Finite Group Databasebeta

← #37507462

Subgroups — #37507462

Order 22912.

216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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#26038971C211yesmaximal, characteristic
2#26038490C211yesmaximal, characteristic, complemented
3#26038461C211yesmaximal, characteristic, complemented
4#26038171C211yesmaximal, characteristic, complemented
5#26038169C211yesmaximal, characteristic, complemented
6D4⋊(C179⋊C8)C211yesmaximal, characteristic, complemented
7D4⋊C8×C179C211yesmaximal, characteristic, complemented
8C2×#15668242—21no—
9#19153106—21no—
10#19153104C411yescharacteristic
11#19153100C411yescharacteristic
12#19153095—21no—
13#19153093C411yescharacteristic
14#19153084C411yescharacteristic
15C4×Dic358C2211yescharacteristic
16C4×C22⋊D179—21no—
17#19153072—21no—
18C42×D179C2211yescharacteristic
19C4⋊(C179⋊C8)C2211yescharacteristic
20Dic179⋊C8—21no—
21Dic179⋊C8—21no—
22(C2×D179)⋊C8—21no—
23C4×C179⋊C8C2211yescharacteristic
24C4×D4×C179C2211yescharacteristic
25C4⋊C8×C179C2211yescharacteristic
26C4×C8×C179C2211yescharacteristic
27C2×Dic358C2×C411yescharacteristic
28C2×C22⋊D179—21no—
29C2×C4×D179C2×C411yescharacteristic
30C2×C4×D179D411yescharacteristic
31C2×C4×D179D411yescharacteristic
32#15668242—42no—
33C2×C179⋊C8—21no—
34C2×C179⋊C8—21no—
35C4⋊Dic179—21no—
36C4⋊Dic179—21no—
37C4⋊Dic179C2×C411yescharacteristic
38Dic179⋊C4—21no—
39Dic179⋊C4—21no—
40C22⋊Dic179—21no—
41C22⋊Dic179—21no—
42C22⋊Dic179—21no—
43(C2×D179)⋊C4—21no—
44C4×Dic179—21no—
45C4×Dic179C2×C411yescharacteristic
46C4×Dic179D411yescharacteristic
47C4×Dic179D411yescharacteristic
48C2×D4×C179C2×C411yescharacteristic
49C22×C4×C179—21no—
50C2×C8×C179—21no—
51C2×C8×C179—21no—
52C4⋊C4×C179C2×C411yescharacteristic
53C22⋊C4×C179—21no—
54C42×C179C2311yescharacteristic
55C22×D179C22⋊C411yescharacteristic
56Dic358—21no—
57Dic358—21no—
58C22⋊D179—42no—
59C2×Dic179—21no—
60C2×Dic179—21no—
61C2×Dic179C22⋊C411yescharacteristic
62C2×Dic179C22⋊C411yescharacteristic
63C2×Dic179C22⋊C411yescharacteristic
64C4×D179—21no—
65C4×D179—21no—
66C4×D179—21no—
67C4×D179—21no—
68C4×D179—41no—
69C179⋊C8—41no—
70C179⋊C8—41no—
71C23×C179—21no—
72D4×C179—21no—
73D4×C179—21no—
74C2×C4×C179—21no—
75C2×C4×C179—41no—
76C2×C4×C179—41no—
77C2×C4×C179C22×C411yescharacteristic
78C2×C4×C179C2×D411yescharacteristic
79C2×C4×C179C2×D411yescharacteristic
80C8×C179—41no—
81C8×C179—41no—
82C22×C179—41no—
83C22×C179—41no—
84C22×C179—41no—
85C22×C179C2×C22⋊C411yescharacteristic
86C2×D179—21no—
87C2×D179—21no—
88C2×D179—21no—
89C4×C179—21no—
90C4×C179—41no—
91C4×C179#13111yescharacteristic
92C4×C179#13111yescharacteristic
93C4×C179AGL(1,ℤ/8)11yescharacteristic
94C4×C179#13711yescharacteristic
95Dic179—21no—
96Dic179—21no—
97Dic179—21no—
98Dic179—41no—
99Dic179—41no—
100C2×C179—81no—
101C2×C179#40811yescharacteristic
