Finite Group Databasebeta

← #34036806

Subgroups — #34036806

Order 18752.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#22627619C211yesmaximal, characteristic, complemented
3#22627613C211yesmaximal, characteristic, complemented
4#22627609C211yesmaximal, characteristic, complemented
5#22627609C211yesmaximal, characteristic, complemented
6#22627608C211yesmaximal, characteristic, complemented
7#22627600C211yesmaximal, characteristic, complemented
8#22627594C211yesmaximal, characteristic
9#22627586C211yesmaximal, characteristic, complemented
10C4×C22⋊D293C211yesmaximal, characteristic, complemented
11#22627582C211yesmaximal, characteristic, complemented
12#22627580C211yesmaximal, characteristic, complemented
13C2×#17989779C211yesmaximal, characteristic, complemented
14C22⋊C4×D293C211yesmaximal, characteristic, complemented
15C22⋊Q8×C293C211yesmaximal, characteristic, complemented
16C23×D293C2211yescharacteristic
17C2×D1172C2211yescharacteristic
18C2×D1172C2211yescharacteristic
19C2×C22⋊D293C2211yescharacteristic
20C22×Dic293C2211yescharacteristic
21C2×C4×D293C2211yescharacteristic
22C2×C4×D293C2211yescharacteristic
23C2×C4×D293C2211yescharacteristic, complemented
24C4⋊Dic293C2211yescharacteristic, complemented
25C4⋊Dic293C2211yescharacteristic, complemented
26#17989781C2211yescharacteristic, complemented
27#17989781C2211yescharacteristic, complemented
28#17989781C2211yescharacteristic, complemented
29C22⋊Dic293C2211yescharacteristic
30#17989779C2211yescharacteristic
31#17989779C2211yescharacteristic
32#17989779C2211yescharacteristic
33#17989779C2211yescharacteristic
34#17989779C2211yescharacteristic
35#17989779C2211yescharacteristic
36#17989779C2211yescharacteristic
37#17989779C2211yescharacteristic
38#17989779C2211yescharacteristic, complemented
39#17989779C2211yescharacteristic, complemented
40#17989779C2211yescharacteristic, complemented
41C4×Dic293C2211yescharacteristic, complemented
42C4×Dic293C2211yescharacteristic, complemented
43C4×Dic293C2211yescharacteristic, complemented
44C2×Q8×C293C2211yescharacteristic, complemented
45C22×C4×C293C2211yescharacteristic
46C4⋊C4×C293C2211yescharacteristic, complemented
47C4⋊C4×C293C2211yescharacteristic, complemented
48C4⋊C4×C293C2211yescharacteristic, complemented
49C22⋊C4×C293C2211yescharacteristic
50C22⋊C4×C293C2211yescharacteristic
51C22×D293—22no—
52C22×D293—22no—
53C22×D293—41no—
54C22×D293C2311yescharacteristic
55C22×D293C2311yescharacteristic
56C22×D293C2311yescharacteristic
57D1172—22no—
58D1172—41no—
59C22⋊D293—22no—
60C2×Dic293—22no—
61C2×Dic293C2311yescharacteristic
62C2×Dic293C2311yescharacteristic
63C2×Dic293C2311yescharacteristic
64C2×Dic293C2311yescharacteristic
65C2×Dic293C2311yescharacteristic
66C4×D293—22no—
67C4×D293—41no—
68C4×D293—41no—
69C23×C293C2311yescharacteristic
70Q8×C293—41no—
71C2×C4×C293—41no—
72C2×C4×C293C2311yescharacteristic
73C2×C4×C293C2311yescharacteristic
74C2×C4×C293C2311yescharacteristic
75C2×C4×C293C2311yescharacteristic
76C2×C4×C293C2311yescharacteristic
77C2×C4×C293C2311yescharacteristic
78C22×C293—21no—
79C22×C293—21no—
80C22×C293#4112yes—
81C22×C293C2411yescharacteristic
82C2×D293—21no—
83C2×D293—21no—
84C2×D293—21no—
85C2×D293—21no—
86C2×D293—21no—
87C2×D293—21no—
88C2×D293—21no—
89C2×D293—21no—
90C2×D293—44no—
91C2×D293#4112yes—
92C4×C293—21no—
93C4×C293—21no—
94C4×C293—21no—
95C4×C293—21no—
96C4×C293—21no—
97C4×C293—21no—
98Dic293—21no—
99Dic293—21no—
100Dic293—21no—
101Dic293—21no—
102Dic293—21no—
103C2×C293—22no—
104C2×C293C2×#4111yescharacteristic
105C2×C293C2×#4111yescharacteristic
106C2×C293H(5,𝔽2)11yescharacteristic
107D293—22no—
108D293—41no—
109D293—41no—
