Finite Group Databasebeta

← #28390540

Subgroups — #28390540

Order 14464.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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#20299434C211yesmaximal, characteristic
2#20298616C212yesmaximal, complemented
3#20298592C212yesmaximal, complemented
4#20298565C211yesmaximal, characteristic, complemented
5#410×C113C211yesmaximal, characteristic, complemented
6#16813670C412yescomplemented
7#16813669—22no—
8#16813668—22no—
9#16813667—22no—
10#16813667C412yescomplemented
11C2×#14268647—22no—
12C2×#14268647C2212yes—
13#41×D113—24no—
14C2×#14268631C2211yescharacteristic, complemented
15C22×#11744751C2211yescharacteristic, complemented
16#16813550—24no—
17#16813545—22no—
18#16813542—22no—
19C22⋊#11744751—22no—
20C2×#41×C113C2211yescharacteristic
21#117×C113C2212yescomplemented
22#99×C113—22no—
23#14268648—24no—
24#14268647—24no—
25#14268647—24no—
26#14268647—24no—
27#14268647—22no—
28#14268647—22no—
29#14268647C2×C414yes—
30#14268647D414yes—
31#14268646—28no—
32#14268646—24no—
33C2×Dic226—22no—
34C2×Dic226D412yes—
35Q8×D113—24no—
36C2×D452—22no—
37C2×D452D412yes—
38C2×C22⋊D113—24no—
39C2×C22⋊D113—22no—
40D4×D113—28no—
41D4×D113—24no—
42C2×C4×D113—24no—
43C2×C4×D113—22no—
44#14268631—22no—
45C2×#11744751—21no—
46C2×#11744751—22no—
47C2×#11744751—21no—
48#41×C113—22no—
49#41×C113—22no—
50C2×Q8×C113C2×C411yescharacteristic
51C2×D4×C113C2×C411yescharacteristic
52C2×D4×C113D412yes—
53C22×C4×C113D412yes—
54C22×C4×C113C2311yescharacteristic
55C4⋊C4×C113—22no—
56C22⋊C4×C113—22no—
57C42×C113—22no—
58C23×C113C22⋊C412yes—
59C23×C113C2×D411yescharacteristic
60C22×D113—24no—
61C22×D113—22no—
62Q8×C113—22no—
63D4×C113—24no—
64D4×C113—22no—
65C2×C4×C113—22no—
66C2×C4×C113—22no—
67C2×C4×C113—42no—
68C2×C4×C113C22⋊C412yes—
69C2×C4×C113C22×C411yescharacteristic
70C2×C4×C113C2×D412yes—
71C2×C4×C113C2×D412yes—
72C2×C4×C113C2×D411yescharacteristic
73C22⋊D113—28no—
74C22⋊D113—24no—
75C22⋊D113—24no—
76C2×Dic113—24no—
77C2×Dic113—22no—
78D452—24no—
79D452—22no—
80D452C22⋊C414yes—
81C4×D113—28no—
82C4×D113—24no—
83C4×D113—24no—
84Dic226—24no—
85Dic226—22no—
86Dic226C22⋊C414yes—
87#11744751—41no—
88#11744751—41no—
89C22×C113—22no—
90C22×C113—41no—
91C22×C113—42no—
92C22×C113C2×C22⋊C411yescharacteristic
93C22×C113#12012yes—
94C2×D113—24no—
95C2×D113—82no—
96C2×D113—84no—
97C4×C113—22no—
98C4×C113—82no—
99C4×C113C2×C22⋊C412yes—
100C4×C113#12011yescharacteristic
101C4×C113#12011yescharacteristic
102Dic113—24no—
103C2×C113—22no—
104C2×C113—21no—
105C2×C113—42no—
106C2×C113#37911yescharacteristic
107D113—44no—
108#1794—1131nomaximal, Sylow
109C113#179411yescharacteristic, complemented, Sylow
110#585—1131no—
111#421—1132no—
112#416—1132no—
113#410D11311yescharacteristic, complemented
114#408—1131no—
1152−1+4—1132no—
1162−1+4—2262no—
117H(5,𝔽2)—1132no—
118H(5,𝔽2)—2262no—
119H(5,𝔽2)—2262no—
120C2×#41—1132no—
121C2×#41—2264no—
122C2×#41—2262no—
123C2×#41C2×D11311yescharacteristic
124C2×M16—1131no—
125C22×C8—1131no—
126#117C2×D11312yescomplemented
127#104—2264no—
128#103—2262no—
129#102—2262no—
130#99—22no—
131C22⋊C8—2262no—
132#41—22no—
133#41—22no—
134#41—1134no—
135#41—1134no—
136#41—2264no—
137#41—2264no—
138#41—2264no—
139#41—2268no—
140#41—2264no—
141#41—2264no—
142#41—2262no—
143#41—2262no—
144C2×Q8—1132no—
145C2×Q8—2262no—
146C2×Q8—2264no—
147C2×Q8C4×D11311yescharacteristic
148C2×D4—1132no—
149C2×D4—2262no—
150C2×D4—2264no—
151C2×D4—2268no—
152C2×D4—2264no—
153C2×D4—2262no—
154C2×D4C4×D11311yescharacteristic
155C2×D4C22⋊D11312yes—
156C22×C4—2264no—
157C22×C4—2262no—
158C22×C4D45212yes—
159C22×C4C22×D11311yescharacteristic
160M16—2262no—
161C2×C8—2262no—
162C2×C8—2261no—
163C2×C8—2261no—
164C4⋊C4—22no—
165C22⋊C4—22no—
166C42—22no—
167C23—2264no—
168C23—2262no—
169C23#1426862412yes—
170C23C2×C22⋊D11311yescharacteristic
171Q8—22no—
172Q8—1134no—
173Q8—2264no—
174Q8—2262no—
175D4—24no—
176D4—22no—
177D4—1134no—
178D4—2264no—
179D4—2268no—
180D4—2264no—
181D4—2264no—
182D4—2262no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—2268no—
187C2×C4—2264no—
188C2×C4—2262no—
189C2×C4—2264no—
190C2×C4—2264no—
191C2×C4#1426862412yes—
192C2×C4C2×C4×D11311yescharacteristic
193C2×C4D4×D11312yes—
194C2×C4D4×D11312yes—
195C2×C4C2×D45211yescharacteristic
196C8—4521no—
197C8—4521no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—9042no—
202C22—9044no—
203C22—2264no—
204C22C2×#1426862411yescharacteristic
205C22#1681359012yes—
206C4—22no—
207C4—82no—
208C4—2264no—
209C4C22⋊C4×D11312yes—
210C4#1681359211yescharacteristic
211C4#1681359211yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—4524no—
216C2#2029845311yescharacteristic
subgroupG/H
centerC4#16813592
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#410×C113C2
socleC2×C113#379
prime radical#20299434C2
cosocleC22×C4×C113C23
hypercenter#410D113
hypocenterC113#1794
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #20298616C2semidirect
3. #20298592C2semidirect
4. #20298565C2semidirect
5. #410×C113C2semidirect
6. #16813670C4semidirect
10. #16813667C4semidirect
14. C2×#14268631C22semidirect
15. C22×#11744751C22semidirect
21. #117×C113C22semidirect
109. C113#1794semidirect
113. #410D113semidirect
126. #117C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994342
#202986162
#202985922
#202985652
#410×C1132
#1794113