Finite Group Databasebeta

← #45688177

Subgroups — #45688177

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#30659695C211yesmaximal, characteristic, complemented
3#30659694C211yesmaximal, characteristic, complemented
4#30659691C211yesmaximal, characteristic, complemented
5#30659690C211yesmaximal, characteristic, complemented
6#30659689C211yesmaximal, characteristic, complemented
7#30659689C211yesmaximal, characteristic, complemented
8#30659687C211yesmaximal, characteristic, complemented
9#30659686C211yesmaximal, characteristic, complemented
10#30659685C211yesmaximal, characteristic, complemented
11#30659685C211yesmaximal, characteristic, complemented
12#30659680C211yesmaximal, characteristic, complemented
13#30659680C211yesmaximal, characteristic, complemented
14#30659679C211yesmaximal, characteristic, complemented
15#121×C521C211yesmaximal, characteristic, complemented
16C2×Dic1042C2211yescharacteristic
17C2×Dic1042C2211yescharacteristic
18C2×C22⋊D521C2211yescharacteristic
19C2×C22⋊D521C2211yescharacteristic
20C2×C22⋊D521C2211yescharacteristic
21C22×Dic521C2211yescharacteristic
22C22×Dic521C2211yescharacteristic
23C2×C4×D521C2211yescharacteristic
24C4⋊Dic521C2211yescharacteristic
25C4⋊Dic521C2211yescharacteristic
26#22552343C2211yescharacteristic
27#22552343C2211yescharacteristic
28#22552343C2211yescharacteristic
29#22552343C2211yescharacteristic
30#22552343C2211yescharacteristic
31#22552343C2211yescharacteristic
32#22552343C2211yescharacteristic
33C22⋊Dic521C2211yescharacteristic
34C22⋊Dic521C2211yescharacteristic
35C22⋊Dic521C2211yescharacteristic
36C22⋊Dic521C2211yescharacteristic
37C22⋊Dic521C2211yescharacteristic
38C22⋊Dic521C2211yescharacteristic
39C22⋊Dic521C2211yescharacteristic
40#22552341C2211yescharacteristic
41#22552341C2211yescharacteristic
42#22552341C2211yescharacteristic
43C4×Dic521C2211yescharacteristic
44C2×D4×C521C2211yescharacteristic
45C2×D4×C521C2211yescharacteristic
46C2×D4×C521C2211yescharacteristic
47C22×C4×C521C2211yescharacteristic
48C4⋊C4×C521C2211yescharacteristic
49C22⋊C4×C521C2211yescharacteristic
50C22⋊C4×C521C2211yescharacteristic
51C22×D521C2311yescharacteristic
52Dic1042—41no—
53Dic1042—41no—
54C22⋊D521—41no—
55C22⋊D521—41no—
56C22⋊D521—41no—
57C2×Dic521—41no—
58C2×Dic521—41no—
59C2×Dic521C2311yescharacteristic
60C2×Dic521C2311yescharacteristic
61C2×Dic521C2311yescharacteristic
62C2×Dic521C2311yescharacteristic
63C2×Dic521C2311yescharacteristic
64C2×Dic521C2311yescharacteristic
65C2×Dic521C2311yescharacteristic
66C4×D521—41no—
67C23×C521C2311yescharacteristic
68C23×C521C2311yescharacteristic
69C23×C521C2311yescharacteristic
70D4×C521—41no—
71D4×C521—41no—
72D4×C521—41no—
73C2×C4×C521—41no—
74C2×C4×C521C2311yescharacteristic
75C2×C4×C521C2311yescharacteristic
76C2×C4×C521C2311yescharacteristic
77C2×C4×C521C2311yescharacteristic
78C22×C521—21no—
79C22×C521—21no—
80C22×C521—21no—
81C22×C521—21no—
82C22×C521—21no—
83C22×C521—21no—
84C22×C521—21no—
85C22×C521—21no—
86C22×C521—21no—
87C22×C521C2411yescharacteristic
88C2×D521—21no—
89C2×D521—21no—
90C2×D521—21no—
91C4×C521—21no—
92C4×C521—21no—
93C4×C521—21no—
94C4×C521—21no—
95Dic521—21no—
96Dic521—21no—
97Dic521—21no—
98Dic521—21no—
99Dic521—21no—
100Dic521—21no—
101Dic521—21no—
102C2×C521—41no—
103C2×C521—41no—
104C2×C521—41no—
105C2×C521H(5,𝔽2)11yescharacteristic
106C2×C521H(5,𝔽2)11yescharacteristic
107C2×C5212−1+411yescharacteristic
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⋊Q8—5211no—
122#121—5211no—
123#121—5211no—
124#121—5211no—
125#121D52111yescharacteristic, complemented
126C2×Q8—5211no—
127C2×Q8—5211no—
128C2×D4—5211no—
129C2×D4—5211no—
130C2×D4—5211no—
131C2×D4C2×D52111yescharacteristic
132C2×D4C2×D52111yescharacteristic
133C2×D4C2×D52111yescharacteristic
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⋊C4—5211no—
146C4⋊C4—5211no—
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—
162C23C22×D52111yescharacteristic
163C23C22×D52111yescharacteristic
164C23C22×D52111yescharacteristic
165Q8—20841no—
166Q8—20841no—
167D4—41no—
168D4—41no—
169D4—41no—
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—5211no—
180C2×C4—5211no—
181C2×C4—20841no—
182C2×C4—20841no—
183C2×C4—20841no—
184C2×C4C22×D52111yescharacteristic
185C2×C4C22×D52111yescharacteristic
186C2×C4C22×D52111yescharacteristic
187C2×C4C22×D52111yescharacteristic
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—10421no—
198C22—10421no—
199C22—10421no—
200C22C23×D52111yescharacteristic
201C4—21no—
202C4—21no—
203C4—21no—
204C4—21no—
205C4—10421no—
206C4—10421no—
207C4—10421no—
208C4—10421no—
209C4—10421no—
210C4—10421no—
211C4—10421no—
212C2—41no—
213C2—41no—
214C2—41no—
215C2—20841no—
216C2#3065975311yescharacteristic
217C2#3065975311yescharacteristic
218C2#3065975511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D521
commutator, socle, cosocleC22×C521C24
Fitting#121×C521C2
hypercenter#121D521
hypocenterC521#562
LCSG ▷ C22×C521 ▷ C521
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #30659698C2semidirect
2. #30659695C2semidirect
3. #30659694C2semidirect
4. #30659691C2semidirect
5. #30659690C2semidirect
6. #30659689C2semidirect
7. #30659689C2semidirect
8. #30659687C2semidirect
9. #30659686C2semidirect
10. #30659685C2semidirect
11. #30659685C2semidirect
12. #30659680C2semidirect
13. #30659680C2semidirect
14. #30659679C2semidirect
15. #121×C521C2semidirect
109. C521#562semidirect
125. #121D521semidirect

Maximal subgroups

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

subgroupindex
#306596982
#306596952
#306596942
#306596912
#306596902
#306596892
#306596872
#306596862
#306596852
#306596802
#306596792
#121×C5212
#562521