Finite Group Databasebeta

← #34036711

Subgroups — #34036711

Order 18752.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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#22627619C211yesmaximal, characteristic, complemented
2#22627617C211yesmaximal, characteristic, complemented
3#22627611C211yesmaximal, characteristic, complemented
4#22627610C211yesmaximal, characteristic, complemented
5#22627607C211yesmaximal, characteristic, complemented
6#22627605C211yesmaximal, characteristic, complemented
7#22627602C211yesmaximal, characteristic, complemented
8#22627596C211yesmaximal, characteristic, complemented
9#22627595C211yesmaximal, characteristic, complemented
10#22627592C211yesmaximal, characteristic, complemented
11#22627592C211yesmaximal, characteristic, complemented
12C4×C22⋊D293C211yesmaximal, characteristic, complemented
13#22627584C211yesmaximal, characteristic, complemented
14C22⋊C4×D293C211yesmaximal, characteristic, complemented
15#121×C293C211yesmaximal, characteristic, complemented
16C23×D293C2211yescharacteristic
17C2×Dic586C2211yescharacteristic, complemented
18C2×C22⋊D293C2211yescharacteristic
19C2×C22⋊D293C2211yescharacteristic
20C2×C22⋊D293C2211yescharacteristic
21C2×C22⋊D293C2211yescharacteristic
22C22×Dic293C2211yescharacteristic, complemented
23C2×C4×D293C2211yescharacteristic
24C2×C4×D293C2211yescharacteristic
25C4⋊Dic293C2211yescharacteristic, complemented
26#17989781C2211yescharacteristic, complemented
27#17989781C2211yescharacteristic, complemented
28#17989781C2211yescharacteristic, complemented
29#17989781C2211yescharacteristic, complemented
30C22⋊Dic293C2211yescharacteristic
31C22⋊Dic293C2211yescharacteristic
32C22⋊Dic293C2211yescharacteristic
33C22⋊Dic293C2211yescharacteristic, complemented
34C22⋊Dic293C2211yescharacteristic, complemented
35C22⋊Dic293C2211yescharacteristic, complemented
36#17989779C2211yescharacteristic
37#17989779C2211yescharacteristic
38#17989779C2211yescharacteristic
39#17989779C2211yescharacteristic
40#17989779C2211yescharacteristic
41#17989779C2211yescharacteristic
42C4×Dic293C2211yescharacteristic, complemented
43C4×Dic293C2211yescharacteristic, complemented
44C2×D4×C293C2211yescharacteristic
45C2×D4×C293C2211yescharacteristic
46C2×D4×C293C2211yescharacteristic, complemented
47C22×C4×C293C2211yescharacteristic, complemented
48C4⋊C4×C293C2211yescharacteristic, complemented
49C22⋊C4×C293C2211yescharacteristic
50C22⋊C4×C293C2211yescharacteristic, complemented
51C22×D293—22no—
52C22×D293—41no—
53C22×D293—41no—
54C22×D293C2311yescharacteristic
55C22×D293C2311yescharacteristic
56Dic586—41no—
57C22⋊D293—22no—
58C22⋊D293—22no—
59C22⋊D293—41no—
60C22⋊D293—41no—
61C2×Dic293—41no—
62C2×Dic293C2311yescharacteristic
63C2×Dic293C2311yescharacteristic
64C2×Dic293C2311yescharacteristic
65C2×Dic293C2311yescharacteristic
66C2×Dic293C2311yescharacteristic
67C2×Dic293C2311yescharacteristic
68C4×D293—41no—
69C4×D293—41no—
70C23×C293C2311yescharacteristic
71C23×C293C2311yescharacteristic
72C23×C293C2311yescharacteristic
73D4×C293—41no—
74D4×C293—41no—
75D4×C293—41no—
76C2×C4×C293—41no—
77C2×C4×C293C2311yescharacteristic
78C2×C4×C293C2311yescharacteristic
79C2×C4×C293C2311yescharacteristic
80C2×C4×C293C2311yescharacteristic
81C22×C293—21no—
82C22×C293—21no—
83C22×C293—21no—
84C22×C293—21no—
85C22×C293—21no—
86C22×C293—21no—
87C22×C293—21no—
88C22×C293—21no—
89C22×C293—21no—
90C22×C293C2411yescharacteristic
91C2×D293—21no—
92C2×D293—21no—
93C2×D293—21no—
94C2×D293—21no—
95C2×D293—21no—
96C2×D293—44no—
97C2×D293#4112yes—
98C4×C293—21no—
99C4×C293—21no—
100C4×C293—21no—
101C4×C293—21no—
102Dic293—21no—
103Dic293—21no—
104Dic293—21no—
105Dic293—21no—
106Dic293—21no—
107Dic293—21no—
108C2×C293—41no—
109C2×C293—41no—
110C2×C293—41no—
