Finite Group Databasebeta

← C2×#11719539 #13128314

Subgroups — C2×#11719539 #13128314

Order 1664.

1736 conjugacy classes of subgroups; only the 573 normal subgroups are shown.

normal subgroups only

This group has 1736 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×C13×#41C211yesmaximal, characteristic, complemented
2C22×#6131C211yesmaximal, characteristic, complemented
3#11719539C2116yesmaximal, direct product factor
4C2×Q8×Dic13C211yesmaximal, characteristic, complemented
5C2×#88194C213yesmaximal, complemented
6C2×#88192C213yesmaximal, complemented
7C2×#88184C213yesmaximal, complemented
8C2×C4×C22⋊D13C213yesmaximal, complemented
9C2×C13×#41—28no—
10C2×C13×#41C2218yescomplemented
11C22×Q8×C13C2211yescharacteristic
12C22×D4×C13C2213yes—
13C23×C4×C13C2213yes—
14C22×C22⋊D13C2213yes—
15C22×C22⋊D13C2216yes—
16C2×#6131—28no—
17C2×#6131C2218yescomplemented
18C22×D52C2213yes—
19C22×C4×D13C2213yes—
20C2×C22⋊Dic13C2213yes—
21Q8×Dic13C2218yescomplemented
22#88194C22124yescomplemented
23#88192C22124yescomplemented
24#88184C22124yescomplemented
25C4×C22⋊D13C22124yescomplemented
26C2×#6103C2213yes—
27C2×C4⋊Dic13C2213yes—
28C2×#6101C2211yescharacteristic
29C2×C4×Dic13C2213yes—
30C24×C13C2313yes—
31C23×D13C2313yes—
32C13×#41—232no—
33C2×Q8×C13D418yescomplemented
34C2×Q8×C13C2314yes—
35C2×D4×C13—212no—
36C2×D4×C13C23112yes—
37C22×C4×C13—212no—
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C23112yes—
40C22×C4×C13C2313yes—
41C2×C22⋊D13—212no—
42C2×C22⋊D13—412no—
43C2×C22⋊D13C23112yes—
44C2×C22⋊D13C23124yes—
45C22×Dic13C2313yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48#6131—232no—
49C2×D52—212no—
50C2×D52C23112yes—
51C2×C4×D13—212no—
52C2×C4×D13C23112yes—
53C22⋊Dic13C23112yes—
54#6103C23112yes—
55C4⋊Dic13C23112yes—
56#6101C2314yes—
57C4×Dic13C23112yes—
58C2×#550—131nomaximal, Sylow
59C23×C13—26no—
60C23×C13—26no—
61C23×C13—26no—
62C23×C13C2416yes—
63C23×C13C2411yescharacteristic
64C22×D13—26no—
65C22×D13—26no—
66C22×D13—26no—
67C22×D13C2416yes—
68Q8×C13C2×D4116yescomplemented
69D4×C13—224no—
70C2×C4×C13—22no—
71C2×C4×C13—224no—
72C2×C4×C13C2×D4112yes—
73C2×C4×C13C2412yes—
74C2×C4×C13C2416yes—
75C22⋊D13—224no—
76C22⋊D13—424no—
77C2×Dic13—22no—
78C2×Dic13—26no—
79C2×Dic13#4114yescomplemented
80C2×Dic13C2416yes—
81C2×Dic13C2412yes—
82C2×Dic13C2412yes—
83D52—224no—
84C4×D13—224no—
85C22×#41—131no—
86C22×#41D1311yescharacteristic, complemented
87#550—1316no—
88C2×#127—133no—
89C2×#121—133no—
90C2×#121—133no—
91C2×C4×Q8—131no—
92C2×C4×D4—133no—
93C22×C13—26no—
94C22×C13—26no—
95C22×C13—26no—
96C22×C13—412no—
97C22×C13C22×D412yes—
98C22×C13C2×#4112yes—
99C22×C13H(5,𝔽2)12yes—
100C22×C13C2511yescharacteristic
101C2×D13—26no—
102C2×D13—26no—
103C2×D13—26no—
104C2×D13—412no—
105C4×C13—22no—
106C4×C13C22×D4112yes—
107Dic13—22no—
108Dic13—26no—
109Dic13C2×#4114yescomplemented
110C2×#41—28no—
111C2×#41—138no—
112C2×#41—268no—
113C2×#41C2×D1318yescomplemented
114C22×Q8C2×D1311yescharacteristic
115C22×D4—133no—
