Finite Group Databasebeta

← #28406736

Subgroups — #28406736

Order 14464.

276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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⋊#108C211yesmaximal, characteristic
2#20299591C212yesmaximal
3D113⋊#101C212yesmaximal
4#20299561C211yesmaximal, characteristic
5C2×Q16×D113C211yesmaximal, characteristic
6D113⋊M16C2212yes—
7D113⋊M16C2211yescharacteristic
8#16813701C2211yescharacteristic
9#16813693—21no—
10#16813692—21no—
11#16813685—24no—
12#16813683—24no—
13#16813676—21no—
14C8×#90673—21no—
15C2×Q8×D113C2212yes—
16C2×Dic452C411yescharacteristic, complemented
17C2×#14268637C412yescomplemented
18Q16×D113—21no—
19Q16×D113—21no—
20Q16×D113—21no—
21Q16×D113—21no—
22C2×C8×D113C2211yescharacteristic
23C2×Q16×C113C411yescharacteristic, complemented
24#14268657—21no—
25#14268657—22no—
26#14268656—22no—
27#14268656D412yes—
28#14268655—21no—
29#14268655—22no—
30C4⋊#90673D412yes—
31C22⋊#90673—21no—
32C4×#90673—21no—
33C2×Dic226—22no—
34C2×Dic226C2×C412yes—
35Q8×D113—22no—
36Q8×D113—22no—
37Q8×D113—22no—
38Q8×D113—22no—
39C2×C4×D113—22no—
40C2×C4×D113C2311yescharacteristic
41Dic452—21no—
42Dic452—21no—
43#14268637—22no—
44#14268637—22no—
45C2×#11744751C2×C411yescharacteristic
46C8×D113D411yescharacteristic
47C8×D113D411yescharacteristic
48C8×D113D411yescharacteristic
49C8×D113D411yescharacteristic
50C2×Q8×C113C2×C412yes—
51Q16×C113—21no—
52Q16×C113—21no—
53C2×C8×C113C2×C411yescharacteristic
54C22×D113#4111yescharacteristic
55C2×#90673—22no—
56Q8×C113—22no—
57Q8×C113—22no—
58C2×C4×C113—22no—
59C2×C4×C113C22×C411yescharacteristic
60C2×Dic113—22no—
61C2×Dic113C2×D411yescharacteristic
62C4×D113—42no—
63C4×D113—42no—
64C4×D113C2×D411yescharacteristic
65C4×D113C2×D411yescharacteristic
66C4×D113C2×D411yescharacteristic
67C4×D113#4111yescharacteristic
68Dic226—22no—
69Dic226—22no—
70Dic226—42no—
71Dic226—42no—
72#11744753—22no—
73#11744753—42no—
74C8×C113C22⋊C411yescharacteristic
75C8×C113C22⋊C411yescharacteristic
76#11744751C22⋊C411yescharacteristic
77#11744751C22⋊C411yescharacteristic
78C22×C113C4×D411yescharacteristic
79C2×D113—22no—
80C2×D113#12111yescharacteristic
81C2×D113#12411yescharacteristic
82#90673—42no—
83C4×C113—42no—
84C4×C113C2×C22⋊C411yescharacteristic
85C4×C113C4×D411yescharacteristic
86Dic113—42no—
87Dic113#12111yescharacteristic
88Dic113#12711yescharacteristic
89C2×C113—21no—
90C2×C113#39011yescharacteristic
91D113—21no—
92D113#47312yes—
93#1979—1131nomaximal, Sylow
94C113#197911yescharacteristic, complemented, Sylow
95C22×Q16—1131no—
96C2×#108—1131no—
97#419—1132no—
98C2×#101—1132no—
99#405—1131no—
100C22×Q8—1132no—
101C2×Q16—1132no—
102C2×Q16—1131no—
103C2×Q16—2261no—
104C2×Q16—2261no—
105C2×Q16—2261no—
106C2×Q16—2261no—
107C2×Q16#9067311yescharacteristic, complemented
108C2×M16—1131no—
109C2×M16—1132no—
110C22×C8—1131no—
111#117—1131no—
112#108—2261no—
113#108—2261no—
114#103—2264no—
115#101—2264no—
116#97—2261no—
117C4×C8—2261no—
118C2×Q8—1132no—
119C2×Q8—2262no—
120C2×Q8—2262no—
121C2×Q8—2262no—
122C2×Q8—2262no—
123C2×Q8—2262no—
124C2×Q8C2×#9067312yes—
125C22×C4—1131no—
126C22×C4—2262no—
127Q16—21no—
128Q16—21no—
129Q16—2262no—
130Q16—2262no—
131Q16—2261no—
132Q16—2261no—
133M16—1132no—
134M16—2262no—
135M16—2262no—
136M16—2261no—
137C2×C8—1131no—
138C2×C8—1131no—
139C2×C8—1131no—
140C2×C8—1131no—
141C2×C8—1131no—
142C2×C8—2262no—
143C2×C8—2261no—
144C2×C8C2×#9067311yescharacteristic
145C4⋊C4—1132no—
146C22⋊C4—2261no—
147C42—2261no—
148C23—1131no—
149Q8—22no—
150Q8—22no—
151Q8—4522no—
152Q8—4522no—
153Q8—2262no—
154Q8—2262no—
155C2×C4—22no—
156C2×C4—1131no—
157C2×C4—1131no—
158C2×C4—1131no—
159C2×C4—1131no—
160C2×C4—1131no—
161C2×C4—4522no—
162C2×C4—4522no—
163C2×C4—2262no—
164C2×C4—2262no—
165C2×C4C22×#9067311yescharacteristic
166C8—1131no—
167C8—1131no—
168C8—4522no—
169C8—2262no—
170C8C22⋊#9067311yescharacteristic
171C8C22⋊#9067311yescharacteristic
172C22—1131no—
173C22—1131no—
174C22—2262no—
175C22D4×#9067311yescharacteristic
176C4—42no—
177C4—1131no—
178C4—1131no—
179C4—4522no—
180C4—4522no—
181C4C2×C22⋊#9067311yescharacteristic
182C4D4×#9067311yescharacteristic
183C2—21no—
184C2—1132no—
185C2—2261no—
186C2#2029955011yescharacteristic
subgroupG/H
centerC2#20299550
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×Q16×C113C4
socleC2×C113#390
prime radicalC22×D113#41
cosocleC2×C4×D113C23
hypercenterC2×Q16#90673
hypocenterC113#1979
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
16. C2×Dic452C4semidirect
17. C2×#14268637C4semidirect
23. C2×Q16×C113C4semidirect
94. C113#1979semidirect
107. C2×Q16#90673semidirect

Maximal subgroups

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

subgroupindex
D113⋊#1082
#202995912
D113⋊#1012
#202995612
C2×Q16×D1132
#1979113