Finite Group Databasebeta

← #37508088

Subgroups — #37508088

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#26038785C211yesmaximal, characteristic, complemented
3#26038631C211yesmaximal, characteristic, complemented
4#26038184C211yesmaximal, characteristic, complemented
5D4⋊(C179⋊C8)C211yesmaximal, characteristic, complemented
6#26038166C211yesmaximal, characteristic, complemented
7#459×C179C211yesmaximal, characteristic, complemented
8C2×#15668259—21no—
9C2×#15668244—21no—
10#19153113C2211yescharacteristic
11#19153095—22no—
12#19153092—21no—
13#19153084—21no—
14C4×D716C2211yescharacteristic
15C4⋊C4×D179—21no—
16C4⋊(C179⋊C8)C2211yescharacteristic
17#19153034—22no—
18#19153034—21no—
19C4×C179⋊C8C2211yescharacteristic
20C2×D8×C179—21no—
21#127×C179C2211yescharacteristic
22C4×D4×C179C2211yescharacteristic
23C4⋊C8×C179C2211yescharacteristic
24#102×C179—21no—
25#15668259—42no—
26#15668259—42no—
27C2×Dic358—21no—
28C2×D716D411yescharacteristic
29C2×C22⋊D179—22no—
30C2×C4×D179—22no—
31C2×C4×D179—21no—
32#15668244—42no—
33C2×C179⋊C8—21no—
34C2×C179⋊C8—21no—
35C4⋊Dic179—21no—
36C4⋊Dic179D411yescharacteristic
37C4⋊Dic179D412yes—
38Dic179⋊C4—22no—
39C22⋊Dic179—22no—
40(C2×D179)⋊C4—21no—
41C2×D4×C179—21no—
42C2×D4×C179—21no—
43C2×D4×C179—21no—
44C2×D4×C179D411yescharacteristic
45C22×C4×C179—21no—
46D8×C179—42no—
47C2×C8×C179—21no—
48C4⋊C4×C179D411yescharacteristic
49C22⋊C4×C179—21no—
50C42×C179C2311yescharacteristic
51C22×D179—21no—
52Dic358—41no—
53Dic358—41no—
54D716—21no—
55D716D812yescomplemented
56C22⋊D179—44no—
57C2×Dic179—21no—
58C2×Dic179—22no—
59C4×D179—44no—
60C4×D179—41no—
61C4×D179—41no—
62C179⋊C8—41no—
63C179⋊C8—41no—
64C23×C179—21no—
65C23×C179—41no—
66D4×C179—21no—
67D4×C179—21no—
68D4×C179—42no—
69D4×C179—41no—
70D4×C179—41no—
71D4×C179—41no—
72D4×C179—41no—
73C2×C4×C179—21no—
74C2×C4×C179—41no—
75C2×C4×C179—41no—
76C2×C4×C179C2×D411yescharacteristic
77C2×C4×C179C2×D411yescharacteristic
78C2×C4×C179C2×D411yescharacteristic
79C8×C179—41no—
80C22×C179—41no—
81C22×C179—41no—
82C22×C179—41no—
83C22×C179—81no—
84C22×C179—81no—
85C22×C179—81no—
86C22×C179#12011yescharacteristic
87C2×D179—22no—
88C2×D179—41no—
89C2×D179—41no—
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—161no—
100C2×C179#44711yescharacteristic
101C2×C179#44911yescharacteristic
102C2×C179#45411yescharacteristic
103D179—42no—
104C179#162511yescharacteristic, complemented, Sylow
105#1625—1791nomaximal, Sylow
106#547—1791no—
107#486—1791no—
108#459—1791no—
109#459D17911yescharacteristic, complemented
110#332—1791no—
111D4⋊C8—1791no—
112D4⋊C8—1791no—
113C2×#41—3581no—
114C2×D8—21no—
115C2×D8—3581no—
116C4⋊Q8—1791no—
117#127C2×D17911yescharacteristic
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—21no—
127#102—3581no—
128#102—3582no—
129C4×C8—1791no—
130#41—7162no—
131#41—7162no—
132C2×Q8—3581no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—3582no—
137C2×D4—1791no—
138C2×D4C22⋊D17911yescharacteristic
139C22×C4—21no—
140C22×C4—3582no—
141C22×C4—3581no—
142D8—42no—
143D8—7162no—
144C2×C8—21no—
145C2×C8—3581no—
146C2×C8—3581no—
147C4⋊C4—3582no—
148C4⋊C4—3581no—
149C4⋊C4—1791no—
150C4⋊C4—1792no—
151C4⋊C4C22⋊D17911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3582no—
154C22⋊C4—3581no—
155C42C22×D17911yescharacteristic
156C23—21no—
157C23—41no—
158C23—3581no—
159Q8—7161no—
160Q8—7161no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—3581no—
169D4—1792no—
170D4—7164no—
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×C22⋊D17911yescharacteristic
182C8—41no—
183C8—7161no—
184C8—7161no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—3582no—
192C22—7161no—
193C22—7161no—
194C22#1915308111yescharacteristic
195C4—21no—
196C4—41no—
197C4—7162no—
198C4—7161no—
199C4D8×D17911yescharacteristic
200C4#1915313311yescharacteristic
201C4#1915313711yescharacteristic
202C4#1915313911yescharacteristic
203C2—81no—
204C2—161no—
205C2—7162no—
206C2#2603857111yescharacteristic
207C2#2603858211yescharacteristic
208C2#2603861011yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#459×C179C2
socleC22×C179#120
hypercenter#459D179
hypocenterC179#1625
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #26039094C2semidirect
2. #26038785C2semidirect
3. #26038631C2semidirect
4. #26038184C2semidirect
5. D4⋊(C179⋊C8)C2semidirect
6. #26038166C2semidirect
7. #459×C179C2semidirect
55. D716D8semidirect
104. C179#1625semidirect
109. #459D179semidirect

Maximal subgroups

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

subgroupindex
#260390942
#260387852
#260386312
#260381842
D4⋊(C179⋊C8)2
#260381662
#459×C1792
#1625179