Finite Group Databasebeta

← #26031201

Subgroups — #26031201

Order 11392.

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

normal subgroups only

This group has 384 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#19152153C211yesmaximal, characteristic
2C4⋊Q8×D89C211yesmaximal, characteristic
3#19151978C211yesmaximal, characteristic, complemented
4#19151977C211yesmaximal, characteristic, complemented
5#19151950C211yesmaximal, characteristic, complemented
6#19151807C214yesmaximal, complemented
7#19151755C214yesmaximal
8#19151649C211yesmaximal, characteristic
9#487×C89C211yesmaximal, characteristic, complemented
10C2×Q8×D89C2212yes—
11C2×Dic356C2214yes—
12C2×#13083564C2214yes—
13#15668012C2211yescharacteristic
14#15668012C2211yescharacteristic
15#15668011—21no—
16#15668011—21no—
17#15668010C2212yes—
18#15668003—21no—
19#15667992C2212yes—
20#15667988—21no—
21Q8×Dic89—21no—
22#15667977C2212yes—
23#15667970—21no—
24C4⋊C4×D89—21no—
25C4⋊C4×D89—21no—
26C42×D89C2211yescharacteristic
27#15667941C2212yes—
28#15667935C2214yes—
29#15667924C2212yes—
30C4×#10623494C2211yescharacteristic
31C4⋊Q8×C89C2211yescharacteristic
32C4⋊Q8×C89C2211yescharacteristic
33#103×C89C2214yes—
34C4×C8×C89C2211yescharacteristic
35C2×Dic178—22no—
36C2×Dic178C2312yes—
37C2×Dic178C2312yes—
38Q8×D89—44no—
39C2×C4×D89—22no—
40C2×C4×D89D411yescharacteristic
41C2×C4×D89D411yescharacteristic
42C2×C4×D89C2311yescharacteristic
43Dic356—44no—
44#13083564—44no—
45C2×#10623494C2312yes—
46C4⋊Dic89—21no—
47C4⋊Dic89—21no—
48C4⋊Dic89—21no—
49C4⋊Dic89—21no—
50C4⋊Dic89—22no—
51#13083553—22no—
52#13083553—22no—
53#13083553—22no—
54#13083551—22no—
55C4×Dic89—22no—
56C4×Dic89D411yescharacteristic
57C4×Dic89D411yescharacteristic
58C4×Dic89C2311yescharacteristic
59C2×Q8×C89—21no—
60C2×Q8×C89C2312yes—
61C2×C8×C89C2312yes—
62C4⋊C4×C89—21no—
63C4⋊C4×C89—21no—
64C4⋊C4×C89—21no—
65C4⋊C4×C89C2312yes—
66C42×C89C2311yescharacteristic
67C22×D89C2×D411yescharacteristic
68Q8×C89—24no—
69Q8×C89—42no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89C2×D411yescharacteristic
73C2×C4×C89C2×D411yescharacteristic
74C2×C4×C89C2411yescharacteristic
75C2×Dic89—22no—
76C2×Dic89—22no—
77C2×Dic89C2×D411yescharacteristic
78C2×Dic89C2×D411yescharacteristic
79C2×Dic89C2×D411yescharacteristic
80C4×D89—22no—
81C4×D89—22no—
82C4×D89—44no—
83C4×D89Q1614yescomplemented
84Dic178—24no—
85Dic178—24no—
86Dic178—44no—
87C8×C89—22no—
88#10623494—22no—
89C22×C89C22×D411yescharacteristic
90C2×D89—21no—
91C2×D89—21no—
92C2×D89C2×Q1612yes—
93C4×C89—42no—
94C4×C89—42no—
95C4×C89C2×Q1612yes—
96C4×C89#13712yes—
97C4×C89H(5,𝔽2)12yes—
98Dic89—21no—
99Dic89—21no—
100Dic89—42no—
101Dic89—42no—
102Dic89C2×Q1612yes—
103C2×C89#53511yescharacteristic
