Finite Group Databasebeta

← #26026127

Subgroups — #26026127

Order 11392.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#15668002C211yesmaximal, characteristic
2C2×Q8×Dic89C211yesmaximal, characteristic
3#19151540C212yesmaximal
4#19151538C211yesmaximal, characteristic
5#19151537C211yesmaximal, characteristic
6#19151531C212yesmaximal
7#19151517C211yesmaximal, characteristic
8#19151484C212yesmaximal
9#19151480C212yesmaximal
10#19151465C211yesmaximal, characteristic
11#395×C89C211yesmaximal, characteristic
12#15668002—24no—
13Q8×Dic89—24no—
14C2×C4⋊Dic89C2211yescharacteristic
15C2×C4⋊Dic89C2212yes—
16C2×C4⋊Dic89C2211yescharacteristic
17C2×#13083553C2211yescharacteristic
18C2×#13083553C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×C4×Dic89C2212yes—
23C2×C4×Dic89C2211yescharacteristic
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26#15667919C2212yes—
27#15667919C2212yes—
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C22×Q8×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2212yes—
34C2×C4⋊C4×C89C2211yescharacteristic
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2311yescharacteristic
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C4⋊Dic89—22no—
44C4⋊Dic89—24no—
45C4⋊Dic89—22no—
46#13083553—22no—
47#13083553—24no—
48#13083553—22no—
49#13083553—22no—
50#13083553—22no—
51C4×Dic89—24no—
52C4×Dic89D414yes—
53C2×Q8×C89—22no—
54C2×Q8×C89—24no—
55C22×C4×C89C2312yes—
56C22×C4×C89C2311yescharacteristic
57C22×C4×C89C2311yescharacteristic
58C22×C4×C89C2311yescharacteristic
59C22×C4×C89C2312yes—
60C4⋊C4×C89—22no—
61C4⋊C4×C89—24no—
62C23×C89C2411yescharacteristic
63Q8×C89—28no—
64C2×C4×C89—22no—
65C2×C4×C89—22no—
66C2×C4×C89—22no—
67C2×C4×C89—21no—
68C2×C4×C89—21no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—21no—
72C2×C4×C89—22no—
73C2×C4×C89—21no—
74C2×C4×C89—22no—
75C2×C4×C89C2×D412yes—
76C2×C4×C89#4114yes—
77C2×Dic89—21no—
78C2×Dic89—21no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—21no—
82C2×Dic89—21no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—21no—
86C2×Dic89—24no—
87C2×Dic89—21no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89C2×D412yes—
91C2×Dic89C2×D412yes—
92C22×C89C22×D411yescharacteristic
93C22×C89C2×#4112yes—
94C22×C892−1+411yescharacteristic
95C22×C892−1+411yescharacteristic
96C22×C892−1+412yes—
97C4×C89—22no—
98C4×C89—24no—
99C4×C89—41no—
100C4×C89—41no—
101C4×C89—42no—
102Dic89—22no—
103Dic89—22no—
104Dic89—41no—
105Dic89—41no—
106Dic89—42no—
107Dic89—42no—
108C2×C89#52511yescharacteristic
109C2×C89#53611yescharacteristic
110C2×C89#53611yescharacteristic
111C2×C89#54112yes—
112C2×C89#54112yes—
113#2634—891nomaximal, Sylow
114C89#263411yescharacteristic, complemented, Sylow
115C2×#125—891no—
116C2×C4×Q8—891no—
117#400—891no—
118#400—891no—
119#400—892no—
120#398—892no—
121#395—891no—
122#395D8911yescharacteristic
123#387—892no—
124#387—892no—
125#383—891no—
126C22×Q8C2×D8911yescharacteristic
127#125—1784no—
128C4×Q8—1784no—
129C2×C4⋊C4—892no—
130C2×C4⋊C4—891no—
131C2×C4⋊C4—891no—
132C2×C4⋊C4—891no—
133C2×C4⋊C4—891no—
134C2×C4⋊C4—891no—
135C2×C4⋊C4—891no—
136C2×C4⋊C4—892no—
137C2×C4⋊C4C2×D8911yescharacteristic
138C2×C4⋊C4C2×D8912yes—
139C2×C42—891no—
140C2×C42—892no—
141#95—892no—
142#95—891no—
143#95—892no—
144#95—892no—
145#95—892no—
146#95—892no—
147#95—892no—
148#95—892no—
149#95C2×D8911yescharacteristic
150#95C2×D8912yes—
151C2×Q8—22no—
152C2×Q8—24no—
153C22×C4—891no—
154C22×C4—891no—
155C22×C4—892no—
156C22×C4—892no—
157C22×C4—891no—
158C22×C4—891no—
159C22×C4C22×D8912yes—
160C22×C4C22×D8911yescharacteristic
161C22×C4C22×D8911yescharacteristic
162C22×C4C22×D8911yescharacteristic
163C22×C4C22×D8912yes—
164C4⋊C4—22no—
165C4⋊C4—24no—
166C4⋊C4—1784no—
167C4⋊C4—1782no—
168C4⋊C4—1782no—
169C4⋊C4—1782no—
170C4⋊C4—1782no—
171C4⋊C4—1782no—
172C4⋊C4—1782no—
173C4⋊C4—1784no—
174C42—894no—
175C42—1784no—
176C23C23×D8911yescharacteristic
177Q8—28no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—892no—
190C2×C4—892no—
191C2×C4—1782no—
192C2×C4—1781no—
193C2×C4—1781no—
194C2×C4—1782no—
195C2×C4—1782no—
196C2×C4—1781no—
197C2×C4—1781no—
198C2×C4—1784no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1781no—
202C2×C4—1781no—
203C2×C4—1782no—
204C2×C4D4×D8912yes—
205C2×C4#1308357314yes—
206C22C2×D4×D8911yescharacteristic
207C22C2×#1308357312yes—
208C22#1566805911yescharacteristic
209C22#1566806011yescharacteristic
210C22#1566806012yes—
211C4—22no—
212C4—24no—
213C4—41no—
214C4—42no—
215C4—41no—
216C4—3561no—
217C4—3562no—
218C4—3562no—
219C4—3561no—
220C4—1782no—
221C4—1782no—
222C2#1915210411yescharacteristic
223C2#1915217111yescharacteristic
224C2#1915217311yescharacteristic
225C2#1915220812yes—
226C2#1915220912yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#395×C89C2
hypercenter#395D89
hypocenterC89#2634
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
114. C89#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#156680022
C2×Q8×Dic892
#191515402
#191515382
#191515372
#191515312
#191515172
#191514842
#191514802
#191514652
#395×C892
#263489