Finite Group Databasebeta

← #26021945

Subgroups — #26021945

Order 11392.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#19152173C211yesmaximal, characteristic
2#19151581C212yesmaximal
3#19151397C211yesmaximal, characteristic, complemented
4#19151396C212yesmaximal, complemented
5#356×C89C211yesmaximal, characteristic, complemented
6C2×#13083575C2211yescharacteristic
7C2×Q8×D89C411yescharacteristic
8M16×D89—22no—
9#15668010C2211yescharacteristic
10#15668001C411yescharacteristic
11#15668000C411yescharacteristic
12#15667997—22no—
13#15667990—22no—
14#15667969C411yescharacteristic
15#15667931C2212yes—
16#15667928—22no—
17C4⋊Q8×C89C2211yescharacteristic
18#101×C89C2212yes—
19#13083575—42no—
20C2×Dic178—21no—
21C2×Dic178C2×C411yescharacteristic
22Q8×D89—42no—
23C2×D356C2×C411yescharacteristic
24C2×D356D412yes—
25C2×C4×D89—21no—
26C2×C4×D89C2×C411yescharacteristic
27C2×C4×D89D412yes—
28#13083558—22no—
29#13083557—42no—
30C8×D89—42no—
31#13083553—22no—
32#13083553—21no—
33#13083551—21no—
34#13083551—22no—
35#13083551—22no—
36C4×Dic89C2×C411yescharacteristic
37C2×Q8×C89C2×C411yescharacteristic
38C2×Q8×C89C2311yescharacteristic
39M16×C89—22no—
40C4⋊C4×C89—22no—
41C42×C89C2×C411yescharacteristic
42C22×D89C22⋊C412yes—
43C22×D89C22⋊C411yescharacteristic
44Q8×C89—41no—
45Q8×C89—41no—
46C2×C4×C89—21no—
47C2×C4×C89—21no—
48C2×C4×C89C22×C411yescharacteristic
49C2×C4×C89C2×D412yes—
50C2×Dic89—21no—
51C2×Dic89—21no—
52C2×Dic89C22⋊C411yescharacteristic
53D356—41no—
54D356—42no—
55C4×D89—22no—
56C4×D89—22no—
57C4×D89—22no—
58C4×D89—42no—
59Dic178—42no—
60Dic178—41no—
61C8×C89—42no—
62#10623494—42no—
63C22×C89C2×C22⋊C411yescharacteristic
64C2×D89—21no—
65C2×D89—22no—
66C2×D89—42no—
67C2×D89—41no—
68C4×C89—22no—
69C4×C89—21no—
70C4×C89—41no—
71C4×C89—41no—
72Dic89—41no—
73Dic89—41no—
74Dic89#9912yes—
75C2×C89—21no—
76C2×C89C2×#9911yescharacteristic
77D89—41no—
78D89—42no—
79#2135—891nomaximal, Sylow
80C89#213511yescharacteristic, complemented, Sylow
81#536—891no—
82#413—892no—
83#356—891no—
84#356—892no—
85#356D8911yescharacteristic, complemented
86C2×#41—891no—
87C22×Q8—891no—
88C2×M16—1782no—
89C4⋊Q8—891no—
90C4⋊Q8C2×D8911yescharacteristic
91#124—891no—
92#124—891no—
93#123—1782no—
94C22⋊Q8—1782no—
95#117—891no—
96#101—892no—
97#101C2×D8912yes—
98#100—1782no—
99#41—3562no—
100C2×Q8—891no—
101C2×Q8—3562no—
102C2×Q8—1781no—
103C2×Q8C4×D8911yescharacteristic
104C2×Q8C22×D8911yescharacteristic
105C2×D4—891no—
106C2×D4—892no—
107C22×C4—891no—
108C22×C4—892no—
109C22×C4—1781no—
110M16—22no—
111M16—3562no—
112M16—1782no—
113C2×C8—3562no—
114C4⋊C4—22no—
115C4⋊C4—1781no—
116C4⋊C4—1782no—
117C22⋊C4—1781no—
118C22⋊C4—1782no—
119C22⋊C4—1782no—
120C42—891no—
121C42C4×D8911yescharacteristic
122C23—892no—
123C23—891no—
124Q8—41no—
125Q8—41no—
126Q8—3561no—
127Q8—3562no—
128D4—3562no—
129D4—3561no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—891no—
133C2×C4—3562no—
134C2×C4—1782no—
135C2×C4—1782no—
136C2×C4—1782no—
137C2×C4—1781no—
138C2×C4—1781no—
139C2×C4C2×C4×D8911yescharacteristic
140C2×C4D4×D8912yes—
141C8—42no—
142C8—3562no—
143C22—3562no—
144C22—3561no—
145C22—1781no—
146C22—1782no—
147C22C22⋊C4×D8911yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—892no—
153C4—3561no—
154C4—3561no—
155C2—21no—
156C2—3561no—
157C2—3562no—
158C2#99×D8911yescharacteristic
subgroupG/H
centerC2#99×D89
commutatorC2×C4×C89C22×C4
FrattiniC2×Q8C22×D89
Fitting#356×C89C2
socleC2×C89C2×#99
prime radicalC2×#13083575C22
cosocleC2×Q8×C89C23
hypercenter#356D89
hypocenterC89#2135
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
3. #19151397C2semidirect
4. #19151396C2semidirect
5. #356×C89C2semidirect
80. C89#2135semidirect
85. #356D89semidirect

Maximal subgroups

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

subgroupindex
#191521732
#191515812
#191513972
#191513962
#356×C892
#213589