Finite Group Databasebeta

← #15764242

Subgroups — #15764242

Order 3328.

600 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11718750C212yesmaximal, complemented
2#13122882C211yesmaximal, characteristic
3C2×#11718056C212yesmaximal, complemented
4#13112717C211yesmaximal, characteristic, complemented
5C13×#1960C211yesmaximal, characteristic, complemented
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×#88129C2212yes—
8C2×C13×#103—22no—
9C2×C13×#97C2211yescharacteristic
10C13×#382C2211yescharacteristic
11#11718750—24no—
12#11718750—24no—
13#11718652—22no—
14C2×#88050—22no—
15C2×#88049—22no—
16C2×#88043C2212yes—
17#11718334—22no—
18#11718332—22no—
19#11718056—24no—
20C22×Q8×C13—21no—
21C22×D52—22no—
22C22×D52D412yes—
23C22×Dic26D412yes—
24C22×C8×C13—21no—
25C13×C4⋊Q8—22no—
26C13×C4⋊Q8—21no—
27C13×C4⋊Q8D412yescomplemented
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4D412yes—
30C2×C42×C13C2311yescharacteristic
31C2×#6103—22no—
32C2×#6103—22no—
33C2×#6103—24no—
34C22×#1055—22no—
35#88129—22no—
36#88129—22no—
37#88129—22no—
38#88129—22no—
39C13×#103—44no—
40C13×#97—22no—
41C13×#95—22no—
42#88071—22no—
43#88050—28no—
44#88049—28no—
45#88043—22no—
46#88043D414yescomplemented
47#10085—131nomaximal, Sylow
48C23×D13—22no—
49C2×Q8×C13—22no—
50C2×Q8×C13—42no—
51C2×Q8×C13—42no—
52C2×Q8×C13—41no—
53C22×C4×C13—22no—
54C22×C4×C13—41no—
55C22×C4×C13C2×D412yes—
56C22×C4×C13C2×D411yescharacteristic
57C22×Dic13—22no—
58C2×D52—22no—
59C2×D52—22no—
60C2×D52—44no—
61C2×D52—82no—
62C2×D52—84no—
63C2×Dic26—22no—
64C2×Dic26—22no—
65C2×Dic26—44no—
66C2×C8×C13—22no—
67C2×C8×C13—41no—
68C2×C8×C13—41no—
69C13×C4⋊C4—24no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—42no—
72C42×C13C2×D411yescharacteristic
73C42×C13C2×D412yes—
74C42×C13#4111yescharacteristic
75#6103—42no—
76#6103—42no—
77#6103—42no—
78#6103—42no—
79#6103—84no—
80C2×#1055—24no—
81C2×#1055—44no—
82C2×#489—132no—
83#2819—131no—
84#1960D1311yescharacteristic, complemented
85C2×#329—132no—
86#1295—131no—
87C23×C13#12011yescharacteristic
88C22×D13—42no—
89C22×D13—42no—
90C22×D13—42no—
91C22×D13—44no—
92C22×D13—44no—
93Q8×C13—44no—
94Q8×C13—82no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—24no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—44no—
101C2×C4×C13—81no—
102C2×C4×C13—81no—
103C2×C4×C13#12012yes—
104C2×C4×C13#12112yes—
105C2×C4×C13#12111yescharacteristic
106C2×C4×C13#12711yescharacteristic
107C2×Dic13—42no—
108C2×Dic13—44no—
109D52—44no—
110D52—82no—
111D52—88no—
112Dic26—44no—
113Dic26—82no—
114C8×C13—42no—
115#1055—44no—
116C2×C4⋊Q8C2×D1311yescharacteristic
117C2×#124—132no—
118#489—264no—
119#489—264no—
120C2×#103—22no—
121C2×#103—262no—
122C2×#102—262no—
123C2×#97—132no—
124C2×#97C2×D1311yescharacteristic
125#394—262no—
126#393—262no—
127#392—262no—
128#382C2×D1311yescharacteristic
129#329—264no—
130C22×C13#39211yescharacteristic
131C22×C13#45311yescharacteristic
132C22×C13#45411yescharacteristic
133C22×C13#45514yes—
