Finite Group Databasebeta

← #26025613

Subgroups — #26025613

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×Q8×Dic89C211yesmaximal, characteristic
2C2×#15667977C211yesmaximal, characteristic
3#19151538C211yesmaximal, characteristic
4#19151537C211yesmaximal, characteristic
5#19151517C211yesmaximal, characteristic
6#19151502C212yesmaximal
7#19151493C212yesmaximal
8#19151485C212yesmaximal
9#19151484C212yesmaximal
10#19151462C211yesmaximal, characteristic
11#395×C89C211yesmaximal, characteristic
12C22×Dic178C2211yescharacteristic
13Q8×Dic89—24no—
14#15667977—24no—
15C2×C4⋊Dic89C2212yes—
16C2×C4⋊Dic89C2211yescharacteristic
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×C4×Dic89C2211yescharacteristic
22C2×C4×Dic89C2211yescharacteristic
23C2×C4×Dic89C2212yes—
24C2×C4×Dic89C2211yescharacteristic
25#15667919C2212yes—
26#15667919C2211yescharacteristic
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—
37C2×Dic178—22no—
38C2×Dic178—22no—
39C2×Dic178Q814yescomplemented
40C22×Dic89C2312yes—
41C22×Dic89C2312yes—
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2311yescharacteristic
46C4⋊Dic89—22no—
47C4⋊Dic89—24no—
48#13083553—22no—
49#13083553—24no—
50#13083553—22no—
51#13083553—24no—
52C4×Dic89—22no—
53C4×Dic89—22no—
54C4×Dic89—24no—
55C4×Dic89D414yes—
56C2×Q8×C89—22no—
57C2×Q8×C89—24no—
58C22×C4×C89C2312yes—
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2311yescharacteristic
61C22×C4×C89C2311yescharacteristic
62C22×C4×C89C2312yes—
63C4⋊C4×C89—22no—
64C4⋊C4×C89—24no—
65C23×C89C2411yescharacteristic
66Q8×C89—28no—
67C2×C4×C89—21no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—21no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89C2×D412yes—
78C2×C4×C89C2×Q812yes—
79C2×C4×C89#4114yes—
80C2×Dic89—21no—
81C2×Dic89—21no—
82C2×Dic89—22no—
83C2×Dic89—21no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89—24no—
89C2×Dic89—22no—
90C2×Dic89C2×D412yes—
91C2×Dic89C2×D412yes—
92C2×Dic89C2×Q812yes—
93C2×Dic89C2×Q812yes—
94C2×Dic89#4112yes—
95Dic178—28no—
96C22×C89C22×D411yescharacteristic
97C22×C89C22×Q811yescharacteristic
98C22×C89C2×#4111yescharacteristic
99C22×C89C2×#4112yes—
100C22×C892−1+412yes—
101C4×C89—22no—
102C4×C89—22no—
103C4×C89—24no—
104C4×C89—41no—
105C4×C89—42no—
106Dic89—22no—
107Dic89—22no—
108Dic89—41no—
109Dic89—42no—
110Dic89—42no—
111Dic89C22⋊Q814yes—
112C2×C89C2×C22⋊Q811yescharacteristic
113C2×C89#52511yescharacteristic
114C2×C89#53611yescharacteristic
115C2×C89#55612yes—
116C2×C89#55712yes—
117#2581—891nomaximal, Sylow
118C89#258111yescharacteristic, complemented, Sylow
119C2×C4×Q8—891no—
120C2×C4×Q8—891no—
121#400—891no—
122#400—891no—
123#395—891no—
124#395D8911yescharacteristic
125#391—892no—
126#389—892no—
127#387—892no—
128#387—892no—
129#382—891no—
130C22×Q8—891no—
131C22×Q8C2×D8911yescharacteristic
132C4×Q8—1784no—
133C4×Q8—1784no—
134C2×C4⋊C4—892no—
135C2×C4⋊C4—891no—
136C2×C4⋊C4—891no—
137C2×C4⋊C4—891no—
138C2×C4⋊C4—892no—
139C2×C4⋊C4—892no—
140C2×C4⋊C4C2×D8911yescharacteristic
141C2×C4⋊C4C2×D8912yes—
142C2×C42—891no—
143C2×C42—891no—
144C2×C42—891no—
145C2×C42—892no—
146#95—892no—
147#95—891no—
148#95—892no—
149#95—892no—
150#95—892no—
151#95—892no—
152#95—892no—
153#95C2×D8911yescharacteristic
154#95C2×D8912yes—
155C2×Q8—22no—
156C2×Q8—24no—
157C2×Q8—894no—
158C2×Q8—1782no—
159C2×Q8—1782no—
160C22×C4—891no—
161C22×C4—891no—
162C22×C4—891no—
163C22×C4—892no—
164C22×C4—892no—
165C22×C4—891no—
166C22×C4C22×D8912yes—
167C22×C4C22×D8911yescharacteristic
168C22×C4C22×D8911yescharacteristic
169C22×C4C22×D8911yescharacteristic
170C22×C4C22×D8912yes—
171C4⋊C4—22no—
172C4⋊C4—24no—
173C4⋊C4—1782no—
174C4⋊C4—1784no—
175C4⋊C4—1784no—
176C4⋊C4—1782no—
177C4⋊C4—1782no—
178C4⋊C4—1784no—
179C42—894no—
180C42—1782no—
181C42—1784no—
182C42—1782no—
183C23C23×D8911yescharacteristic
184Q8—28no—
185Q8—1788no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—892no—
197C2×C4—892no—
198C2×C4—892no—
199C2×C4—892no—
200C2×C4—892no—
201C2×C4—1782no—
202C2×C4—1781no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4—1784no—
207C2×C4—1782no—
208C2×C4—1781no—
209C2×C4—1781no—
210C2×C4—1782no—
211C2×C4D4×D8912yes—
212C2×C4Q8×D8912yes—
213C2×C4#1308357314yes—
214C22C2×D4×D8911yescharacteristic
215C22C2×Q8×D8911yescharacteristic
216C22#41×D8911yescharacteristic
217C22C2×#1308357312yes—
218C22#1566806012yes—
219C4—22no—
220C4—22no—
221C4—24no—
222C4—42no—
223C4—41no—
224C4—894no—
225C4—3562no—
226C4—3562no—
227C4—3561no—
228C4—1782no—
229C4—1782no—
230C2C22⋊Q8×D8911yescharacteristic
231C2#1915210411yescharacteristic
232C2#1915217311yescharacteristic
233C2#1915231912yes—
234C2#1915232312yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#395×C89C2
hypercenter#395D89
hypocenterC89#2581
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
39. C2×Dic178Q8semidirect
118. C89#2581semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic892
C2×#156679772
#191515382
#191515372
#191515172
#191515022
#191514932
#191514852
#191514842
#191514622
#395×C892
#258189