Finite Group Databasebeta

← #28406479

Subgroups — #28406479

Order 14464.

300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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#20299566C211yesmaximal, characteristic
2#20299540C211yesmaximal, characteristic
3#20299471C212yesmaximal, complemented
4#20299471C212yesmaximal, complemented
5#117×D113C211yesmaximal, characteristic
6C2×#14268655C2212yes—
7C2×C4⋊#90673C2212yes—
8C2×C22⋊#90673—21no—
9#16813679—21no—
10C22⋊#11744753—21no—
11(C2×#90673)⋊C4—21no—
12C22×C4×D113C2211yescharacteristic
13#16813581C411yescharacteristic, complemented
14#16813580C411yescharacteristic, complemented
15#16813580C411yescharacteristic, complemented
16#16813579—21no—
17#16813578—21no—
18C4⋊C4×D113C2211yescharacteristic
19C4⋊C4×D113C2211yescharacteristic
20C22⋊C4×D113—21no—
21C42×D113—21no—
22#117×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24#14268655—24no—
25C2×#11744753—22no—
26C4⋊#90673—24no—
27C22⋊#90673—42no—
28C23×D113D411yescharacteristic
29C22×Dic113D411yescharacteristic
30C2×C4×D113—24no—
31C2×C4×D113—21no—
32C2×C4×D113—21no—
33C2×C4×D113C2×C411yescharacteristic
34C2×C4×D113D411yescharacteristic
35C2×C4×D113D411yescharacteristic
36C2×C4×D113C2311yescharacteristic
37C4⋊Dic113C2×C411yescharacteristic
38C4⋊Dic113C2×C411yescharacteristic
39#14268626—21no—
40#14268626—21no—
41C22⋊Dic113—21no—
42#14268624—21no—
43#14268624—21no—
44C4×Dic113—21no—
45C4×Dic113—21no—
46C4×Dic113—21no—
47C22×C4×C113C2×C411yescharacteristic
48C4⋊C4×C113C2×C411yescharacteristic
49C4⋊C4×C113C2×C411yescharacteristic
50C22⋊C4×C113—21no—
51C42×C113—21no—
52C23×C113C22⋊C411yescharacteristic
53C22×D113—22no—
54C22×D113—22no—
55C22×D113—21no—
56C22×D113—21no—
57C22×D113C22⋊C411yescharacteristic
58C22×D113C2×D411yescharacteristic
59C2×#90673—42no—
60C2×#90673—42no—
61C2×#90673—42no—
62C2×C4×C113—22no—
63C2×C4×C113—21no—
64C2×C4×C113—21no—
65C2×C4×C113C22⋊C411yescharacteristic
66C2×C4×C113C22×C411yescharacteristic
67C2×Dic113—22no—
68C2×Dic113—21no—
69C2×Dic113—21no—
70C2×Dic113C22⋊C411yescharacteristic
71C2×Dic113C2×D411yescharacteristic
72C4×D113—22no—
73C4×D113—22no—
74C4×D113—22no—
75C4×D113—42no—
76C4×D113—41no—
77C4×D113—41no—
78C4×D113#4114yes—
79#11744753—42no—
80C22×C113—21no—
81C22×C113—21no—
82C22×C113—21no—
83C22×C113C2×C22⋊C411yescharacteristic
84C2×D113—21no—
85C2×D113—21no—
86C2×D113—21no—
87C2×D113—42no—
88C2×D113—42no—
89C2×D113#12312yes—
90C2×D113#13512yes—
91C2×D113AGL(1,ℤ/8)11yescharacteristic
92C2×D113#13711yescharacteristic
93#90673—82no—
94C4×C113—21no—
95C4×C113—41no—
96C4×C113—41no—
97C4×C113#11712yes—
98Dic113—21no—
99Dic113—41no—
100Dic113—41no—
101Dic113#12312yes—
102C2×C113—41no—
103C2×C113#38111yescharacteristic
104C2×C113#41611yescharacteristic
105C2×C113#41711yescharacteristic
106D113—41no—
107D113#48212yes—
108D113#48512yes—
109#1825—1131nomaximal, Sylow
110C113#182511yescharacteristic, complemented, Sylow
111C2×#117—1131no—
112C2×C22⋊C8—1131no—
113#380—1131no—
114#340—1132no—
115#340—1132no—
116C23×C4—1131no—
117C22×C8—1132no—
118#117—1131no—
119#117—1131no—
120#117—1131no—
121#117—2261no—
122#117—2261no—
123#117#9067311yescharacteristic, complemented
124C2×C4⋊C4—1131no—
125C2×C4⋊C4—1131no—
126C2×C4⋊C4—1132no—
127C2×C22⋊C4—2261no—
128C2×C22⋊C4—2261no—
129C2×C42—2261no—
130C22⋊C8—2261no—
131C22⋊C8—2261no—
132#95—2261no—
133C24—1131no—
134C22×C4—1131no—
135C22×C4—1131no—
136C22×C4—1131no—
137C22×C4—1131no—
138C22×C4—1131no—
139C22×C4—2264no—
140C22×C4—2261no—
141C22×C4—2261no—
142C22×C4—2262no—
143C22×C4C2×#9067311yescharacteristic
144C2×C8—2262no—
145C2×C8—2264no—
146C4⋊C4—1131no—
147C4⋊C4—1131no—
148C4⋊C4—2261no—
149C4⋊C4—2261no—
150C4⋊C4—2264no—
151C4⋊C4C2×#9067311yescharacteristic
152C4⋊C4C2×#9067311yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—4522no—
155C22⋊C4—2261no—
156C22⋊C4—2261no—
157C22⋊C4—2261no—
158C42—21no—
159C42—2261no—
160C42—2261no—
161C42—2261no—
162C23—1131no—
163C23—1131no—
164C23—2261no—
165C23—2262no—
166C23—2262no—
167C23—2261no—
168C23C22⋊#9067311yescharacteristic
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—1131no—
173C2×C4—1134no—
174C2×C4—1131no—
175C2×C4—4522no—
176C2×C4—4521no—
177C2×C4—4521no—
178C2×C4—4522no—
179C2×C4—4522no—
180C2×C4—4522no—
181C2×C4—2262no—
182C2×C4—2262no—
183C2×C4—2262no—
184C2×C4—2261no—
185C2×C4—2261no—
186C2×C4—2262no—
187C2×C4C22⋊#9067311yescharacteristic
188C2×C4C22×#9067311yescharacteristic
189C8—4522no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—1132no—
194C22—1132no—
195C22—1131no—
196C22—1131no—
197C22—4522no—
198C22—4522no—
199C22—2261no—
200C22—2261no—
201C22—2261no—
202C22C2×C22⋊#9067311yescharacteristic
203C4—21no—
204C4—41no—
205C4—41no—
206C4—1132no—
207C4—9042no—
208C4—4521no—
209C4—4521no—
210C4—2261no—
211C4#1681370112yes—
212C2—41no—
213C2—1132no—
214C2—1132no—
215C2—4521no—
216C2#2029954111yescharacteristic
217C2#2029958811yescharacteristic
218C2#2029958911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#117×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC23×D113D4
cosocleC2×C4×D113C23
hypercenter#117#90673
hypocenterC113#1825
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #20299471C2semidirect
4. #20299471C2semidirect
13. #16813581C4semidirect
14. #16813580C4semidirect
15. #16813580C4semidirect
22. #117×C113C4semidirect
110. C113#1825semidirect
123. #117#90673semidirect

Maximal subgroups

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

subgroupindex
#202995662
#202995402
#202994712
#117×D1132
#1825113