Finite Group Databasebeta

← #28389115

Subgroups — #28389115

Order 14464.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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#20299109C211yesmaximal, characteristic
2#20298562C211yesmaximal, characteristic, complemented
3#20298334C212yesmaximal, complemented
4#20298331C212yesmaximal, complemented
5#380×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C411yescharacteristic, complemented
7C2×#14268631—21no—
8#16813605—21no—
9#16813601C411yescharacteristic, complemented
10#16813601C2211yescharacteristic
11#16813596C411yescharacteristic, complemented
12#16813596C2211yescharacteristic
13#16813591—21no—
14C4×C22⋊D113—21no—
15C4×C22⋊D113—21no—
16#16813581C411yescharacteristic, complemented
17C22⋊#11744751—21no—
18C22⋊#11744751C2212yes—
19C23×C4×C113C2211yescharacteristic
20C2×C4⋊C4×C113—21no—
21C2×C22⋊C4×C113—21no—
22#95×C113C2212yes—
23#14268647—42no—
24C2×Dic226C2×C411yescharacteristic
25C2×D452C2×C411yescharacteristic
26C2×C22⋊D113—21no—
27C2×C22⋊D113—21no—
28C2×C22⋊D113—21no—
29C2×C4×D113—21no—
30#14268631—42no—
31C2×#11744751—22no—
32C4⋊Dic113C2×C411yescharacteristic
33C4⋊Dic113C2×C411yescharacteristic
34#14268626—21no—
35#14268626—21no—
36C22⋊Dic113—21no—
37C22⋊Dic113—21no—
38C22⋊Dic113—21no—
39#14268624—21no—
40#14268624—21no—
41C4×Dic113—21no—
42C24×C113D411yescharacteristic
43C22×C4×C113—22no—
44C22×C4×C113—42no—
45C22×C4×C113C2×C411yescharacteristic
46C22×C4×C113C2×C411yescharacteristic
47C22×C4×C113D411yescharacteristic
48C22×C4×C113D411yescharacteristic
49C22×C4×C113D411yescharacteristic
50C22×C4×C113C2311yescharacteristic
51C4⋊C4×C113—42no—
52C22⋊C4×C113—42no—
53C23×C113—21no—
54C23×C113—21no—
55C23×C113—41no—
56C23×C113—41no—
57C23×C113C22⋊C411yescharacteristic
58C23×C113C22⋊C411yescharacteristic
59C23×C113C2×D411yescharacteristic
60C22×D113—21no—
61C2×C4×C113—22no—
62C2×C4×C113—22no—
63C2×C4×C113—22no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113—41no—
67C2×C4×C113—42no—
68C2×C4×C113—42no—
69C2×C4×C113—42no—
70C2×C4×C113C22⋊C411yescharacteristic
71C2×C4×C113C22⋊C411yescharacteristic
72C2×C4×C113C22×C411yescharacteristic
73C2×C4×C113C2×D411yescharacteristic
74C22⋊D113—42no—
75C22⋊D113—42no—
76C22⋊D113—41no—
77C22⋊D113—41no—
78C2×Dic113—21no—
79C2×Dic113—21no—
80C2×Dic113—21no—
81D452—41no—
82C4×D113—42no—
83Dic226—41no—
84#11744751—42no—
85C22×C113—21no—
86C22×C113—21no—
87C22×C113—21no—
88C22×C113—21no—
89C22×C113—21no—
90C22×C113—21no—
91C22×C113—21no—
92C22×C113—21no—
93C22×C113—42no—
94C22×C113—42no—
95C22×C113C2×C22⋊C411yescharacteristic
96C22×C113AGL(1,ℤ/8)11yescharacteristic
97C22×C113#13711yescharacteristic
98C2×D113—41no—
99C2×D113—41no—
100C2×D113—41no—
101C4×C113—21no—
102C4×C113—21no—
103C4×C113—21no—
104C4×C113—82no—
105C4×C113#9912yes—
106Dic113—41no—
107Dic113—41no—
108Dic113—41no—
109C2×C113—21no—
110C2×C113—21no—
111C2×C113—41no—
112C2×C113—41no—
113C2×C113C2×#9911yescharacteristic
114C2×C113#41711yescharacteristic
115C2×C113#42111yescharacteristic
116D113—81no—
117#1513—1131nomaximal, Sylow
118C113#151311yescharacteristic, complemented, Sylow
119#525—1131no—
120#407—1131no—
121#380D11311yescharacteristic, complemented
122#328—1132no—
123#327—1132no—
124C2×#41—1131no—
125C23×C4C2×D11311yescharacteristic
126C2×M16—2261no—
127#123—2261no—
128C22⋊Q8—1131no—
129C22⋊Q8—1131no—
130#121—1131no—
131#121—1131no—
132#120—2261no—
133C4×D4—2261no—
134C4×D4—2261no—
135#117—1131no—
136C2×C4⋊C4—21no—
137C2×C22⋊C4—21no—
138C22⋊C8—1132no—
139C22⋊C8—2261no—
140#95C2×D11312yes—
141C24C22⋊D11311yescharacteristic
142#41—4522no—
143C2×Q8—1131no—
144C2×D4—1131no—
145C2×D4—2261no—
146C2×D4—2261no—
147C2×D4—2261no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—2261no—
151C22×C4C4×D11311yescharacteristic
152C22×C4C4×D11311yescharacteristic
153C22×C4D45211yescharacteristic
154C22×C4D45211yescharacteristic
155C22×C4C22⋊D11311yescharacteristic
156C22×C4C22×D11311yescharacteristic
157M16—4522no—
158C2×C8—2262no—
159C4⋊C4—42no—
160C4⋊C4—1131no—
161C4⋊C4—1131no—
162C4⋊C4—2261no—
163C4⋊C4—2261no—
164C22⋊C4—42no—
165C22⋊C4—2261no—
166C22⋊C4—2261no—
167C22⋊C4—2261no—
168C22⋊C4—2261no—
169C22⋊C4—2261no—
170C42—2261no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—2261no—
176C23#1426862411yescharacteristic
177C23#1426862411yescharacteristic
178C23C2×C22⋊D11311yescharacteristic
179Q8—4521no—
180D4—4521no—
181D4—4522no—
182D4—4522no—
183D4—4521no—
184D4—4521no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—4522no—
195C2×C4—2261no—
196C2×C4—2261no—
197C2×C4—2261no—
198C2×C4#1426862411yescharacteristic
199C2×C4#1426862411yescharacteristic
200C2×C4C2×C4×D11311yescharacteristic
201C2×C4C2×D45211yescharacteristic
202C8—4522no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—4521no—
214C22—4521no—
215C22—4521no—
216C22C2×#1426862411yescharacteristic
217C22#1681364811yescharacteristic
218C22#1681365311yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—82no—
223C4—4521no—
224C4—4521no—
225C4—4521no—
226C4#1681353612yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—9041no—
232C2C2×#1681353611yescharacteristic
233C2#2029859711yescharacteristic
234C2#2029861611yescharacteristic
subgroupG/H
centerC22C2×#14268624
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#380×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299109C2
cosocleC22×C4×C113C23
hypercenter#380D113
hypocenterC113#1513
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #20298562C2semidirect
3. #20298334C2semidirect
4. #20298331C2semidirect
5. #380×C113C2semidirect
6. C2×#14268647C4semidirect
9. #16813601C4semidirect
11. #16813596C4semidirect
16. #16813581C4semidirect
118. C113#1513semidirect
121. #380D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
#202985622
#202983342
#202983312
#380×C1132
#1513113