Finite Group Databasebeta

← #26028081

Subgroups — #26028081

Order 11392.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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#19151537C211yesmaximal, characteristic, complemented
2#19151520C212yesmaximal, complemented
3#19151515C212yesmaximal
4#19151515C211yesmaximal, characteristic
5#19151489C212yesmaximal, complemented
6#19151488C212yesmaximal, complemented
7#19151488C212yesmaximal, complemented
8#19151479C212yesmaximal, complemented
9#384×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12C2×#13083553C2212yes—
13C2×#13083551C2212yes—
14C2×#13083551C2212yes—
15C2×#13083551C2212yes—
16C2×#13083551C2212yes—
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×C4×Dic89C2212yes—
20#15667919C2211yescharacteristic
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2211yescharacteristic
25#15667919C2212yes—
26C2×C4⋊C4×C89C2212yes—
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C4⋊C4×C89C2212yes—
29C2×C4⋊C4×C89C2211yescharacteristic
30C2×C42×C89C2211yescharacteristic
31C23×D89C2312yes—
32C2×D356—41no—
33C2×D356—42no—
34C22×Dic89C2312yes—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C4⋊Dic89—41no—
38#13083553—24no—
39#13083551—24no—
40#13083551—24no—
41#13083551—24no—
42#13083551—42no—
43#13083551—42no—
44#13083551—42no—
45C4×Dic89—42no—
46C22×C4×C89C2311yescharacteristic
47C22×C4×C89C2312yes—
48C22×C4×C89C2311yescharacteristic
49C22×C4×C89C2311yescharacteristic
50C22×C4×C89C2312yes—
51C4⋊C4×C89—42no—
52C4⋊C4×C89—41no—
53C4⋊C4×C89—42no—
54C4⋊C4×C89—41no—
55C42×C89—22no—
56C23×C89C2411yescharacteristic
57C22×D89—22no—
58C22×D89—22no—
59C22×D89—22no—
60C22×D89—22no—
61C22×D89—22no—
62C22×D89—22no—
63C22×D89—22no—
64C2×C4×C89—22no—
65C2×C4×C89—21no—
66C2×C4×C89—22no—
67C2×C4×C89—21no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—21no—
73C2×C4×C89—21no—
74C2×C4×C89—22no—
75C2×C4×C89#4112yes—
76C2×C4×C89#4114yes—
77C2×Dic89—22no—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86D356—44no—
87C22×C89C2×#4111yescharacteristic
88C22×C89C2×#4112yes—
89C22×C89H(5,𝔽2)11yescharacteristic
90C22×C89H(5,𝔽2)12yes—
91C22×C892−1+411yescharacteristic
92C2×D89—42no—
93C2×D89—42no—
94C2×D89—42no—
95C2×D89—42no—
96C2×D89—42no—
97C2×D89—42no—
98C2×D89—42no—
99C4×C89—22no—
100C4×C89—24no—
101C4×C89—41no—
102C4×C89—42no—
103C4×C89—41no—
104Dic89—42no—
105Dic89—42no—
106Dic89—42no—
107C2×C89#53911yescharacteristic
108C2×C89#54212yes—
109C2×C89#55312yes—
110C2×C89#55511yescharacteristic
111C2×C89#56011yescharacteristic
112D89—82no—
113#2795—891nomaximal, Sylow
114C89#279511yescharacteristic, complemented, Sylow
115#400—891no—
116#396—892no—
117#394—891no—
118#394—892no—
119#388—892no—
120#388—892no—
121#388—892no—
122#387—892no—
123#384D8911yescharacteristic, complemented
124C22×D4—891no—
125C2×C4⋊C4—891no—
126C2×C4⋊C4—892no—
127C2×C4⋊C4C2×D8912yes—
128C2×C4⋊C4C2×D8911yescharacteristic
129C2×C4⋊C4C2×D8912yes—
130C2×C4⋊C4C2×D8911yescharacteristic
131C2×C22⋊C4—892no—
132C2×C22⋊C4—892no—
133C2×C22⋊C4—892no—
134C2×C22⋊C4—892no—
135C2×C22⋊C4—892no—
136C2×C22⋊C4—892no—
137C2×C42—892no—
138C2×C42C2×D8911yescharacteristic
139#95—891no—
140#95—892no—
141#95—892no—
142#95—892no—
143#95—891no—
144#95—892no—
145C24—892no—
146C2×D4—3561no—
147C2×D4—3562no—
148C22×C4—892no—
149C22×C4—892no—
150C22×C4—892no—
151C22×C4C22×D8911yescharacteristic
152C22×C4C22×D8912yes—
153C22×C4C22×D8911yescharacteristic
154C22×C4C22×D8911yescharacteristic
155C22×C4C22×D8912yes—
156C4⋊C4—42no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—41no—
160C4⋊C4—3561no—
161C4⋊C4—1784no—
162C22⋊C4—3562no—
163C22⋊C4—3562no—
164C22⋊C4—3562no—
165C22⋊C4—1784no—
166C22⋊C4—1784no—
167C22⋊C4—1784no—
168C42—22no—
169C42—3562no—
170C23—1782no—
171C23—1782no—
172C23—1782no—
173C23—1782no—
174C23—1782no—
175C23—1782no—
176C23—1782no—
177C23C23×D8911yescharacteristic
178D4—3564no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—1782no—
191C2×C4—1782no—
192C2×C4—1782no—
193C2×C4—1782no—
194C2×C4—1782no—
195C2×C4—1782no—
196C2×C4—1782no—
197C2×C4—1782no—
198C2×C4—1782no—
199C2×C4#1308357412yes—
200C2×C4#1308357514yes—
201C22—3562no—
202C22—3562no—
203C22—3562no—
204C22—3562no—
205C22—3562no—
206C22—3562no—
207C22—3562no—
208C22C2×#1308357411yescharacteristic
209C22C2×#1308357512yes—
210C22#1566805711yescharacteristic
211C22#1566805712yes—
212C22#1566806011yescharacteristic
213C4—22no—
214C4—24no—
215C4—41no—
216C4—42no—
217C4—41no—
218C4—3562no—
219C4—3562no—
220C4—3562no—
221C2—7122no—
222C2#1915219511yescharacteristic
223C2#1915222212yes—
224C2#1915229612yes—
225C2#1915231411yescharacteristic
226C2#1915233511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#384×C89C2
prime radicalC22×D356C22
hypercenter#384D89
hypocenterC89#2795
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #19151537C2semidirect
2. #19151520C2semidirect
5. #19151489C2semidirect
6. #19151488C2semidirect
7. #19151488C2semidirect
8. #19151479C2semidirect
9. #384×C89C2semidirect
114. C89#2795semidirect
123. #384D89semidirect

Maximal subgroups

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

subgroupindex
#191515372
#191515202
#191515152
#191514892
#191514882
#191514792
#384×C892
#279589