Finite Group Databasebeta

← #26019341

Subgroups — #26019341

Order 11392.

256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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#19151946C211yesmaximal, characteristic, complemented
2#19151793C211yesmaximal, characteristic, complemented
3#19151793C211yesmaximal, characteristic, complemented
4#19151344C211yesmaximal, characteristic, complemented
5D4⋊#10623494C211yesmaximal, characteristic, complemented
6D4⋊#10623494C211yesmaximal, characteristic, complemented
7#547×C89C211yesmaximal, characteristic, complemented
8C2×#13083559—21no—
9C2×#13083559—21no—
10#15668009C2211yescharacteristic
11C4⋊#10623494C2211yescharacteristic
12C4⋊#10623494C2211yescharacteristic
13#15667932—22no—
14#15667932—21no—
15#15667932—21no—
16C4×#10623494C2211yescharacteristic
17C2×#41×C89—21no—
18C4⋊Q8×C89C2211yescharacteristic
19#123×C89—22no—
20C22⋊Q8×C89—21no—
21#121×C89—21no—
22C4×D4×C89C2211yescharacteristic
23C4×D4×C89C2211yescharacteristic
24C2×C4⋊C4×C89—21no—
25C2×D356—21no—
26C2×D356—21no—
27C2×D356—21no—
28#13083559—42no—
29#13083559—42no—
30C2×#10623494—21no—
31C2×#10623494—21no—
32C2×#10623494—21no—
33#41×C89—42no—
34#41×C89—42no—
35C2×Q8×C89—21no—
36C2×D4×C89—22no—
37C2×D4×C89D411yescharacteristic
38C2×D4×C89D411yescharacteristic
39C22×C4×C89—22no—
40C22×C4×C89—21no—
41C22×C4×C89—21no—
42C4⋊C4×C89—22no—
43C4⋊C4×C89—21no—
44C4⋊C4×C89D411yescharacteristic
45C4⋊C4×C89D411yescharacteristic
46C4⋊C4×C89D412yes—
47C22⋊C4×C89—22no—
48C22⋊C4×C89—21no—
49C22⋊C4×C89—21no—
50C42×C89C2311yescharacteristic
51C23×C89—21no—
52C23×C89—21no—
53C22×D89—41no—
54Q8×C89—41no—
55Q8×C89—41no—
56D4×C89—21no—
57D4×C89—21no—
58D4×C89—21no—
59D4×C89—44no—
60D4×C89D812yescomplemented
61C2×C4×C89—21no—
62C2×C4×C89—21no—
63C2×C4×C89—22no—
64C2×C4×C89—44no—
65C2×C4×C89—41no—
66C2×C4×C89—41no—
67C2×C4×C89—41no—
68C2×C4×C89—41no—
69C2×C4×C89C2×D411yescharacteristic
70C2×C4×C89C2×D411yescharacteristic
71C2×C4×C89C2×D411yescharacteristic
72D356—42no—
73D356—41no—
74D356—41no—
75D356—41no—
76D356—41no—
77#10623494—41no—
78#10623494—41no—
79#10623494—41no—
80C22×C89—22no—
81C22×C89—41no—
82C22×C89—41no—
83C22×C89—41no—
84C22×C89—41no—
85C22×C89—41no—
86C22×C89#12011yescharacteristic
87C2×D89—81no—
88C2×D89—81no—
89C2×D89—81no—
90C4×C89—21no—
91C4×C89—41no—
92C4×C89—42no—
93C4×C89—41no—
94C4×C89C2×D811yescharacteristic
95C4×C89#13511yescharacteristic
96C4×C89AGL(1,ℤ/8)11yescharacteristic
97C4×C89AGL(1,ℤ/8)11yescharacteristic
98C2×C89—42no—
99C2×C89—81no—
100C2×C89#44711yescharacteristic
101C2×C89#44911yescharacteristic
102C2×C89#45411yescharacteristic
103D89—161no—
104#1625—891nomaximal, Sylow
105C89#162511yescharacteristic, complemented, Sylow
106#547D8911yescharacteristic, complemented
107#486—891no—
108#459—891no—
109#459—891no—
110#332—891no—
111D4⋊C8—891no—
112D4⋊C8—891no—
113C2×#41—21no—
114C2×D8—1781no—
115C2×D8—1781no—
116C4⋊Q8C2×D8911yescharacteristic
117#127—891no—
118#123—22no—
119C22⋊Q8—21no—
120#121—21no—
121C4×D4C2×D8911yescharacteristic
122C4×D4C2×D8911yescharacteristic
123C2×C4⋊C4—21no—
124C4⋊C8—891no—
125C4⋊C8—891no—
126#102—1781no—
127#102—1781no—
128#102—1782no—
129C4×C8—891no—
130#41—42no—
131#41—42no—
132C2×Q8—21no—
133C2×D4—22no—
134C2×D4—1781no—
135C2×D4—1781no—
136C2×D4—1781no—
137C2×D4C22⋊D8911yescharacteristic
138C2×D4C22⋊D8911yescharacteristic
139C22×C4—22no—
140C22×C4—21no—
141C22×C4—21no—
142D8—3562no—
143D8—3562no—
144C2×C8—1781no—
145C2×C8—1781no—
146C2×C8—1781no—
147C4⋊C4—22no—
148C4⋊C4—21no—
149C4⋊C4C22⋊D8911yescharacteristic
150C4⋊C4C22⋊D8911yescharacteristic
151C4⋊C4C22⋊D8912yes—
152C22⋊C4—22no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C22×D8911yescharacteristic
156C23—21no—
157C23—21no—
158C23—3561no—
159Q8—41no—
160Q8—41no—
161D4—21no—
162D4—21no—
163D4—21no—
164D4—44no—
165D4—3562no—
166D4—3561no—
167D4—3561no—
168D4—3561no—
169D4—3561no—
170D4#1308355912yescomplemented
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—44no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4C2×C22⋊D8911yescharacteristic
180C2×C4C2×C22⋊D8911yescharacteristic
181C2×C4C2×C22⋊D8911yescharacteristic
182C8—3561no—
183C8—3561no—
184C8—3561no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—7121no—
192C22—7121no—
193C22—7121no—
194C22#1566798111yescharacteristic
195C4—21no—
196C4—41no—
197C4—42no—
198C4—41no—
199C4C2×#1308355911yescharacteristic
200C4#1566803211yescharacteristic
201C4#1566803711yescharacteristic
202C4#1566803811yescharacteristic
203C2—42no—
204C2—81no—
205C2—14241no—
206C2#1915173211yescharacteristic
207C2#1915174311yescharacteristic
208C2#1915177111yescharacteristic
subgroupG/H
centerC22#15667981
commutator, cosocleC42×C89C23
FrattiniC42C22×D89
Fitting#547×C89C2
socleC22×C89#120
hypercenter#547D89
hypocenterC89#1625
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #19151946C2semidirect
2. #19151793C2semidirect
3. #19151793C2semidirect
4. #19151344C2semidirect
5. D4⋊#10623494C2semidirect
6. D4⋊#10623494C2semidirect
7. #547×C89C2semidirect
60. D4×C89D8semidirect
105. C89#1625semidirect
106. #547D89semidirect
170. D4#13083559semidirect

Maximal subgroups

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

subgroupindex
#191519462
#191517932
#191513442
D4⋊#106234942
#547×C892
#162589