Finite Group Databasebeta

← #28399054

Subgroups — #28399054

Order 14464.

704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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
2#20299364C212yesmaximal, complemented
3#20298581C214yesmaximal, complemented
4#20298580C212yesmaximal, complemented
5C2×#16813541C211yesmaximal, characteristic, complemented
6#101×D113C214yesmaximal, complemented
7C2×#101×C113C211yesmaximal, characteristic, complemented
8#16813670—24no—
9#16813670—24no—
10C2×#14268648C412yes—
11C2×#14268648C2212yes—
12C2×#14268647C414yes—
13C2×#14268647C2211yescharacteristic
14C2×#14268647C2211yescharacteristic
15C2×Q8×D113C412yes—
16C2×Q8×D113C2212yes—
17#16813630—24no—
18#16813628—24no—
19C2×#14268631C2212yes—
20M16×D113C2218yes—
21#16813541C2214yes—
22#16813540C2214yes—
23#16813538C2214yes—
24C22×Q8×C113C2211yescharacteristic
25C2×M16×C113C2212yes—
26#101×C113C2214yes—
27#14268648—28no—
28#14268648—28no—
29#14268647—22no—
30#14268647—22no—
31#14268647—28no—
32#14268647—28no—
33#14268647D414yes—
34#14268647D414yes—
35C2×Dic226C2×C414yes—
36C2×Dic226C2×C411yescharacteristic
37C2×Dic226C2311yescharacteristic
38Q8×D113—28no—
39Q8×D113—28no—
40C2×D452C2×C414yes—
41C2×D452C2×C411yescharacteristic
42C2×D452C2311yescharacteristic
43C2×C22⋊D113C2×C412yes—
44C2×C22⋊D113C2×C412yes—
45C2×C4×D113C2×C414yes—
46C2×C4×D113C2×C412yes—
47C2×C4×D113C2×C414yes—
48C2×C4×D113C2312yes—
49#14268631—22no—
50#14268631C2314yes—
51#14268630—28no—
52C2×#11744751—22no—
53C8×D113—28no—
54C2×Q8×C113—22no—
55C2×Q8×C113—22no—
56C2×Q8×C113C2×C412yes—
57C2×Q8×C113C2312yes—
58C22×C4×C113C2×C412yes—
59C22×C4×C113C2311yescharacteristic
60M16×C113—22no—
61M16×C113C2314yes—
62C2×C8×C113—22no—
63C23×C113C22×C411yescharacteristic
64C22×D113C22×C412yes—
65C22×D113C22×C412yes—
66Q8×C113—24no—
67Q8×C113—24no—
68C2×C4×C113—22no—
69C2×C4×C113—22no—
70C2×C4×C113C22×C414yes—
71C2×C4×C113C22×C411yescharacteristic
72C2×C4×C113C2×D412yes—
73C2×C4×C113C2×D412yes—
74C2×C4×C113C2411yescharacteristic
75C22⋊D113—22no—
76C22⋊D113—22no—
77C22⋊D113C22⋊C414yes—
78C22⋊D113C22⋊C414yes—
79C2×Dic113C22×C412yes—
80C2×Dic113C22×C412yes—
81D452—28no—
82D452—22no—
83D452C22⋊C414yes—
84C4×D113—28no—
85C4×D113—24no—
86C4×D113—28no—
87C4×D113C2×D418yes—
88Dic226—22no—
89Dic226—28no—
90Dic226C22⋊C414yes—
91C8×C113—24no—
92#11744751—24no—
93C22×C113—41no—
94C22×C113C2×C22⋊C411yescharacteristic
95C22×C113C2×C22⋊C411yescharacteristic
96C22×C113C23×C411yescharacteristic
97C2×D113—22no—
98C2×D113—42no—
99C2×D113—42no—
100C2×D113C2×C22⋊C414yes—
101C4×C113—24no—
102C4×C113C2×C22⋊C412yes—
103C4×C113C22×D412yes—
104Dic113—22no—
105Dic113C2×C22⋊C414yes—
106C2×C113—21no—
107C2×C113—21no—
108C2×C113—21no—
109C2×C113C22×C22⋊C411yescharacteristic
110D113—24no—
111D113—42no—
