Finite Group Databasebeta

← #34036772

Subgroups — #34036772

Order 18752.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C2×#17989803C211yesmaximal, characteristic, complemented
2C2×D4×D293C211yesmaximal, characteristic, complemented
3#22627606C212yesmaximal, complemented
4#22627600C211yesmaximal, characteristic, complemented
5#22627597C212yesmaximal, complemented
6#22627595C211yesmaximal, characteristic, complemented
7#22627594C212yesmaximal, complemented
8C4×D1172C211yesmaximal, characteristic, complemented
9C4×D1172C211yesmaximal, characteristic, complemented
10C22⋊C4×D293C212yesmaximal, complemented
11#124×C293C211yesmaximal, characteristic, complemented
12C23×D293C2212yes—
13#17989803—24no—
14C2×D1172C2211yescharacteristic
15C2×D1172C2211yescharacteristic
16C2×D1172C2212yescomplemented
17C2×C22⋊D293C2212yes—
18C2×C22⋊D293C2212yescomplemented
19D4×D293—24no—
20C2×C4×D293C2211yescharacteristic
21C2×C4×D293C2211yescharacteristic, complemented
22C2×C4×D293C2212yescomplemented
23C2×C4×D293C2212yescomplemented
24C4⋊Dic293C2211yescharacteristic, complemented
25C4⋊Dic293C2211yescharacteristic, complemented
26#17989781C2212yescomplemented
27C22⋊Dic293C2212yescomplemented
28#17989779C2211yescharacteristic
29#17989779C2212yes—
30#17989779C2212yescomplemented
31#17989779C2211yescharacteristic, complemented
32C2×Q8×C293C2211yescharacteristic, complemented
33C2×D4×C293C2211yescharacteristic
34C22⋊C4×C293C2212yescomplemented
35C22⋊C4×C293C2212yescomplemented
36C42×C293C2211yescharacteristic, complemented
37C22×D293—24no—
38C22×D293—24no—
39C22×D293—42no—
40C22×D293C2311yescharacteristic
41C22×D293C2312yes—
42C22×D293C2311yescharacteristic
43D1172—24no—
44D1172—22no—
45D1172D414yescomplemented
46C22⋊D293—24no—
47C22⋊D293—42no—
48C2×Dic293C2312yes—
49C2×Dic293C2311yescharacteristic
50C2×Dic293C2311yescharacteristic
51C4×D293—24no—
52C4×D293—22no—
53C4×D293—22no—
54C4×D293—42no—
55C23×C293C2312yes—
56Q8×C293—22no—
57D4×C293—22no—
58C2×C4×C293C2311yescharacteristic
59C2×C4×C293C2311yescharacteristic
60C2×C4×C293C2312yes—
61C2×C4×C293C2311yescharacteristic
62C22×C293—22no—
63C22×C293—22no—
64C22×C293—22no—
65C22×C293C2411yescharacteristic
66C2×D293—21no—
67C2×D293—22no—
68C2×D293—22no—
69C2×D293—21no—
70C2×D293—21no—
71C2×D293—21no—
72C2×D293—21no—
73C2×D293—48no—
74C2×D293C2×D414yes—
75C2×D293#4112yescomplemented
76C4×C293—22no—
77C4×C293—21no—
78C4×C293—21no—
79C4×C293C2×D412yes—
80Dic293—21no—
81Dic293—21no—
82Dic293—22no—
83C2×C293—42no—
84C2×C293C22×D411yescharacteristic
85C2×C293C2×#4111yescharacteristic
86C2×C293H(5,𝔽2)11yescharacteristic
87D293—22no—
88D293—24no—
89D293—41no—
90C293#54611yescharacteristic, complemented, Sylow
91#546—2931nomaximal, Sylow
92C2×#41—2931no—
93C22×D4—2931no—
94#124D29311yescharacteristic, complemented
95#123—2932no—
