Finite Group Databasebeta

← #45688178

Subgroups — #45688178

Order 33344.

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#30659698C211yesmaximal, characteristic, complemented
2#30659697C211yesmaximal, characteristic, complemented
3#30659694C211yesmaximal, characteristic, complemented
4#30659693C211yesmaximal, characteristic, complemented
5#30659693C211yesmaximal, characteristic, complemented
6#30659691C211yesmaximal, characteristic, complemented
7#30659690C211yesmaximal, characteristic, complemented
8#30659688C211yesmaximal, characteristic, complemented
9#30659686C211yesmaximal, characteristic, complemented
10#30659684C211yesmaximal, characteristic, complemented
11#30659683C211yesmaximal, characteristic, complemented
12#30659682C211yesmaximal, characteristic, complemented
13#30659681C211yesmaximal, characteristic, complemented
14#30659681C211yesmaximal, characteristic, complemented
15C22⋊Q8×C521C211yesmaximal, characteristic, complemented
16C2×Dic1042C2211yescharacteristic
17C2×D2084C2211yescharacteristic
18C2×D2084C2211yescharacteristic
19C2×D2084C2211yescharacteristic
20C2×C22⋊D521C2211yescharacteristic
21C2×C22⋊D521C2211yescharacteristic
22C2×C22⋊D521C2211yescharacteristic
23C2×C4×D521C2211yescharacteristic
24C2×C4×D521C2211yescharacteristic
25C2×C4×D521C2211yescharacteristic
26C4⋊Dic521C2211yescharacteristic
27C4⋊Dic521C2211yescharacteristic
28#22552343C2211yescharacteristic
29#22552343C2211yescharacteristic
30#22552343C2211yescharacteristic
31#22552343C2211yescharacteristic
32#22552343C2211yescharacteristic
33C22⋊Dic521C2211yescharacteristic
34#22552341C2211yescharacteristic
35#22552341C2211yescharacteristic
36#22552341C2211yescharacteristic
37#22552341C2211yescharacteristic
38#22552341C2211yescharacteristic
39#22552341C2211yescharacteristic
40#22552341C2211yescharacteristic
41#22552341C2211yescharacteristic
42#22552341C2211yescharacteristic
43C4×Dic521C2211yescharacteristic
44C2×Q8×C521C2211yescharacteristic
45C22×C4×C521C2211yescharacteristic
46C4⋊C4×C521C2211yescharacteristic
47C4⋊C4×C521C2211yescharacteristic
48C4⋊C4×C521C2211yescharacteristic
49C22⋊C4×C521C2211yescharacteristic
50C22⋊C4×C521C2211yescharacteristic
51C22×D521C2311yescharacteristic
52C22×D521C2311yescharacteristic
53C22×D521C2311yescharacteristic
54Dic1042—41no—
55D2084—41no—
56D2084—41no—
57D2084—41no—
58C22⋊D521—41no—
59C22⋊D521—41no—
60C22⋊D521—41no—
61C2×Dic521C2311yescharacteristic
62C2×Dic521C2311yescharacteristic
63C2×Dic521C2311yescharacteristic
64C2×Dic521C2311yescharacteristic
65C2×Dic521C2311yescharacteristic
66C4×D521—41no—
67C4×D521—41no—
68C4×D521—41no—
69C23×C521C2311yescharacteristic
70Q8×C521—41no—
71C2×C4×C521—41no—
72C2×C4×C521C2311yescharacteristic
73C2×C4×C521C2311yescharacteristic
74C2×C4×C521C2311yescharacteristic
75C2×C4×C521C2311yescharacteristic
76C2×C4×C521C2311yescharacteristic
77C2×C4×C521C2311yescharacteristic
78C22×C521—21no—
79C22×C521—21no—
80C22×C521—21no—
81C22×C521C2411yescharacteristic
82C2×D521—21no—
83C2×D521—21no—
84C2×D521—21no—
85C2×D521—21no—
86C2×D521—21no—
87C2×D521—21no—
88C2×D521—21no—
89C2×D521—21no—
90C2×D521—21no—
91C4×C521—21no—
92C4×C521—21no—
93C4×C521—21no—
94C4×C521—21no—
95C4×C521—21no—
96C4×C521—21no—
97Dic521—21no—
98Dic521—21no—
99Dic521—21no—
100Dic521—21no—
