Finite Group Databasebeta

← #46830974

Subgroups — #46830974

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×#22575837C211yesmaximal, characteristic, complemented
2#41×D541C211yesmaximal, characteristic, complemented
3#31772660C212yesmaximal, complemented
4#31772659C211yesmaximal, characteristic, complemented
5#31772656C211yesmaximal, characteristic, complemented
6#31772655C212yesmaximal, complemented
7#31772653C211yesmaximal, characteristic, complemented
8#31772651C212yesmaximal, complemented
9#31772649C212yesmaximal, complemented
10M16×D541C211yesmaximal, characteristic, complemented
11#137×C541C211yesmaximal, characteristic, complemented
12#22575837—21no—
13#22575837—21no—
14#22575837C2212yes—
15#22575837C2212yescomplemented
16#22575837C2211yescharacteristic, complemented
17#22575836—21no—
18#22575836C2211yescharacteristic
19#22575835—21no—
20#22575835C2211yescharacteristic, complemented
21Q8×D541C2211yescharacteristic, complemented
22C2×D2164—21no—
23C2×D2164C2211yescharacteristic, complemented
24D4×D541—21no—
25D4×D541C2211yescharacteristic, complemented
26C2×C4×D541—21no—
27C2×C4×D541—21no—
28C2×C4×D541C2211yescharacteristic
29#22575826C2212yescomplemented
30#22575825C2212yescomplemented
31#22575823C2212yescomplemented
32#22575823C2212yescomplemented
33D4328C2212yescomplemented
34#22575821C2212yescomplemented
35#22575820C2211yescharacteristic, complemented
36#22575819C2212yescomplemented
37C8×D541C2212yescomplemented
38#41×C541C2211yescharacteristic
39C2×Q8×C541C2211yescharacteristic, complemented
40Q16×C541C2212yescomplemented
41SD16×C541C2212yescomplemented
42M16×C541C2211yescharacteristic, complemented
43C22×D541—21no—
44C22×D541—21no—
45C22×D541D411yescharacteristic
46Dic1082—21no—
47Dic1082C2311yescharacteristic
48D2164—21no—
49D2164—22no—
50D2164—22no—
51D2164—21no—
52D2164C2312yes—
53D2164C2311yescharacteristic
54C22⋊D541—21no—
55C22⋊D541—21no—
56C22⋊D541—21no—
57C2×Dic541—21no—
58C2×Dic541D411yescharacteristic
59C4×D541—21no—
60C4×D541—21no—
61C4×D541—21no—
62C4×D541—22no—
63C4×D541—22no—
64C4×D541D411yescharacteristic
65C4×D541D411yescharacteristic
66C4×D541C2311yescharacteristic
67C4×D541C2311yescharacteristic
68#16864513C2312yes—
69Q8×C541—21no—
70Q8×C541C2312yes—
71Q8×C541C2311yescharacteristic
72D4×C541—21no—
73D4×C541C2311yescharacteristic
74C2×C4×C541—21no—
75C2×C4×C541—21no—
76C2×C4×C541C2311yescharacteristic
77C8×C541C2312yes—
78C22×C541—21no—
79C22×C541C2×D411yescharacteristic
80C2×D541—21no—
81C2×D541—22no—
82C2×D541—41no—
83C2×D541—42no—
84C2×D541—42no—
85C2×D541C2×D411yescharacteristic
86C2×D541C2×D411yescharacteristic
87C4×C541—22no—
88C4×C541—21no—
89C4×C541C2×D411yescharacteristic
90C4×C541C2411yescharacteristic
91Dic541—21no—
92Dic541C2×D411yescharacteristic
93Dic541C2×D411yescharacteristic
94C2×C541—21no—
95C2×C541—41no—
96C2×C541C22×D411yescharacteristic
97D541—21no—
98D541—21no—
99D541—41no—
100D541—42no—
101C541#57511yescharacteristic, complemented, Sylow
102#575—5411nomaximal, Sylow
103C2×#41—5411no—
104C2×#41—5411no—
105#137—5411no—
106#137—5412no—
