Finite Group Databasebeta

← #28390547

Subgroups — #28390547

Order 14464.

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

normal subgroups only

This group has 536 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
1C2×#16813669C211yesmaximal, characteristic
2#20298616C212yesmaximal, complemented
3#20298606C212yesmaximal, complemented
4#20298582C211yesmaximal, characteristic, complemented
5#410×C113C211yesmaximal, characteristic, complemented
6#16813669—24no—
7#16813669—24no—
8C2×#14268647C412yescomplemented
9C2×#14268647C2211yescharacteristic
10C2×#14268646—21no—
11C2×#14268646—22no—
12C22×Dic226C412yescomplemented
13C22×Dic226C2211yescharacteristic
14C2×Q8×D113—21no—
15C2×#14268631C2212yes—
16#16813550—24no—
17#16813545—24no—
18#16813541—21no—
19#16813539—21no—
20C2×#41×C113C2211yescharacteristic
21#117×C113C2212yes—
22#99×C113—22no—
23#14268647—22no—
24#14268647—24no—
25#14268647—24no—
26#14268647D414yes—
27#14268646—216no—
28#14268646—28no—
29C2×Dic226—22no—
30C2×Dic226—21no—
31C2×Dic226—22no—
32C2×Dic226—24no—
33C2×Dic226—24no—
34C2×Dic226C2×C411yescharacteristic
35C2×Dic226C2×C412yes—
36C2×Dic226D414yes—
37Q8×D113—28no—
38C2×D452C2×C411yescharacteristic
39C2×C22⋊D113—22no—
40C2×C22⋊D113—21no—
41C22×Dic113—22no—
42C22×Dic113—21no—
43C2×C4×D113—22no—
44C2×C4×D113—21no—
45#14268631—22no—
46#14268631—22no—
47C2×#11744751—22no—
48#41×C113—22no—
49#41×C113—22no—
50C2×Q8×C113D411yescharacteristic
51C2×D4×C113D411yescharacteristic
52C2×D4×C113D412yes—
53C22×C4×C113C2×C412yes—
54C22×C4×C113C2311yescharacteristic
55C4⋊C4×C113—22no—
56C22⋊C4×C113—22no—
57C42×C113—22no—
58C23×C113C22⋊C412yes—
59C23×C113C2×D411yescharacteristic
60C22×D113—21no—
61Q8×C113—22no—
62D4×C113—24no—
63D4×C113—22no—
64C2×C4×C113—22no—
65C2×C4×C113—22no—
66C2×C4×C113—42no—
67C2×C4×C113C22⋊C412yes—
68C2×C4×C113C22×C411yescharacteristic
69C2×C4×C113C2×D412yes—
70C2×C4×C113C2×D412yes—
71C2×C4×C113C2×D411yescharacteristic
72C22⋊D113—28no—
73C22⋊D113—24no—
74C2×Dic113—28no—
75C2×Dic113—22no—
76C2×Dic113—21no—
77C2×Dic113—24no—
78D452—21no—
79D452C22⋊C412yes—
80C4×D113—28no—
81C4×D113—24no—
82Dic226—28no—
83Dic226—22no—
84Dic226—21no—
85Dic226—24no—
86Dic226C22⋊C412yes—
87Dic226C22⋊C414yes—
88#11744751—42no—
89C22×C113—22no—
90C22×C113—41no—
91C22×C113—42no—
92C22×C113C2×C22⋊C411yescharacteristic
93C22×C113#12012yes—
94C2×D113—22no—
95C2×D113—42no—
96C4×C113—22no—
97C4×C113—82no—
98C4×C113C2×C22⋊C411yescharacteristic
99C4×C113C2×C22⋊C411yescharacteristic
100C4×C113#12012yes—
101Dic113—22no—
102Dic113—24no—
103C2×C113—22no—
104C2×C113—21no—
105C2×C113—42no—
106C2×C113#37911yescharacteristic
107D113—42no—
108#1796—1131nomaximal, Sylow
109C113#179611yescharacteristic, complemented, Sylow
110C2×2−1+4—1131no—
111#421—1132no—
112#419—1132no—
113#413—1131no—
114#410D11311yescharacteristic, complemented
1152−1+4—2264no—
1162−1+4—2264no—
117C2×#41—1132no—
118C2×#41—1131no—
119C2×#41—2261no—
120C2×#41—2262no—
121C2×#41C2×D11311yescharacteristic
122C22×Q8—1132no—
123C22×Q8—1131no—
124C22×Q8—2261no—
125C2×M16—1132no—
126#117C2×D11312yes—
127#104—2264no—
128#103—2264no—
129#101—2261no—
130#100—2261no—
131#99—22no—
132#41—22no—
133#41—22no—
134#41—1134no—
135#41—2264no—
136#41—2264no—
137#41—22616no—
138#41—2268no—
139#41—2262no—
140C2×Q8—1132no—
141C2×Q8—1131no—
142C2×Q8—1134no—
143C2×Q8—2264no—
144C2×Q8—2264no—
145C2×Q8—2268no—
146C2×Q8—2262no—
147C2×Q8—2262no—
148C2×Q8—2261no—
149C2×Q8D45211yescharacteristic
150C2×D4—1131no—
151C2×D4—2262no—
152C2×D4—2261no—
153C2×D4D45211yescharacteristic
154C2×D4C22⋊D11312yes—
155C22×C4—2262no—
156C22×C4—2261no—
157C22×C4—2262no—
158C22×C4—2261no—
159C22×C4C4×D11312yes—
160C22×C4C22×D11311yescharacteristic
161M16—2262no—
162M16—2262no—
163C2×C8—2262no—
164C4⋊C4—22no—
165C22⋊C4—22no—
166C42—22no—
167C23—2261no—
168C23#1426862412yes—
169C23C2×C22⋊D11311yescharacteristic
170Q8—22no—
171Q8—1134no—
172Q8—1132no—
173Q8—2268no—
174Q8—2262no—
175Q8—2261no—
176Q8—2264no—
177D4—24no—
178D4—22no—
179D4—1132no—
180D4—2268no—
181D4—2264no—
182D4—2261no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—2268no—
187C2×C4—2268no—
188C2×C4—2261no—
189C2×C4—2262no—
190C2×C4—2264no—
191C2×C4—2264no—
192C2×C4#1426862412yes—
193C2×C4C2×C4×D11311yescharacteristic
194C2×C4D4×D11312yes—
195C2×C4D4×D11312yes—
196C2×C4C2×D45211yescharacteristic
197C8—4522no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—4522no—
202C22—2262no—
203C22C2×#1426862411yescharacteristic
204C22#1681359012yes—
205C4—22no—
206C4—82no—
207C4—2264no—
208C4—2262no—
209C4C22⋊C4×D11311yescharacteristic
210C4C22⋊C4×D11311yescharacteristic
211C4#1681359212yes—
212C2—22no—
213C2—21no—
214C2—42no—
215C2—4522no—
216C2#2029845311yescharacteristic
subgroupG/H
centerC2#20298453
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#410×C113C2
socleC2×C113#379
prime radicalC2×#16813669C2
cosocleC22×C4×C113C23
hypercenter#410D113
hypocenterC113#1796
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. #20298616C2semidirect
3. #20298606C2semidirect
4. #20298582C2semidirect
5. #410×C113C2semidirect
8. C2×#14268647C4semidirect
12. C22×Dic226C4semidirect
109. C113#1796semidirect
114. #410D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136692
#202986162
#202986062
#202985822
#410×C1132
#1796113