Finite Group Databasebeta

← #28406001

Subgroups — #28406001

Order 14464.

284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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, complemented
2#20299541C211yesmaximal, characteristic, complemented
3#20299452C212yesmaximal, complemented
4#20299450C212yesmaximal, complemented
5#20299111C211yesmaximal, characteristic
6C2×#14268655—21no—
7C2×C22⋊#90673—21no—
8#16813679C2212yes—
9C22⋊#11744753—21no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4C2212yes—
12C2×#14268648C411yescharacteristic, complemented
13C22×C4×D113C2211yescharacteristic
14#16813607—21no—
15#16813598C2211yescharacteristic
16#16813597C2211yescharacteristic
17#16813596C411yescharacteristic, complemented
18#16813592—21no—
19#16813584—21no—
20#16813582—21no—
21#16813580C411yescharacteristic, complemented
22C22⋊Q8×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24#14268655—42no—
25C2×#11744753—22no—
26C22⋊#90673—42no—
27C23×D113D411yescharacteristic
28#14268648—42no—
29C2×D452—21no—
30C2×D452—21no—
31C2×D452C2×C411yescharacteristic
32C2×C22⋊D113—21no—
33C22×Dic113D411yescharacteristic
34C2×C4×D113—21no—
35C2×C4×D113—42no—
36C2×C4×D113C2×C411yescharacteristic
37C2×C4×D113D411yescharacteristic
38C2×C4×D113D411yescharacteristic
39C2×C4×D113C2311yescharacteristic
40C4⋊Dic113C2×C411yescharacteristic
41#14268626—21no—
42#14268624—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—21no—
46C4×Dic113—21no—
47C2×Q8×C113C2×C411yescharacteristic
48C22×C4×C113C2×C411yescharacteristic
49C4⋊C4×C113—21no—
50C4⋊C4×C113C2×C411yescharacteristic
51C22⋊C4×C113—21no—
52C23×C113C22⋊C411yescharacteristic
53C22×D113—22no—
54C22×D113—22no—
55C22×D113—21no—
56C22×D113—41no—
57C22×D113C22⋊C411yescharacteristic
58C22×D113C2×D411yescharacteristic
59C2×#90673—42no—
60C2×#90673—42no—
61C2×#90673—42no—
62Q8×C113—41no—
63C2×C4×C113—21no—
64C2×C4×C113—21no—
65C2×C4×C113—41no—
66C2×C4×C113C22⋊C411yescharacteristic
67C2×C4×C113C22×C411yescharacteristic
68C22⋊D113—42no—
69C2×Dic113—21no—
70C2×Dic113—41no—
71C2×Dic113C22⋊C411yescharacteristic
72C2×Dic113C2×D411yescharacteristic
73D452—41no—
74D452—42no—
75D452—42no—
76C4×D113—22no—
77C4×D113—22no—
78C4×D113—41no—
79C4×D113—41no—
80C4×D113—42no—
81#11744753—42no—
82C22×C113—21no—
83C22×C113—21no—
84C22×C113—21no—
85C22×C113C2×C22⋊C411yescharacteristic
86C2×D113—21no—
87C2×D113—21no—
88C2×D113—21no—
89C2×D113—21no—
90C2×D113—44no—
91C2×D113—41no—
92C2×D113—41no—
93C2×D113—41no—
94C2×D113#9912yes—
95C2×D113#13512yes—
96#90673—82no—
97C4×C113—21no—
98C4×C113—21no—
99C4×C113—41no—
100C4×C113—41no—
101Dic113—21no—
102Dic113—21no—
103Dic113—41no—
104C2×C113—41no—
105C2×C113C2×#9911yescharacteristic
106C2×C113#41611yescharacteristic
107C2×C113#42111yescharacteristic
108D113—22no—
109D113—22no—
110D113—81no—
111#1516—1131nomaximal, Sylow
112C113#151611yescharacteristic, complemented, Sylow
113#525—1131no—
114C2×C22⋊C8—1131no—
115#381—1131no—
116#328—1132no—
117#327—1132no—
118C2×#41—1131no—
119C23×C4—1131no—
120C22×C8—2261no—
121#123—2261no—
122C22⋊Q8—1131no—
123C22⋊Q8#9067311yescharacteristic, complemented
124#121—1131no—
125#121—1131no—
126#120—2261no—
127C4×D4—2261no—
128C4×D4—2261no—
129#117—1131no—
130C2×C22⋊C4—2261no—
131C22⋊C8—1132no—
132C22⋊C8—2261no—
133#95—1132no—
134#95—2261no—
135C24—1131no—
136#41—4522no—
137C2×Q8C2×#9067311yescharacteristic
138C2×D4—1131no—
139C2×D4—2261no—
140C2×D4—2261no—
141C2×D4—2261no—
142C22×C4—1131no—
143C22×C4—1131no—
144C22×C4—1131no—
145C22×C4—1131no—
146C22×C4—1131no—
147C22×C4—4522no—
148C22×C4—2261no—
149C22×C4—2262no—
150C22×C4C2×#9067311yescharacteristic
151C2×C8—4522no—
152C2×C8—2262no—
153C4⋊C4—21no—
154C4⋊C4—1131no—
155C4⋊C4—2261no—
156C4⋊C4C2×#9067311yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—4522no—
159C22⋊C4—2261no—
160C22⋊C4—2261no—
161C22⋊C4—2261no—
162C22⋊C4—2261no—
163C42—2261no—
164C23—1131no—
165C23—1131no—
166C23—4521no—
167C23—2262no—
168C23—2262no—
169C23—2261no—
170C23C22⋊#9067311yescharacteristic
171Q8—41no—
172D4—4521no—
173D4—4522no—
174D4—4522no—
175D4—4522no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—1131no—
180C2×C4—1131no—
181C2×C4—4521no—
182C2×C4—4521no—
183C2×C4—4522no—
184C2×C4—4522no—
185C2×C4—4522no—
186C2×C4—4522no—
187C2×C4—4521no—
188C2×C4—2262no—
189C2×C4—2262no—
190C2×C4—2261no—
191C2×C4C22⋊#9067311yescharacteristic
192C2×C4C22×#9067311yescharacteristic
193C8—4522no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—1132no—
198C22—1132no—
199C22—4524no—
200C22—4521no—
201C22—4521no—
202C22—4521no—
203C22—2261no—
204C22—2261no—
205C22—2261no—
206C22—2261no—
207C22C2×C22⋊#9067311yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—9042no—
213C4—4521no—
214C4—2261no—
215C4—2261no—
216C2—41no—
217C2—9041no—
218C2—2262no—
219C2—2262no—
220C2D113⋊#9911yescharacteristic
221C2#2029958811yescharacteristic
222C2#2029959711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC22⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299111C2
cosocleC2×C4×D113C23
hypercenterC22⋊Q8#90673
hypocenterC113#1516
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #20299566C2semidirect
2. #20299541C2semidirect
3. #20299452C2semidirect
4. #20299450C2semidirect
12. C2×#14268648C4semidirect
17. #16813596C4semidirect
21. #16813580C4semidirect
22. C22⋊Q8×C113C4semidirect
112. C113#1516semidirect
123. C22⋊Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202995662
#202995412
#202994522
#202994502
#202991112
#1516113