Finite Group Databasebeta

← #34036713

Subgroups — #34036713

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#22627618C211yesmaximal, characteristic, complemented
2#22627617C211yesmaximal, characteristic, complemented
3#22627613C211yesmaximal, characteristic, complemented
4#22627608C211yesmaximal, characteristic, complemented
5#22627606C211yesmaximal, characteristic, complemented
6#22627600C211yesmaximal, characteristic, complemented
7#22627597C211yesmaximal, characteristic, complemented
8#22627597C211yesmaximal, characteristic, complemented
9#22627596C211yesmaximal, characteristic, complemented
10#22627594C211yesmaximal, characteristic, complemented
11#22627592C211yesmaximal, characteristic, complemented
12C4×D1172C211yesmaximal, characteristic, complemented
13#22627584C211yesmaximal, characteristic, complemented
14C22⋊C4×D293C211yesmaximal, characteristic, complemented
15#124×C293C211yesmaximal, characteristic, complemented
16C23×D293C2211yescharacteristic
17C2×D1172C2211yescharacteristic
18C2×D1172C2211yescharacteristic
19C2×C22⋊D293C2211yescharacteristic
20C2×C22⋊D293C2211yescharacteristic
21C2×C22⋊D293C2211yescharacteristic
22C2×C22⋊D293C2211yescharacteristic, complemented
23C22×Dic293C2211yescharacteristic, complemented
24C2×C4×D293C2211yescharacteristic
25C2×C4×D293C2211yescharacteristic
26C2×C4×D293C2211yescharacteristic, complemented
27C4⋊Dic293C2211yescharacteristic, complemented
28C4⋊Dic293C2211yescharacteristic, complemented
29#17989781C2211yescharacteristic, complemented
30#17989781C2211yescharacteristic, complemented
31#17989781C2211yescharacteristic, complemented
32#17989781C2211yescharacteristic, complemented
33C22⋊Dic293C2211yescharacteristic
34C22⋊Dic293C2211yescharacteristic
35#17989779C2211yescharacteristic
36#17989779C2211yescharacteristic
37#17989779C2211yescharacteristic
38#17989779C2211yescharacteristic
39#17989779C2211yescharacteristic
40#17989779C2211yescharacteristic
41#17989779C2211yescharacteristic, complemented
42#17989779C2211yescharacteristic, complemented
43C4×Dic293C2211yescharacteristic, complemented
44C2×Q8×C293C2211yescharacteristic, complemented
45C2×D4×C293C2211yescharacteristic
46C22⋊C4×C293C2211yescharacteristic
47C22⋊C4×C293C2211yescharacteristic
48C22⋊C4×C293C2211yescharacteristic, complemented
49C22⋊C4×C293C2211yescharacteristic, complemented
50C42×C293C2211yescharacteristic, complemented
51C22×D293—22no—
52C22×D293—41no—
53C22×D293—41no—
54C22×D293C2311yescharacteristic
55C22×D293C2311yescharacteristic
56C22×D293C2311yescharacteristic
57D1172—22no—
58D1172—41no—
59C22⋊D293—22no—
60C22⋊D293—41no—
61C22⋊D293—41no—
62C22⋊D293—41no—
63C2×Dic293—41no—
64C2×Dic293C2311yescharacteristic
65C2×Dic293C2311yescharacteristic
66C2×Dic293C2311yescharacteristic
67C2×Dic293C2311yescharacteristic
68C2×Dic293C2311yescharacteristic
69C4×D293—41no—
70C4×D293—41no—
71C4×D293—41no—
72C23×C293C2311yescharacteristic
73C23×C293C2311yescharacteristic
74Q8×C293—41no—
75D4×C293—41no—
76C2×C4×C293C2311yescharacteristic
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×C293C2411yescharacteristic
88C2×D293—21no—
89C2×D293—21no—
90C2×D293—21no—
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—
102C4×C293—21no—
103Dic293—21no—
104Dic293—21no—
105Dic293—21no—
106Dic293—21no—
107Dic293—21no—
108C2×C293—41no—
109C2×C293—41no—
110C2×C293C2×#4111yescharacteristic
111C2×C293H(5,𝔽2)11yescharacteristic
112C2×C293H(5,𝔽2)11yescharacteristic
