Finite Group Databasebeta

← #26026178

Subgroups — #26026178

Order 11392.

520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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, complemented
2C2×#15667974C211yesmaximal, characteristic
3#19151528C211yesmaximal, characteristic, complemented
4#19151525C211yesmaximal, characteristic, complemented
5#19151524C212yesmaximal, complemented
6#19151516C212yesmaximal
7#19151509C211yesmaximal, characteristic, complemented
8#19151480C212yesmaximal, complemented
9#19151469C212yesmaximal, complemented
10#19151460C211yesmaximal, characteristic, complemented
11#395×C89C211yesmaximal, characteristic, complemented
12C22×D356C2211yescharacteristic
13C22×C4×D89C2211yescharacteristic
14C22×C4×D89C2211yescharacteristic
15#15667988—24no—
16#15667974—24no—
17C2×C4⋊Dic89C2211yescharacteristic
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2211yescharacteristic
22C2×#13083551C2212yes—
23C2×#13083551C2211yescharacteristic
24C2×#13083551C2212yes—
25C2×#13083551C2212yes—
26C2×C4×Dic89C2211yescharacteristic
27#15667919C2212yes—
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
38C23×D89C2311yescharacteristic
39C2×D356—22no—
40C2×D356—22no—
41C2×D356—22no—
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2312yes—
44C22×Dic89C2312yes—
45C22×Dic89C2311yescharacteristic
46C2×C4×D89—22no—
47C2×C4×D89—42no—
48C2×C4×D89—42no—
49C2×C4×D89D414yes—
50C4⋊Dic89—22no—
51#13083553—24no—
52#13083553—24no—
53#13083551—22no—
54#13083551—24no—
55#13083551—24no—
56#13083551—22no—
57#13083551—42no—
58#13083551—42no—
59C4×Dic89—22no—
60C2×Q8×C89—22no—
61C2×Q8×C89—42no—
62C22×C4×C89C2311yescharacteristic
63C22×C4×C89C2312yes—
64C22×C4×C89C2312yes—
65C22×C4×C89C2311yescharacteristic
66C22×C4×C89C2311yescharacteristic
67C4⋊C4×C89—22no—
68C4⋊C4×C89—42no—
69C23×C89C2411yescharacteristic
70C22×D89—21no—
71C22×D89—21no—
72C22×D89—21no—
73C22×D89—21no—
74C22×D89—22no—
75C22×D89—22no—
76C22×D89—22no—
77C22×D89—22no—
78C22×D89C2×D412yes—
79C22×D89#4112yes—
80Q8×C89—44no—
81C2×C4×C89—21no—
82C2×C4×C89—21no—
83C2×C4×C89—22no—
84C2×C4×C89—21no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89—22no—
90C2×C4×C89—22no—
91C2×C4×C89—22no—
92C2×C4×C89C2×D412yes—
93C2×C4×C89#4112yes—
94C2×Dic89—22no—
95C2×Dic89—21no—
96C2×Dic89—22no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89—22no—
102C2×Dic89—22no—
103C2×Dic89C2×D412yes—
104D356—28no—
105C4×D89—44no—
106C4×D89—44no—
107C22×C89C22×D411yescharacteristic
108C22×C89C2×#4111yescharacteristic
109C22×C89C2×#4111yescharacteristic
110C22×C89H(5,𝔽2)12yes—
111C22×C892−1+412yes—
112C2×D89—22no—
113C2×D89—22no—
114C2×D89—22no—
115C2×D89—22no—
116C2×D89—24no—
117C2×D89—41no—
118C2×D89—41no—
119C2×D89—42no—
120C2×D89—42no—
121C2×D89—42no—
122C4×C89—22no—
123C4×C89—22no—
124C4×C89—41no—
125C4×C89—42no—
126C4×C89—42no—
127Dic89—22no—
128Dic89—42no—
129Dic89—41no—
130Dic89—42no—
131C2×C89#52511yescharacteristic
132C2×C89#53411yescharacteristic
133C2×C89#53611yescharacteristic
134C2×C89#53912yes—
135C2×C89#54212yes—
136D89—42no—
137D89—42no—
138#2638—891nomaximal, Sylow
