Finite Group Databasebeta

← #26019237

Subgroups — #26019237

Order 11392.

280 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 53 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#19152160C211yesmaximal, characteristic
2#19151911C212yesmaximal, complemented
3#19151331C212yesmaximal, complemented
4#19151322C211yesmaximal, characteristic, complemented
5#397×C89C211yesmaximal, characteristic, complemented
6C22×C22⋊D89—21no—
7#15667996—22no—
8#15667986—21no—
9#15667986C2212yes—
10#15667982—22no—
11#15667945—22no—
12#15667932—22no—
13C22⋊#10623494C2212yescomplemented
14C2×C4⋊C4×C89C2211yescharacteristic, complemented
15C2×C22⋊C4×C89—21no—
16C2×C22⋊C4×C89C2211yescharacteristic
17#95×C89—21no—
18#95×C89C2211yescharacteristic, complemented
19C23×D89—21no—
20C2×D356—21no—
21C2×D356D412yes—
22C2×C22⋊D89—22no—
23C2×C22⋊D89—22no—
24C2×C22⋊D89—42no—
25C2×C22⋊D89—42no—
26C22×Dic89—21no—
27C2×#10623494—22no—
28C4⋊Dic89—21no—
29C4⋊Dic89D412yes—
30#13083551—22no—
31#13083551—22no—
32C24×C89D411yescharacteristic
33C22×C4×C89—21no—
34C22×C4×C89—21no—
35C22×C4×C89D411yescharacteristic
36C22×C4×C89C2311yescharacteristic
37C4⋊C4×C89—22no—
38C22⋊C4×C89—22no—
39C22⋊C4×C89—42no—
40C23×C89—21no—
41C23×C89—21no—
42C23×C89—41no—
43C23×C89—41no—
44C23×C89D812yes—
45C23×C89C2×D411yescharacteristic
46C22×D89—22no—
47C22×D89—42no—
48C22×D89—81no—
49C22×D89—81no—
50C2×C4×C89—21no—
51C2×C4×C89—41no—
52C2×C4×C89—41no—
53C2×C4×C89—41no—
54C2×C4×C89—41no—
55C2×C4×C89—41no—
56C2×C4×C89—41no—
57C2×C4×C89—41no—
58C2×C4×C89—41no—
59C2×C4×C89C2×D412yes—
60C22⋊D89—44no—
61C22⋊D89—42no—
62C22⋊D89—42no—
63C2×Dic89—22no—
64C2×Dic89—42no—
65D356—42no—
66D356—81no—
67#10623494—42no—
68C22×C89—21no—
69C22×C89—21no—
70C22×C89—22no—
71C22×C89—42no—
72C22×C89—41no—
73C22×C89—41no—
74C22×C89—81no—
75C22×C89#12011yescharacteristic
76C22×C89C2×D811yescharacteristic
77C22×C89AGL(1,ℤ/8)11yescharacteristic
78C2×D89—42no—
79C2×D89—42no—
80C2×D89—42no—
81C2×D89—84no—
82C4×C89—22no—
83C4×C89—41no—
84C4×C89—81no—
85C4×C89—81no—
86Dic89—42no—
87C2×C89—21no—
88C2×C89—21no—
89C2×C89—42no—
90C2×C89#44711yescharacteristic
91C2×C89#45511yescharacteristic
92C2×C89#45811yescharacteristic
93D89—82no—
94#1607—891nomaximal, Sylow
95C89#160711yescharacteristic, complemented, Sylow
96#534—891no—
97#480—892no—
98#397D8911yescharacteristic, complemented
99#327—892no—
100#323—891no—
101C22×D4—1781no—
102#123—1782no—
103#121—892no—
104#121—1781no—
105#120—1782no—
106C2×C4⋊C4C2×D8911yescharacteristic, complemented
107C2×C22⋊C4—21no—
108C2×C22⋊C4C2×D8911yescharacteristic
109#107—1782no—
110#102—1782no—
111C22⋊C8—892no—
112#95—21no—
113#95C2×D8911yescharacteristic, complemented
114C24—1781no—
115C24C22⋊D8911yescharacteristic
116C2×D4—892no—
117C2×D4—3562no—
118C2×D4—3562no—
119C2×D4—1781no—
120C2×D4—1782no—
121C2×D4—1782no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—1781no—
125C22×C4C22⋊D8911yescharacteristic
126C22×C4C22×D8911yescharacteristic
127C2×C8—1782no—
128C4⋊C4—22no—
129C4⋊C4—892no—
130C4⋊C4—1781no—
131C22⋊C4—22no—
132C22⋊C4—42no—
133C22⋊C4—1782no—
134C22⋊C4—1782no—
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23—3562no—
140C23—1782no—
141C23—7121no—
142C23—7121no—
143C23#1308355912yes—
144C23C2×C22⋊D8911yescharacteristic
145D4—3562no—
146D4—3564no—
147D4—3562no—
148D4—3562no—
149D4—7121no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—3562no—
160C2×C4—1782no—
161C2×C4D4×D8912yes—
162C8—3562no—
163C22—21no—
164C22—21no—
165C22—22no—
166C22—42no—
167C22—41no—
168C22—41no—
169C22—81no—
170C22—3562no—
171C22—3562no—
172C22—3562no—
173C22—7124no—
174C22#1566798011yescharacteristic
175C22C2×#1308355911yescharacteristic
176C22#1566803711yescharacteristic
177C4—22no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—3562no—
182C2—21no—
183C2—21no—
184C2—42no—
185C2—7122no—
186C2#1915173111yescharacteristic
187C2#1915177511yescharacteristic
188C2#1915178711yescharacteristic
subgroupG/H
centerC22#15667980
commutator, cosocleC22×C4×C89C23
FrattiniC22×C4C22×D89
Fitting#397×C89C2
socleC22×C89#120
prime radical#19152160C2
hypercenter#397D89
hypocenterC89#1607
LCSG ▷ C22×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #19151911C2semidirect
3. #19151331C2semidirect
4. #19151322C2semidirect
5. #397×C89C2semidirect
13. C22⋊#10623494C22semidirect
14. C2×C4⋊C4×C89C22semidirect
18. #95×C89C22semidirect
95. C89#1607semidirect
98. #397D89semidirect
106. C2×C4⋊C4C2×D89semidirect
113. #95C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191521602
#191519112
#191513312
#191513222
#397×C892
#160789