113D293—22no—
114D293—41no—
115D293—41no—
116C293#53811yescharacteristic, complemented, Sylow
117#538—2931nomaximal, Sylow
118#126—2931no—
119#126—2931no—
120#124—2931no—
121#124D29311yescharacteristic, complemented
122#123—2931no—
123#123—2931no—
124C22⋊Q8—2931no—
125#121—2931no—
126#121—2931no—
127#121—2931no—
128#120—2931no—
129#120—2931no—
130C4×D4—2931no—
131C4×D4—2931no—
132C2×C22⋊C4—2931no—
133C24—2931no—
134C2×Q8C2×D29311yescharacteristic, complemented
135C2×D4—2931no—
136C2×D4—2931no—
137C2×D4—2931no—
138C2×D4—2931no—
139C2×D4—2931no—
140C2×D4—2931no—
141C2×D4C2×D29311yescharacteristic
142C22×C4—2931no—
143C22×C4—2931no—
144C22×C4—2931no—
145C22×C4—2931no—
146C4⋊C4—2931no—
147C4⋊C4—2931no—
148C4⋊C4—2931no—
149C4⋊C4—2931no—
150C4⋊C4—2931no—
151C4⋊C4—2931no—
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⋊C4C2×D29311yescharacteristic
163C22⋊C4C2×D29311yescharacteristic
164C22⋊C4C2×D29311yescharacteristic, complemented
165C22⋊C4C2×D29311yescharacteristic, complemented
166C42—2931no—
167C42C2×D29311yescharacteristic, complemented
168C23—2931no—
169C23—2931no—
170C23—2931no—
171C23—5862no—
172C23—11721no—
173C23—11721no—
174C23C22×D29311yescharacteristic
175C23C22×D29311yescharacteristic
176Q8—41no—
177D4—41no—
178D4—5862no—
179D4—5862no—
180D4—11721no—
181D4—11721no—
182D4—11721no—
183D4—11721no—
184C2×C4—2931no—
185C2×C4—2931no—
186C2×C4—2931no—
187C2×C4—2931no—
188C2×C4—2931no—
189C2×C4—11721no—
190C2×C4—11721no—
191C2×C4—11721no—
192C2×C4—11721no—
193C2×C4C22×D29311yescharacteristic
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—2932no—
205C22—5861no—
206C22—5861no—
207C22—5861no—
208C22—5861no—
209C22—5861no—
210C22—5861no—
211C22—5861no—
212C22—5861no—
213C22—11724no—
214C22C23×D29311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—5861no—
221C4—5861no—
222C4—5861no—
223C4—5861no—
224C4—5861no—
225C2—41no—
226C2—41no—
227C2—5862no—
228C2—11721no—
229C2—11721no—
230C2#41×D29311yescharacteristic
231C2#2262766911yescharacteristic
232C2#2262767011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
Fitting#124×C293C2
hypercenter#124D293
hypocenterC293#538
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #22627618C2semidirect
2. #22627617C2semidirect
3. #22627613C2semidirect
4. #22627608C2semidirect
5. #22627606C2semidirect
6. #22627600C2semidirect
7. #22627597C2semidirect
8. #22627597C2semidirect
9. #22627596C2semidirect
10. #22627594C2semidirect
11. #22627592C2semidirect
12. C4×D1172C2semidirect
13. #22627584C2semidirect
14. C22⋊C4×D293C2semidirect
15. #124×C293C2semidirect
22. C2×C22⋊D293C22semidirect
23. C22×Dic293C22semidirect
26. C2×C4×D293C22semidirect
27. C4⋊Dic293C22semidirect
28. C4⋊Dic293C22semidirect
29. #17989781C22semidirect
30. #17989781C22semidirect
31. #17989781C22semidirect
32. #17989781C22semidirect
41. #17989779C22semidirect
42. #17989779C22semidirect
43. C4×Dic293C22semidirect
44. C2×Q8×C293C22semidirect
48. C22⋊C4×C293C22semidirect
49. C22⋊C4×C293C22semidirect
50. C42×C293C22semidirect
116. C293#538semidirect
121. #124D293semidirect
134. C2×Q8C2×D293semidirect
164. C22⋊C4C2×D293semidirect
165. C22⋊C4C2×D293semidirect
167. C42C2×D293semidirect

Maximal subgroups

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

subgroupindex
#226276182
#226276172
#226276132
#226276082
#226276062
#226276002
#226275972
#226275962
#226275942
#226275922
C4×D11722
#226275842
C22⋊C4×D2932
#124×C2932
#538293