Finite Group Databasebeta

← #13124819

Subgroups — #13124819

Order 1664.

398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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#11719215C211yesmaximal, characteristic
2#11719209C211yesmaximal, characteristic, complemented
3C2×C13×#107C211yesmaximal, characteristic, complemented
4#11718774C211yesmaximal, characteristic, complemented
5#11718771C211yesmaximal, characteristic, complemented
6#11718627C211yesmaximal, characteristic, complemented
7#11718625C211yesmaximal, characteristic, complemented
8#11718549C212yesmaximal, complemented
9#11718546C212yesmaximal, complemented
10#11718545C212yesmaximal, complemented
11#11718543C212yesmaximal, complemented
12C2×#6127C2211yescharacteristic
13C2×#6127C2211yescharacteristic
14C22×C8×C13C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17#88184—22no—
18C4×C22⋊D13—22no—
19#88180C2211yescharacteristic
20C2×#6099C2211yescharacteristic
21#88151—21no—
22#88151C2212yes—
23#88149—21no—
24#88149C2212yes—
25#88147—21no—
26#88146C2212yes—
27C4⋊C4×D13C2212yes—
28#88141—21no—
29C13×#107C2212yes—
30C13×#107C2212yes—
31#88061C2211yescharacteristic
32#88061C2211yescharacteristic
33#88060C2212yes—
34#88060C2212yes—
35#88056C2211yescharacteristic
36#88056C2211yescharacteristic
37#88050C2212yes—
38#88049C2212yes—
39#88048C2212yes—
40#88047C2212yes—
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13C2311yescharacteristic
44C2×C22⋊D13—21no—
45C2×C22⋊D13D412yes—
46#6127—22no—
47#6127—22no—
48#6127—22no—
49#6127—22no—
50C2×D52—22no—
51C2×D52D411yescharacteristic
52C2×D52C2311yescharacteristic
53C2×C4×D13—21no—
54C2×C4×D13—22no—
55C2×C4×D13C2312yes—
56C2×Dic26D411yescharacteristic
57C2×Dic26C2311yescharacteristic
58C2×C8×C13—22no—
59C2×C8×C13C2311yescharacteristic
60C2×C8×C13C2311yescharacteristic
61C13×C4⋊C4—21no—
62C13×C4⋊C4—21no—
63C13×C4⋊C4C2312yes—
64C13×C4⋊C4C2312yes—
65C22⋊Dic13—21no—
66#6103—22no—
67#6103—22no—
68#6103—22no—
69C4⋊Dic13—22no—
70C4⋊Dic13C2311yescharacteristic
71C4⋊Dic13C2311yescharacteristic
72#6101—22no—
73C4×Dic13—21no—
74C4×Dic13—22no—
75#6099—22no—
76C2×#1055C2312yes—
77#3098—131nomaximal, Sylow
78C23×C13C2×D411yescharacteristic
79C22×D13—21no—
80C22×D13C2×D412yes—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13#4112yes—
87C2×C4×C13#4112yes—
88C2×C4×C13C2411yescharacteristic
89C22⋊D13—24no—
90C22⋊D13—42no—
91C2×Dic13—21no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13C2×D412yes—
95D52—22no—
96D52—21no—
97D52—21no—
98D52—82no—
99C4×D13—22no—
100C4×D13—22no—
101C4×D13—42no—
102C4×D13—82no—
103Dic26—22no—
104Dic26—21no—
105Dic26—21no—
106C8×C13—21no—
107C8×C13—21no—
108#1055—22no—
109#537—131no—
110#520—131no—
111#485—132no—
112#484—132no—
113#482—132no—
114#480—132no—
115#428—131no—
116C2×#107D1311yescharacteristic, complemented
117#417—131no—
118#416—131no—
119#408—131no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13#12312yes—
123C22×C13C22×D411yescharacteristic
124C2×D13—22no—
125C2×D13—22no—
126C2×D13—22no—
127C2×D13—41no—
128C2×D13—41no—
129C2×D13—41no—
130C4×C13—42no—
131C4×C13—42no—
132C4×C13#12312yes—
