Finite Group Databasebeta

← #37508000

Subgroups — #37508000

Order 22912.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#26039038C211yesmaximal, characteristic
2#26038767C211yesmaximal, characteristic, complemented
3#26038753C211yesmaximal, characteristic
4#26038371C211yesmaximal, characteristic, complemented
5#26038172C211yesmaximal, characteristic
6#26038164C211yesmaximal, characteristic, complemented
7#328×C179C211yesmaximal, characteristic, complemented
8#19153108—21no—
9#19153104—21no—
10#19153098—21no—
11#19153097—21no—
12#19153089—21no—
13#19153087C2211yescharacteristic
14(C22⋊D179)⋊C4—21no—
15C2×C4⋊Dic179—21no—
16C2×C4⋊Dic179C2211yescharacteristic
17C2×Dic179⋊C4C2211yescharacteristic
18#19153047—21no—
19#19153044—21no—
20#19153037—21no—
21#19153035—21no—
22C22⋊(C179⋊C8)C2211yescharacteristic
23C179⋊#95—21no—
24C22⋊Q8×C179C2211yescharacteristic
25C22⋊C8×C179C2211yescharacteristic
26#95×C179C2211yescharacteristic
27C2×D716D411yescharacteristic
28C2×C22⋊D179—21no—
29C22×Dic179—21no—
30C22×Dic179D411yescharacteristic
31C22×Dic179D411yescharacteristic
32C2×C4×D179—21no—
33C2×C179⋊C8—21no—
34C4⋊Dic179—21no—
35C4⋊Dic179—21no—
36C4⋊Dic179—21no—
37C4⋊Dic179—21no—
38C4⋊Dic179—42no—
39C4⋊Dic179D411yescharacteristic
40Dic179⋊C4—21no—
41Dic179⋊C4—21no—
42Dic179⋊C4—21no—
43(C2×D179)⋊C4—21no—
44(C2×D179)⋊C4—21no—
45(C2×D179)⋊C4—21no—
46(C2×D179)⋊C4—21no—
47C4×Dic179—21no—
48C2×Q8×C179D411yescharacteristic
49C22×C4×C179—21no—
50C22×C4×C179C2311yescharacteristic
51C2×C8×C179—21no—
52C4⋊C4×C179—21no—
53C4⋊C4×C179D411yescharacteristic
54C22⋊C4×C179—21no—
55C22×D179—21no—
56D716—41no—
57C22⋊D179—41no—
58C22⋊D179—41no—
59C2×Dic179—21no—
60C2×Dic179—21no—
61C2×Dic179—21no—
62C2×Dic179—21no—
63C2×Dic179—21no—
64C2×Dic179—41no—
65C2×Dic179—41no—
66C2×Dic179—41no—
67C2×Dic179—41no—
68C4×D179—81no—
69C179⋊C8—41no—
70C23×C179C2×D411yescharacteristic
71Q8×C179—41no—
72C2×C4×C179—22no—
73C2×C4×C179—21no—
74C2×C4×C179—21no—
75C2×C4×C179—41no—
76C2×C4×C179—41no—
77C2×C4×C179—41no—
78C2×C4×C179C2×D411yescharacteristic
79C2×C4×C179C2×D411yescharacteristic
80C8×C179—41no—
81C22×C179—21no—
82C22×C179—21no—
83C22×C179#12011yescharacteristic
84C22×C179#13511yescharacteristic
85C22×C179AGL(1,ℤ/8)11yescharacteristic
86C2×D179—41no—
87C2×D179—41no—
88C2×D179—41no—
89C4×C179—21no—
90C4×C179—21no—
91C4×C179—42no—
92C4×C179—41no—
93C4×C179—41no—
94Dic179—41no—
95Dic179—41no—
96Dic179—41no—
97Dic179—81no—
98C2×C179—21no—
99C2×C179—21no—
100C2×C179#44911yescharacteristic
101C2×C179#45611yescharacteristic
102C2×C179#45811yescharacteristic
103D179—81no—
104C179#160911yescharacteristic, complemented, Sylow
105#1609—1791nomaximal, Sylow
106#539—1791no—
107#483—1791no—
108#480—1791no—
109#398—1791no—
110#328D17911yescharacteristic, complemented
111#327—1791no—
112#324—1791no—
113#126—3581no—
114#125—3581no—
115#123—3581no—
116#123—3581no—
117C22⋊Q8—3581no—
118C22⋊Q8C2×D17911yescharacteristic
119#121—1791no—
120C4×D4—3581no—
121C2×C4⋊C4—3581no—
122C2×C4⋊C4—1791no—
123C2×C4⋊C4—1791no—
124#107—3581no—
125#106—3581no—
126#103—3581no—
127#102—3581no—
128C22⋊C8—1791no—
129C22⋊C8C2×D17911yescharacteristic
130#95—3581no—
131#95C2×D17911yescharacteristic
132C2×Q8D71611yescharacteristic
133C2×D4—3581no—
134C2×D4—1791no—
135C22×C4—21no—
136C22×C4—3581no—
137C22×C4—3581no—
138C22×C4—1791no—
139C22×C4—1791no—
140C22×C4C22×D17911yescharacteristic
141C2×C8—21no—
142C2×C8—3581no—
143C4⋊C4—21no—
144C4⋊C4—3581no—
145C4⋊C4—3581no—
146C4⋊C4—3581no—
147C4⋊C4—3581no—
148C4⋊C4—3581no—
149C4⋊C4—3581no—
150C4⋊C4—3581no—
151C4⋊C4—1791no—
152C4⋊C4—7162no—
153C4⋊C4D71611yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—3581no—
156C22⋊C4—3581no—
157C22⋊C4—3581no—
158C22⋊C4—3581no—
159C42—3581no—
160C23—3581no—
161C23D4×D17911yescharacteristic
162Q8—41no—
163D4—7161no—
164D4—7161no—
165D4—7161no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3581no—
173C2×C4—3581no—
174C2×C4—3581no—
175C2×C4—3581no—
176C2×C4—3581no—
177C2×C4—14321no—
178C2×C4—7161no—
179C2×C4—7161no—
180C2×C4—7161no—
181C2×C4—7161no—
182C2×C4D4×D17911yescharacteristic
183C2×C4C2×D71611yescharacteristic
184C8—41no—
185C8—7161no—
186C22—21no—
187C22—21no—
188C22—7161no—
189C22—7161no—
190C22—7161no—
191C22#1915308311yescharacteristic
192C22#1915313611yescharacteristic
193C22#1915314011yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—14321no—
200C4—7161no—
201C4—7161no—
202C4—7161no—
203C2—21no—
204C2—21no—
205C2—14321no—
206C2#2603858711yescharacteristic
207C2#2603862311yescharacteristic
208C2#2603863011yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#328×C179C2
socleC22×C179#120
prime radical#19153087C22
hypercenter#328D179
hypocenterC179#1609
LCSG ▷ C22×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #26038767C2semidirect
4. #26038371C2semidirect
6. #26038164C2semidirect
7. #328×C179C2semidirect
104. C179#1609semidirect
110. #328D179semidirect

Maximal subgroups

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

subgroupindex
#260390382
#260387672
#260387532
#260383712
#260381722
#260381642
#328×C1792
#1609179