Finite Group Databasebeta

← #37508100

Subgroups — #37508100

Order 22912.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#26039104C211yesmaximal, characteristic, complemented
2#26038636C211yesmaximal, characteristic, complemented
3#26038631C211yesmaximal, characteristic
4#26038185C211yesmaximal, characteristic, complemented
5#26038171C211yesmaximal, characteristic, complemented
6#26038168C211yesmaximal, characteristic, complemented
7#486×C179C211yesmaximal, characteristic, complemented
8C2×Q8×D179—21no—
9C2×#15668247—21no—
10C2×#15668244—21no—
11#19153112—21no—
12#19153091—22no—
13#19153089—21no—
14C4×Dic358C2211yescharacteristic
15C4×D716C2211yescharacteristic
16#19153075—21no—
17C4⋊(C179⋊C8)C2211yescharacteristic
18C4⋊(C179⋊C8)C2211yescharacteristic
19#19153034—21no—
20#19153034—21no—
21C4⋊Q8×C179C2211yescharacteristic
22#127×C179C2211yescharacteristic
23#102×C179—22no—
24C4×C8×C179C2211yescharacteristic
25C2×Dic358—22no—
26C2×Dic358D411yescharacteristic
27Q8×D179—42no—
28Q8×D179—42no—
29C2×D716D411yescharacteristic
30C2×C4×D179—22no—
31C2×C4×D179—21no—
32#15668247—42no—
33#15668244—42no—
34C2×C179⋊C8—21no—
35C2×C179⋊C8—21no—
36C4⋊Dic179D411yescharacteristic
37C4⋊Dic179D411yescharacteristic
38Dic179⋊C4—22no—
39Dic179⋊C4—21no—
40(C2×D179)⋊C4—22no—
41(C2×D179)⋊C4—21no—
42C4×Dic179—21no—
43C2×Q8×C179—21no—
44C2×D4×C179—21no—
45C2×D4×C179—21no—
46C2×D4×C179—21no—
47C2×C8×C179—21no—
48C4⋊C4×C179—21no—
49C4⋊C4×C179D412yes—
50C42×C179C2311yescharacteristic
51C22×D179—21no—
52Dic358—21no—
53Dic358—44no—
54Dic358D812yescomplemented
55D716—21no—
56D716SD1612yescomplemented
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—21no—
60C4×D179—44no—
61C4×D179—41no—
62C4×D179—41no—
63C179⋊C8—41no—
64C179⋊C8—41no—
65C23×C179—41no—
66Q8×C179—41no—
67Q8×C179—41no—
68D4×C179—42no—
69D4×C179—41no—
70D4×C179—41no—
71D4×C179—41no—
72D4×C179—41no—
73C2×C4×C179—22no—
74C2×C4×C179C2×D411yescharacteristic
75C2×C4×C179C2×D411yescharacteristic
76C2×C4×C179C2×D411yescharacteristic
77C8×C179—41no—
78C22×C179—81no—
79C22×C179—81no—
80C22×C179—81no—
81C22×C179#12011yescharacteristic
82C2×D179—22no—
83C2×D179—41no—
84C2×D179—41no—
85C4×C179—21no—
86C4×C179—42no—
87C4×C179C2×D811yescharacteristic
88C4×C179C2×SD1611yescharacteristic
89C4×C179AGL(1,ℤ/8)11yescharacteristic
90C4×C179#13711yescharacteristic
91Dic179—22no—
92Dic179—41no—
93Dic179—41no—
94C2×C179—161no—
95C2×C179#44711yescharacteristic
96C2×C179#44811yescharacteristic
97C2×C179#45411yescharacteristic
98D179—42no—
99C179#162711yescharacteristic, complemented, Sylow
100#1627—1791nomaximal, Sylow
101D4×Q8—1791no—
102#486D17911yescharacteristic, complemented
103#460—1791no—
104#459—1791no—
105#332—1791no—
106Q8⋊C8—1791no—
107D4⋊C8—1791no—
108C22×Q8—3581no—
109C2×SD16—3581no—
110C2×D8—3581no—
111C4⋊Q8—3581no—
112C4⋊Q8C2×D17911yescharacteristic
113#127C2×D17911yescharacteristic
114C22⋊Q8—3581no—
115C22⋊Q8—3582no—
116C4×Q8—1791no—
117C4×D4—3581no—
118C4×D4—1791no—
119C4⋊C8—1791no—
120C4⋊C8—1791no—
121#102—22no—
122#102—3581no—
123#102—3581no—
124C4×C8C2×D17911yescharacteristic
125C2×Q8—21no—
126C2×Q8—3582no—
127C2×Q8—1791no—
128C2×Q8—7162no—
129C2×Q8—7162no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—1791no—
134C22×C4—3582no—
135C22×C4—3581no—
136SD16—7162no—
137D8—7162no—
138C2×C8—21no—
139C2×C8—3581no—
140C2×C8—3581no—
141C4⋊C4—21no—
142C4⋊C4—3582no—
143C4⋊C4—3581no—
144C4⋊C4—1791no—
145C4⋊C4—1791no—
146C4⋊C4C22⋊D17912yes—
147C22⋊C4—3582no—
148C22⋊C4—3581no—
149C42—3581no—
150C42C22×D17911yescharacteristic
151C23—41no—
152C23—3581no—
153Q8—41no—
154Q8—41no—
155Q8—3581no—
156Q8—1792no—
157Q8—7164no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—3581no—
164D4—1792no—
165C2×C4—22no—
166C2×C4—3581no—
167C2×C4—3581no—
168C2×C4—3581no—
169C2×C4—7164no—
170C2×C4—7161no—
171C2×C4—7161no—
172C2×C4D4×D17911yescharacteristic
173C2×C4D4×D17911yescharacteristic
174C2×C4C2×C22⋊D17911yescharacteristic
175C8—41no—
176C8—7161no—
177C8—7161no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—3582no—
182C22—7161no—
183C22—7161no—
184C22#1915308111yescharacteristic
185C4—21no—
186C4—42no—
187C4—3582no—
188C4—7161no—
189C4—7161no—
190C4D8×D17911yescharacteristic
191C4SD16×D17911yescharacteristic
192C4#1915313711yescharacteristic
193C4#1915314211yescharacteristic
194C2—161no—
195C2—7162no—
196C2#2603857111yescharacteristic
197C2#2603857611yescharacteristic
198C2#2603861111yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#486×C179C2
socleC22×C179#120
prime radical#26038631C2
hypercenter#486D179
hypocenterC179#1627
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #26039104C2semidirect
2. #26038636C2semidirect
4. #26038185C2semidirect
5. #26038171C2semidirect
6. #26038168C2semidirect
7. #486×C179C2semidirect
54. Dic358D8semidirect
56. D716SD16semidirect
99. C179#1627semidirect
102. #486D179semidirect

Maximal subgroups

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

subgroupindex
#260391042
#260386362
#260386312
#260381852
#260381712
#260381682
#486×C1792
#1627179