Finite Group Databasebeta

← #28392225

Subgroups — #28392225

Order 14464.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#20299162C211yesmaximal, characteristic
2#20298572C211yesmaximal, characteristic, complemented
3#20298386C214yesmaximal, complemented
4#413×C113C211yesmaximal, characteristic, complemented
5C22×D452C411yescharacteristic, complemented
6#16813618—21no—
7#16813611—21no—
8#16813596—21no—
9#16813596—21no—
10#16813590C412yescomplemented
11#16813590C2212yes—
12#16813581—21no—
13#16813581C411yescharacteristic, complemented
14#16813537—21no—
15#16813537C2212yes—
16C2×#41×C113C2211yescharacteristic
17C2×M16×C113—21no—
18#101×C113—21no—
19#100×C113C2212yes—
20C23×D113C2×C412yes—
21C2×D452—21no—
22C2×D452—21no—
23C2×D452—41no—
24C2×D452—41no—
25C2×C22⋊D113—22no—
26C2×C22⋊D113—22no—
27C4⋊Dic113—21no—
28C4⋊Dic113—41no—
29C22⋊Dic113—22no—
30C22⋊Dic113C2×C412yes—
31#14268624—22no—
32#14268624—22no—
33C4×Dic113—21no—
34C4×Dic113—41no—
35#41×C113—41no—
36#41×C113—41no—
37C2×Q8×C113D411yescharacteristic
38C2×D4×C113C2×C411yescharacteristic
39C2×D4×C113D411yescharacteristic
40C2×D4×C113C2311yescharacteristic
41C22×C4×C113C2×C411yescharacteristic
42C22×C4×C113D411yescharacteristic
43C22×C4×C113D411yescharacteristic
44M16×C113—22no—
45M16×C113—41no—
46C2×C8×C113—41no—
47C23×C113C22⋊C411yescharacteristic
48C23×C113C22×C411yescharacteristic
49C23×C113C2×D411yescharacteristic
50C22×D113—22no—
51C22×D113—42no—
52C22×D113—82no—
53Q8×C113—41no—
54D4×C113—41no—
55D4×C113—41no—
56D4×C113—41no—
57C2×C4×C113—21no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—21no—
61C2×C4×C113—21no—
62C2×C4×C113—21no—
63C2×C4×C113C22⋊C411yescharacteristic
64C2×C4×C113C22⋊C411yescharacteristic
65C2×C4×C113C22⋊C411yescharacteristic
66C2×C4×C113C2×D411yescharacteristic
67C22⋊D113—82no—
68C22⋊D113—82no—
69C2×Dic113—22no—
70C2×Dic113—42no—
71D452—42no—
72D452—41no—
73D452—41no—
74C8×C113—42no—
75C22×C113—21no—
76C22×C113—21no—
77C22×C113—21no—
78C22×C113—41no—
79C22×C113—41no—
80C22×C113—41no—
81C22×C113C2×C22⋊C411yescharacteristic
82C2×D113—42no—
83C2×D113—42no—
84C2×D113—42no—
85C2×D113—84no—
86C4×C113—21no—
87C4×C113—21no—
88C4×C113—21no—
89C4×C113#9911yescharacteristic
90C4×C113#9911yescharacteristic
91Dic113—42no—
92Dic113—82no—
93C2×C113—21no—
94C2×C113—41no—
95C2×C113—41no—
96C2×C113—41no—
97C2×C113C2×#9911yescharacteristic
98D113—82no—
99#2122—1131nomaximal, Sylow
100C113#212211yescharacteristic, complemented, Sylow
101#535—1131no—
102#413D11311yescharacteristic, complemented
103#410—1131no—
104AΣL(1,𝔽16)—1134no—
105C2×#41C2×D11311yescharacteristic
106C22×D4—1131no—
107C2×M16—21no—
108#127—2261no—
109#124—2261no—
110#121—2261no—
111#121—2261no—
112#120—1132no—
113#120—1132no—
114#117—1131no—
115#117—2261no—
116#101—21no—
117#100C2×D11312yes—
118#99—1132no—
119#99—2261no—
120C24—1132no—
121#41—41no—
122#41—41no—
123C2×Q8C22⋊D11311yescharacteristic
124C2×D4—4521no—
125C2×D4—4521no—
126C2×D4—2262no—
127C2×D4—2262no—
128C2×D4—2261no—
129C2×D4—2261no—
130C2×D4C4×D11311yescharacteristic
131C2×D4D45211yescharacteristic
132C2×D4C22×D11311yescharacteristic
133C22×C4C4×D11311yescharacteristic
134C22×C4D45211yescharacteristic
135C22×C4C22⋊D11311yescharacteristic
136M16—22no—
137M16—41no—
138C2×C8—41no—
139C4⋊C4—4521no—
140C4⋊C4—2261no—
141C22⋊C4—1132no—
142C22⋊C4—2262no—
143C22⋊C4—2262no—
144C22⋊C4—2262no—
145C42—4521no—
146C42—2261no—
147C23—9042no—
148C23—4522no—
149C23—2262no—
150C23#1426862411yescharacteristic
151C23C2×C4×D11311yescharacteristic
152C23C2×D45211yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—9042no—
158D4—9042no—
159D4—4522no—
160D4—4521no—
161D4—4521no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—4522no—
169C2×C4—2262no—
170C2×C4#1426862411yescharacteristic
171C2×C4#1426862411yescharacteristic
172C2×C4#1426862411yescharacteristic
173C2×C4C2×C22⋊D11311yescharacteristic
174C8—42no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—9044no—
182C22—4522no—
183C22—4522no—
184C22—4522no—
185C22C2×#1426862411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—9042no—
190C4—4522no—
191C4#1681353611yescharacteristic
192C4#1681353611yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—9042no—
198C2C2×#1681353611yescharacteristic
subgroupG/H
centerC2C2×#16813536
commutatorC23×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#413×C113C2
socleC2×C113C2×#99
prime radical#20299162C2
cosocleC2×D4×C113C23
hypercenter#413D113
hypocenterC113#2122
LCSG ▷ C23×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #20298572C2semidirect
3. #20298386C2semidirect
4. #413×C113C2semidirect
5. C22×D452C4semidirect
10. #16813590C4semidirect
13. #16813581C4semidirect
100. C113#2122semidirect
102. #413D113semidirect

Maximal subgroups

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

subgroupindex
#202991622
#202985722
#202983862
#413×C1132
#2122113