Finite Group Databasebeta

← #15780342

Subgroups — #15780342

Order 3328.

456 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13127939C211yesmaximal, characteristic, complemented
2C2×#11718158C211yesmaximal, characteristic, complemented
3#13116564C211yesmaximal, characteristic, complemented
4#13114895C211yesmaximal, characteristic, complemented
5#13112947C211yesmaximal, characteristic, complemented
6#13112936C211yesmaximal, characteristic, complemented
7C13×#3067C211yesmaximal, characteristic
8C13×#575—21no—
9C2×C13×#135C2211yescharacteristic
10C2×C13×#131C2211yescharacteristic
11C13×#473C412yescomplemented
12C13×#472C412yescomplemented
13C13×#471—22no—
14C2×C13×#108C2211yescharacteristic
15C13×#413—21no—
16#11718893—21no—
17#11718801—22no—
18#11718801—22no—
19C2×#88059C2211yescharacteristic
20C2×#88057C2211yescharacteristic
21C2×#88052—22no—
22C2×#88052C2211yescharacteristic
23C2×#88052C2211yescharacteristic
24#11718159—22no—
25#11718158—22no—
26#11718146—21no—
27C2×C13×#41—21no—
28C2×C13×#41D411yescharacteristic
29C13×#137—22no—
30C13×#137—41no—
31C13×AGL(1,ℤ/8)—22no—
32C13×AGL(1,ℤ/8)—41no—
33C13×#135—21no—
34C13×#135—21no—
35C13×#135—21no—
36C13×#135—21no—
37C13×#135—42no—
38C2×C13×Q16C2×C411yescharacteristic
39C2×C13×SD16—21no—
40C2×C13×D8C2×C411yescharacteristic
41C13×#131—21no—
42C13×#131—21no—
43C13×#131C2×C412yes—
44C13×#131D412yes—
45C2×C13×M16—21no—
46C2×C13×M16—21no—
47C2×C13×M16D411yescharacteristic
48C22×C8×C13—21no—
49C22×C8×C13C2311yescharacteristic
50C2×C4⋊Dic13—21no—
51C2×#6099—21no—
52C13×#108—21no—
53C13×#108C2×C412yes—
54C13×#101—22no—
55C13×#100—22no—
56#88075—41no—
57#88072—41no—
58#88059—21no—
59#88059—21no—
60#88057—21no—
61#88057—21no—
62#88052—24no—
63#88052—21no—
64#88052—21no—
65#88052—21no—
66#88052D412yes—
67C2×#6090—24no—
68C2×#6090—21no—
69C2×#6090D412yes—
70#13070—131nomaximal, Sylow
71C13×#41—21no—
72C13×#41—21no—
73C13×#41—41no—
74C13×#41—41no—
75C13×#41—41no—
76C13×#41—41no—
77C13×#41C22⋊C412yes—
78C13×#41SD1612yes—
79C2×Q8×C13—21no—
80C2×Q8×C13D811yescharacteristic
81C2×D4×C13—21no—
82C2×D4×C13—21no—
83C2×D4×C13—41no—
84C2×D4×C13D811yescharacteristic
85C22×C4×C13—21no—
86C22×C4×C13—41no—
87C22×C4×C13C2×D411yescharacteristic
88C22×Dic13—41no—
89C13×Q16—21no—
90C13×Q16—21no—
91C13×Q16—42no—
92C13×SD16—42no—
93C13×SD16—42no—
94C13×SD16—41no—
95C13×SD16—41no—
96C13×D8—21no—
97C13×D8—21no—
98C13×D8—42no—
99C13×M16—21no—
100C13×M16—22no—
101C13×M16—22no—
102C13×M16—22no—
103C13×M16—41no—
104C13×M16C22⋊C412yes—
105C2×C8×C13—21no—
106C2×C8×C13—22no—
107C2×C8×C13—22no—
108C2×C8×C13—41no—
109C2×C8×C13C22×C411yescharacteristic
110C2×C8×C13C2×D411yescharacteristic
111C2×C8×C13C2×D411yescharacteristic
112C2×C8×C13C2×D411yescharacteristic
113C2×C8×C13#4111yescharacteristic
114C2×C8×C13#4111yescharacteristic
115C4⋊Dic13—41no—
116C4⋊Dic13—41no—
117#6099—41no—
118#6099—41no—
119C2×#1055—41no—
120#6090—22no—
121#6090—22no—
122#3407—131no—
123#3067D1311yescharacteristic
124C2×#360—131no—
125#2143—131no—
126#1815—131no—
127#1388—131no—
128#1383—131no—
129C23×C13—21no—
130C23×C13—41no—
131C23×C13#13511yescharacteristic
132Q8×C13—21no—
133Q8×C13—41no—
134Q8×C13—41no—
135Q8×C13#10212yes—
136D4×C13—22no—
137D4×C13—22no—
138D4×C13—21no—
139D4×C13—41no—
140D4×C13—41no—
141D4×C13—81no—
142D4×C13—81no—
143D4×C13#10212yes—
144C2×C4×C13—21no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—41no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13C2×C22⋊C411yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13C2×D811yescharacteristic
154C2×C4×C13C2×SD1611yescharacteristic
155C2×C4×C13#13511yescharacteristic
156C2×Dic13—81no—
157C2×Dic13—161no—
158C8×C13—22no—
159C8×C13—42no—
160C8×C13C4×D411yescharacteristic
161C8×C13C4×D411yescharacteristic
162C8×C13#12011yescharacteristic
163C8×C13#12311yescharacteristic
164#1055—81no—
165#575—21no—
166C2×#135C2×D1311yescharacteristic
167C2×#131C2×D1311yescharacteristic
168#504—262no—
169#504—262no—
170C2×M32—131no—
171C2×M32—131no—
172C2×M32—262no—
173#473Dic1312yescomplemented
174#472Dic1312yescomplemented
175#471—22no—
176C2×#108—131no—
177C2×#108C2×D1311yescharacteristic
178C2×#106—131no—
179#417—261no—
