Finite Group Databasebeta

← #28392226

Subgroups — #28392226

Order 14464.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299170C211yesmaximal, characteristic
2#20298579C211yesmaximal, characteristic
3#20298570C211yesmaximal, characteristic
4#20298389C211yesmaximal, characteristic, complemented
5#20298388C211yesmaximal, characteristic, complemented
6#20298387C211yesmaximal, characteristic, complemented
7#352×C113C211yesmaximal, characteristic, complemented
8C2×#14268646C2211yescharacteristic
9C22×Dic226C411yescharacteristic, complemented
10M16×D113—21no—
11#16813621—21no—
12#16813608—21no—
13#16813606C411yescharacteristic, complemented
14#16813605C411yescharacteristic, complemented
15#16813603C2211yescharacteristic
16#16813600—21no—
17#16813599—21no—
18#16813578—21no—
19#16813578C411yescharacteristic, complemented
20#16813540—21no—
21#16813539C2211yescharacteristic
22#16813537C2211yescharacteristic
23#16813536—21no—
24#123×C113C2211yescharacteristic
25#100×C113C2211yescharacteristic
26#99×C113C2211yescharacteristic
27#14268646—41no—
28#14268646—41no—
29C2×Dic226—21no—
30C2×Dic226—21no—
31C2×Dic226—41no—
32C2×Dic226—41no—
33C2×Dic226D411yescharacteristic
34C2×C22⋊D113C2×C411yescharacteristic
35C2×C22⋊D113D411yescharacteristic
36C22×Dic113C2×C411yescharacteristic
37C22×Dic113C2×C411yescharacteristic
38C22×Dic113D411yescharacteristic
39C2×C4×D113D411yescharacteristic
40#14268631—21no—
41#14268630—41no—
42C8×D113—41no—
43C4⋊Dic113—21no—
44#14268626—21no—
45#14268626—21no—
46#14268626—21no—
47#14268626—41no—
48C22⋊Dic113—21no—
49C22⋊Dic113—21no—
50C22⋊Dic113C2×C411yescharacteristic
51#14268624—21no—
52#14268624—21no—
53C4×Dic113—21no—
54C4×Dic113—41no—
55C2×D4×C113C2311yescharacteristic
56C22×C4×C113C2×C411yescharacteristic
57M16×C113—21no—
58C4⋊C4×C113—21no—
59C22⋊C4×C113—21no—
60C22⋊C4×C113—21no—
61C22⋊C4×C113C2×C411yescharacteristic
62C23×C113C22×C411yescharacteristic
63C23×C113C2×D411yescharacteristic
64C22×D113C22⋊C411yescharacteristic
65D4×C113—41no—
66C2×C4×C113—21no—
67C2×C4×C113—21no—
68C2×C4×C113—41no—
69C2×C4×C113—41no—
70C2×C4×C113C2×D411yescharacteristic
71C22⋊D113—41no—
72C22⋊D113—41no—
73C2×Dic113—21no—
74C2×Dic113—21no—
75C2×Dic113—21no—
76C2×Dic113—21no—
77C2×Dic113—21no—
78C2×Dic113—21no—
79C2×Dic113—41no—
80C2×Dic113—41no—
81C2×Dic113C22⋊C411yescharacteristic
82C2×Dic113C22⋊C411yescharacteristic
83C2×Dic113C22⋊C411yescharacteristic
84C4×D113—21no—
85C4×D113—21no—
86Dic226—41no—
87Dic226—42no—
88Dic226—41no—
89Dic226—41no—
90C8×C113—41no—
91#11744751—41no—
92C22×C113—21no—
93C22×C113—21no—
94C22×C113—41no—
95C22×C113—41no—
96C22×C113C2×C22⋊C411yescharacteristic
97C2×D113—21no—
98C2×D113—41no—
99C4×C113—21no—
100C4×C113—41no—
101C4×C113—41no—
102C4×C113—81no—
103Dic113—21no—
104Dic113—21no—
105Dic113—41no—
106Dic113—41no—
107Dic113—81no—
108Dic113#9911yescharacteristic
109Dic113#9911yescharacteristic
