Finite Group Databasebeta

← #3584⋊C3 #85639

Subgroups — #3584⋊C3 #85639

Order 384.

334 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 58 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#5945C212yesmaximal, complemented
2#578⋊C3C211yesmaximal, characteristic, complemented
3#577⋊C3C212yesmaximal, complemented
4#576⋊C3C211yesmaximal, characteristic, complemented
5C2×#131⋊C3C211yesmaximal, characteristic, complemented
6#3584C311yesmaximal, characteristic, complemented, Sylow
72−1+4⋊C3—22no—
82−1+4⋊C3C2212yescomplemented
9#994C2212yescomplemented
10C2×#41⋊C3—22no—
11C2×#41⋊C3C2211yescharacteristic
12C3×#135—41nomaximal
13#131⋊C3C2211yescharacteristic, complemented
14#131⋊C3C2211yescharacteristic, complemented
15#585C2×C312yescomplemented
16#578—31no—
17#578C2×C311yescharacteristic, complemented
18#577—32no—
19#577C2×C312yescomplemented
20#576—31no—
21#576C2×C311yescharacteristic, complemented
22#575—32no—
23C2×#135—31no—
24C2×#135—31no—
25C2×#131C2×C311yescharacteristic, complemented
26C3×#41—42no—
27#41⋊C3—22no—
28#41⋊C3D411yescharacteristic
29#41⋊C3C2311yescharacteristic
30C2×SL(2,𝔽3)—22no—
31C2×SL(2,𝔽3)D411yescharacteristic
32C3×Q16—41no—
33C3×SD16—42no—
34C3×D8—41no—
35C2×C3×C8—41no—
362−1+4—22no—
372−1+4—32no—
382−1+4C22×C312yes—
39H(5,𝔽2)—32no—
40H(5,𝔽2)—62no—
41H(5,𝔽2)C22×C312yes—
42C2×#41—22no—
43C2×#41—32no—
44C2×#41—32no—
45C2×#41—62no—
46C2×#41C22×C311yescharacteristic
47#137—34no—
48#137—32no—
49#137—32no—
50AGL(1,ℤ/8)—34no—
51AGL(1,ℤ/8)—32no—
52AGL(1,ℤ/8)—32no—
53#135—32no—
54#135—32no—
55#135—32no—
56#135—32no—
57#135—31no—
58#135—32no—
59#135—31no—
60#135—31no—
61#135A411yescharacteristic
62C2×Q16—31no—
63C2×Q16—31no—
64C2×SD16—32no—
65C2×SD16—32no—
66C2×D8—31no—
67C2×D8—31no—
68#131—31no—
69#131—31no—
70#131C22×C311yescharacteristic
71#131C22×C311yescharacteristic
72C2×M16—31no—
73C22×C8—31no—
74C3×Q8—42no—
75C3×D4—42no—
76C3×D4—82no—
77C2×C3×C4—41no—
78C2×C3×C4—82no—
79SL(2,𝔽3)C2×D411yescharacteristic
80C3×C8—41no—
81C3×C8—41no—
82#41—22no—
83#41—31no—
84#41—31no—
85#41—34no—
86#41—32no—
87#41—32no—
88#41—32no—
89#41—62no—
90#41—62no—
91#41—62no—
92#41—62no—
93#41—64no—
94#41—62no—
95#41—62no—
96#41—62no—
97#41C3×D411yescharacteristic
98#41C2×A412yes—
99#41C23×C311yescharacteristic
100C2×Q8—22no—
101C2×Q8—32no—
102C2×Q8—32no—
103C2×Q8—62no—
104C2×Q8C3×D411yescharacteristic
105C2×D4—31no—
106C2×D4—32no—
107C2×D4—32no—
108C2×D4—62no—
109C2×D4—62no—
110C2×D4—64no—
111C2×D4—62no—
112C2×D4—62no—
113C22×C4—31no—
114C22×C4—62no—
115C22×C4—62no—
116Q16—32no—
117Q16—32no—
118Q16—31no—
119Q16C2×A411yescharacteristic
120SD16—34no—
121SD16—32no—
122SD16—32no—
123SD16—32no—
124SD16C2×A412yes—
125D8—32no—
126D8—32no—
127D8—31no—
128D8C2×A411yescharacteristic
129M16—32no—
130M16—31no—
131M16—31no—
132C2×C8—31no—
133C2×C8—31no—
134C2×C8—31no—
135C2×C8—31no—
136C2×C8—31no—
137C2×C8C2×A411yescharacteristic
138C22×C3—41no—
139C22×C3—82no—
140C3×C4—41no—
141C3×C4—41no—
142C3×C4—82no—
143C23—31no—
144C23—62no—
145C23—62no—
146Q8—31no—
147Q8—32no—
148Q8—62no—
149Q8—62no—
150Q8C2×C3×D411yescharacteristic
151Q8C22×A412yes—
152D4—22no—
153D4—31no—
154D4—31no—
155D4—32no—
156D4—32no—
157D4—62no—
158D4—62no—
159D4—62no—
160D4—62no—
161D4—64no—
162D4—62no—
163D4C22×A412yes—
164C2×C4—22no—
165C2×C4—31no—
166C2×C4—31no—
167C2×C4—31no—
168C2×C4—31no—
169C2×C4—31no—
170C2×C4—62no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—64no—
174C2×C4—62no—
175C2×C4—62no—
176C2×C4C22×A411yescharacteristic
177C8—31no—
178C8—31no—
179C8C22×A411yescharacteristic
180C8C22×A411yescharacteristic
181C2×C3—41no—
182C2×C3—81no—
183C2×C3—162no—
184C22—22no—
185C22—31no—
186C22—31no—
187C22—62no—
188C22—121no—
189C22—242no—
190C22—242no—
191C22D4×A411yescharacteristic
192C4—22no—
193C4—31no—
194C4—31no—
195C4—62no—
196C4D4×A411yescharacteristic
197C4C23×A411yescharacteristic
198C3—41noSylow
199C2—21no—
200C2—42no—
201C2—61no—
202C2—61no—
203C2—122no—
204C2C2×D4×A411yescharacteristic
subgroupG/H
centerC4D4×A4
commutator, cosocle#41C23×C3
FrattiniC4C23×A4
Fitting#3584C3
socleC2C2×D4×A4
hypercenter#135A4
hypocenterQ8C2×C3×D4
LCSG ▷ #41 ▷ Q8
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #5945C2semidirect
2. #578⋊C3C2semidirect
3. #577⋊C3C2semidirect
4. #576⋊C3C2semidirect
5. C2×#131⋊C3C2semidirect
6. #3584C3semidirect
8. 2−1+4⋊C3C22semidirect
9. #994C22semidirect
13. #131⋊C3C22semidirect
14. #131⋊C3C22semidirect
15. #585C2×C3semidirect
17. #578C2×C3semidirect
19. #577C2×C3semidirect
21. #576C2×C3semidirect
25. C2×#131C2×C3semidirect

Maximal subgroups

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

subgroupindex
#59452
#578⋊C32
#577⋊C32
#576⋊C32
C2×#131⋊C32
#35843
C3×#1354