Finite Group Databasebeta

← #26026118

Subgroups — #26026118

Order 11392.

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

normal subgroups only

This group has 500 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×#15668001C211yesmaximal, characteristic
2C2×#15667977C211yesmaximal, characteristic, complemented
3#19151533C212yesmaximal, complemented
4#19151517C211yesmaximal, characteristic, complemented
5#19151516C211yesmaximal, characteristic
6#19151515C211yesmaximal, characteristic
7#19151511C212yesmaximal, complemented
8#19151488C212yesmaximal, complemented
9#19151487C212yesmaximal, complemented
10#19151465C211yesmaximal, characteristic, complemented
11#395×C89C211yesmaximal, characteristic, complemented
12C22×Dic178C2211yescharacteristic
13C22×D356C2211yescharacteristic
14#15668001—24no—
15#15667977—24no—
16C2×#13083553C2211yescharacteristic
17C2×#13083553C2211yescharacteristic
18C2×#13083553C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×#13083551C2212yes—
22C2×#13083551C2212yes—
23C2×#13083551C2212yes—
24C2×#13083551C2212yes—
25C2×C4×Dic89C2211yescharacteristic
26C2×C4×Dic89C2211yescharacteristic
27C2×C4×Dic89C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2211yescharacteristic
31#15667919C2212yes—
32C22×Q8×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C4⋊C4×C89C2212yes—
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C23×D89C2312yes—
38C2×Dic178—22no—
39C2×Dic178—22no—
40C2×Dic178—22no—
41C2×D356—22no—
42C2×D356—42no—
43C22×Dic89C2312yes—
44C22×Dic89C2311yescharacteristic
45C22×Dic89C2311yescharacteristic
46C22×Dic89C2311yescharacteristic
47C22×Dic89C2311yescharacteristic
48#13083553—22no—
49#13083553—22no—
50#13083553—42no—
51#13083551—24no—
52#13083551—24no—
53#13083551—24no—
54#13083551—24no—
55#13083551—42no—
56#13083551—42no—
57C4×Dic89—22no—
58C4×Dic89—22no—
59C4×Dic89D414yes—
60C2×Q8×C89—22no—
61C2×Q8×C89—42no—
62C22×C4×C89C2312yes—
63C22×C4×C89C2312yes—
64C22×C4×C89C2311yescharacteristic
65C22×C4×C89C2311yescharacteristic
66C22×C4×C89C2311yescharacteristic
67C4⋊C4×C89—22no—
68C4⋊C4×C89—42no—
69C23×C89C2411yescharacteristic
70C22×D89—22no—
71C22×D89—22no—
72C22×D89—22no—
73C22×D89—22no—
74C22×D89—22no—
75C22×D89—22no—
76C22×D89—22no—
77Q8×C89—44no—
78C2×C4×C89—21no—
79C2×C4×C89—21no—
80C2×C4×C89—22no—
81C2×C4×C89—21no—
82C2×C4×C89—22no—
83C2×C4×C89—22no—
84C2×C4×C89—22no—
85C2×C4×C89—22no—
86C2×C4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89—22no—
89C2×C4×C89C2×D412yes—
90C2×C4×C89#4112yes—
91C2×Dic89—21no—
92C2×Dic89—21no—
93C2×Dic89—21no—
94C2×Dic89—21no—
95C2×Dic89—22no—
96C2×Dic89—21no—
97C2×Dic89—22no—
98C2×Dic89—22no—
99C2×Dic89—22no—
100C2×Dic89—22no—
101C2×Dic89C2×D412yes—
102C2×Dic89C2×D412yes—
103C2×Dic89#4112yes—
104D356—44no—
105Dic178—28no—
106C22×C89C22×D411yescharacteristic
107C22×C89C2×#4111yescharacteristic
108C22×C89C2×#4111yescharacteristic
109C22×C89H(5,𝔽2)12yes—
110C22×C892−1+412yes—
111C2×D89—42no—
112C2×D89—42no—
113C2×D89—42no—
114C2×D89—42no—
115C2×D89—42no—
116C2×D89—42no—
117C2×D89—42no—
118C4×C89—22no—
119C4×C89—22no—
120C4×C89—41no—
121C4×C89—42no—
122C4×C89—42no—
123Dic89—22no—
124Dic89—22no—
125Dic89—22no—
126Dic89—41no—
