Finite Group Databasebeta

← #26028399

Subgroups — #26028399

Order 11392.

408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#19151527C212yesmaximal, complemented
2#19151525C212yesmaximal, complemented
3#19151520C212yesmaximal, complemented
4#19151518C211yesmaximal, characteristic, complemented
5#19151515C212yesmaximal
6#19151511C212yesmaximal, complemented
7#19151499C211yesmaximal, characteristic
8#19151484C212yesmaximal, complemented
9#398×C89C211yesmaximal, characteristic, complemented
10C22×Dic178C2211yescharacteristic
11C22×D356C2211yescharacteristic
12C2×C4⋊Dic89C2212yes—
13C2×#13083553C2212yes—
14C2×#13083551C2212yes—
15C2×#13083551C2212yes—
16C2×#13083551C2212yes—
17C2×#13083551C2212yes—
18C2×#13083551C2212yes—
19C2×#13083551C2212yes—
20C2×C4×Dic89C2211yescharacteristic
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26C2×C4⋊C4×C89C2212yes—
27C2×C4⋊C4×C89C2211yescharacteristic
28C2×C4⋊C4×C89C2211yescharacteristic
29#95×C89C2212yes—
30#95×C89C2211yescharacteristic
31C23×D89C2312yes—
32C2×Dic178—41no—
33C2×Dic178—42no—
34C2×D356—22no—
35C2×D356—41no—
36C2×D356—41no—
37C22×Dic89C2312yes—
38C22×Dic89C2312yes—
39C22×Dic89C2312yes—
40C4⋊Dic89—42no—
41#13083553—42no—
42#13083551—42no—
43#13083551—42no—
44#13083551—42no—
45#13083551—42no—
46#13083551—42no—
47#13083551—42no—
48C4×Dic89—41no—
49C22×C4×C89C2311yescharacteristic
50C22×C4×C89C2312yes—
51C22×C4×C89C2312yes—
52C22×C4×C89C2311yescharacteristic
53C22×C4×C89C2311yescharacteristic
54C4⋊C4×C89—24no—
55C4⋊C4×C89—41no—
56C4⋊C4×C89—41no—
57C23×C89C2411yescharacteristic
58C22×D89—22no—
59C22×D89—22no—
60C22×D89—22no—
61C22×D89—22no—
62C22×D89—22no—
63C22×D89—22no—
64C22×D89—22no—
65C2×C4×C89—21no—
66C2×C4×C89—21no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89—21no—
70C2×C4×C89—22no—
71C2×C4×C89—21no—
72C2×C4×C89—22no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89#4112yes—
78C2×Dic89—22no—
79C2×Dic89—22no—
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—22no—
83C2×Dic89—22no—
84C2×Dic89—22no—
85C2×Dic89—22no—
86C2×Dic89—22no—
87D356—44no—
88Dic178—44no—
89C22×C89C2×#4111yescharacteristic
90C22×C89H(5,𝔽2)11yescharacteristic
91C22×C89H(5,𝔽2)11yescharacteristic
92C22×C89H(5,𝔽2)12yes—
93C22×C892−1+412yes—
94C2×D89—42no—
95C2×D89—42no—
96C2×D89—42no—
97C2×D89—42no—
98C2×D89—42no—
99C2×D89—42no—
100C2×D89—42no—
101C4×C89—22no—
102C4×C89—42no—
103C4×C89—42no—
104C4×C89—41no—
105C4×C89—41no—
106Dic89—42no—
107Dic89—42no—
108Dic89—42no—
109C2×C89#53811yescharacteristic
110C2×C89#54212yes—
111C2×C89#56011yescharacteristic
112C2×C89#56212yes—
113C2×C89#56311yescharacteristic
114D89—82no—
115#2830—891nomaximal, Sylow
116C89#283011yescharacteristic, complemented, Sylow
117#398D8911yescharacteristic, complemented
118#397—892no—
119#397—892no—
120#396—892no—
121#395—891no—
122#394—892no—
123#393—892no—
124#390—891no—
125#387—892no—
126C22×Q8—891no—
127C22×D4—891no—
128C2×C4⋊C4—892no—
129C2×C4⋊C4—892no—
130C2×C4⋊C4C2×D8912yes—
131C2×C4⋊C4C2×D8911yescharacteristic
132C2×C4⋊C4C2×D8911yescharacteristic
133C2×C22⋊C4—892no—
134C2×C22⋊C4—892no—
135C2×C22⋊C4—892no—
136C2×C22⋊C4—892no—
137C2×C22⋊C4—892no—
138C2×C22⋊C4—892no—
139C2×C42—891no—
140#95—892no—
141#95—892no—
142#95—892no—
143#95—892no—
144#95—891no—
145#95C2×D8912yes—
146#95C2×D8911yescharacteristic
147C24—892no—
148C2×Q8—3561no—
149C2×Q8—3562no—
150C2×D4—3561no—
151C2×D4—3561no—
152C2×D4—1782no—
153C22×C4—892no—
154C22×C4—892no—
155C22×C4—892no—
156C22×C4C22×D8912yes—
157C22×C4C22×D8911yescharacteristic
158C22×C4C22×D8912yes—
159C22×C4C22×D8911yescharacteristic
160C22×C4C22×D8911yescharacteristic
161C4⋊C4—24no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—3562no—
165C4⋊C4—3562no—
166C22⋊C4—3562no—
167C22⋊C4—3562no—
168C22⋊C4—3562no—
169C22⋊C4—3562no—
170C22⋊C4—3562no—
171C22⋊C4—3562no—
172C42—3561no—
173C23—1782no—
174C23—1782no—
175C23—1782no—
176C23—1782no—
177C23—1782no—
178C23—1782no—
179C23—1782no—
180C23C23×D8911yescharacteristic
181Q8—3564no—
182D4—3564no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
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—22no—
195C2×C4—1782no—
196C2×C4—1782no—
197C2×C4—1782no—
198C2×C4—1782no—
199C2×C4—1782no—
200C2×C4—1782no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4#1308357312yes—
205C22—3562no—
206C22—3562no—
207C22—3562no—
208C22—3562no—
209C22—3562no—
210C22—3562no—
211C22—3562no—
212C22C2×#1308357311yescharacteristic
213C22#1566805711yescharacteristic
214C22#1566805811yescharacteristic
215C22#1566805812yes—
216C22#1566806012yes—
217C4—22no—
218C4—42no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—3562no—
223C4—3562no—
224C4—3562no—
225C2—7122no—
226C2#1915218511yescharacteristic
227C2#1915222112yes—
228C2#1915233811yescharacteristic
229C2#1915234612yes—
230C2#1915234711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, cosocleC23×C89C24
Fitting#398×C89C2
prime radicalC22×D356C22
hypercenter#398D89
hypocenterC89#2830
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #19151527C2semidirect
2. #19151525C2semidirect
3. #19151520C2semidirect
4. #19151518C2semidirect
6. #19151511C2semidirect
8. #19151484C2semidirect
9. #398×C89C2semidirect
116. C89#2830semidirect
117. #398D89semidirect

Maximal subgroups

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

subgroupindex
#191515272
#191515252
#191515202
#191515182
#191515152
#191515112
#191514992
#191514842
#398×C892
#283089