180#413—21no—
181#360—262no—
182#359—262no—
183#343—261no—
184C22×C13—22no—
185C22×C13—41no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13—161no—
189C22×C13#41611yescharacteristic
190C22×C13#46511yescharacteristic
191C22×C13#46611yescharacteristic
192C4×C13—22no—
193C4×C13—81no—
194C4×C13#38611yescharacteristic
195C4×C13C2×#10211yescharacteristic
196C4×C13#46511yescharacteristic
197C4×C13#46611yescharacteristic
198Dic13—161no—
199C2×#41—21no—
200C2×#41C22⋊D1311yescharacteristic
201#137—22no—
202#137—41no—
203AGL(1,ℤ/8)—22no—
204AGL(1,ℤ/8)—41no—
205#135—21no—
206#135—21no—
207#135—21no—
208#135—21no—
209#135—42no—
210C2×Q16C2×Dic1311yescharacteristic
211C2×SD16—21no—
212C2×D8C2×Dic1311yescharacteristic
213#131—21no—
214#131—21no—
215#131C2×Dic1312yes—
216#131C22⋊D1312yes—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—261no—
220C2×M16C22⋊D1311yescharacteristic
221C22×C8—21no—
222C22×C8C22×D1311yescharacteristic
223C2×C4⋊C4—261no—
224M32—132no—
225M32—264no—
226M32—261no—
227M32—261no—
228M32—261no—
229C2×C16—132no—
230C2×C16—264no—
231C2×C16—261no—
232#108—21no—
233#108—261no—
234#108—261no—
235#108C2×Dic1312yes—
236#106—261no—
237#106—261no—
238#103—521no—
239#102—521no—
240#101—22no—
241#100—22no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13—21no—
245C2×C13—42no—
246C2×C13—161no—
247C2×C13#189311yescharacteristic
248#41—21no—
249#41—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41#610512yes—
255#41C22⋊Dic1312yes—
256C2×Q8—21no—
257C2×Q8#610411yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4#610411yescharacteristic
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—521no—
265C22×C4C2×C22⋊D1311yescharacteristic
266Q16—21no—
267Q16—21no—
268Q16—42no—
269SD16—42no—
270SD16—42no—
271SD16—41no—
272SD16—41no—
273D8—21no—
274D8—21no—
275D8—42no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—22no—
280M16—41no—
281M16—521no—
282M16—521no—
283M16C22⋊Dic1312yes—
284C2×C8—21no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—521no—
289C2×C8D4×D1311yescharacteristic
290C2×C8D4×D1311yescharacteristic
291C2×C8#612911yescharacteristic
292C2×C8#612911yescharacteristic
293C2×C8C22×Dic1311yescharacteristic
294C2×C8C2×C22⋊D1311yescharacteristic
295C4⋊C4—521no—
296C4⋊C4—521no—
297C16—262no—
298C16—262no—
299C13#1307011yescharacteristic, complemented, Sylow
300C23—21no—
301C23—41no—
302C23#8820411yescharacteristic
303Q8—21no—
304Q8—41no—
305Q8—41no—
306Q8#8807212yes—
307D4—22no—
308D4—22no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—81no—
313D4—81no—
314D4#8807212yes—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—1041no—
322C2×C4—2081no—
323C2×C4C2×#610411yescharacteristic
324C2×C4C2×#610511yescharacteristic
325C2×C4#8819311yescharacteristic
326C2×C4#8819311yescharacteristic
327C2×C4#8820411yescharacteristic
328C2×C4C2×C22⋊Dic1311yescharacteristic
329C8—22no—
330C8—42no—
331C8—1041no—
332C8D4×Dic1311yescharacteristic
333C8D4×Dic1311yescharacteristic
334C8#8818911yescharacteristic
335C8#8819111yescharacteristic
336C22—22no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22—161no—
341C22#1171869911yescharacteristic
342C22#1171870211yescharacteristic
343C22#1171889411yescharacteristic
344C4—22no—
345C4—81no—
346C4—2081no—
347C4#1171869911yescharacteristic
348C4#1171870211yescharacteristic
349C4C2×#8807211yescharacteristic
350C4#1171888111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—161no—
356C2#1311526511yescharacteristic
subgroupG/H
centerC2#13115265
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
Fitting, prime radicalC13×#3067C2
socleC2×C13#1893
cosocleC22×C8×C13C23
hypercenter#3067D13
hypocenterC13#13070
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. #13127939C2semidirect
2. C2×#11718158C2semidirect
3. #13116564C2semidirect
4. #13114895C2semidirect
5. #13112947C2semidirect
6. #13112936C2semidirect
11. C13×#473C4semidirect
12. C13×#472C4semidirect
173. #473Dic13semidirect
174. #472Dic13semidirect
299. C13#13070semidirect

Maximal subgroups

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

subgroupindex
#131279392
C2×#117181582
#131165642
#131148952
#131129472
#131129362
C13×#30672
#1307013