Finite Group Databasebeta

← #37566040

Subgroups — #37566040

Order 24256.

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×#20258605C211yesmaximal, characteristic, complemented
2#41×D379C211yesmaximal, characteristic, complemented
3#27131364C211yesmaximal, characteristic, complemented
4#27131361C211yesmaximal, characteristic, complemented
5#27131360C212yesmaximal, complemented
6#27131357C211yesmaximal, characteristic, complemented
7#27131355C212yesmaximal, complemented
8#27131352C212yesmaximal, complemented
9#27131350C212yesmaximal, complemented
10M16×D379C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C379C211yesmaximal, characteristic, complemented
12#20258607C2211yescharacteristic, complemented
13#20258606—21no—
14#20258606C2211yescharacteristic
15#20258605—21no—
16#20258605—21no—
17#20258605—21no—
18#20258605C2212yes—
19#20258605C2211yescharacteristic, complemented
20#20258605C2212yescomplemented
21C2×Dic758C2211yescharacteristic, complemented
22Q8×D379C2211yescharacteristic, complemented
23C2×C22⋊D379—21no—
24D4×D379—21no—
25D4×D379C2211yescharacteristic, complemented
26C22×Dic379—21no—
27C2×C4×D379—21no—
28C2×C4×D379C2211yescharacteristic
29Dic1516C2212yescomplemented
30#20258596C2212yescomplemented
31#20258595C2212yescomplemented
32#20258594C2212yescomplemented
33#20258594C2212yescomplemented
34#20258591C2212yescomplemented
35#20258590C2211yescharacteristic, complemented
36#20258589C2212yescomplemented
37C8×D379C2212yescomplemented
38#41×C379C2211yescharacteristic
39C2×D4×C379C2211yescharacteristic, complemented
40SD16×C379C2212yescomplemented
41D8×C379C2212yescomplemented
42M16×C379C2211yescharacteristic, complemented
43C22×D379—21no—
44C22×D379D411yescharacteristic
45Dic758—21no—
46Dic758—21no—
47Dic758C2311yescharacteristic
48Dic758C2312yes—
49D1516—21no—
50D1516C2311yescharacteristic
51C22⋊D379—21no—
52C22⋊D379—21no—
53C22⋊D379—22no—
54C22⋊D379—22no—
55C22⋊D379—21no—
56C2×Dic379—21no—
57C2×Dic379—21no—
58C2×Dic379—22no—
59C2×Dic379—22no—
60C2×Dic379D411yescharacteristic
61C4×D379—21no—
62C4×D379—21no—
63C4×D379—21no—
64C4×D379D411yescharacteristic
65C4×D379D411yescharacteristic
66C4×D379C2311yescharacteristic
67C4×D379C2311yescharacteristic
68C379⋊C8C2312yes—
69C23×C379—21no—
70Q8×C379C2311yescharacteristic
71D4×C379—21no—
72D4×C379—21no—
73D4×C379C2311yescharacteristic
74D4×C379C2312yes—
75C2×C4×C379—21no—
76C2×C4×C379C2311yescharacteristic
77C8×C379C2312yes—
78C22×C379—21no—
79C22×C379—22no—
80C22×C379—42no—
81C22×C379C2×D411yescharacteristic
82C2×D379—21no—
83C2×D379—41no—
84C2×D379—42no—
85C2×D379C2×D411yescharacteristic
86C2×D379C2×D411yescharacteristic
87C4×C379—21no—
88C4×C379C2×D411yescharacteristic
89C4×C379C2411yescharacteristic
90Dic379—21no—
91Dic379—22no—
92Dic379C2×D411yescharacteristic
93Dic379C2×D411yescharacteristic
94C2×C379—21no—
95C2×C379—41no—
96C2×C379—42no—
97C2×C379C22×D411yescharacteristic
98D379—21no—
99D379—21no—
100D379—41no—
101C379#57511yescharacteristic, complemented, Sylow
102#575—3791nomaximal, Sylow
103C2×#41—3791no—
104C2×#41—3791no—
105#137—3791no—
106#137—3792no—
107#137—3791no—
108AGL(1,ℤ/8)—3791no—
