Finite Group Databasebeta

← #28406337

Subgroups — #28406337

Order 14464.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×#16813686C212yesmaximal
2C4×#14268657C211yesmaximal, characteristic, complemented
3#20299534C211yesmaximal, characteristic, complemented
4#20299468C212yesmaximal, complemented
5C4×#14268646C211yesmaximal, characteristic
6C2×#14268657C2212yes—
7C2×C4×#90673C2212yes—
8#16813686C418yescomplemented
9#16813677—21no—
10C4×#11744753—21no—
11(C2×#90673)⋊C4—21no—
12(C2×#90673)⋊C4—21no—
13C2×#14268646C2211yescharacteristic
14C4×Dic226C411yescharacteristic, complemented
15#16813587C411yescharacteristic, complemented
16D4×Dic113C411yescharacteristic, complemented
17C4×C22⋊D113—21no—
18#16813582—21no—
19#16813580C2211yescharacteristic
20#16813578—21no—
21C2×C4×Dic113—21no—
22C42×D113C2211yescharacteristic
23C4×D4×C113C411yescharacteristic, complemented
24C22×#90673—22no—
25#14268657—22no—
26#14268657C2×C414yescomplemented
27C2×#11744753—22no—
28C4×#90673—22no—
29C4×#90673C2×C414yescomplemented
30#14268646—22no—
31#14268646C2×C414yes—
32C2×Dic226C2×C411yescharacteristic
33C2×C22⋊D113—21no—
34C22×Dic113—21no—
35C22×Dic113—21no—
36C2×C4×D113D411yescharacteristic
37C2×C4×D113D411yescharacteristic
38C2×C4×D113C2311yescharacteristic
39C4⋊Dic113C2×C411yescharacteristic
40#14268626—21no—
41#14268626—21no—
42C22⋊Dic113—21no—
43#14268624—21no—
44C4×Dic113—21no—
45C4×Dic113—21no—
46C4×Dic113—21no—
47C4×Dic113C2×C411yescharacteristic
48C4×Dic113D411yescharacteristic
49C4×Dic113D411yescharacteristic
50C2×D4×C113C2×C411yescharacteristic
51C22×C4×C113—21no—
52C4⋊C4×C113C2×C411yescharacteristic
53C22⋊C4×C113—21no—
54C42×C113C2×C411yescharacteristic
55C23×C113—21no—
56C22×D113C2×D411yescharacteristic
57C2×#90673—24no—
58C2×#90673—42no—
59C2×#90673—42no—
60D4×C113—21no—
61D4×C113C4212yes—
62C2×C4×C113—21no—
63C2×C4×C113—42no—
64C2×C4×C113C22⋊C411yescharacteristic
65C2×C4×C113C22⋊C411yescharacteristic
66C2×C4×C113C22×C411yescharacteristic
67C22⋊D113—24no—
68C2×Dic113—21no—
69C2×Dic113—24no—
70C2×Dic113—21no—
71C2×Dic113—42no—
72C2×Dic113C22⋊C411yescharacteristic
73C2×Dic113C22⋊C411yescharacteristic
74C2×Dic113C2×D411yescharacteristic
75C4×D113—41no—
76C4×D113—41no—
77C4×D113C22×C412yes—
78C4×D113#4112yes—
79Dic226—21no—
80Dic226C4212yes—
81#11744753—24no—
82C22×C113—22no—
83C22×C113—41no—
84C22×C113—41no—
85C22×C113C2×C22⋊C411yescharacteristic
86C2×D113—21no—
87C2×D113—21no—
88C2×D113C4×D412yes—
89#90673—44no—
90C4×C113—21no—
91C4×C113—21no—
92C4×C113—41no—
93C4×C113C2×C4211yescharacteristic
94C4×C113#11711yescharacteristic
95Dic113—22no—
96Dic113—21no—
97Dic113—21no—
98Dic113—41no—
99Dic113C4×D412yes—
100C2×C113—42no—
101C2×C113C4×C22⋊C411yescharacteristic
102C2×C113#42111yescharacteristic
103C2×C113#42111yescharacteristic
104D113—22no—
