Finite Group Databasebeta

← #26025930

Subgroups — #26025930

Order 11392.

540 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15667970C212yesmaximal, complemented
2#19151520C212yesmaximal, complemented
3#19151515C211yesmaximal, characteristic
4#19151488C212yesmaximal, complemented
5#19151485C212yesmaximal, complemented
6#19151476C212yesmaximal
7#19151472C212yesmaximal, complemented
8#19151463C211yesmaximal, characteristic, complemented
9#398×C89C211yesmaximal, characteristic, complemented
10C22×D356C2211yescharacteristic
11C22×C4×D89C2212yes—
12#15667970—28no—
13C2×C4⋊Dic89C2212yes—
14C2×C4⋊Dic89C2211yescharacteristic
15C2×#13083553C2212yes—
16C2×#13083551C2212yes—
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×#13083551C2212yes—
21C2×C4×Dic89C2212yes—
22C2×C4×Dic89C2211yescharacteristic
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26#15667919C2212yes—
27C2×C4⋊C4×C89C2212yes—
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C4⋊C4×C89C2211yescharacteristic
30#95×C89C2211yescharacteristic
31#95×C89C2212yes—
32C23×D89C2312yes—
33C2×D356—24no—
34C2×D356—41no—
35C22×Dic89C2312yes—
36C22×Dic89C2312yes—
37C22×Dic89C2312yes—
38C2×C4×D89—24no—
39C2×C4×D89—24no—
40C2×C4×D89—24no—
41C4⋊Dic89—24no—
42C4⋊Dic89—41no—
43#13083553—24no—
44#13083551—24no—
45#13083551—24no—
46#13083551—24no—
47#13083551—24no—
48#13083551—42no—
49C4×Dic89—24no—
50C4×Dic89D414yescomplemented
51C22×C4×C89C2311yescharacteristic
52C22×C4×C89C2311yescharacteristic
53C22×C4×C89C2312yes—
54C22×C4×C89C2311yescharacteristic
55C22×C4×C89C2312yes—
56C4⋊C4×C89—24no—
57C4⋊C4×C89—41no—
58C4⋊C4×C89—41no—
59C23×C89C2411yescharacteristic
60C22×D89—22no—
61C22×D89—22no—
62C22×D89—22no—
63C22×D89—22no—
64C22×D89—22no—
65C22×D89—22no—
66C22×D89#4114yes—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—21no—
70C2×C4×C89—21no—
71C2×C4×C89—22no—
72C2×C4×C89—22no—
73C2×C4×C89—22no—
74C2×C4×C89—21no—
75C2×C4×C89—22no—
76C2×C4×C89—21no—
77C2×C4×C89—22no—
78C2×C4×C89C2×D412yes—
79C2×C4×C89#4114yes—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87C2×Dic89—22no—
88C2×Dic89C2×D414yes—
89D356—44no—
90C4×D89—216no—
91C22×C89C22×D411yescharacteristic
92C22×C89C2×#4112yes—
93C22×C89C2×#4112yes—
94C22×C89H(5,𝔽2)11yescharacteristic
95C22×C892−1+411yescharacteristic
96C2×D89—24no—
97C2×D89—24no—
98C2×D89—24no—
99C2×D89—42no—
100C2×D89—42no—
101C2×D89—42no—
102C2×D89—42no—
103C4×C89—24no—
104C4×C89—22no—
105C4×C89—42no—
106C4×C89—41no—
107C4×C89—41no—
108Dic89—24no—
109Dic89—42no—
110Dic89—42no—
111C2×C89#52512yes—
112C2×C89#53711yescharacteristic
113C2×C89#55111yescharacteristic
114C2×C89#55212yes—
115C2×C89#55511yescharacteristic
116D89—44no—
117#2609—891nomaximal, Sylow
118C89#260911yescharacteristic, complemented, Sylow
119C2×#117—892no—
120#398D8911yescharacteristic, complemented
121#396—892no—
122#394—891no—
123#388—892no—
124#387—892no—
125#386—892no—
126#385—892no—
127#382—891no—
128C22×D4—891no—
129C23×C4—892no—
130#117—1788no—
131C2×C4⋊C4—891no—
132C2×C4⋊C4—892no—
133C2×C4⋊C4—892no—
134C2×C4⋊C4C2×D8912yes—
135C2×C4⋊C4C2×D8911yescharacteristic
136C2×C4⋊C4C2×D8911yescharacteristic
137C2×C22⋊C4—892no—
138C2×C22⋊C4—892no—
139C2×C22⋊C4—892no—
140C2×C22⋊C4—892no—
141C2×C22⋊C4—892no—
142C2×C42—891no—
143C2×C42—892no—
144#95—892no—
145#95—892no—
146#95—891no—
147#95—892no—
148#95C2×D8911yescharacteristic
149#95C2×D8912yes—
150C24—892no—
151C2×D4—3561no—
152C2×D4—1784no—
153C22×C4—892no—
154C22×C4—892no—
155C22×C4—892no—
156C22×C4—1784no—
157C22×C4—1784no—
158C22×C4—1784no—
159C22×C4C22×D8911yescharacteristic
160C22×C4C22×D8911yescharacteristic
161C22×C4C22×D8912yes—
162C22×C4C22×D8911yescharacteristic
163C22×C4C22×D8912yes—
164C4⋊C4—24no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—3561no—
168C4⋊C4—1784no—
169C4⋊C4—1784no—
170C22⋊C4—3562no—
171C22⋊C4—1784no—
172C22⋊C4—1784no—
173C22⋊C4—1784no—
174C22⋊C4—1784no—
175C42—894no—
176C42—1784no—
177C23—894no—
178C23—1782no—
179C23—1782no—
180C23—1782no—
181C23—1782no—
182C23—1782no—
183C23—1782no—
184C23C23×D8911yescharacteristic
185D4—3564no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—894no—
198C2×C4—17816no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4—1782no—
207C2×C4D4×D8912yes—
208C2×C4#1308357514yes—
209C22—3562no—
210C22—3562no—
211C22—3562no—
212C22—3562no—
213C22—1784no—
214C22—1784no—
215C22—1784no—
216C22C2×D4×D8911yescharacteristic
217C22#41×D8912yes—
218C22C2×#1308357512yes—
219C22#1566805711yescharacteristic
220C22#1566805911yescharacteristic
221C4—22no—
222C4—24no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—3562no—
227C4—3562no—
228C4—1784no—
229C2—3564no—
230C2#1915211112yes—
231C2#1915217511yescharacteristic
232C2#1915227611yescharacteristic
233C2#1915228612yes—
234C2#1915231411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC22×D356C22
hypercenter#398D89
hypocenterC89#2609
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#15667970C2semidirect
2. #19151520C2semidirect
4. #19151488C2semidirect
5. #19151485C2semidirect
7. #19151472C2semidirect
8. #19151463C2semidirect
9. #398×C89C2semidirect
50. C4×Dic89D4semidirect
118. C89#2609semidirect
120. #398D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156679702
#191515202
#191515152
#191514882
#191514852
#191514762
#191514722
#191514632
#398×C892
#260989