Finite Group Databasebeta

← #46830971

Subgroups — #46830971

Order 34624.

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×#22575835C211yesmaximal, characteristic, complemented
2#41×D541C211yesmaximal, characteristic, complemented
3#31772661C211yesmaximal, characteristic, complemented
4#31772658C211yesmaximal, characteristic, complemented
5#31772657C212yesmaximal, complemented
6#31772654C211yesmaximal, characteristic, complemented
7#31772652C212yesmaximal, complemented
8#31772649C212yesmaximal, complemented
9#31772647C212yesmaximal, complemented
10M16×D541C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C541C211yesmaximal, characteristic, complemented
12#22575837C2211yescharacteristic, complemented
13#22575836—21no—
14#22575836C2211yescharacteristic
15#22575835—21no—
16#22575835—21no—
17#22575835—21no—
18#22575835C2212yes—
19#22575835C2211yescharacteristic, complemented
20#22575835C2212yescomplemented
21C2×Dic1082C2211yescharacteristic, complemented
22Q8×D541C2211yescharacteristic, complemented
23C2×C22⋊D541—21no—
24D4×D541—21no—
25D4×D541C2211yescharacteristic, complemented
26C22×Dic541—21no—
27C2×C4×D541—21no—
28C2×C4×D541C2211yescharacteristic
29Dic2164C2212yescomplemented
30#22575826C2212yescomplemented
31#22575825C2212yescomplemented
32#22575824C2212yescomplemented
33#22575824C2212yescomplemented
34#22575821C2212yescomplemented
35#22575820C2211yescharacteristic, complemented
36#22575819C2212yescomplemented
37C8×D541C2212yescomplemented
38#41×C541C2211yescharacteristic
39C2×D4×C541C2211yescharacteristic, complemented
40SD16×C541C2212yescomplemented
41D8×C541C2212yescomplemented
42M16×C541C2211yescharacteristic, complemented
43C22×D541—21no—
44C22×D541D411yescharacteristic
45Dic1082—21no—
46Dic1082—21no—
47Dic1082C2311yescharacteristic
48Dic1082C2312yes—
49D2164—21no—
50D2164C2311yescharacteristic
51C22⋊D541—21no—
52C22⋊D541—21no—
53C22⋊D541—22no—
54C22⋊D541—22no—
55C22⋊D541—21no—
56C2×Dic541—21no—
57C2×Dic541—21no—
58C2×Dic541—22no—
59C2×Dic541—22no—
60C2×Dic541D411yescharacteristic
61C4×D541—21no—
62C4×D541—21no—
63C4×D541—21no—
64C4×D541D411yescharacteristic
65C4×D541D411yescharacteristic
66C4×D541C2311yescharacteristic
67C4×D541C2311yescharacteristic
68#16864513C2312yes—
69C23×C541—21no—
70Q8×C541C2311yescharacteristic
71D4×C541—21no—
72D4×C541—21no—
73D4×C541C2311yescharacteristic
74D4×C541C2312yes—
75C2×C4×C541—21no—
76C2×C4×C541C2311yescharacteristic
77C8×C541C2312yes—
78C22×C541—22no—
79C22×C541—21no—
80C22×C541—42no—
81C22×C541C2×D411yescharacteristic
82C2×D541—21no—
83C2×D541—41no—
84C2×D541—42no—
85C2×D541C2×D411yescharacteristic
86C2×D541C2×D411yescharacteristic
87C4×C541—21no—
88C4×C541C2×D411yescharacteristic
89C4×C541C2411yescharacteristic
90Dic541—21no—
91Dic541—22no—
92Dic541C2×D411yescharacteristic
93Dic541C2×D411yescharacteristic
94C2×C541—21no—
95C2×C541—41no—
96C2×C541—42no—
97C2×C541C22×D411yescharacteristic
98D541—21no—
99D541—21no—
100D541—41no—
101C541#57511yescharacteristic, complemented, Sylow
102#575—5411nomaximal, Sylow
103C2×#41—5411no—
104C2×#41—5411no—
105#137—5411no—
106#137—5412no—
107#137—5411no—
108AGL(1,ℤ/8)—5411no—
