Finite Group Databasebeta

← #28390499

Subgroups — #28390499

Order 14464.

584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#14268646C211yesmaximal, characteristic
2C2×#16813540C212yesmaximal, complemented
3C2×#16813539C211yesmaximal, characteristic, complemented
4#20298561C212yesmaximal, complemented
5C2×#100×C113C211yesmaximal, characteristic, complemented
6C2×#14268646—24no—
7C2×#14268646—24no—
8C2×#14268646—22no—
9C2×#14268646—22no—
10C22×Dic226C2211yescharacteristic
11C22×C22⋊D113C412yes—
12C23×Dic113C412yes—
13C22×C4×D113C2211yescharacteristic
14C2×#14268631C2212yes—
15#16813540—24no—
16#16813539—22no—
17#16813534—24no—
18C22×D4×C113C2211yescharacteristic
19C2×M16×C113C2212yes—
20#100×C113—22no—
21C23×D113C2×C411yescharacteristic
22#14268646—216no—
23#14268646—216no—
24C2×Dic226—22no—
25C2×Dic226—21no—
26C2×Dic226—21no—
27C2×Dic226D414yes—
28C2×C22⋊D113—24no—
29C2×C22⋊D113—24no—
30C2×C22⋊D113—24no—
31C22×Dic113—24no—
32C22×Dic113—24no—
33C22×Dic113—24no—
34C22×Dic113C2×C411yescharacteristic
35C22×Dic113C2×C412yes—
36C2×C4×D113—22no—
37C2×C4×D113—21no—
38C2×C4×D113—21no—
39C2×C4×D113D414yes—
40#14268631—22no—
41#14268631—22no—
42C2×#11744751—22no—
43C24×C113C2×C412yes—
44C2×D4×C113—22no—
45C2×D4×C113—22no—
46C2×D4×C113D412yes—
47C2×D4×C113D412yes—
48C22×C4×C113C2311yescharacteristic
49M16×C113—22no—
50M16×C113—22no—
51C2×C8×C113—22no—
52C23×C113—22no—
53C23×C113—22no—
54C23×C113—44no—
55C23×C113C22⋊C414yes—
56C23×C113C22×C411yescharacteristic
57C22×D113—21no—
58C22×D113—21no—
59C22×D113—42no—
60C22×D113C22⋊C412yes—
61D4×C113—24no—
62D4×C113—24no—
63C2×C4×C113C2×D412yes—
64C2×C4×C113C2×D412yes—
65C2×C4×C113C2×D411yescharacteristic
66C2×C4×C113C2×D411yescharacteristic
67C22⋊D113—216no—
68C2×Dic113—216no—
69C2×Dic113—21no—
70C2×Dic113—21no—
71C2×Dic113—22no—
72C2×Dic113—22no—
73C2×Dic113C22⋊C412yes—
74C2×Dic113C22⋊C414yes—
75C4×D113—24no—
76C4×D113—24no—
77Dic226—24no—
78Dic226—24no—
79C8×C113—42no—
80#11744751—42no—
81C22×C113—22no—
82C22×C113—24no—
83C22×C113—44no—
84C22×C113—44no—
85C22×C113—44no—
86C22×C113C2×C22⋊C411yescharacteristic
87C22×C113C2×C22⋊C411yescharacteristic
88C22×C113C2×C22⋊C411yescharacteristic
89C2×D113—22no—
90C2×D113—24no—
91C2×D113—42no—
92C2×D113—42no—
93C4×C113#12012yes—
94C4×C113#12012yes—
95Dic113—24no—
96Dic113—22no—
97C2×C113—21no—
98C2×C113—21no—
99C2×C113—44no—
100C2×C113#37911yescharacteristic
101C2×C113#41312yes—
102D113—42no—
103#1785—1131nomaximal, Sylow
104C113#178511yescharacteristic, complemented, Sylow
105C22×#41—1131no—
106C2×#101—1132no—
107C2×#100—1131no—
108C2×#100D11311yescharacteristic, complemented
109#407—1132no—
110C2×#41—2264no—
111C2×#41—2264no—
112C2×#41—2262no—
113C2×#41—2262no—
114C22×Q8—1131no—
115C22×D4—1132no—
116C22×D4C2×D11311yescharacteristic
117C23×C4—1131no—
118C23×C4—1132no—
119C2×M16—1132no—
120C2×M16C2×D11312yes—
121#101—2264no—
122#100—22no—
123#100—2262no—
124C22⋊C8—2264no—
125C24—1131no—
126C24C4×D11312yes—
127#41—22616no—
128#41—22616no—
129C2×Q8—1134no—
130C2×Q8—2262no—
131C2×Q8—2261no—
132C2×Q8—2261no—
133C2×D4—22no—
134C2×D4—22no—
135C2×D4—2264no—
136C2×D4—2264no—
137C2×D4—2264no—
138C2×D4D45212yes—
139C2×D4C22⋊D11312yes—
140C22×C4—1131no—
141C22×C4—1132no—
142C22×C4—1134no—
143C22×C4—2264no—
144C22×C4—2264no—
145C22×C4—2264no—
146C22×C4—2262no—
147C22×C4—2261no—
148C22×C4—2261no—
149C22×C4C22×D11311yescharacteristic
150M16—22no—
151M16—22no—
152M16—2262no—
153M16—2262no—
154C2×C8—22no—
155C2×C8—2262no—
156C23—22no—
157C23—22no—
158C23—44no—
159C23—1132no—
160C23—4522no—
161C23—2261no—
162C23—2261no—
163C23#1426862414yes—
164C23C2×C4×D11311yescharacteristic
165Q8—2264no—
166Q8—2264no—
167D4—24no—
168D4—24no—
169D4—22616no—
170C2×C4—1134no—
171C2×C4—1132no—
172C2×C4—22616no—
173C2×C4—2261no—
174C2×C4—2262no—
175C2×C4—2261no—
176C2×C4—2262no—
177C2×C4—2264no—
178C2×C4—2264no—
179C2×C4D4×D11312yes—
180C2×C4D4×D11312yes—
181C2×C4C2×C22⋊D11311yescharacteristic
182C2×C4C2×D45211yescharacteristic
183C8—42no—
184C8—4522no—
185C22—22no—
186C22—24no—
187C22—44no—
188C22—44no—
189C22—44no—
190C22—4522no—
191C22—4522no—
192C22—2264no—
193C22—2262no—
194C22C22⋊C4×D11311yescharacteristic
195C22C22⋊C4×D11311yescharacteristic
196C22C2×#1426862411yescharacteristic
197C4—2262no—
198C4—2264no—
199C4#1681359012yes—
200C4#1681359212yes—
201C2—21no—
202C2—21no—
203C2—44no—
204C2—4522no—
205C2#2029845311yescharacteristic
206C2#2029857912yes—
subgroupG/H
centerC22C22⋊C4×D113
commutatorC23×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#100×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×#14268646C2
cosocleC22×C4×C113C23
hypercenterC2×#100D113
hypocenterC113#1785
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×#16813540C2semidirect
3. C2×#16813539C2semidirect
4. #20298561C2semidirect
5. C2×#100×C113C2semidirect
104. C113#1785semidirect
108. C2×#100D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686462
C2×#168135402
C2×#168135392
#202985612
C2×#100×C1132
#1785113