Finite Group Databasebeta

← #26021812

Subgroups — #26021812

Order 11392.

214 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 81 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#19151467C211yesmaximal, 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×#13083553—21no—
13C2×#13083553—21no—
14C2×C4×Dic89C2211yescharacteristic
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—
31#13083553—42no—
32#13083553—42no—
33C4×Dic89—21no—
34C4×Dic89—21no—
35C22×C4×C89—21no—
36C22×C4×C89—21no—
37C22×C4×C89C2311yescharacteristic
38C2×C8×C89—21no—
39C2×C8×C89—21no—
40C2×C8×C89—21no—
41C4⋊C4×C89—21no—
42C4⋊C4×C89—21no—
43C4⋊C4×C89—21no—
44C4⋊C4×C89—21no—
45C23×C89C2×D411yescharacteristic
46C2×C4×C89—41no—
47C2×C4×C89—41no—
48C2×C4×C89—41no—
49C2×C4×C89—41no—
50C2×C4×C89—41no—
51C2×C4×C89—41no—
52C2×C4×C89C2×Q811yescharacteristic
53C2×C4×C89#4111yescharacteristic
54C2×C4×C89#4111yescharacteristic
55C2×C4×C89#4111yescharacteristic
56C2×C4×C89#4111yescharacteristic
57C2×C4×C89#4111yescharacteristic
58C2×Dic89—21no—
59C2×Dic89—21no—
60C2×Dic89—21no—
61C2×Dic89—21no—
62C2×Dic89—22no—
63C2×Dic89—41no—
64C2×Dic89—41no—
65C2×Dic89—41no—
66C2×Dic89—41no—
67C2×Dic89—41no—
68C2×Dic89D812yes—
69C2×Dic89SD1612yes—
70C8×C89—41no—
71#10623494—41no—
72C22×C89C22⋊Q811yescharacteristic
73C22×C89#12311yescharacteristic
74C22×C89#12411yescharacteristic
75C22×C89C2×D811yescharacteristic
76C22×C89C2×SD1611yescharacteristic
77C22×C89#13711yescharacteristic
78C22×C89#13711yescharacteristic
79C4×C89—81no—
80C4×C89—81no—
81C4×C89#12511yescharacteristic
82C4×C89#12511yescharacteristic
83C4×C89#12611yescharacteristic
84C4×C89#12611yescharacteristic
85Dic89—22no—
86Dic89—22no—
87Dic89—42no—
88Dic89—81no—
89C2×C89#40011yescharacteristic
90C2×C89#47411yescharacteristic
91C2×C89#47511yescharacteristic
92C2×C89#48011yescharacteristic
93C2×C89#48311yescharacteristic
94C2×C89#48611yescharacteristic
95C2×C89#49111yescharacteristic
96#2099—891nomaximal, Sylow
97C89#209911yescharacteristic, complemented, Sylow
98#389—891no—
99#384—891no—
100#340—891no—
101#340—891no—
102#340—891no—
103#340D8911yescharacteristic
104#336—891no—
105C22×C8—891no—
106C22×C8C2×D8911yescharacteristic
107C2×C4⋊C4—891no—
108C2×C4⋊C4—891no—
109C2×C4⋊C4—1781no—
110C2×C4⋊C4—1781no—
111C2×C4⋊C4—1781no—
112C2×C4⋊C4C2×D8911yescharacteristic
113C2×C4⋊C4C2×D8911yescharacteristic
114C2×C42—891no—
115#95—1781no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—891no—
119C22×C4—891no—
120C22×C4—1781no—
121C22×C4—1781no—
122C22×C4C22×D8911yescharacteristic
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—1781no—
127C2×C8—1781no—
128C2×C8—1781no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—892no—
134C4⋊C4—3562no—
135C4⋊C4—3562no—
136C4⋊C4—3562no—
137C4⋊C4—1781no—
138C4⋊C4—1781no—
139C4⋊C4—1781no—
140C42—1781no—
141C42—1781no—
142C23D4×D8911yescharacteristic
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—892no—
150C2×C4—892no—
151C2×C4—3561no—
152C2×C4—3561no—
153C2×C4—3561no—
154C2×C4—3561no—
155C2×C4—3561no—
156C2×C4—1782no—
157C2×C4—1781no—
158C2×C4—1781no—
159C2×C4—1781no—
160C2×C4—1781no—
161C2×C4Q8×D8911yescharacteristic
162C2×C4#1308357311yescharacteristic
163C2×C4#1308357311yescharacteristic
164C2×C4#1308357411yescharacteristic
165C2×C4#1308357411yescharacteristic
166C2×C4#1308357411yescharacteristic
167C8—41no—
168C8—3561no—
169C22#1566799011yescharacteristic
170C22#1566799411yescharacteristic
171C22#1566799811yescharacteristic
172C22D8×D8911yescharacteristic
173C22SD16×D8911yescharacteristic
174C22#1566804111yescharacteristic
175C22#1566804411yescharacteristic
176C4—81no—
177C4—81no—
178C4—3562no—
179C4—1782no—
180C4—1782no—
181C4—7121no—
182C4#1566800211yescharacteristic
183C4#1566800211yescharacteristic
184C4#1566800511yescharacteristic
185C4#1566800611yescharacteristic
186C2#1915153911yescharacteristic
187C2#1915187711yescharacteristic
188C2#1915188211yescharacteristic
189C2#1915191011yescharacteristic
190C2#1915192711yescharacteristic
191C2#1915194311yescharacteristic
192C2#1915196511yescharacteristic
subgroupG/H
centerC23D4×D89
commutator, cosocleC22×C4×C89C23
FrattiniC22×C4C22×D89
Fitting#340×C89C2
socle, prime radicalC23×C89C2×D4
hypercenter#340D89
hypocenterC89#2099
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
97. C89#2099semidirect

Maximal subgroups

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

subgroupindex
#191514942
#191514672
#191513612
#191513602
#191513522
#340×C892
#209989