Finite Group Databasebeta

← #26025249

Subgroups — #26025249

Order 11392.

604 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 157 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, complemented
2C2×#15668001C211yesmaximal, characteristic
3C2×#15668000C211yesmaximal, characteristic
4C2×#15667974C211yesmaximal, characteristic
5#19151527C214yesmaximal, complemented
6#19151503C211yesmaximal, characteristic, complemented
7#19151457C214yesmaximal, complemented
8C4×#13083553C211yesmaximal, characteristic, complemented
9#391×C89C211yesmaximal, characteristic, complemented
10C22×Dic178C2211yescharacteristic
11C22×D356C2211yescharacteristic
12C22×C4×D89C2212yes—
13#15668010—24no—
14#15668001—24no—
15#15668000—24no—
16#15667974—24no—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2212yes—
20C2×#13083551C2214yes—
21C2×#13083551C2214yes—
22C2×#13083551C2212yes—
23C2×C4×Dic89C2211yescharacteristic
24C2×C4×Dic89C2211yescharacteristic
25#15667919C2212yes—
26#15667919C2214yes—
27C22×Q8×C89C2211yescharacteristic
28C2×C4⋊C4×C89C2211yescharacteristic
29C2×C42×C89C2211yescharacteristic
30#95×C89C2214yes—
31C23×D89C2312yes—
32C2×Dic178—22no—
33C2×Dic178—22no—
34C2×Dic178—22no—
35C2×D356—22no—
36C2×D356—22no—
37C2×D356D414yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2311yescharacteristic
42C2×C4×D89—24no—
43C2×C4×D89—28no—
44#13083553—24no—
45#13083553—24no—
46#13083553—24no—
47#13083551—28no—
48#13083551—28no—
49#13083551—24no—
50C4×Dic89—22no—
51C4×Dic89D414yes—
52C2×Q8×C89—22no—
53C2×Q8×C89—22no—
54C2×Q8×C89—22no—
55C22×C4×C89C2312yes—
56C22×C4×C89C2312yes—
57C22×C4×C89C2312yes—
58C22×C4×C89C2311yescharacteristic
59C4⋊C4×C89—22no—
60C42×C89—22no—
61C23×C89C2411yescharacteristic
62C22×D89—22no—
63C22×D89—24no—
64C22×D89—22no—
65C22×D89—24no—
66C22×D89C2×D414yes—
67Q8×C89—44no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—22no—
72C2×C4×C89—22no—
73C2×C4×C89—22no—
74C2×C4×C89—24no—
75C2×C4×C89—22no—
76C2×C4×C89C2×D412yes—
77C2×C4×C89C2×D412yes—
78C2×C4×C89#4112yes—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89C2×D412yes—
87C2×Dic89C2×D412yes—
88C2×Dic89#4114yes—
89D356—28no—
90C4×D89—48no—
91Dic178—44no—
92C22×C89C22×D411yescharacteristic
93C22×C89C22×D411yescharacteristic
94C22×C89C2×#4111yescharacteristic
95C22×C89C2×#4112yes—
96C22×C892−1+412yes—
97C2×D89—24no—
98C2×D89—28no—
99C2×D89—42no—
100C2×D89—42no—
101C2×D89—44no—
102C4×C89—42no—
103C4×C89—42no—
104C4×C89—42no—
105C4×C89#12114yes—
106Dic89—22no—
107Dic89—42no—
108Dic89—42no—
109Dic89#12414yescomplemented
110C2×C89C2×#12111yescharacteristic
111C2×C89C2×#12411yescharacteristic
112C2×C89#53611yescharacteristic
113C2×C89#54712yes—
114C2×C89#55612yes—
115D89—44no—
116#2547—891nomaximal, Sylow
117C89#254711yescharacteristic, complemented, Sylow
118C2×C4⋊Q8—891no—
119C2×#124—891no—
120C2×#124—891no—
121C2×C4×D4—891no—
122#397—894no—
123#391—891no—
124#391D8911yescharacteristic, complemented
125#380—894no—
126C4×C4⋊C4—891no—
127C22×Q8—891no—
128C22×Q8C2×D8911yescharacteristic
129C22×D4—891no—
130C23×C4—892no—
131C4⋊Q8—1784no—
132#124—1784no—
133#124—1784no—
134C4×D4—1784no—
135C2×C4⋊C4—892no—
136C2×C4⋊C4—892no—
137C2×C4⋊C4—892no—
138C2×C4⋊C4C2×D8911yescharacteristic
139C2×C22⋊C4—892no—
140C2×C22⋊C4—894no—
141C2×C22⋊C4—894no—
142C2×C42—891no—
143C2×C42—891no—
144C2×C42C2×D8911yescharacteristic
145#95—892no—
146#95—894no—
147#95C2×D8914yes—
148C24—892no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—1782no—
153C2×Q8—1782no—
154C2×Q8—1782no—
155C2×D4—894no—
156C2×D4—1782no—
157C2×D4—1782no—
158C22×C4—891no—
159C22×C4—891no—
160C22×C4—892no—
161C22×C4—892no—
162C22×C4—1784no—
163C22×C4—1788no—
164C22×C4C22×D8912yes—
165C22×C4C22×D8912yes—
166C22×C4C22×D8912yes—
167C22×C4C22×D8911yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—1784no—
170C4⋊C4—1784no—
171C4⋊C4—1784no—
172C22⋊C4—1784no—
173C22⋊C4—1788no—
174C22⋊C4—1788no—
175C42—22no—
176C42—894no—
177C42—1782no—
178C23—894no—
179C23—1782no—
180C23—1784no—
181C23—1782no—
182C23—1784no—
183C23C23×D8911yescharacteristic
184Q8—44no—
185Q8—3564no—
186D4—1788no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—892no—
196C2×C4—894no—
197C2×C4—892no—
198C2×C4—3568no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4—1782no—
206C2×C4D4×D8912yes—
207C2×C4D4×D8912yes—
208C2×C4#1308357412yes—
209C22—3562no—
210C22—3564no—
211C22—3562no—
212C22—1788no—
213C22—1784no—
214C22C2×D4×D8911yescharacteristic
215C22C2×D4×D8911yescharacteristic
216C22#41×D8912yes—
217C22C2×#1308357411yescharacteristic
218C22#1566806012yes—
219C4—42no—
220C4—42no—
221C4—42no—
222C4—894no—
223C4—3562no—
224C4—3562no—
225C4—1782no—
226C4#1566798514yes—
227C2—3564no—
228C2C2×#1566798511yescharacteristic
229C2#124×D8911yescharacteristic
230C2#1915217311yescharacteristic
231C2#1915225012yes—
232C2#1915232012yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#391×C89C2
prime radicalC22×D356C22
hypercenter#391D89
hypocenterC89#2547
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#15668010C2semidirect
5. #19151527C2semidirect
6. #19151503C2semidirect
7. #19151457C2semidirect
8. C4×#13083553C2semidirect
9. #391×C89C2semidirect
109. Dic89#124semidirect
117. C89#2547semidirect
124. #391D89semidirect

Maximal subgroups

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

subgroupindex
C2×#156680102
C2×#156680012
C2×#156680002
C2×#156679742
#191515272
#191515032
#191514572
C4×#130835532
#391×C892
#254789