
44C4⋊Dic113C2312yes—
45#14268626—22no—
46#14268626—22no—
47#14268626—22no—
48C22⋊Dic113—22no—
49C22⋊Dic113—22no—
50C22⋊Dic113—22no—
51C22⋊Dic113—22no—
52C22⋊Dic113D412yes—
53C4×Dic113—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
66D4×C113—22no—
67D4×C113—22no—
68D4×C113—82no—
69C2×C4×C113—21no—
70C2×C4×C113—21no—
71C2×C4×C113—22no—
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2411yescharacteristic
74C2×Dic113—22no—
75C2×Dic113—22no—
76C2×Dic113—82no—
77C2×Dic113C2×D412yes—
78C2×Dic113C2×D412yes—
79Dic226—22no—
80Dic226—22no—
81Dic226—82no—
82C8×C113—21no—
83C8×C113—21no—
84#11744751—22no—
85C22×C113—21no—
86C22×C113—21no—
87C22×C113—21no—
88C22×C113—42no—
89C22×C113—42no—
90C22×C113—42no—
91C22×C113C22×D411yescharacteristic
92C4×C113—21no—
93C4×C113—42no—
94C4×C113H(5,𝔽2)11yescharacteristic
95C4×C1132−1+411yescharacteristic
96Dic113—22no—
97Dic113—22no—
98Dic113—42no—
99Dic113—42no—
100C2×C113—41no—
101C2×C113—82no—
102C2×C113#53711yescharacteristic
103C2×C113#57611yescharacteristic
104C2×C113#57811yescharacteristic
105#3262—1131nomaximal, Sylow
106C113#326211yescharacteristic, complemented, Sylow
107#542—1132no—
108#477—1132no—
109#474—1132no—
110#468—1132no—
111#467—1131no—
112#466D11311yescharacteristic
113#464—1132no—
114#463—1132no—
115#424—1131no—
116C2×Q16—1131no—
117C2×SD16—1132no—
118C2×D8C2×D11311yescharacteristic
119C2×M16—1131no—
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#121C2×D11312yes—
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#103—1132no—
139#102—1132no—
140#102C2×D11312yes—
141C2×Q8—1132no—
142C2×Q8—2262no—
143C2×D4—22no—
144C2×D4C22×D11312yes—
145C22×C4—2262no—
146C22×C4C22×D11311yescharacteristic
147Q16—4521no—
148SD16—4522no—
149D8—41no—
150M16—4521no—
151C2×C8—41no—
152C2×C8—1132no—
153C2×C8C22×D11311yescharacteristic
154C2×C8C22×D11311yescharacteristic
155C4⋊C4—1131no—
156C4⋊C4—1131no—
157C4⋊C4—1132no—
158C4⋊C4—2262no—
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—22no—
171C23D4×D11311yescharacteristic
172Q8—9042no—
173Q8—2262no—
174Q8—2262no—
175D4—22no—
176D4—22no—
177D4—82no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—1132no—
182C2×C4—1132no—
183C2×C4—9042no—
184C2×C4—2262no—
185C2×C4—2262no—
186C2×C4D4×D11311yescharacteristic
187C2×C4C23×D11311yescharacteristic
188C8—21no—
189C8—21no—
190C8—2262no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C2×D4×D11311yescharacteristic
198C4—21no—
199C4—42no—
200C4—4522no—
201C4—4522no—
202C4—2262no—
203C4—2262no—
204C4#1681366711yescharacteristic
205C4#1681366911yescharacteristic
206C2—41no—
207C2—82no—
208C2#2029917511yescharacteristic
209C2#2029939911yescharacteristic
210C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radical#466×C113C2
socleC22×C113C22×D4
hypercenter#466D113
hypocenterC113#3262
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. #20299215C2semidirect
2. #20298892C2semidirect
3. #20298876C2semidirect
4. #20298842C2semidirect
5. #20298839C2semidirect
6. #20298819C2semidirect
7. #20298811C2semidirect
8. #20298624C2semidirect
106. C113#3262semidirect

Maximal subgroups

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

subgroupindex
#202992152
#202988922
#202988762
#202988422
#202988392
#202988192
#202988112
#202986242
#466×C1132
#3262113