Finite Group Databasebeta

← #14581082

Subgroups — #14581082

Order 2624.

220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 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#13050154C211yesmaximal, characteristic, complemented
2#13050153C211yesmaximal, characteristic, complemented
3#13050150C211yesmaximal, characteristic, complemented
4#13050149C211yesmaximal, characteristic, complemented
5#13050149C211yesmaximal, characteristic, complemented
6#13050147C211yesmaximal, characteristic, complemented
7#13050146C211yesmaximal, characteristic, complemented
8#13050144C211yesmaximal, characteristic, complemented
9#13050142C211yesmaximal, characteristic, complemented
10#13050140C211yesmaximal, characteristic, complemented
11#13050139C211yesmaximal, characteristic, complemented
12#13050138C211yesmaximal, characteristic, complemented
13#13050137C211yesmaximal, characteristic, complemented
14#13050137C211yesmaximal, characteristic, complemented
15C22⋊Q8×C41C211yesmaximal, characteristic, complemented
16C2×Q8×C41C2211yescharacteristic
17C22×C4×C41C2211yescharacteristic
18C2×C22⋊D41C2211yescharacteristic
19C2×C22⋊D41C2211yescharacteristic
20C2×C22⋊D41C2211yescharacteristic
21C2×D164C2211yescharacteristic
22C2×D164C2211yescharacteristic
23C2×D164C2211yescharacteristic
24C2×C4×D41C2211yescharacteristic
25C2×C4×D41C2211yescharacteristic
26C2×C4×D41C2211yescharacteristic
27C2×Dic82C2211yescharacteristic
28C4⋊C4×C41C2211yescharacteristic
29C4⋊C4×C41C2211yescharacteristic
30C4⋊C4×C41C2211yescharacteristic
31C22⋊C4×C41C2211yescharacteristic
32C22⋊C4×C41C2211yescharacteristic
33C22⋊Dic41C2211yescharacteristic
34#10620281C2211yescharacteristic
35#10620281C2211yescharacteristic
36#10620281C2211yescharacteristic
37#10620281C2211yescharacteristic
38#10620281C2211yescharacteristic
39#10620281C2211yescharacteristic
40#10620281C2211yescharacteristic
41#10620281C2211yescharacteristic
42#10620281C2211yescharacteristic
43C4⋊Dic41C2211yescharacteristic
44C4⋊Dic41C2211yescharacteristic
45#10620279C2211yescharacteristic
46#10620279C2211yescharacteristic
47#10620279C2211yescharacteristic
48#10620279C2211yescharacteristic
49#10620279C2211yescharacteristic
50C4×Dic41C2211yescharacteristic
51C23×C41C2311yescharacteristic
52C22×D41C2311yescharacteristic
53C22×D41C2311yescharacteristic
54C22×D41C2311yescharacteristic
55Q8×C41—41no—
56C2×C4×C41—41no—
57C2×C4×C41C2311yescharacteristic
58C2×C4×C41C2311yescharacteristic
59C2×C4×C41C2311yescharacteristic
60C2×C4×C41C2311yescharacteristic
61C2×C4×C41C2311yescharacteristic
62C2×C4×C41C2311yescharacteristic
63C22⋊D41—41no—
64C22⋊D41—41no—
65C22⋊D41—41no—
66C2×Dic41C2311yescharacteristic
67C2×Dic41C2311yescharacteristic
68C2×Dic41C2311yescharacteristic
69C2×Dic41C2311yescharacteristic
70C2×Dic41C2311yescharacteristic
71D164—41no—
72D164—41no—
73D164—41no—
74C4×D41—41no—
75C4×D41—41no—
76C4×D41—41no—
77Dic82—41no—
78C22×C41—21no—
79C22×C41—21no—
80C22×C41—21no—
81C22×C41C2411yescharacteristic
82C2×D41—21no—
83C2×D41—21no—
84C2×D41—21no—
85C2×D41—21no—
86C2×D41—21no—
87C2×D41—21no—
88C2×D41—21no—
89C2×D41—21no—
90C2×D41—21no—
91C4×C41—21no—
92C4×C41—21no—
93C4×C41—21no—
94C4×C41—21no—
