Finite Group Databasebeta

← #28391093

Subgroups — #28391093

Order 14464.

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

normal subgroups only

This group has 312 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
1#20299364C211yesmaximal, characteristic
2#20299172C211yesmaximal, characteristic
3#20298607C211yesmaximal, characteristic, complemented
4#20298571C211yesmaximal, characteristic
5#20298355C211yesmaximal, characteristic, complemented
6#20298354C211yesmaximal, characteristic, complemented
7#419×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9#16813630—22no—
10#16813628—22no—
11C2×#14268631C2211yescharacteristic
12M16×D113—22no—
13#16813620C412yescomplemented
14#16813611C412yescomplemented
15#16813605—22no—
16#16813598—22no—
17#16813581C2211yescharacteristic
18#16813581C2211yescharacteristic
19#16813546—22no—
20#16813536—22no—
21C22×Q8×C113C2211yescharacteristic
22C2×M16×C113C2211yescharacteristic
23#117×C113C2211yescharacteristic
24#103×C113—22no—
25#14268647—21no—
26#14268647—21no—
27#14268647—21no—
28#14268647—21no—
29C2×Dic226C2×C411yescharacteristic
30C2×D452C2×C411yescharacteristic
31C2×C22⋊D113D412yes—
32C2×C4×D113D412yes—
33#14268631—21no—
34#14268631—21no—
35#14268630—24no—
36C2×#11744751D412yes—
37C8×D113—24no—
38C4⋊Dic113—21no—
39C4⋊Dic113—21no—
40#14268626—24no—
41C22⋊Dic113—21no—
42C22⋊Dic113—21no—
43#14268624—24no—
44C4×Dic113—21no—
45C4×Dic113C2×C412yes—
46C2×Q8×C113—21no—
47C2×Q8×C113—21no—
48C2×Q8×C113—21no—
49C2×Q8×C113—21no—
50C2×Q8×C113—21no—
51C2×Q8×C113C2×C412yes—
52C22×C4×C113—21no—
53C22×C4×C113C2311yescharacteristic
54M16×C113—21no—
55M16×C113—21no—
56C2×C8×C113D412yes—
57C4⋊C4×C113—21no—
58C22⋊C4×C113—21no—
59C42×C113—21no—
60C23×C113C2×D411yescharacteristic
61C22×D113C22⋊C412yes—
62Q8×C113—22no—
63Q8×C113—22no—
64Q8×C113—41no—
65Q8×C113—41no—
66C2×C4×C113—22no—
67C2×C4×C113—41no—
68C2×C4×C113—41no—
69C2×C4×C113—41no—
70C2×C4×C113C22×C411yescharacteristic
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113C2×D411yescharacteristic
73C2×C4×C113C2×D411yescharacteristic
74C2×C4×C113#4111yescharacteristic
75C2×C4×C113#4111yescharacteristic
76C22⋊D113—22no—
77C22⋊D113—22no—
78C2×Dic113—22no—
79C2×Dic113—41no—
80C2×Dic113C22⋊C412yes—
81D452—21no—
82D452—21no—
83C4×D113—22no—
84C4×D113—22no—
85Dic226—21no—
86Dic226—21no—
87C8×C113—22no—
88#11744751—22no—
89C22×C113—41no—
90C22×C113C2×C22⋊C411yescharacteristic
91C22×C113#12111yescharacteristic
92C22×C113#12111yescharacteristic
93C2×D113—22no—
94C2×D113—42no—
95C4×C113—42no—
96C4×C113—81no—
97C4×C113C4×D411yescharacteristic
98C4×C113C4×D411yescharacteristic
99C4×C113#12011yescharacteristic
100C4×C113#12311yescharacteristic
101Dic113—22no—
102Dic113—42no—
103Dic113—81no—
104C2×C113—21no—
105C2×C113—21no—
106C2×C113—21no—
107C2×C113#38611yescharacteristic
108D113—42no—
109#1909—1131nomaximal, Sylow
110C113#190911yescharacteristic, complemented, Sylow
111#568—1131no—
112#536—1131no—
113#419—1131no—
114#419D11311yescharacteristic, complemented
115#410—1131no—
116H(3,ℤ/4)—1131no—
117H(3,ℤ/4)—1131no—
118C2×#41—1131no—
119C22×Q8C2×D11311yescharacteristic
120#131—2262no—
121#131—2262no—
122C2×M16—1131no—
123C2×M16—2262no—
124C2×M16C2×D11311yescharacteristic
125C4⋊Q8—1132no—
126#124—1132no—
127#123—2262no—
128C22⋊Q8—2262no—
129#117—1131no—
130#117—1131no—
131#117C2×D11311yescharacteristic
132#103—22no—
133#103—2262no—
134#99—2262no—
135#41—2261no—
136#41—2261no—
137#41—2261no—
138#41—2261no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—1131no—
145C2×Q8C4×D11312yes—
146C2×D4—1132no—
147C2×D4—1131no—
148C22×C4—21no—
149C22×C4—1132no—
150C22×C4C22×D11311yescharacteristic
151M16—21no—
152M16—21no—
153M16—2264no—
154M16—2261no—
155M16—2261no—
156C2×C8—1132no—
157C2×C8—2264no—
158C2×C8C22⋊D11312yes—
159C4⋊C4—21no—
160C4⋊C4—2264no—
161C4⋊C4—2261no—
162C4⋊C4—2261no—
163C22⋊C4—21no—
164C22⋊C4—2264no—
165C22⋊C4—2261no—
166C22⋊C4—2261no—
167C42—21no—
168C42—1132no—
169C42—2261no—
170C23—1132no—
171C23D4×D11311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—2261no—
177Q8—2261no—
178D4—2262no—
179D4—2262no—
180D4—2261no—
181D4—2261no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1132no—
187C2×C4—4521no—
188C2×C4—2262no—
189C2×C4—2262no—
190C2×C4—2262no—
191C2×C4C2×C4×D11311yescharacteristic
192C2×C4D4×D11311yescharacteristic
193C2×C4D4×D11311yescharacteristic
194C2×C4C2×C22⋊D11311yescharacteristic
195C2×C4#1426864611yescharacteristic
196C2×C4#1426864711yescharacteristic
197C8—22no—
198C8—2262no—
199C22—41no—
200C22—4522no—
201C22—2262no—
202C22C22⋊C4×D11311yescharacteristic
203C22#1681359311yescharacteristic
204C22#1681359511yescharacteristic
205C4—42no—
206C4—81no—
207C4—9041no—
208C4—4522no—
209C4—2262no—
210C4#1681358211yescharacteristic
211C4C4×C22⋊D11311yescharacteristic
212C4#1681359011yescharacteristic
213C4#1681360411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—4522no—
218C2#2029847411yescharacteristic
subgroupG/H
centerC2#20298474
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#419×C113C2
socleC2×C113#386
prime radicalC2×#14268647C22
cosocleC22×C4×C113C23
hypercenter#419D113
hypocenterC113#1909
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #20298607C2semidirect
5. #20298355C2semidirect
6. #20298354C2semidirect
7. #419×C113C2semidirect
13. #16813620C4semidirect
14. #16813611C4semidirect
110. C113#1909semidirect
114. #419D113semidirect

Maximal subgroups

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

subgroupindex
#202993642
#202991722
#202986072
#202985712
#202983552
#202983542
#419×C1132
#1909113