Finite Group Databasebeta

← #34036939

Subgroups — #34036939

Order 18752.

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

normal subgroups only

This group has 258 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
1#22627671C211yesmaximal, characteristic, complemented
2#22627669C211yesmaximal, characteristic, complemented
3#22627657C211yesmaximal, characteristic, complemented
4#22627653C212yesmaximal, complemented
5#22627648C212yesmaximal, complemented
6#22627644C211yesmaximal, characteristic, complemented
7#22627643C212yesmaximal, complemented
8C2×#17989790C211yesmaximal, characteristic, complemented
9SD16×D293C212yesmaximal, complemented
10#22627632C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C293C211yesmaximal, characteristic, complemented
12#17989802—21no—
13#17989802C2211yescharacteristic
14#17989802C2211yescharacteristic
15#17989801—21no—
16#17989801—22no—
17#17989801C2212yes—
18#17989801C2212yescomplemented
19C2×Dic586—21no—
20C2×Dic586C2211yescharacteristic, complemented
21Q8×D293C2212yescomplemented
22C2×C22⋊D293—22no—
23D4×D293—21no—
24D4×D293C2212yes—
25Dic1172C2212yescomplemented
26#17989792C2211yescharacteristic, complemented
27#17989791C2212yescomplemented
28#17989790C2212yescomplemented
29#17989790C2212yescomplemented
30#17989790C2211yescharacteristic, complemented
31#17989789C2211yescharacteristic, complemented
32#17989787C2211yescharacteristic, complemented
33#17989785C2212yescomplemented
34C2×#14556873C2211yescharacteristic, complemented
35C8×D293C2212yescomplemented
36#41×C293C2211yescharacteristic, complemented
37C2×D4×C293C2211yescharacteristic
38SD16×C293C2212yescomplemented
39D8×C293C2212yescomplemented
40M16×C293C2211yescharacteristic, complemented
41C22×D293—22no—
42Dic586—21no—
43Dic586—22no—
44Dic586D411yescharacteristic
45Dic586C2312yes—
46Dic586C2311yescharacteristic
47D1172D411yescharacteristic
48D1172C2311yescharacteristic
49C22⋊D293—21no—
50C22⋊D293—22no—
51C22⋊D293—22no—
52C22⋊D293—22no—
53C22⋊D293D412yes—
54C2×Dic293—21no—
55C2×Dic293—22no—
56C2×Dic293—22no—
57C4×D293—22no—
58C4×D293—21no—
59C4×D293C2312yes—
60#14556873C2311yescharacteristic
61#14556873C2311yescharacteristic
62C23×C293—21no—
63Q8×C293C2311yescharacteristic
64D4×C293—21no—
65D4×C293—21no—
66D4×C293C2311yescharacteristic
67D4×C293C2312yes—
68C2×C4×C293—21no—
69C2×C4×C293C2311yescharacteristic
70C8×C293C2312yes—
71C22×C293—21no—
72C22×C293—22no—
73C22×C293—81no—
74C22×C293C2×D411yescharacteristic
75C2×D293—21no—
76C2×D293—82no—
77C2×D293C2×D412yes—
78C4×C293—21no—
79C4×C293C2×D411yescharacteristic
80C4×C293C2411yescharacteristic
81Dic293—21no—
82Dic293—22no—
83Dic293C2×D412yes—
84C2×C293—21no—
85C2×C293—42no—
86C2×C293—41no—
87C2×C293C22×D411yescharacteristic
88D293—22no—
89D293—41no—
90C293#57711yescharacteristic, complemented, Sylow
91#577—2931nomaximal, Sylow
922−1+4—2931no—
93H(5,𝔽2)—2931no—
94#137—2932no—
95#137—2931no—
96AGL(1,ℤ/8)—2932no—
