Finite Group Databasebeta

← #37508222

Subgroups — #37508222

Order 22912.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#26039169C211yesmaximal, characteristic
2#26038789C211yesmaximal, characteristic
3#26038725C211yesmaximal, characteristic
4#26038650C211yesmaximal, characteristic
5#26038169C211yesmaximal, characteristic
6#26038169C211yesmaximal, characteristic
7#333×C179C211yesmaximal, characteristic
8C2×Dic716—21no—
9#19153113C2211yescharacteristic
10#19153112—21no—
11#19153112—21no—
12#19153111—22no—
13C4×Dic358C2211yescharacteristic
14C4×Dic358C2211yescharacteristic
15#19153078—21no—
16#19153078—21no—
17#19153045—21no—
18#19153038—21no—
19#19153038—21no—
20#19153037—22no—
21C4×C179⋊C8C2211yescharacteristic
22C4⋊Q8×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24C4⋊C8×C179C2211yescharacteristic
25C2×Dic358—22no—
26C2×Dic358—21no—
27C2×Dic358D411yescharacteristic
28C2×Dic358D411yescharacteristic
29Dic716—42no—
30C2×C179⋊C8—21no—
31C4⋊Dic179—21no—
32C4⋊Dic179—21no—
33C4⋊Dic179D411yescharacteristic
34C4⋊Dic179D411yescharacteristic
35Dic179⋊C4—22no—
36Dic179⋊C4—22no—
37Dic179⋊C4—21no—
38Dic179⋊C4—21no—
39C4×Dic179—22no—
40C4×Dic179—21no—
41C4×Dic179—21no—
42C2×Q8×C179D412yes—
43C2×C8×C179—21no—
44C2×C8×C179—21no—
45C4⋊C4×C179—21no—
46C4⋊C4×C179—21no—
47C42×C179C2311yescharacteristic
48Dic358—21no—
49Dic358—21no—
50Dic358—41no—
51Dic358—41no—
52Dic358—82no—
53Dic358SD1612yes—
54Dic358Q1612yescomplemented
55C2×Dic179—21no—
56C2×Dic179—21no—
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—41no—
60C179⋊C8—41no—
61Q8×C179—42no—
62C2×C4×C179—22no—
63C2×C4×C179C2×D411yescharacteristic
64C2×C4×C179C2×D411yescharacteristic
65C2×C4×C179C2×D411yescharacteristic
66C8×C179—41no—
67C8×C179—41no—
68C22×C179#12011yescharacteristic
69C4×C179—21no—
70C4×C179—42no—
71C4×C179C2×SD1611yescharacteristic
72C4×C179C2×Q1611yescharacteristic
73C4×C179#13711yescharacteristic
74C4×C179#13711yescharacteristic
75Dic179—22no—
76Dic179—22no—
77Dic179—41no—
78Dic179—41no—
79Dic179—81no—
80C2×C179#44811yescharacteristic
81C2×C179#45111yescharacteristic
82C2×C179#45511yescharacteristic
83C179#164511yescharacteristic, complemented, Sylow
84#1645—1791nomaximal, Sylow
85Q82—1791no—
86#487—1791no—
87#475—1791no—
88#462—1791no—
89#333D17911yescharacteristic
90Q8⋊C8—1791no—
91Q8⋊C8—1791no—
92C2×Q16—3581no—
93C4⋊Q8—3581no—
94C4⋊Q8—3581no—
95C4⋊Q8—3582no—
96C4⋊Q8—1791no—
97C4⋊Q8C2×D17911yescharacteristic
98C4×Q8—3581no—
99C4×Q8—3581no—
100C4×Q8—1791no—
101C4×Q8—1791no—
102#106—3581no—
103C4⋊C8C2×D17911yescharacteristic
104C4⋊C8C2×D17911yescharacteristic
105#103—3581no—
106#103—3582no—
107#103—3581no—
108C4×C8—1791no—
109C2×Q8—3582no—
110C2×Q8—3581no—
111C2×Q8—1791no—
112C2×Q8—1791no—
113C2×Q8D71612yes—
114Q16—7162no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—3581no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—3582no—
121C4⋊C4—3582no—
122C4⋊C4—3581no—
123C4⋊C4—3581no—
124C4⋊C4—3581no—
125C4⋊C4—3581no—
126C4⋊C4—1791no—
127C4⋊C4—1791no—
128C42—3582no—
129C42—3581no—
130C42—3581no—
131C42C22×D17911yescharacteristic
132Q8—42no—
133Q8—3581no—
134Q8—3581no—
135Q8—14322no—
136Q8—1792no—
137Q8—1792no—
138Q8—7161no—
139Q8—7161no—
140C2×C4—22no—
141C2×C4—3581no—
142C2×C4—3581no—
143C2×C4—3581no—
144C2×C4—3581no—
145C2×C4—7161no—
146C2×C4D4×D17911yescharacteristic
147C2×C4D4×D17911yescharacteristic
148C2×C4C2×D71611yescharacteristic
149C8—41no—
150C8—41no—
151C8—7161no—
152C22#1915308311yescharacteristic
153C4—21no—
154C4—42no—
155C4—3582no—
156C4—3582no—
157C4—14321no—
158C4—7161no—
159C4—7161no—
160C4SD16×D17911yescharacteristic
161C4Q16×D17911yescharacteristic
162C4#1915314211yescharacteristic
163C4#1915314511yescharacteristic
164C2#2603857911yescharacteristic
165C2#2603859611yescharacteristic
166C2#2603861911yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#333×C179C2
socle, prime radicalC22×C179#120
hypercenter#333D179
hypocenterC179#1645
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
54. Dic358Q16semidirect
83. C179#1645semidirect

Maximal subgroups

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

subgroupindex
#260391692
#260387892
#260387252
#260386502
#260381692
#333×C1792
#1645179