Finite Group Databasebeta

← #26025463

Subgroups — #26025463

Order 11392.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×#15668011C211yesmaximal, characteristic
2C2×#15667977C211yesmaximal, characteristic
3#19151538C211yesmaximal, characteristic
4#19151537C211yesmaximal, characteristic
5#19151536C211yesmaximal, characteristic
6#19151502C212yesmaximal
7#19151502C212yesmaximal
8#19151502C212yesmaximal
9#19151462C212yesmaximal
10#19151449C211yesmaximal, characteristic
11#400×C89C211yesmaximal, characteristic
12C22×Dic178C2212yes—
13C22×Dic178C2211yescharacteristic
14#15668011—24no—
15#15667977—24no—
16C2×C4⋊Dic89C2211yescharacteristic
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×C4×Dic89C2212yes—
22C2×C4×Dic89C2211yescharacteristic
23C2×C4×Dic89C2211yescharacteristic
24C2×C4×Dic89C2211yescharacteristic
25#15667919C2211yescharacteristic
26#15667919C2212yes—
27#15667919C2212yes—
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C2×C4⋊C4×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34#95×C89C2211yescharacteristic
35#95×C89C2212yes—
36#95×C89C2212yes—
37C2×Dic178—22no—
38C2×Dic178—22no—
39C2×Dic178—24no—
40C2×Dic178—28no—
41C2×Dic178Q814yescomplemented
42C22×Dic89C2312yes—
43C22×Dic89C2312yes—
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2311yescharacteristic
47C22×Dic89C2311yescharacteristic
48C4⋊Dic89—22no—
49#13083553—22no—
50#13083553—22no—
51#13083553—24no—
52#13083553—24no—
53C4×Dic89—22no—
54C4×Dic89—22no—
55C4×Dic89—24no—
56C4×Dic89D414yes—
57C22×C4×C89C2312yes—
58C22×C4×C89C2312yes—
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2311yescharacteristic
61C22×C4×C89C2311yescharacteristic
62C4⋊C4×C89—22no—
63C4⋊C4×C89—22no—
64C23×C89C2411yescharacteristic
65C2×C4×C89—21no—
66C2×C4×C89—21no—
67C2×C4×C89—22no—
68C2×C4×C89—21no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—24no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89C2×D412yes—
76C2×C4×C89C2×Q812yes—
77C2×Dic89—21no—
78C2×Dic89—21no—
79C2×Dic89—21no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—24no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89C2×D412yes—
87C2×Dic89C2×D412yes—
88C2×Dic89C2×Q812yes—
89C2×Dic89C2×Q812yes—
90C2×Dic89#4112yes—
91C2×Dic89#4114yes—
92Dic178—28no—
93Dic178—48no—
94C22×C89C22×D411yescharacteristic
95C22×C89C22×Q811yescharacteristic
96C22×C89C2×#4111yescharacteristic
97C22×C89C2×#4112yes—
98C22×C892−1+412yes—
99C4×C89—22no—
100C4×C89—22no—
101C4×C89—42no—
102C4×C89—41no—
103C4×C89—42no—
104Dic89—22no—
105Dic89—42no—
106Dic89—41no—
107Dic89—42no—
108Dic89C22⋊Q814yes—
109Dic89#12414yes—
110C2×C89C2×C22⋊Q811yescharacteristic
111C2×C89C2×#12411yescharacteristic
112C2×C89#53611yescharacteristic
113C2×C89#55612yes—
114C2×C89#55712yes—
115#2568—891nomaximal, Sylow
116C89#256811yescharacteristic, complemented, Sylow
117C2×C4⋊Q8—891no—
118C2×C4×Q8—891no—
119#400—891no—
120#400—891no—
121#400—891no—
122#400D8911yescharacteristic
123#391—892no—
124#391—892no—
125#391—892no—
126#382—892no—
127C4×C4⋊C4—891no—
128C22×Q8—891no—
129C22×Q8—892no—
130C4⋊Q8—1784no—
131C4×Q8—1784no—
132C2×C4⋊C4—891no—
133C2×C4⋊C4—891no—
134C2×C4⋊C4—892no—
135C2×C4⋊C4—891no—
136C2×C4⋊C4—892no—
137C2×C4⋊C4C2×D8911yescharacteristic
138C2×C4⋊C4C2×D8911yescharacteristic
139C2×C42—891no—
140C2×C42—891no—
141C2×C42—891no—
142C2×C42—892no—
143#95—891no—
144#95—892no—
145#95—892no—
146#95—892no—
147#95—892no—
148#95—892no—
149#95—892no—
150#95C2×D8911yescharacteristic
151#95C2×D8912yes—
152#95C2×D8912yes—
153C2×Q8—894no—
154C2×Q8—1784no—
155C2×Q8—1788no—
156C2×Q8—1782no—
157C2×Q8—1782no—
158C22×C4—891no—
159C22×C4—891no—
160C22×C4—891no—
161C22×C4—892no—
162C22×C4—891no—
163C22×C4—892no—
164C22×C4C22×D8912yes—
165C22×C4C22×D8911yescharacteristic
166C22×C4C22×D8912yes—
167C22×C4C22×D8911yescharacteristic
168C22×C4C22×D8911yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—1782no—
172C4⋊C4—1784no—
173C4⋊C4—1784no—
174C4⋊C4—1782no—
175C4⋊C4—1782no—
176C42—894no—
177C42—1782no—
178C42—1782no—
179C42—1784no—
180C23C23×D8911yescharacteristic
181Q8—3568no—
182Q8—1788no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—892no—
194C2×C4—892no—
195C2×C4—892no—
196C2×C4—892no—
197C2×C4—894no—
198C2×C4—892no—
199C2×C4—1781no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1784no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4—1781no—
207C2×C4—1781no—
208C2×C4D4×D8912yes—
209C2×C4Q8×D8912yes—
210C22C2×D4×D8911yescharacteristic
211C22C2×Q8×D8911yescharacteristic
212C22#41×D8911yescharacteristic
213C22#41×D8912yes—
214C22#1566805912yes—
215C4—22no—
216C4—22no—
217C4—41no—
218C4—42no—
219C4—42no—
220C4—894no—
221C4—894no—
222C4—3561no—
223C4—3562no—
224C4—3562no—
225C4—1782no—
226C2C22⋊Q8×D8911yescharacteristic
227C2#124×D8911yescharacteristic
228C2#1915217011yescharacteristic
229C2#1915231512yes—
230C2#1915232512yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#400×C89C2
hypercenter#400D89
hypocenterC89#2568
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
41. C2×Dic178Q8semidirect
116. C89#2568semidirect

Maximal subgroups

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

subgroupindex
C2×#156680112
C2×#156679772
#191515382
#191515372
#191515362
#191515022
#191514622
#191514492
#400×C892
#256889