Finite Group Databasebeta

← #26025628

Subgroups — #26025628

Order 11392.

544 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 159 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×#15667988C211yesmaximal, characteristic
2C2×C4⋊C4×D89C211yesmaximal, characteristic
3#19151530C211yesmaximal, characteristic, complemented
4#19151528C211yesmaximal, characteristic, complemented
5#19151517C211yesmaximal, characteristic, complemented
6#19151495C212yesmaximal, complemented
7#19151494C212yesmaximal, complemented
8#19151472C212yesmaximal
9#19151469C212yesmaximal
10#19151445C211yesmaximal, characteristic
11#395×C89C211yesmaximal, characteristic, complemented
12C22×C4×D89C2211yescharacteristic
13C22×C4×D89C2211yescharacteristic
14C22×C4×D89C2211yescharacteristic
15#15667988—24no—
16C2×C4⋊Dic89C2212yes—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×C4⋊Dic89C2211yescharacteristic
19C2×#13083553C2212yes—
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2212yes—
22C2×#13083553C2211yescharacteristic
23C2×#13083553C2212yes—
24C4⋊C4×D89—24no—
25C2×#13083551C2212yes—
26C2×#13083551C2212yes—
27C2×C4×Dic89C2212yes—
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—
37C23×D89C2311yescharacteristic
38C22×Dic89C2311yescharacteristic
39C22×Dic89C2312yes—
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2312yes—
42C22×Dic89C2311yescharacteristic
43C2×C4×D89—22no—
44C2×C4×D89—22no—
45C2×C4×D89—22no—
46C2×C4×D89—22no—
47C2×C4×D89—42no—
48C2×C4×D89—42no—
49C2×C4×D89D414yes—
50C4⋊Dic89—22no—
51C4⋊Dic89—22no—
52C4⋊Dic89—24no—
53#13083553—22no—
54#13083553—24no—
55#13083553—24no—
56#13083553—22no—
57#13083553—42no—
58#13083551—24no—
59#13083551Q818yescomplemented
60C4×Dic89—42no—
61C2×Q8×C89—22no—
62C2×Q8×C89—42no—
63C22×C4×C89C2311yescharacteristic
64C22×C4×C89C2312yes—
65C22×C4×C89C2311yescharacteristic
66C22×C4×C89C2312yes—
67C22×C4×C89C2311yescharacteristic
68C4⋊C4×C89—22no—
69C4⋊C4×C89—42no—
70C23×C89C2411yescharacteristic
71C22×D89—21no—
72C22×D89—21no—
73C22×D89—22no—
74C22×D89C2×D412yes—
75C22×D89C2×Q814yes—
76Q8×C89—44no—
77C2×C4×C89—21no—
78C2×C4×C89—22no—
79C2×C4×C89—21no—
80C2×C4×C89—22no—
81C2×C4×C89—22no—
82C2×C4×C89—21no—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89C2×D412yes—
88C2×C4×C89C2×Q814yes—
89C2×C4×C89#4112yes—
90C2×Dic89—21no—
91C2×Dic89—22no—
92C2×Dic89—21no—
93C2×Dic89—22no—
94C2×Dic89—22no—
95C2×Dic89—22no—
96C2×Dic89—21no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C2×Dic89C2×D412yes—
101C2×Dic89C2×Q814yes—
102C2×Dic89#4112yes—
103C4×D89—28no—
104C4×D89—44no—
105C4×D89—44no—
106C22×C89C22×D411yescharacteristic
107C22×C89C22×Q812yes—
108C22×C89C2×#4111yescharacteristic
109C22×C89C2×#4111yescharacteristic
110C22×C89H(5,𝔽2)12yes—
111C2×D89—22no—
112C2×D89—22no—
113C2×D89—24no—
114C2×D89—24no—
115C2×D89C4⋊Q814yes—
116C4×C89—22no—
117C4×C89—22no—
118C4×C89—24no—
119C4×C89—41no—
120C4×C89—42no—
121Dic89—22no—
122Dic89—22no—
123Dic89—24no—
124Dic89—42no—
125Dic89—41no—
126C2×C89#52511yescharacteristic
127C2×C89C2×C4⋊Q811yescharacteristic
128C2×C89#53411yescharacteristic