101Dic521—21no—
102C2×C521—41no—
103C2×C521H(5,𝔽2)11yescharacteristic
104C2×C521H(5,𝔽2)11yescharacteristic
105C2×C5212−1+411yescharacteristic
106D521—41no—
107D521—41no—
108D521—41no—
109C521#56211yescharacteristic, complemented, Sylow
110#562—5211nomaximal, Sylow
111#125—5211no—
112#124—5211no—
113#124—5211no—
114#123—5211no—
115#123—5211no—
116#123—5211no—
117#123—5211no—
118C22⋊Q8—5211no—
119C22⋊Q8—5211no—
120C22⋊Q8—5211no—
121C22⋊Q8D52111yescharacteristic, complemented
122#121—5211no—
123#121—5211no—
124#121—5211no—
125#121—5211no—
126C2×Q8—5211no—
127C2×Q8C2×D52111yescharacteristic
128C2×D4—5211no—
129C2×D4—5211no—
130C2×D4—5211no—
131C2×D4—5211no—
132C2×D4—5211no—
133C2×D4—5211no—
134C22×C4—5211no—
135C22×C4—5211no—
136C22×C4—5211no—
137C22×C4C2×D52111yescharacteristic
138C4⋊C4—5211no—
139C4⋊C4—5211no—
140C4⋊C4—5211no—
141C4⋊C4—5211no—
142C4⋊C4—5211no—
143C4⋊C4—5211no—
144C4⋊C4—5211no—
145C4⋊C4C2×D52111yescharacteristic
146C4⋊C4C2×D52111yescharacteristic
147C4⋊C4C2×D52111yescharacteristic
148C22⋊C4—5211no—
149C22⋊C4—5211no—
150C22⋊C4—5211no—
151C22⋊C4—5211no—
152C22⋊C4—5211no—
153C22⋊C4—5211no—
154C22⋊C4—5211no—
155C22⋊C4—5211no—
156C22⋊C4—5211no—
157C22⋊C4—5211no—
158C22⋊C4C2×D52111yescharacteristic
159C22⋊C4C2×D52111yescharacteristic
160C42—5211no—
161C23—5211no—
162C23—5211no—
163C23—5211no—
164C23C22×D52111yescharacteristic
165Q8—41no—
166Q8—20841no—
167D4—20841no—
168D4—20841no—
169D4—20841no—
170D4—20841no—
171D4—20841no—
172D4—20841no—
173C2×C4—41no—
174C2×C4—5211no—
175C2×C4—5211no—
176C2×C4—5211no—
177C2×C4—5211no—
178C2×C4—5211no—
179C2×C4—20841no—
180C2×C4—20841no—
181C2×C4—20841no—
182C2×C4C22×D52111yescharacteristic
183C2×C4C22×D52111yescharacteristic
184C2×C4C22×D52111yescharacteristic
185C2×C4C22×D52111yescharacteristic
186C2×C4C22×D52111yescharacteristic
187C2×C4C22×D52111yescharacteristic
188C22—21no—
189C22—21no—
190C22—21no—
191C22—10421no—
192C22—10421no—
193C22—10421no—
194C22—10421no—
195C22—10421no—
196C22—10421no—
197C22—10421no—
198C22—10421no—
199C22—10421no—
200C22C23×D52111yescharacteristic
201C4—21no—
202C4—21no—
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—10421no—
208C4—10421no—
209C4—10421no—
210C4—10421no—
211C4—10421no—
212C2—41no—
213C2—20841no—
214C2—20841no—
215C2—20841no—
216C2#3065975311yescharacteristic
217C2#3065975411yescharacteristic
218C2#3065975611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D521
commutator, socle, cosocleC22×C521C24
FittingC22⋊Q8×C521C2
hypercenterC22⋊Q8D521
hypocenterC521#562
LCSG ▷ C22×C521 ▷ C521
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #30659698C2semidirect
2. #30659697C2semidirect
3. #30659694C2semidirect
4. #30659693C2semidirect
5. #30659693C2semidirect
6. #30659691C2semidirect
7. #30659690C2semidirect
8. #30659688C2semidirect
9. #30659686C2semidirect
10. #30659684C2semidirect
11. #30659683C2semidirect
12. #30659682C2semidirect
13. #30659681C2semidirect
14. #30659681C2semidirect
15. C22⋊Q8×C521C2semidirect
109. C521#562semidirect
121. C22⋊Q8D521semidirect

Maximal subgroups

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

subgroupindex
#306596982
#306596972
#306596942
#306596932
#306596912
#306596902
#306596882
#306596862
#306596842
#306596832
#306596822
#306596812
C22⋊Q8×C5212
#562521