96C22⋊Q8—2931no—
97#121—2931no—
98#121—2932no—
99#120—2932no—
100C4×D4—2931no—
101C4×D4—2931no—
102C2×C22⋊C4—2932no—
103C24—2932no—
104#41—5864no—
105C2×Q8C2×D29311yescharacteristic, complemented
106C2×D4—2932no—
107C2×D4—2932no—
108C2×D4—2931no—
109C2×D4—2931no—
110C2×D4—2932no—
111C2×D4—5864no—
112C2×D4C2×D29311yescharacteristic
113C22×C4—2932no—
114C22×C4—2931no—
115C22×C4—2931no—
116C22×C4—2932no—
117C4⋊C4—2931no—
118C4⋊C4—2931no—
119C4⋊C4—2932no—
120C22⋊C4—2932no—
121C22⋊C4—2931no—
122C22⋊C4—2932no—
123C22⋊C4—2932no—
124C22⋊C4—2931no—
125C22⋊C4C2×D29312yescomplemented
126C22⋊C4C2×D29312yescomplemented
127C42C2×D29311yescharacteristic, complemented
128C23—2931no—
129C23—2932no—
130C23—2931no—
131C23—5864no—
132C23—5864no—
133C23—11722no—
134C23C22×D29312yes—
135Q8—22no—
136D4—22no—
137D4—2934no—
138D4—5864no—
139D4—5862no—
140D4—5864no—
141D4—11722no—
142C2×C4—2932no—
143C2×C4—2931no—
144C2×C4—2931no—
145C2×C4—5864no—
146C2×C4—5862no—
147C2×C4—5862no—
148C2×C4—11722no—
149C2×C4C22×D29311yescharacteristic
150C2×C4C22×D29311yescharacteristic
151C2×C4C22×D29312yes—
152C2×C4C22×D29311yescharacteristic
153C22—22no—
154C22—22no—
155C22—22no—
156C22—2934no—
157C22—2932no—
158C22—5861no—
159C22—5862no—
160C22—5862no—
161C22—5861no—
162C22—5861no—
163C22—5861no—
164C22—5861no—
165C22—11728no—
166C22C23×D29311yescharacteristic
167C4—22no—
168C4—21no—
169C4—21no—
170C4—5861no—
171C4—5861no—
172C4—5862no—
173C4D4×D29312yes—
174C2—42no—
175C2—5862no—
176C2—5864no—
177C2—11721no—
178C2C2×D4×D29311yescharacteristic
179C2#41×D29311yescharacteristic
180C2#2262767011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
Fitting#124×C293C2
hypercenter#124D293
hypocenterC293#546
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#17989803C2semidirect
2. C2×D4×D293C2semidirect
3. #22627606C2semidirect
4. #22627600C2semidirect
5. #22627597C2semidirect
6. #22627595C2semidirect
7. #22627594C2semidirect
8. C4×D1172C2semidirect
9. C4×D1172C2semidirect
10. C22⋊C4×D293C2semidirect
11. #124×C293C2semidirect
16. C2×D1172C22semidirect
18. C2×C22⋊D293C22semidirect
21. C2×C4×D293C22semidirect
22. C2×C4×D293C22semidirect
23. C2×C4×D293C22semidirect
24. C4⋊Dic293C22semidirect
25. C4⋊Dic293C22semidirect
26. #17989781C22semidirect
27. C22⋊Dic293C22semidirect
30. #17989779C22semidirect
31. #17989779C22semidirect
32. C2×Q8×C293C22semidirect
34. C22⋊C4×C293C22semidirect
35. C22⋊C4×C293C22semidirect
36. C42×C293C22semidirect
45. D1172D4semidirect
75. C2×D293#41semidirect
90. C293#546semidirect
94. #124D293semidirect
105. C2×Q8C2×D293semidirect
125. C22⋊C4C2×D293semidirect
126. C22⋊C4C2×D293semidirect
127. C42C2×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#179898032
C2×D4×D2932
#226276062
#226276002
#226275972
#226275952
#226275942
C4×D11722
C22⋊C4×D2932
#124×C2932
#546293