Finite Group Databasebeta

← #49183514

Subgroups — #49183514

Order 37952.

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×#23748734C211yesmaximal, characteristic, complemented
2#41×D593C211yesmaximal, characteristic, complemented
3#34039317C212yesmaximal, complemented
4#34039316C211yesmaximal, characteristic, complemented
5#34039313C211yesmaximal, characteristic, complemented
6#34039312C212yesmaximal, complemented
7#34039310C211yesmaximal, characteristic, complemented
8#34039308C212yesmaximal, complemented
9#34039306C212yesmaximal, complemented
10M16×D593C211yesmaximal, characteristic, complemented
11#137×C593C211yesmaximal, characteristic, complemented
12#23748734—21no—
13#23748734—21no—
14#23748734C2212yes—
15#23748734C2212yescomplemented
16#23748734C2211yescharacteristic, complemented
17#23748733—21no—
18#23748733C2211yescharacteristic
19#23748732—21no—
20#23748732C2211yescharacteristic, complemented
21Q8×D593C2211yescharacteristic, complemented
22C2×D2372—21no—
23C2×D2372C2211yescharacteristic, complemented
24D4×D593—21no—
25D4×D593C2211yescharacteristic, complemented
26C2×C4×D593—21no—
27C2×C4×D593—21no—
28C2×C4×D593C2211yescharacteristic
29#23748723C2212yescomplemented
30#23748722C2212yescomplemented
31#23748720C2212yescomplemented
32#23748720C2212yescomplemented
33D4744C2212yescomplemented
34#23748718C2212yescomplemented
35#23748717C2211yescharacteristic, complemented
36#23748716C2212yescomplemented
37C8×D593C2212yescomplemented
38#41×C593C2211yescharacteristic
39C2×Q8×C593C2211yescharacteristic, complemented
40Q16×C593C2212yescomplemented
41SD16×C593C2212yescomplemented
42M16×C593C2211yescharacteristic, complemented
43C22×D593—21no—
44C22×D593—21no—
45C22×D593D411yescharacteristic
46Dic1186—21no—
47Dic1186C2311yescharacteristic
48D2372—21no—
49D2372—22no—
50D2372—22no—
51D2372—21no—
52D2372C2312yes—
53D2372C2311yescharacteristic
54C22⋊D593—21no—
55C22⋊D593—21no—
56C22⋊D593—21no—
57C2×Dic593—21no—
58C2×Dic593D411yescharacteristic
59C4×D593—21no—
60C4×D593—21no—
61C4×D593—21no—
62C4×D593—22no—
63C4×D593—22no—
64C4×D593D411yescharacteristic
65C4×D593D411yescharacteristic
66C4×D593C2311yescharacteristic
67C4×D593C2311yescharacteristic
68#18011654C2312yes—
69Q8×C593—21no—
70Q8×C593C2312yes—
71Q8×C593C2311yescharacteristic
72D4×C593—21no—
73D4×C593C2311yescharacteristic
74C2×C4×C593—21no—
75C2×C4×C593—21no—
76C2×C4×C593C2311yescharacteristic
77C8×C593C2312yes—
78C22×C593—21no—
79C22×C593C2×D411yescharacteristic
80C2×D593—21no—
81C2×D593—22no—
82C2×D593—41no—
83C2×D593—42no—
84C2×D593—42no—
85C2×D593C2×D411yescharacteristic
86C2×D593C2×D411yescharacteristic
87C4×C593—21no—
88C4×C593—22no—
89C4×C593C2×D411yescharacteristic
90C4×C593C2411yescharacteristic
91Dic593—21no—
92Dic593C2×D411yescharacteristic
93Dic593C2×D411yescharacteristic
94C2×C593—21no—
95C2×C593—41no—
96C2×C593C22×D411yescharacteristic
97D593—21no—
98D593—21no—
99D593—41no—
100D593—42no—
101C593#57511yescharacteristic, complemented, Sylow
102#575—5931nomaximal, Sylow
103C2×#41—5931no—
104C2×#41—5931no—
105#137—5931no—
106#137—5932no—
107#137D59311yescharacteristic, complemented
