Finite Group Databasebeta

← #26025456

Subgroups — #26025456

Order 11392.

500 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 171 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×#15668010C211yesmaximal, characteristic
2C2×#15667977C211yesmaximal, characteristic
3#19151519C211yesmaximal, characteristic
4#19151518C211yesmaximal, characteristic
5#19151517C211yesmaximal, characteristic
6#19151502C212yesmaximal
7#19151495C212yesmaximal
8#19151493C212yesmaximal
9#19151467C212yesmaximal
10#19151449C211yesmaximal, characteristic
11#395×C89C211yesmaximal, characteristic
12C22×Dic178C2211yescharacteristic
13C22×Dic178C2211yescharacteristic
14#15668010—24no—
15#15667977—24no—
16C2×C4⋊Dic89C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2212yes—
22C2×#13083553C2212yes—
23C2×#13083553C2212yes—
24C2×C4×Dic89C2212yes—
25C2×C4×Dic89C2211yescharacteristic
26C2×C4×Dic89C2211yescharacteristic
27C2×C4×Dic89C2211yescharacteristic
28#15667919C2211yescharacteristic
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C22×Q8×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C4⋊C4×C89C2212yes—
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C2×Dic178—22no—
38C2×Dic178—22no—
39C2×Dic178—22no—
40C2×Dic178—42no—
41C2×Dic178Q814yescomplemented
42C22×Dic89C2312yes—
43C22×Dic89C2311yescharacteristic
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2312yes—
46C22×Dic89C2311yescharacteristic
47C22×Dic89C2311yescharacteristic
48C4⋊Dic89—42no—
49#13083553—22no—
50#13083553—22no—
51#13083553—24no—
52#13083553—24no—
53#13083553—42no—
54#13083553—42no—
55#13083553Q818yescomplemented
56C4×Dic89—22no—
57C4×Dic89—22no—
58C4×Dic89—24no—
59C4×Dic89D414yes—
60C2×Q8×C89—22no—
61C2×Q8×C89—42no—
62C22×C4×C89C2312yes—
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2311yescharacteristic
65C22×C4×C89C2311yescharacteristic
66C22×C4×C89C2312yes—
67C4⋊C4×C89—22no—
68C4⋊C4×C89—42no—
69C23×C89C2411yescharacteristic
70Q8×C89—44no—
71C2×C4×C89—21no—
72C2×C4×C89—22no—
73C2×C4×C89—21no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—21no—
77C2×C4×C89—22no—
78C2×C4×C89—22no—
79C2×C4×C89—22no—
80C2×C4×C89—22no—
81C2×C4×C89C2×D412yes—
82C2×C4×C89C2×Q814yes—
83C2×C4×C89C2×Q812yes—
84C2×Dic89—21no—
85C2×Dic89—22no—
86C2×Dic89—21no—
87C2×Dic89—22no—
88C2×Dic89—21no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—22no—
92C2×Dic89—22no—
93C2×Dic89C2×D412yes—
94C2×Dic89C2×D412yes—
95C2×Dic89C2×Q814yes—
96C2×Dic89C2×Q812yes—
97C2×Dic89C2×Q812yes—
98C2×Dic89C2×Q814yes—
99C2×Dic89#4112yes—
100Dic178—28no—
101Dic178—44no—
102C22×C89C22×D411yescharacteristic
103C22×C89C22×Q811yescharacteristic
104C22×C89C22×Q812yes—
105C22×C89C2×#4111yescharacteristic
106C22×C89H(5,𝔽2)12yes—
107C4×C89—22no—
108C4×C89—22no—
109C4×C89—24no—
110C4×C89—41no—
111C4×C89—42no—
112Dic89—22no—
113Dic89—24no—
114Dic89—42no—
115Dic89—41no—
116Dic89C22⋊Q814yes—
