Finite Group Databasebeta

← #28405667

Subgroups — #28405667

Order 14464.

232 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D113⋊#99C211yesmaximal, characteristic
2#20299550C211yesmaximal, characteristic
3#99×D113C211yesmaximal, characteristic
4C2×C4⋊#90673C411yescharacteristic, complemented
5C2×C22⋊#90673—21no—
6C2×C22⋊#90673—21no—
7C2×C22⋊#90673—21no—
8C2×C4×#90673C411yescharacteristic, complemented
9#16813681C412yescomplemented
10#16813680—21no—
11C2×D4×D113C2211yescharacteristic
12C22⋊C4×D113—21no—
13#16813537C411yescharacteristic, complemented
14#16813536—21no—
15#99×C113C411yescharacteristic, complemented
16C22×#90673—21no—
17C22×#90673—21no—
18C22×#90673—41no—
19C4⋊#90673—41no—
20C22⋊#90673—22no—
21C22⋊#90673—42no—
22C22⋊#90673—42no—
23C22⋊#90673—41no—
24C4×#90673—41no—
25C23×D113D411yescharacteristic
26C23×D113D411yescharacteristic
27C2×D452C2×C411yescharacteristic
28C2×C22⋊D113D411yescharacteristic
29C2×C22⋊D113Q811yescharacteristic
30D4×D113—41no—
31D4×D113—41no—
32C2×C4×D113—41no—
33C2×C4×D113C2×C411yescharacteristic
34C22⋊Dic113—21no—
35#14268624—41no—
36C2×D4×C113C2×C411yescharacteristic
37C22⋊C4×C113—21no—
38C23×C113C22⋊C411yescharacteristic
39C23×C113C4⋊C411yescharacteristic
40C22×D113—21no—
41C22×D113—21no—
42C22×D113—21no—
43C22×D113—21no—
44C22×D113—41no—
45C22×D113—41no—
46C22×D113—41no—
47C22×D113—41no—
48C22×D113C22⋊C411yescharacteristic
49C22×D113C22⋊C411yescharacteristic
50C22×D113C4⋊C411yescharacteristic
51C2×#90673—22no—
52C2×#90673—41no—
53C2×#90673—41no—
54C2×#90673—42no—
55C2×#90673—41no—
56C2×#90673—41no—
57C2×#90673—41no—
58C2×#90673—81no—
59C2×#90673—81no—
60D4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113C4211yescharacteristic
63C22⋊D113—41no—
64C22⋊D113—41no—
65C2×Dic113—41no—
66C2×Dic113C4⋊C411yescharacteristic
67D452—41no—
68C4×D113—21no—
69C4×D113—21no—
70C4×D113—81no—
71C4×D113—81no—
72C22×C113—21no—
73C22×C113—21no—
74C22×C113—41no—
75C22×C113—41no—
76C22×C113#9511yescharacteristic
77C2×D113—21no—
78C2×D113—21no—
79C2×D113—21no—
80C2×D113—21no—
81C2×D113—41no—
82C2×D113—41no—
83C2×D113—41no—
84C2×D113—41no—
85C2×D113—41no—
86C2×D113—41no—
87C2×D113—81no—
88C2×D113—81no—
89C2×D113#9911yescharacteristic
90C2×D113#9911yescharacteristic
91#90673—42no—
92#90673—82no—
93#90673—81no—
94C4×C113—21no—
95C4×C113—81no—
96Dic113—21no—
97Dic113—81no—
98C2×C113—21no—
99C2×C113—41no—
100C2×C113—41no—
101C2×C113#34211yescharacteristic
102D113—21no—
103D113—41no—
104D113—41no—
105D113#35311yescharacteristic
106D113#35411yescharacteristic
107#1393—1131nomaximal, Sylow
108C113#139311yescharacteristic, complemented, Sylow
109C2×#99—1131no—
110C2×#99—1131no—
111#390—1131no—
112C22×D4—1131no—
113C2×C4⋊C4—1131no—
114C2×C22⋊C4—2261no—
115C2×C22⋊C4—2261no—
116C2×C22⋊C4—2261no—
117C2×C22⋊C4—2261no—
118C2×C42—1131no—
119#99—1132no—
120#99—1131no—
121#99—2261no—
122#99—2261no—
123#99#9067311yescharacteristic, complemented
124C24—1131no—
125C24—1131no—
126C2×D4—1131no—
127C2×D4—1131no—
128C2×D4—1131no—
129C2×D4—4521no—
130C2×D4—4521no—
131C2×D4C2×#9067311yescharacteristic
132C22×C4—1131no—
133C22×C4—4521no—
134C22×C4—4521no—
135C22×C4—2261no—
136C22×C4—2261no—
137C4⋊C4—4521no—
138C22⋊C4—21no—
139C22⋊C4—4521no—
140C22⋊C4—4521no—
141C22⋊C4—4522no—
142C22⋊C4—4522no—
143C22⋊C4—2262no—
144C22⋊C4—2261no—
145C42—4521no—
146C23—1131no—
147C23—1131no—
148C23—1131no—
149C23—4521no—
150C23—4521no—
151C23—4521no—
152C23—4521no—
153C23—2261no—
154C23—2261no—
155C23—2261no—
156C23—2261no—
157C23C22⋊#9067311yescharacteristic
158C23C4⋊#9067311yescharacteristic
159D4—41no—
160D4—4521no—
161D4—4521no—
162D4—4521no—
163C2×C4—41no—
164C2×C4—1131no—
165C2×C4—9041no—
166C2×C4—9041no—
167C2×C4—9041no—
168C2×C4—9041no—
169C2×C4—4521no—
170C2×C4—4521no—
171C2×C4—4521no—
172C2×C4—4521no—
173C2×C4—4522no—
174C2×C4—4521no—
175C2×C4—4521no—
176C2×C4—2261no—
177C2×C4—2261no—
178C2×C4—2262no—
179C2×C4C4×#9067311yescharacteristic
180C22—21no—
181C22—21no—
182C22—41no—
183C22—41no—
184C22—1131no—
185C22—1131no—
186C22—9041no—
187C22—9041no—
188C22—4521no—
189C22—4521no—
190C22—4521no—
191C22—4521no—
192C22—4521no—
193C22—4521no—
194C22—2261no—
195C22—2261no—
196C22—2261no—
197C22—2261no—
198C22(C2×#90673)⋊C411yescharacteristic
199C4—21no—
200C4—81no—
201C4—9041no—
202C4—9041no—
203C4—9042no—
204C4—4522no—
205C4—2261no—
206C2—21no—
207C2—41no—
208C2—41no—
209C2—1131no—
210C2—1131no—
211C2—4521no—
212C2—4521no—
213C2—2261no—
214C2#2029947511yescharacteristic
subgroupG/H
centerC2#20299475
commutatorC2×C4×C113C42
FrattiniC2×D4C2×#90673
Fitting#99×C113C4
socleC2×C113#342
prime radical, cosocleC2×D4×D113C22
hypercenter#99#90673
hypocenterC113#1393
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊#90673C4semidirect
8. C2×C4×#90673C4semidirect
9. #16813681C4semidirect
13. #16813537C4semidirect
15. #99×C113C4semidirect
108. C113#1393semidirect
123. #99#90673semidirect

Maximal subgroups

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

subgroupindex
D113⋊#992
#202995502
#99×D1132
#1393113