Finite Group Databasebeta

← D113⋊#356 #28406863

Subgroups — D113⋊#356 #28406863

Order 14464.

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

normal subgroups only

This group has 240 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
1D113⋊#101C212yesmaximal
2#20299509C212yesmaximal, complemented
3#20299508C212yesmaximal, complemented
4C4⋊Q8×D113C211yesmaximal, characteristic
5D113⋊M16—22no—
6#16813683—22no—
7#16813683C2214yes—
8C2×Q8×D113C411yescharacteristic
9C2×Q8×D113C2211yescharacteristic
10#16813622C2211yescharacteristic
11#16813621—22no—
12#16813620C411yescharacteristic
13#16813620C2211yescharacteristic
14C4⋊C4×D113—22no—
15C42×D113C411yescharacteristic
16C4⋊Q8×C113C411yescharacteristic
17#14268657—42no—
18#14268656—24no—
19#14268655—42no—
20C2×Dic226—21no—
21C2×Dic226C2×C411yescharacteristic
22C2×Dic226D412yes—
23C2×Dic226C2311yescharacteristic
24Q8×D113—41no—
25Q8×D113—41no—
26Q8×D113—41no—
27Q8×D113—41no—
28C2×C4×D113—21no—
29C2×C4×D113—21no—
30C2×C4×D113C2×C411yescharacteristic
31C2×C4×D113D412yes—
32C4⋊Dic113—22no—
33#14268626—22no—
34#14268626—22no—
35C4×Dic113—21no—
36C4×Dic113C2×C411yescharacteristic
37C2×Q8×C113C2×C411yescharacteristic
38C2×Q8×C113C2×C411yescharacteristic
39C4⋊C4×C113—22no—
40C42×C113C2×C411yescharacteristic
41C22×D113C22⋊C411yescharacteristic
42Q8×C113—41no—
43Q8×C113—41no—
44C2×C4×C113—21no—
45C2×C4×C113—21no—
46C2×C4×C113C22⋊C412yes—
47C2×C4×C113C22×C411yescharacteristic
48C2×Dic113—21no—
49C2×Dic113—21no—
50C2×Dic113C22⋊C411yescharacteristic
51C2×Dic113C2×D412yes—
52C4×D113—24no—
53C4×D113—21no—
54C4×D113—21no—
55C4×D113—22no—
56C4×D113—22no—
57C4×D113—41no—
58C4×D113—41no—
59Dic226—42no—
60Dic226—41no—
61Dic226—42no—
62Dic226—41no—
63#11744753—44no—
64C22×C113C2×C22⋊C411yescharacteristic
65C2×D113—22no—
66C2×D113#9911yescharacteristic
67C2×D113#9911yescharacteristic
68C4×C113—22no—
69C4×C113—21no—
70C4×C113—22no—
71C4×C113—41no—
72Dic113—22no—
73Dic113—22no—
74Dic113—21no—
75Dic113—41no—
76C2×C113—21no—
77C2×C113C2×#9911yescharacteristic
78D113—21no—
79D113#35612yescomplemented
80C2×#356—1131nomaximal, Sylow
81C113C2×#35611yescharacteristic, complemented, Sylow
82C2×C4⋊Q8—1131no—
83C2×#101—1132no—
84#356—1132no—
85#356—1132no—
86C22×Q8—1131no—
87C22×Q8—1131no—
88C2×M16—2262no—
89C4⋊Q8—1131no—
90C4⋊Q8—1131no—
91C4⋊Q8—1131no—
92C4⋊Q8—2262no—
93C4⋊Q8#9067311yescharacteristic
94C2×C4⋊C4—2262no—
95C2×C42—1131no—
96#101—1134no—
97#101—2262no—
98C2×Q8—1132no—
99C2×Q8—1131no—
100C2×Q8—1131no—
101C2×Q8—4521no—
102C2×Q8—4521no—
103C2×Q8—4521no—
104C2×Q8—4521no—
105C2×Q8—2261no—
106C2×Q8C2×#9067311yescharacteristic
107C2×Q8C2×#9067311yescharacteristic
108C22×C4—1132no—
109C22×C4—1131no—
110C22×C4—2261no—
111C22×C4—2261no—
112M16—4522no—
113M16—2264no—
114C2×C8—4522no—
115C4⋊C4—22no—
116C4⋊C4—2262no—
117C4⋊C4—2262no—
118C4⋊C4—2262no—
119C42—1131no—
120C42—2261no—
121C42C2×#9067311yescharacteristic
122C23—1131no—
123Q8—41no—
124Q8—41no—
125Q8—4521no—
126Q8—4522no—
127Q8—4521no—
128Q8—4522no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—1131no—
132C2×C4—1132no—
133C2×C4—4521no—
134C2×C4—4521no—
135C2×C4—2262no—
136C2×C4—2262no—
137C2×C4—2261no—
138C2×C4—2261no—
139C2×C4—2264no—
140C2×C4—2261no—
141C2×C4—2261no—
142C2×C4C22⋊#9067312yes—
143C2×C4C22×#9067311yescharacteristic
144C8—4524no—
145C22—1131no—
146C22—1131no—
147C22—2262no—
148C22C2×C22⋊#9067311yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—41no—
153C4—4521no—
154C4—2262no—
155C4—2262no—
156C4—2261no—
157C2—21no—
158C2—1132no—
159C2—2261no—
160C2D113⋊#9911yescharacteristic
subgroupG/H
centerC2D113⋊#99
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4⋊Q8×C113C4
socleC2×C113C2×#99
prime radicalC22×D113C22⋊C4
cosocleC2×Dic226C23
hypercenterC4⋊Q8#90673
hypocenterC113C2×#356
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #20299509C2semidirect
3. #20299508C2semidirect
79. D113#356semidirect
81. C113C2×#356semidirect

Maximal subgroups

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

subgroupindex
D113⋊#1012
#202995092
#202995082
C4⋊Q8×D1132
C2×#356113