Finite Group Databasebeta

← #15779442

Subgroups — #15779442

Order 3328.

424 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 135 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#13123426C211yesmaximal, characteristic
2#13116624C212yesmaximal, complemented
3#13114869C211yesmaximal, characteristic
4#13112942C212yesmaximal, complemented
5C2×C13×#349C211yesmaximal, characteristic
6C22×C13×M16C2211yescharacteristic
7C2×#88180—21no—
8C2×C13×M32C2212yes—
9#11718873—21no—
10#11718782—22no—
11#11718782—22no—
12#11718767—21no—
13#11718767C2212yes—
14C2×#88058C2211yescharacteristic
15C2×#88057C2211yescharacteristic
16C13×#349C414yescomplemented
17#11718143—21no—
18#11718097—22no—
19#11718096—22no—
20C23×C4×C13D411yescharacteristic
21C2×C13×M16—22no—
22C2×C13×M16—22no—
23C2×C13×M16C2×C412yes—
24C2×C13×M16Q812yes—
25C22×C8×C13D411yescharacteristic
26C22×C8×C13C2311yescharacteristic
27C2×C22⋊Dic13—41no—
28C2×C22⋊Dic13—41no—
29#88180—22no—
30#88180—22no—
31#88180—41no—
32#88180—41no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4×Dic13—41no—
38C13×M32—22no—
39C13×M32C2×C414yescomplemented
40C2×C13×C16—22no—
41#88071—41no—
42#88058—21no—
43#88058—21no—
44#88058—22no—
45#88058D412yes—
46#88058D412yes—
47#88057—22no—
48#88057—22no—
49#88057—22no—
50#12923—131nomaximal, Sylow
51C24×C13D811yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13C4⋊C412yes—
57C22×C4×C13D811yescharacteristic
58C22×C4×C13Q1612yes—
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—41no—
61C22×Dic13—41no—
62C22×Dic13—41no—
63C22×Dic13—41no—
64C13×M16—24no—
65C13×M16—24no—
66C2×C8×C13—21no—
67C2×C8×C13—21no—
68C2×C8×C13C4⋊C412yes—
69C2×C8×C13C22×C411yescharacteristic
70C2×C8×C13C2×D412yes—
71C2×C8×C13C2×Q811yescharacteristic
72C2×C8×C13#4112yes—
73C22⋊Dic13—42no—
74C22⋊Dic13—42no—
75C22⋊Dic13—82no—
76C4⋊Dic13—22no—
77C4⋊Dic13—22no—
78C4⋊Dic13—41no—
79C4⋊Dic13—41no—
80C4⋊Dic13—41no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84C4×Dic13—42no—
85C4×Dic13—42no—
86C13×C16—24no—
87#2911—131no—
88#2159—132no—
89C2×#349D1311yescharacteristic
90#1809—131no—
91#1386—132no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13#10712yes—
97C23×C13C2×D811yescharacteristic
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13#10712yes—
105C2×C4×C13C2×C4⋊C411yescharacteristic
106C2×C4×C13#12011yescharacteristic
107C2×C4×C13#12311yescharacteristic
108C2×C4×C13C2×Q1611yescharacteristic
109C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C13#13711yescharacteristic
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—82no—
114C2×Dic13—82no—
115C2×Dic13—81no—
116C2×Dic13—81no—
117C2×Dic13—81no—
118C2×Dic13—81no—
119C2×Dic13—81no—
120C2×Dic13—81no—
121C8×C13—22no—
122C8×C13C4×D412yes—
123C8×C13C22⋊Q812yes—
124C22×M16C2×D1311yescharacteristic
125C2×#117—261no—
126C2×M32C2×D1312yes—
127#428—262no—
128#428—262no—
129#427—132no—
130#427—261no—
131C2×#107—131no—
132C2×#106—131no—
133#380—261no—
134#367—262no—
135#366—262no—
136#349Dic1314yescomplemented
137#340—261no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13—22no—
141C22×C13—42no—
142C22×C13—41no—
143C22×C13—41no—
144C22×C13—81no—
145C22×C13C2×#10711yescharacteristic
146C22×C13#44711yescharacteristic
147C22×C13#48011yescharacteristic
148C4×C13—22no—
149C4×C13#38511yescharacteristic
