Finite Group Databasebeta

← #26027747

Subgroups — #26027747

Order 11392.

344 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 121 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#19151540C212yesmaximal
2#19151531C212yesmaximal
3#19151528C211yesmaximal, characteristic
4#19151495C212yesmaximal
5#19151485C212yesmaximal
6#19151483C212yesmaximal
7#19151465C212yesmaximal
8#19151463C211yesmaximal, characteristic
9#400×C89C211yesmaximal, characteristic
10C2×C4⋊Dic89C2212yes—
11C2×C4⋊Dic89C2211yescharacteristic
12C2×C4⋊Dic89C2211yescharacteristic
13C2×#13083553C2212yes—
14C2×#13083553C2212yes—
15C2×#13083553C2212yes—
16C2×C4×Dic89C2211yescharacteristic
17C2×C4×Dic89C2212yes—
18#15667919C2212yes—
19#15667919C2212yes—
20#15667919C2212yes—
21#15667919C2212yes—
22#15667919C2212yes—
23#15667919C2212yes—
24#15667919C2212yes—
25#15667919C2211yescharacteristic
26C2×C4⋊C4×C89C2211yescharacteristic
27C2×C4⋊C4×C89C2211yescharacteristic
28#95×C89C2211yescharacteristic
29#95×C89C2212yes—
30#95×C89C2212yes—
31C22×Dic89C2312yes—
32C22×Dic89C2312yes—
33C22×Dic89C2312yes—
34C22×Dic89C2312yes—
35C4⋊Dic89—24no—
36C4⋊Dic89—41no—
37C4⋊Dic89—41no—
38#13083553—24no—
39#13083553—24no—
40#13083553—42no—
41C4×Dic89—22no—
42C4×Dic89—24no—
43C22×C4×C89C2312yes—
44C22×C4×C89C2311yescharacteristic
45C22×C4×C89C2312yes—
46C22×C4×C89C2311yescharacteristic
47C22×C4×C89C2311yescharacteristic
48C4⋊C4×C89—41no—
49C4⋊C4×C89—41no—
50C23×C89C2411yescharacteristic
51C2×C4×C89—21no—
52C2×C4×C89—21no—
53C2×C4×C89—22no—
54C2×C4×C89—22no—
55C2×C4×C89—22no—
56C2×C4×C89—21no—
57C2×C4×C89—22no—
58C2×C4×C89—21no—
59C2×C4×C89—22no—
60C2×C4×C89—22no—
61C2×C4×C89—22no—
62C2×C4×C89—22no—
63C2×C4×C89#4112yes—
64C2×Dic89—22no—
65C2×Dic89—22no—
66C2×Dic89—22no—
67C2×Dic89—22no—
68C2×Dic89—22no—
69C2×Dic89—22no—
70C2×Dic89—22no—
71C2×Dic89—22no—
72C2×Dic89—22no—
73C2×Dic89—22no—
74C2×Dic89—22no—
75C2×Dic89#4114yes—
76C22×C89C2×#4111yescharacteristic
77C22×C89C2×#4112yes—
78C22×C89H(5,𝔽2)11yescharacteristic
79C22×C892−1+411yescharacteristic
80C22×C892−1+412yes—
81C4×C89—22no—
82C4×C89—42no—
83C4×C89—42no—
84C4×C89—41no—
85C4×C89—41no—
86Dic89—24no—
87Dic89—42no—
88Dic89—42no—
89Dic89—42no—
90C2×C89#53911yescharacteristic
91C2×C89#54112yes—
92C2×C89#55212yes—
93C2×C89#55511yescharacteristic
94C2×C89#56311yescharacteristic
95#2769—891nomaximal, Sylow
96C89#276911yescharacteristic, complemented, Sylow
97#400—892no—
98#400D8911yescharacteristic
99#398—891no—
100#398—892no—
101#389—892no—
102#387—892no—
103#387—892no—
104#383—892no—
105#382—891no—
106C2×C4⋊C4—891no—
107C2×C4⋊C4—892no—
108C2×C4⋊C4—891no—
109C2×C4⋊C4—892no—
110C2×C4⋊C4—892no—
111C2×C4⋊C4—892no—
112C2×C4⋊C4C2×D8911yescharacteristic
113C2×C4⋊C4C2×D8911yescharacteristic
114C2×C42—891no—
115C2×C42—892no—
116#95—892no—
117#95—892no—
118#95—892no—
119#95—892no—
120#95—892no—
121#95—892no—
122#95—891no—
123#95—892no—
124#95C2×D8911yescharacteristic
125#95C2×D8912yes—
126#95C2×D8912yes—
127C22×C4—892no—
128C22×C4—892no—
129C22×C4—892no—
130C22×C4—892no—
131C22×C4C22×D8911yescharacteristic
132C22×C4C22×D8912yes—
133C22×C4C22×D8911yescharacteristic
134C22×C4C22×D8912yes—
135C22×C4C22×D8911yescharacteristic
136C4⋊C4—41no—
137C4⋊C4—41no—
138C4⋊C4—3562no—
139C4⋊C4—3561no—
140C4⋊C4—3561no—
141C4⋊C4—1784no—
142C4⋊C4—1784no—
143C4⋊C4—1784no—
144C42—1784no—
145C42—1782no—
146C23C23×D8911yescharacteristic
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—894no—
160C2×C4—1782no—
161C2×C4—1782no—
162C2×C4—1782no—
163C2×C4—1782no—
164C2×C4—1782no—
165C2×C4—1782no—
166C2×C4—1782no—
167C2×C4—1782no—
168C2×C4—1782no—
169C2×C4—1782no—
170C2×C4—1782no—
171C2×C4#1308357512yes—
172C22#41×D8912yes—
173C22C2×#1308357511yescharacteristic
174C22#1566805711yescharacteristic
175C22#1566805911yescharacteristic
176C22#1566805912yes—
177C4—22no—
178C4—42no—
179C4—42no—
180C4—41no—
181C4—41no—
182C4—3562no—
183C4—3562no—
184C4—3562no—
185C4—1784no—
186C2#1915219711yescharacteristic
187C2#1915220512yes—
188C2#1915228612yes—
189C2#1915231011yescharacteristic
190C2#1915235111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#400×C89C2
hypercenter#400D89
hypocenterC89#2769
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
96. C89#2769semidirect

Maximal subgroups

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

subgroupindex
#191515402
#191515312
#191515282
#191514952
#191514852
#191514832
#191514652
#191514632
#400×C892
#276989