111C2×C293C2×#4111yescharacteristic
112C2×C293H(5,𝔽2)11yescharacteristic
113C2×C293H(5,𝔽2)11yescharacteristic
114D293—22no—
115D293—41no—
116C293#53811yescharacteristic, complemented, Sylow
117#538—2931nomaximal, Sylow
118#126—2931no—
119#126—2931no—
120#124—2931no—
121#124—2931no—
122#123—2931no—
123#123—2931no—
124C22⋊Q8—2931no—
125#121—2931no—
126#121—2931no—
127#121D29311yescharacteristic, complemented
128#120—2931no—
129#120—2931no—
130C4×D4—2931no—
131C4×D4—2931no—
132C2×C22⋊C4—2931no—
133C24—2931no—
134C2×Q8—2931no—
135C2×D4—2931no—
136C2×D4—2931no—
137C2×D4—2931no—
138C2×D4—2931no—
139C2×D4C2×D29311yescharacteristic
140C2×D4C2×D29311yescharacteristic
141C2×D4C2×D29311yescharacteristic, complemented
142C22×C4—2931no—
143C22×C4—2931no—
144C22×C4—2931no—
145C22×C4C2×D29311yescharacteristic, complemented
146C4⋊C4—2931no—
147C4⋊C4—2931no—
148C4⋊C4—2931no—
149C4⋊C4—2931no—
150C4⋊C4—2931no—
151C4⋊C4C2×D29311yescharacteristic, complemented
152C22⋊C4—2931no—
153C22⋊C4—2931no—
154C22⋊C4—2931no—
155C22⋊C4—2931no—
156C22⋊C4—2931no—
157C22⋊C4—2931no—
158C22⋊C4—2931no—
159C22⋊C4—2931no—
160C22⋊C4—2931no—
161C22⋊C4—2931no—
162C22⋊C4—2931no—
163C22⋊C4—2931no—
164C22⋊C4C2×D29311yescharacteristic
165C22⋊C4C2×D29311yescharacteristic, complemented
166C42—2931no—
167C42—2931no—
168C23—2931no—
169C23—2931no—
170C23—5862no—
171C23—11721no—
172C23—11721no—
173C23C22×D29311yescharacteristic
174C23C22×D29311yescharacteristic
175C23C22×D29311yescharacteristic
176Q8—11721no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—5862no—
181D4—5862no—
182D4—11721no—
183D4—11721no—
184C2×C4—41no—
185C2×C4—2931no—
186C2×C4—2931no—
187C2×C4—2931no—
188C2×C4—2931no—
189C2×C4—2931no—
190C2×C4—2931no—
191C2×C4—11721no—
192C2×C4—11721no—
193C2×C4—11721no—
194C2×C4C22×D29311yescharacteristic
195C2×C4C22×D29311yescharacteristic
196C2×C4C22×D29311yescharacteristic
197C2×C4C22×D29311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—2932no—
208C22—5861no—
209C22—5861no—
210C22—5861no—
211C22—5861no—
212C22—5861no—
213C22—11724no—
214C22C23×D29311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—5861no—
220C4—5861no—
221C4—5861no—
222C4—5861no—
223C4—5861no—
224C4—5861no—
225C2—41no—
226C2—41no—
227C2—41no—
228C2—5862no—
229C2—11721no—
230C2#41×D29311yescharacteristic
231C2#2262766911yescharacteristic
232C2#2262766911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
Fitting#121×C293C2
hypercenter#121D293
hypocenterC293#538
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #22627619C2semidirect
2. #22627617C2semidirect
3. #22627611C2semidirect
4. #22627610C2semidirect
5. #22627607C2semidirect
6. #22627605C2semidirect
7. #22627602C2semidirect
8. #22627596C2semidirect
9. #22627595C2semidirect
10. #22627592C2semidirect
11. #22627592C2semidirect
12. C4×C22⋊D293C2semidirect
13. #22627584C2semidirect
14. C22⋊C4×D293C2semidirect
15. #121×C293C2semidirect
17. C2×Dic586C22semidirect
22. C22×Dic293C22semidirect
25. C4⋊Dic293C22semidirect
26. #17989781C22semidirect
27. #17989781C22semidirect
28. #17989781C22semidirect
29. #17989781C22semidirect
33. C22⋊Dic293C22semidirect
34. C22⋊Dic293C22semidirect
35. C22⋊Dic293C22semidirect
42. C4×Dic293C22semidirect
43. C4×Dic293C22semidirect
46. C2×D4×C293C22semidirect
47. C22×C4×C293C22semidirect
48. C4⋊C4×C293C22semidirect
50. C22⋊C4×C293C22semidirect
116. C293#538semidirect
127. #121D293semidirect
141. C2×D4C2×D293semidirect
145. C22×C4C2×D293semidirect
151. C4⋊C4C2×D293semidirect
165. C22⋊C4C2×D293semidirect

Maximal subgroups

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

subgroupindex
#226276192
#226276172
#226276112
#226276102
#226276072
#226276052
#226276022
#226275962
#226275952
#226275922
C4×C22⋊D2932
#226275842
C22⋊C4×D2932
#121×C2932
#538293