139C89#263811yescharacteristic, complemented, Sylow
140C2×C22⋊Q8—891no—
141C2×C4×D4—891no—
142#398—891no—
143#397—892no—
144#397—891no—
145#395D8911yescharacteristic, complemented
146#394—892no—
147#393—891no—
148#387—892no—
149#385—892no—
150#381—891no—
151C22×Q8C2×D8911yescharacteristic
152C22×D4—891no—
153C23×C4—891no—
154C23×C4—891no—
155C22⋊Q8—1784no—
156C4×D4—1784no—
157C2×C4⋊C4—892no—
158C2×C4⋊C4—891no—
159C2×C4⋊C4—892no—
160C2×C4⋊C4C2×D8911yescharacteristic
161C2×C4⋊C4C2×D8912yes—
162C2×C22⋊C4—892no—
163C2×C22⋊C4—892no—
164C2×C22⋊C4—891no—
165C2×C22⋊C4—891no—
166C2×C22⋊C4—892no—
167C2×C22⋊C4—892no—
168C2×C42—891no—
169#95—892no—
170#95—891no—
171#95—892no—
172#95—892no—
173#95—892no—
174#95C2×D8911yescharacteristic
175#95C2×D8912yes—
176C24—891no—
177C24—891no—
178C2×Q8—22no—
179C2×Q8—42no—
180C2×D4—1782no—
181C2×D4—1782no—
182C2×D4—1782no—
183C22×C4—891no—
184C22×C4—894no—
185C22×C4—891no—
186C22×C4—892no—
187C22×C4—892no—
188C22×C4—3562no—
189C22×C4—3562no—
190C22×C4—1782no—
191C22×C4C22×D8912yes—
192C22×C4C22×D8911yescharacteristic
193C22×C4C22×D8912yes—
194C22×C4C22×D8911yescharacteristic
195C22×C4C22×D8911yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—42no—
198C4⋊C4—1784no—
199C4⋊C4—1782no—
200C4⋊C4—1784no—
201C22⋊C4—3562no—
202C22⋊C4—3562no—
203C22⋊C4—1782no—
204C22⋊C4—1784no—
205C22⋊C4—1784no—
206C22⋊C4—1782no—
207C42—1782no—
208C23—892no—
209C23—892no—
210C23—1781no—
211C23—1781no—
212C23—1781no—
213C23—1781no—
214C23—1782no—
215C23—1782no—
216C23—1782no—
217C23—1782no—
218C23C23×D8911yescharacteristic
219Q8—44no—
220D4—1788no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—892no—
233C2×C4—3564no—
234C2×C4—3564no—
235C2×C4—1781no—
236C2×C4—1782no—
237C2×C4—1782no—
238C2×C4—1782no—
239C2×C4—1782no—
240C2×C4—1782no—
241C2×C4—1782no—
242C2×C4—1782no—
243C2×C4—1782no—
244C2×C4D4×D8912yes—
245C2×C4#1308357512yes—
246C22—3561no—
247C22—3561no—
248C22—3562no—
249C22—3562no—
250C22—3562no—
251C22—1782no—
252C22—1782no—
253C22—1784no—
254C22—1782no—
255C22—1782no—
256C22C2×D4×D8911yescharacteristic
257C22#41×D8911yescharacteristic
258C22C2×#1308357511yescharacteristic
259C22#1566805712yes—
260C22#1566806012yes—
261C4—22no—
262C4—22no—
263C4—41no—
264C4—42no—
265C4—42no—
266C4—3561no—
267C4—3562no—
268C4—3562no—
269C4—1782no—
270C2—3562no—
271C2—3562no—
272C2#1915211111yescharacteristic
273C2#1915215811yescharacteristic
274C2#1915217311yescharacteristic
275C2#1915219412yes—
276C2#1915222212yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#395×C89C2
prime radicalC22×D356C22
hypercenter#395D89
hypocenterC89#2638
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#15667988C2semidirect
3. #19151528C2semidirect
4. #19151525C2semidirect
5. #19151524C2semidirect
7. #19151509C2semidirect
8. #19151480C2semidirect
9. #19151469C2semidirect
10. #19151460C2semidirect
11. #395×C89C2semidirect
139. C89#2638semidirect
145. #395D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679882
C2×#156679742
#191515282
#191515252
#191515242
#191515162
#191515092
#191514802
#191514692
#191514602
#395×C892
#263889