95C4×C41—21no—
96C4×C41—21no—
97Dic41—21no—
98Dic41—21no—
99Dic41—21no—
100Dic41—21no—
101Dic41—21no—
102C2×C41—41no—
103C2×C41H(5,𝔽2)11yescharacteristic
104C2×C41H(5,𝔽2)11yescharacteristic
105C2×C412−1+411yescharacteristic
106D41—41no—
107D41—41no—
108D41—41no—
109#562—411nomaximal, Sylow
110C41#56211yescharacteristic, complemented, Sylow
111#125—411no—
112#124—411no—
113#124—411no—
114#123—411no—
115#123—411no—
116#123—411no—
117#123—411no—
118C22⋊Q8—411no—
119C22⋊Q8—411no—
120C22⋊Q8—411no—
121C22⋊Q8D4111yescharacteristic, complemented
122#121—411no—
123#121—411no—
124#121—411no—
125#121—411no—
126C2×Q8—411no—
127C2×Q8C2×D4111yescharacteristic
128C2×D4—411no—
129C2×D4—411no—
130C2×D4—411no—
131C2×D4—411no—
132C2×D4—411no—
133C2×D4—411no—
134C22×C4—411no—
135C22×C4—411no—
136C22×C4—411no—
137C22×C4C2×D4111yescharacteristic
138C4⋊C4—411no—
139C4⋊C4—411no—
140C4⋊C4—411no—
141C4⋊C4—411no—
142C4⋊C4—411no—
143C4⋊C4—411no—
144C4⋊C4—411no—
145C4⋊C4C2×D4111yescharacteristic
146C4⋊C4C2×D4111yescharacteristic
147C4⋊C4C2×D4111yescharacteristic
148C22⋊C4—411no—
149C22⋊C4—411no—
150C22⋊C4—411no—
151C22⋊C4—411no—
152C22⋊C4—411no—
153C22⋊C4—411no—
154C22⋊C4—411no—
155C22⋊C4—411no—
156C22⋊C4—411no—
157C22⋊C4—411no—
158C22⋊C4C2×D4111yescharacteristic
159C22⋊C4C2×D4111yescharacteristic
160C42—411no—
161C23—411no—
162C23—411no—
163C23—411no—
164C23C22×D4111yescharacteristic
165Q8—41no—
166Q8—1641no—
167D4—1641no—
168D4—1641no—
169D4—1641no—
170D4—1641no—
171D4—1641no—
172D4—1641no—
173C2×C4—41no—
174C2×C4—411no—
175C2×C4—411no—
176C2×C4—411no—
177C2×C4—411no—
178C2×C4—411no—
179C2×C4—1641no—
180C2×C4—1641no—
181C2×C4—1641no—
182C2×C4C22×D4111yescharacteristic
183C2×C4C22×D4111yescharacteristic
184C2×C4C22×D4111yescharacteristic
185C2×C4C22×D4111yescharacteristic
186C2×C4C22×D4111yescharacteristic
187C2×C4C22×D4111yescharacteristic
188C22—21no—
189C22—21no—
190C22—21no—
191C22—821no—
192C22—821no—
193C22—821no—
194C22—821no—
195C22—821no—
196C22—821no—
197C22—821no—
198C22—821no—
199C22—821no—
200C22C23×D4111yescharacteristic
201C4—21no—
202C4—21no—
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—821no—
208C4—821no—
209C4—821no—
210C4—821no—
211C4—821no—
212C2—41no—
213C2—1641no—
214C2—1641no—
215C2—1641no—
216C2#1305020911yescharacteristic
217C2#1305021011yescharacteristic
218C2#1305021211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
FittingC22⋊Q8×C41C2
hypercenterC22⋊Q8D41
hypocenterC41#562
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13050154C2semidirect
2. #13050153C2semidirect
3. #13050150C2semidirect
4. #13050149C2semidirect
5. #13050149C2semidirect
6. #13050147C2semidirect
7. #13050146C2semidirect
8. #13050144C2semidirect
9. #13050142C2semidirect
10. #13050140C2semidirect
11. #13050139C2semidirect
12. #13050138C2semidirect
13. #13050137C2semidirect
14. #13050137C2semidirect
15. C22⋊Q8×C41C2semidirect
110. C41#562semidirect
121. C22⋊Q8D41semidirect

Maximal subgroups

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

subgroupindex
#130501542
#130501532
#130501502
#130501492
#130501472
#130501462
#130501442
#130501422
#130501402
#130501392
#130501382
#130501372
C22⋊Q8×C412
#56241