150C4×C13#42811yescharacteristic
151C4×C13#45111yescharacteristic
152C4×C13#48411yescharacteristic
153Dic13—82no—
154Dic13—82no—
155Dic13—161no—
156Dic13—161no—
157C23×C4D5211yescharacteristic
158C2×M16—22no—
159C2×M16—22no—
160C2×M16Dic2612yes—
161C2×M16C2×Dic1312yes—
162C22×C8D5211yescharacteristic
163C22×C8C22×D1311yescharacteristic
164#117—262no—
165#117—262no—
166#117—521no—
167#117—521no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—261no—
172C2×C22⋊C4—521no—
173C2×C22⋊C4—521no—
174C2×C42—521no—
175M32—22no—
176M32C2×Dic1314yescomplemented
177C2×C16—22no—
178#107—132no—
179#107—132no—
180#107—261no—
181#107—261no—
182#107—262no—
183#106—262no—
184#106—262no—
185#106—262no—
186#95—521no—
187C2×C13—21no—
188C2×C13—21no—
189C2×C13—42no—
190C2×C13#185211yescharacteristic
191C2×C13#219011yescharacteristic
192C2×C13#219111yescharacteristic
193C24D10411yescharacteristic
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—521no—
199C22×C4—521no—
200C22×C4—521no—
201C22×C4—521no—
202C22×C4D10411yescharacteristic
203C22×C4Dic5212yes—
204C22×C4C4⋊Dic1312yes—
205C22×C4C2×D5211yescharacteristic
206M16—24no—
207M16—24no—
208C2×C8—21no—
209C2×C8—21no—
210C2×C8C4⋊Dic1312yes—
211C2×C8C2×Dic2611yescharacteristic
212C2×C8D4×D1312yes—
213C2×C8#612912yes—
214C2×C8C22×Dic1311yescharacteristic
215C4⋊C4—262no—
216C4⋊C4—262no—
217C4⋊C4—521no—
218C4⋊C4—521no—
219C4⋊C4—521no—
220C4⋊C4—521no—
221C4⋊C4—521no—
222C4⋊C4—521no—
223C22⋊C4—522no—
224C22⋊C4—522no—
225C22⋊C4—1042no—
226C42—522no—
227C42—522no—
228C16—24no—
229C13#1292311yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—41no—
233C23—41no—
234C23#8805812yes—
235C23C2×D10411yescharacteristic
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4—1042no—
245C2×C4—1042no—
246C2×C4—1041no—
247C2×C4—1041no—
248C2×C4—1041no—
249C2×C4—1041no—
250C2×C4—1041no—
251C2×C4—1041no—
252C2×C4#8805812yes—
253C2×C4#8813611yescharacteristic
254C2×C4#8814011yescharacteristic
255C2×C4C2×Dic5211yescharacteristic
256C2×C4#8816211yescharacteristic
257C2×C4#8816311yescharacteristic
258C2×C4C2×C4⋊Dic1311yescharacteristic
259C8—22no—
260C8#8813212yes—
261C8D4×Dic1312yes—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—42no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1171839311yescharacteristic
270C22#1171839711yescharacteristic
271C22C2×#8805811yescharacteristic
272C4—22no—
273C4—1042no—
274C4—1042no—
275C4—2081no—
276C4—2081no—
277C4#1171838311yescharacteristic
278C4#1171840011yescharacteristic
279C4#1171861111yescharacteristic
280C4#1171878211yescharacteristic
281C2—21no—
282C2—21no—
283C2—42no—
284C2#1311502611yescharacteristic
285C2#1311678411yescharacteristic
286C2#1311678911yescharacteristic
subgroupG/H
centerC22#11718393
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#349C2
socleC22×C13#447
prime radicalC24×C13D8
cosocleC22×C8×C13C23
hypercenterC2×#349D13
hypocenterC13#12923
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. #13116624C2semidirect
4. #13112942C2semidirect
16. C13×#349C4semidirect
39. C13×M32C2×C4semidirect
136. #349Dic13semidirect
176. M32C2×Dic13semidirect
229. C13#12923semidirect

Maximal subgroups

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

subgroupindex
#131234262
#131166242
#131148692
#131129422
C2×C13×#3492
#1292313