Finite Group Databasebeta

← #28401205

Subgroups — #28401205

Order 14464.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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#20299209C211yesmaximal, characteristic, complemented
2#20299204C211yesmaximal, characteristic
3#20298997C211yesmaximal, characteristic, complemented
4#20298972C211yesmaximal, characteristic, complemented
5#20298963C211yesmaximal, characteristic, complemented
6#20298847C212yesmaximal, complemented
7#20298830C212yesmaximal, complemented
8#20298701C212yesmaximal, complemented
9#20298683C212yesmaximal, complemented
10#20298555C211yesmaximal, characteristic, complemented
11#491×C113C211yesmaximal, characteristic, complemented
12C2×#14268634C2212yes—
13C2×#14268634C2212yes—
14C2×#14268630C2211yescharacteristic
15C2×C8×D113C2211yescharacteristic
16#16813619C2211yescharacteristic
17#16813617—22no—
18#16813614C2211yescharacteristic
19#16813612—22no—
20#16813607—22no—
21#16813598C2212yes—
22#16813597—22no—
23#16813597C2212yes—
24Q8×Dic113C2212yes—
25#16813584C2212yes—
26#16813579C2211yescharacteristic
27#16813555C2212yes—
28#16813553C2212yes—
29#16813544C2212yes—
30#16813544C2212yes—
31#16813532C2211yescharacteristic
32C4×#11744751C2211yescharacteristic
33C8×Dic113C2211yescharacteristic
34C4⋊Q8×C113C2211yescharacteristic
35#125×C113C2211yescharacteristic
36#103×C113C2212yes—
37#103×C113C2212yes—
38#97×C113C2211yescharacteristic
39C2×D452—22no—
40C2×D452—22no—
41C2×D452C2312yes—
42C2×C4×D113—22no—
43C2×C4×D113C2311yescharacteristic
44#14268634—24no—
45#14268634—24no—
46#14268630—22no—
47C2×#11744751C2311yescharacteristic
48C2×#11744751C2311yescharacteristic
49C8×D113—22no—
50C4⋊Dic113—22no—
51C4⋊Dic113C2312yes—
52#14268626—22no—
53#14268626—22no—
54#14268626D412yes—
55#14268624—22no—
56#14268624—22no—
57#14268624—22no—
58#14268624D412yes—
59C4×Dic113—22no—
60C4×Dic113C2311yescharacteristic
61C2×Q8×C113C2312yes—
62C2×C8×C113C2311yescharacteristic
63C2×C8×C113C2311yescharacteristic
64C4⋊C4×C113—22no—
65C4⋊C4×C113—22no—
66C4⋊C4×C113C2312yes—
67C42×C113C2311yescharacteristic
68C22×D113—22no—
69C22×D113C2×D411yescharacteristic
70Q8×C113—22no—
71Q8×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113—22no—
74C2×C4×C113C2×D412yes—
75C2×C4×C113C2411yescharacteristic
76C2×Dic113—22no—
77C2×Dic113C2×D412yes—
78C2×Dic113C2×D411yescharacteristic
79D452—22no—
80D452—22no—
81D452—82no—
82D452—82no—
83C4×D113—21no—
84C4×D113—21no—
85C4×D113—82no—
86C8×C113—21no—
87C8×C113—21no—
88#11744751#4112yes—
89#11744751#4112yes—
90C22×C113C22×D411yescharacteristic
91C2×D113—21no—
92C2×D113—22no—
93C2×D113—42no—
94C2×D113—42no—
95C2×D113—42no—
96C4×C113—22no—
97C4×C113—42no—
98C4×C113—42no—
99C4×C113C2×#4111yescharacteristic
100C4×C113C2×#4111yescharacteristic
101Dic113—21no—
102Dic113—22no—
103Dic113—42no—
104C2×C113#53211yescharacteristic
105C2×C113#57712yes—
106D113—41no—
107D113—82no—
108#3174—1131nomaximal, Sylow
109C113#317411yescharacteristic, complemented, Sylow
110#541—1131no—
111#540—1131no—
112#499—1131no—
113#492—1131no—
114#491D11311yescharacteristic, complemented
115#490—1131no—
116#468—1132no—
117#465—1132no—
118#440—1132no—
119C4×SD16—1132no—
120#405—1131no—
121C2×SD16—1132no—
122C2×SD16—1132no—
123C2×M16—1131no—
124C22×C8—1131no—
125C4⋊Q8C2×D11311yescharacteristic
126#127—1131no—
127#126—2262no—
128#125—1131no—
129#125—2262no—
130#125C2×D11311yescharacteristic
131#123—2262no—
132C22⋊Q8—1132no—
133#121—1132no—
134#121—2262no—
135C4×Q8—1132no—
136C4×D4—1132no—
137#117—1131no—
138#107—1132no—
139#106—1132no—
140#103C2×D11312yes—
141#103C2×D11312yes—
142#102—1132no—
143#102—1132no—
144#97—1131no—
145#97C2×D11311yescharacteristic
146C4×C8—1131no—
147C4×C8—1131no—
148C2×Q8C22×D11312yes—
149C2×D4—1132no—
150C2×D4—2262no—
151C2×D4—2262no—
152C22×C4—1131no—
153C22×C4—2262no—
154SD16—2264no—
155SD16—2264no—
156M16—2262no—
157C2×C8—1131no—
158C2×C8—1131no—
159C2×C8—2262no—
160C2×C8C22×D11311yescharacteristic
161C2×C8C22×D11311yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—1132no—
165C4⋊C4—1132no—
166C4⋊C4—2262no—
167C4⋊C4—2262no—
168C4⋊C4—2262no—
169C4⋊C4C22×D11312yes—
170C22⋊C4—1132no—
171C22⋊C4—2262no—
172C22⋊C4—2262no—
173C22⋊C4—2262no—
174C42—1131no—
175C42—2262no—
176C42C22×D11311yescharacteristic
177C23—1131no—
178C23—2262no—
179Q8—22no—
180Q8—22no—
181D4—9042no—
182D4—9042no—
183D4—2262no—
184D4—2262no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—1132no—
188C2×C4—1131no—
189C2×C4—9042no—
190C2×C4—2262no—
191C2×C4—2261no—
192C2×C4—2261no—
193C2×C4D4×D11312yes—
194C2×C4C23×D11311yescharacteristic
195C8—21no—
196C8—21no—
197C8—1132no—
198C8—1132no—
199C22—4522no—
200C22—4522no—
201C22—4522no—
202C22—2261no—
203C22—2262no—
204C22C2×D4×D11311yescharacteristic
205C4—22no—
206C4—42no—
207C4—42no—
208C4—4522no—
209C4—2261no—
210C4—2262no—
211C4#41×D11311yescharacteristic
212C4#41×D11311yescharacteristic
213C2—9042no—
214C2—4521no—
215C2#2029914711yescharacteristic
216C2#2029940712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#491×C113C2
socleC22×C113C22×D4
prime radical#20299204C2
hypercenter#491D113
hypocenterC113#3174
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #20299209C2semidirect
3. #20298997C2semidirect
4. #20298972C2semidirect
5. #20298963C2semidirect
6. #20298847C2semidirect
7. #20298830C2semidirect
8. #20298701C2semidirect
9. #20298683C2semidirect
10. #20298555C2semidirect
11. #491×C113C2semidirect
109. C113#3174semidirect
114. #491D113semidirect

Maximal subgroups

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

subgroupindex
#202992092
#202992042
#202989972
#202989722
#202989632
#202988472
#202988302
#202987012
#202986832
#202985552
#491×C1132
#3174113