Finite Group Databasebeta

← #36368985

Subgroups — #36368985

Order 22144.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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#26012513C211yesmaximal, characteristic
2#26012436C211yesmaximal, characteristic
3#26012345C212yesmaximal
4#26012344C212yesmaximal
5#26012045C211yesmaximal, characteristic
6C4⋊#13063443—21no—
7#19149736C2212yes—
8#19149734—21no—
9(C2×#10621924)⋊C4—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—
25C2×Dic346—21no—
26C2×Dic346C2×C411yescharacteristic
27C2×C4×D173D411yescharacteristic
28C2×C4×D173D411yescharacteristic
29C2×C4×D173C2311yescharacteristic
30C4⋊Dic173—21no—
31C4⋊Dic173C2×C411yescharacteristic
32#14583805—21no—
33#14583805—21no—
34#14583805—21no—
35#14583805—21no—
36#14583805—21no—
37#14583803—21no—
38#14583803—21no—
39C4×Dic173—21no—
40C4×Dic173C2×C411yescharacteristic
41C4×Dic173D411yescharacteristic
42C4×Dic173D411yescharacteristic
43C2×Q8×C173C2×C411yescharacteristic
44C4⋊C4×C173—21no—
45C4⋊C4×C173C2×C411yescharacteristic
46C42×C173—21no—
47C42×C173C2×C411yescharacteristic
48C2×#10621924—42no—
49C2×#10621924—42no—
50C2×#10621924—42no—
51#13063443—42no—
52C22×D173C2×D411yescharacteristic
53Dic346—42no—
54Dic346—41no—
55C2×Dic173—21no—
56C2×Dic173—21no—
57C2×Dic173C22⋊C411yescharacteristic
58C2×Dic173C22⋊C411yescharacteristic
59C2×Dic173C2×D411yescharacteristic
60C4×D173—22no—
61C4×D173—41no—
62C4×D173—41no—
63Q8×C173—41no—
64C2×C4×C173—21no—
65C2×C4×C173—21no—
66C2×C4×C173C22⋊C411yescharacteristic
67C2×C4×C173C22⋊C411yescharacteristic
68C2×C4×C173C22×C411yescharacteristic
69C22×C173C2×C22⋊C411yescharacteristic
70C2×D173—21no—
71C2×D173—21no—
72C2×D173#13712yes—
73#10621924—82no—
74C4×C173—21no—
75C4×C173—21no—
76C4×C173—21no—
77C4×C173—41no—
78C4×C173—41no—
79Dic173—21no—
80Dic173—21no—
81Dic173—21no—
82Dic173—41no—
83Dic173—41no—
84C2×C173#41011yescharacteristic
85C2×C173#41911yescharacteristic
86C2×C173#42111yescharacteristic
87D173—22no—
88C173#151511yescharacteristic, complemented, Sylow
89#1515—1731nomaximal, Sylow
90#533—1731no—
91#432—1731no—
92#383—1731no—
93#328—1732no—
94#328—1732no—
95C4⋊Q8—1731no—
96C4⋊Q8—1731no—
97#125—3461no—
98C22⋊Q8—3461no—
99C22⋊Q8—1731no—
100C22⋊Q8—1731no—
101C4×Q8—3461no—
102C4×Q8—1731no—
103C4×Q8#1062192411yescharacteristic, complemented
104#117—3461no—
105C2×C42—1731no—
106C4⋊C8—3461no—
107C22⋊C8—1732no—
108#97—3461no—
109#95—3461no—
110#95—3461no—
111#95—1732no—
112C2×Q8—3461no—
113C2×Q8—1731no—
114C2×Q8C2×#1062192411yescharacteristic
115C22×C4—3462no—
116C22×C4—1731no—
117C22×C4—1731no—
118C22×C4—1731no—
119C2×C8—3462no—
120C4⋊C4—21no—
121C4⋊C4—3461no—
122C4⋊C4—3461no—
123C4⋊C4—3461no—
124C4⋊C4—3461no—
125C4⋊C4—3461no—
126C4⋊C4—3461no—
127C4⋊C4—1731no—
128C4⋊C4C2×#1062192411yescharacteristic
129C22⋊C4—3461no—
130C22⋊C4—3461no—
131C42—21no—
132C42—3461no—
133C42—1731no—
134C42—1731no—
135C42—1731no—
136C42C2×#1062192411yescharacteristic
137C23—1731no—
138Q8—41no—
139Q8—6921no—
140Q8—6922no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—3462no—
144C2×C4—3461no—
145C2×C4—3461no—
146C2×C4—1731no—
147C2×C4—1731no—
148C2×C4—1731no—
149C2×C4—6921no—
150C2×C4—6921no—
151C2×C4—6922no—
152C2×C4—6922no—
153C2×C4—6922no—
154C2×C4C22⋊#1062192411yescharacteristic
155C2×C4C22⋊#1062192411yescharacteristic
156C2×C4C22×#1062192411yescharacteristic
157C8—6922no—
158C22—3461no—
159C22—3461no—
160C22—1732no—
161C22C2×C22⋊#1062192411yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—3461no—
168C4—3461no—
169C4—3461no—
170C4—13842no—
171C4—6921no—
172C4—6921no—
173C2—3462no—
174C2#2601247011yescharacteristic
175C2#2601248411yescharacteristic
176C2#2601248811yescharacteristic
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#1515
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
88. C173#1515semidirect
103. C4×Q8#10621924semidirect

Maximal subgroups

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

subgroupindex
#260125132
#260124362
#260123452
#260123442
#260120452
#1515173