109AGL(1,ℤ/8)—3792no—
110AGL(1,ℤ/8)D37911yescharacteristic, complemented
111#135—3792no—
112#135—3792no—
113C2×M16—3791no—
114#41—3791no—
115#41—3792no—
116#41—3792no—
117#41—3791no—
118#41—3791no—
119#41—7581no—
120#41—7581no—
121#41—7581no—
122#41—7581no—
123#41C2×D37911yescharacteristic
124C2×Q8—3791no—
125C2×Q8—3791no—
126C2×D4—3791no—
127C2×D4—7581no—
128C2×D4—7581no—
129C2×D4C2×D37911yescharacteristic, complemented
130C22×C4—3791no—
131C22×C4—7581no—
132C22×C4—7581no—
133Q16—3792no—
134Q16—3792no—
135SD16—3792no—
136SD16—3792no—
137SD16—3792no—
138SD16C2×D37912yescomplemented
139D8—3792no—
140D8C2×D37912yescomplemented
141M16—3791no—
142M16—3792no—
143M16C2×D37911yescharacteristic, complemented
144C2×C8—3792no—
145C23—21no—
146C23—3791no—
147C23—7581no—
148Q8—3791no—
149Q8—3792no—
150Q8—7581no—
151Q8—7581no—
152Q8C22×D37911yescharacteristic
153D4—21no—
154D4—21no—
155D4—3791no—
156D4—7581no—
157D4—7581no—
158D4—7581no—
159D4—7582no—
160D4—7582no—
161D4—7581no—
162D4C22×D37912yes—
163D4C22×D37911yescharacteristic
164C2×C4—21no—
165C2×C4—3791no—
166C2×C4—3791no—
167C2×C4—3791no—
168C2×C4—3791no—
169C2×C4—3791no—
170C2×C4—7581no—
171C2×C4—7581no—
172C2×C4—7581no—
173C2×C4—7582no—
174C2×C4—7582no—
175C2×C4—7581no—
176C2×C4—7581no—
177C2×C4C22×D37911yescharacteristic
178C8—3792no—
179C8C22×D37912yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—3791no—
184C22—3791no—
185C22—15161no—
186C22—15162no—
187C22—7581no—
188C22D4×D37911yescharacteristic
189C4—21no—
190C4—3791no—
191C4—3791no—
192C4—7581no—
193C4—7582no—
194C4D4×D37911yescharacteristic
195C4C23×D37911yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—15161no—
200C2—7581no—
201C2—7581no—
202C2C2×D4×D37911yescharacteristic
subgroupG/H
centerC2C2×D4×D379
commutator, cosocleC4×C379C24
FrattiniC4C23×D379
FittingAGL(1,ℤ/8)×C379C2
socleC2×C379C22×D4
hypercenterAGL(1,ℤ/8)D379
hypocenterC379#575
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#20258605C2semidirect
2. #41×D379C2semidirect
3. #27131364C2semidirect
4. #27131361C2semidirect
5. #27131360C2semidirect
6. #27131357C2semidirect
7. #27131355C2semidirect
8. #27131352C2semidirect
9. #27131350C2semidirect
10. M16×D379C2semidirect
11. AGL(1,ℤ/8)×C379C2semidirect
12. #20258607C22semidirect
19. #20258605C22semidirect
20. #20258605C22semidirect
21. C2×Dic758C22semidirect
22. Q8×D379C22semidirect
25. D4×D379C22semidirect
29. Dic1516C22semidirect
30. #20258596C22semidirect
31. #20258595C22semidirect
32. #20258594C22semidirect
33. #20258594C22semidirect
34. #20258591C22semidirect
35. #20258590C22semidirect
36. #20258589C22semidirect
37. C8×D379C22semidirect
39. C2×D4×C379C22semidirect
40. SD16×C379C22semidirect
41. D8×C379C22semidirect
42. M16×C379C22semidirect
101. C379#575semidirect
110. AGL(1,ℤ/8)D379semidirect
129. C2×D4C2×D379semidirect
138. SD16C2×D379semidirect
140. D8C2×D379semidirect
143. M16C2×D379semidirect

Maximal subgroups

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

subgroupindex
C2×#202586052
#41×D3792
#271313642
#271313612
#271313602
#271313572
#271313552
#271313522
#271313502
M16×D3792
AGL(1,ℤ/8)×C3792
#575379