Finite Group Databasebeta

← #15780328

Subgroups — #15780328

Order 3328.

470 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127939C211yesmaximal, characteristic, complemented
2C2×#11718155C211yesmaximal, characteristic, complemented
3#13116552C211yesmaximal, characteristic, complemented
4#13114890C211yesmaximal, characteristic, complemented
5#13112950C211yesmaximal, characteristic, complemented
6#13112939C211yesmaximal, characteristic, complemented
7C2×C13×#472C211yesmaximal, characteristic
8C2×C13×AGL(1,ℤ/8)—21no—
9C22×C13×D8C2211yescharacteristic
10C2×C13×#131C2211yescharacteristic
11C13×#472—22no—
12C13×#472C414yescomplemented
13C2×C13×#108C2211yescharacteristic
14C2×C13×#100—21no—
15#11718897—21no—
16#11718801—22no—
17#11718801—22no—
18C2×#88059C2211yescharacteristic
19#11718767C2211yescharacteristic
20C2×#88052—22no—
21C2×#88052C2211yescharacteristic
22C2×#88052C2211yescharacteristic
23#11718155—22no—
24#11718154—22no—
25#11718151—21no—
26C2×C13×#41D411yescharacteristic
27C22×D4×C13—21no—
28C13×AGL(1,ℤ/8)—24no—
29C13×AGL(1,ℤ/8)—42no—
30C2×C13×SD16—41no—
31C2×C13×D8—21no—
32C2×C13×D8—21no—
33C2×C13×D8—21no—
34C2×C13×D8—21no—
35C2×C13×D8—21no—
36C2×C13×D8—41no—
37C2×C13×D8C2×C412yes—
38C13×#131—21no—
39C13×#131—21no—
40C13×#131C2×C412yes—
41C13×#131D412yes—
42C2×C13×M16—21no—
43C2×C13×M16—21no—
44C2×C13×M16D411yescharacteristic
45C22×C8×C13—21no—
46C22×C8×C13C2311yescharacteristic
47#88180—21no—
48C2×#6099—21no—
49C13×#108—21no—
50C13×#108C2×C412yes—
51C13×#100—24no—
52#88077—42no—
53#88059—21no—
54#88059—21no—
55#88058—21no—
56#88057—21no—
57#88052—24no—
58#88052—21no—
59#88052—21no—
60#88052—21no—
61#88052D412yes—
62C2×#6090—24no—
63C2×#6090—21no—
64C2×#6090D412yes—
65#13068—131nomaximal, Sylow
66C24×C13—41no—
67C13×#41—21no—
68C13×#41—21no—
69C13×#41C22⋊C412yes—
70C13×#41D812yes—
71C2×Q8×C13SD1611yescharacteristic
72C2×D4×C13—21no—
73C2×D4×C13—22no—
74C2×D4×C13—41no—
75C2×D4×C13—41no—
76C2×D4×C13—41no—
77C2×D4×C13—41no—
78C2×D4×C13—41no—
79C2×D4×C13SD1611yescharacteristic
80C22×C4×C13—21no—
81C22×C4×C13C2×D411yescharacteristic
82C13×SD16—44no—
83C13×D8—22no—
84C13×D8—22no—
85C13×D8—44no—
86C13×D8—41no—
87C13×D8—41no—
88C13×M16—21no—
89C13×M16—22no—
90C13×M16—22no—
91C13×M16—22no—
92C13×M16—41no—
93C13×M16C22⋊C412yes—
94C2×C8×C13—21no—
95C2×C8×C13—22no—
96C2×C8×C13—22no—
97C2×C8×C13—41no—
98C2×C8×C13C22×C411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13#4111yescharacteristic
103C2×C8×C13#4111yescharacteristic
104C22⋊Dic13—41no—
105C4⋊Dic13—41no—
106C4×Dic13—41no—
107#6099—41no—
108#6099—41no—
109C2×#1055—41no—
110#6090—22no—
111#6090—22no—
112#3407—131no—
113C2×#472D1311yescharacteristic
114C2×#361—131no—
115#2140—131no—
116#1814—131no—
117#1389—131no—
118#1385—131no—
119C23×C13—21no—
120C23×C13—42no—
121C23×C13—81no—
122C23×C13—81no—
123C23×C13—162no—
124C23×C13#13511yescharacteristic
125Q8×C13—21no—
126Q8×C13#10212yes—
127D4×C13—22no—
128D4×C13—22no—
129D4×C13—21no—
130D4×C13—42no—
131D4×C13—42no—
132D4×C13—81no—
133D4×C13—81no—
134D4×C13#10212yes—
135C2×C4×C13—21no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13C2×C22⋊C411yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13C2×D811yescharacteristic
142C2×C4×C13C2×SD1611yescharacteristic
143C2×C4×C13#13511yescharacteristic
144C2×Dic13—81no—
145C8×C13—22no—
146C8×C13—42no—
147C8×C13C4×D411yescharacteristic
148C8×C13C4×D411yescharacteristic
149C8×C13#12011yescharacteristic
150C8×C13#12311yescharacteristic
151#1055—81no—
152C2×AGL(1,ℤ/8)—21no—
153C22×D8C2×D1311yescharacteristic
154C2×#131C2×D1311yescharacteristic
155#504—262no—
156#504—262no—
157C2×M32—131no—
158C2×M32—131no—
159C2×M32—262no—
160#472—22no—
161#472Dic1314yescomplemented
162C2×#108—131no—
163C2×#108C2×D1311yescharacteristic
164#427—131no—
165#421—261no—
166C2×#100—21no—
167#361—262no—
168#357—262no—
169#344—261no—
