Finite Group Databasebeta

← #26031702

Subgroups — #26031702

Order 11392.

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

normal subgroups only

This group has 322 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#19152210C211yesmaximal, characteristic
2#19151905C212yesmaximal, complemented
3#19151902C212yesmaximal, complemented
4#19151854C212yesmaximal
5#19151837C212yesmaximal
6#19151808C212yesmaximal, complemented
7#19151805C212yesmaximal, complemented
8#19151625C211yesmaximal, characteristic
9#541×C89C211yesmaximal, characteristic
10C2×#13083564C2212yes—
11C2×#13083564C2212yes—
12C2×#13083558C2211yescharacteristic
13C22×#10623494C2211yescharacteristic
14#15668012C2211yescharacteristic
15#15668005—22no—
16#15668004C2211yescharacteristic
17#15668002—22no—
18#15667991C2212yes—
19C4×Dic178C2212yes—
20#15667945C2212yes—
21#15667943C2212yes—
22C4⋊#10623494C2212yes—
23C4⋊#10623494C2212yes—
24#15667936C2212yes—
25#15667936C2212yes—
26#15667935C2212yes—
27#15667935C2212yes—
28C4⋊Q8×C89C2211yescharacteristic
29#126×C89—22no—
30#125×C89—22no—
31#125×C89C2211yescharacteristic
32C22⋊Q8×C89C2212yes—
33C4×Q8×C89C2212yes—
34#117×C89C2211yescharacteristic
35C2×Dic178C2312yes—
36#13083564—42no—
37#13083564—42no—
38#13083558—41no—
39C2×#10623494—41no—
40C2×#10623494C2312yes—
41C2×#10623494C2312yes—
42C4⋊Dic89—22no—
43C4⋊Dic89C2312yes—
44#13083553—22no—
45#13083553—22no—
46#13083553—22no—
47C22⋊Dic89—22no—
48C4×Dic89—22no—
49C2×Q8×C89C2312yes—
50C22×C4×C89C2311yescharacteristic
51C4⋊C4×C89—22no—
52C4⋊C4×C89—22no—
53C4⋊C4×C89—22no—
54C4⋊C4×C89—22no—
55C4⋊C4×C89D412yes—
56C4⋊C4×C89C2312yes—
57C22⋊C4×C89—22no—
58C22⋊C4×C89D412yes—
59C42×C89—22no—
60C42×C89C2311yescharacteristic
61C42×C89C2311yescharacteristic
62C23×C89C2×D411yescharacteristic
63Q8×C89—22no—
64Q8×C89—22no—
65C2×C4×C89—21no—
66C2×C4×C89—21no—
67C2×C4×C89—22no—
68C2×C4×C89—22no—
69C2×C4×C89C2×D412yes—
70C2×C4×C89C2×D412yes—
71C2×C4×C89C2×D411yescharacteristic
72C2×C4×C89C2411yescharacteristic
73C2×Dic89—22no—
74C2×Dic89—22no—
75Dic178—22no—
76Dic178—22no—
77#10623494—22no—
78#10623494—22no—
79C22×C89—21no—
80C22×C89—22no—
81C22×C89C22×D411yescharacteristic
82C4×C89—21no—
83C4×C89—22no—
84C4×C89—22no—
85C4×C89—42no—
86C4×C89—42no—
87C4×C89H(5,𝔽2)11yescharacteristic
88C4×C892−1+411yescharacteristic
89Dic89—42no—
90Dic89—42no—
91C2×C89—41no—
92C2×C89#53711yescharacteristic
93C2×C89#57812yes—
94#3261—891nomaximal, Sylow
95C89#326111yescharacteristic, complemented, Sylow
96#541—891no—
97#541D8911yescharacteristic
98#479—892no—
99#479—892no—
100#470—892no—
101#467—892no—
102#462—892no—
103#462—892no—
104#424—891no—
105C2×Q16—892no—
106C2×Q16—892no—
107C2×M16—891no—
108C22×C8—891no—
109C4⋊Q8—891no—
110C4⋊Q8C2×D8911yescharacteristic
111#126—22no—
112#126—1782no—
113#125—22no—
114#125—891no—
115#125—1782no—
116#125C2×D8911yescharacteristic
117C22⋊Q8—892no—
118C22⋊Q8C2×D8912yes—
119C4×Q8—892no—
120C4×Q8C2×D8912yes—
121#117C2×D8911yescharacteristic
122#107—892no—
123#106—892no—
124C4⋊C8—892no—
125C4⋊C8—892no—
126#103—892no—
127#103—892no—
128#103—892no—
129#103—892no—
130C2×Q8—892no—
131C2×Q8C22×D8912yes—
132C22×C4C22×D8911yescharacteristic
133Q16—3562no—
134Q16—3562no—
135M16—3561no—
136C2×C8—892no—
137C2×C8—892no—
138C2×C8—3561no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—892no—
144C4⋊C4—1782no—
145C4⋊C4—1782no—
146C4⋊C4—1782no—
147C4⋊C4—1782no—
148C4⋊C4C22⋊D8912yes—
149C4⋊C4C22×D8912yes—
150C22⋊C4—22no—
151C22⋊C4—1782no—
152C22⋊C4C22⋊D8912yes—
153C42—22no—
154C42—1782no—
155C42C22×D8911yescharacteristic
156C42C22×D8911yescharacteristic
157C23C2×C22⋊D8911yescharacteristic
158Q8—22no—
159Q8—22no—
160Q8—1782no—
161Q8—1782no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—1782no—
167C2×C4—1782no—
168C2×C4C2×C22⋊D8912yes—
169C2×C4C2×C22⋊D8912yes—
170C2×C4C2×C22⋊D8911yescharacteristic
171C2×C4C23×D8911yescharacteristic
172C8—1782no—
173C8—1782no—
174C22—22no—
175C22—21no—
176C22C22×C22⋊D8911yescharacteristic
177C4—22no—
178C4—22no—
179C4—21no—
180C4—42no—
181C4—42no—
182C4—3562no—
183C4—3562no—
184C4#1566805811yescharacteristic
185C4#1566805911yescharacteristic
186C2—41no—
187C2#1915217611yescharacteristic
188C2#1915241312yes—
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#541×C89C2
socleC22×C89C22×D4
prime radicalC23×C89C2×D4
hypercenter#541D89
hypocenterC89#3261
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #19151905C2semidirect
3. #19151902C2semidirect
6. #19151808C2semidirect
7. #19151805C2semidirect
95. C89#3261semidirect

Maximal subgroups

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

subgroupindex
#191522102
#191519052
#191519022
#191518542
#191518372
#191518082
#191518052
#191516252
#541×C892
#326189