116C22×D4—136no—
117C22×D4—133no—
118C22×D4C2×D1313yes—
119C23×C4—133no—
120C23×C4C2×D1313yes—
121#127—1324no—
122#121—1324no—
123#121—1324no—
124C4×Q8—138no—
125C4×D4—1324no—
126C2×C4⋊C4—131no—
127C2×C4⋊C4—133no—
128C2×C22⋊C4—133no—
129C2×C22⋊C4—133no—
130C2×C42—133no—
131C2×C13—46no—
132C2×C13#55014yescomplemented
133C2×C13C23×D411yescharacteristic
134C2×C13C22×#4111yescharacteristic
135C2×C13C2×H(5,𝔽2)11yescharacteristic
136D13—46no—
137C24—133no—
138C24C22×D1313yes—
139#41—232no—
140#41—2632no—
141C2×Q8C22⋊D1318yescomplemented
142C2×Q8C22×D1314yes—
143C2×D4—212no—
144C2×D4—1312no—
145C2×D4—1324no—
146C2×D4—1312no—
147C2×D4—2612no—
148C2×D4—2612no—
149C2×D4—5212no—
150C2×D4C22×D13112yes—
151C22×C4—212no—
152C22×C4—131no—
153C22×C4—133no—
154C22×C4—131no—
155C22×C4—1312no—
156C22×C4—2612no—
157C22×C4C22×D13112yes—
158C22×C4C22×D1311yescharacteristic
159C22×C4C22×D1313yes—
160C4⋊C4—134no—
161C4⋊C4—1312no—
162C22⋊C4—1312no—
163C22⋊C4—1312no—
164C42—1312no—
165C13C2×#55011yescharacteristic, complemented, Sylow
166C23—26no—
167C23—26no—
168C23—26no—
169C23—136no—
170C23—266no—
171C23—266no—
172C23—266no—
173C23C23×D1316yes—
174C23C23×D1311yescharacteristic
175Q8C2×C22⋊D13116yescomplemented
176D4—224no—
177D4—2624no—
178D4—2624no—
179D4—5224no—
180C2×C4—22no—
181C2×C4—224no—
182C2×C4—134no—
183C2×C4—132no—
184C2×C4—136no—
185C2×C4—132no—
186C2×C4—266no—
187C2×C4—262no—
188C2×C4—2624no—
189C2×C4C2×C22⋊D13112yes—
190C2×C4C23×D1312yes—
191C2×C4C23×D1316yes—
192C22—26no—
193C22—26no—
194C22—26no—
195C22—412no—
196C22—266no—
197C22—266no—
198C22—266no—
199C22—5212no—
200C22#41×D1312yes—
201C22#8825612yes—
202C22C22×C22⋊D1312yes—
203C22C24×D1311yescharacteristic
204C4—22no—
205C4—134no—
206C4—266no—
207C4—262no—
208C4C22×C22⋊D13112yes—
209C2—46no—
210C2—526no—
211C2#1171953914yesdirect product factor
212C2C2×#41×D1311yescharacteristic
213C2C2×#8825611yescharacteristic
214C2C23×C22⋊D1311yescharacteristic
subgroupG/H
centerC23C23×D13
commutator, cosocleC22×C13C25
FrattiniC22C24×D13
FittingC22×C13×#41C2
socleC23×C13C24
hypercenterC22×#41D13
hypocenterC13C2×#550
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C13×#41C2semidirect
2. C22×#6131C2semidirect
3. #11719539C2direct (N × H)
4. C2×Q8×Dic13C2semidirect
5. C2×#88194C2semidirect
6. C2×#88192C2semidirect
7. C2×#88184C2semidirect
8. C2×C4×C22⋊D13C2semidirect
10. C2×C13×#41C22semidirect
17. C2×#6131C22semidirect
21. Q8×Dic13C22semidirect
22. #88194C22semidirect
23. #88192C22semidirect
24. #88184C22semidirect
25. C4×C22⋊D13C22semidirect
33. C2×Q8×C13D4semidirect
68. Q8×C13C2×D4semidirect
79. C2×Dic13#41semidirect
86. C22×#41D13semidirect
109. Dic13C2×#41semidirect
113. C2×#41C2×D13semidirect
132. C2×C13#550semidirect
141. C2×Q8C22⋊D13semidirect
165. C13C2×#550semidirect
175. Q8C2×C22⋊D13semidirect
211. C2#11719539direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×#412
C22×#61312
#117195392
C2×Q8×Dic132
C2×#881942
C2×#881922
C2×#881842
C2×C4×C22⋊D132
C2×#55013