Finite Group Databasebeta

← #26020700

Subgroups — #26020700

Order 11392.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#19152109C211yesmaximal, characteristic
2C2×#15667940C212yesmaximal, complemented
3#19151562C211yesmaximal, characteristic, complemented
4#19151358C212yesmaximal, complemented
5C2×#117×C89C211yesmaximal, characteristic, complemented
6C2×#13083574C2211yescharacteristic
7C2×#13083558C2212yes—
8#15667995—21no—
9#15667991C412yescomplemented
10#15667986C412yescomplemented
11#15667981—21no—
12C4×C22⋊D89—22no—
13#15667971C2211yescharacteristic
14#15667940—24no—
15C22⋊#10623494—22no—
16C23×C4×C89C2211yescharacteristic
17#117×C89—24no—
18C2×C4⋊C4×C89—21no—
19C2×C22⋊C4×C89—21no—
20C2×C42×C89C2212yes—
21#13083574—22no—
22#13083574—22no—
23C2×Dic178C2×C411yescharacteristic
24C2×D356C2×C411yescharacteristic
25C2×C22⋊D89—22no—
26C2×C22⋊D89—21no—
27C2×C4×D89—21no—
28#13083558—22no—
29#13083558—22no—
30C2×#10623494—22no—
31C4⋊Dic89C2×C412yes—
32#13083553—22no—
33C22⋊Dic89—22no—
34C22⋊Dic89—21no—
35#13083551—22no—
36C4×Dic89—21no—
37C24×C89D411yescharacteristic
38C22×C4×C89—22no—
39C22×C4×C89—22no—
40C22×C4×C89—22no—
41C22×C4×C89C2×C412yes—
42C22×C4×C89D411yescharacteristic
43C22×C4×C89D412yes—
44C22×C4×C89C2311yescharacteristic
45C4⋊C4×C89—24no—
46C22⋊C4×C89—24no—
47C42×C89—22no—
48C42×C89D414yescomplemented
49C23×C89—21no—
50C23×C89—21no—
51C23×C89—42no—
52C23×C89C22⋊C412yes—
53C23×C89C2×D411yescharacteristic
54C22×D89—21no—
55C2×C4×C89—21no—
56C2×C4×C89—21no—
57C2×C4×C89—24no—
58C2×C4×C89—24no—
59C2×C4×C89—24no—
60C2×C4×C89—44no—
61C2×C4×C89C22⋊C412yes—
62C2×C4×C89C22×C411yescharacteristic
63C2×C4×C89C2×D412yes—
64C2×C4×C89C2×D411yescharacteristic
65C2×C4×C89#4112yes—
66C22⋊D89—44no—
67C22⋊D89—41no—
68C22⋊D89—41no—
69C2×Dic89—22no—
70C2×Dic89—21no—
71D356—22no—
72C4×D89—42no—
73Dic178—22no—
74#10623494—42no—
75C22×C89—22no—
76C22×C89—22no—
77C22×C89—22no—
78C22×C89—22no—
79C22×C89—42no—
80C22×C89—42no—
81C22×C89C2×C22⋊C411yescharacteristic
82C22×C89#12011yescharacteristic
83C22×C89#12311yescharacteristic
84C2×D89—41no—
85C2×D89—42no—
86C4×C89—22no—
87C4×C89—44no—
88C4×C89C4×D412yes—
89C4×C89#12112yes—
90Dic89—41no—
91Dic89—42no—
92C2×C89—21no—
93C2×C89—21no—
94C2×C89—42no—
95C2×C89#38611yescharacteristic
96C2×C89#42112yes—
97D89—81no—
98#1897—891nomaximal, Sylow
99C89#189711yescharacteristic, complemented, Sylow
100#525—891no—
101C2×#117D8911yescharacteristic, complemented
102C2×#104—892no—
103#407—891no—
104#339—892no—
105C2×#41—891no—
106C23×C4C2×D8911yescharacteristic
107C2×M16—892no—
108#123—1781no—
109C22⋊Q8—892no—
110#121—892no—
111#120—1781no—
112C4×D4—1782no—
113#117—24no—
114#117—891no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D8912yes—
118#104—1784no—
119C22⋊C8—1782no—
120C24C22⋊D8911yescharacteristic
121#41—1782no—
122#41—1782no—
123C2×Q8—891no—
124C2×D4—891no—
125C2×D4—1782no—
126C2×D4—1781no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—1781no—
131C22×C4C4×D8912yes—
132C22×C4D35612yes—
133C22×C4C22⋊D8911yescharacteristic
134C22×C4C22×D8911yescharacteristic
135M16—1782no—
136M16—1782no—
137C2×C8—1782no—
138C4⋊C4—24no—
139C4⋊C4—892no—
140C4⋊C4—1782no—
141C22⋊C4—24no—
142C22⋊C4—1782no—
143C22⋊C4—1781no—
144C22⋊C4—1782no—
145C42—22no—
146C42—1781no—
147C42C22⋊D8914yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—1781no—
152C23#1308355112yes—
153C23C2×C22⋊D8911yescharacteristic
154Q8—1782no—
155D4—3564no—
156D4—3561no—
157D4—3561no—
158D4—1782no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—3562no—
166C2×C4—1782no—
167C2×C4—1781no—
168C2×C4#1308355112yes—
169C2×C4C2×C4×D8911yescharacteristic
170C2×C4C2×C22⋊D8912yes—
171C2×C4C2×D35611yescharacteristic
172C2×C4#1308357412yes—
173C8—3562no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—3562no—
181C22—3561no—
182C22C2×#1308355111yescharacteristic
183C22#1566798111yescharacteristic
184C22#1566799511yescharacteristic
185C4—22no—
186C4—44no—
187C4—3562no—
188C4—3561no—
189C4C4×C22⋊D8912yes—
190C4#1566798612yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—7121no—
195C2#1915147711yescharacteristic
196C2#1915161612yes—
subgroupG/H
centerC2×C4C2×D356
commutatorC2×C4×C89C22×C4
FrattiniC22×C4C22×D89
FittingC2×#117×C89C2
socleC22×C89C2×C22⋊C4
prime radical#19152109C2
cosocleC22×C4×C89C23
hypercenterC2×#117D89
hypocenterC89#1897
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#15667940C2semidirect
3. #19151562C2semidirect
4. #19151358C2semidirect
5. C2×#117×C89C2semidirect
9. #15667991C4semidirect
10. #15667986C4semidirect
48. C42×C89D4semidirect
99. C89#1897semidirect
101. C2×#117D89semidirect
147. C42C22⋊D89semidirect

Maximal subgroups

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

subgroupindex
#191521092
C2×#156679402
#191515622
#191513582
C2×#117×C892
#189789