108AGL(1,ℤ/8)—5931no—
109AGL(1,ℤ/8)—5932no—
110AGL(1,ℤ/8)—5931no—
111#135—5932no—
112#135—5932no—
113C2×M16—5931no—
114#41—5932no—
115#41—5931no—
116#41—5932no—
117#41—5931no—
118#41—5931no—
119#41—11861no—
120#41—11861no—
121#41—11861no—
122#41—11861no—
123#41C2×D59311yescharacteristic
124C2×Q8—5931no—
125C2×Q8C2×D59311yescharacteristic, complemented
126C2×D4—5931no—
127C2×D4—5931no—
128C2×D4—11861no—
129C2×D4—11861no—
130C22×C4—5931no—
131C22×C4—11861no—
132C22×C4—11861no—
133Q16—5932no—
134Q16C2×D59312yescomplemented
135SD16—5932no—
136SD16—5932no—
137SD16—5932no—
138SD16C2×D59312yescomplemented
139D8—5932no—
140D8—5932no—
141M16—5931no—
142M16—5932no—
143M16C2×D59311yescharacteristic, complemented
144C2×C8—5932no—
145C23—5931no—
146C23—11861no—
147C23—11861no—
148Q8—21no—
149Q8—5931no—
150Q8—11861no—
151Q8C22×D59311yescharacteristic
152Q8C22×D59312yes—
153D4—21no—
154D4—5932no—
155D4—5931no—
156D4—11861no—
157D4—11862no—
158D4—11862no—
159D4—11861no—
160D4—11861no—
161D4—11861no—
162D4—11861no—
163D4C22×D59311yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—5931no—
167C2×C4—5931no—
168C2×C4—5931no—
169C2×C4—5931no—
170C2×C4—5931no—
171C2×C4—11861no—
172C2×C4—11862no—
173C2×C4—11862no—
174C2×C4—11861no—
175C2×C4—11861no—
176C2×C4—11861no—
177C2×C4C22×D59311yescharacteristic
178C8—5932no—
179C8C22×D59312yes—
180C22—21no—
181C22—23722no—
182C22—23721no—
183C22—23722no—
184C22—5931no—
185C22—5931no—
186C22—11862no—
187C22—11861no—
188C22D4×D59311yescharacteristic
189C4—21no—
190C4—22no—
191C4—5931no—
192C4—5931no—
193C4—11861no—
194C4D4×D59311yescharacteristic
195C4C23×D59311yescharacteristic
196C2—21no—
197C2—41no—
198C2—23722no—
199C2—23721no—
200C2—11861no—
201C2—11861no—
202C2C2×D4×D59311yescharacteristic
subgroupG/H
centerC2C2×D4×D593
commutator, cosocleC4×C593C24
FrattiniC4C23×D593
Fitting#137×C593C2
socleC2×C593C22×D4
hypercenter#137D593
hypocenterC593#575
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#23748734C2semidirect
2. #41×D593C2semidirect
3. #34039317C2semidirect
4. #34039316C2semidirect
5. #34039313C2semidirect
6. #34039312C2semidirect
7. #34039310C2semidirect
8. #34039308C2semidirect
9. #34039306C2semidirect
10. M16×D593C2semidirect
11. #137×C593C2semidirect
15. #23748734C22semidirect
16. #23748734C22semidirect
20. #23748732C22semidirect
21. Q8×D593C22semidirect
23. C2×D2372C22semidirect
25. D4×D593C22semidirect
29. #23748723C22semidirect
30. #23748722C22semidirect
31. #23748720C22semidirect
32. #23748720C22semidirect
33. D4744C22semidirect
34. #23748718C22semidirect
35. #23748717C22semidirect
36. #23748716C22semidirect
37. C8×D593C22semidirect
39. C2×Q8×C593C22semidirect
40. Q16×C593C22semidirect
41. SD16×C593C22semidirect
42. M16×C593C22semidirect
101. C593#575semidirect
107. #137D593semidirect
125. C2×Q8C2×D593semidirect
134. Q16C2×D593semidirect
138. SD16C2×D593semidirect
143. M16C2×D593semidirect

Maximal subgroups

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

subgroupindex
C2×#237487342
#41×D5932
#340393172
#340393162
#340393132
#340393122
#340393102
#340393082
#340393062
M16×D5932
#137×C5932
#575593