117Dic89C4⋊Q814yes—
118C2×C89C2×C22⋊Q811yescharacteristic
119C2×C89C2×C4⋊Q811yescharacteristic
120C2×C89#53511yescharacteristic
121C2×C89#55412yes—
122C2×C89Q8212yes—
123#2567—891nomaximal, Sylow
124C89#256711yescharacteristic, complemented, Sylow
125C2×C4⋊Q8—891no—
126C2×C4×Q8—891no—
127#395—891no—
128#395—891no—
129#395—891no—
130#395D8911yescharacteristic
131#391—892no—
132#389—892no—
133#389—892no—
134#384—892no—
135C4×C4⋊C4—891no—
136C22×Q8—891no—
137C22×Q8—891no—
138C22×Q8C2×D8911yescharacteristic
139C4⋊Q8—1784no—
140C4×Q8—1784no—
141C2×C4⋊C4—892no—
142C2×C4⋊C4—892no—
143C2×C4⋊C4—892no—
144C2×C4⋊C4—892no—
145C2×C4⋊C4—891no—
146C2×C4⋊C4—891no—
147C2×C4⋊C4—892no—
148C2×C4⋊C4—892no—
149C2×C4⋊C4C2×D8911yescharacteristic
150C2×C4⋊C4C2×D8912yes—
151C2×C42—891no—
152C2×C42—891no—
153C2×C42—891no—
154C2×C42—892no—
155#95—891no—
156#95—892no—
157#95—892no—
158#95—892no—
159#95C2×D8911yescharacteristic
160#95C2×D8912yes—
161C2×Q8—22no—
162C2×Q8—42no—
163C2×Q8—894no—
164C2×Q8—3562no—
165C2×Q8—1782no—
166C2×Q8—1782no—
167C2×Q8—1782no—
168C22×C4—891no—
169C22×C4—891no—
170C22×C4—891no—
171C22×C4—892no—
172C22×C4—892no—
173C22×C4—891no—
174C22×C4C22×D8912yes—
175C22×C4C22×D8911yescharacteristic
176C22×C4C22×D8911yescharacteristic
177C22×C4C22×D8911yescharacteristic
178C22×C4C22×D8912yes—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—898no—
182C4⋊C4—3562no—
183C4⋊C4—3562no—
184C4⋊C4—3562no—
185C4⋊C4—1782no—
186C4⋊C4—1784no—
187C4⋊C4—1784no—
188C4⋊C4—1782no—
189C42—894no—
190C42—1782no—
191C42—1782no—
192C42—1784no—
193C23C23×D8911yescharacteristic
194Q8—44no—
195Q8—3564no—
196Q8—1788no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—892no—
208C2×C4—892no—
209C2×C4—894no—
210C2×C4—892no—
211C2×C4—892no—
212C2×C4—894no—
213C2×C4—892no—
214C2×C4—1781no—
215C2×C4—1782no—
216C2×C4—1782no—
217C2×C4—1782no—
218C2×C4—1782no—
219C2×C4—1781no—
220C2×C4—1782no—
221C2×C4—1781no—
222C2×C4—1782no—
223C2×C4D4×D8912yes—
224C2×C4Q8×D8914yes—
225C2×C4Q8×D8912yes—
226C22C2×D4×D8911yescharacteristic
227C22C2×Q8×D8912yes—
228C22C2×Q8×D8911yescharacteristic
229C22#41×D8911yescharacteristic
230C22#1566805712yes—
231C4—22no—
232C4—24no—
233C4—22no—
234C4—42no—
235C4—41no—
236C4—894no—
237C4—894no—
238C4—3562no—
239C4—3561no—
240C4—1784no—
241C4—1782no—
242C2C22⋊Q8×D8911yescharacteristic
243C2C4⋊Q8×D8911yescharacteristic
244C2#1915216311yescharacteristic
245C2#1915230212yes—
246C2#1915232812yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#395×C89C2
hypercenter#395D89
hypocenterC89#2567
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
41. C2×Dic178Q8semidirect
55. #13083553Q8semidirect
124. C89#2567semidirect

Maximal subgroups

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

subgroupindex
C2×#156680102
C2×#156679772
#191515192
#191515182
#191515172
#191515022
#191514952
#191514932
#191514672
#191514492
#395×C892
#256789