Finite Group Databasebeta

← #28389539

Subgroups — #28389539

Order 14464.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#20299195C211yesmaximal, characteristic
2#20298756C211yesmaximal, characteristic, complemented
3#20298739C211yesmaximal, characteristic
4#20298518C211yesmaximal, characteristic, complemented
5#20298336C211yesmaximal, characteristic, complemented
6#20298333C211yesmaximal, characteristic
7#324×C113C211yesmaximal, characteristic, complemented
8C22×Dic226C2211yescharacteristic
9C2×Dic452—21no—
10C2×#14268636—21no—
11#16813617—21no—
12#16813612—21no—
13#16813607—21no—
14#16813605—21no—
15#16813601C2211yescharacteristic
16#16813600—21no—
17#16813596C2211yescharacteristic
18C4×C22⋊D113—21no—
19C2×#14268626—21no—
20#16813547—21no—
21#16813547—21no—
22#16813529—21no—
23#16813529C2211yescharacteristic
24C2×C4⋊C4×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26C22⋊C8×C113C2211yescharacteristic
27C2×Dic226—21no—
28C2×Dic226—21no—
29C2×Dic226—42no—
30C2×Dic226D411yescharacteristic
31C2×D452D411yescharacteristic
32C2×C22⋊D113—21no—
33C22×Dic113—21no—
34C22×Dic113—21no—
35C2×C4×D113—21no—
36Dic452—42no—
37#14268636—42no—
38C4⋊Dic113D411yescharacteristic
39C4⋊Dic113D411yescharacteristic
40#14268626—21no—
41#14268626—21no—
42#14268626—21no—
43#14268626—21no—
44#14268626—42no—
45C22⋊Dic113—21no—
46#14268624—21no—
47#14268624—21no—
48#14268624—21no—
49#14268624—21no—
50C4×Dic113—21no—
51C22×C4×C113D411yescharacteristic
52C22×C4×C113D411yescharacteristic
53C22×C4×C113C2311yescharacteristic
54C2×C8×C113—21no—
55C2×C8×C113—21no—
56C4⋊C4×C113—21no—
57C4⋊C4×C113—21no—
58C23×C113C2×D411yescharacteristic
59C22×D113—21no—
60C2×C4×C113—21no—
61C2×C4×C113—21no—
62C2×C4×C113—21no—
63C2×C4×C113—21no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C22⋊D113—41no—
69C22⋊D113—41no—
70C2×Dic113—22no—
71C2×Dic113—22no—
72C2×Dic113—21no—
73C2×Dic113—21no—
74C2×Dic113—21no—
75C2×Dic113—41no—
76C2×Dic113—41no—
77C2×Dic113—41no—
78C2×Dic113—41no—
79D452—41no—
80C4×D113—81no—
81Dic226—22no—
82Dic226—22no—
83Dic226—41no—
84Dic226—41no—
85Dic226—41no—
86C8×C113—41no—
87C8×C113—41no—
88C22×C113—21no—
89C22×C113—21no—
90C22×C113#12011yescharacteristic
91C22×C113#13511yescharacteristic
92C22×C113#13711yescharacteristic
93C2×D113—41no—
94C2×D113—41no—
95C2×D113—41no—
96C4×C113—21no—
97C4×C113—21no—
98C4×C113—41no—
99C4×C113—41no—
100Dic113—42no—
101Dic113—41no—
102Dic113—41no—
103Dic113—42no—
104Dic113—41no—
105C2×C113—21no—
106C2×C113—21no—
107C2×C113#45211yescharacteristic
108C2×C113#45611yescharacteristic
109C2×C113B(4,𝔽2)11yescharacteristic
110D113—81no—
111#1603—1131nomaximal, Sylow
112C113#160311yescharacteristic, complemented, Sylow
113#539—1131no—
114#451—1131no—
115#448—1131no—
116#395—1131no—
117#328—1131no—
118#327—1131no—
119#324D11311yescharacteristic, complemented
120C22×Q8—1131no—
121C2×Q16—2261no—
122C2×SD16—2261no—
123#126—2261no—
124#125—2261no—
125#123—2261no—
126#123—2261no—
127C22⋊Q8—1131no—
128C22⋊Q8—2261no—
129#121—1131no—
130C4×D4—2261no—
131C2×C4⋊C4—2261no—
132C2×C4⋊C4C2×D11311yescharacteristic
133#103—2261no—
134#103—2261no—
135C22⋊C8C2×D11311yescharacteristic
136C22⋊C8C2×D11311yescharacteristic
137#95—1131no—
138#95—2261no—
139C2×Q8—1131no—
140C2×Q8—4522no—
141C2×Q8—2261no—
142C2×Q8—2261no—
143C2×D4—1131no—
144C2×D4—2261no—
145C22×C4—2261no—
146C22×C4—2261no—
147C22×C4—2261no—
148C22×C4D45211yescharacteristic
149C22×C4D45211yescharacteristic
150C22×C4C22×D11311yescharacteristic
151Q16—4522no—
152SD16—4522no—
153C2×C8—21no—
154C2×C8—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—1131no—
158C4⋊C4—1131no—
159C4⋊C4—4522no—
160C4⋊C4—2261no—
161C4⋊C4—2261no—
162C4⋊C4—2261no—
163C4⋊C4—2261no—
164C22⋊C4—2261no—
165C22⋊C4—2261no—
166C22⋊C4—2261no—
167C22⋊C4—2261no—
168C22⋊C4—2261no—
169C42—2261no—
170C23—2261no—
171C23C2×D45211yescharacteristic
172Q8—4521no—
173Q8—4521no—
174Q8—4521no—
175Q8—2262no—
176Q8—2262no—
177D4—4521no—
178D4—4521no—
179D4—4521no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—9041no—
187C2×C4—4521no—
188C2×C4—4521no—
189C2×C4—4521no—
190C2×C4—4521no—
191C2×C4—2262no—
192C2×C4—2262no—
193C2×C4—2261no—
194C2×C4—2261no—
195C2×C4—2261no—
196C2×C4D4×D11311yescharacteristic
197C2×C4D4×D11311yescharacteristic
198C8—41no—
199C8—41no—
200C22—21no—
201C22—21no—
202C22—4521no—
203C22—4521no—
204C22—4521no—
205C22#1681359211yescharacteristic
206C22#1681364411yescharacteristic
207C22#1681365511yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—4522no—
213C4—4521no—
214C4—4521no—
215C4—4521no—
216C4—4522no—
217C2—21no—
218C2—21no—
219C2—9041no—
220C2#2029876211yescharacteristic
221C2#2029878311yescharacteristic
222C2#2029878611yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113#120
prime radical#16813596C22
hypercenter#324D113
hypocenterC113#1603
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20298756C2semidirect
4. #20298518C2semidirect
5. #20298336C2semidirect
7. #324×C113C2semidirect
112. C113#1603semidirect
119. #324D113semidirect

Maximal subgroups

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

subgroupindex
#202991952
#202987562
#202987392
#202985182
#202983362
#202983332
#324×C1132
#1603113