97AGL(1,ℤ/8)D29311yescharacteristic, complemented
98#135—2931no—
99#135—2932no—
100C2×SD16—2931no—
101C2×SD16—2932no—
102#131—2931no—
103#41—2931no—
104#41—2932no—
105#41—2932no—
106#41—2931no—
107#41—5861no—
108#41—5862no—
109#41—5861no—
110#41C2×D29311yescharacteristic, complemented
111C2×Q8—2932no—
112C2×Q8—2931no—
113C2×Q8—5861no—
114C2×D4—2932no—
115C2×D4—5861no—
116C2×D4—5862no—
117C2×D4C2×D29311yescharacteristic
118Q16—2931no—
119Q16—2932no—
120SD16—2931no—
121SD16—2932no—
122SD16—2932no—
123SD16—2931no—
124SD16—2932no—
125SD16C2×D29312yescomplemented
126D8—2931no—
127D8C2×D29312yescomplemented
128M16—2932no—
129M16C2×D29311yescharacteristic, complemented
130C2×C8—2931no—
131C2×C8—2932no—
132C23—21no—
133C23—5862no—
134Q8—2931no—
135Q8—2932no—
136Q8—2931no—
137Q8—5862no—
138Q8—5861no—
139Q8C22×D29311yescharacteristic
140D4—21no—
141D4—21no—
142D4—2932no—
143D4—2931no—
144D4—2931no—
145D4—5862no—
146D4—5862no—
147D4—5862no—
148D4—5861no—
149D4C22×D29311yescharacteristic
150D4C22×D29312yes—
151C2×C4—21no—
152C2×C4—2932no—
153C2×C4—5862no—
154C2×C4—5862no—
155C2×C4—5862no—
156C2×C4—5861no—
157C2×C4—5861no—
158C2×C4C22×D29311yescharacteristic
159C8—2931no—
160C8—2931no—
161C8C22×D29312yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—2932no—
166C22—23442no—
167C22—5861no—
168C22D4×D29311yescharacteristic
169C4—21no—
170C4—2932no—
171C4—5861no—
172C4—5862no—
173C4D4×D29311yescharacteristic
174C4C23×D29311yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—5862no—
179C2—11721no—
180C2C2×D4×D29311yescharacteristic
subgroupG/H
centerC2C2×D4×D293
commutator, cosocleC4×C293C24
FrattiniC4C23×D293
FittingAGL(1,ℤ/8)×C293C2
socleC2×C293C22×D4
hypercenterAGL(1,ℤ/8)D293
hypocenterC293#577
LCSG ▷ C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #22627671C2semidirect
2. #22627669C2semidirect
3. #22627657C2semidirect
4. #22627653C2semidirect
5. #22627648C2semidirect
6. #22627644C2semidirect
7. #22627643C2semidirect
8. C2×#17989790C2semidirect
9. SD16×D293C2semidirect
10. #22627632C2semidirect
11. AGL(1,ℤ/8)×C293C2semidirect
18. #17989801C22semidirect
20. C2×Dic586C22semidirect
21. Q8×D293C22semidirect
25. Dic1172C22semidirect
26. #17989792C22semidirect
27. #17989791C22semidirect
28. #17989790C22semidirect
29. #17989790C22semidirect
30. #17989790C22semidirect
31. #17989789C22semidirect
32. #17989787C22semidirect
33. #17989785C22semidirect
34. C2×#14556873C22semidirect
35. C8×D293C22semidirect
36. #41×C293C22semidirect
38. SD16×C293C22semidirect
39. D8×C293C22semidirect
40. M16×C293C22semidirect
90. C293#577semidirect
97. AGL(1,ℤ/8)D293semidirect
110. #41C2×D293semidirect
125. SD16C2×D293semidirect
127. D8C2×D293semidirect
129. M16C2×D293semidirect

Maximal subgroups

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

subgroupindex
#226276712
#226276692
#226276572
#226276532
#226276482
#226276442
#226276432
C2×#179897902
SD16×D2932
#226276322
AGL(1,ℤ/8)×C2932
#577293