Finite Group Databasebeta

← #28390535

Subgroups — #28390535

Order 14464.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16813670C211yesmaximal, characteristic
2C2×#16813548C212yesmaximal, complemented
3#20298600C212yesmaximal, complemented
4#20298505C211yesmaximal, characteristic, complemented
5C2×#101×C113C211yesmaximal, characteristic, complemented
6#16813670—24no—
7#16813670—22no—
8#16813670C414yescomplemented
9C2×#14268648—22no—
10C2×#14268647—22no—
11C2×#14268647C2212yes—
12C2×Q8×D113—22no—
13C2×C4⋊Dic113C2211yescharacteristic
14C2×C4×Dic113C2211yescharacteristic
15#16813548—24no—
16#16813547—22no—
17#16813544—22no—
18#16813529—22no—
19C22×Q8×C113C2211yescharacteristic
20C2×M16×C113C2212yes—
21#101×C113—22no—
22#14268648—28no—
23#14268648—28no—
24#14268647—28no—
25#14268647—28no—
26#14268647—22no—
27#14268647—22no—
28#14268647C2×C414yes—
29#14268647D414yes—
30C2×Dic226—22no—
31C2×Dic226D412yes—
32Q8×D113—28no—
33Q8×D113—28no—
34C2×D452—22no—
35C2×D452D412yes—
36C2×C22⋊D113—22no—
37C22×Dic113—21no—
38C22×Dic113—21no—
39C2×C4×D113—24no—
40C2×C4×D113—22no—
41C4⋊Dic113—22no—
42C4×Dic113—22no—
43C2×Q8×C113—22no—
44C2×Q8×C113—22no—
45C2×Q8×C113C2×C412yes—
46C2×Q8×C113D412yes—
47C22×C4×C113D412yes—
48C22×C4×C113C2311yescharacteristic
49M16×C113—22no—
50M16×C113—22no—
51C2×C8×C113—22no—
52C23×C113C2×D411yescharacteristic
53C22×D113—22no—
54Q8×C113—24no—
55Q8×C113—24no—
56C2×C4×C113—22no—
57C2×C4×C113—22no—
58C2×C4×C113C22⋊C414yes—
59C2×C4×C113C22×C411yescharacteristic
60C2×C4×C113C2×D412yes—
61C2×C4×C113C2×D412yes—
62C2×C4×C113C2×D411yescharacteristic
63C22⋊D113—24no—
64C22⋊D113—24no—
65C2×Dic113—22no—
66C2×Dic113—22no—
67C2×Dic113—41no—
68C2×Dic113—41no—
69C2×Dic113—42no—
70C2×Dic113—41no—
71D452—28no—
72D452—22no—
73D452C22⋊C414yes—
74C4×D113—216no—
75C4×D113—24no—
76C4×D113—24no—
77Dic226—28no—
78Dic226—22no—
79Dic226C22⋊C414yes—
80C8×C113—42no—
81C22×C113—21no—
82C22×C113—21no—
83C22×C113C2×C22⋊C411yescharacteristic
84C22×C113#12011yescharacteristic
85C22×C113#12011yescharacteristic
86C2×D113—24no—
87C2×D113—42no—
88C2×D113—42no—
89C4×C113—24no—
90C4×C113C2×C22⋊C412yes—
91C4×C113#12012yes—
92Dic113—24no—
93Dic113—42no—
94Dic113—81no—
95C2×C113—21no—
96C2×C113—21no—
97C2×C113#37911yescharacteristic
98C2×C113#45411yescharacteristic
99C2×C113#45611yescharacteristic
100D113—44no—
101#1793—1131nomaximal, Sylow
102C113#179311yescharacteristic, complemented, Sylow
103C2×2−1+4—1131no—
104C2×#104—1132no—
105#417—1132no—
106C2×#101D11311yescharacteristic, complemented
107#391—1131no—
1082−1+4—1134no—
1092−1+4—2264no—
1102−1+4—2262no—
111C2×#41—1132no—
112C2×#41—2262no—
113C2×#41—2262no—
114C22×Q8—2262no—
115C22×Q8C2×D11311yescharacteristic
116C2×M16C2×D11312yes—
117C2×C4⋊C4—1131no—
118C2×C42—1131no—
119#104—2264no—
120#103—2262no—
121#102—2262no—
122#101—22no—
123#95—2262no—
124#41—1134no—
125#41—1134no—
126#41—2268no—
127#41—2268no—
128#41—2268no—
129#41—2268no—
130#41—2262no—
131#41—2262no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—1132no—
135C2×Q8—2262no—
136C2×Q8—2268no—
137C2×Q8—2268no—
138C2×Q8C4×D11312yes—
139C2×Q8C22⋊D11312yes—
140C2×D4—1132no—
141C2×D4—2262no—
142C2×D4—2262no—
143C22×C4—2264no—
144C22×C4—2261no—
145C22×C4—2261no—
146C22×C4—2262no—
147C22×C4D45212yes—
148C22×C4C22×D11311yescharacteristic
149M16—22no—
150M16—22no—
151C2×C8—22no—
152C4⋊C4—2262no—
153C42—2262no—
154C23—2262no—
155C23C2×D45211yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—1134no—
159Q8—2268no—
160Q8—2262no—
161D4—1134no—
162D4—2268no—
163D4—2264no—
164D4—2264no—
165D4—2262no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—4522no—
169C2×C4—4521no—
170C2×C4—4521no—
171C2×C4—4521no—
172C2×C4—22616no—
173C2×C4—2262no—
174C2×C4—2262no—
175C2×C4—2264no—
176C2×C4—2264no—
177C2×C4#1426862414yes—
178C2×C4C2×C4×D11311yescharacteristic
179C2×C4D4×D11312yes—
180C2×C4D4×D11312yes—
181C2×C4C2×C22⋊D11311yescharacteristic
182C8—42no—
183C22—21no—
184C22—21no—
185C22—4522no—
186C22—4522no—
187C22—2264no—
188C22C2×#1426862411yescharacteristic
189C22#1681359211yescharacteristic
190C22#1681359211yescharacteristic
191C4—24no—
192C4—9041no—
193C4—4522no—
194C4—2264no—
195C4C22⋊C4×D11312yes—
196C4#1681359012yes—
197C2—21no—
198C2—21no—
199C2—4524no—
200C2#2029845311yescharacteristic
201C2#2029877311yescharacteristic
202C2#2029878311yescharacteristic
subgroupG/H
centerC22#16813592
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#101×C113C2
socleC22×C113#120
prime radicalC2×#16813670C2
cosocleC22×C4×C113C23
hypercenterC2×#101D113
hypocenterC113#1793
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#16813548C2semidirect
3. #20298600C2semidirect
4. #20298505C2semidirect
5. C2×#101×C113C2semidirect
8. #16813670C4semidirect
102. C113#1793semidirect
106. C2×#101D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136702
C2×#168135482
#202986002
#202985052
C2×#101×C1132
#1793113