Finite Group Databasebeta

← #49148745

Subgroups — #49148745

Order 36928.

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×#22604417C211yesmaximal, characteristic, complemented
2#41×D577C211yesmaximal, characteristic, complemented
3#32914697C211yesmaximal, characteristic, complemented
4#32914694C211yesmaximal, characteristic, complemented
5#32914693C212yesmaximal, complemented
6#32914690C211yesmaximal, characteristic, complemented
7#32914688C212yesmaximal, complemented
8#32914685C212yesmaximal, complemented
9#32914683C212yesmaximal, complemented
10M16×D577C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C577C211yesmaximal, characteristic, complemented
12#22604419C2211yescharacteristic, complemented
13#22604418—21no—
14#22604418C2211yescharacteristic
15#22604417—21no—
16#22604417—21no—
17#22604417—21no—
18#22604417C2212yes—
19#22604417C2211yescharacteristic, complemented
20#22604417C2212yescomplemented
21C2×Dic1154C2211yescharacteristic, complemented
22Q8×D577C2211yescharacteristic, complemented
23C2×C22⋊D577—21no—
24D4×D577—21no—
25D4×D577C2211yescharacteristic, complemented
26C22×Dic577—21no—
27C2×C4×D577—21no—
28C2×C4×D577C2211yescharacteristic
29Dic2308C2212yescomplemented
30#22604408C2212yescomplemented
31#22604407C2212yescomplemented
32#22604406C2212yescomplemented
33#22604406C2212yescomplemented
34#22604403C2212yescomplemented
35#22604402C2211yescharacteristic, complemented
36#22604401C2212yescomplemented
37C8×D577C2212yescomplemented
38#41×C577C2211yescharacteristic
39C2×D4×C577C2211yescharacteristic, complemented
40SD16×C577C2212yescomplemented
41D8×C577C2212yescomplemented
42M16×C577C2211yescharacteristic, complemented
43C22×D577—21no—
44C22×D577D411yescharacteristic
45Dic1154—21no—
46Dic1154—21no—
47Dic1154C2311yescharacteristic
48Dic1154C2312yes—
49D2308—21no—
50D2308C2311yescharacteristic
51C22⋊D577—21no—
52C22⋊D577—21no—
53C22⋊D577—22no—
54C22⋊D577—22no—
55C22⋊D577—21no—
56C2×Dic577—21no—
57C2×Dic577—21no—
58C2×Dic577—22no—
59C2×Dic577—22no—
60C2×Dic577D411yescharacteristic
61C4×D577—21no—
62C4×D577—21no—
63C4×D577—21no—
64C4×D577D411yescharacteristic
65C4×D577D411yescharacteristic
66C4×D577C2311yescharacteristic
67C4×D577C2311yescharacteristic
68#17987230C2312yes—
69C23×C577—21no—
70Q8×C577C2311yescharacteristic
71D4×C577—21no—
72D4×C577—21no—
73D4×C577C2311yescharacteristic
74D4×C577C2312yes—
75C2×C4×C577—21no—
76C2×C4×C577C2311yescharacteristic
77C8×C577C2312yes—
78C22×C577—21no—
79C22×C577—22no—
80C22×C577—42no—
81C22×C577C2×D411yescharacteristic
82C2×D577—21no—
83C2×D577—41no—
84C2×D577—42no—
85C2×D577C2×D411yescharacteristic
86C2×D577C2×D411yescharacteristic
87C4×C577—21no—
88C4×C577C2×D411yescharacteristic
89C4×C577C2411yescharacteristic
90Dic577—21no—
91Dic577—22no—
92Dic577C2×D411yescharacteristic
93Dic577C2×D411yescharacteristic
94C2×C577—21no—
95C2×C577—41no—
96C2×C577—42no—
97C2×C577C22×D411yescharacteristic
98D577—21no—
99D577—21no—
100D577—41no—
101C577#57511yescharacteristic, complemented, Sylow
102#575—5771nomaximal, Sylow
103C2×#41—5771no—
104C2×#41—5771no—
105#137—5771no—
106#137—5772no—
107#137—5771no—
108AGL(1,ℤ/8)—5771no—
109AGL(1,ℤ/8)—5772no—
