Finite Group Databasebeta

← #26021743

Subgroups — #26021743

Order 11392.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#15667945C211yesmaximal, characteristic
2C2×C4⋊#10623494C211yesmaximal, characteristic
3#19151496C211yesmaximal, characteristic
4#19151360C211yesmaximal, characteristic
5#19151360C211yesmaximal, characteristic
6#19151360C211yesmaximal, characteristic
7#389×C89C211yesmaximal, characteristic
8C22×#10623494C2211yescharacteristic
9C22×#10623494C2211yescharacteristic
10C2×C4⋊Dic89C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12C2×#13083553—21no—
13#15667945—22no—
14C4⋊#10623494—22no—
15#15667919—21no—
16C2×C4⋊C4×C89—21no—
17C2×C4⋊C4×C89C2211yescharacteristic
18C2×C4⋊C4×C89C2211yescharacteristic
19C2×C42×C89C2211yescharacteristic
20#95×C89—21no—
21C22×Dic89—21no—
22C22×Dic89—21no—
23C2×#10623494—21no—
24C2×#10623494—21no—
25C2×#10623494—21no—
26C2×#10623494—21no—
27C2×#10623494—21no—
28C2×#10623494D412yes—
29C4⋊Dic89—21no—
30C4⋊Dic89—21no—
31C4⋊Dic89—21no—
32C4⋊Dic89Q812yes—
33#13083553—42no—
34C22×C4×C89—21no—
35C22×C4×C89—21no—
36C22×C4×C89D411yescharacteristic
37C22×C4×C89D411yescharacteristic
38C22×C4×C89C2311yescharacteristic
39C4⋊C4×C89—21no—
40C4⋊C4×C89—21no—
41C4⋊C4×C89—21no—
42C4⋊C4×C89—42no—
43C4⋊C4×C89Q812yes—
44C42×C89—21no—
45C42×C89—21no—
46C23×C89C2×D411yescharacteristic
47C2×C4×C89—21no—
48C2×C4×C89—21no—
49C2×C4×C89—21no—
50C2×C4×C89—22no—
51C2×C4×C89—21no—
52C2×C4×C89—21no—
53C2×C4×C89—41no—
54C2×C4×C89—41no—
55C2×C4×C89—41no—
56C2×C4×C89—41no—
57C2×C4×C89—41no—
58C2×C4×C89D812yes—
59C2×C4×C89C2×D411yescharacteristic
60C2×C4×C89C2×Q811yescharacteristic
61C2×C4×C89C2×Q811yescharacteristic
62C2×C4×C89#4111yescharacteristic
63C2×C4×C89#4111yescharacteristic
64C2×C4×C89#4111yescharacteristic
65C2×Dic89—22no—
66C2×Dic89—41no—
67C2×Dic89—41no—
68C2×Dic89—41no—
69C2×Dic89—41no—
70C2×Dic89—41no—
71#10623494—22no—
72#10623494—41no—
73C22×C89#12111yescharacteristic
74C22×C89C22⋊Q811yescharacteristic
75C22×C89C22⋊Q811yescharacteristic
76C22×C89C2×D811yescharacteristic
77C22×C89#13511yescharacteristic
78C22×C89#13711yescharacteristic
79C22×C89#13711yescharacteristic
80C4×C89—22no—
81C4×C89—41no—
82C4×C89—42no—
83C4×C89—81no—
84C4×C89#12311yescharacteristic
85C4×C89#12511yescharacteristic
86C4×C89#12511yescharacteristic
87C4×C89C4⋊Q811yescharacteristic
88Dic89—42no—
89Dic89—81no—
90C2×C89#39811yescharacteristic
91C2×C89#46611yescharacteristic
92C2×C89#47011yescharacteristic
93C2×C89#47411yescharacteristic
94C2×C89#47411yescharacteristic
95C2×C89#47911yescharacteristic
96C2×C89#47911yescharacteristic
97#2086—891nomaximal, Sylow
98C89#208611yescharacteristic, complemented, Sylow
99C2×#107—891no—
100C2×C4⋊C8—891no—
101#389—891no—
102#389D8911yescharacteristic
103#340—891no—
104#340—891no—
105#340—891no—
106C22×C8—891no—
107C22×C8—891no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—891no—
110C2×C4⋊C4—891no—
111C2×C4⋊C4—1781no—
112C2×C4⋊C4C2×D8911yescharacteristic
113C2×C4⋊C4C2×D8911yescharacteristic
114C2×C42C2×D8911yescharacteristic
115#107—1782no—
116C4⋊C8—1782no—
117#95—21no—
118#95—1781no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—1781no—
122C22×C4—1781no—
123C22×C4C22⋊D8911yescharacteristic
124C22×C4C22⋊D8911yescharacteristic
125C22×C4C22×D8911yescharacteristic
126C2×C8—892no—
127C2×C8—1781no—
128C2×C8—1781no—
129C2×C8—1781no—
130C2×C8—1781no—
131C2×C8—1781no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—42no—
136C4⋊C4—892no—
137C4⋊C4—3562no—
138C4⋊C4—1781no—
139C4⋊C4—1781no—
140C4⋊C4—1781no—
141C4⋊C4Dic17812yes—
142C42—21no—
143C42—21no—
144C23C2×C22⋊D8911yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—3561no—
157C2×C4—3561no—
158C2×C4—3561no—
159C2×C4—3561no—
160C2×C4—3561no—
161C2×C4—1782no—
162C2×C4#1308355912yes—
163C2×C4D4×D8911yescharacteristic
164C2×C4Q8×D8911yescharacteristic
165C2×C4C2×Dic17811yescharacteristic
166C2×C4#1308357311yescharacteristic
167C2×C4#1308357411yescharacteristic
168C2×C4#1308357511yescharacteristic
169C8—3561no—
170C8—1782no—
171C22#1566798411yescharacteristic
172C22#1566798811yescharacteristic
173C22#1566799111yescharacteristic
174C22C2×#1308355911yescharacteristic
175C22#1566803211yescharacteristic
176C22#1566804211yescharacteristic
177C22#1566804311yescharacteristic
178C4—22no—
179C4—42no—
180C4—41no—
181C4—81no—
182C4—3562no—
183C4—7121no—
184C4#1566799711yescharacteristic
185C4#1566800211yescharacteristic
186C4#1566800311yescharacteristic
187C4#1566801111yescharacteristic
188C2#1915153111yescharacteristic
189C2#1915183211yescharacteristic
190C2#1915185411yescharacteristic
191C2#1915187511yescharacteristic
192C2#1915187811yescharacteristic
193C2#1915190211yescharacteristic
194C2#1915190511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D89
commutator, cosocleC22×C4×C89C23
FrattiniC22×C4C22×D89
Fitting#389×C89C2
socle, prime radicalC23×C89C2×D4
hypercenter#389D89
hypocenterC89#2086
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
98. C89#2086semidirect

Maximal subgroups

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

subgroupindex
C2×#156679452
C2×C4⋊#106234942
#191514962
#191513602
#389×C892
#208689