Finite Group Databasebeta

← #37508337

Subgroups — #37508337

Order 22912.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#26039189C211yesmaximal, characteristic
2#26038848C211yesmaximal, characteristic, complemented
3#26038808C211yesmaximal, characteristic, complemented
4#26038798C211yesmaximal, characteristic
5#26038180C211yesmaximal, characteristic, complemented
6#26038180C211yesmaximal, characteristic, complemented
7#329×C179C211yesmaximal, characteristic
8#19153113C2211yescharacteristic
9#19153111—21no—
10#19153106—21no—
11#19153106—21no—
12#19153105C2211yescharacteristic
13#19153105C2211yescharacteristic
14#19153094—21no—
15#19153090—21no—
16#19153090—21no—
17#19153047—21no—
18#19153045—21no—
19#19153038—21no—
20#19153038—21no—
21#19153037—21no—
22#19153034—21no—
23#19153024C2211yescharacteristic
24#124×C179C2211yescharacteristic
25#97×C179C2211yescharacteristic
26#97×C179C2211yescharacteristic
27C2×Dic358—21no—
28C2×Dic358—21no—
29C22×Dic179—21no—
30C2×C179⋊C8—21no—
31C4⋊Dic179—21no—
32C4⋊Dic179—21no—
33C4⋊Dic179D411yescharacteristic
34C4⋊Dic179D411yescharacteristic
35C4⋊Dic179D411yescharacteristic
36C4⋊Dic179D411yescharacteristic
37Dic179⋊C4—21no—
38Dic179⋊C4—21no—
39Dic179⋊C4—21no—
40Dic179⋊C4—21no—
41Dic179⋊C4—21no—
42Dic179⋊C4—21no—
43C22⋊Dic179—21no—
44C22⋊Dic179—21no—
45C22⋊Dic179—21no—
46C4×Dic179—21no—
47C2×Q8×C179D411yescharacteristic
48C2×D4×C179D411yescharacteristic
49C2×C8×C179—21no—
50C2×C8×C179—21no—
51C22⋊C4×C179—21no—
52C22⋊C4×C179—21no—
53C42×C179C2311yescharacteristic
54Dic358—42no—
55Dic358—81no—
56C2×Dic179—21no—
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—21no—
60C2×Dic179—41no—
61C2×Dic179—81no—
62C179⋊C8—41no—
63C23×C179—21no—
64Q8×C179—41no—
65D4×C179—41no—
66C2×C4×C179—21no—
67C2×C4×C179C2×D411yescharacteristic
68C2×C4×C179C2×D411yescharacteristic
69C2×C4×C179C2×D411yescharacteristic
70C8×C179—22no—
71C8×C179—41no—
72C22×C179—41no—
73C22×C179—41no—
74C22×C179—41no—
75C22×C179#12011yescharacteristic
76C4×C179—21no—
77C4×C179—21no—
78C4×C179—21no—
79C4×C179—41no—
80Dic179—41no—
81Dic179—41no—
82Dic179—41no—
83Dic179—41no—
84Dic179—81no—
85C2×C179—81no—
86C2×C179#45411yescharacteristic
87C2×C179#45511yescharacteristic
88C2×C179#45611yescharacteristic
89C179#166411yescharacteristic, complemented, Sylow
90#1664—1791nomaximal, Sylow
91#563—1791no—
92#501—1791no—
93#491—1791no—
94#489—1791no—
95#330—1791no—
96#330—1791no—
97#329D17911yescharacteristic
98C4⋊Q8—3581no—
99C4⋊Q8—1791no—
100#126—3581no—
101#126—3581no—
102#125—1791no—
103#125—1791no—
104#124C2×D17911yescharacteristic
105#123—3581no—
106C22⋊Q8—3581no—
107C22⋊Q8—3581no—
108#107—3581no—
109#106—3581no—
110#103—3581no—
111#103—3581no—
112#103—3581no—
113#102—3581no—
114#97—1791no—
115#97C2×D17911yescharacteristic
116#97C2×D17911yescharacteristic
117C2×Q8—3581no—
118C2×Q8—3581no—
119C2×Q8D71611yescharacteristic
120C2×D4D71611yescharacteristic
121C22×C4—3581no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—3581no—
125C4⋊C4—3581no—
126C4⋊C4—3581no—
127C4⋊C4—3581no—
128C4⋊C4—3581no—
129C4⋊C4—3581no—
130C4⋊C4—3581no—
131C4⋊C4—3581no—
132C4⋊C4—3581no—
133C4⋊C4—1791no—
134C4⋊C4—1791no—
135C4⋊C4—1791no—
136C4⋊C4—1791no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—3581no—
140C22⋊C4—3581no—
141C22⋊C4—3581no—
142C42—3581no—
143C42C22×D17911yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—14321no—
147Q8—7162no—
148D4—41no—
149C2×C4—21no—
150C2×C4—3581no—
151C2×C4—3581no—
152C2×C4—3581no—
153C2×C4—3581no—
154C2×C4—14321no—
155C2×C4—7161no—
156C2×C4D4×D17911yescharacteristic
157C2×C4D4×D17911yescharacteristic
158C2×C4C2×D71611yescharacteristic
159C8—22no—
160C8—41no—
161C8—7161no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1915308311yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—14321no—
171C4—7161no—
172C4—7161no—
173C4—7161no—
174C4—7161no—
175C2—81no—
176C2#2603861311yescharacteristic
177C2#2603861911yescharacteristic
178C2#2603862311yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#329×C179C2
socleC22×C179#120
prime radicalC2×D4×C179D4
hypercenter#329D179
hypocenterC179#1664
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #26038848C2semidirect
3. #26038808C2semidirect
5. #26038180C2semidirect
6. #26038180C2semidirect
89. C179#1664semidirect

Maximal subgroups

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

subgroupindex
#260391892
#260388482
#260388082
#260387982
#260381802
#329×C1792
#1664179