Finite Group Databasebeta

← #26021822

Subgroups — #26021822

Order 11392.

198 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 77 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#19151494C211yesmaximal, characteristic
2#19151463C211yesmaximal, characteristic
3#19151361C211yesmaximal, characteristic
4#19151360C211yesmaximal, characteristic
5#19151360C211yesmaximal, characteristic
6#19151352C211yesmaximal, characteristic
7#340×C89C211yesmaximal, characteristic
8C22×#10623494C2211yescharacteristic
9C2×C4⋊Dic89C2211yescharacteristic
10C2×C4⋊Dic89C2211yescharacteristic
11C2×#13083553—21no—
12C2×C4×Dic89C2211yescharacteristic
13#15667919—21no—
14#15667919—21no—
15#15667919—21no—
16C22×C8×C89C2211yescharacteristic
17C2×C4⋊C4×C89C2211yescharacteristic
18C2×C4⋊C4×C89C2211yescharacteristic
19C22×Dic89—21no—
20C22×Dic89—21no—
21C22×Dic89D411yescharacteristic
22C22×Dic89D411yescharacteristic
23C2×#10623494—21no—
24C2×#10623494—21no—
25C2×#10623494—21no—
26C4⋊Dic89—21no—
27C4⋊Dic89—21no—
28C4⋊Dic89—21no—
29C4⋊Dic89Q812yes—
30#13083553—42no—
31C4×Dic89—21no—
32C4×Dic89—21no—
33C22×C4×C89—21no—
34C22×C4×C89—21no—
35C22×C4×C89C2311yescharacteristic
36C2×C8×C89—21no—
37C2×C8×C89—21no—
38C2×C8×C89—21no—
39C4⋊C4×C89—21no—
40C4⋊C4×C89—21no—
41C4⋊C4×C89—21no—
42C4⋊C4×C89—21no—
43C23×C89C2×D411yescharacteristic
44C2×C4×C89—41no—
45C2×C4×C89—41no—
46C2×C4×C89—41no—
47C2×C4×C89—41no—
48C2×C4×C89—41no—
49C2×C4×C89—41no—
50C2×C4×C89C2×Q811yescharacteristic
51C2×C4×C89#4111yescharacteristic
52C2×C4×C89#4111yescharacteristic
53C2×C4×C89#4111yescharacteristic
54C2×C4×C89#4111yescharacteristic
55C2×C4×C89#4111yescharacteristic
56C2×Dic89—22no—
57C2×Dic89—21no—
58C2×Dic89—21no—
59C2×Dic89—21no—
60C2×Dic89—21no—
61C2×Dic89—21no—
62C2×Dic89—21no—
63C2×Dic89—41no—
64C2×Dic89—41no—
65C2×Dic89—41no—
66C2×Dic89—41no—
67C2×Dic89—41no—
68C8×C89—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—81no—
78C4×C89—81no—
79C4×C89#12511yescharacteristic
80C4×C89#12511yescharacteristic
81C4×C89#12611yescharacteristic
82C4×C89#12611yescharacteristic
83Dic89—42no—
84Dic89—41no—
85Dic89—41no—
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#382—891no—
98#340—891no—
99#340—891no—
100#340—891no—
101#340D8911yescharacteristic
102#336—891no—
103C22×C8—891no—
104C22×C8C2×D8911yescharacteristic
105C2×C4⋊C4—891no—
106C2×C4⋊C4—891no—
107C2×C4⋊C4—1781no—
108C2×C4⋊C4C2×D8911yescharacteristic
109C2×C4⋊C4C2×D8911yescharacteristic
110C2×C42—891no—
111#95—1781no—
112#95—1781no—
113#95—1781no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—891no—
117C22×C4—891no—
118C22×C4—1781no—
119C22×C4—1781no—
120C22×C4C22×D8911yescharacteristic
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
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—1781no—
137C42—1781no—
138C23D4×D8911yescharacteristic
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—3561no—
146C2×C4—3561no—
147C2×C4—3561no—
148C2×C4—3561no—
149C2×C4—3561no—
150C2×C4—1782no—
151C2×C4—1781no—
152C2×C4—1781no—
153C2×C4—1781no—
154C2×C4—1781no—
155C2×C4—1781no—
156C2×C4—1781no—
157C2×C4Q8×D8911yescharacteristic
158C2×C4#1308357311yescharacteristic
159C2×C4#1308357311yescharacteristic
160C2×C4#1308357411yescharacteristic
161C2×C4#1308357411yescharacteristic
162C2×C4#1308357411yescharacteristic
163C8—41no—
164C8—3561no—
165C22#1566799011yescharacteristic
166C22#1566799411yescharacteristic
167C22#1566799811yescharacteristic
168C22#1566803111yescharacteristic
169C22#1566803311yescharacteristic
170C22#1566803911yescharacteristic
171C22#1566804411yescharacteristic
172C4—81no—
173C4—81no—
174C4—3562no—
175C4—3561no—
176C4—3561no—
177C4—7121no—
178C4#1566800211yescharacteristic
179C4#1566800211yescharacteristic
180C4#1566800511yescharacteristic
181C4#1566800611yescharacteristic
182C2#1915153911yescharacteristic
183C2#1915189711yescharacteristic
184C2#1915190411yescharacteristic
185C2#1915192011yescharacteristic
186C2#1915193711yescharacteristic
187C2#1915195111yescharacteristic
188C2#1915195911yescharacteristic
subgroupG/H
centerC23D4×D89
commutator, cosocleC22×C4×C89C23
FrattiniC22×C4C22×D89
Fitting#340×C89C2
socle, prime radicalC23×C89C2×D4
hypercenter#340D89
hypocenterC89#2101
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

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
#191514942
#191514632
#191513612
#191513602
#191513522
#340×C892
#210189