Finite Group Databasebeta

← #37507539

Subgroups — #37507539

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#26038305C211yesmaximal, characteristic, complemented
3#26038177C212yesmaximal, complemented
4#26038174C212yesmaximal
5#432×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—
16C2×C4⋊Dic179—21no—
17C179⋊#95—21no—
18C179⋊#95C2212yes—
19C2×C42×C179C2211yescharacteristic
20C4⋊C8×C179—21no—
21C22⋊C8×C179C2212yes—
22#97×C179—21no—
23C2×Dic358C2×C411yescharacteristic
24C2×D716C2×C411yescharacteristic
25C2×C22⋊D179—21no—
26C22×Dic179—22no—
27C2×C4×D179—21no—
28C4⋊Dic179—42no—
29C4⋊Dic179C2×C411yescharacteristic
30C4⋊Dic179C2×C411yescharacteristic
31Dic179⋊C4—21no—
32Dic179⋊C4—21no—
33Dic179⋊C4—21no—
34Dic179⋊C4—21no—
35C22⋊Dic179—21no—
36(C2×D179)⋊C4—21no—
37(C2×D179)⋊C4—21no—
38(C2×D179)⋊C4—21no—
39(C2×D179)⋊C4—21no—
40C4×Dic179—21no—
41C22×C4×C179D411yescharacteristic
42C22×C4×C179D411yescharacteristic
43C22×C4×C179C2311yescharacteristic
44C2×C8×C179—22no—
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—
57C2×Dic179—42no—
58C2×Dic179—42no—
59C2×Dic179—42no—
60C4×D179—42no—
61C23×C179C2×D411yescharacteristic
62C2×C4×C179—21no—
63C2×C4×C179—21no—
64C2×C4×C179—41no—
65C2×C4×C179—41no—
66C2×C4×C179C22⋊C411yescharacteristic
67C2×C4×C179C22⋊C411yescharacteristic
68C2×C4×C179C22⋊C411yescharacteristic
69C2×C4×C179C22⋊C411yescharacteristic
70C2×C4×C179C22×C411yescharacteristic
71C2×C4×C179C2×D411yescharacteristic
72C8×C179—42no—
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—
87Dic179—41no—
88Dic179—41no—
89Dic179—41no—
90Dic179—82no—
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#432D17911yescharacteristic, complemented
101#382—1791no—
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—3581no—
115C2×C42C2×D17911yescharacteristic
116C4⋊C8—21no—
117C22⋊C8C2×D17912yes—
118#97—21no—
119#95—3581no—
120#95—1792no—
121C2×Q8—1791no—
122C2×D4—3581no—
123C2×D4—1791no—
124C22×C4—3581no—
125C22×C4—3582no—
126C22×C4D71611yescharacteristic
127C22×C4D71611yescharacteristic
128C22×C4C22×D17911yescharacteristic
129C2×C8—22no—
130C4⋊C4—3581no—
131C4⋊C4—3581no—
132C4⋊C4—3581no—
133C4⋊C4—3581no—
134C4⋊C4—1791no—
135C4⋊C4—1791no—
136C4⋊C4—7162no—
137C22⋊C4—3581no—
138C22⋊C4—3581no—
139C22⋊C4—3581no—
140C22⋊C4—3581no—
141C22⋊C4—3581no—
142C42—3581no—
143C42C4×D17911yescharacteristic
144C42C4×D17911yescharacteristic
145C42C22⋊D17911yescharacteristic
146C42C22⋊D17911yescharacteristic
147C23—3581no—
148C23C2×D71611yescharacteristic
149Q8—7161no—
150D4—7161no—
151D4—7161no—
152D4—7161no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—3581no—
158C2×C4—3581no—
159C2×C4—3581no—
160C2×C4—7162no—
161C2×C4—7162no—
162C2×C4—7162no—
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×C22⋊D17911yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—7161no—
174C22—7161no—
175C22—7161no—
176C22C2×(C2×D179)⋊C411yescharacteristic
177C22#1915314111yescharacteristic
178C22#1915314611yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—14322no—
186C4—7161no—
187C4—7161no—
188C4—7161no—
189C2—21no—
190C2—21no—
191C2—14321no—
192C2#2603841211yescharacteristic
193C2#2603844111yescharacteristic
194C2#2603845511yescharacteristic
subgroupG/H
centerC22C2×(C2×D179)⋊C4
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
Fitting#432×C179C2
socleC22×C179C2×C22⋊C4
prime radical#19153087C22
cosocleC22×C4×C179C23
hypercenter#432D179
hypocenterC179#1512
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #26038305C2semidirect
3. #26038177C2semidirect
5. #432×C179C2semidirect
7. #19153105C4semidirect
8. #19153101C4semidirect
12. C4×Dic358C4semidirect
13. C4×D716C4semidirect
97. C179#1512semidirect
100. #432D179semidirect

Maximal subgroups

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

subgroupindex
#260389732
#260383052
#260381772
#260381742
#432×C1792
#1512179