Finite Group Databasebeta

← #37507622

Subgroups — #37507622

Order 22912.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D179C211yesmaximal, characteristic
2#26038494C212yesmaximal, complemented
3#26038179C211yesmaximal, characteristic, complemented
4#26038178C212yesmaximal, complemented
5#329×C179C211yesmaximal, characteristic, complemented
6C2×Q8×D179C411yescharacteristic
7C2×D4×D179C411yescharacteristic
8#19153102C411yescharacteristic
9#19153101C2211yescharacteristic
10#19153100C411yescharacteristic
11#19153099—22no—
12C22⋊C4×D179—22no—
13C42×D179C2211yescharacteristic
14Dic179⋊C8—22no—
15(C2×D179)⋊C8—22no—
16#19153024C2212yescomplemented
17#124×C179C2211yescharacteristic
18#97×C179C2212yescomplemented
19C23×D179—21no—
20C2×Dic358—21no—
21C2×Dic358C2×C411yescharacteristic
22Q8×D179—42no—
23C2×D716C2×C411yescharacteristic
24C2×C22⋊D179—21no—
25D4×D179—42no—
26C2×C4×D179—21no—
27C2×C4×D179C2×C411yescharacteristic
28C2×C4×D179D412yes—
29C2×C179⋊C8—22no—
30C22⋊Dic179—22no—
31(C2×D179)⋊C4—22no—
32(C2×D179)⋊C4—22no—
33C4×Dic179C2×C411yescharacteristic
34C4×Dic179D412yes—
35C2×Q8×C179C2×C411yescharacteristic
36C2×D4×C179C2×C411yescharacteristic
37C2×C8×C179—22no—
38C22⋊C4×C179—22no—
39C42×C179C2311yescharacteristic
40C22×D179—21no—
41C22×D179—44no—
42C22×D179—42no—
43C22×D179C22⋊C411yescharacteristic
44Dic358—42no—
45Dic358—41no—
46D716—41no—
47C22⋊D179—42no—
48C2×Dic179—21no—
49C2×Dic179C22⋊C412yes—
50C2×Dic179C22⋊C411yescharacteristic
51C4×D179—22no—
52C4×D179—42no—
53C4×D179—42no—
54C179⋊C8—42no—
55C23×C179—21no—
56Q8×C179—41no—
57D4×C179—41no—
58C2×C4×C179—21no—
59C2×C4×C179C22×C411yescharacteristic
60C2×C4×C179C2×D412yes—
61C8×C179—42no—
62C22×C179—41no—
63C22×C179—42no—
64C22×C179C2×C22⋊C411yescharacteristic
65C2×D179—22no—
66C2×D179—41no—
67C2×D179—42no—
68C2×D179—84no—
69C2×D179#10012yes—
70C4×C179—21no—
71C4×C179—22no—
72C4×C179—41no—
73Dic179—21no—
74Dic179—22no—
75Dic179—41no—
76C2×C179—81no—
77C2×C179C2×#10011yescharacteristic
78C2×C179#42112yes—
79D179—22no—
80D179—81no—
81C179#153311yescharacteristic, complemented, Sylow
82#1533—1791nomaximal, Sylow
83C2×#124—1791no—
84#432—1792no—
85#329—1791no—
86#329—1792no—
87#329D17911yescharacteristic, complemented
88C22×Q8—1791no—
89C22×D4—1791no—
90#124—3582no—
91#124—1791no—
92#124—1791no—
93#124—1791no—
94#124C2×D17911yescharacteristic
95C2×C22⋊C4—3582no—
96C2×C42—1791no—
97C4⋊C8—3582no—
98C22⋊C8—3582no—
99#97—1792no—
100#97C2×D17912yescomplemented
101C24—3581no—
102C2×Q8—3581no—
103C2×Q8—1791no—
104C2×Q8—7162no—
105C2×Q8C4×D17911yescharacteristic
106C2×D4—3581no—
107C2×D4—1791no—
108C2×D4—7162no—
109C2×D4C4×D17911yescharacteristic
110C22×C4—3581no—
111C22×C4—1791no—
112C22×C4—1792no—
113C2×C8—22no—
114C2×C8—3582no—
115C22⋊C4—22no—
116C22⋊C4—3582no—
117C22⋊C4—3582no—
118C22⋊C4—3582no—
119C42—1791no—
120C42—1792no—
121C42C22×D17911yescharacteristic
122C23—21no—
123C23—3581no—
124C23—1791no—
125C23—7164no—
126C23—7162no—
127Q8—41no—
128Q8—7161no—
129Q8—7162no—
130D4—41no—
131D4—7161no—
132D4—7162no—
133C2×C4—21no—
134C2×C4—3582no—
135C2×C4—3581no—
136C2×C4—1792no—
137C2×C4—1791no—
138C2×C4—7162no—
139C2×C4—7162no—
140C2×C4C2×C4×D17911yescharacteristic
141C2×C4D4×D17912yes—
142C8—42no—
143C8—7162no—
144C22—41no—
145C22—42no—
146C22—3582no—
147C22—14324no—
148C22—1792no—
149C22—7161no—
150C22—7162no—
151C22C22⋊C4×D17911yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—3581no—
156C4—3582no—
157C4—7161no—
158C2—81no—
159C2—3582no—
160C2—14321no—
161C2#100×D17911yescharacteristic
162C2#2603845412yes—
subgroupG/H
centerC22C22⋊C4×D179
commutatorC2×C4×C179C22×C4
FrattiniC42C22×D179
Fitting#329×C179C2
socleC22×C179C2×C22⋊C4
prime radicalC2×D4×D179C4
cosocleC42×C179C23
hypercenter#329D179
hypocenterC179#1533
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #26038494C2semidirect
3. #26038179C2semidirect
4. #26038178C2semidirect
5. #329×C179C2semidirect
16. #19153024C22semidirect
18. #97×C179C22semidirect
81. C179#1533semidirect
87. #329D179semidirect
100. #97C2×D179semidirect

Maximal subgroups

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

subgroupindex
#124×D1792
#260384942
#260381792
#260381782
#329×C1792
#1533179