Finite Group Databasebeta

← C2×#5831 #87270

Subgroups — C2×#5831 #87270

Order 384.

1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.

normal subgroups only

This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 573 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
1C22×C3×#41C211yesmaximal, characteristic, complemented
2C22×D3×Q8C211yesmaximal, characteristic, complemented
3#5831C2116yesmaximal, direct product factor
4C2×Q8×Dic3C211yesmaximal, characteristic, complemented
5C2×#938C213yesmaximal, complemented
6C2×#936C213yesmaximal, complemented
7C2×C4×#67C213yesmaximal, complemented
8C2×#924C213yesmaximal, complemented
9C2×#548—31nomaximal, Sylow
10C2×C3×#41—28no—
11C2×C3×#41C2218yescomplemented
12C22×C3×Q8C2211yescharacteristic
13C22×C3×D4C2213yes—
14C23×C3×C4C2213yes—
15C22×#67C2213yes—
16C2×D3×Q8—28no—
17C2×D3×Q8C2218yescomplemented
18C22×C4×D3C2213yes—
19C22×Dic6C2213yes—
20C2×#217C2216yes—
21C2×#217C2213yes—
22Q8×Dic3C2218yescomplemented
23#938C22124yescomplemented
24#936C22124yescomplemented
25C4×#67C22124yescomplemented
26C2×(C2×D3)⋊C4C2211yescharacteristic
27C2×C4⋊Dic3C2213yes—
28#924C22124yescomplemented
29C2×Dic3⋊C4C2213yes—
30C2×C4×Dic3C2213yes—
31C22×#41D311yescharacteristic, complemented
32C23×Q8—31no—
33#548—316no—
34C2×#124—33no—
35C2×C22⋊Q8—33no—
36C2×#121—33no—
37C2×C4×Q8—31no—
38C2×C4×D4—33no—
39C24×C3C2313yes—
40C23×D3C2311yescharacteristic
41C3×#41—232no—
42C2×C3×Q8D418yescomplemented
43C2×C3×Q8C2314yes—
44C2×C3×D4—212no—
45C2×C3×D4C23112yes—
46C22×C3×C4—212no—
47C22×C3×C4C2311yescharacteristic
48C22×C3×C4C23112yes—
49C22×C3×C4C2313yes—
50C2×#67—212no—
51C2×#67C23112yes—
52C22×Dic3C2311yescharacteristic
53C22×Dic3C2313yes—
54C22×Dic3C2313yes—
55D3×Q8—232no—
56C2×C4×D3—212no—
57C2×C4×D3C23112yes—
58C2×Dic6—212no—
59C2×Dic6C23112yes—
60#217C23124yes—
61#217C23112yes—
62(C2×D3)⋊C4C2314yes—
63C4⋊Dic3C23112yes—
64Dic3⋊C4C23112yes—
65C4×Dic3C23112yes—
66C2×#41—28no—
67C2×#41C2×D318yescomplemented
68C22×Q8—38no—
69C22×Q8—33no—
70C22×Q8—68no—
71C22×Q8C2×D311yescharacteristic
72C22×D4—33no—
73C22×D4C2×D313yes—
74C23×C4—33no—
75C23×C4C2×D313yes—
76#124—324no—
77C22⋊Q8—324no—
78#121—324no—
79C4×Q8—38no—
80C4×D4—324no—
81C2×C4⋊C4—33no—
82C2×C4⋊C4—33no—
83C2×C22⋊C4—33no—
84C2×C22⋊C4—36no—
85C2×C22⋊C4—31no—
86C2×C42—33no—
87C23×C3—26no—
88C23×C3—26no—
89C23×C3—26no—
90C23×C3C2416yes—
91C23×C3C2411yescharacteristic
92C22×D3—22no—
93C22×D3—22no—
94C22×D3#4114yescomplemented
95C22×D3C2412yes—
96C3×Q8C2×D4116yescomplemented
97C3×D4—224no—
98C2×C3×C4—22no—
99C2×C3×C4—224no—
100C2×C3×C4C2×D4112yes—
101C2×C3×C4C2412yes—
102C2×C3×C4C2416yes—
103#67—224no—
104C2×Dic3—26no—
105C2×Dic3—26no—
106C2×Dic3—22no—
107C2×Dic3C2412yes—
108C2×Dic3C2416yes—
109C2×Dic3C2416yes—
110C4×D3—224no—
111Dic6—224no—
112C24—31no—
113C24C22×D313yes—
