Finite Group Databasebeta

← #26021819

Subgroups — #26021819

Order 11392.

198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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#19151496C211yesmaximal, characteristic
2#19151360C211yesmaximal, characteristic
3#19151360C211yesmaximal, characteristic
4#19151360C211yesmaximal, characteristic
5#19151360C211yesmaximal, characteristic
6#19151353C211yesmaximal, characteristic
7#382×C89C211yesmaximal, characteristic
8C22×#10623494C2211yescharacteristic
9C22×#10623494C2211yescharacteristic
10C2×C4⋊Dic89C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12C2×#13083553—21no—
13#15667919—21no—
14C2×C4⋊C4×C89C2211yescharacteristic
15C2×C4⋊C4×C89C2211yescharacteristic
16C2×C42×C89C2211yescharacteristic
17#95×C89—21no—
18#95×C89—21no—
19C22×Dic89—21no—
20C22×Dic89—21no—
21C2×#10623494—21no—
22C2×#10623494—21no—
23C2×#10623494—21no—
24C2×#10623494—21no—
25C2×#10623494—21no—
26C2×#10623494—21no—
27C4⋊Dic89—21no—
28C4⋊Dic89—21no—
29C4⋊Dic89—21no—
30C4⋊Dic89Q812yes—
31#13083553—42no—
32C22×C4×C89—21no—
33C22×C4×C89—21no—
34C22×C4×C89D411yescharacteristic
35C22×C4×C89D411yescharacteristic
36C22×C4×C89C2311yescharacteristic
37C4⋊C4×C89—21no—
38C4⋊C4×C89—21no—
39C4⋊C4×C89—21no—
40C4⋊C4×C89—21no—
41C42×C89—21no—
42C42×C89—21no—
43C23×C89C2×D411yescharacteristic
44C2×C4×C89—21no—
45C2×C4×C89—21no—
46C2×C4×C89—21no—
47C2×C4×C89—21no—
48C2×C4×C89—21no—
49C2×C4×C89—21no—
50C2×C4×C89—41no—
51C2×C4×C89—41no—
52C2×C4×C89—41no—
53C2×C4×C89—41no—
54C2×C4×C89—41no—
55C2×C4×C89—41no—
56C2×C4×C89C2×Q811yescharacteristic
57C2×C4×C89#4111yescharacteristic
58C2×C4×C89#4111yescharacteristic
59C2×C4×C89#4111yescharacteristic
60C2×C4×C89#4111yescharacteristic
61C2×C4×C89#4111yescharacteristic
62C2×Dic89—22no—
63C2×Dic89—41no—
64C2×Dic89—41no—
65C2×Dic89—41no—
66C2×Dic89—41no—
67C2×Dic89—41no—
68#10623494—41no—
69#10623494—41no—
70C22×C89C22⋊Q811yescharacteristic
71C22×C89#12311yescharacteristic
72C22×C89#12411yescharacteristic
73C22×C89#13511yescharacteristic
74C22×C89#13511yescharacteristic
75C22×C89AGL(1,ℤ/8)11yescharacteristic
76C22×C89#13711yescharacteristic
77C4×C89—41no—
78C4×C89—41no—
79C4×C89—81no—
80C4×C89—81no—
81C4×C89#12511yescharacteristic
82C4×C89#12511yescharacteristic
83C4×C89#12611yescharacteristic
84C4×C89#12611yescharacteristic
85Dic89—42no—
86Dic89—81no—
87C2×C89#40011yescharacteristic
88C2×C89#47811yescharacteristic
89C2×C89#47911yescharacteristic
90C2×C89#48211yescharacteristic
91C2×C89#48511yescharacteristic
92C2×C89#48811yescharacteristic
93C2×C89#48911yescharacteristic
94#2101—891nomaximal, Sylow
95C89#210111yescharacteristic, complemented, Sylow
96#389—891no—
97#382D8911yescharacteristic
98#340—891no—
99#340—891no—
100#340—891no—
101#340—891no—
102#336—891no—
103C22×C8—891no—
104C22×C8—891no—
105C2×C4⋊C4—891no—
106C2×C4⋊C4—891no—
107C2×C4⋊C4—1781no—
108C2×C4⋊C4C2×D8911yescharacteristic
109C2×C4⋊C4C2×D8911yescharacteristic
110C2×C42C2×D8911yescharacteristic
111#95—21no—
112#95—21no—
113#95—1781no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—1781no—
117C22×C4—1781no—
118C22×C4C22⋊D8911yescharacteristic
119C22×C4C22⋊D8911yescharacteristic
120C22×C4C22×D8911yescharacteristic
121C2×C8—1781no—
122C2×C8—1781no—
123C2×C8—1781no—
124C2×C8—1781no—
125C2×C8—1781no—
126C2×C8—1781no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—892no—
132C4⋊C4—3562no—
133C4⋊C4—1781no—
134C4⋊C4—1781no—
135C4⋊C4—1781no—
136C42—21no—
137C42—21no—
138C23C2×C22⋊D8911yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—3561no—
152C2×C4—3561no—
153C2×C4—3561no—
154C2×C4—3561no—
155C2×C4—3561no—
156C2×C4—1782no—
157C2×C4Q8×D8911yescharacteristic
158C2×C4#1308357311yescharacteristic
159C2×C4#1308357311yescharacteristic
160C2×C4#1308357411yescharacteristic
161C2×C4#1308357411yescharacteristic
162C2×C4#1308357511yescharacteristic
163C8—3561no—
164C8—3561no—
165C22#1566798811yescharacteristic
166C22#1566799511yescharacteristic
167C22#1566799911yescharacteristic
168C22#1566803211yescharacteristic
169C22#1566803211yescharacteristic
170C22#1566803711yescharacteristic
171C22#1566804211yescharacteristic
172C4—41no—
173C4—41no—
174C4—81no—
175C4—81no—
176C4—3562no—
177C4—7121no—
178C4#1566800211yescharacteristic
179C4#1566800211yescharacteristic
180C4#1566800711yescharacteristic
181C4#1566800711yescharacteristic
182C2#1915153611yescharacteristic
183C2#1915189511yescharacteristic
184C2#1915190211yescharacteristic
185C2#1915192211yescharacteristic
186C2#1915193911yescharacteristic
187C2#1915195211yescharacteristic
188C2#1915195711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D89
commutator, cosocleC22×C4×C89C23
FrattiniC22×C4C22×D89
Fitting#382×C89C2
socle, prime radicalC23×C89C2×D4
hypercenter#382D89
hypocenterC89#2101
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
95. C89#2101semidirect

Maximal subgroups

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

subgroupindex
#191514962
#191513602
#191513532
#382×C892
#210189