170C22×C13—22no—
171C22×C13—41no—
172C22×C13—81no—
173C22×C13—82no—
174C22×C13—162no—
175C22×C13—162no—
176C22×C13—162no—
177C22×C13#41611yescharacteristic
178C22×C13#46511yescharacteristic
179C22×C13#46611yescharacteristic
180C4×C13—22no—
181C4×C13#38611yescharacteristic
182C4×C13C2×#10211yescharacteristic
183C4×C13#46511yescharacteristic
184C4×C13#46611yescharacteristic
185Dic13—161no—
186C2×#41C22⋊D1311yescharacteristic
187C22×D4—21no—
188AGL(1,ℤ/8)—24no—
189AGL(1,ℤ/8)—42no—
190C2×SD16—41no—
191C2×D8—21no—
192C2×D8—21no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—41no—
197C2×D8C2×Dic1312yes—
198#131—21no—
199#131—21no—
200#131C2×Dic1312yes—
201#131C22⋊D1312yes—
202C2×M16—21no—
203C2×M16—21no—
204C2×M16—261no—
205C2×M16C22⋊D1311yescharacteristic
206C22×C8—21no—
207C22×C8C22×D1311yescharacteristic
208#117—261no—
209M32—132no—
210M32—264no—
211M32—261no—
212M32—261no—
213M32—261no—
214C2×C16—132no—
215C2×C16—264no—
216C2×C16—261no—
217#108—21no—
218#108—261no—
219#108—261no—
220#108C2×Dic1312yes—
221#107—261no—
222#106—261no—
223#104—522no—
224#100—24no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—42no—
229C2×C13—162no—
230C2×C13#189311yescharacteristic
231C24—41no—
232#41—21no—
233#41—21no—
234#41#610412yes—
235#41C22⋊Dic1312yes—
236C2×Q8#610511yescharacteristic
237C2×D4—21no—
238C2×D4—22no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4#610511yescharacteristic
245C22×C4—21no—
246C22×C4C2×C22⋊D1311yescharacteristic
247SD16—44no—
248D8—22no—
249D8—22no—
250D8—44no—
251D8—41no—
252D8—41no—
253M16—21no—
254M16—22no—
255M16—22no—
256M16—22no—
257M16—41no—
258M16—521no—
259M16—521no—
260M16C22⋊Dic1312yes—
261C2×C8—21no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—521no—
266C2×C8D4×D1311yescharacteristic
267C2×C8D4×D1311yescharacteristic
268C2×C8#612911yescharacteristic
269C2×C8#612911yescharacteristic
270C2×C8C22×Dic1311yescharacteristic
271C2×C8C2×C22⋊D1311yescharacteristic
272C4⋊C4—521no—
273C22⋊C4—521no—
274C42—521no—
275C16—262no—
276C16—262no—
277C13#1306811yescharacteristic, complemented, Sylow
278C23—21no—
279C23—42no—
280C23—81no—
281C23—81no—
282C23—162no—
283C23#8820411yescharacteristic
284Q8—21no—
285Q8#8807212yes—
286D4—22no—
287D4—22no—
288D4—21no—
289D4—42no—
290D4—42no—
291D4—81no—
292D4—81no—
293D4#8807212yes—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—1041no—
298C2×C4C2×#610411yescharacteristic
299C2×C4C2×#610511yescharacteristic
300C2×C4#8819311yescharacteristic
301C2×C4#8819311yescharacteristic
302C2×C4#8820411yescharacteristic
303C2×C4C2×C22⋊Dic1311yescharacteristic
304C8—22no—
305C8—42no—
306C8—1041no—
307C8D4×Dic1311yescharacteristic
308C8D4×Dic1311yescharacteristic
309C8#8818911yescharacteristic
310C8#8819111yescharacteristic
311C22—22no—
312C22—41no—
313C22—81no—
314C22—82no—
315C22—162no—
316C22—162no—
317C22—162no—
318C22#1171869911yescharacteristic
319C22#1171870211yescharacteristic
320C22#1171889411yescharacteristic
321C4—22no—
322C4—2081no—
323C4#1171869911yescharacteristic
324C4#1171870211yescharacteristic
325C4C2×#8807211yescharacteristic
326C4#1171888111yescharacteristic
327C2—21no—
328C2—21no—
329C2—21no—
330C2—42no—
331C2—162no—
332C2#1311526511yescharacteristic
subgroupG/H
centerC2#13115265
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC2×C13×#472C2
socleC2×C13#1893
cosocleC22×C8×C13C23
hypercenterC2×#472D13
hypocenterC13#13068
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. #13127939C2semidirect
2. C2×#11718155C2semidirect
3. #13116552C2semidirect
4. #13114890C2semidirect
5. #13112950C2semidirect
6. #13112939C2semidirect
12. C13×#472C4semidirect
161. #472Dic13semidirect
277. C13#13068semidirect

Maximal subgroups

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

subgroupindex
#131279392
C2×#117181552
#131165522
#131148902
#131129502
#131129392
C2×C13×#4722
#1306813