Finite Group Databasebeta

← #15779858

Subgroups — #15779858

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88058C211yesmaximal, characteristic, complemented
2C2×#11718154C212yesmaximal, complemented
3C2×C22⋊#6090C211yesmaximal, characteristic, complemented
4#13112927C212yesmaximal, complemented
5C2×C13×#466C211yesmaximal, characteristic
6C22×C13×D8C2211yescharacteristic
7C23×C8×C13C2211yescharacteristic
8C2×C13×#121—21no—
9C22×C4⋊Dic13—21no—
10C13×#466—22no—
11C13×#466C414yescomplemented
12C2×C13×#107C2211yescharacteristic
13C2×C13×#102—21no—
14C2×#88058—24no—
15C2×#88058—21no—
16C2×#88058C2212yes—
17C22×#6090C2212yes—
18#11718154—24no—
19C22⋊#6090—22no—
20C22×D4×C13—21no—
21C22×D4×C13—41no—
22C23×C4×C13D411yescharacteristic
23C23×Dic13—41no—
24C2×C13×D8—22no—
25C2×C13×D8—21no—
26C2×C13×D8—22no—
27C2×C13×D8C2×C412yescomplemented
28C22×C8×C13—22no—
29C22×C8×C13—22no—
30C22×C8×C13C2×C412yes—
31C22×C8×C13D411yescharacteristic
32C22×C8×C13D412yes—
33C22×C8×C13C2311yescharacteristic
34C13×#121—24no—
35C13×#121—42no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C22⋊C4—41no—
38C2×C4⋊Dic13—24no—
39C2×C4⋊Dic13—22no—
40C2×C4⋊Dic13—42no—
41C2×C4⋊Dic13—41no—
42C13×#107—21no—
43C13×#107C2×C412yescomplemented
44C13×#102—24no—
45#88058—24no—
46#88058—22no—
47#88058D414yescomplemented
48C2×#6090—22no—
49C2×#6090—22no—
50C2×#6090—22no—
51#12991—131nomaximal, Sylow
52C24×C13—41no—
53C24×C13D811yescharacteristic
54C2×D4×C13—22no—
55C2×D4×C13—44no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C2×D4×C13—82no—
62C2×D4×C13—82no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—41no—
68C22×C4×C13C22⋊C412yes—
69C22×C4×C13D811yescharacteristic
70C22×C4×C13SD1612yes—
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—44no—
73C22×Dic13—42no—
74C22×Dic13—82no—
75C22×Dic13—82no—
76C13×D8—24no—
77C13×D8—42no—
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13—24no—
81C2×C8×C13—24no—
82C2×C8×C13C22⋊C412yes—
83C2×C8×C13C22×C411yescharacteristic
84C2×C8×C13C2×D412yes—
85C2×C8×C13C2×D411yescharacteristic
86C2×C8×C13#4112yes—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—44no—
90C4⋊Dic13—24no—
91C4⋊Dic13—44no—
92C4⋊Dic13—42no—
93#6090—42no—
94C2×#466D1311yescharacteristic
95C22×#107—131no—
96C2×#357—132no—
97C2×C22⋊C16—131no—
98#1380—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—42no—
104C23×C13—81no—
105C23×C13—81no—
106C23×C13—81no—
107C23×C13—81no—
108C23×C13—81no—
109C23×C13—81no—
110C23×C13#10212yes—
111C23×C13D1612yes—
112C23×C13SD3212yes—
113C23×C13C2×D811yescharacteristic
114D4×C13—42no—
115D4×C13—42no—
116D4×C13—88no—
117D4×C13—81no—
118D4×C13—81no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—42no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13#10212yes—
129C2×C4×C13C2×C22⋊C411yescharacteristic
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12311yescharacteristic
132C2×C4×C13C2×SD1611yescharacteristic
133C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×Dic13—44no—
136C2×Dic13—88no—
137C2×Dic13—82no—
138C2×Dic13—82no—
139C8×C13—22no—
140C8×C13C4×D412yes—
141C8×C13#12112yes—
142C22×D8C2×D1311yescharacteristic
143C23×C8C2×D1311yescharacteristic
144C2×#121—21no—
145C22×C4⋊C4—261no—
146C22×C16—132no—
147#466—22no—
148#466Dic1314yescomplemented
149C2×#107—132no—
150C2×#107—264no—
151C2×#107—261no—
152C2×#107C2×D1311yescharacteristic
153C2×#102—21no—
154#357—264no—
155C22⋊C16—262no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—82no—
163C22×C13—82no—
164C22×C13—82no—
165C22×C13—161no—
166C22×C13—161no—
167C22×C13—161no—
168C22×C13—161no—
169C22×C13#35714yescomplemented
170C22×C13C2×#10211yescharacteristic
171C22×C13#44711yescharacteristic
172C22×C13#48011yescharacteristic
173C22×C13C2×D1611yescharacteristic
174C22×C13C2×SD3211yescharacteristic
175C22×C13#50911yescharacteristic
176C22×C13#51011yescharacteristic
177C4×C13—22no—
178C4×C13—82no—
179C4×C13#38611yescharacteristic
180C4×C13#41711yescharacteristic
181C4×C13#44811yescharacteristic
