Finite Group Databasebeta

← #36369740

Subgroups — #36369740

Order 22144.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#14583836C211yesmaximal, characteristic
2C4×C4⋊#10621924C211yesmaximal, characteristic
3#26012361C212yesmaximal
4#26012361C212yesmaximal
5#26012047C211yesmaximal, characteristic
6C2×#14583836C2212yes—
7C2×C4⋊#10621924—21no—
8C2×C4×#10621924C2212yes—
9#19149734—21no—
10C4×#13063443—21no—
11(C2×#10621924)⋊C4—21no—
12#19149678C411yescharacteristic, complemented
13#19149678C411yescharacteristic, complemented
14#19149671C411yescharacteristic, complemented
15#19149657—21no—
16#19149657—21no—
17#19149644—21no—
18#19149644—21no—
19#19149637C2211yescharacteristic
20#19149637C2211yescharacteristic
21C42×D173C2211yescharacteristic
22#125×C173C411yescharacteristic, complemented
23C22×#10621924—22no—
24#14583836—22no—
25#14583836Q814yescomplemented
26C2×#13063443—22no—
27C4⋊#10621924—24no—
28C4×#10621924—24no—
29C2×Dic346—21no—
30C2×Dic346—21no—
31C2×C4×D173D411yescharacteristic
32C2×C4×D173D411yescharacteristic
33C2×C4×D173C2311yescharacteristic
34C4⋊Dic173C2×C411yescharacteristic
35C4⋊Dic173C2×C411yescharacteristic
36#14583805—21no—
37#14583805—21no—
38#14583805—21no—
39#14583805—21no—
40#14583803—21no—
41#14583803—21no—
42C4×Dic173—21no—
43C4×Dic173—21no—
44C4×Dic173C2×C411yescharacteristic
45C4×Dic173D411yescharacteristic
46C4×Dic173D411yescharacteristic
47C4⋊C4×C173—21no—
48C4⋊C4×C173—21no—
49C4⋊C4×C173C2×C411yescharacteristic
50C4⋊C4×C173C2×C411yescharacteristic
51C42×C173C2×C411yescharacteristic
52C2×#10621924—24no—
53C2×#10621924—42no—
54C2×#10621924—42no—
55#13063443—24no—
56C22×D173C2×D411yescharacteristic
57Dic346—42no—
58Dic346—42no—
59C2×Dic173—21no—
60C2×Dic173—21no—
61C2×Dic173C22⋊C411yescharacteristic
62C2×Dic173C22⋊C411yescharacteristic
63C2×Dic173C2×D411yescharacteristic
64C4×D173—22no—
65C4×D173—41no—
66C4×D173C2×Q812yes—
67C4×D173#4112yes—
68C2×C4×C173—21no—
69C2×C4×C173—21no—
70C2×C4×C173C22⋊C411yescharacteristic
71C2×C4×C173C22⋊C411yescharacteristic
72C2×C4×C173C22×C411yescharacteristic
73C22×C173C2×C22⋊C411yescharacteristic
74C2×D173—21no—
75C2×D173—21no—
76C2×D173#12411yescharacteristic
77C2×D173C4⋊Q811yescharacteristic
78#10621924—44no—
79C4×C173—21no—
80C4×C173—21no—
81C4×C173—41no—
82C4×C173—41no—
83C4×C173C4×Q812yes—
84Dic173—21no—
85Dic173—41no—
86Dic173—41no—
87Dic173#10412yes—
88Dic173C22⋊Q812yes—
89C2×C173#39111yescharacteristic
90C2×C173C2×#10411yescharacteristic
91C2×C173#42111yescharacteristic
92D173—21no—
93D173—21no—
94C173#198611yescharacteristic, complemented, Sylow
95#1986—1731nomaximal, Sylow
96#533—1731no—
97C4×M16—1731no—
98C4×C4⋊C4—1731no—
99#339—1732no—
100#339—1732no—
101C2×M16—1732no—
102C4⋊Q8—1731no—
103C4⋊Q8—1731no—
104#125—1731no—
105#125#1062192411yescharacteristic, complemented
106C22⋊Q8—3461no—
107C22⋊Q8—3461no—
108C4×Q8—3461no—
109C4×Q8—3461no—
110#117—1731no—
111#117—1731no—
112C2×C4⋊C4—3461no—
113C2×C42—1732no—
114C2×C42—1731no—
115#97—3461no—
116C4×C8—3461no—
117#95—3461no—
118C2×Q8—3461no—
119C2×Q8—3461no—
120C22×C4—3462no—
121C22×C4—1731no—
122C22×C4—1731no—
123C22×C4—1731no—
124M16—3462no—
125M16—1734no—
126C2×C8—3462no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—3461no—
130C4⋊C4—3461no—
131C4⋊C4—3464no—
132C4⋊C4—3461no—
133C4⋊C4—3461no—
134C4⋊C4—1731no—
135C4⋊C4—1731no—
136C4⋊C4C2×#1062192411yescharacteristic
137C4⋊C4C2×#1062192411yescharacteristic
138C22⋊C4—3461no—
139C22⋊C4—3461no—
140C42—3461no—
141C42—3461no—
142C42—3464no—
143C42—1731no—
144C42—1731no—
145C42—1731no—
146C42C2×#1062192411yescharacteristic
147C23—1731no—
148Q8—6922no—
149Q8—6922no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—3462no—
153C2×C4—3464no—
154C2×C4—3461no—
155C2×C4—3461no—
156C2×C4—1731no—
157C2×C4—1731no—
158C2×C4—1731no—
159C2×C4—1732no—
160C2×C4—1732no—
161C2×C4—6921no—
162C2×C4—6922no—
163C2×C4—6922no—
164C2×C4C22⋊#1062192411yescharacteristic
165C2×C4C22⋊#1062192411yescharacteristic
166C2×C4C22×#1062192411yescharacteristic
167C8—3464no—
168C22—3461no—
169C22—3461no—
170C22—1731no—
171C22—1731no—
172C22C2×C22⋊#1062192411yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—3461no—
178C4—1732no—
179C4—1732no—
180C4—6924no—
181C4—6921no—
182C4—6921no—
183C4Q8×#1062192412yes—
184C2—3461no—
185C2—3461no—
186C2(C2×#10621924)⋊Q811yescharacteristic
187C2D173⋊#10411yescharacteristic
188C2#2601248811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10621924
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
Fitting#125×C173C4
socleC22×C173C2×C22⋊C4
prime radicalC22×D173C2×D4
cosocleC2×C4×D173C23
hypercenter#125#10621924
hypocenterC173#1986
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #19149678C4semidirect
13. #19149678C4semidirect
14. #19149671C4semidirect
22. #125×C173C4semidirect
25. #14583836Q8semidirect
94. C173#1986semidirect
105. #125#10621924semidirect

Maximal subgroups

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

subgroupindex
C4×#145838362
C4×C4⋊#106219242
#260123612
#260120472
#1986173