Finite Group Databasebeta

← #37507519

Subgroups — #37507519

Order 22912.

294 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×#19153092C211yesmaximal, characteristic
2#26038403C211yesmaximal, characteristic
3#26038175C214yesmaximal, complemented
4C4×C22⋊C4×C179C211yesmaximal, characteristic
5C22×Dic358C411yescharacteristic, complemented
6C2×#15668243—21no—
7#19153092—21no—
8#19153092—21no—
9#19153092C412yescomplemented
10#19153092C2212yes—
11C2×C4⋊Dic179C411yescharacteristic, complemented
12C2×Dic179⋊C4—21no—
13C2×C22⋊Dic179—21no—
14C22⋊(C179⋊C8)—21no—
15C22⋊(C179⋊C8)C2212yes—
16C23×C4×C179C2211yescharacteristic
17C2×C22⋊C4×C179—21no—
18C2×C42×C179—21no—
19#95×C179C2212yes—
20C2×Dic358—21no—
21C2×Dic358—42no—
22C2×Dic358C2×C412yes—
23C22×Dic179—21no—
24C22×Dic179—21no—
25#15668243—42no—
26C2×C179⋊C8—22no—
27C4⋊Dic179—21no—
28C4⋊Dic179C2×C412yes—
29Dic179⋊C4—22no—
30Dic179⋊C4—22no—
31C22⋊Dic179—22no—
32C22⋊Dic179—22no—
33C24×C179D411yescharacteristic
34C22×C4×C179—22no—
35C22×C4×C179—42no—
36C22×C4×C179C2×C411yescharacteristic
37C22×C4×C179C2×C411yescharacteristic
38C22×C4×C179D411yescharacteristic
39C22×C4×C179D411yescharacteristic
40C22×C4×C179D411yescharacteristic
41C22×C4×C179C2311yescharacteristic
42C22⋊C4×C179—24no—
43C42×C179—42no—
44Dic358—42no—
45Dic358—42no—
46C2×Dic179—22no—
47C2×Dic179—22no—
48C2×Dic179—42no—
49C2×Dic179—42no—
50C179⋊C8—42no—
51C23×C179—22no—
52C23×C179—22no—
53C23×C179—41no—
54C23×C179C22⋊C411yescharacteristic
55C23×C179C22⋊C411yescharacteristic
56C23×C179C2×D411yescharacteristic
57C2×C4×C179—22no—
58C2×C4×C179—22no—
59C2×C4×C179—22no—
60C2×C4×C179—24no—
61C2×C4×C179—41no—
62C2×C4×C179—41no—
63C2×C4×C179—41no—
64C2×C4×C179—42no—
65C2×C4×C179—42no—
66C2×C4×C179C22⋊C411yescharacteristic
67C2×C4×C179C22⋊C411yescharacteristic
68C2×C4×C179C22×C411yescharacteristic
69C2×C4×C179C2×D411yescharacteristic
70C22×C179—21no—
71C22×C179—21no—
72C22×C179—21no—
73C22×C179—21no—
74C22×C179—21no—
75C22×C179—21no—
76C22×C179—21no—
77C22×C179—44no—
78C22×C179#10412yes—
79C22×C179C2×C22⋊C411yescharacteristic
80C22×C179#13712yes—
81C4×C179—21no—
82C4×C179—21no—
83C4×C179—21no—
84C4×C179—44no—
85C4×C179#9912yes—
86Dic179—42no—
87Dic179—42no—
88C2×C179—22no—
89C2×C179—22no—
90C2×C179—41no—
91C2×C179C2×#9911yescharacteristic
92C2×C179#41911yescharacteristic
93C2×C179C2×#10411yescharacteristic
94C179#150811yescharacteristic, complemented, Sylow
95#1508—1791nomaximal, Sylow
96C2×C22⋊Q8—1791no—
97#407—1791no—
98C4×C22⋊C4D17911yescharacteristic
99#328—1794no—
100C22×Q8—1791no—
101C23×C4C2×D17911yescharacteristic
102C2×M16—3581no—
103C22⋊Q8—3581no—
104C22⋊Q8—3581no—
105C22⋊Q8—1792no—
106C22⋊Q8—1792no—
107C2×C4⋊C4—3581no—
108C2×C4⋊C4—1791no—
109C2×C22⋊C4—21no—
110C2×C22⋊C4—3581no—
111C2×C42—21no—
112C22⋊C8—3581no—
113C22⋊C8—1792no—
114#95C2×D17912yes—
115C24C22⋊D17911yescharacteristic
116C2×Q8—3581no—
117C2×Q8—1792no—
118C2×Q8—7162no—
119C22×C4—22no—
120C22×C4—42no—
121C22×C4—3581no—
122C22×C4—3581no—
123C22×C4C4×D17911yescharacteristic
124C22×C4C4×D17911yescharacteristic
125C22×C4C22⋊D17911yescharacteristic
126C22×C4D71611yescharacteristic
127C22×C4D71611yescharacteristic
128C22×C4C22×D17911yescharacteristic
129M16—7162no—
130C2×C8—3582no—
131C4⋊C4—3582no—
132C4⋊C4—3581no—
133C4⋊C4—3582no—
134C4⋊C4—1792no—
135C22⋊C4—24no—
136C22⋊C4—3582no—
137C22⋊C4—3582no—
138C42—42no—
139C23—22no—
140C23—22no—
141C23—41no—
142C23(C2×D179)⋊C411yescharacteristic
143C23(C2×D179)⋊C411yescharacteristic
144C23C2×C22⋊D17911yescharacteristic
145Q8—7162no—
146Q8—7162no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—3582no—
157C2×C4—3582no—
158C2×C4—7162no—
159C2×C4—7162no—
160C2×C4(C2×D179)⋊C411yescharacteristic
161C2×C4(C2×D179)⋊C411yescharacteristic
162C2×C4C2×C4×D17911yescharacteristic
163C2×C4C2×D71611yescharacteristic
164C8—7162no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—44no—
173C22#1915304112yes—
174C22C2×(C2×D179)⋊C411yescharacteristic
175C22#1915314312yes—
176C4—21no—
177C4—21no—
178C4—21no—
179C4—44no—
180C4—7162no—
181C4—7162no—
182C4#1915302712yes—
183C2—22no—
184C2—22no—
185C2—41no—
186C2C2×#1915302711yescharacteristic
187C2#2603844711yescharacteristic
188C2C2×#1915304111yescharacteristic
subgroupG/H
centerC22C2×(C2×D179)⋊C4
commutatorC2×C4×C179C22×C4
FrattiniC22×C4C22×D179
FittingC4×C22⋊C4×C179C2
socleC22×C179C2×C22⋊C4
prime radicalC24×C179D4
cosocleC22×C4×C179C23
hypercenterC4×C22⋊C4D179
hypocenterC179#1508
LCSG ▷ C2×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #26038175C2semidirect
5. C22×Dic358C4semidirect
9. #19153092C4semidirect
11. C2×C4⋊Dic179C4semidirect
94. C179#1508semidirect

Maximal subgroups

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

subgroupindex
C2×#191530922
#260384032
#260381752
C4×C22⋊C4×C1792
#1508179