Finite Group Databasebeta

← #36368996

Subgroups — #36368996

Order 22144.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#26012510C211yesmaximal, characteristic
2#26012435C211yesmaximal, characteristic
3#26012345C212yesmaximal
4#26012344C212yesmaximal
5#26012045C211yesmaximal, characteristic
6C2×C4⋊#10621924—21no—
7C4⋊#13063443—21no—
8#19149736C2212yes—
9C4×#13063443—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—42no—
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—42no—
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—41no—
62C4×D173—41no—
63C4×D173SD1612yes—
64C4×D173Q1612yes—
65Q8×C173—41no—
66C2×C4×C173—21no—
67C2×C4×C173—21no—
68C2×C4×C173C22⋊C411yescharacteristic
69C2×C4×C173C22⋊C411yescharacteristic
70C2×C4×C173C22×C411yescharacteristic
71C22×C173C2×C22⋊C411yescharacteristic
72C2×D173—21no—
73C2×D173—21no—
74C2×D173C2×SD1611yescharacteristic
75C2×D173C2×Q1611yescharacteristic
76#10621924—82no—
77C4×C173—21no—
78C4×C173—21no—
79C4×C173—41no—
80C4×C173—41no—
81C4×C173#10312yes—
82Dic173—21no—
83Dic173—21no—
84Dic173—41no—
85Dic173—41no—
86Dic173#10312yes—
87C2×C173#41011yescharacteristic
88C2×C173C2×#10311yescharacteristic
89C2×C173#42111yescharacteristic
90D173—21no—
91D173—21no—
92C173#151811yescharacteristic, complemented, Sylow
93#1518—1731nomaximal, Sylow
94#533—1731no—
95#431—1731no—
96#382—1731no—
97#328—1732no—
98#328—1732no—
99C4⋊Q8—1731no—
100C4⋊Q8—1731no—
101#125—3461no—
102C22⋊Q8—3461no—
103C22⋊Q8—1731no—
104C22⋊Q8—1731no—
105C4×Q8—3461no—
106C4×Q8—1731no—
107C4×Q8#1062192411yescharacteristic, complemented
108#117—3461no—
109C2×C4⋊C4—3461no—
110C2×C42—1731no—
111C4⋊C8—3461no—
112C22⋊C8—1732no—
113C4×C8—3461no—
114#95—3461no—
115#95—1732no—
116C2×Q8—3461no—
117C2×Q8—1731no—
118C2×Q8C2×#1062192411yescharacteristic
119C22×C4—3462no—
120C22×C4—1731no—
121C22×C4—1731no—
122C22×C4—1731no—
123C2×C8—3462no—
124C4⋊C4—21no—
125C4⋊C4—3461no—
126C4⋊C4—3461no—
127C4⋊C4—3461no—
128C4⋊C4—3461no—
129C4⋊C4—3461no—
130C4⋊C4—3461no—
131C4⋊C4—1731no—
132C4⋊C4—6922no—
133C4⋊C4C2×#1062192411yescharacteristic
134C22⋊C4—3461no—
135C22⋊C4—3461no—
136C42—21no—
137C42—3461no—
138C42—1731no—
139C42—1731no—
140C42—1731no—
141C42C2×#1062192411yescharacteristic
142C23—1731no—
143Q8—41no—
144Q8—6921no—
145Q8—6922no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—3461no—
149C2×C4—3461no—
150C2×C4—1731no—
151C2×C4—1731no—
152C2×C4—1731no—
153C2×C4—1732no—
154C2×C4—1732no—
155C2×C4—6921no—
156C2×C4—6921no—
157C2×C4—6922no—
158C2×C4—6922no—
159C2×C4—6922no—
160C2×C4C22⋊#1062192411yescharacteristic
161C2×C4C22⋊#1062192411yescharacteristic
162C2×C4C22×#1062192411yescharacteristic
163C8—6922no—
164C22—3461no—
165C22—3461no—
166C22—1731no—
167C22—1731no—
168C22C2×C22⋊#1062192411yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—3461no—
174C4—3461no—
175C4—13842no—
176C4—1732no—
177C4—6921no—
178C4—6921no—
179C4#1914974212yes—
180C2—3461no—
181C2—3461no—
182C2#2601247011yescharacteristic
183C2C2×#1914974211yescharacteristic
184C2#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#1518
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
92. C173#1518semidirect
107. C4×Q8#10621924semidirect

Maximal subgroups

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

subgroupindex
#260125102
#260124352
#260123452
#260123442
#260120452
#1518173