Finite Group Databasebeta

← #36368944

Subgroups — #36368944

Order 22144.

284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 70 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, complemented
2C4×C4⋊#10621924C211yesmaximal, characteristic, complemented
3#26012343C214yesmaximal, complemented
4#26012042C211yesmaximal, characteristic
5C2×C4⋊#10621924—21no—
6C2×C4×#10621924—21no—
7C4⋊#13063443—21no—
8#19149736C2212yes—
9C4×#13063443—21no—
10(C2×#10621924)⋊C4C2212yes—
11C2×#14583827—21no—
12#19149676C411yescharacteristic, complemented
13#19149668—21no—
14#19149654—21no—
15#19149654C2212yes—
16#19149641—21no—
17#19149641C412yescomplemented
18C42×D173C2211yescharacteristic
19C4⋊Q8×C173C411yescharacteristic, complemented
20C22×#10621924—22no—
21C2×#13063443—22no—
22C4⋊#10621924—24no—
23C4×#10621924—42no—
24#14583827—42no—
25#14583827—42no—
26C2×D692—22no—
27C2×D692—21no—
28C2×D692—21no—
29C2×D692C2×C412yes—
30C2×C4×D173—22no—
31C2×C4×D173D411yescharacteristic
32C2×C4×D173D411yescharacteristic
33C2×C4×D173C2311yescharacteristic
34#14583803—22no—
35#14583803—22no—
36C4×Dic173C2×C411yescharacteristic
37C4×Dic173D411yescharacteristic
38C4×Dic173D411yescharacteristic
39C2×Q8×C173—21no—
40C4⋊C4×C173—21no—
41C4⋊C4×C173C2×C412yes—
42C42×C173C2×C411yescharacteristic
43C2×#10621924—24no—
44C2×#10621924—42no—
45C2×#10621924—42no—
46#13063443—42no—
47C22×D173—22no—
48C22×D173C2×D411yescharacteristic
49D692—42no—
50D692—42no—
51D692—42no—
52D692—42no—
53D692—42no—
54C2×Dic173C22⋊C411yescharacteristic
55C2×Dic173C22⋊C411yescharacteristic
56C2×Dic173C2×D411yescharacteristic
57C4×D173—22no—
58C4×D173—41no—
59C4×D173—44no—
60C4×D173D812yes—
61C4×D173SD1612yes—
62Q8×C173—42no—
63C2×C4×C173—22no—
64C2×C4×C173C22⋊C411yescharacteristic
65C2×C4×C173C22⋊C411yescharacteristic
66C2×C4×C173C22×C411yescharacteristic
67C22×C173C2×C22⋊C411yescharacteristic
68C2×D173—21no—
69C2×D173—21no—
70C2×D173—42no—
71C2×D173—42no—
72C2×D173—42no—
73C2×D173C2×D811yescharacteristic
74C2×D173C2×SD1611yescharacteristic
75#10621924—44no—
76C4×C173—21no—
77C4×C173—42no—
78C4×C173#10212yes—
79C4×C173#10412yes—
80Dic173—21no—
81Dic173—21no—
82Dic173#10212yes—
83C2×C173#41011yescharacteristic
84C2×C173C2×#10211yescharacteristic
85C2×C173C2×#10411yescharacteristic
86D173—21no—
87D173—21no—
88D173—82no—
89C173#150211yescharacteristic, complemented, Sylow
90#1502—1731nomaximal, Sylow
91#532—1731no—
92#431—1731no—
93C4×C4⋊C4—1731no—
94#327—1734no—
95C2×#41—3461no—
96C4⋊Q8#1062192411yescharacteristic, complemented
97#127—1731no—
98#124—3461no—
99#121—3461no—
100#121—1732no—
101C4×D4—3461no—
102C4×D4—1732no—
103C2×C4⋊C4—3461no—
104C2×C42—3461no—
105C2×C42—1731no—
106C4⋊C8—3461no—
107C22⋊C8—1732no—
108C4×C8—3461no—
109#95—1732no—
110#41—6922no—
111#41—6922no—
112C2×Q8—21no—
113C2×D4—3462no—
114C2×D4—3461no—
115C2×D4—3461no—
116C2×D4—1732no—
117C22×C4—3462no—
118C22×C4—3462no—
119C22×C4—1731no—
120C22×C4—1731no—
121C22×C4—1731no—
122C2×C8—3462no—
123C4⋊C4—21no—
124C4⋊C4—3464no—
125C4⋊C4C2×#1062192412yes—
126C22⋊C4—3462no—
127C22⋊C4—3462no—
128C42—1731no—
129C42—1731no—
130C42—1731no—
131C42—6922no—
132C42C2×#1062192411yescharacteristic
133C23—3462no—
134C23—1731no—
135Q8—42no—
136D4—6922no—
137D4—6922no—
138D4—6922no—
139D4—6922no—
140D4—6922no—
141C2×C4—22no—
142C2×C4—3462no—
143C2×C4—3464no—
144C2×C4—1731no—
145C2×C4—1731no—
146C2×C4—1731no—
147C2×C4—1732no—
148C2×C4—1732no—
149C2×C4—6921no—
150C2×C4—6924no—
151C2×C4—6922no—
152C2×C4—6922no—
153C2×C4C22⋊#1062192411yescharacteristic
154C2×C4C22⋊#1062192411yescharacteristic
155C2×C4C22×#1062192411yescharacteristic
156C8—6922no—
157C22—3461no—
158C22—3461no—
159C22—1731no—
160C22—1731no—
161C22—6922no—
162C22—6922no—
163C22—6922no—
164C22C2×C22⋊#1062192411yescharacteristic
165C4—21no—
166C4—42no—
167C4—3461no—
168C4—3461no—
169C4—1732no—
170C4—6924no—
171C4#1914974112yes—
172C4#1914974412yes—
173C2—3461no—
174C2—3461no—
175C2—13842no—
176C2#2601247211yescharacteristic
177C2C2×#1914974111yescharacteristic
178C2C2×#1914974411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10621924
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
FittingC4⋊Q8×C173C4
socleC22×C173C2×C22⋊C4
prime radical#26012042C2
cosocleC2×C4×D173C23
hypercenterC4⋊Q8#10621924
hypocenterC173#1502
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
1. #26012510C2semidirect
2. C4×C4⋊#10621924C2semidirect
3. #26012343C2semidirect
12. #19149676C4semidirect
17. #19149641C4semidirect
19. C4⋊Q8×C173C4semidirect
89. C173#1502semidirect
96. C4⋊Q8#10621924semidirect

Maximal subgroups

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

subgroupindex
#260125102
C4×C4⋊#106219242
#260123432
#260120422
#1502173