Finite Group Databasebeta

← #26019477

Subgroups — #26019477

Order 11392.

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

normal subgroups only

This group has 212 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#19152314C211yesmaximal, characteristic
2#19151875C211yesmaximal, characteristic, complemented
3#19151800C211yesmaximal, characteristic, complemented
4#19151347C211yesmaximal, characteristic, complemented
5#19151327C211yesmaximal, characteristic, complemented
6#19151327C211yesmaximal, characteristic, complemented
7#487×C89C211yesmaximal, characteristic, complemented
8C2×#13083561—21no—
9#15668001—22no—
10#15667987—21no—
11#15667987—21no—
12C4×D356C2211yescharacteristic
13C4×D356C2211yescharacteristic
14#15667970—21no—
15#15667970—21no—
16#15667945—21no—
17C4⋊#10623494C2211yescharacteristic
18C4⋊#10623494C2211yescharacteristic
19#15667936—21no—
20#15667932—21no—
21C4⋊Q8×C89C2211yescharacteristic
22C4⋊Q8×C89C2211yescharacteristic
23#103×C89—22no—
24C4×C8×C89C2211yescharacteristic
25C2×D356—22no—
26C2×D356D411yescharacteristic
27C2×D356D411yescharacteristic
28C2×C4×D89—21no—
29C2×C4×D89—21no—
30#13083561—42no—
31C2×#10623494—21no—
32C2×#10623494—21no—
33C4⋊Dic89D411yescharacteristic
34C4⋊Dic89D411yescharacteristic
35#13083551—22no—
36#13083551—22no—
37#13083551—21no—
38#13083551—21no—
39C4×Dic89—22no—
40C2×Q8×C89—21no—
41C2×Q8×C89D412yes—
42C2×C8×C89—21no—
43C4⋊C4×C89—21no—
44C4⋊C4×C89—21no—
45C4⋊C4×C89—21no—
46C4⋊C4×C89—21no—
47C42×C89C2311yescharacteristic
48C22×D89—21no—
49C22×D89—21no—
50Q8×C89—42no—
51Q8×C89—41no—
52Q8×C89—41no—
53C2×C4×C89—22no—
54C2×C4×C89—41no—
55C2×C4×C89C2×D411yescharacteristic
56C2×C4×C89C2×D411yescharacteristic
57C2×C4×C89C2×D411yescharacteristic
58C2×Dic89—21no—
59C2×Dic89—21no—
60D356—21no—
61D356—21no—
62D356—21no—
63D356—21no—
64D356—82no—
65C4×D89—41no—
66C4×D89—41no—
67C4×D89—41no—
68C4×D89—41no—
69C8×C89—41no—
70#10623494—41no—
71#10623494—41no—
72C22×C89#12011yescharacteristic
73C2×D89—41no—
74C2×D89—41no—
75C2×D89—41no—
76C2×D89—41no—
77C2×D89—41no—
78C2×D89—41no—
79C4×C89—21no—
80C4×C89—42no—
81C4×C89—81no—
82C4×C89#13511yescharacteristic
83C4×C89#13511yescharacteristic
84C4×C89AGL(1,ℤ/8)11yescharacteristic
85C4×C89#13711yescharacteristic
86Dic89—41no—
87Dic89—41no—
88C2×C89#44911yescharacteristic
89C2×C89#45211yescharacteristic
90C2×C89#45511yescharacteristic
91D89—81no—
92D89—81no—
93#1646—891nomaximal, Sylow
94C89#164611yescharacteristic, complemented, Sylow
95#555—891no—
96#487D8911yescharacteristic, complemented
97#474—891no—
98#461—891no—
99#333—891no—
100D4⋊C8—891no—
101D4⋊C8—891no—
102C2×SD16—1781no—
103C4⋊Q8C2×D8911yescharacteristic
104C4⋊Q8C2×D8911yescharacteristic
105#124—1782no—
106#121—1781no—
107#121—1781no—
108C4×D4—891no—
109C4×D4—891no—
110#117—1781no—
111#117—1781no—
112#107—1781no—
113C4⋊C8—891no—
114C4⋊C8—891no—
115#103—22no—
116#103—1781no—
117#102—1781no—
118C4×C8C2×D8911yescharacteristic
119C2×Q8—21no—
120C2×Q8C22⋊D8912yes—
121C2×D4—891no—
122C2×D4—891no—
123C2×D4—1782no—
124C22×C4—1781no—
125C22×C4—1781no—
126SD16—3562no—
127C2×C8—21no—
128C2×C8—1781no—
129C2×C8—1781no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—891no—
135C4⋊C4—891no—
136C22⋊C4—1782no—
137C22⋊C4—1782no—
138C22⋊C4—1781no—
139C22⋊C4—1781no—
140C42—1782no—
141C42C22×D8911yescharacteristic
142C23—1781no—
143C23—1781no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—1781no—
148D4—1781no—
149D4—1781no—
150D4—1781no—
151D4—7122no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—3561no—
155C2×C4—3561no—
156C2×C4—3561no—
157C2×C4—3561no—
158C2×C4—1781no—
159C2×C4—1781no—
160C2×C4D4×D8911yescharacteristic
161C2×C4D4×D8911yescharacteristic
162C2×C4C2×C22⋊D8911yescharacteristic
163C8—41no—
164C8—3561no—
165C8—3561no—
166C22—3561no—
167C22—3561no—
168C22—3561no—
169C22—3561no—
170C22—3561no—
171C22—3561no—
172C22#1566798011yescharacteristic
173C4—21no—
174C4—42no—
175C4—81no—
176C4—3561no—
177C4—3561no—
178C4#1566803311yescharacteristic
179C4#1566803511yescharacteristic
180C4#1566803911yescharacteristic
181C4#1566804411yescharacteristic
182C2—7121no—
183C2—7121no—
184C2#1915174211yescharacteristic
185C2#1915175911yescharacteristic
186C2#1915177511yescharacteristic
subgroupG/H
centerC22#15667980
commutator, cosocleC42×C89C23
FrattiniC42C22×D89
Fitting#487×C89C2
socleC22×C89#120
prime radical#19152314C2
hypercenter#487D89
hypocenterC89#1646
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #19151875C2semidirect
3. #19151800C2semidirect
4. #19151347C2semidirect
5. #19151327C2semidirect
6. #19151327C2semidirect
7. #487×C89C2semidirect
94. C89#1646semidirect
96. #487D89semidirect

Maximal subgroups

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

subgroupindex
#191523142
#191518752
#191518002
#191513472
#191513272
#487×C892
#164689