Finite Group Databasebeta

← #45688228

Subgroups — #45688228

Order 33344.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#22552363C211yesmaximal, characteristic, complemented
2#41×D521C211yesmaximal, characteristic, complemented
3#30659741C211yesmaximal, characteristic, complemented
4#30659738C211yesmaximal, characteristic, complemented
5#30659737C212yesmaximal, complemented
6#30659734C211yesmaximal, characteristic, complemented
7#30659732C212yesmaximal, complemented
8#30659729C212yesmaximal, complemented
9#30659727C212yesmaximal, complemented
10M16×D521C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C521C211yesmaximal, characteristic, complemented
12#22552365C2211yescharacteristic, complemented
13#22552364—21no—
14#22552364C2211yescharacteristic
15#22552363—21no—
16#22552363—21no—
17#22552363—21no—
18#22552363C2212yes—
19#22552363C2211yescharacteristic, complemented
20#22552363C2212yescomplemented
21C2×Dic1042C2211yescharacteristic, complemented
22Q8×D521C2211yescharacteristic, complemented
23C2×C22⋊D521—21no—
24D4×D521—21no—
25D4×D521C2211yescharacteristic, complemented
26C22×Dic521—21no—
27C2×C4×D521—21no—
28C2×C4×D521C2211yescharacteristic
29Dic2084C2212yescomplemented
30#22552354C2212yescomplemented
31#22552353C2212yescomplemented
32#22552352C2212yescomplemented
33#22552352C2212yescomplemented
34#22552349C2212yescomplemented
35#22552348C2211yescharacteristic, complemented
36#22552347C2212yescomplemented
37C8×D521C2212yescomplemented
38#41×C521C2211yescharacteristic
39C2×D4×C521C2211yescharacteristic, complemented
40SD16×C521C2212yescomplemented
41D8×C521C2212yescomplemented
42M16×C521C2211yescharacteristic, complemented
43C22×D521—21no—
44C22×D521D411yescharacteristic
45Dic1042—21no—
46Dic1042—21no—
47Dic1042C2311yescharacteristic
48Dic1042C2312yes—
49D2084—21no—
50D2084C2311yescharacteristic
51C22⋊D521—21no—
52C22⋊D521—21no—
53C22⋊D521—22no—
54C22⋊D521—22no—
55C22⋊D521—21no—
56C2×Dic521—21no—
57C2×Dic521—21no—
58C2×Dic521—22no—
59C2×Dic521—22no—
60C2×Dic521D411yescharacteristic
61C4×D521—21no—
62C4×D521—21no—
63C4×D521—21no—
64C4×D521D411yescharacteristic
65C4×D521D411yescharacteristic
66C4×D521C2311yescharacteristic
67C4×D521C2311yescharacteristic
68#16861960C2312yes—
69C23×C521—21no—
70Q8×C521C2311yescharacteristic
71D4×C521—21no—
72D4×C521—21no—
73D4×C521C2311yescharacteristic
74D4×C521C2312yes—
75C2×C4×C521—21no—
76C2×C4×C521C2311yescharacteristic
77C8×C521C2312yes—
78C22×C521—21no—
79C22×C521—22no—
80C22×C521—42no—
81C22×C521C2×D411yescharacteristic
82C2×D521—21no—
83C2×D521—41no—
84C2×D521—42no—
85C2×D521C2×D411yescharacteristic
86C2×D521C2×D411yescharacteristic
87C4×C521—21no—
88C4×C521C2×D411yescharacteristic
89C4×C521C2411yescharacteristic
90Dic521—21no—
91Dic521—22no—
92Dic521C2×D411yescharacteristic
93Dic521C2×D411yescharacteristic
94C2×C521—21no—
95C2×C521—41no—
96C2×C521—42no—
97C2×C521C22×D411yescharacteristic
98D521—21no—
99D521—21no—
100D521—41no—
101C521#57511yescharacteristic, complemented, Sylow
102#575—5211nomaximal, Sylow
103C2×#41—5211no—
104C2×#41—5211no—
105#137—5211no—
106#137—5212no—
107#137—5211no—
108AGL(1,ℤ/8)—5211no—
109AGL(1,ℤ/8)—5212no—
