Finite Group Databasebeta

← #36368956

Subgroups — #36368956

Order 22144.

228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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#26012514C211yesmaximal, characteristic
2#26012427C211yesmaximal, characteristic
3#26012345C212yesmaximal
4#26012344C212yesmaximal
5#26012045C211yesmaximal, characteristic
6C2×C4×#10621924—21no—
7#19149746—21no—
8#19149736C2212yes—
9#19149734—21no—
10(C2×#10621924)⋊C4—21no—
11(C2×#10621924)⋊C4C2212yes—
12#19149678C411yescharacteristic, complemented
13#19149677C411yescharacteristic, complemented
14#19149669—21no—
15#19149659C2211yescharacteristic
16#19149657—21no—
17#19149655C2211yescharacteristic
18C4×Dic346—21no—
19C4×Dic346C411yescharacteristic, complemented
20#19149636—21no—
21C42×D173C2211yescharacteristic
22C4×Q8×C173C411yescharacteristic, complemented
23C22×#10621924—22no—
24C2×#13063443—22no—
25C4×#10621924—24no—
26C2×Dic346—21no—
27C2×Dic346C2×C411yescharacteristic
28C2×C4×D173D411yescharacteristic
29C2×C4×D173D411yescharacteristic
30C2×C4×D173C2311yescharacteristic
31C4⋊Dic173—21no—
32C4⋊Dic173C2×C411yescharacteristic
33#14583805—21no—
34#14583805—21no—
35#14583805—21no—
36#14583805—21no—
37#14583805—21no—
38#14583803—21no—
39#14583803—21no—
40C4×Dic173—21no—
41C4×Dic173C2×C411yescharacteristic
42C4×Dic173D411yescharacteristic
43C4×Dic173D411yescharacteristic
44C2×Q8×C173C2×C411yescharacteristic
45C4⋊C4×C173—21no—
46C4⋊C4×C173C2×C411yescharacteristic
47C42×C173—21no—
48C42×C173C2×C411yescharacteristic
49C2×#10621924—24no—
50C2×#10621924—42no—
51C2×#10621924—42no—
52#13063443—42no—
53C22×D173C2×D411yescharacteristic
54Dic346—42no—
55Dic346—41no—
56C2×Dic173—21no—
57C2×Dic173—21no—
58C2×Dic173C22⋊C411yescharacteristic
59C2×Dic173C22⋊C411yescharacteristic
60C2×Dic173C2×D411yescharacteristic
61C4×D173—22no—
62C4×D173—22no—
63C4×D173—41no—
64Q8×C173—41no—
65C2×C4×C173—21no—
66C2×C4×C173—21no—
67C2×C4×C173C22⋊C411yescharacteristic
68C2×C4×C173C22⋊C411yescharacteristic
69C2×C4×C173C22×C411yescharacteristic
70C22×C173C2×C22⋊C411yescharacteristic
71C2×D173—21no—
72C2×D173—21no—
73C2×D173#13712yes—
74#10621924—44no—
75C4×C173—21no—
76C4×C173—21no—
77C4×C173—21no—
78C4×C173—41no—
79C4×C173—41no—
80Dic173—21no—
81Dic173—21no—
82Dic173—41no—
83Dic173—41no—
84Dic173#10412yes—
85C2×C173#41011yescharacteristic
86C2×C173#41911yescharacteristic
87C2×C173C2×#10411yescharacteristic
88D173—22no—
89C173#150611yescharacteristic, complemented, Sylow
90#1506—1731nomaximal, Sylow
91#533—1731no—
92#432—1731no—
93#376—1731no—
94#328—1732no—
95#328—1732no—
96C4⋊Q8—1731no—
97C4⋊Q8—1731no—
98#125—3461no—
99C22⋊Q8—3461no—
100C22⋊Q8—1731no—
101C22⋊Q8—1731no—
102C4×Q8—3461no—
103C4×Q8—1731no—
104C4×Q8#1062192411yescharacteristic, complemented
105#117—3461no—
106C2×C42—3461no—
107C2×C42—1731no—
108C4⋊C8—3461no—
109C22⋊C8—1732no—
110#97—3461no—
111#95—3461no—
112#95—1732no—
113C2×Q8—3461no—
114C2×Q8—1731no—
115C2×Q8C2×#1062192411yescharacteristic
116C22×C4—3462no—
117C22×C4—1731no—
118C22×C4—1731no—
119C22×C4—1731no—
120C2×C8—3462no—
121C4⋊C4—21no—
122C4⋊C4—3461no—
123C4⋊C4—3461no—
124C4⋊C4—3461no—
125C4⋊C4—3461no—
126C4⋊C4—3461no—
127C4⋊C4—3461no—
128C4⋊C4—1731no—
129C4⋊C4C2×#1062192411yescharacteristic
130C22⋊C4—3461no—
131C22⋊C4—3461no—
132C42—21no—
133C42—3464no—
134C42—3461no—
135C42—1731no—
136C42—1731no—
137C42—1731no—
138C42C2×#1062192411yescharacteristic
139C23—1731no—
140Q8—41no—
141Q8—6921no—
142Q8—6922no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—3462no—
146C2×C4—3462no—
147C2×C4—3464no—
148C2×C4—3461no—
149C2×C4—3461no—
150C2×C4—1731no—
151C2×C4—1731no—
152C2×C4—1731no—
153C2×C4—6921no—
154C2×C4—6922no—
155C2×C4—6922no—
156C2×C4C22⋊#1062192411yescharacteristic
157C2×C4C22⋊#1062192411yescharacteristic
158C2×C4C22×#1062192411yescharacteristic
159C8—6922no—
160C22—3461no—
161C22—3461no—
162C22—1732no—
163C22C2×C22⋊#1062192411yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—3461no—
170C4—3461no—
171C4—1732no—
172C4—6924no—
173C4—6921no—
174C4—6921no—
175C2—3462no—
176C2#2601247011yescharacteristic
177C2#2601248411yescharacteristic
178C2D173⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10621924
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
FittingC4×Q8×C173C4
socleC22×C173C2×C22⋊C4
prime radicalC22×D173C2×D4
cosocleC2×C4×D173C23
hypercenterC4×Q8#10621924
hypocenterC173#1506
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #19149678C4semidirect
13. #19149677C4semidirect
19. C4×Dic346C4semidirect
22. C4×Q8×C173C4semidirect
89. C173#1506semidirect
104. C4×Q8#10621924semidirect

Maximal subgroups

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

subgroupindex
#260125142
#260124272
#260123452
#260123442
#260120452
#1506173