Finite Group Databasebeta

← #37509101

Subgroups — #37509101

Order 22912.

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

normal subgroups only

This group has 262 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#41×Dic179C211yesmaximal, characteristic
2#26038423C211yesmaximal, characteristic
3#26038198C212yesmaximal, complemented
4#26038195C212yesmaximal, complemented
5#410×C179C211yesmaximal, characteristic
6C2×#15668243C2212yes—
7Q8×Dic179—21no—
8D4×Dic179—22no—
9D4×Dic179—21no—
10#19153072C412yescomplemented
11#19153072C2211yescharacteristic
12C2×C4×Dic179C412yescomplemented
13C2×C4×Dic179C2211yescharacteristic
14#19153032—21no—
15#19153030—21no—
16C2×#41×C179C2211yescharacteristic
17#117×C179C2212yes—
18#99×C179—22no—
19C22×Dic179—22no—
20C22×Dic179—21no—
21#15668243—22no—
22#15668243—22no—
23C2×C179⋊C8—22no—
24C4⋊Dic179—22no—
25C4⋊Dic179—21no—
26C22⋊Dic179—22no—
27C22⋊Dic179—21no—
28C4×Dic179—22no—
29C4×Dic179—21no—
30C4×Dic179C2×C411yescharacteristic
31C4×Dic179C2×C412yes—
32C4×Dic179C2×C411yescharacteristic
33#41×C179—22no—
34#41×C179—22no—
35C2×Q8×C179D411yescharacteristic
36C2×D4×C179D412yes—
37C2×D4×C179D411yescharacteristic
38C22×C4×C179C2×C412yes—
39C22×C4×C179C2311yescharacteristic
40C4⋊C4×C179—22no—
41C22⋊C4×C179—22no—
42C42×C179—22no—
43C2×Dic179—21no—
44C2×Dic179—22no—
45C2×Dic179—21no—
46C2×Dic179—42no—
47C2×Dic179—44no—
48C179⋊C8—42no—
49C23×C179C22⋊C412yes—
50C23×C179C2×D411yescharacteristic
51Q8×C179—22no—
52D4×C179—24no—
53D4×C179—22no—
54C2×C4×C179—22no—
55C2×C4×C179—22no—
56C2×C4×C179—42no—
57C2×C4×C179C22⋊C412yes—
58C2×C4×C179C22×C411yescharacteristic
59C2×C4×C179C2×D411yescharacteristic
60C2×C4×C179#4112yes—
61C2×C4×C179#4112yes—
62C22×C179—22no—
63C22×C179—41no—
64C22×C179—42no—
65C22×C179C2×C22⋊C411yescharacteristic
66C22×C179#12312yes—
67C4×C179—22no—
68C4×C179—82no—
69C4×C179#11711yescharacteristic
70C4×C179#11711yescharacteristic
71C4×C179#12312yes—
72Dic179—22no—
73Dic179—42no—
74Dic179—41no—
75C2×C179—21no—
76C2×C179—22no—
77C2×C179—42no—
78C2×C179#38111yescharacteristic
79C179#182711yescharacteristic, complemented, Sylow
80#1827—1791nomaximal, Sylow
81C4×#41—1791no—
82#413—1791no—
83#410D17911yescharacteristic
84#339—1792no—
85H(3,ℤ/4)—1792no—
86C2×#41C2×D17911yescharacteristic
87C2×M16—1792no—
88C4×Q8—3581no—
89C4×D4—3582no—
90C4×D4—3581no—
91#117—1792no—
92#117—1791no—
93#117C2×D17912yes—
94C2×C42—1792no—
95C2×C42—1791no—
96#101—3581no—
97#100—3581no—
98#99—22no—
99#41—22no—
100#41—22no—
101C2×Q8D71611yescharacteristic
102C2×D4C22⋊D17912yes—
103C2×D4D71611yescharacteristic
104C22×C4—3582no—
105C22×C4—3581no—
106C22×C4C4×D17912yes—
107C22×C4C22×D17911yescharacteristic
108M16—3582no—
109M16—3582no—
110C2×C8—3582no—
111C4⋊C4—22no—
112C4⋊C4—3582no—
113C4⋊C4—3581no—
114C22⋊C4—22no—
115C22⋊C4—3582no—
116C22⋊C4—3581no—
117C42—22no—
118C42—3582no—
119C42—3581no—
120C42—1791no—
121C42—1792no—
122C42—1791no—
123C23(C2×D179)⋊C412yes—
124C23C2×C22⋊D17911yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—3581no—
132C2×C4—3582no—
133C2×C4—3581no—
134C2×C4—7162no—
135C2×C4—7164no—
136C2×C4(C2×D179)⋊C412yes—
137C2×C4C2×C4×D17911yescharacteristic
138C2×C4C2×D71611yescharacteristic
139C2×C4#1566825812yes—
140C2×C4#1566825812yes—
141C8—7162no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×(C2×D179)⋊C411yescharacteristic
146C22#1915309412yes—
147C4—22no—
148C4—82no—
149C4—3582no—
150C4—7162no—
151C4—7161no—
152C4#1915306911yescharacteristic
153C4#1915306911yescharacteristic
154C4#1915309712yes—
155C2—22no—
156C2—21no—
157C2—42no—
158C2#2603830011yescharacteristic
subgroupG/H
centerC4#19153069
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#410×C179C2
socleC2×C179#381
prime radicalC2×#41×C179C22
cosocleC22×C4×C179C23
hypercenter#410D179
hypocenterC179#1827
LCSG ▷ C2×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #26038198C2semidirect
4. #26038195C2semidirect
10. #19153072C4semidirect
12. C2×C4×Dic179C4semidirect
79. C179#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic1792
#260384232
#260381982
#260381952
#410×C1792
#1827179