Finite Group Databasebeta

← #28391071

Subgroups — #28391071

Order 14464.

310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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×#16813652C211yesmaximal, characteristic
2#20299075C211yesmaximal, characteristic, complemented
3#20298615C211yesmaximal, characteristic
4#20298606C211yesmaximal, characteristic, complemented
5#20298368C211yesmaximal, characteristic, complemented
6#20298354C211yesmaximal, characteristic, complemented
7#410×C113C211yesmaximal, characteristic
8C22×Dic226C2211yescharacteristic
9#16813652—22no—
10#16813652—22no—
11C2×#14268637C412yescomplemented
12C2×#14268635C412yescomplemented
13C2×#14268631C2211yescharacteristic
14C2×#14268631C2211yescharacteristic
15C4×Dic226—22no—
16#16813587—22no—
17#16813581C2211yescharacteristic
18#16813578—22no—
19#16813549—22no—
20#16813545—22no—
21C2×#41×C113C2211yescharacteristic
22#117×C113C2211yescharacteristic
23#117×C113C2211yescharacteristic
24#99×C113—22no—
25C2×Dic226—21no—
26C2×Dic226—21no—
27C2×Dic226—21no—
28C2×Dic226C2×C412yes—
29C2×Dic226D412yes—
30C2×Dic226D412yes—
31C22×Dic113—21no—
32#14268637—24no—
33#14268635—24no—
34#14268631—21no—
35#14268631—21no—
36#14268631—21no—
37#14268631—21no—
38C2×#11744751—21no—
39C2×#11744751C2×C412yes—
40C4⋊Dic113—21no—
41#14268626—24no—
42C22⋊Dic113—21no—
43C4×Dic113—24no—
44C4×Dic113D412yes—
45#41×C113—21no—
46#41×C113—21no—
47#41×C113—21no—
48#41×C113—21no—
49C2×Q8×C113C2×C411yescharacteristic
50C2×D4×C113—21no—
51C2×D4×C113C2×C411yescharacteristic
52C22×C4×C113—21no—
53C22×C4×C113C2311yescharacteristic
54C4⋊C4×C113—21no—
55C4⋊C4×C113—21no—
56C22⋊C4×C113—21no—
57C22⋊C4×C113D412yes—
58C42×C113—21no—
59C42×C113—21no—
60C23×C113—21no—
61C23×C113C2×D411yescharacteristic
62Q8×C113—21no—
63Q8×C113—21no—
64D4×C113—21no—
65D4×C113—21no—
66D4×C113—41no—
67D4×C113—41no—
68C2×C4×C113—21no—
69C2×C4×C113—22no—
70C2×C4×C113—41no—
71C2×C4×C113—41no—
72C2×C4×C113—41no—
73C2×C4×C113C22×C411yescharacteristic
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2×D411yescharacteristic
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113#4111yescharacteristic
78C2×C4×C113#4111yescharacteristic
79C2×Dic113—22no—
80C2×Dic113—22no—
81C2×Dic113—22no—
82C2×Dic113—22no—
83Dic226—22no—
84Dic226—22no—
85Dic226—22no—
86Dic226C22⋊C414yes—
87#11744751—22no—
88#11744751—41no—
89C22×C113—41no—
90C22×C113—41no—
91C22×C113—81no—
92C22×C113C4×D411yescharacteristic
93C22×C113#12011yescharacteristic
94C22×C113#12111yescharacteristic
95C4×C113—42no—
96C4×C113—41no—
97C4×C113—81no—
98C4×C113C2×C22⋊C411yescharacteristic
99C4×C113C4×D411yescharacteristic
100C4×C113#12111yescharacteristic
101C4×C113#12311yescharacteristic
102Dic113—24no—
103Dic113—42no—
104C2×C113—21no—
105C2×C113—21no—
106C2×C113—21no—
107C2×C113—81no—
108C2×C113#38611yescharacteristic
109#1905—1131nomaximal, Sylow
110C113#190511yescharacteristic, complemented, Sylow
111C2×#137—1131no—
112#519—1131no—
113#421—1131no—
114#419—1131no—
115#410D11311yescharacteristic
116#344—1131no—
117H(3,ℤ/4)—1131no—
118C2×#41C2×D11311yescharacteristic
119C22×Q8—1131no—
120#137—2262no—
121#137—2262no—
122C2×Q16—1132no—
123C2×SD16—1132no—
124C2×M16—1131no—
125C2×M16—1131no—
126C4×Q8—2262no—
127C4×Q8—2262no—
128#117—1131no—
129#117—2262no—
130#117C2×D11311yescharacteristic
131#117C2×D11311yescharacteristic
132#104—2262no—
133#103—2262no—
134#99—22no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—1132no—
140C2×Q8—1132no—
141C2×Q8—1132no—
142C2×Q8—2261no—
143C2×Q8—2261no—
144C2×Q8—2261no—
145C2×Q8C4×D11311yescharacteristic
146C2×D4—21no—
147C2×D4C4×D11311yescharacteristic
148C22×C4—21no—
149C22×C4—2261no—
150C22×C4C22×D11311yescharacteristic
151Q16—2264no—
152SD16—2264no—
153M16—2261no—
154M16—2261no—
155M16—2261no—
156M16—2261no—
157C2×C8—1132no—
158C2×C8—2261no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—2264no—
162C4⋊C4—2261no—
163C22⋊C4—21no—
164C22⋊C4—2261no—
165C22⋊C4C22⋊D11312yes—
166C42—21no—
167C42—21no—
168C42—1132no—
169C42—2264no—
170C23—21no—
171C23C2×C22⋊D11311yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—1134no—
175Q8—2262no—
176Q8—2262no—
177Q8—2262no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—2262no—
188C2×C4—2262no—
189C2×C4—2262no—
190C2×C4—2262no—
191C2×C4C2×C4×D11311yescharacteristic
192C2×C4D4×D11311yescharacteristic
193C2×C4D4×D11311yescharacteristic
194C2×C4D4×D11311yescharacteristic
195C2×C4#1426864611yescharacteristic
196C2×C4#1426864711yescharacteristic
197C8—4521no—
198C8—2262no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22C4×C22⋊D11311yescharacteristic
203C22#1681359011yescharacteristic
204C22#1681359311yescharacteristic
205C4—42no—
206C4—41no—
207C4—81no—
208C4—4522no—
209C4—2264no—
210C4C22⋊C4×D11311yescharacteristic
211C4#1681358211yescharacteristic
212C4#1681359511yescharacteristic
213C4#1681360411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#2029847411yescharacteristic
subgroupG/H
centerC2#20298474
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#410×C113C2
socleC2×C113#386
prime radicalC2×#41×C113C22
cosocleC22×C4×C113C23
hypercenter#410D113
hypocenterC113#1905
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #20299075C2semidirect
4. #20298606C2semidirect
5. #20298368C2semidirect
6. #20298354C2semidirect
11. C2×#14268637C4semidirect
12. C2×#14268635C4semidirect
110. C113#1905semidirect

Maximal subgroups

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

subgroupindex
C2×#168136522
#202990752
#202986152
#202986062
#202983682
#202983542
#410×C1132
#1905113