Finite Group Databasebeta

← #26021615

Subgroups — #26021615

Order 11392.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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×#15667947C211yesmaximal, characteristic
2#19151640C211yesmaximal, characteristic
3#19151626C211yesmaximal, characteristic
4#19151607C211yesmaximal, characteristic
5C2×#15667936C211yesmaximal, characteristic
6#19151366C211yesmaximal, characteristic
7C2×#101×C89C211yesmaximal, characteristic
8C2×#13083558C2211yescharacteristic
9C22×#10623494C2211yescharacteristic
10#15667971C2211yescharacteristic
11C2×C4⋊Dic89C2211yescharacteristic
12#15667947—22no—
13#15667946—21no—
14#15667944—21no—
15#15667941—22no—
16#15667936—22no—
17#15667936—21no—
18#15667936—21no—
19C22×Q8×C89C2211yescharacteristic
20C2×M16×C89C2211yescharacteristic
21C2×M16×C89C2211yescharacteristic
22#101×C89—22no—
23C22×Dic89—21no—
24#13083558—21no—
25#13083558—21no—
26C2×#10623494—21no—
27C2×#10623494—21no—
28C2×#10623494—21no—
29C2×#10623494D412yes—
30C4⋊Dic89—21no—
31C4⋊Dic89—21no—
32C4⋊Dic89D411yescharacteristic
33C4⋊Dic89D411yescharacteristic
34C22⋊Dic89—21no—
35C4×Dic89—21no—
36C2×Q8×C89—21no—
37C2×Q8×C89—21no—
38C2×Q8×C89—21no—
39C2×Q8×C89—21no—
40C2×Q8×C89—21no—
41C2×Q8×C89Q812yes—
42C22×C4×C89—21no—
43C22×C4×C89C2311yescharacteristic
44M16×C89—21no—
45M16×C89—21no—
46M16×C89—21no—
47M16×C89D412yes—
48C2×C8×C89—21no—
49C2×C8×C89—21no—
50C23×C89#4111yescharacteristic
51Q8×C89—22no—
52Q8×C89—22no—
53Q8×C89—41no—
54Q8×C89—41no—
55C2×C4×C89—22no—
56C2×C4×C89—41no—
57C2×C4×C89—41no—
58C2×C4×C89C2×D411yescharacteristic
59C2×C4×C89C2×D411yescharacteristic
60C2×C4×C89C2×D411yescharacteristic
61C2×C4×C89C2×Q811yescharacteristic
62C2×C4×C89#4111yescharacteristic
63C2×C4×C89#4111yescharacteristic
64C2×Dic89—21no—
65C2×Dic89—21no—
66C2×Dic89—41no—
67C2×Dic89—81no—
68C8×C89—22no—
69C8×C89—41no—
70#10623494—22no—
71#10623494—41no—
72C22×C89—21no—
73C22×C89—21no—
74C22×C89#12111yescharacteristic
75C22×C89C22⋊Q811yescharacteristic
76C22×C89#12611yescharacteristic
77C4×C89—42no—
78C4×C89#12111yescharacteristic
79C4×C89#12111yescharacteristic
80C4×C89C22⋊Q811yescharacteristic
81C4×C89C22⋊Q811yescharacteristic
82Dic89—41no—
83Dic89—41no—
84Dic89—81no—
85C2×C89—21no—
86C2×C89—21no—
87C2×C89#39611yescharacteristic
88C2×C89#47111yescharacteristic
89C2×C89#47311yescharacteristic
90#2064—891nomaximal, Sylow
91C89#206411yescharacteristic, complemented, Sylow
92C2×#108—891no—
93#428—891no—
94#424—891no—
95#419—891no—
96C2×#103—891no—
97C2×#101D8911yescharacteristic
98#343—891no—
99C22×Q8C2×D8911yescharacteristic
100C2×M16—891no—
101C2×M16C2×D8911yescharacteristic
102C2×M16C2×D8911yescharacteristic
103C22×C8—891no—
104#117—891no—
105C2×C4⋊C4—891no—
106#108—1782no—
107#107—1781no—
108#106—1781no—
109C4⋊C8—1782no—
110#103—1781no—
111#103—1781no—
112#103—1782no—
113#101—22no—
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8Dic17812yes—
120C22×C4—21no—
121C22×C4—1781no—
122C22×C4C22×D8911yescharacteristic
123M16—21no—
124M16—21no—
125M16—21no—
126M16—1781no—
127M16—1781no—
128M16C22⋊D8912yes—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—892no—
132C2×C8—1781no—
133C2×C8—1781no—
134C2×C8—1781no—
135C4⋊C4—891no—
136C4⋊C4—891no—
137C4⋊C4—1781no—
138C4⋊C4—1781no—
139C22⋊C4—1781no—
140C42—1781no—
141C23#1308357411yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—41no—
145Q8—41no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—3561no—
150C2×C4—1781no—
151C2×C4—1781no—
152C2×C4—7121no—
153C2×C4D4×D8911yescharacteristic
154C2×C4D4×D8911yescharacteristic
155C2×C4C2×C22⋊D8911yescharacteristic
156C2×C4C2×Dic17811yescharacteristic
157C2×C4#1308357311yescharacteristic
158C2×C4#1308357311yescharacteristic
159C8—22no—
160C8—41no—
161C8—3561no—
162C8—1782no—
163C22—21no—
164C22—21no—
165C22#1566798511yescharacteristic
166C22#1566799111yescharacteristic
167C22#1566800511yescharacteristic
168C4—42no—
169C4—3561no—
170C4—3561no—
171C4—7121no—
172C4#1566798311yescharacteristic
173C4#1566798411yescharacteristic
174C4#1566798911yescharacteristic
175C4#1566798911yescharacteristic
176C2—21no—
177C2—21no—
178C2#1915152111yescharacteristic
179C2#1915186411yescharacteristic
180C2#1915187211yescharacteristic
subgroupG/H
centerC22#15667985
commutator, cosocleC22×C4×C89C23
FrattiniC22×C4C22×D89
FittingC2×#101×C89C2
socleC22×C89#121
prime radicalC23×C89#41
hypercenterC2×#101D89
hypocenterC89#2064
LCSG ▷ C22×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
91. C89#2064semidirect

Maximal subgroups

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

subgroupindex
C2×#156679472
#191516402
#191516262
#191516072
C2×#156679362
#191513662
C2×#101×C892
#206489