110C293#55111yescharacteristic, complemented, Sylow
111#551—2931nomaximal, Sylow
112#126—2931no—
113#126—2931no—
114#124—2931no—
115#123—2931no—
116#123—2931no—
117#123—2931no—
118C22⋊Q8—2931no—
119C22⋊Q8D29311yescharacteristic, complemented
120#120—2931no—
121C4×D4—2931no—
122C4×D4—2931no—
123#117—2931no—
124#117—2931no—
125C2×C22⋊C4—2931no—
126C2×C22⋊C4—2931no—
127C24—2931no—
128C2×Q8C2×D29311yescharacteristic, complemented
129C2×D4—2931no—
130C2×D4—2931no—
131C2×D4—2931no—
132C22×C4—2931no—
133C22×C4—2931no—
134C22×C4—2931no—
135C22×C4—2931no—
136C22×C4C2×D29311yescharacteristic
137C4⋊C4—2931no—
138C4⋊C4—2931no—
139C4⋊C4—2931no—
140C4⋊C4—2931no—
141C4⋊C4—2931no—
142C4⋊C4C2×D29311yescharacteristic, complemented
143C4⋊C4C2×D29311yescharacteristic, complemented
144C4⋊C4C2×D29311yescharacteristic, complemented
145C22⋊C4—2931no—
146C22⋊C4—2931no—
147C22⋊C4—2931no—
148C22⋊C4—2931no—
149C22⋊C4—2931no—
150C22⋊C4—2931no—
151C22⋊C4—2931no—
152C22⋊C4—2931no—
153C22⋊C4—2931no—
154C22⋊C4—2931no—
155C22⋊C4—2931no—
156C22⋊C4—2931no—
157C22⋊C4C2×D29311yescharacteristic
158C22⋊C4C2×D29311yescharacteristic
159C42—2931no—
160C42—2931no—
161C42—2931no—
162C23—2931no—
163C23—2931no—
164C23—2931no—
165C23—5862no—
166C23—5862no—
167C23—11721no—
168C23C22×D29311yescharacteristic
169Q8—41no—
170D4—5862no—
171D4—5862no—
172D4—11721no—
173C2×C4—41no—
174C2×C4—2931no—
175C2×C4—2931no—
176C2×C4—2931no—
177C2×C4—2931no—
178C2×C4—2931no—
179C2×C4—5862no—
180C2×C4—5862no—
181C2×C4—11721no—
182C2×C4—11721no—
183C2×C4C22×D29311yescharacteristic
184C2×C4C22×D29311yescharacteristic
185C2×C4C22×D29311yescharacteristic
186C2×C4C22×D29311yescharacteristic
187C2×C4C22×D29311yescharacteristic
188C2×C4C22×D29311yescharacteristic
189C22—21no—
190C22—21no—
191C22—2932no—
192C22—5861no—
193C22—5861no—
194C22—5861no—
195C22—5861no—
196C22—5861no—
197C22—5861no—
198C22—5861no—
199C22—5861no—
200C22—11724no—
201C22#1798980312yes—
202C22C23×D29311yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—5861no—
210C4—5861no—
211C4—5861no—
212C4—5861no—
213C4—5861no—
214C2—22no—
215C2—5862no—
216C2—11721no—
217C2—11721no—
218C2#41×D29311yescharacteristic
219C2C2×#1798980311yescharacteristic
220C2#2262766911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D293
commutator, socle, cosocleC22×C293C24
FittingC22⋊Q8×C293C2
prime radical#22627594C2
hypercenterC22⋊Q8D293
hypocenterC293#551
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #22627619C2semidirect
2. #22627619C2semidirect
3. #22627613C2semidirect
4. #22627609C2semidirect
5. #22627609C2semidirect
6. #22627608C2semidirect
7. #22627600C2semidirect
9. #22627586C2semidirect
10. C4×C22⋊D293C2semidirect
11. #22627582C2semidirect
12. #22627580C2semidirect
13. C2×#17989779C2semidirect
14. C22⋊C4×D293C2semidirect
15. C22⋊Q8×C293C2semidirect
23. C2×C4×D293C22semidirect
24. C4⋊Dic293C22semidirect
25. C4⋊Dic293C22semidirect
26. #17989781C22semidirect
27. #17989781C22semidirect
28. #17989781C22semidirect
38. #17989779C22semidirect
39. #17989779C22semidirect
40. #17989779C22semidirect
41. C4×Dic293C22semidirect
42. C4×Dic293C22semidirect
43. C4×Dic293C22semidirect
44. C2×Q8×C293C22semidirect
46. C4⋊C4×C293C22semidirect
47. C4⋊C4×C293C22semidirect
48. C4⋊C4×C293C22semidirect
110. C293#551semidirect
119. C22⋊Q8D293semidirect
128. C2×Q8C2×D293semidirect
142. C4⋊C4C2×D293semidirect
143. C4⋊C4C2×D293semidirect
144. C4⋊C4C2×D293semidirect

Maximal subgroups

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

subgroupindex
#226276192
#226276132
#226276092
#226276082
#226276002
#226275942
#226275862
C4×C22⋊D2932
#226275822
#226275802
C2×#179897792
C22⋊C4×D2932
C22⋊Q8×C2932
#551293