Finite Group Databasebeta

← #28389063

Subgroups — #28389063

Order 14464.

304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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#20299109C211yesmaximal, characteristic
2C2×C22⋊#11744751C211yesmaximal, characteristic, complemented
3#20298334C212yesmaximal, complemented
4#20298331C212yesmaximal, complemented
5C4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C411yescharacteristic, complemented
7C22×#11744751—21no—
8#16813605—21no—
9#16813601C411yescharacteristic, complemented
10#16813601C2211yescharacteristic
11#16813596C411yescharacteristic, complemented
12#16813596C2211yescharacteristic
13#16813591—21no—
14C4×C22⋊D113—21no—
15C4×C22⋊D113—21no—
16#16813581C411yescharacteristic, complemented
17C22⋊#11744751—21no—
18C22⋊#11744751C2212yes—
19C23×C4×C113C2211yescharacteristic
20C2×C22⋊C4×C113—21no—
21C2×C42×C113—21no—
22#95×C113C2212yes—
23#14268647—42no—
24C2×Dic226C2×C411yescharacteristic
25C2×D452C2×C411yescharacteristic
26C2×C22⋊D113—21no—
27C2×C22⋊D113—21no—
28C2×C22⋊D113—21no—
29C2×C4×D113—21no—
30C2×#11744751—22no—
31C2×#11744751—42no—
32C4⋊Dic113C2×C411yescharacteristic
33C4⋊Dic113C2×C411yescharacteristic
34#14268626—21no—
35#14268626—21no—
36C22⋊Dic113—21no—
37C22⋊Dic113—21no—
38C22⋊Dic113—21no—
39#14268624—21no—
40#14268624—21no—
41C4×Dic113—21no—
42C24×C113D411yescharacteristic
43C22×C4×C113—22no—
44C22×C4×C113—42no—
45C22×C4×C113C2×C411yescharacteristic
46C22×C4×C113C2×C411yescharacteristic
47C22×C4×C113D411yescharacteristic
48C22×C4×C113D411yescharacteristic
49C22×C4×C113D411yescharacteristic
50C22×C4×C113C2311yescharacteristic
51C22⋊C4×C113—24no—
52C42×C113—42no—
53C23×C113—22no—
54C23×C113—22no—
55C23×C113—41no—
56C23×C113C22⋊C411yescharacteristic
57C23×C113C22⋊C411yescharacteristic
58C23×C113C2×D411yescharacteristic
59C22×D113—21no—
60C2×C4×C113—22no—
61C2×C4×C113—22no—
62C2×C4×C113—22no—
63C2×C4×C113—24no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113—41no—
67C2×C4×C113—42no—
68C2×C4×C113—42no—
69C2×C4×C113C22⋊C411yescharacteristic
70C2×C4×C113C22⋊C411yescharacteristic
71C2×C4×C113C22×C411yescharacteristic
72C2×C4×C113C2×D411yescharacteristic
73C22⋊D113—42no—
74C22⋊D113—42no—
75C22⋊D113—42no—
76C2×Dic113—21no—
77C2×Dic113—21no—
78C2×Dic113—21no—
79D452—41no—
80C4×D113—42no—
81Dic226—41no—
82#11744751—42no—
83C22×C113—21no—
84C22×C113—21no—
85C22×C113—21no—
86C22×C113—21no—
87C22×C113—21no—
88C22×C113—21no—
89C22×C113—21no—
90C22×C113—44no—
91C22×C113#10412yes—
92C22×C113C2×C22⋊C411yescharacteristic
93C22×C113#13512yes—
94C2×D113—41no—
95C2×D113—41no—
96C2×D113—41no—
97C4×C113—21no—
98C4×C113—21no—
99C4×C113—21no—
100C4×C113—44no—
101C4×C113#9912yes—
102Dic113—41no—
103Dic113—41no—
104Dic113—41no—
105C2×C113—22no—
106C2×C113—22no—
107C2×C113—41no—
108C2×C113C2×#9911yescharacteristic
109C2×C113#41611yescharacteristic
110C2×C113C2×#10411yescharacteristic
111D113—81no—
112#1501—1131nomaximal, Sylow
113C113#150111yescharacteristic, complemented, Sylow
114#525—1131no—
115C2×C22⋊C8—1131no—
116C4×C22⋊C4D11311yescharacteristic, complemented
117#328—1132no—
118#327—1132no—
119C2×#41—1131no—
120C23×C4C2×D11311yescharacteristic
121C22×C8—2261no—
122#123—2261no—
123C22⋊Q8—1131no—
124C22⋊Q8—1131no—
125#121—1131no—
126#121—1131no—
127#120—2261no—
128C4×D4—2261no—
129C4×D4—2261no—
130#117—1131no—
131C2×C22⋊C4—21no—
132C2×C42—21no—
133C22⋊C8—1132no—
134C22⋊C8—2261no—
135#95C2×D11312yes—
136C24C22⋊D11311yescharacteristic
137#41—4522no—
138C2×Q8—1131no—
139C2×D4—1131no—
140C2×D4—2261no—
141C2×D4—2261no—
142C2×D4—2261no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—2261no—
146C22×C4C4×D11311yescharacteristic
147C22×C4C4×D11311yescharacteristic
148C22×C4D45211yescharacteristic
149C22×C4D45211yescharacteristic
150C22×C4C22⋊D11311yescharacteristic
151C22×C4C22×D11311yescharacteristic
152C2×C8—4522no—
153C2×C8—2262no—
154C4⋊C4—1131no—
155C4⋊C4—1131no—
156C4⋊C4—2261no—
157C4⋊C4—2261no—
158C22⋊C4—24no—
159C22⋊C4—2261no—
160C22⋊C4—2261no—
161C22⋊C4—2261no—
162C22⋊C4—2261no—
163C22⋊C4—2261no—
164C42—42no—
165C42—2261no—
166C23—22no—
167C23—22no—
168C23—41no—
169C23—2261no—
170C23#1426862411yescharacteristic
171C23#1426862411yescharacteristic
172C23C2×C22⋊D11311yescharacteristic
173Q8—4521no—
174D4—4521no—
175D4—4522no—
176D4—4522no—
177D4—4522no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—4522no—
188C2×C4—2261no—
189C2×C4—2261no—
190C2×C4—2261no—
191C2×C4#1426862411yescharacteristic
192C2×C4#1426862411yescharacteristic
193C2×C4C2×C4×D11311yescharacteristic
194C2×C4C2×D45211yescharacteristic
195C8—4522no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22—4521no—
205C22—4521no—
206C22—4521no—
207C22#1681355012yes—
208C22C2×#1426862411yescharacteristic
209C22#1681364212yes—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—44no—
214C4—4521no—
215C4—4521no—
216C4—4521no—
217C4#1681353612yes—
218C2—22no—
219C2—22no—
220C2—41no—
221C2—9041no—
222C2C2×#1681353611yescharacteristic
223C2#2029859211yescharacteristic
224C2C2×#1681355011yescharacteristic
subgroupG/H
centerC2×C4#14268624
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC4×C22⋊C4×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299109C2
cosocleC22×C4×C113C23
hypercenterC4×C22⋊C4D113
hypocenterC113#1501
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#11744751C2semidirect
3. #20298334C2semidirect
4. #20298331C2semidirect
5. C4×C22⋊C4×C113C2semidirect
6. C2×#14268647C4semidirect
9. #16813601C4semidirect
11. #16813596C4semidirect
16. #16813581C4semidirect
113. C113#1501semidirect
116. C4×C22⋊C4D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
C2×C22⋊#117447512
#202983342
#202983312
C4×C22⋊C4×C1132
#1501113