110AGL(1,ℤ/8)D52111yescharacteristic, complemented
111#135—5212no—
112#135—5212no—
113C2×M16—5211no—
114#41—5211no—
115#41—5212no—
116#41—5212no—
117#41—5211no—
118#41—5211no—
119#41—10421no—
120#41—10421no—
121#41—10421no—
122#41—10421no—
123#41C2×D52111yescharacteristic
124C2×Q8—5211no—
125C2×Q8—5211no—
126C2×D4—5211no—
127C2×D4—10421no—
128C2×D4—10421no—
129C2×D4C2×D52111yescharacteristic, complemented
130C22×C4—5211no—
131C22×C4—10421no—
132C22×C4—10421no—
133Q16—5212no—
134Q16—5212no—
135SD16—5212no—
136SD16—5212no—
137SD16—5212no—
138SD16C2×D52112yescomplemented
139D8—5212no—
140D8C2×D52112yescomplemented
141M16—5211no—
142M16—5212no—
143M16C2×D52111yescharacteristic, complemented
144C2×C8—5212no—
145C23—21no—
146C23—5211no—
147C23—10421no—
148Q8—5211no—
149Q8—5212no—
150Q8—10421no—
151Q8—10421no—
152Q8C22×D52111yescharacteristic
153D4—21no—
154D4—21no—
155D4—5211no—
156D4—10421no—
157D4—10421no—
158D4—10421no—
159D4—10422no—
160D4—10422no—
161D4—10421no—
162D4C22×D52112yes—
163D4C22×D52111yescharacteristic
164C2×C4—21no—
165C2×C4—5211no—
166C2×C4—5211no—
167C2×C4—5211no—
168C2×C4—5211no—
169C2×C4—5211no—
170C2×C4—10421no—
171C2×C4—10421no—
172C2×C4—10421no—
173C2×C4—10422no—
174C2×C4—10422no—
175C2×C4—10421no—
176C2×C4—10421no—
177C2×C4C22×D52111yescharacteristic
178C8—5212no—
179C8C22×D52112yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—5211no—
184C22—5211no—
185C22—10421no—
186C22—20841no—
187C22—20842no—
188C22D4×D52111yescharacteristic
189C4—21no—
190C4—5211no—
191C4—5211no—
192C4—10421no—
193C4—10422no—
194C4D4×D52111yescharacteristic
195C4C23×D52111yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—10421no—
200C2—10421no—
201C2—20841no—
202C2C2×D4×D52111yescharacteristic
subgroupG/H
centerC2C2×D4×D521
commutator, cosocleC4×C521C24
FrattiniC4C23×D521
FittingAGL(1,ℤ/8)×C521C2
socleC2×C521C22×D4
hypercenterAGL(1,ℤ/8)D521
hypocenterC521#575
LCSG ▷ C4×C521 ▷ C2×C521 ▷ C521
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#22552363C2semidirect
2. #41×D521C2semidirect
3. #30659741C2semidirect
4. #30659738C2semidirect
5. #30659737C2semidirect
6. #30659734C2semidirect
7. #30659732C2semidirect
8. #30659729C2semidirect
9. #30659727C2semidirect
10. M16×D521C2semidirect
11. AGL(1,ℤ/8)×C521C2semidirect
12. #22552365C22semidirect
19. #22552363C22semidirect
20. #22552363C22semidirect
21. C2×Dic1042C22semidirect
22. Q8×D521C22semidirect
25. D4×D521C22semidirect
29. Dic2084C22semidirect
30. #22552354C22semidirect
31. #22552353C22semidirect
32. #22552352C22semidirect
33. #22552352C22semidirect
34. #22552349C22semidirect
35. #22552348C22semidirect
36. #22552347C22semidirect
37. C8×D521C22semidirect
39. C2×D4×C521C22semidirect
40. SD16×C521C22semidirect
41. D8×C521C22semidirect
42. M16×C521C22semidirect
101. C521#575semidirect
110. AGL(1,ℤ/8)D521semidirect
129. C2×D4C2×D521semidirect
138. SD16C2×D521semidirect
140. D8C2×D521semidirect
143. M16C2×D521semidirect

Maximal subgroups

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

subgroupindex
C2×#225523632
#41×D5212
#306597412
#306597382
#306597372
#306597342
#306597322
#306597292
#306597272
M16×D5212
AGL(1,ℤ/8)×C5212
#575521