Finite Group Databasebeta

← #37509984

Subgroups — #37509984

Order 22912.

324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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
2C4×C22⋊Dic179C211yesmaximal, characteristic
3#26038205C214yesmaximal
4#380×C179C211yesmaximal, characteristic
5C22×Dic358C411yescharacteristic, complemented
6#19153092—21no—
7#19153092—21no—
8#19153092—21no—
9#19153092—21no—
10C2×C4⋊Dic179C411yescharacteristic, complemented
11C2×Dic179⋊C4C412yescomplemented
12C2×C22⋊Dic179C2212yes—
13C2×C22⋊Dic179C2212yes—
14C2×C4×Dic179—21no—
15C179⋊#95—21no—
16C23×C4×C179C2211yescharacteristic
17C2×C4⋊C4×C179—21no—
18C2×C22⋊C4×C179C2212yes—
19#95×C179—21no—
20C2×Dic358—21no—
21C2×Dic358—21no—
22C2×Dic358—42no—
23C22×Dic179—22no—
24C22×Dic179C2×C412yes—
25C22×Dic179C2×C412yes—
26C4⋊Dic179—21no—
27C4⋊Dic179—21no—
28Dic179⋊C4—22no—
29Dic179⋊C4—22no—
30C22⋊Dic179—22no—
31C22⋊Dic179—22no—
32C22⋊Dic179—22no—
33C22⋊Dic179Q814yescomplemented
34C4×Dic179—42no—
35C24×C179C2311yescharacteristic
36C22×C4×C179—22no—
37C22×C4×C179—42no—
38C22×C4×C179C2×C411yescharacteristic
39C22×C4×C179C2×C411yescharacteristic
40C22×C4×C179D411yescharacteristic
41C22×C4×C179D411yescharacteristic
42C22×C4×C179D411yescharacteristic
43C22×C4×C179D411yescharacteristic
44C4⋊C4×C179—42no—
45C22⋊C4×C179—24no—
46Dic358—42no—
47Dic358—42no—
48C2×Dic179—22no—
49C2×Dic179—22no—
50C2×Dic179—24no—
51C2×Dic179—42no—
52C2×Dic179—42no—
53C2×Dic179—42no—
54C2×Dic179—42no—
55C23×C179—41no—
56C23×C179—41no—
57C23×C179C22×C411yescharacteristic
58C23×C179C2×D411yescharacteristic
59C23×C179C2×D411yescharacteristic
60C23×C179C2×Q812yes—
61C23×C179#4112yes—
62C2×C4×C179—22no—
63C2×C4×C179—22no—
64C2×C4×C179—22no—
65C2×C4×C179—41no—
66C2×C4×C179—41no—
67C2×C4×C179—41no—
68C2×C4×C179—42no—
69C2×C4×C179—42no—
70C2×C4×C179—42no—
71C2×C4×C179C22⋊C411yescharacteristic
72C2×C4×C179C22⋊C411yescharacteristic
73C2×C4×C179C22⋊C411yescharacteristic
74C2×C4×C179C22⋊C411yescharacteristic
75C22×C179—21no—
76C22×C179—21no—
77C22×C179—21no—
78C22×C179—21no—
79C22×C179—21no—
80C22×C179—21no—
81C22×C179—42no—
82C22×C179—42no—
83C22×C179C2×C22⋊C411yescharacteristic
84C22×C179C4×Q812yes—
85C22×C179C22⋊Q812yes—
86C22×C179#12411yescharacteristic
87C22×C179C4⋊Q811yescharacteristic
88C4×C179—21no—
89C4×C179—21no—
90C4×C179—21no—
91C4×C179—82no—
92C4×C179#9912yes—
93Dic179—44no—
94Dic179—42no—
95Dic179—42no—
96C2×C179—22no—
97C2×C179—21no—
98C2×C179—22no—
99C2×C179—21no—
100C2×C179#39111yescharacteristic
101C2×C179C2×#9911yescharacteristic
102C2×C179#41011yescharacteristic
103C179#199611yescharacteristic, complemented, Sylow
104#1996—1791nomaximal, Sylow
105C2×C22⋊Q8—1791no—
106#380D17911yescharacteristic
107C4×C22⋊C4—1791no—
108#342—1794no—
109C22×Q8—1791no—
110C23×C4C2×D17911yescharacteristic
111C22⋊Q8—3581no—
112C22⋊Q8—3581no—
113C22⋊Q8—3581no—
114C22⋊Q8—3581no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—1792no—
117C2×C4⋊C4—1791no—
118C2×C22⋊C4—1792no—
119C2×C22⋊C4—1792no—
120C2×C22⋊C4C2×D17912yes—
121C2×C42—3581no—
122#95—21no—
123#95—3581no—
124C24C22×D17911yescharacteristic
125C2×Q8—3581no—
126C2×Q8—3581no—
127C2×Q8—7162no—
128C22×C4—22no—
129C22×C4—42no—
130C22×C4—3582no—
131C22×C4—1792no—
132C22×C4—1792no—
133C22×C4C4×D17911yescharacteristic
134C22×C4C4×D17911yescharacteristic
135C22×C4C22⋊D17911yescharacteristic
136C22×C4C22⋊D17911yescharacteristic
137C22×C4D71611yescharacteristic
138C22×C4D71611yescharacteristic
139C4⋊C4—42no—
140C4⋊C4—3582no—
141C4⋊C4—3582no—
142C4⋊C4—3581no—
143C4⋊C4—3581no—
144C22⋊C4—24no—
145C22⋊C4—3582no—
146C22⋊C4—3582no—
147C22⋊C4—3582no—
148C22⋊C4—1794no—
149C42—7162no—
150C23—41no—
151C23—41no—
152C23C2×C4×D17911yescharacteristic
153C23C2×C22⋊D17911yescharacteristic
154C23C2×D71611yescharacteristic
155C23Q8×D17912yes—
156C23#1566825812yes—
157Q8—7162no—
158Q8—7162no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—3582no—
169C2×C4—3582no—
170C2×C4—3584no—
171C2×C4—7162no—
172C2×C4—7162no—
173C2×C4—7162no—
174C2×C4—7162no—
175C2×C4(C2×D179)⋊C411yescharacteristic
176C2×C4(C2×D179)⋊C411yescharacteristic
177C2×C4(C2×D179)⋊C411yescharacteristic
178C2×C4(C2×D179)⋊C411yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C2×(C2×D179)⋊C411yescharacteristic
188C22#1915307812yes—
189C22#1915309312yes—
190C22#1915310011yescharacteristic
191C22#1915311111yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—82no—
196C4—7164no—
197C4—7162no—
198C4—7162no—
199C4#1915302712yes—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2#2603834411yescharacteristic
205C2C2×#1915302711yescharacteristic
206C2#2603841211yescharacteristic
subgroupG/H
centerC22C2×(C2×D179)⋊C4
commutatorC23×C179C22×C4
FrattiniC24C22×D179
Fitting#380×C179C2
socleC22×C179C2×C22⋊C4
prime radical, cosocleC24×C179C23
hypercenter#380D179
hypocenterC179#1996
LCSG ▷ C23×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
5. C22×Dic358C4semidirect
10. C2×C4⋊Dic179C4semidirect
11. C2×Dic179⋊C4C4semidirect
33. C22⋊Dic179Q8semidirect
103. C179#1996semidirect

Maximal subgroups

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

subgroupindex
C2×#191530922
C4×C22⋊Dic1792
#260382052
#380×C1792
#1996179