Finite Group Databasebeta

← #37508294

Subgroups — #37508294

Order 22912.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#26039183C211yesmaximal, characteristic, complemented
2#26038829C211yesmaximal, characteristic, complemented
3#26038828C211yesmaximal, characteristic, complemented
4#26038804C211yesmaximal, characteristic, complemented
5#26038180C211yesmaximal, characteristic, complemented
6#26038178C211yesmaximal, characteristic, complemented
7#329×C179C211yesmaximal, characteristic, complemented
8C2×#15668248—21no—
9C2×#15668246—21no—
10C2×D1432—21no—
11C2×#15668244—21no—
12#19153110C2211yescharacteristic
13#19153105C2211yescharacteristic
14#19153101C2211yescharacteristic
15#19153097—21no—
16#19153095—21no—
17#19153090—21no—
18#19153089—21no—
19#19153086—21no—
20#19153085—21no—
21#19153035—21no—
22#19153035—21no—
23#19153024C2211yescharacteristic
24#124×C179C2211yescharacteristic
25#97×C179C2211yescharacteristic
26#97×C179C2211yescharacteristic
27C2×Dic358D411yescharacteristic
28C2×D716—21no—
29C2×D716—21no—
30C2×D716—21no—
31C2×D716D411yescharacteristic
32C2×C22⋊D179—21no—
33C2×C22⋊D179—21no—
34C22×Dic179—21no—
35C2×C4×D179—21no—
36#15668248—42no—
37#15668246—42no—
38D1432—42no—
39#15668244—42no—
40C2×C179⋊C8—21no—
41C4⋊Dic179—21no—
42C4⋊Dic179D411yescharacteristic
43C4⋊Dic179D411yescharacteristic
44Dic179⋊C4—21no—
45Dic179⋊C4—21no—
46Dic179⋊C4—21no—
47C22⋊Dic179—21no—
48(C2×D179)⋊C4—21no—
49(C2×D179)⋊C4—21no—
50(C2×D179)⋊C4—21no—
51C2×Q8×C179D411yescharacteristic
52C2×D4×C179D411yescharacteristic
53C2×C8×C179—21no—
54C2×C8×C179—21no—
55C22⋊C4×C179—21no—
56C22⋊C4×C179—21no—
57C42×C179C2311yescharacteristic
58C22×D179—21no—
59C22×D179—41no—
60Dic358—41no—
61D716—41no—
62D716—41no—
63D716—41no—
64D716—41no—
65D716—41no—
66D716—42no—
67C22⋊D179—81no—
68C22⋊D179—81no—
69C2×Dic179—21no—
70C2×Dic179—21no—
71C2×Dic179—21no—
72C2×Dic179—81no—
73C4×D179—81no—
74C179⋊C8—22no—
75C23×C179—21no—
76Q8×C179—41no—
77D4×C179—41no—
78C2×C4×C179—21no—
79C2×C4×C179C2×D411yescharacteristic
80C2×C4×C179C2×D411yescharacteristic
81C2×C4×C179C2×D411yescharacteristic
82C8×C179—22no—
83C8×C179—41no—
84C22×C179—41no—
85C22×C179—41no—
86C22×C179—41no—
87C22×C179#12011yescharacteristic
88C2×D179—41no—
89C2×D179—41no—
90C2×D179—41no—
91C2×D179—81no—
92C2×D179—81no—
93C2×D179—81no—
94C4×C179—21no—
95C4×C179—21no—
96C4×C179—21no—
97C4×C179—41no—
98Dic179—41no—
99Dic179—41no—
100Dic179—41no—
101C2×C179—81no—
102C2×C179#45311yescharacteristic
103C2×C179#45311yescharacteristic
104C2×C179#45411yescharacteristic
105D179—81no—
106D179—161no—
107C179#165611yescharacteristic, complemented, Sylow
108#1656—1791nomaximal, Sylow
109#562—1791no—
110#496—1791no—
111#496—1791no—
112#490—1791no—
113#330—1791no—
114#329—1791no—
115#329D17911yescharacteristic, complemented
116C2×SD16—3581no—
117C2×SD16—3581no—
118C2×D8—3581no—
119C2×D8—3581no—
120#127—1791no—
121#125—1791no—
122#124—1791no—
123#124C2×D17911yescharacteristic
124#123—3581no—
125#123—3581no—
126C22⋊Q8—3581no—
127C22⋊Q8—3581no—
128#121—3581no—
129#121—3581no—
130#102—3581no—
131#102—3581no—
132#97—1791no—
133#97C2×D17911yescharacteristic
134#97C2×D17911yescharacteristic
135C2×Q8—1791no—
136C2×Q8D71611yescharacteristic
137C2×D4—3581no—
138C2×D4—3581no—
139C2×D4—3581no—
140C2×D4—3581no—
141C2×D4—3581no—
142C2×D4—1791no—
143C2×D4D71611yescharacteristic
144C22×C4—3581no—
145C22×C4—3581no—
146SD16—7162no—
147SD16—7162no—
148D8—7162no—
149D8—7162no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3581no—
153C4⋊C4—3581no—
154C4⋊C4—3581no—
155C4⋊C4—3581no—
156C4⋊C4—3581no—
157C4⋊C4—1791no—
158C4⋊C4—1791no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—3581no—
162C22⋊C4—3581no—
163C22⋊C4—3581no—
164C22⋊C4—3581no—
165C42C22×D17911yescharacteristic
166C23—21no—
167C23—3581no—
168C23—7161no—
169Q8—41no—
170Q8—7161no—
171D4—41no—
172D4—14321no—
173D4—14321no—
174D4—7161no—
175D4—7161no—
176D4—7161no—
177D4—7161no—
178D4—7162no—
179D4—7161no—
180C2×C4—21no—
181C2×C4—3581no—
182C2×C4—3581no—
183C2×C4—3581no—
184C2×C4—14321no—
185C2×C4—14321no—
186C2×C4D4×D17911yescharacteristic
187C2×C4D4×D17911yescharacteristic
188C2×C4C2×D71611yescharacteristic
189C8—22no—
190C8—41no—
191C8—3582no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—14321no—
196C22—14321no—
197C22—14321no—
198C22—7161no—
199C22—7161no—
200C22—7161no—
201C22#1915308311yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—7161no—
207C4—7161no—
208C4—7161no—
209C2—81no—
210C2—28641no—
211C2—14321no—
212C2#2603860811yescharacteristic
213C2#2603860911yescharacteristic
214C2#2603861311yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#329×C179C2
socleC22×C179#120
hypercenter#329D179
hypocenterC179#1656
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #26039183C2semidirect
2. #26038829C2semidirect
3. #26038828C2semidirect
4. #26038804C2semidirect
5. #26038180C2semidirect
6. #26038178C2semidirect
7. #329×C179C2semidirect
107. C179#1656semidirect
115. #329D179semidirect

Maximal subgroups

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

subgroupindex
#260391832
#260388292
#260388282
#260388042
#260381802
#260381782
#329×C1792
#1656179