Finite Group Databasebeta

← #28405992

Subgroups — #28405992

Order 14464.

286 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 58 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#20299570C211yesmaximal, characteristic, complemented
2#20299540C211yesmaximal, characteristic, complemented
3#20299452C212yesmaximal, complemented
4#20299450C212yesmaximal, complemented
5#20299111C211yesmaximal, characteristic
6C2×#14268656—21no—
7C2×C4⋊#90673—21no—
8C2×C22⋊#90673—21no—
9#16813679—21no—
10#16813679C2212yes—
11(C2×#90673)⋊C4C2212yes—
12C2×#14268648C411yescharacteristic, complemented
13C22×C4×D113C2211yescharacteristic
14#16813607—21no—
15#16813598C2211yescharacteristic
16#16813597C2211yescharacteristic
17#16813596C411yescharacteristic, complemented
18#16813592—21no—
19#16813584—21no—
20#16813582—21no—
21#16813580C411yescharacteristic, complemented
22C22⋊Q8×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24#14268656—42no—
25C2×#11744753—22no—
26C4⋊#90673—42no—
27C22⋊#90673—42no—
28C23×D113D411yescharacteristic
29#14268648—42no—
30C2×D452—21no—
31C2×D452—21no—
32C2×D452C2×C411yescharacteristic
33C2×C22⋊D113—21no—
34C22×Dic113D411yescharacteristic
35C2×C4×D113—21no—
36C2×C4×D113—42no—
37C2×C4×D113C2×C411yescharacteristic
38C2×C4×D113D411yescharacteristic
39C2×C4×D113D411yescharacteristic
40C2×C4×D113C2311yescharacteristic
41C4⋊Dic113C2×C411yescharacteristic
42#14268626—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—21no—
46#14268624—21no—
47C4×Dic113—21no—
48C2×Q8×C113C2×C411yescharacteristic
49C22×C4×C113C2×C411yescharacteristic
50C4⋊C4×C113—21no—
51C4⋊C4×C113C2×C411yescharacteristic
52C22⋊C4×C113—21no—
53C23×C113C22⋊C411yescharacteristic
54C22×D113—21no—
55C22×D113—21no—
56C22×D113—21no—
57C22×D113—41no—
58C22×D113—41no—
59C22×D113C22⋊C411yescharacteristic
60C22×D113C2×D411yescharacteristic
61C2×#90673—42no—
62C2×#90673—42no—
63C2×#90673—42no—
64Q8×C113—41no—
65C2×C4×C113—21no—
66C2×C4×C113—21no—
67C2×C4×C113—41no—
68C2×C4×C113C22⋊C411yescharacteristic
69C2×C4×C113C22×C411yescharacteristic
70C22⋊D113—42no—
71C2×Dic113—22no—
72C2×Dic113—21no—
73C2×Dic113C22⋊C411yescharacteristic
74C2×Dic113C2×D411yescharacteristic
75D452—41no—
76D452—42no—
77D452—41no—
78D452—41no—
79C4×D113—22no—
80C4×D113—22no—
81C4×D113—41no—
82C4×D113—41no—
83C4×D113—42no—
84#11744753—42no—
85C22×C113—21no—
86C22×C113—21no—
87C22×C113—21no—
88C22×C113C2×C22⋊C411yescharacteristic
89C2×D113—21no—
90C2×D113—21no—
91C2×D113—21no—
92C2×D113—21no—
93C2×D113—21no—
94C2×D113—42no—
95C2×D113—42no—
96C2×D113—41no—
97C2×D113—41no—
98C2×D113—41no—
99C2×D113AGL(1,ℤ/8)11yescharacteristic
100C2×D113#13711yescharacteristic
101#90673—82no—
102C4×C113—21no—
103C4×C113—21no—
104C4×C113—41no—
105C4×C113—41no—
106Dic113—21no—
107Dic113—41no—
108Dic113#9912yes—
109C2×C113—41no—
110C2×C113C2×#9911yescharacteristic
111C2×C113#41711yescharacteristic