105#1759—1131nomaximal, Sylow
106C113#175911yescharacteristic, complemented, Sylow
107C4×#41—1131no—
108C2×#104—1132no—
109C4×M16—1131no—
110#376—1131no—
111#339—1132no—
112C2×#41—1131no—
113C2×M16—1132no—
114C4×Q8—1131no—
115C4×Q8—1131no—
116C4×D4—1131no—
117C4×D4—2261no—
118C4×D4—2261no—
119C4×D4#9067311yescharacteristic, complemented
120#117—1131no—
121#117—2261no—
122C2×C42—1131no—
123C2×C42—1132no—
124C2×C42—2261no—
125#104—1138no—
126#97—2261no—
127C4×C8—2261no—
128#95—2261no—
129#95—2261no—
130#41—1134no—
131#41—2262no—
132C2×Q8—1131no—
133C2×D4—2261no—
134C2×D4C2×#9067311yescharacteristic
135C22×C4—21no—
136C22×C4—1131no—
137C22×C4—1131no—
138C22×C4—1131no—
139C22×C4—2261no—
140C22×C4—2261no—
141C22×C4—2262no—
142M16—1134no—
143M16—2262no—
144C2×C8—2262no—
145C4⋊C4—1131no—
146C4⋊C4—2261no—
147C4⋊C4—2261no—
148C4⋊C4C2×#9067311yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—2261no—
151C22⋊C4—2261no—
152C42—1131no—
153C42—1131no—
154C42—1131no—
155C42—1134no—
156C42—2261no—
157C42—2261no—
158C42—2262no—
159C42—2261no—
160C42C2×#9067311yescharacteristic
161C23—21no—
162C23—1131no—
163Q8—1132no—
164Q8—2261no—
165D4—21no—
166D4—2264no—
167D4C4×#9067312yes—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—1131no—
171C2×C4—1132no—
172C2×C4—1132no—
173C2×C4—1131no—
174C2×C4—1131no—
175C2×C4—4521no—
176C2×C4—4521no—
177C2×C4—4522no—
178C2×C4—4522no—
179C2×C4—4522no—
180C2×C4—2264no—
181C2×C4—2264no—
182C2×C4—2261no—
183C2×C4—2261no—
184C2×C4C22⋊#9067311yescharacteristic
185C2×C4C22⋊#9067311yescharacteristic
186C2×C4C22×#9067311yescharacteristic
187C8—2264no—
188C22—22no—
189C22—41no—
190C22—41no—
191C22—1132no—
192C22—2261no—
193C22—2261no—
194C22C2×C22⋊#9067311yescharacteristic
195C4—21no—
196C4—21no—
197C4—41no—
198C4—1132no—
199C4—4524no—
200C4—4521no—
201C4—2262no—
202C4—2261no—
203C4—2261no—
204C4C2×C4×#9067311yescharacteristic
205C4#1681370111yescharacteristic
206C2—42no—
207C2—2262no—
208C2C4×C22⋊#9067311yescharacteristic
209C2#2029959511yescharacteristic
210C2#2029959611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC4×C113C2×C42
FrattiniC2×C4C22×#90673
FittingC4×D4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC2×#14268646C22
cosocleC2×C4×D113C23
hypercenterC4×D4#90673
hypocenterC113#1759
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×#14268657C2semidirect
3. #20299534C2semidirect
4. #20299468C2semidirect
8. #16813686C4semidirect
14. C4×Dic226C4semidirect
15. #16813587C4semidirect
16. D4×Dic113C4semidirect
23. C4×D4×C113C4semidirect
26. #14268657C2×C4semidirect
29. C4×#90673C2×C4semidirect
106. C113#1759semidirect
119. C4×D4#90673semidirect

Maximal subgroups

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

subgroupindex
C2×#168136862
C4×#142686572
#202995342
#202994682
C4×#142686462
#1759113