133C4×C13C2×#4111yescharacteristic
134C4×C13C2×#4111yescharacteristic
135Dic13—22no—
136Dic13—41no—
137Dic13—41no—
138Dic13—41no—
139C2×#41—131no—
140C2×#41—131no—
141C2×M16—131no—
142C22×C8C2×D1311yescharacteristic
143C22⋊Q8—132no—
144C22⋊Q8—261no—
145#121—132no—
146#121—261no—
147#121—262no—
148C4×Q8—261no—
149C4×D4—261no—
150C4×D4—262no—
151#117—131no—
152#117—132no—
153C2×C4⋊C4—132no—
154C2×C4⋊C4C2×D1311yescharacteristic
155C2×C4⋊C4C2×D1311yescharacteristic
156#107—132no—
157#107C2×D1312yes—
158#107C2×D1312yes—
159#106—132no—
160#103—131no—
161#103—131no—
162#103—132no—
163#102—131no—
164#102—131no—
165#102—132no—
166C22⋊C8—132no—
167C22⋊C8—132no—
168C2×C13—22no—
169C2×C13C2×#12311yescharacteristic
170C2×C13#57611yescharacteristic
171C2×C13#57811yescharacteristic
172D13—42no—
173D13—81no—
174#41—262no—
175#41—262no—
176#41—262no—
177#41—262no—
178C2×Q8—131no—
179C2×Q8—131no—
180C2×D4—132no—
181C2×D4—131no—
182C2×D4—131no—
183C2×D4—262no—
184C2×D4—261no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—132no—
188C22×C4—262no—
189C22×C4—261no—
190C22×C4C22×D1311yescharacteristic
191M16—262no—
192C2×C8—22no—
193C2×C8—132no—
194C2×C8C22×D1311yescharacteristic
195C2×C8C22×D1311yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—131no—
199C4⋊C4—131no—
200C4⋊C4—262no—
201C4⋊C4—262no—
202C4⋊C4C22×D1312yes—
203C4⋊C4C22×D1312yes—
204C22⋊C4—262no—
205C22⋊C4—262no—
206C22⋊C4—262no—
207C22⋊C4—261no—
208C42—262no—
209C42—261no—
210C13#309811yescharacteristic, complemented, Sylow
211C23—132no—
212C23—261no—
213C23D4×D1311yescharacteristic
214Q8—262no—
215Q8—261no—
216Q8—261no—
217D4—264no—
218D4—262no—
219D4—261no—
220D4—261no—
221D4—522no—
222D4—1042no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—132no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—522no—
234C2×C4—1042no—
235C2×C4#612712yes—
236C2×C4D4×D1311yescharacteristic
237C2×C4#613112yes—
238C2×C4C23×D1311yescharacteristic
239C8—21no—
240C8—21no—
241C8—262no—
242C22—21no—
243C22—21no—
244C22—262no—
245C22—262no—
246C22—262no—
247C22—521no—
248C22—521no—
249C22—521no—
250C22#8814812yes—
251C22C2×D4×D1311yescharacteristic
252C4—42no—
253C4—42no—
254C4—262no—
255C4—521no—
256C4—521no—
257C4—521no—
258C4#8814812yes—
259C4C2×#612711yescharacteristic
260C4C2×#613111yescharacteristic
261C2—22no—
262C2—522no—
263C2—1041no—
264C2C2×#8814811yescharacteristic
265C2#1171946211yescharacteristic
266C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#107C2
socleC22×C13C22×D4
prime radical#11719215C2
hypercenterC2×#107D13
hypocenterC13#3098
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #11719209C2semidirect
3. C2×C13×#107C2semidirect
4. #11718774C2semidirect
5. #11718771C2semidirect
6. #11718627C2semidirect
7. #11718625C2semidirect
8. #11718549C2semidirect
9. #11718546C2semidirect
10. #11718545C2semidirect
11. #11718543C2semidirect
116. C2×#107D13semidirect
210. C13#3098semidirect

Maximal subgroups

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

subgroupindex
#117192152
#117192092
C2×C13×#1072
#117187742
#117187712
#117186272
#117186252
#117185492
#117185462
#117185452
#117185432
#309813