Finite Group Databasebeta

← #26028419

Subgroups — #26028419

Order 11392.

416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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#19151539C212yesmaximal, complemented
2#19151527C212yesmaximal, complemented
3#19151518C211yesmaximal, characteristic, complemented
4#19151516C212yesmaximal
5#19151515C211yesmaximal, characteristic
6#19151511C212yesmaximal, complemented
7#19151509C212yesmaximal, complemented
8#19151489C212yesmaximal, complemented
9#391×C89C211yesmaximal, characteristic, complemented
10C22×Dic178C2211yescharacteristic
11C22×D356C2211yescharacteristic
12C2×#13083553C2212yes—
13C2×#13083553C2212yes—
14C2×#13083551C2212yes—
15C2×#13083551C2212yes—
16C2×#13083551C2212yes—
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2211yescharacteristic
25#15667919C2211yescharacteristic
26C22×Q8×C89C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C42×C89C2211yescharacteristic
29#95×C89C2212yes—
30#95×C89C2212yes—
31C23×D89C2312yes—
32C2×Dic178—41no—
33C2×Dic178—42no—
34C2×D356—41no—
35C2×D356—42no—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39#13083553—42no—
40#13083553—42no—
41#13083551—24no—
42#13083551—42no—
43#13083551—42no—
44#13083551—42no—
45#13083551—42no—
46#13083551—42no—
47C2×Q8×C89—22no—
48C2×Q8×C89—41no—
49C2×Q8×C89—41no—
50C22×C4×C89C2311yescharacteristic
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2312yes—
53C22×C4×C89C2312yes—
54C22×C4×C89C2311yescharacteristic
55C4⋊C4×C89—41no—
56C42×C89—41no—
57C23×C89C2411yescharacteristic
58C22×D89—22no—
59C22×D89—22no—
60C22×D89—22no—
61C22×D89—22no—
62C22×D89—22no—
63C22×D89—22no—
64C22×D89—22no—
65Q8×C89—44no—
66C2×C4×C89—21no—
67C2×C4×C89—21no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—21no—
71C2×C4×C89—21no—
72C2×C4×C89—22no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89#4112yes—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88D356—44no—
89Dic178—44no—
90C22×C89C2×#4111yescharacteristic
91C22×C89H(5,𝔽2)11yescharacteristic
92C22×C89H(5,𝔽2)11yescharacteristic
93C22×C89H(5,𝔽2)12yes—
94C22×C892−1+412yes—
95C2×D89—42no—
96C2×D89—42no—
97C2×D89—42no—
98C2×D89—42no—
99C2×D89—42no—
100C2×D89—42no—
101C2×D89—42no—
102C4×C89—22no—
103C4×C89—42no—
104C4×C89—41no—
105C4×C89—41no—
106C4×C89—42no—
107Dic89—42no—
108Dic89—42no—
109Dic89—42no—
110C2×C89#53811yescharacteristic
111C2×C89#54212yes—
112C2×C89H(3,𝔽4)11yescharacteristic
113C2×C89#56212yes—
114C2×C89#56311yescharacteristic
115D89—82no—
116#2832—891nomaximal, Sylow
117C89#283211yescharacteristic, complemented, Sylow
118#400—892no—
119#397—892no—
120#395—891no—
121#394—891no—
122#394—892no—
123#393—892no—
124#393—892no—
125#391D8911yescharacteristic, complemented
126#388—892no—
127C22×Q8—891no—
128C22×Q8C2×D8911yescharacteristic
129C22×D4—891no—
130C2×C4⋊C4—892no—
131C2×C4⋊C4—892no—
132C2×C4⋊C4C2×D8911yescharacteristic
133C2×C22⋊C4—892no—
134C2×C22⋊C4—892no—
135C2×C22⋊C4—892no—
136C2×C22⋊C4—892no—
137C2×C22⋊C4—892no—
138C2×C22⋊C4—892no—
139C2×C42C2×D8911yescharacteristic
140#95—892no—
141#95—892no—
142#95—892no—
143#95—892no—
144#95—891no—
145#95—891no—
146#95C2×D8912yes—
147#95C2×D8912yes—
148C24—892no—
149C2×Q8—22no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—3561no—
153C2×Q8—3562no—
154C2×D4—3561no—
155C2×D4—3562no—
156C22×C4—892no—
157C22×C4—892no—
158C22×C4—892no—
159C22×C4C22×D8912yes—
160C22×C4C22×D8912yes—
161C22×C4C22×D8911yescharacteristic
162C22×C4C22×D8911yescharacteristic
163C22×C4C22×D8911yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—3562no—
166C4⋊C4—3562no—
167C22⋊C4—3562no—
168C22⋊C4—3562no—
169C22⋊C4—3562no—
170C22⋊C4—3562no—
171C22⋊C4—3562no—
172C22⋊C4—1784no—
173C42—41no—
174C23—1782no—
175C23—1782no—
176C23—1782no—
177C23—1782no—
178C23—1782no—
179C23—1782no—
180C23—1782no—
181C23C23×D8911yescharacteristic
182Q8—44no—
183Q8—3564no—
184D4—3564no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—1782no—
198C2×C4—1782no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4#1308357412yes—
207C22—3562no—
208C22—3562no—
209C22—3562no—
210C22—3562no—
211C22—3562no—
212C22—3562no—
213C22—3562no—
214C22C2×#1308357411yescharacteristic
215C22#1566805711yescharacteristic
216C22#1566805711yescharacteristic
217C22#1566805812yes—
218C22#1566806012yes—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—42no—
224C4—3562no—
225C4—3562no—
226C4—3562no—
227C2—7122no—
228C2#1915218611yescharacteristic
229C2#1915222012yes—
230C2#1915234011yescharacteristic
231C2#1915234412yes—
232C2#1915234711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#391×C89C2
prime radicalC22×D356C22
hypercenter#391D89
hypocenterC89#2832
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #19151539C2semidirect
2. #19151527C2semidirect
3. #19151518C2semidirect
6. #19151511C2semidirect
7. #19151509C2semidirect
8. #19151489C2semidirect
9. #391×C89C2semidirect
117. C89#2832semidirect
125. #391D89semidirect

Maximal subgroups

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

subgroupindex
#191515392
#191515272
#191515182
#191515162
#191515152
#191515112
#191515092
#191514892
#391×C892
#283289