102C2×C179#41711yescharacteristic
103C2×C179#42111yescharacteristic
104D179—41no—
105C179#149511yescharacteristic, complemented, Sylow
106#1495—1791nomaximal, Sylow
107#529—1791no—
108#431—1791no—
109#423—1791no—
110Q8⋊C8—1791no—
111Q8⋊C8—1791no—
112D4⋊C8—1791no—
113D4⋊C8D17911yescharacteristic, complemented
114C2×M16—3581no—
115#126—3581no—
116#125—1791no—
117#124—1791no—
118#123—3581no—
119C22⋊Q8—1791no—
120#121—1791no—
121C4×Q8—1791no—
122C4×D4—3581no—
123C4×D4C2×D17911yescharacteristic
124#117—3581no—
125C2×C42—1791no—
126C4⋊C8—3581no—
127C4⋊C8—3581no—
128C4⋊C8—1791no—
129C4⋊C8C2×D17911yescharacteristic
130C22⋊C8—3581no—
131C4×C8—1791no—
132C4×C8C2×D17911yescharacteristic
133C2×Q8—1791no—
134C2×D4—3581no—
135C2×D4C4×D17911yescharacteristic
136C22×C4—21no—
137C22×C4—1791no—
138C22×C4—1791no—
139C22×C4—1791no—
140M16—7162no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—3581no—
144C2×C8—3581no—
145C4⋊C4—3581no—
146C4⋊C4—3581no—
147C4⋊C4—3581no—
148C4⋊C4—3581no—
149C4⋊C4—1791no—
150C4⋊C4C4×D17911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3581no—
153C22⋊C4—3581no—
154C22⋊C4—3581no—
155C22⋊C4—3581no—
156C42—3581no—
157C42—1791no—
158C42—1791no—
159C42—1791no—
160C42C22×D17911yescharacteristic
161C23—21no—
162C23—1791no—
163Q8—3581no—
164Q8—3581no—
165D4—21no—
166D4—21no—
167D4—7162no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—3581no—
172C2×C4—3581no—
173C2×C4—3581no—
174C2×C4—3581no—
175C2×C4—3581no—
176C2×C4—3581no—
177C2×C4—1791no—
178C2×C4—1791no—
179C2×C4—1791no—
180C2×C4—7161no—
181C2×C4C2×C4×D17911yescharacteristic
182C2×C4D4×D17911yescharacteristic
183C2×C4D4×D17911yescharacteristic
184C8—41no—
185C8—41no—
186C8—7161no—
187C8—7161no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—3581no—
192C22—3581no—
193C22—3581no—
194C22C22⋊C4×D17911yescharacteristic
195C4—21no—
196C4—41no—
197C4—3581no—
198C4—3581no—
199C4—3581no—
200C4—7161no—
201C4—7161no—
202C4#1915311911yescharacteristic
203C4#1915312111yescharacteristic
204C4#1915313711yescharacteristic
205C4#1915314211yescharacteristic
206C2—81no—
207C2—7161no—
208C2#2603840411yescharacteristic
209C2#2603843711yescharacteristic
210C2#2603845411yescharacteristic
subgroupG/H
centerC2×C4D4×D179
commutatorC2×C4×C179C22×C4
FrattiniC42C22×D179
FittingD4⋊C8×C179C2
socleC22×C179C2×C22⋊C4
prime radical#19153084C4
cosocleC42×C179C23
hypercenterD4⋊C8D179
hypocenterC179#1495
LCSG ▷ C2×C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #26038490C2semidirect
3. #26038461C2semidirect
4. #26038171C2semidirect
5. #26038169C2semidirect
6. D4⋊(C179⋊C8)C2semidirect
7. D4⋊C8×C179C2semidirect
105. C179#1495semidirect
113. D4⋊C8D179semidirect

Maximal subgroups

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

subgroupindex
#260389712
#260384902
#260384612
#260381712
#260381692
D4⋊(C179⋊C8)2
D4⋊C8×C1792
#1495179