Finite Group Databasebeta

← #37508092

Subgroups — #37508092

Order 22912.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#26039094C211yesmaximal, characteristic, complemented
2#26038786C211yesmaximal, characteristic, complemented
3#26038635C211yesmaximal, characteristic, complemented
4#26038634C211yesmaximal, characteristic, complemented
5#26038186C211yesmaximal, characteristic, complemented
6#26038168C211yesmaximal, characteristic, complemented
7D4⋊C8×C179C211yesmaximal, characteristic, complemented
8C2×#15668259—21no—
9C2×D1432—21no—
10C2×#15668244—21no—
11#19153113C2211yescharacteristic
12#19153110C2211yescharacteristic
13#19153095—22no—
14#19153092—21no—
15#19153084—21no—
16C4×D716C2211yescharacteristic
17C4⋊C4×D179—21no—
18C4⋊(C179⋊C8)C2211yescharacteristic
19#19153035—22no—
20#19153035—21no—
21#19153033—21no—
22C4×D4×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24C4×C8×C179C2211yescharacteristic
25#15668259—42no—
26#15668259—42no—
27C2×Dic358—21no—
28C2×D716—21no—
29C2×D716—21no—
30C2×D716—21no—
31C2×D716D411yescharacteristic
32C2×C22⋊D179—22no—
33C2×C4×D179—22no—
34C2×C4×D179—21no—
35D1432—42no—
36#15668244—42no—
37C2×C179⋊C8—21no—
38C4⋊Dic179—21no—
39C4⋊Dic179D411yescharacteristic
40C4⋊Dic179D412yes—
41Dic179⋊C4—22no—
42C22⋊Dic179—22no—
43(C2×D179)⋊C4—21no—
44C2×D4×C179D411yescharacteristic
45C22×C4×C179—21no—
46C2×C8×C179—21no—
47C2×C8×C179—21no—
48C4⋊C4×C179D411yescharacteristic
49C22⋊C4×C179—21no—
50C42×C179C2311yescharacteristic
51C22×D179—21no—
52C22×D179—41no—
53Dic358—41no—
54Dic358—41no—
55D716—21no—
56D716—42no—
57D716—41no—
58D716—41no—
59D716—41no—
60D716—41no—
61D716D812yescomplemented
62C22⋊D179—44no—
63C2×Dic179—21no—
64C2×Dic179—22no—
65C4×D179—44no—
66C4×D179—41no—
67C4×D179—41no—
68C179⋊C8—41no—
69C23×C179—21no—
70D4×C179—21no—
71D4×C179—21no—
72C2×C4×C179—21no—
73C2×C4×C179—41no—
74C2×C4×C179—41no—
75C2×C4×C179C2×D411yescharacteristic
76C2×C4×C179C2×D411yescharacteristic
77C2×C4×C179C2×D411yescharacteristic
78C8×C179—41no—
79C8×C179—41no—
80C22×C179—41no—
81C22×C179—41no—
82C22×C179—41no—
83C22×C179#12011yescharacteristic
84C2×D179—22no—
85C2×D179—41no—
86C2×D179—41no—
87C2×D179—81no—
88C2×D179—81no—
89C2×D179—81no—
90C4×C179—21no—
91C4×C179—41no—
92C4×C179C2×D811yescharacteristic
93C4×C179#13511yescharacteristic
94C4×C179AGL(1,ℤ/8)11yescharacteristic
95C4×C179AGL(1,ℤ/8)11yescharacteristic
96Dic179—42no—
97Dic179—41no—
98C2×C179—81no—
99C2×C179#44711yescharacteristic
100C2×C179#44911yescharacteristic
101C2×C179#45411yescharacteristic
102D179—42no—
103D179—161no—
104C179#162511yescharacteristic, complemented, Sylow
105#1625—1791nomaximal, Sylow
106#547—1791no—
107#486—1791no—
108#459—1791no—
109#459—1791no—
110#332—1791no—
111D4⋊C8—1791no—
112D4⋊C8D17911yescharacteristic, complemented
113C2×#41—3581no—
114C2×D8—3581no—
115C2×D8—3581no—
116C4⋊Q8—1791no—
117#127—1791no—
118#123—3582no—
119C22⋊Q8—3581no—
120#121—3581no—
121C4×D4—1791no—
122C4×D4C2×D17911yescharacteristic
123C2×C4⋊C4—3581no—
124C4⋊C8—1791no—
125C4⋊C8C2×D17911yescharacteristic
126#102—3581no—
127#102—3582no—
128#102—3581no—
129C4×C8C2×D17911yescharacteristic
130#41—7162no—
131#41—7162no—
132C2×Q8—3581no—
133C2×D4—3582no—
134C2×D4—3581no—
135C2×D4—3581no—
136C2×D4—3581no—
137C2×D4—1791no—
138C2×D4D71611yescharacteristic
139C22×C4—21no—
140C22×C4—3582no—
141C22×C4—3581no—
142D8—7162no—
143D8—7162no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—3581no—
147C4⋊C4—3582no—
148C4⋊C4—3581no—
149C4⋊C4—1791no—
150C4⋊C4—1792no—
151C4⋊C4D71611yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3582no—
154C22⋊C4—3581no—
155C42C22×D17911yescharacteristic
156C23—21no—
157C23—3581no—
158C23—7161no—
159Q8—7161no—
160Q8—7161no—
161D4—21no—
162D4—21no—
163D4—3581no—
164D4—1792no—
165D4—7162no—
166D4—7164no—
167D4—7161no—
168D4—7161no—
169D4—7161no—
170D4—7161no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3581no—
175C2×C4—3582no—
176C2×C4—7164no—
177C2×C4—7161no—
178C2×C4—7161no—
179C2×C4D4×D17911yescharacteristic
180C2×C4D4×D17911yescharacteristic
181C2×C4C2×D71611yescharacteristic
182C8—41no—
183C8—41no—
184C8—7161no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—3582no—
189C22—14321no—
190C22—14321no—
191C22—14321no—
192C22—7161no—
193C22—7161no—
194C22#1915308311yescharacteristic
195C4—21no—
196C4—41no—
197C4—7162no—
198C4—7161no—
199C4D8×D17911yescharacteristic
200C4#1915313511yescharacteristic
201C4#1915314011yescharacteristic
202C4#1915314111yescharacteristic
203C2—81no—
204C2—28641no—
205C2—7162no—
206C2#2603857411yescharacteristic
207C2#2603858611yescharacteristic
208C2#2603861311yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
FittingD4⋊C8×C179C2
socleC22×C179#120
hypercenterD4⋊C8D179
hypocenterC179#1625
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #26039094C2semidirect
2. #26038786C2semidirect
3. #26038635C2semidirect
4. #26038634C2semidirect
5. #26038186C2semidirect
6. #26038168C2semidirect
7. D4⋊C8×C179C2semidirect
61. D716D8semidirect
104. C179#1625semidirect
112. D4⋊C8D179semidirect

Maximal subgroups

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

subgroupindex
#260390942
#260387862
#260386352
#260386342
#260381862
#260381682
D4⋊C8×C1792
#1625179