112C2×C113#42111yescharacteristic
113D113—21no—
114D113—21no—
115D113—41no—
116D113—81no—
117#1513—1131nomaximal, Sylow
118C113#151311yescharacteristic, complemented, Sylow
119#525—1131no—
120#407—1131no—
121#380—1131no—
122#328—1132no—
123#327—1132no—
124C2×#41—1131no—
125C23×C4—1131no—
126C2×M16—2261no—
127#123—2261no—
128C22⋊Q8—1131no—
129C22⋊Q8#9067311yescharacteristic, complemented
130#121—1131no—
131#121—1131no—
132#120—2261no—
133C4×D4—2261no—
134C4×D4—2261no—
135#117—1131no—
136C2×C4⋊C4—2261no—
137C2×C22⋊C4—2261no—
138C22⋊C8—1132no—
139C22⋊C8—2261no—
140#95—1132no—
141C24—1131no—
142#41—4522no—
143C2×Q8C2×#9067311yescharacteristic
144C2×D4—1131no—
145C2×D4—2261no—
146C2×D4—2261no—
147C2×D4—2261no—
148C22×C4—1131no—
149C22×C4—1131no—
150C22×C4—1131no—
151C22×C4—1131no—
152C22×C4—1131no—
153C22×C4—4522no—
154C22×C4—2261no—
155C22×C4—2262no—
156C22×C4C2×#9067311yescharacteristic
157M16—4522no—
158C2×C8—2262no—
159C4⋊C4—21no—
160C4⋊C4—1131no—
161C4⋊C4—4522no—
162C4⋊C4—2261no—
163C4⋊C4C2×#9067311yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—4522no—
166C22⋊C4—2261no—
167C22⋊C4—2261no—
168C22⋊C4—2261no—
169C22⋊C4—2261no—
170C42—2261no—
171C23—1131no—
172C23—1131no—
173C23—4521no—
174C23—4521no—
175C23—2261no—
176C23—2261no—
177C23—2261no—
178C23C22⋊#9067311yescharacteristic
179Q8—41no—
180D4—4521no—
181D4—4521no—
182D4—4521no—
183D4—4522no—
184D4—4522no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—1131no—
189C2×C4—1131no—
190C2×C4—4521no—
191C2×C4—4521no—
192C2×C4—4522no—
193C2×C4—4522no—
194C2×C4—4522no—
195C2×C4—4522no—
196C2×C4—2262no—
197C2×C4—2262no—
198C2×C4—2262no—
199C2×C4—2261no—
200C2×C4C22⋊#9067311yescharacteristic
201C2×C4C22×#9067311yescharacteristic
202C8—4522no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—1131no—
207C22—1131no—
208C22—4522no—
209C22—4522no—
210C22—4521no—
211C22—4521no—
212C22—4521no—
213C22—2261no—
214C22—2261no—
215C22—2261no—
216C22—2261no—
217C22—2261no—
218C22C2×C22⋊#9067311yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—41no—
223C4—1132no—
224C4—9042no—
225C4—4521no—
226C4—2261no—
227C2—41no—
228C2—9041no—
229C2—4521no—
230C2—2261no—
231C2—2261no—
232C2D113⋊#9911yescharacteristic
233C2#2029958911yescharacteristic
234C2#2029959711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC22⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299111C2
cosocleC2×C4×D113C23
hypercenterC22⋊Q8#90673
hypocenterC113#1513
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #20299570C2semidirect
2. #20299540C2semidirect
3. #20299452C2semidirect
4. #20299450C2semidirect
12. C2×#14268648C4semidirect
17. #16813596C4semidirect
21. #16813580C4semidirect
22. C22⋊Q8×C113C4semidirect
118. C113#1513semidirect
129. C22⋊Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202995702
#202995402
#202994522
#202994502
#202991112
#1513113