Finite Group Databasebeta

← #26028197

Subgroups — #26028197

Order 11392.

480 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 129 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#19151511C212yesmaximal, complemented
3#19151511C212yesmaximal, complemented
4#19151502C212yesmaximal, complemented
5#19151499C211yesmaximal, characteristic
6#19151476C212yesmaximal
7#19151472C212yesmaximal, complemented
8#19151469C212yesmaximal, complemented
9#400×C89C211yesmaximal, characteristic, complemented
10C22×Dic178C2212yes—
11C22×D356C2211yescharacteristic
12C22×C4×D89C2212yes—
13C2×C4⋊Dic89C2211yescharacteristic
14C2×#13083553C2212yes—
15C2×#13083551C2212yes—
16C2×#13083551C2212yes—
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×C4×Dic89C2211yescharacteristic
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26C2×C4⋊C4×C89C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28#95×C89C2212yes—
29#95×C89C2212yes—
30#95×C89C2211yescharacteristic
31C23×D89C2312yes—
32C2×Dic178—24no—
33C2×Dic178—42no—
34C2×Dic178—42no—
35C2×D356—41no—
36C2×D356—41no—
37C2×D356Q814yescomplemented
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C22×Dic89C2312yes—
41C2×C4×D89—42no—
42C2×C4×D89—42no—
43C2×C4×D89—42no—
44C4⋊Dic89—41no—
45#13083553—42no—
46#13083551—24no—
47#13083551—24no—
48#13083551—42no—
49#13083551—42no—
50#13083551—42no—
51C4×Dic89—41no—
52C22×C4×C89C2312yes—
53C22×C4×C89C2312yes—
54C22×C4×C89C2311yescharacteristic
55C22×C4×C89C2311yescharacteristic
56C22×C4×C89C2311yescharacteristic
57C4⋊C4×C89—41no—
58C4⋊C4×C89—41no—
59C23×C89C2411yescharacteristic
60C22×D89—22no—
61C22×D89—22no—
62C22×D89—22no—
63C22×D89—22no—
64C22×D89—22no—
65C22×D89—22no—
66C22×D89C2×Q814yes—
67C2×C4×C89—21no—
68C2×C4×C89—21no—
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—22no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89C2×Q812yes—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89#4114yes—
89D356—44no—
90C4×D89—48no—
91Dic178—48no—
92C22×C89C22×Q811yescharacteristic
93C22×C89C2×#4112yes—
94C22×C89H(5,𝔽2)11yescharacteristic
95C22×C89H(5,𝔽2)12yes—
96C22×C89H(5,𝔽2)11yescharacteristic
97C2×D89—24no—
98C2×D89—24no—
99C2×D89—24no—
100C2×D89—42no—
101C2×D89—42no—
102C2×D89—42no—
103C2×D89—42no—
104C4×C89—22no—
105C4×C89—42no—
106C4×C89—41no—
107C4×C89—41no—
108C4×C89—42no—
109Dic89—24no—
110Dic89—42no—
111Dic89—42no—
112C2×C89#53812yes—
113C2×C89#54311yescharacteristic
114C2×C89#55412yes—
115C2×C89#55911yescharacteristic
116C2×C89H(3,𝔽4)11yescharacteristic
117D89—44no—
118#2804—891nomaximal, Sylow
119C89#280411yescharacteristic, complemented, Sylow
120#400—891no—
121#400D8911yescharacteristic, complemented
122#393—892no—
123#393—892no—
124#391—892no—
125#390—891no—
126#386—892no—
127#385—892no—
128#385—892no—
129C22×Q8—892no—
130C22×D4—891no—
131C23×C4—892no—
132C2×C4⋊C4—892no—
133C2×C4⋊C4—891no—
134C2×C4⋊C4C2×D8911yescharacteristic
135C2×C4⋊C4C2×D8911yescharacteristic
136C2×C22⋊C4—892no—
137C2×C22⋊C4—892no—
138C2×C22⋊C4—892no—
139C2×C22⋊C4—892no—
140C2×C22⋊C4—892no—
141C2×C42—891no—
142#95—892no—
143#95—892no—
144#95—892no—
145#95—892no—
146#95—891no—
147#95C2×D8912yes—
148#95C2×D8912yes—
149#95C2×D8911yescharacteristic
150C24—892no—
151C2×Q8—3562no—
152C2×Q8—3562no—
153C2×Q8—1784no—
154C2×D4—894no—
155C2×D4—3561no—
156C2×D4—3561no—
157C22×C4—892no—
158C22×C4—892no—
159C22×C4—892no—
160C22×C4—3562no—
161C22×C4—3562no—
162C22×C4—3562no—
163C22×C4C22×D8911yescharacteristic
164C22×C4C22×D8912yes—
165C22×C4C22×D8911yescharacteristic
166C22×C4C22×D8912yes—
167C22×C4C22×D8911yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—3562no—
171C4⋊C4—3561no—
172C22⋊C4—3562no—
173C22⋊C4—3562no—
174C22⋊C4—3562no—
175C22⋊C4—1784no—
176C22⋊C4—1784no—
177C42—3561no—
178C23—894no—
179C23—1782no—
180C23—1782no—
181C23—1782no—
182C23—1782no—
183C23—1782no—
184C23—1782no—
185C23C23×D8911yescharacteristic
186Q8—3568no—
187D4—3564no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—894no—
201C2×C4—3568no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4—1782no—
207C2×C4—1782no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4Q8×D8912yes—
211C22—3562no—
212C22—3562no—
213C22—3562no—
214C22—3562no—
215C22—1784no—
216C22—1784no—
217C22—1784no—
218C22C2×Q8×D8911yescharacteristic
219C22#41×D8912yes—
220C22#1566805711yescharacteristic
221C22#1566805811yescharacteristic
222C22#1566805812yes—
223C4—22no—
224C4—42no—
225C4—41no—
226C4—41no—
227C4—42no—
228C4—3562no—
229C4—3562no—
230C4—1784no—
231C2—3564no—
232C2#1915218712yes—
233C2#1915222311yescharacteristic
234C2#1915230412yes—
235C2#1915233211yescharacteristic
236C2#1915234011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#400×C89C2
prime radicalC22×D356C22
hypercenter#400D89
hypocenterC89#2804
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #19151537C2semidirect
2. #19151511C2semidirect
3. #19151511C2semidirect
4. #19151502C2semidirect
7. #19151472C2semidirect
8. #19151469C2semidirect
9. #400×C89C2semidirect
37. C2×D356Q8semidirect
119. C89#2804semidirect
121. #400D89semidirect

Maximal subgroups

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

subgroupindex
#191515372
#191515112
#191515022
#191514992
#191514762
#191514722
#191514692
#400×C892
#280489