Finite Group Databasebeta

← #37508300

Subgroups — #37508300

Order 22912.

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

normal subgroups only

This group has 206 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#26039193C211yesmaximal, characteristic, complemented
2#26038828C211yesmaximal, characteristic
3#26038805C211yesmaximal, characteristic, complemented
4#26038804C211yesmaximal, characteristic, complemented
5#26038180C211yesmaximal, characteristic, complemented
6#26038178C211yesmaximal, characteristic, complemented
7#330×C179C211yesmaximal, characteristic, complemented
8C2×#15668248—21no—
9C2×D1432—21no—
10#19153112—21no—
11#19153110C2211yescharacteristic
12#19153108—21no—
13#19153108—21no—
14#19153105C2211yescharacteristic
15#19153101C2211yescharacteristic
16#19153098—21no—
17#19153093—21no—
18#19153091—21no—
19#19153035—21no—
20#19153035—21no—
21#19153033—21no—
22#19153033—21no—
23#19153024C2211yescharacteristic
24#125×C179C2211yescharacteristic
25#97×C179C2211yescharacteristic
26#97×C179C2211yescharacteristic
27C2×Dic358—21no—
28C2×Dic358D411yescharacteristic
29C2×D716—21no—
30C2×D716—21no—
31C2×D716—21no—
32C2×D716D411yescharacteristic
33C2×C4×D179—21no—
34#15668248—42no—
35D1432—42no—
36C2×C179⋊C8—21no—
37C4⋊Dic179—21no—
38C4⋊Dic179D411yescharacteristic
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—
47(C2×D179)⋊C4—21no—
48C4×Dic179—21no—
49C2×C8×C179—21no—
50C2×C8×C179—21no—
51C4⋊C4×C179—21no—
52C4⋊C4×C179—21no—
53C4⋊C4×C179D411yescharacteristic
54C4⋊C4×C179D411yescharacteristic
55C42×C179C2311yescharacteristic
56C22×D179—21no—
57C22×D179—41no—
58Dic358—41no—
59Dic358—81no—
60D716—41no—
61D716—41no—
62D716—41no—
63D716—42no—
64D716—42no—
65C2×Dic179—21no—
66C2×Dic179—21no—
67C2×Dic179—21no—
68C4×D179—81no—
69C179⋊C8—41no—
70C2×C4×C179—21no—
71C2×C4×C179—21no—
72C2×C4×C179C2×D411yescharacteristic
73C2×C4×C179C2×D411yescharacteristic
74C2×C4×C179C2×D411yescharacteristic
75C8×C179—22no—
76C8×C179—41no—
77C22×C179#12011yescharacteristic
78C2×D179—41no—
79C2×D179—41no—
80C2×D179—41no—
81C2×D179—81no—
82C2×D179—81no—
83C2×D179—81no—
84C4×C179—21no—
85C4×C179—21no—
86C4×C179—21no—
87C4×C179—41no—
88C4×C179—41no—
89Dic179—41no—
90Dic179—41no—
91Dic179—41no—
92C2×C179#45311yescharacteristic
93C2×C179#45411yescharacteristic
94C2×C179#45411yescharacteristic
95D179—81no—
96D179—161no—
97C179#165711yescharacteristic, complemented, Sylow
98#1657—1791nomaximal, Sylow
99#563—1791no—
100#496—1791no—
101#490—1791no—
102#490—1791no—
103#330—1791no—
104#330D17911yescharacteristic, complemented
105#329—1791no—
106C2×SD16—3581no—
107C2×D8—3581no—
108C4⋊Q8—3581no—
109#127—1791no—
110#126—3581no—
111#126—3581no—
112#125—1791no—
113#125C2×D17911yescharacteristic
114#124—1791no—
115#123—3581no—
116C22⋊Q8—3581no—
117C22⋊Q8—3581no—
118#102—3581no—
119#102—3581no—
120#102—3581no—
121#102—3581no—
122#97—1791no—
123#97C2×D17911yescharacteristic
124#97C2×D17911yescharacteristic
125C2×Q8—3581no—
126C2×Q8—1791no—
127C2×D4—3581no—
128C2×D4—3581no—
129C2×D4—3581no—
130C2×D4—1791no—
131C22×C4—3581no—
132SD16—7162no—
133D8—7162no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—3581no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—3581no—
140C4⋊C4—3581no—
141C4⋊C4—3581no—
142C4⋊C4—3581no—
143C4⋊C4—1791no—
144C4⋊C4—1791no—
145C4⋊C4D71611yescharacteristic
146C4⋊C4D71611yescharacteristic
147C22⋊C4—3581no—
148C22⋊C4—3581no—
149C22⋊C4—3581no—
150C22⋊C4—3581no—
151C22⋊C4—3581no—
152C42—3581no—
153C42C22×D17911yescharacteristic
154C23—3581no—
155C23—7161no—
156Q8—14321no—
157Q8—7161no—
158D4—7161no—
159D4—7161no—
160D4—7162no—
161D4—7162no—
162D4—7161no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—3581no—
166C2×C4—3581no—
167C2×C4—3581no—
168C2×C4—14321no—
169C2×C4D4×D17911yescharacteristic
170C2×C4D4×D17911yescharacteristic
171C2×C4C2×D71611yescharacteristic
172C8—22no—
173C8—41no—
174C8—7161no—
175C22—14321no—
176C22—14321no—
177C22—14321no—
178C22—7161no—
179C22—7161no—
180C22—7161no—
181C22#1915308311yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—7161no—
188C4—7161no—
189C4—7161no—
190C2—28641no—
191C2—14321no—
192C2#2603860811yescharacteristic
193C2#2603861311yescharacteristic
194C2#2603861411yescharacteristic
subgroupG/H
centerC22#19153083
commutator, cosocleC42×C179C23
FrattiniC42C22×D179
Fitting#330×C179C2
socleC22×C179#120
prime radical#26038828C2
hypercenter#330D179
hypocenterC179#1657
LCSG ▷ C42×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #26039193C2semidirect
3. #26038805C2semidirect
4. #26038804C2semidirect
5. #26038180C2semidirect
6. #26038178C2semidirect
7. #330×C179C2semidirect
97. C179#1657semidirect
104. #330D179semidirect

Maximal subgroups

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

subgroupindex
#260391932
#260388282
#260388052
#260388042
#260381802
#260381782
#330×C1792
#1657179