Finite Group Databasebeta

← #37507536

Subgroups — #37507536

Order 22912.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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#26038973C211yesmaximal, characteristic
2#26038496C211yesmaximal, characteristic, complemented
3#26038175C212yesmaximal, complemented
4#26038172C212yesmaximal
5#382×C179C211yesmaximal, characteristic, complemented
6#19153107—21no—
7#19153105C411yescharacteristic, complemented
8#19153101C411yescharacteristic, complemented
9#19153096—21no—
10#19153092C2211yescharacteristic
11#19153087C2211yescharacteristic
12C4×Dic358C411yescharacteristic, complemented
13C4×D716C411yescharacteristic, complemented
14C4×C22⋊D179—21no—
15#19153070—21no—
16C4⋊(C179⋊C8)—21no—
17C22⋊(C179⋊C8)C2212yes—
18#19153024—21no—
19C2×C4⋊C4×C179—21no—
20C2×C42×C179C2211yescharacteristic
21#95×C179—21no—
22#95×C179C2212yes—
23C2×Dic358C2×C411yescharacteristic
24C2×D716C2×C411yescharacteristic
25C2×C22⋊D179—21no—
26C2×C4×D179—21no—
27C2×C179⋊C8—22no—
28C4⋊Dic179C2×C411yescharacteristic
29C4⋊Dic179C2×C411yescharacteristic
30Dic179⋊C4—21no—
31Dic179⋊C4—21no—
32Dic179⋊C4—21no—
33Dic179⋊C4—21no—
34C22⋊Dic179—21no—
35(C2×D179)⋊C4—21no—
36(C2×D179)⋊C4—21no—
37(C2×D179)⋊C4—21no—
38(C2×D179)⋊C4—21no—
39C4×Dic179—21no—
40C22×C4×C179—22no—
41C22×C4×C179D411yescharacteristic
42C22×C4×C179D411yescharacteristic
43C22×C4×C179C2311yescharacteristic
44C4⋊C4×C179—42no—
45C42×C179C2×C411yescharacteristic
46C42×C179C2×C411yescharacteristic
47C42×C179D411yescharacteristic
48C42×C179D411yescharacteristic
49C22×D179—21no—
50Dic358—41no—
51D716—41no—
52C22⋊D179—41no—
53C22⋊D179—41no—
54C2×Dic179—21no—
55C2×Dic179—21no—
56C2×Dic179—21no—
57C4×D179—42no—
58C179⋊C8—42no—
59C23×C179C2×D411yescharacteristic
60C2×C4×C179—21no—
61C2×C4×C179—21no—
62C2×C4×C179—41no—
63C2×C4×C179—41no—
64C2×C4×C179—42no—
65C2×C4×C179—42no—
66C2×C4×C179—42no—
67C2×C4×C179C22⋊C411yescharacteristic
68C2×C4×C179C22⋊C411yescharacteristic
69C2×C4×C179C22⋊C411yescharacteristic
70C2×C4×C179C22⋊C411yescharacteristic
71C2×C4×C179C22×C411yescharacteristic
72C2×C4×C179C2×D411yescharacteristic
73C22×C179—21no—
74C22×C179—21no—
75C22×C179C2×C22⋊C411yescharacteristic
76C22×C179AGL(1,ℤ/8)11yescharacteristic
77C22×C179#13711yescharacteristic
78C2×D179—41no—
79C2×D179—41no—
80C2×D179—41no—
81C4×C179—21no—
82C4×C179—21no—
83C4×C179—21no—
84C4×C179—21no—
85C4×C179—21no—
86C4×C179—21no—
87C4×C179—82no—
88Dic179—41no—
89Dic179—41no—
90Dic179—41no—
91C2×C179—21no—
92C2×C179—21no—
93C2×C179#41011yescharacteristic
94C2×C179#41711yescharacteristic
95C2×C179#42111yescharacteristic
96D179—81no—
97C179#151211yescharacteristic, complemented, Sylow
98#1512—1791nomaximal, Sylow
99#529—1791no—
100#432—1791no—
101#382D17911yescharacteristic, complemented
102#328—1792no—
103#327—1792no—
104#126—3581no—
105#125—1791no—
106#124—1791no—
107#123—3581no—
108C22⋊Q8—1791no—
109#121—1791no—
110C4×Q8—1791no—
111C4×D4—3581no—
112C4×D4—1791no—
113#117—3581no—
114C2×C4⋊C4—21no—
115C2×C42C2×D17911yescharacteristic
116C4⋊C8—3581no—
117C22⋊C8—1792no—
118#97—3581no—
119#95—21no—
120#95C2×D17912yes—
121C2×Q8—1791no—
122C2×D4—3581no—
123C2×D4—1791no—
124C22×C4—22no—
125C22×C4—3581no—
126C22×C4C22⋊D17911yescharacteristic
127C22×C4C22⋊D17911yescharacteristic
128C22×C4C22×D17911yescharacteristic
129C2×C8—3582no—
130C4⋊C4—42no—
131C4⋊C4—3581no—
132C4⋊C4—3581no—
133C4⋊C4—3581no—
134C4⋊C4—3581no—
135C4⋊C4—1791no—
136C4⋊C4—1791no—
137C22⋊C4—3581no—
138C22⋊C4—3581no—
139C22⋊C4—3581no—
140C22⋊C4—3581no—
141C22⋊C4—3581no—
142C42—3581no—
143C42C4×D17911yescharacteristic
144C42C4×D17911yescharacteristic
145C42D71611yescharacteristic
146C42D71611yescharacteristic
147C23—3581no—
148C23C2×C22⋊D17911yescharacteristic
149Q8—7161no—
150D4—7161no—
151D4—7161no—
152D4—7161no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—3581no—
161C2×C4—3581no—
162C2×C4—3581no—
163C2×C4—7162no—
164C2×C4(C2×D179)⋊C411yescharacteristic
165C2×C4(C2×D179)⋊C411yescharacteristic
166C2×C4(C2×D179)⋊C411yescharacteristic
167C2×C4(C2×D179)⋊C411yescharacteristic
168C2×C4C2×C4×D17911yescharacteristic
169C2×C4C2×D71611yescharacteristic
170C8—7162no—
171C22—21no—
172C22—21no—
173C22—7161no—
174C22—7161no—
175C22—7161no—
176C22C2×(C2×D179)⋊C411yescharacteristic
177C22#1915313911yescharacteristic
178C22#1915314411yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—82no—
186C4—7161no—
187C4—7161no—
188C4—7161no—
189C2—21no—
190C2—21no—
191C2—14321no—
192C2#2603841211yescharacteristic
193C2#2603843811yescharacteristic
194C2#2603845711yescharacteristic
subgroupG/H
centerC22C2×(C2×D179)⋊C4
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#382×C179C2
socleC22×C179C2×C22⋊C4
prime radical#19153087C22
cosocleC22×C4×C179C23
hypercenter#382D179
hypocenterC179#1512
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #26038496C2semidirect
3. #26038175C2semidirect
5. #382×C179C2semidirect
7. #19153105C4semidirect
8. #19153101C4semidirect
12. C4×Dic358C4semidirect
13. C4×D716C4semidirect
97. C179#1512semidirect
101. #382D179semidirect

Maximal subgroups

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

subgroupindex
#260389732
#260384962
#260381752
#260381722
#382×C1792
#1512179