109AGL(1,ℤ/8)—5412no—
110AGL(1,ℤ/8)D54111yescharacteristic, complemented
111#135—5412no—
112#135—5412no—
113C2×M16—5411no—
114#41—5411no—
115#41—5412no—
116#41—5411no—
117#41—5412no—
118#41—5411no—
119#41—10821no—
120#41—10821no—
121#41—10821no—
122#41—10821no—
123#41C2×D54111yescharacteristic
124C2×Q8—5411no—
125C2×Q8—5411no—
126C2×D4—5411no—
127C2×D4—10821no—
128C2×D4—10821no—
129C2×D4C2×D54111yescharacteristic, complemented
130C22×C4—5411no—
131C22×C4—10821no—
132C22×C4—10821no—
133Q16—5412no—
134Q16—5412no—
135SD16—5412no—
136SD16—5412no—
137SD16—5412no—
138SD16C2×D54112yescomplemented
139D8—5412no—
140D8C2×D54112yescomplemented
141M16—5411no—
142M16—5412no—
143M16C2×D54111yescharacteristic, complemented
144C2×C8—5412no—
145C23—21no—
146C23—5411no—
147C23—10821no—
148Q8—5411no—
149Q8—5412no—
150Q8—10821no—
151Q8—10821no—
152Q8C22×D54111yescharacteristic
153D4—21no—
154D4—21no—
155D4—5411no—
156D4—10821no—
157D4—10821no—
158D4—10821no—
159D4—10822no—
160D4—10822no—
161D4—10821no—
162D4C22×D54112yes—
163D4C22×D54111yescharacteristic
164C2×C4—21no—
165C2×C4—5411no—
166C2×C4—5411no—
167C2×C4—5411no—
168C2×C4—5411no—
169C2×C4—5411no—
170C2×C4—10821no—
171C2×C4—10821no—
172C2×C4—10821no—
173C2×C4—10822no—
174C2×C4—10822no—
175C2×C4—10821no—
176C2×C4—10821no—
177C2×C4C22×D54111yescharacteristic
178C8—5412no—
179C8C22×D54112yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—5411no—
184C22—5411no—
185C22—10821no—
186C22—21641no—
187C22—21642no—
188C22D4×D54111yescharacteristic
189C4—21no—
190C4—5411no—
191C4—5411no—
192C4—10821no—
193C4—10822no—
194C4D4×D54111yescharacteristic
195C4C23×D54111yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—10821no—
200C2—10821no—
201C2—21641no—
202C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC2C2×D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
FittingAGL(1,ℤ/8)×C541C2
socleC2×C541C22×D4
hypercenterAGL(1,ℤ/8)D541
hypocenterC541#575
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#22575835C2semidirect
2. #41×D541C2semidirect
3. #31772661C2semidirect
4. #31772658C2semidirect
5. #31772657C2semidirect
6. #31772654C2semidirect
7. #31772652C2semidirect
8. #31772649C2semidirect
9. #31772647C2semidirect
10. M16×D541C2semidirect
11. AGL(1,ℤ/8)×C541C2semidirect
12. #22575837C22semidirect
19. #22575835C22semidirect
20. #22575835C22semidirect
21. C2×Dic1082C22semidirect
22. Q8×D541C22semidirect
25. D4×D541C22semidirect
29. Dic2164C22semidirect
30. #22575826C22semidirect
31. #22575825C22semidirect
32. #22575824C22semidirect
33. #22575824C22semidirect
34. #22575821C22semidirect
35. #22575820C22semidirect
36. #22575819C22semidirect
37. C8×D541C22semidirect
39. C2×D4×C541C22semidirect
40. SD16×C541C22semidirect
41. D8×C541C22semidirect
42. M16×C541C22semidirect
101. C541#575semidirect
110. AGL(1,ℤ/8)D541semidirect
129. C2×D4C2×D541semidirect
138. SD16C2×D541semidirect
140. D8C2×D541semidirect
143. M16C2×D541semidirect

Maximal subgroups

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

subgroupindex
C2×#225758352
#41×D5412
#317726612
#317726582
#317726572
#317726542
#317726522
#317726492
#317726472
M16×D5412
AGL(1,ℤ/8)×C5412
#575541