Finite Group Databasebeta

← #37508006

Subgroups — #37508006

Order 22912.

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

normal subgroups only

This group has 210 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#26039068C211yesmaximal, characteristic
2#26038769C211yesmaximal, characteristic
3#26038370C211yesmaximal, characteristic
4#26038177C211yesmaximal, characteristic
5#26038176C211yesmaximal, characteristic
6#26038164C211yesmaximal, characteristic
7#483×C179C211yesmaximal, characteristic
8#19153112—21no—
9#19153111—21no—
10#19153103—21no—
11#19153103—21no—
12#19153092C2211yescharacteristic
13#19153090—21no—
14#19153069—21no—
15C2×Dic179⋊C4—21no—
16C2×Dic179⋊C4C2211yescharacteristic
17#19153044—21no—
18#19153036—21no—
19C22⋊(C179⋊C8)C2211yescharacteristic
20C179⋊#95—21no—
21C179⋊#95C2211yescharacteristic
22C22⋊Q8×C179C2211yescharacteristic
23C2×C4⋊C4×C179C2211yescharacteristic
24#106×C179—21no—
25#103×C179—21no—
26C22⋊C8×C179C2211yescharacteristic
27C2×Dic358—21no—
28C2×Dic358D411yescharacteristic
29C22×Dic179—21no—
30C22×Dic179D411yescharacteristic
31C22×Dic179D411yescharacteristic
32C2×C179⋊C8—21no—
33C4⋊Dic179—21no—
34C4⋊Dic179D411yescharacteristic
35Dic179⋊C4—21no—
36Dic179⋊C4—21no—
37Dic179⋊C4—21no—
38Dic179⋊C4—21no—
39Dic179⋊C4—21no—
40Dic179⋊C4—21no—
41Dic179⋊C4—21no—
42Dic179⋊C4—42no—
43C22⋊Dic179—21no—
44C4×Dic179—21no—
45C4×Dic179—21no—
46C2×Q8×C179D411yescharacteristic
47C22×C4×C179—21no—
48C22×C4×C179C2311yescharacteristic
49C2×C8×C179—21no—
50C4⋊C4×C179—21no—
51C4⋊C4×C179—21no—
52C4⋊C4×C179—21no—
53C4⋊C4×C179D411yescharacteristic
54C22⋊C4×C179—21no—
55Dic358—41no—
56Dic358—81no—
57C2×Dic179—21no—
58C2×Dic179—21no—
59C2×Dic179—22no—
60C2×Dic179—21no—
61C2×Dic179—21no—
62C2×Dic179—21no—
63C2×Dic179—41no—
64C2×Dic179—41no—
65C2×Dic179—41no—
66C2×Dic179SD1612yes—
67C179⋊C8—41no—
68C23×C179C2×D411yescharacteristic
69Q8×C179—41no—
70C2×C4×C179—21no—
71C2×C4×C179—21no—
72C2×C4×C179—41no—
73C2×C4×C179—41no—
74C2×C4×C179—41no—
75C2×C4×C179—41no—
76C2×C4×C179C2×D411yescharacteristic
77C2×C4×C179C2×D411yescharacteristic
78C8×C179—41no—
79C22×C179—21no—
80C22×C179—21no—
81C22×C179#12011yescharacteristic
82C22×C179C2×SD1611yescharacteristic
83C22×C179#13711yescharacteristic
84C4×C179—21no—
85C4×C179—21no—
86C4×C179—41no—
87C4×C179—41no—
88C4×C179—81no—
89Dic179—22no—
90Dic179—42no—
91Dic179—41no—
92Dic179—41no—
93Dic179—41no—
94C2×C179—21no—
95C2×C179—21no—
96C2×C179#44811yescharacteristic
97C2×C179#45611yescharacteristic
98C2×C179#45811yescharacteristic
99C179#161111yescharacteristic, complemented, Sylow
100#1611—1791nomaximal, Sylow
101#544—1791no—
102#483—1791no—
103#483D17911yescharacteristic
104#398—1791no—
105#328—1791no—
106#328—1791no—
107#324—1791no—
108C4⋊Q8—3581no—
109C4⋊Q8—3581no—
110#125—3581no—
111#125—3581no—
112C22⋊Q8—3581no—
113C22⋊Q8—1791no—
114C22⋊Q8C2×D17911yescharacteristic
115#117—3581no—
116C2×C4⋊C4—3581no—
117C2×C4⋊C4—1791no—
118C2×C4⋊C4C2×D17911yescharacteristic
119#106—21no—
120#106—3581no—
121#103—21no—
122#103—3581no—
123C22⋊C8—1791no—
124C22⋊C8C2×D17911yescharacteristic
125#95—3581no—
126#95—1791no—
127C2×Q8—3581no—
128C2×Q8—1791no—
129C2×Q8C22⋊D17911yescharacteristic
130C22×C4—21no—
131C22×C4—3581no—
132C22×C4—1791no—
133C22×C4—1791no—
134C22×C4C22×D17911yescharacteristic
135C2×C8—21no—
136C2×C8—3581no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—3581no—
141C4⋊C4—3581no—
142C4⋊C4—3581no—
143C4⋊C4—3581no—
144C4⋊C4—3581no—
145C4⋊C4—3581no—
146C4⋊C4—3581no—
147C4⋊C4—3581no—
148C4⋊C4—1791no—
149C4⋊C4—7162no—
150C4⋊C4C22⋊D17911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3581no—
153C42—3581no—
154C42—3581no—
155C23D4×D17911yescharacteristic
156Q8—41no—
157Q8—14321no—
158Q8—7161no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—3581no—
166C2×C4—3581no—
167C2×C4—3582no—
168C2×C4—3581no—
169C2×C4—3581no—
170C2×C4—3581no—
171C2×C4—1792no—
172C2×C4—7161no—
173C2×C4—7161no—
174C2×C4—7161no—
175C2×C4D4×D17911yescharacteristic
176C2×C4C2×C22⋊D17911yescharacteristic
177C8—41no—
178C8—7161no—
179C22—21no—
180C22—21no—
181C22#1915308111yescharacteristic
182C22SD16×D17911yescharacteristic
183C22#1915314211yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—81no—
189C4—3582no—
190C4—7162no—
191C4—7161no—
192C4—7161no—
193C4—7161no—
194C2—21no—
195C2—21no—
196C2#2603857611yescharacteristic
197C2#2603862011yescharacteristic
198C2#2603862811yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#483×C179C2
socleC22×C179#120
prime radicalC23×C179C2×D4
hypercenter#483D179
hypocenterC179#1611
LCSG ▷ C22×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
99. C179#1611semidirect

Maximal subgroups

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

subgroupindex
#260390682
#260387692
#260383702
#260381772
#260381762
#260381642
#483×C1792
#1611179