Finite Group Databasebeta

← #34036637

Subgroups — #34036637

Order 18752.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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×#17989801C211yesmaximal, characteristic, complemented
2C22×C4×D293C211yesmaximal, characteristic, complemented
3#22627607C211yesmaximal, characteristic, complemented
4#22627602C212yesmaximal, complemented
5#22627597C212yesmaximal, complemented
6#22627594C211yesmaximal, characteristic, complemented
7#22627592C211yesmaximal, characteristic, complemented
8#22627586C212yesmaximal, complemented
9#22627584C212yesmaximal, complemented
10#22627580C211yesmaximal, characteristic, complemented
11#123×C293C211yesmaximal, characteristic, complemented
12C23×D293C2211yescharacteristic
13#17989801—24no—
14C2×Dic586C2211yescharacteristic, complemented
15C2×D1172C2212yes—
16C2×C22⋊D293C2212yes—
17C2×C22⋊D293C2211yescharacteristic
18C2×C22⋊D293C2211yescharacteristic, complemented
19C22×Dic293C2211yescharacteristic
20C22×Dic293C2211yescharacteristic, complemented
21C2×C4×D293—24no—
22C2×C4×D293C2212yes—
23C2×C4×D293C2212yes—
24C2×C4×D293C2211yescharacteristic, complemented
25#17989781C2212yescomplemented
26#17989781C2212yescomplemented
27C22⋊Dic293C2211yescharacteristic
28#17989779C2212yes—
29#17989779C2212yes—
30#17989779C2212yescomplemented
31C4×Dic293C2212yescomplemented
32C2×D4×C293C2211yescharacteristic
33C22×C4×C293C2211yescharacteristic
34C4⋊C4×C293C2212yescomplemented
35C22⋊C4×C293C2211yescharacteristic
36C22⋊C4×C293C2212yescomplemented
37C22×D293—22no—
38C22×D293—24no—
39C22×D293C2311yescharacteristic
40C22×D293C2312yes—
41Dic586—22no—
42D1172—24no—
43C22⋊D293—22no—
44C22⋊D293—24no—
45C22⋊D293—22no—
46C2×Dic293—22no—
47C2×Dic293D414yescomplemented
48C2×Dic293C2312yes—
49C2×Dic293C2311yescharacteristic
50C2×Dic293C2311yescharacteristic
51C2×Dic293C2311yescharacteristic
52C4×D293—24no—
53C4×D293—24no—
54C4×D293—22no—
55C23×C293C2311yescharacteristic
56C23×C293C2311yescharacteristic
57D4×C293—22no—
58C2×C4×C293—22no—
59C2×C4×C293C2312yes—
60C2×C4×C293C2312yes—
61C2×C4×C293C2311yescharacteristic
62C22×C293—22no—
63C22×C293—21no—
64C22×C293—22no—
65C22×C293C2×D412yes—
66C22×C293C2411yescharacteristic
67C2×D293—28no—
68C2×D293—22no—
69C2×D293—22no—
70C2×D293—21no—
71C2×D293—22no—
72C2×D293#4114yescomplemented
73C4×C293—22no—
74C4×C293—21no—
75C4×C293—22no—
76Dic293—21no—
77Dic293—22no—
78Dic293C2×D412yes—
79Dic293C2×D412yes—
80C2×C293—22no—
81C2×C293—41no—
82C2×C293C22×D411yescharacteristic
83C2×C293C2×#4112yes—
84D293—24no—
85D293—41no—
86C293#52511yescharacteristic, complemented, Sylow
87#525—2931nomaximal, Sylow
88C2×#41—2931no—
89C23×C4—2931no—
90#123—2931no—
91#123D29311yescharacteristic, complemented
92C22⋊Q8—2932no—
93#121—2932no—
94#120—2931no—
95#120—2931no—
96C4×D4—2932no—
97C4×D4—2932no—
98#117—2931no—
99C24—2931no—
100#41—5864no—
101C2×Q8—2931no—
102C2×D4—2932no—
103C2×D4—2931no—
104C2×D4—2931no—
105C2×D4—2932no—
106C2×D4C2×D29311yescharacteristic
107C22×C4—2931no—
108C22×C4—2931no—
109C22×C4—2932no—
110C22×C4—2931no—
111C22×C4—2932no—
112C22×C4—5864no—
113C22×C4C2×D29311yescharacteristic
114C4⋊C4—2932no—
115C4⋊C4—2932no—
116C4⋊C4C2×D29312yescomplemented
117C22⋊C4—2931no—
118C22⋊C4—2932no—
119C22⋊C4—2932no—
120C22⋊C4—2932no—
121C22⋊C4C2×D29311yescharacteristic
122C22⋊C4C2×D29312yescomplemented
123C42—2932no—
124C23—2932no—
125C23—2931no—
126C23—5864no—
127C23—5862no—
128C23C22×D29311yescharacteristic
129C23C22×D29311yescharacteristic
130Q8—5862no—
131D4—22no—
132D4—5864no—
133D4—5862no—
134D4—5864no—
135D4—5862no—
136C2×C4—22no—
137C2×C4—2934no—
138C2×C4—2931no—
139C2×C4—2931no—
140C2×C4—2932no—
141C2×C4—2931no—
142C2×C4—5864no—
143C2×C4—5864no—
144C2×C4—5862no—
145C2×C4—5862no—
146C2×C4C22×D29312yes—
147C2×C4C22×D29311yescharacteristic
148C2×C4C22×D29312yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—2934no—
153C22—5868no—
154C22—5862no—
155C22—5862no—
156C22—5861no—
157C22—5862no—
158C22D4×D29312yes—
159C22C23×D29311yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—2932no—
164C4—2932no—
165C4—5861no—
166C4—5862no—
167C2—22no—
168C2—41no—
169C2—5864no—
170C2—11721no—
171C2C2×D4×D29311yescharacteristic
172C2#41×D29312yes—
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
Fitting#123×C293C2
hypercenter#123D293
hypocenterC293#525
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#17989801C2semidirect
2. C22×C4×D293C2semidirect
3. #22627607C2semidirect
4. #22627602C2semidirect
5. #22627597C2semidirect
6. #22627594C2semidirect
7. #22627592C2semidirect
8. #22627586C2semidirect
9. #22627584C2semidirect
10. #22627580C2semidirect
11. #123×C293C2semidirect
14. C2×Dic586C22semidirect
18. C2×C22⋊D293C22semidirect
20. C22×Dic293C22semidirect
24. C2×C4×D293C22semidirect
25. #17989781C22semidirect
26. #17989781C22semidirect
30. #17989779C22semidirect
31. C4×Dic293C22semidirect
34. C4⋊C4×C293C22semidirect
36. C22⋊C4×C293C22semidirect
47. C2×Dic293D4semidirect
72. C2×D293#41semidirect
86. C293#525semidirect
91. #123D293semidirect
116. C4⋊C4C2×D293semidirect
122. C22⋊C4C2×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#179898012
C22×C4×D2932
#226276072
#226276022
#226275972
#226275942
#226275922
#226275862
#226275842
#226275802
#123×C2932
#525293