104C2×C89C22×Q1611yescharacteristic
105C2×C89C2×#13711yescharacteristic
106D89—22no—
107#3209—891nomaximal, Sylow
108C89#320911yescharacteristic, complemented, Sylow
109#533—891no—
110C2×C4⋊Q8—891no—
111#494—891no—
112#494—891no—
113#487—891no—
114#487D8911yescharacteristic, complemented
115#462—894no—
116#451—894no—
117#431—891no—
118C22×Q8—892no—
119C2×Q16—894no—
120C2×Q16—894no—
121C4⋊Q8—892no—
122C4⋊Q8—891no—
123C4⋊Q8—891no—
124C4⋊Q8—1781no—
125C4⋊Q8—1781no—
126C4⋊Q8C2×D8911yescharacteristic
127C4⋊Q8C2×D8911yescharacteristic
128#125—1781no—
129C22⋊Q8—892no—
130C22⋊Q8—1781no—
131C4×Q8—892no—
132C4×Q8—1781no—
133#117—1781no—
134C2×C4⋊C4—1781no—
135C2×C4⋊C4—1781no—
136C2×C42—891no—
137C4⋊C8—892no—
138#103—894no—
139#103C2×D8914yes—
140C22⋊C8—892no—
141C4×C8—891no—
142C4×C8C2×D8911yescharacteristic
143C2×Q8—21no—
144C2×Q8—892no—
145C2×Q8—892no—
146C2×Q8—3564no—
147C2×Q8—1782no—
148C2×Q8C22×D8912yes—
149C22×C4—891no—
150C22×C4—891no—
151C22×C4—891no—
152C22×C4—1782no—
153Q16—3564no—
154Q16—3564no—
155C2×C8—892no—
156C2×C8C22×D8912yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—1782no—
161C4⋊C4—1782no—
162C4⋊C4—1782no—
163C4⋊C4—1782no—
164C4⋊C4—1781no—
165C4⋊C4—1781no—
166C4⋊C4—1781no—
167C4⋊C4—1781no—
168C4⋊C4C22×D8912yes—
169C22⋊C4—1782no—
170C42—891no—
171C42—891no—
172C42—891no—
173C42—1782no—
174C42C22×D8911yescharacteristic
175C23—891no—
176Q8—24no—
177Q8—42no—
178Q8—3564no—
179Q8—1784no—
180Q8—1784no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—891no—
184C2×C4—894no—
185C2×C4—891no—
186C2×C4—891no—
187C2×C4—3564no—
188C2×C4—1782no—
189C2×C4—1782no—
190C2×C4—1782no—
191C2×C4—1782no—
192C2×C4D4×D8911yescharacteristic
193C2×C4D4×D8911yescharacteristic
194C2×C4C23×D8911yescharacteristic
195C8—22no—
196C8—1782no—
197C22—892no—
198C22—1781no—
199C22—1781no—
200C22C2×D4×D8911yescharacteristic
201C4—42no—
202C4—42no—
203C4—892no—
204C4—3562no—
205C4—3562no—
206C4—1781no—
207C4—1781no—
208C4Q16×D8912yes—
209C4#1566804112yes—
210C4#1566805812yes—
211C2—1782no—
212C2#1915216611yescharacteristic
213C2C2×Q16×D8911yescharacteristic
214C2C2×#1566804111yescharacteristic
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#487×C89C2
socleC22×C89C22×D4
prime radicalC22×D89C2×D4
hypercenter#487D89
hypocenterC89#3209
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #19151978C2semidirect
4. #19151977C2semidirect
5. #19151950C2semidirect
6. #19151807C2semidirect
9. #487×C89C2semidirect
83. C4×D89Q16semidirect
108. C89#3209semidirect
114. #487D89semidirect

Maximal subgroups

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

subgroupindex
#191521532
C4⋊Q8×D892
#191519782
#191519772
#191519502
#191518072
#191517552
#191516492
#487×C892
#320989