112#2889—1131nomaximal, Sylow
113C113#288911yescharacteristic, complemented, Sylow
114C2×2−1+4—1131no—
115#568—1132no—
116#413—1132no—
117#413—1134no—
118C2×#101—1131no—
119C2×#101—1134no—
120C2×#101D11311yescharacteristic, complemented
1212−1+4—2264no—
1222−1+4—2264no—
123C2×#41—1132no—
124C2×#41—1132no—
125C2×#41—1134no—
126C2×#41—1131no—
127C2×#41—1131no—
128C22×Q8—1132no—
129C22×Q8—1132no—
130C22×Q8C2×D11311yescharacteristic
131#131—2264no—
132#131—2264no—
133C2×M16—1132no—
134C2×M16—1138no—
135C2×M16C2×D11312yes—
136#101—1134no—
137#101—1134no—
138#101C2×D11314yes—
139#100—1134no—
140#41—1134no—
141#41—1134no—
142#41—2268no—
143#41—2268no—
144#41—2268no—
145#41—2268no—
146#41—2262no—
147#41—2262no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—1131no—
151C2×Q8—1134no—
152C2×Q8—1131no—
153C2×Q8—2268no—
154C2×Q8—2268no—
155C2×Q8C4×D11312yes—
156C2×Q8C22×D11312yes—
157C2×D4—1132no—
158C2×D4—1132no—
159C2×D4—1131no—
160C2×D4—1134no—
161C2×D4—1131no—
162C22×C4—1132no—
163C22×C4—1134no—
164C22×C4—1134no—
165C22×C4—1132no—
166C22×C4C4×D11312yes—
167C22×C4C22×D11311yescharacteristic
168M16—22no—
169M16—1134no—
170M16—2268no—
171M16—2262no—
172M16C22×D11314yes—
173C2×C8—22no—
174C2×C8—2268no—
175C2×C8—2262no—
176C23—1132no—
177C23—1132no—
178C23C2×C4×D11311yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—1134no—
182Q8—2268no—
183Q8—2262no—
184D4—1134no—
185D4—1134no—
186D4—1134no—
187D4—2268no—
188D4—2262no—
189D4—2262no—
190D4—2262no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—1132no—
194C2×C4—1138no—
195C2×C4—1132no—
196C2×C4—2268no—
197C2×C4—2268no—
198C2×C4—2264no—
199C2×C4C2×C4×D11314yes—
200C2×C4C2×C4×D11311yescharacteristic
201C2×C4D4×D11312yes—
202C2×C4D4×D11312yes—
203C2×C4C23×D11311yescharacteristic
204C8—24no—
205C8—2264no—
206C22—41no—
207C22—1134no—
208C22—4522no—
209C22—4522no—
210C22—2262no—
211C22C22⋊C4×D11311yescharacteristic
212C22C22⋊C4×D11311yescharacteristic
213C22C22×C4×D11311yescharacteristic
214C4—24no—
215C4—1134no—
216C4—2262no—
217C4C22⋊C4×D11312yes—
218C4C2×D4×D11312yes—
219C2—21no—
220C2—21no—
221C2—21no—
222C2—4522no—
223C2—2264no—
224C2C2×C22⋊C4×D11311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D113
commutatorC22×C113C23×C4
FrattiniC2×C4C23×D113
FittingC2×#101×C113C2
socleC2×C113C22×C22⋊C4
prime radicalC2×#16813670C2
cosocleC2×C4×C113C24
hypercenterC2×#101D113
hypocenterC113#2889
LCSG ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #20299364C2semidirect
3. #20298581C2semidirect
4. #20298580C2semidirect
5. C2×#16813541C2semidirect
6. #101×D113C2semidirect
7. C2×#101×C113C2semidirect
113. C113#2889semidirect
120. C2×#101D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136702
#202993642
#202985812
#202985802
C2×#168135412
#101×D1132
C2×#101×C1132
#2889113