110AGL(1,ℤ/8)D57711yescharacteristic, complemented
111#135—5772no—
112#135—5772no—
113C2×M16—5771no—
114#41—5771no—
115#41—5772no—
116#41—5772no—
117#41—5771no—
118#41—5771no—
119#41—11541no—
120#41—11541no—
121#41—11541no—
122#41—11541no—
123#41C2×D57711yescharacteristic
124C2×Q8—5771no—
125C2×Q8—5771no—
126C2×D4—5771no—
127C2×D4—11541no—
128C2×D4—11541no—
129C2×D4C2×D57711yescharacteristic, complemented
130C22×C4—5771no—
131C22×C4—11541no—
132C22×C4—11541no—
133Q16—5772no—
134Q16—5772no—
135SD16—5772no—
136SD16—5772no—
137SD16—5772no—
138SD16C2×D57712yescomplemented
139D8—5772no—
140D8C2×D57712yescomplemented
141M16—5771no—
142M16—5772no—
143M16C2×D57711yescharacteristic, complemented
144C2×C8—5772no—
145C23—21no—
146C23—5771no—
147C23—11541no—
148Q8—5771no—
149Q8—5772no—
150Q8—11541no—
151Q8—11541no—
152Q8C22×D57711yescharacteristic
153D4—21no—
154D4—21no—
155D4—5771no—
156D4—11541no—
157D4—11541no—
158D4—11541no—
159D4—11542no—
160D4—11542no—
161D4—11541no—
162D4C22×D57712yes—
163D4C22×D57711yescharacteristic
164C2×C4—21no—
165C2×C4—5771no—
166C2×C4—5771no—
167C2×C4—5771no—
168C2×C4—5771no—
169C2×C4—5771no—
170C2×C4—11541no—
171C2×C4—11541no—
172C2×C4—11541no—
173C2×C4—11542no—
174C2×C4—11542no—
175C2×C4—11541no—
176C2×C4—11541no—
177C2×C4C22×D57711yescharacteristic
178C8—5772no—
179C8C22×D57712yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—23081no—
184C22—23082no—
185C22—5771no—
186C22—5771no—
187C22—11541no—
188C22D4×D57711yescharacteristic
189C4—21no—
190C4—5771no—
191C4—5771no—
192C4—11541no—
193C4—11542no—
194C4D4×D57711yescharacteristic
195C4C23×D57711yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—23081no—
200C2—11541no—
201C2—11541no—
202C2C2×D4×D57711yescharacteristic
subgroupG/H
centerC2C2×D4×D577
commutator, cosocleC4×C577C24
FrattiniC4C23×D577
FittingAGL(1,ℤ/8)×C577C2
socleC2×C577C22×D4
hypercenterAGL(1,ℤ/8)D577
hypocenterC577#575
LCSG ▷ C4×C577 ▷ C2×C577 ▷ C577
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#22604417C2semidirect
2. #41×D577C2semidirect
3. #32914697C2semidirect
4. #32914694C2semidirect
5. #32914693C2semidirect
6. #32914690C2semidirect
7. #32914688C2semidirect
8. #32914685C2semidirect
9. #32914683C2semidirect
10. M16×D577C2semidirect
11. AGL(1,ℤ/8)×C577C2semidirect
12. #22604419C22semidirect
19. #22604417C22semidirect
20. #22604417C22semidirect
21. C2×Dic1154C22semidirect
22. Q8×D577C22semidirect
25. D4×D577C22semidirect
29. Dic2308C22semidirect
30. #22604408C22semidirect
31. #22604407C22semidirect
32. #22604406C22semidirect
33. #22604406C22semidirect
34. #22604403C22semidirect
35. #22604402C22semidirect
36. #22604401C22semidirect
37. C8×D577C22semidirect
39. C2×D4×C577C22semidirect
40. SD16×C577C22semidirect
41. D8×C577C22semidirect
42. M16×C577C22semidirect
101. C577#575semidirect
110. AGL(1,ℤ/8)D577semidirect
129. C2×D4C2×D577semidirect
138. SD16C2×D577semidirect
140. D8C2×D577semidirect
143. M16C2×D577semidirect

Maximal subgroups

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

subgroupindex
C2×#226044172
#41×D5772
#329146972
#329146942
#329146932
#329146902
#329146882
#329146852
#329146832
M16×D5772
AGL(1,ℤ/8)×C5772
#575577