Finite Group Databasebeta

← #37507992

Subgroups — #37507992

Order 22912.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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#26039064C211yesmaximal, characteristic
2#26038770C211yesmaximal, characteristic, complemented
3#26038767C211yesmaximal, characteristic, complemented
4#26038366C211yesmaximal, characteristic
5#26038175C211yesmaximal, characteristic, complemented
6#26038162C211yesmaximal, characteristic
7#328×C179C211yesmaximal, characteristic, complemented
8#19153093—21no—
9#19153092C2211yescharacteristic
10#19153091—21no—
11#19153091—21no—
12#19153090—21no—
13#19153089—21no—
14C2×C4⋊Dic179C2211yescharacteristic
15C2×(C2×D179)⋊C4—21no—
16C2×(C2×D179)⋊C4C2211yescharacteristic
17C22⋊C4×D179—21no—
18#19153045—21no—
19#19153044—21no—
20#19153038—21no—
21#19153037—21no—
22C22⋊(C179⋊C8)C2211yescharacteristic
23C179⋊#95—21no—
24C22⋊Q8×C179C2211yescharacteristic
25C22⋊C8×C179C2211yescharacteristic
26#95×C179C2211yescharacteristic
27C23×D179D411yescharacteristic
28C2×Dic358—21no—
29C2×Dic358D411yescharacteristic
30C22×Dic179—21no—
31C22×Dic179D411yescharacteristic
32C2×C4×D179—21no—
33C2×C4×D179—21no—
34C2×C179⋊C8—21no—
35C4⋊Dic179—21no—
36C4⋊Dic179—21no—
37C4⋊Dic179—21no—
38C4⋊Dic179D411yescharacteristic
39Dic179⋊C4—21no—
40Dic179⋊C4—21no—
41Dic179⋊C4—21no—
42C22⋊Dic179—21no—
43(C2×D179)⋊C4—21no—
44(C2×D179)⋊C4—21no—
45(C2×D179)⋊C4—21no—
46(C2×D179)⋊C4—21no—
47(C2×D179)⋊C4—42no—
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—
56C22×D179—21no—
57C22×D179—41no—
58C22×D179—41no—
59C22×D179SD1612yes—
60Dic358—41no—
61Dic358—81no—
62C2×Dic179—21no—
63C2×Dic179—21no—
64C2×Dic179—21no—
65C2×Dic179—41no—
66C2×Dic179—41no—
67C2×Dic179—41no—
68C2×Dic179—41no—
69C4×D179—81no—
70C4×D179—81no—
71C179⋊C8—41no—
72C23×C179C2×D411yescharacteristic
73Q8×C179—41no—
74C2×C4×C179—21no—
75C2×C4×C179—21no—
76C2×C4×C179—41no—
77C2×C4×C179—41no—
78C2×C4×C179—41no—
79C2×C4×C179—41no—
80C2×C4×C179C2×D411yescharacteristic
81C2×C4×C179C2×D411yescharacteristic
82C8×C179—41no—
83C22×C179—21no—
84C22×C179—21no—
85C22×C179#12011yescharacteristic
86C22×C179C2×SD1611yescharacteristic
87C22×C179#13711yescharacteristic
88C2×D179—22no—
89C2×D179—41no—
90C2×D179—41no—
91C2×D179—42no—
92C2×D179—81no—
93C4×C179—21no—
94C4×C179—21no—
95C4×C179—41no—
96C4×C179—41no—
97C4×C179—81no—
98Dic179—41no—
99Dic179—41no—
100Dic179—41no—
101Dic179—81no—
102C2×C179—21no—
103C2×C179—21no—
104C2×C179#44811yescharacteristic
105C2×C179#45511yescharacteristic
106C2×C179#45811yescharacteristic
107D179—42no—
108C179#160811yescharacteristic, complemented, Sylow
109#1608—1791nomaximal, Sylow
110#543—1791no—
111#483—1791no—
112#483—1791no—
113#397—1791no—
114#328—1791no—
115#328D17911yescharacteristic, complemented
116#323—1791no—
117C22⋊Q8—3581no—
118C22⋊Q8—3581no—
119C22⋊Q8—3581no—
120C22⋊Q8—3581no—
121C22⋊Q8—3581no—
122C22⋊Q8—1791no—
123C22⋊Q8C2×D17911yescharacteristic
124C2×C4⋊C4—1791no—
125C2×C22⋊C4—3581no—
126C2×C22⋊C4—3581no—
127C2×C22⋊C4—1791no—
128#106—3581no—
129#106—3581no—
130#103—3581no—
131#103—3581no—
132C22⋊C8—1791no—
133C22⋊C8C2×D17911yescharacteristic
134#95—3581no—
135#95C2×D17911yescharacteristic
136C24—1791no—
137C2×Q8—3581no—
138C2×Q8—1791no—
139C2×Q8D71611yescharacteristic
140C22×C4—21no—
141C22×C4—3581no—
142C22×C4—3581no—
143C22×C4—3581no—
144C22×C4—1791no—
145C22×C4C22×D17911yescharacteristic
146C2×C8—21no—
147C2×C8—3581no—
148C4⋊C4—21no—
149C4⋊C4—3581no—
150C4⋊C4—3581no—
151C4⋊C4—3581no—
152C4⋊C4—3581no—
153C4⋊C4—3581no—
154C4⋊C4—3581no—
155C4⋊C4—1791no—
156C4⋊C4D71611yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—3581no—
159C22⋊C4—3581no—
160C22⋊C4—3581no—
161C22⋊C4—3581no—
162C22⋊C4—3581no—
163C22⋊C4—7162no—
164C23—3581no—
165C23—3581no—
166C23—1792no—
167C23—7161no—
168C23—7161no—
169C23D4×D17911yescharacteristic
170Q8—41no—
171Q8—14321no—
172Q8—7161no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—3581no—
180C2×C4—3581no—
181C2×C4—3581no—
182C2×C4—14321no—
183C2×C4—14321no—
184C2×C4—7161no—
185C2×C4—7161no—
186C2×C4—7161no—
187C2×C4—7161no—
188C2×C4D4×D17911yescharacteristic
189C2×C4C2×D71611yescharacteristic
190C8—41no—
191C8—7161no—
192C22—21no—
193C22—21no—
194C22—3582no—
195C22—14321no—
196C22—7162no—
197C22—7161no—
198C22—7161no—
199C22#1915308311yescharacteristic
200C22SD16×D17911yescharacteristic
201C22#1915314511yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—14321no—
208C4—7161no—
209C4—7161no—
210C4—7161no—
211C2—21no—
212C2—21no—
213C2—7162no—
214C2#2603857911yescharacteristic
215C2#2603861811yescharacteristic
216C2#2603863011yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#328×C179C2
socleC22×C179#120
prime radicalC23×D179D4
hypercenter#328D179
hypocenterC179#1608
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. #26038770C2semidirect
3. #26038767C2semidirect
5. #26038175C2semidirect
7. #328×C179C2semidirect
108. C179#1608semidirect
115. #328D179semidirect

Maximal subgroups

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

subgroupindex
#260390642
#260387702
#260387672
#260383662
#260381752
#260381622
#328×C1792
#1608179