107#137D54111yescharacteristic, complemented
108AGL(1,ℤ/8)—5411no—
109AGL(1,ℤ/8)—5412no—
110AGL(1,ℤ/8)—5411no—
111#135—5412no—
112#135—5412no—
113C2×M16—5411no—
114#41—5411no—
115#41—5412no—
116#41—5412no—
117#41—5411no—
118#41—5411no—
119#41—10821no—
120#41—10821no—
121#41—10821no—
122#41—10821no—
123#41C2×D54111yescharacteristic
124C2×Q8—5411no—
125C2×Q8C2×D54111yescharacteristic, complemented
126C2×D4—5411no—
127C2×D4—5411no—
128C2×D4—10821no—
129C2×D4—10821no—
130C22×C4—5411no—
131C22×C4—10821no—
132C22×C4—10821no—
133Q16—5412no—
134Q16C2×D54112yescomplemented
135SD16—5412no—
136SD16—5412no—
137SD16—5412no—
138SD16C2×D54112yescomplemented
139D8—5412no—
140D8—5412no—
141M16—5411no—
142M16—5412no—
143M16C2×D54111yescharacteristic, complemented
144C2×C8—5412no—
145C23—5411no—
146C23—10821no—
147C23—10821no—
148Q8—21no—
149Q8—5411no—
150Q8—10821no—
151Q8C22×D54111yescharacteristic
152Q8C22×D54112yes—
153D4—21no—
154D4—5412no—
155D4—5411no—
156D4—10821no—
157D4—10822no—
158D4—10822no—
159D4—10821no—
160D4—10821no—
161D4—10821no—
162D4—10821no—
163D4C22×D54111yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—5411no—
167C2×C4—5411no—
168C2×C4—5411no—
169C2×C4—5411no—
170C2×C4—5411no—
171C2×C4—10821no—
172C2×C4—10822no—
173C2×C4—10822no—
174C2×C4—10821no—
175C2×C4—10821no—
176C2×C4—10821no—
177C2×C4C22×D54111yescharacteristic
178C8—5412no—
179C8C22×D54112yes—
180C22—21no—
181C22—5411no—
182C22—5411no—
183C22—10822no—
184C22—10821no—
185C22—21641no—
186C22—21642no—
187C22—21642no—
188C22D4×D54111yescharacteristic
189C4—21no—
190C4—22no—
191C4—5411no—
192C4—5411no—
193C4—10821no—
194C4D4×D54111yescharacteristic
195C4C23×D54111yescharacteristic
196C2—21no—
197C2—41no—
198C2—10821no—
199C2—10821no—
200C2—21642no—
201C2—21641no—
202C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC2C2×D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
Fitting#137×C541C2
socleC2×C541C22×D4
hypercenter#137D541
hypocenterC541#575
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#22575837C2semidirect
2. #41×D541C2semidirect
3. #31772660C2semidirect
4. #31772659C2semidirect
5. #31772656C2semidirect
6. #31772655C2semidirect
7. #31772653C2semidirect
8. #31772651C2semidirect
9. #31772649C2semidirect
10. M16×D541C2semidirect
11. #137×C541C2semidirect
15. #22575837C22semidirect
16. #22575837C22semidirect
20. #22575835C22semidirect
21. Q8×D541C22semidirect
23. C2×D2164C22semidirect
25. D4×D541C22semidirect
29. #22575826C22semidirect
30. #22575825C22semidirect
31. #22575823C22semidirect
32. #22575823C22semidirect
33. D4328C22semidirect
34. #22575821C22semidirect
35. #22575820C22semidirect
36. #22575819C22semidirect
37. C8×D541C22semidirect
39. C2×Q8×C541C22semidirect
40. Q16×C541C22semidirect
41. SD16×C541C22semidirect
42. M16×C541C22semidirect
101. C541#575semidirect
107. #137D541semidirect
125. C2×Q8C2×D541semidirect
134. Q16C2×D541semidirect
138. SD16C2×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×#225758372
#41×D5412
#317726602
#317726592
#317726562
#317726552
#317726532
#317726512
#317726492
M16×D5412
#137×C5412
#575541