Finite Group Databasebeta

← #28392237

Subgroups — #28392237

Order 14464.

258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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#20299144C211yesmaximal, characteristic
2#20298572C211yesmaximal, characteristic, complemented
3#20298392C212yesmaximal, complemented
4#20298390C212yesmaximal, complemented
5#410×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C411yescharacteristic, complemented
7#16813620C411yescharacteristic, complemented
8#16813618C2211yescharacteristic
9#16813611C411yescharacteristic, complemented
10#16813609C2211yescharacteristic
11#16813594—21no—
12#16813594—21no—
13C4×C22⋊D113—21no—
14C4×C22⋊D113—21no—
15#16813581—21no—
16C2×C4×Dic113C411yescharacteristic, complemented
17#16813537—21no—
18#16813537C2212yes—
19C2×#41×C113C2211yescharacteristic
20#117×C113—21no—
21#99×C113—21no—
22#99×C113C2212yes—
23#14268647—41no—
24#14268647—41no—
25C2×Dic226C2×C411yescharacteristic
26C2×D452C2×C411yescharacteristic
27C2×C22⋊D113—21no—
28C2×C22⋊D113—21no—
29C2×C22⋊D113—21no—
30C22×Dic113—21no—
31C2×C4×D113—21no—
32C4⋊Dic113—41no—
33#14268626—21no—
34#14268626—21no—
35C22⋊Dic113—21no—
36C22⋊Dic113—21no—
37C22⋊Dic113—22no—
38#14268624—21no—
39#14268624—21no—
40C4×Dic113—21no—
41C4×Dic113—41no—
42C4×Dic113C2×C411yescharacteristic
43C4×Dic113C2×C411yescharacteristic
44#41×C113—41no—
45#41×C113—41no—
46C2×Q8×C113C2×C411yescharacteristic
47C2×D4×C113D411yescharacteristic
48C2×D4×C113D411yescharacteristic
49C2×D4×C113C2311yescharacteristic
50C22×C4×C113C2×C411yescharacteristic
51C22×C4×C113D411yescharacteristic
52C22×C4×C113D411yescharacteristic
53C4⋊C4×C113—41no—
54C22⋊C4×C113—22no—
55C42×C113—41no—
56C23×C113C22⋊C411yescharacteristic
57C23×C113C2×D411yescharacteristic
58C23×C113C2×D411yescharacteristic
59C22×D113—21no—
60Q8×C113—41no—
61D4×C113—41no—
62D4×C113—41no—
63D4×C113—41no—
64C2×C4×C113—21no—
65C2×C4×C113—21no—
66C2×C4×C113—21no—
67C2×C4×C113—21no—
68C2×C4×C113—21no—
69C2×C4×C113—21no—
70C2×C4×C113—42no—
71C2×C4×C113C22⋊C411yescharacteristic
72C2×C4×C113C22⋊C411yescharacteristic
73C2×C4×C113C22⋊C411yescharacteristic
74C2×C4×C113C22×C411yescharacteristic
75C22⋊D113—42no—
76C22⋊D113—42no—
77C22⋊D113—42no—
78C2×Dic113—21no—
79C2×Dic113—21no—
80C2×Dic113—21no—
81C2×Dic113—42no—
82C2×Dic113—42no—
83D452—41no—
84C4×D113—41no—
85C4×D113—41no—
86Dic226—41no—
87C22×C113—21no—
88C22×C113—21no—
89C22×C113—21no—
90C22×C113—41no—
91C22×C113—41no—
92C22×C113—41no—
93C22×C113C2×C22⋊C411yescharacteristic
94C2×D113—41no—
95C2×D113—41no—
96C2×D113—41no—
97C4×C113—21no—
98C4×C113—21no—
99C4×C113—21no—
100C4×C113—82no—
101C4×C113#9911yescharacteristic
102C4×C113#9911yescharacteristic
103Dic113—22no—
104Dic113—41no—
105Dic113—41no—
106Dic113—82no—
107C2×C113—21no—
108C2×C113—41no—
109C2×C113—41no—
110C2×C113—41no—
111C2×C113C2×#9911yescharacteristic
112D113—81no—
113#2126—1131nomaximal, Sylow
114C113#212611yescharacteristic, complemented, Sylow
115#532—1131no—
116#410—1131no—
117#410D11311yescharacteristic, complemented
118#354—1132no—
119#353—1132no—
120C2×#41—1131no—
121C2×#41C2×D11311yescharacteristic
122C4⋊Q8—1131no—
123#127—1131no—
124#124—1131no—
125#124—1131no—
126#121—2261no—
127#121—2261no—
128C4×D4—2261no—
129C4×D4—2261no—
130#117—21no—
131#117—2261no—
132C2×C42—1131no—
133#99—21no—
134#99—1132no—
135#99—2261no—
136#99C2×D11312yes—
137#41—41no—
138#41—41no—
139#41—4521no—
140#41—4521no—
141C2×Q8—1131no—
142C2×Q8C4×D11311yescharacteristic
143C2×D4—1131no—
144C2×D4—2261no—
145C2×D4—2261no—
146C2×D4—2261no—
147C2×D4D45211yescharacteristic
148C2×D4C22⋊D11311yescharacteristic
149C2×D4C22×D11311yescharacteristic
150C22×C4—2261no—
151C22×C4—2261no—
152C22×C4C4×D11311yescharacteristic
153C22×C4D45211yescharacteristic
154C22×C4C22⋊D11311yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—4521no—
157C4⋊C4—2261no—
158C4⋊C4—2261no—
159C22⋊C4—22no—
160C22⋊C4—2262no—
161C22⋊C4—2261no—
162C22⋊C4—2261no—
163C22⋊C4—2261no—
164C22⋊C4—2261no—
165C42—41no—
166C42—1131no—
167C42—1131no—
168C42—4521no—
169C42—2261no—
170C23—2261no—
171C23#1426862411yescharacteristic
172C23C2×C22⋊D11311yescharacteristic
173C23C2×D45211yescharacteristic
174Q8—41no—
175Q8—4521no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—4521no—
180D4—4522no—
181D4—4522no—
182D4—4522no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—4522no—
191C2×C4—4522no—
192C2×C4—4521no—
193C2×C4—4521no—
194C2×C4—2261no—
195C2×C4—2261no—
196C2×C4—2261no—
197C2×C4#1426862411yescharacteristic
198C2×C4#1426862411yescharacteristic
199C2×C4#1426862411yescharacteristic
200C2×C4C2×C4×D11311yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—4521no—
208C22—4521no—
209C22—4521no—
210C22C2×#1426862411yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—9042no—
216C4—4521no—
217C4—4521no—
218C4—2262no—
219C4#1681353611yescharacteristic
220C4#1681353611yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—9041no—
226C2C2×#1681353611yescharacteristic
subgroupG/H
centerC4#16813536
commutatorC2×C4×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#410×C113C2
socleC2×C113C2×#99
prime radical#20299144C2
cosocleC2×D4×C113C23
hypercenter#410D113
hypocenterC113#2126
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #20298572C2semidirect
3. #20298392C2semidirect
4. #20298390C2semidirect
5. #410×C113C2semidirect
6. C2×#14268647C4semidirect
7. #16813620C4semidirect
9. #16813611C4semidirect
16. C2×C4×Dic113C4semidirect
114. C113#2126semidirect
117. #410D113semidirect

Maximal subgroups

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

subgroupindex
#202991442
#202985722
#202983922
#202983902
#410×C1132
#2126113