129C2×C89#55412yes—
130C2×C89#55412yes—
131D89—24no—
132#2583—891nomaximal, Sylow
133C89#258311yescharacteristic, complemented, Sylow
134C2×C22⋊Q8—891no—
135C22×C4⋊C4—891no—
136#398—891no—
137#398—891no—
138#395—891no—
139#395D8911yescharacteristic, complemented
140#389—892no—
141#389—892no—
142#385—892no—
143#385—892no—
144C4×C22⋊C4—891no—
145C22×Q8C2×D8911yescharacteristic
146C23×C4—891no—
147C23×C4—891no—
148C23×C4—891no—
149C22⋊Q8—1784no—
150C2×C4⋊C4—892no—
151C2×C4⋊C4—891no—
152C2×C4⋊C4—891no—
153C2×C4⋊C4—891no—
154C2×C4⋊C4—892no—
155C2×C4⋊C4—891no—
156C2×C4⋊C4—892no—
157C2×C4⋊C4—892no—
158C2×C4⋊C4—1784no—
159C2×C4⋊C4C2×D8911yescharacteristic
160C2×C4⋊C4C2×D8912yes—
161C2×C22⋊C4—892no—
162C2×C22⋊C4—892no—
163C2×C42—892no—
164#95—891no—
165#95—892no—
166#95—892no—
167#95—892no—
168#95C2×D8911yescharacteristic
169#95C2×D8912yes—
170C24—891no—
171C2×Q8—22no—
172C2×Q8—42no—
173C22×C4—892no—
174C22×C4—891no—
175C22×C4—891no—
176C22×C4—894no—
177C22×C4—892no—
178C22×C4—891no—
179C22×C4—3562no—
180C22×C4—3562no—
181C22×C4—1782no—
182C22×C4—1782no—
183C22×C4—1782no—
184C22×C4—1782no—
185C22×C4C22×D8911yescharacteristic
186C22×C4C22×D8912yes—
187C22×C4C22×D8911yescharacteristic
188C22×C4C22×D8912yes—
189C22×C4C22×D8911yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—3562no—
193C4⋊C4—1782no—
194C4⋊C4—1782no—
195C4⋊C4—1784no—
196C4⋊C4—1784no—
197C4⋊C4—1782no—
198C4⋊C4—1782no—
199C4⋊C4—1784no—
200C22⋊C4—898no—
201C22⋊C4—1784no—
202C42—3562no—
203C23—892no—
204C23—894no—
205C23—1781no—
206C23—1781no—
207C23—1782no—
208C23C23×D8911yescharacteristic
209Q8—44no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—892no—
221C2×C4—894no—
222C2×C4—892no—
223C2×C4—3564no—
224C2×C4—3564no—
225C2×C4—1788no—
226C2×C4—1782no—
227C2×C4—1781no—
228C2×C4—1782no—
229C2×C4—1782no—
230C2×C4—1782no—
231C2×C4—1781no—
232C2×C4—1782no—
233C2×C4—1781no—
234C2×C4—1782no—
235C2×C4—1782no—
236C2×C4D4×D8912yes—
237C2×C4Q8×D8914yes—
238C2×C4#1308357512yes—
239C22—894no—
240C22—1782no—
241C22—1784no—
242C22—1784no—
243C22—1782no—
244C22C2×D4×D8911yescharacteristic
245C22C2×Q8×D8912yes—
246C22#41×D8911yescharacteristic
247C22C2×#1308357511yescharacteristic
248C22#1566805712yes—
249C4—22no—
250C4—24no—
251C4—22no—
252C4—41no—
253C4—42no—
254C4—3561no—
255C4—3562no—
256C4—1782no—
257C4—1784no—
258C4—1782no—
259C2—1784no—
260C2#1915211111yescharacteristic
261C2C4⋊Q8×D8911yescharacteristic
262C2#1915215811yescharacteristic
263C2#1915230212yes—
264C2#1915230912yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#395×C89C2
prime radicalC23×D89C23
hypercenter#395D89
hypocenterC89#2583
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #19151530C2semidirect
4. #19151528C2semidirect
5. #19151517C2semidirect
6. #19151495C2semidirect
7. #19151494C2semidirect
11. #395×C89C2semidirect
59. #13083551Q8semidirect
133. C89#2583semidirect
139. #395D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679882
C2×C4⋊C4×D892
#191515302
#191515282
#191515172
#191514952
#191514942
#191514722
#191514692
#191514452
#395×C892
#258389