110C2×C113—21no—
111C2×C113—41no—
112C2×C113—41no—
113C2×C113C2×#9911yescharacteristic
114D113—41no—
115#2123—1131nomaximal, Sylow
116C113#212311yescharacteristic, complemented, Sylow
117#536—1131no—
118#413—1131no—
119#410—1131no—
120#352—1131no—
121#352—1131no—
122#352—1131no—
123#352D11311yescharacteristic, complemented
124C2×#41—1131no—
125C22×Q8—1131no—
126C2×M16—2261no—
127C4⋊Q8—2261no—
128#124—2261no—
129#123—1131no—
130#123—1131no—
131#123—1131no—
132#123C2×D11311yescharacteristic
133C22⋊Q8—2261no—
134C22⋊Q8—2261no—
135#117—1131no—
136#117—2261no—
137#101—2261no—
138#100—1131no—
139#100C2×D11311yescharacteristic
140#99—1131no—
141#99—2261no—
142#99C2×D11311yescharacteristic
143#41—4521no—
144#41—4521no—
145C2×Q8—1131no—
146C2×Q8—4521no—
147C2×Q8—4521no—
148C2×Q8—2261no—
149C2×Q8—2261no—
150C2×D4—1131no—
151C2×D4—1131no—
152C2×D4C22×D11311yescharacteristic
153C22×C4—1131no—
154C22×C4—1131no—
155C22×C4—1131no—
156C22×C4—1131no—
157C22×C4C4×D11311yescharacteristic
158M16—21no—
159M16—4521no—
160M16—2261no—
161C2×C8—4521no—
162C4⋊C4—21no—
163C4⋊C4—4521no—
164C4⋊C4—2261no—
165C4⋊C4—2261no—
166C4⋊C4—2261no—
167C4⋊C4—2261no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—1131no—
171C22⋊C4—2261no—
172C22⋊C4—2261no—
173C22⋊C4—2261no—
174C22⋊C4—2261no—
175C22⋊C4C4×D11311yescharacteristic
176C42—4521no—
177C42—2261no—
178C23—1131no—
179C23C2×C4×D11311yescharacteristic
180C23D4×D11311yescharacteristic
181Q8—4521no—
182Q8—4521no—
183Q8—4521no—
184Q8—4522no—
185D4—41no—
186D4—4521no—
187D4—4521no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—1131no—
193C2×C4—1131no—
194C2×C4—1131no—
195C2×C4—4521no—
196C2×C4—4521no—
197C2×C4—2261no—
198C2×C4—2261no—
199C2×C4—2261no—
200C2×C4—2261no—
201C2×C4—2261no—
202C2×C4—2261no—
203C2×C4—2261no—
204C2×C4—2261no—
205C2×C4D4×D11311yescharacteristic
206C8—41no—
207C8—4521no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—4521no—
213C22—2261no—
214C22C22⋊C4×D11311yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—1131no—
220C4—1131no—
221C4—9041no—
222C4—4521no—
223C4—4521no—
224C4—2261no—
225C4—2261no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—4521no—
230C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC23×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#352×C113C2
socleC2×C113C2×#99
prime radicalC2×#14268646C22
cosocleC2×D4×C113C23
hypercenter#352D113
hypocenterC113#2123
LCSG ▷ C23×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #20298389C2semidirect
5. #20298388C2semidirect
6. #20298387C2semidirect
7. #352×C113C2semidirect
9. C22×Dic226C4semidirect
13. #16813606C4semidirect
14. #16813605C4semidirect
19. #16813578C4semidirect
116. C113#2123semidirect
123. #352D113semidirect

Maximal subgroups

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

subgroupindex
#202991702
#202985792
#202985702
#202983892
#202983882
#202983872
#352×C1132
#2123113