114#41—232no—
115C2×Q8—312no—
116C2×Q8—632no—
117C2×Q8—612no—
118C2×Q8#6718yescomplemented
119C2×Q8C22×D314yes—
120C2×D4—212no—
121C2×D4—312no—
122C2×D4—612no—
123C2×D4C22×D3112yes—
124C22×C4—212no—
125C22×C4—31no—
126C22×C4—33no—
127C22×C4—33no—
128C22×C4—312no—
129C22×C4—612no—
130C22×C4C22×D3112yes—
131C22×C4C22×D311yescharacteristic
132C22×C4C22×D313yes—
133C4⋊C4—312no—
134C4⋊C4—312no—
135C22⋊C4—312no—
136C22⋊C4—324no—
137C22⋊C4—34no—
138C42—312no—
139C22×C3—26no—
140C22×C3—26no—
141C22×C3—26no—
142C22×C3—412no—
143C22×C3C22×D412yes—
144C22×C3C2×#4112yes—
145C22×C32−1+412yes—
146C22×C3C2511yescharacteristic
147C2×D3—28no—
148C2×D3—22no—
149C2×D3—22no—
150C2×D3C2×#4114yescomplemented
151C3×C4—22no—
152C3×C4C22×D4112yes—
153Dic3—26no—
154Dic3—26no—
155Dic3—22no—
156C23—26no—
157C23—26no—
158C23—26no—
159C23—34no—
160C23—32no—
161C23—62no—
162C23—62no—
163C23C23×D316yes—
164C23C23×D311yescharacteristic
165Q8—624no—
166Q8C2×#67116yescomplemented
167D4—224no—
168D4—624no—
169C2×C4—22no—
170C2×C4—224no—
171C2×C4—32no—
172C2×C4—36no—
173C2×C4—36no—
174C2×C4—66no—
175C2×C4—62no—
176C2×C4—66no—
177C2×C4—624no—
178C2×C4C2×#67112yes—
179C2×C4C23×D312yes—
180C2×C4C23×D316yes—
181C2×C3—46no—
182C2×C3#54814yescomplemented
183C2×C3C23×D411yescharacteristic
184C2×C3C22×#4111yescharacteristic
185C2×C3C2×2−1+411yescharacteristic
186D3—24no—
187C22—26no—
188C22—26no—
189C22—26no—
190C22—34no—
191C22—412no—
192C22—62no—
193C22—62no—
194C22—68no—
195C22D3×#4112yes—
196C22#101012yes—
197C22C22×#6712yes—
198C22C24×D311yescharacteristic
199C4—22no—
200C4—66no—
201C4—62no—
202C4—66no—
203C4C22×#67112yes—
204C3C2×#54811yescharacteristic, complemented, Sylow
205C2—46no—
206C2—64no—
207C2#583114yesdirect product factor
208C2C2×D3×#4111yescharacteristic
209C2C2×#101011yescharacteristic
210C2C23×#6711yescharacteristic
subgroupG/H
centerC23C23×D3
commutator, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC22×C3×#41C2
socleC23×C3C24
hypercenterC22×#41D3
hypocenterC3C2×#548
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×#41C2semidirect
2. C22×D3×Q8C2semidirect
3. #5831C2direct (N × H)
4. C2×Q8×Dic3C2semidirect
5. C2×#938C2semidirect
6. C2×#936C2semidirect
7. C2×C4×#67C2semidirect
8. C2×#924C2semidirect
11. C2×C3×#41C22semidirect
17. C2×D3×Q8C22semidirect
22. Q8×Dic3C22semidirect
23. #938C22semidirect
24. #936C22semidirect
25. C4×#67C22semidirect
28. #924C22semidirect
31. C22×#41D3semidirect
42. C2×C3×Q8D4semidirect
67. C2×#41C2×D3semidirect
94. C22×D3#41semidirect
96. C3×Q8C2×D4semidirect
118. C2×Q8#67semidirect
150. C2×D3C2×#41semidirect
166. Q8C2×#67semidirect
182. C2×C3#548semidirect
204. C3C2×#548semidirect
207. C2#5831direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#412
C22×D3×Q82
#58312
C2×Q8×Dic32
C2×#9382
C2×#9362
C2×C4×#672
C2×#9242
C2×#5483