134C2×D13—84no—
135C2×D13—84no—
136C2×D13—82no—
137C2×D13—82no—
138C2×D13—82no—
139C4×C13—22no—
140C4×C13—22no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—82no—
144C4×C13—82no—
145Dic13—82no—
146C22×Q8—21no—
147C22×Q8—132no—
148C22×D4—132no—
149C22×D4—262no—
150C22×C8—21no—
151C22×C8—262no—
152C4⋊Q8—21no—
153C4⋊Q8—22no—
154C4⋊Q8D5212yescomplemented
155#124—262no—
156#124—262no—
157#124—262no—
158#124—262no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4C22⋊D1312yes—
161C2×C22⋊C4—262no—
162C2×C22⋊C4—262no—
163C2×C22⋊C4—264no—
164C2×C42C22×D1311yescharacteristic
165#103—44no—
166#103—268no—
167#102—268no—
168#97—22no—
169#97—134no—
170#97—262no—
171#95—22no—
172#95—262no—
173C2×C13#165912yes—
174C2×C13#166212yes—
175C2×C13#200412yes—
176C2×C13#200611yescharacteristic
177D13—162no—
178C24—262no—
179C2×Q8—22no—
180C2×Q8—42no—
181C2×Q8—42no—
182C2×Q8—41no—
183C2×Q8—262no—
184C2×Q8—262no—
185C2×Q8—524no—
186C2×D4—262no—
187C2×D4—262no—
188C2×D4—524no—
189C2×D4—1042no—
190C2×D4—1044no—
191C22×C4—22no—
192C22×C4—41no—
193C22×C4—262no—
194C22×C4D4×D1312yes—
195C22×C4C2×C22⋊D1311yescharacteristic
196C2×C8—22no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—264no—
200C2×C8—524no—
201C4⋊C4—24no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C22⋊C4—522no—
205C22⋊C4—522no—
206C22⋊C4—522no—
207C22⋊C4—522no—
208C22⋊C4—1044no—
209C42C2×D5211yescharacteristic
210C42#612711yescharacteristic
211C42D4×D1312yes—
212C13#1008511yescharacteristic, complemented, Sylow
213C23—522no—
214C23—522no—
215C23—524no—
216C23—524no—
217C23—522no—
218C23#8819111yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—524no—
222Q8—1042no—
223D4—524no—
224D4—1042no—
225D4—1048no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—24no—
229C2×C4—42no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—524no—
235C2×C4—522no—
236C2×C4#8813612yes—
237C2×C4#8813812yes—
238C2×C4#8818411yescharacteristic
239C2×C4#8819411yescharacteristic
240C8—42no—
241C8—524no—
242C22—1044no—
243C22—1044no—
244C22—1042no—
245C22—1042no—
246C22—1042no—
247C22#1171862111yescharacteristic
248C22#1171872311yescharacteristic
249C22#1171873811yescharacteristic
250C22#1171886314yes—
251C4—22no—
252C4—22no—
253C4—21no—
254C4—21no—
255C4—82no—
256C4—82no—
257C4—1042no—
258C2—2082no—
259C2#1311414012yes—
260C2#1311415712yes—
261C2#1311586612yes—
262C2#1311587711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1960C2
socleC23×C13#120
prime radical#13122882C2
hypercenter#1960D13
hypocenterC13#10085
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
1. C2×#11718750C2semidirect
3. C2×#11718056C2semidirect
4. #13112717C2semidirect
5. C13×#1960C2semidirect
27. C13×C4⋊Q8D4semidirect
46. #88043D4semidirect
84. #1960D13semidirect
154. C4⋊Q8D52semidirect
212. C13#10085semidirect

Maximal subgroups

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

subgroupindex
C2×#117187502
#131228822
C2×#117180562
#131127172
C13×#19602
#1008513