127Dic89—42no—
128C2×C89#52511yescharacteristic
129C2×C89#53511yescharacteristic
130C2×C89#53611yescharacteristic
131C2×C89#54212yes—
132C2×C89#54212yes—
133D89—82no—
134#2632—891nomaximal, Sylow
135C89#263211yescharacteristic, complemented, Sylow
136C2×#124—891no—
137C2×C4×Q8—891no—
138#399—892no—
139#395—891no—
140#395D8911yescharacteristic, complemented
141#394—891no—
142#394—891no—
143#393—892no—
144#388—892no—
145#388—892no—
146#383—891no—
147C22×Q8—891no—
148C22×Q8C2×D8911yescharacteristic
149C22×D4—891no—
150#124—1784no—
151C4×Q8—1784no—
152C2×C4⋊C4—892no—
153C2×C4⋊C4—891no—
154C2×C4⋊C4—891no—
155C2×C4⋊C4C2×D8911yescharacteristic
156C2×C4⋊C4C2×D8912yes—
157C2×C22⋊C4—892no—
158C2×C22⋊C4—892no—
159C2×C22⋊C4—892no—
160C2×C22⋊C4—892no—
161C2×C22⋊C4—892no—
162C2×C22⋊C4—892no—
163C2×C42—891no—
164C2×C42—891no—
165C2×C42—891no—
166#95—892no—
167#95—892no—
168#95—891no—
169#95—892no—
170#95C2×D8911yescharacteristic
171#95C2×D8912yes—
172C24—892no—
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—1782no—
176C2×Q8—1782no—
177C2×Q8—1782no—
178C2×D4—3562no—
179C2×D4—1782no—
180C22×C4—891no—
181C22×C4—891no—
182C22×C4—891no—
183C22×C4—892no—
184C22×C4—891no—
185C22×C4C22×D8912yes—
186C22×C4C22×D8912yes—
187C22×C4C22×D8911yescharacteristic
188C22×C4C22×D8911yescharacteristic
189C22×C4C22×D8911yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—3562no—
193C4⋊C4—1782no—
194C4⋊C4—1782no—
195C22⋊C4—3562no—
196C22⋊C4—3562no—
197C22⋊C4—1784no—
198C22⋊C4—1784no—
199C22⋊C4—1784no—
200C22⋊C4—1784no—
201C42—894no—
202C42—1782no—
203C42—1782no—
204C23—1782no—
205C23—1782no—
206C23—1782no—
207C23—1782no—
208C23—1782no—
209C23—1782no—
210C23—1782no—
211C23C23×D8911yescharacteristic
212Q8—44no—
213Q8—1788no—
214D4—3564no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—892no—
227C2×C4—892no—
228C2×C4—892no—
229C2×C4—1781no—
230C2×C4—1782no—
231C2×C4—1782no—
232C2×C4—1782no—
233C2×C4—1782no—
234C2×C4—1781no—
235C2×C4—1781no—
236C2×C4—1781no—
237C2×C4—1781no—
238C2×C4—1782no—
239C2×C4D4×D8912yes—
240C2×C4#1308357512yes—
241C22—3562no—
242C22—3562no—
243C22—3562no—
244C22—3562no—
245C22—3562no—
246C22—3562no—
247C22—3562no—
248C22C2×D4×D8911yescharacteristic
249C22#41×D8911yescharacteristic
250C22C2×#1308357511yescharacteristic
251C22#1566805712yes—
252C22#1566806012yes—
253C4—22no—
254C4—22no—
255C4—42no—
256C4—41no—
257C4—42no—
258C4—3561no—
259C4—3562no—
260C4—1782no—
261C4—1782no—
262C4—1782no—
263C2—7122no—
264C2#1915211111yescharacteristic
265C2#1915216311yescharacteristic
266C2#1915217311yescharacteristic
267C2#1915221812yes—
268C2#1915222212yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#395×C89C2
prime radicalC22×D356C22
hypercenter#395D89
hypocenterC89#2632
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#15667977C2semidirect
3. #19151533C2semidirect
4. #19151517C2semidirect
7. #19151511C2semidirect
8. #19151488C2semidirect
9. #19151487C2semidirect
10. #19151465C2semidirect
11. #395×C89C2semidirect
135. C89#2632semidirect
140. #395D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680012
C2×#156679772
#191515332
#191515172
#191515162
#191515152
#191515112
#191514882
#191514872
#191514652
#395×C892
#263289