182C4×C13#48111yescharacteristic
183Dic13—84no—
184C22×D4—21no—
185C22×D4—41no—
186C23×C4—521no—
187C23×C4C22⋊D1311yescharacteristic
188C2×D8—22no—
189C2×D8—22no—
190C2×D8—21no—
191C2×D8C2×Dic1312yescomplemented
192C22×C8—22no—
193C22×C8—22no—
194C22×C8C2×Dic1312yes—
195C22×C8C22⋊D1311yescharacteristic
196C22×C8C22⋊D1312yes—
197C22×C8C22×D1311yescharacteristic
198#121—24no—
199#121—42no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—264no—
202C2×C4⋊C4—262no—
203C2×C4⋊C4—522no—
204C2×C4⋊C4—521no—
205C2×C22⋊C4—41no—
206C2×C16—262no—
207C2×C16—262no—
208C2×C16—262no—
209#107—21no—
210#107—134no—
211#107—264no—
212#107—262no—
213#107C2×Dic1312yescomplemented
214#102—24no—
215C2×C13—24no—
216C2×C13—162no—
217C2×C13#187411yescharacteristic
218C2×C13C2×#35711yescharacteristic
219C2×C13#213911yescharacteristic
220C2×C13#218411yescharacteristic
221C2×C13#218511yescharacteristic
222C2×C13#223211yescharacteristic
223C2×C13#223311yescharacteristic
224C24—41no—
225C24#610411yescharacteristic
226C2×D4—22no—
227C2×D4—44no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—82no—
234C2×D4—82no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4—524no—
241C22×C4—522no—
242C22×C4—1042no—
243C22×C4—1042no—
244C22×C4#610411yescharacteristic
245C22×C4#610512yes—
246C22×C4C22⋊Dic1312yes—
247C22×C4C2×C22⋊D1311yescharacteristic
248D8—24no—
249D8—42no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—24no—
253C2×C8—24no—
254C2×C8C22⋊Dic1312yes—
255C2×C8D4×D1312yes—
256C2×C8#612912yes—
257C2×C8C22×Dic1311yescharacteristic
258C2×C8C2×C22⋊D1311yescharacteristic
259C4⋊C4—22no—
260C4⋊C4—41no—
261C4⋊C4—264no—
262C4⋊C4—524no—
263C4⋊C4—522no—
264C22⋊C4—44no—
265C16—522no—
266C13#1299111yescharacteristic, complemented, Sylow
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23—81no—
277C23—81no—
278C23#8806612yes—
279C23#8806712yes—
280C23#8807212yes—
281C23C2×#610411yescharacteristic
282D4—42no—
283D4—42no—
284D4—88no—
285D4—81no—
286D4—81no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—524no—
297C2×C4—1048no—
298C2×C4—1042no—
299C2×C4—1042no—
300C2×C4#8807212yes—
301C2×C4C2×#610511yescharacteristic
302C2×C4#8818911yescharacteristic
303C2×C4#8819111yescharacteristic
304C2×C4#8820311yescharacteristic
305C2×C4#8820511yescharacteristic
306C2×C4C2×C22⋊Dic1311yescharacteristic
307C8—22no—
308C8D4×Dic1312yes—
309C8#8819312yes—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—82no—
317C22—82no—
318C22—82no—
319C22—161no—
320C22—161no—
321C22—161no—
322C22—161no—
323C22#1171815414yescomplemented
324C22#1171869411yescharacteristic
325C22#1171869711yescharacteristic
326C22C2×#8806611yescharacteristic
327C22C2×#8806711yescharacteristic
328C22#1171885411yescharacteristic
329C22#1171885611yescharacteristic
330C22C2×#8807211yescharacteristic
331C4—22no—
332C4—82no—
333C4—1044no—
334C4#1171869511yescharacteristic
335C4#1171870111yescharacteristic
336C4#1171888111yescharacteristic
337C4#1171889311yescharacteristic
338C2—24no—
339C2—162no—
340C2#1311515411yescharacteristic
341C2C2×#1171815411yescharacteristic
342C2#1311654811yescharacteristic
343C2#1311674711yescharacteristic
344C2#1311675211yescharacteristic
345C2#1311701411yescharacteristic
346C2#1311701911yescharacteristic
subgroupG/H
centerC23C2×#6104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC2×C13×#466C2
socleC23×C13C2×D8
cosocleC22×C8×C13C23
hypercenterC2×#466D13
hypocenterC13#12991
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C22×#88058C2semidirect
2. C2×#11718154C2semidirect
3. C2×C22⋊#6090C2semidirect
4. #13112927C2semidirect
11. C13×#466C4semidirect
27. C2×C13×D8C2×C4semidirect
43. C13×#107C2×C4semidirect
47. #88058D4semidirect
148. #466Dic13semidirect
169. C22×C13#357semidirect
191. C2×D8C2×Dic13semidirect
213. #107C2×Dic13semidirect
266. C13#12991semidirect
323. C22#11718154semidirect

Maximal subgroups

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

subgroupindex
C22×#880582
C2×#117181542
C2×C22⋊#60902
#131129272
C2×C13×#4662
#1299113