Finite Group Databasebeta

← #28406865

Subgroups — #28406865

Order 14464.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#20299584C212yesmaximal, complemented
2#20299508C212yesmaximal, complemented
3#20299506C212yesmaximal, complemented
4#20299144C211yesmaximal, characteristic
5D113⋊M16—22no—
6#16813683C2214yes—
7#16813682—22no—
8C2×#14268647C2211yescharacteristic
9#16813620C2211yescharacteristic
10#16813618C411yescharacteristic
11#16813611C411yescharacteristic
12#16813609C2211yescharacteristic
13#16813594—22no—
14C4×C22⋊D113—22no—
15C2×C4×Dic113C411yescharacteristic
16C2×#41×C113C411yescharacteristic
17#14268657—42no—
18#14268656—24no—
19#14268655—42no—
20#14268647—41no—
21#14268647—41no—
22C2×Dic226C2311yescharacteristic
23C2×D452C2×C411yescharacteristic
24C2×C22⋊D113—22no—
25C2×C22⋊D113D412yes—
26C22×Dic113—21no—
27C2×C4×D113D412yes—
28#14268626—22no—
29C22⋊Dic113—22no—
30#14268624—22no—
31C4×Dic113—21no—
32C4×Dic113C2×C411yescharacteristic
33C4×Dic113C2×C411yescharacteristic
34#41×C113—41no—
35#41×C113—41no—
36C2×Q8×C113C2×C411yescharacteristic
37C2×D4×C113—21no—
38C2×D4×C113C2×C411yescharacteristic
39C22×C4×C113—21no—
40C22×C4×C113C2×C411yescharacteristic
41C23×C113—21no—
42C23×C113C22⋊C411yescharacteristic
43C22×D113C22⋊C412yes—
44Q8×C113—41no—
45D4×C113—41no—
46D4×C113—42no—
47C2×C4×C113—21no—
48C2×C4×C113—21no—
49C2×C4×C113—21no—
50C2×C4×C113—41no—
51C2×C4×C113—41no—
52C2×C4×C113C22⋊C411yescharacteristic
53C2×C4×C113C22×C411yescharacteristic
54C22⋊D113—42no—
55C22⋊D113—44no—
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—42no—
59C2×Dic113C2×D412yes—
60D452—41no—
61C4×D113—22no—
62C4×D113—22no—
63Dic226—41no—
64#11744753—44no—
65C22×C113—21no—
66C22×C113—41no—
67C22×C113—42no—
68C22×C113—41no—
69C22×C113C2×C22⋊C411yescharacteristic
70C2×D113—22no—
71C2×D113—42no—
72C4×C113—21no—
73C4×C113—41no—
74C4×C113#9911yescharacteristic
75C4×C113#9911yescharacteristic
76Dic113—22no—
77Dic113—22no—
78Dic113—41no—
79C2×C113—21no—
80C2×C113—41no—
81C2×C113—81no—
82C2×C113C2×#9911yescharacteristic
83D113—42no—
84#2132—1131nomaximal, Sylow
85C113#213211yescharacteristic, complemented, Sylow
86#532—1131no—
87#413—1132no—
88#356—1132no—
89#355—1132no—
90C2×#41—1131no—
91C2×#41#9067311yescharacteristic
92C2×M16—2262no—
93C4⋊Q8—1131no—
94#127—1131no—
95#124—1131no—
96#124—1131no—
97#121—2262no—
98C4×D4—2262no—
99C2×C42—1131no—
100#101—1134no—
101#100—2262no—
102#41—41no—
103#41—41no—
104#41—4521no—
105#41—4521no—
106C2×Q8—1131no—
107C2×Q8C2×#9067311yescharacteristic
108C2×D4—21no—
109C2×D4—1132no—
110C2×D4—1131no—
111C2×D4—2262no—
112C2×D4C2×#9067311yescharacteristic
113C22×C4—21no—
114C22×C4—1132no—
115C22×C4—2261no—
116C22×C4C2×#9067311yescharacteristic
117M16—4522no—
118M16—2264no—
119C2×C8—4522no—
120C4⋊C4—2262no—
121C22⋊C4—2262no—
122C22⋊C4—2262no—
123C42—1131no—
124C42—1131no—
125C42—2261no—
126C23—21no—
127C23—1132no—
128C23C22⋊#9067311yescharacteristic
129Q8—41no—
130Q8—4521no—
131D4—41no—
132D4—42no—
133D4—4521no—
134D4—4522no—
135D4—4524no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—1132no—
142C2×C4—4522no—
143C2×C4—2261no—
144C2×C4—2261no—
145C2×C4—2262no—
146C2×C4—2262no—
147C2×C4C22⋊#9067311yescharacteristic
148C2×C4C22×#9067311yescharacteristic
149C8—4524no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—4522no—
155C22—2262no—
156C22C2×C22⋊#9067311yescharacteristic
157C4—21no—
158C4—41no—
159C4—4521no—
160C4—2262no—
161C4—2262no—
162C4#1681368011yescharacteristic
163C4#1681368011yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—4522no—
168C2C2×#1681368011yescharacteristic
subgroupG/H
centerC4#16813680
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×#41×C113C4
socleC2×C113C2×#99
prime radical#20299144C2
cosocleC2×Dic226C23
hypercenterC2×#41#90673
hypocenterC113#2132
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #20299584C2semidirect
2. #20299508C2semidirect
3. #20299506C2semidirect
85. C113#2132semidirect

Maximal subgroups

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

subgroupindex
#202995842
#202995082
#202995062
#202991442
#2132113