Finite Group Databasebeta

← #15779983

Subgroups — #15779983

Order 3328.

526 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88068C211yesmaximal, characteristic
2C2×#11718156C211yesmaximal, characteristic, complemented
3C2×#11718083C211yesmaximal, characteristic
4#13115702C211yesmaximal, characteristic
5#13112927C211yesmaximal, characteristic, complemented
6#13112914C211yesmaximal, characteristic, complemented
7C2×C4×C13×Q16C211yesmaximal, characteristic, complemented
8C22×C13×Q16C2211yescharacteristic
9C2×C4×Q8×C13—21no—
10C22×D104C2211yescharacteristic
11C4×C13×Q16—22no—
12C4×C13×Q16—22no—
13C2×C13×#107C2211yescharacteristic
14C2×C13×#103—21no—
15C2×C4×C8×C13C2211yescharacteristic
16C2×#88068—22no—
17C2×#88068—22no—
18C2×#88068C414yescomplemented
19C2×#88061—21no—
20C2×#88058C2211yescharacteristic
21C22×#6090C2211yescharacteristic
22C22×#6090C2211yescharacteristic
23#11718600—21no—
24#11718156—22no—
25#11718083—22no—
26C22×Q8×C13—21no—
27C22×D52—21no—
28C2×C13×Q16—21no—
29C2×C13×Q16—21no—
30C2×C13×Q16—21no—
31C2×C13×Q16C2×C412yes—
32C2×C13×Q16D412yes—
33C2×C13×Q16D412yes—
34C22×C8×C13D411yescharacteristic
35C22×C8×C13C2311yescharacteristic
36C4×Q8×C13—24no—
37C4×Q8×C13—42no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—41no—
40C2×C42×C13—41no—
41C2×C42×C13D411yescharacteristic
42C2×#6103—41no—
43C2×#6103—41no—
44C2×C4⋊Dic13—21no—
45C2×D104—21no—
46C2×D104—21no—
47C2×D104—21no—
48C2×D104—21no—
49C2×D104—21no—
50C2×D104C2×C412yes—
51C13×#107—21no—
52C13×#107D412yes—
53C13×#103—24no—
54C4×C8×C13—21no—
55C4×C8×C13—21no—
56#88068—28no—
57#88061—42no—
58#88058—21no—
59#88058—21no—
60C2×#6090—21no—
61C2×#6090—21no—
62C2×#6090—21no—
63C2×#6090—21no—
64C2×#6090—21no—
65C2×#6090C2×C412yes—
66#13013—131nomaximal, Sylow
67C23×D13—41no—
68C2×Q8×C13—22no—
69C2×Q8×C13—22no—
70C2×Q8×C13—22no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13D811yescharacteristic
77C22×C4×C13D811yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—41no—
80C2×D52—22no—
81C2×D52—41no—
82C2×D52—41no—
83C2×D52—41no—
84C2×D52—41no—
85C2×D52—41no—
86C13×Q16—22no—
87C13×Q16—22no—
88C13×Q16—22no—
89C13×Q16C22⋊C414yescomplemented
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13C22×C411yescharacteristic
94C2×C8×C13C2×D411yescharacteristic
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13C2×D411yescharacteristic
97C2×C8×C13#4111yescharacteristic
98C2×C8×C13#4111yescharacteristic
99C13×C4⋊C4—22no—
100C13×C4⋊C4—44no—
101C13×C4⋊C4—41no—
102C42×C13—21no—
103C42×C13—21no—
104C42×C13—44no—
105#6103—82no—
106#6103—82no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109D104—22no—
110D104—22no—
111D104—41no—
112D104—41no—
113#6090—22no—
114#6090—41no—
115C22×SD32—131no—
116C2×C4×Q16D1311yescharacteristic, complemented
117C2×#358—131no—
118C2×#357—131no—
119#1970—131no—
120#1380—131no—
121#1374—131no—
122C23×C13C2×D811yescharacteristic
123C22×D13—42no—
124C22×D13—81no—
125C22×D13—81no—
126C22×D13—81no—
127C22×D13—81no—
128C22×D13—81no—
129C22×D13—81no—
130Q8×C13—24no—
131Q8×C13—42no—
132Q8×C13—42no—
133Q8×C13—42no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13SD3212yescomplemented
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#13511yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×Dic13—81no—
153C2×Dic13—81no—
154C2×Dic13—81no—
155D52—42no—
156D52—42no—
157D52—81no—
158D52—81no—
159C8×C13—41no—
160C8×C13C2×C22⋊C411yescharacteristic
161C8×C13C4×D411yescharacteristic
162C8×C13#12111yescharacteristic
163C8×C13#12311yescharacteristic
164C22×Q16C2×D1311yescharacteristic
165C22×D8—131no—
166C2×C4×Q8—21no—
167C2×SD32—134no—
168C2×SD32—262no—
169C2×SD32—262no—
170C22×C16—131no—
171C22×C16—131no—
172C4×Q16—22no—
173C4×Q16—22no—
174C2×#107—131no—
175C2×#107C2×D1311yescharacteristic
176C2×#103—21no—
177C2×#102—261no—
178C2×C4×C8C2×D1311yescharacteristic
179#390—261no—
180#358—262no—
181#357—262no—
182C22×C13C4×D811yescharacteristic
183C22×C13#44711yescharacteristic
184C22×C13#45911yescharacteristic
185C22×C13C2×SD3211yescharacteristic
186C22×C13#50811yescharacteristic
187C22×C13#50911yescharacteristic
188C22×C13#51011yescharacteristic
189C2×D13—82no—
190C2×D13—82no—
191C2×D13—82no—
192C2×D13—161no—
193C2×D13—161no—
194C2×D13—161no—
195C2×D13—161no—
196C4×C13—22no—
197C4×C13—44no—
198C4×C13—41no—
199C4×C13—82no—
200C4×C13#38611yescharacteristic
201C4×C13#44211yescharacteristic
202C4×C13#44911yescharacteristic
203C4×C13#46311yescharacteristic
204Dic13—161no—
205C22×Q8—21no—
206C22×D4—261no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16C4×D1312yes—
211C2×Q16D5212yes—
212C2×Q16C22⋊D1312yes—
213C2×D8—132no—
214C2×D8—261no—
215C2×D8—261no—
216C2×D8—261no—
217C2×D8—261no—
218C2×D8—261no—
219C22×C8C22⋊D1311yescharacteristic
220C22×C8C22×D1311yescharacteristic
221C4×Q8—24no—
222C4×Q8—42no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—261no—
226C2×C22⋊C4—521no—
227C2×C22⋊C4—521no—
228C2×C42—41no—
229C2×C42C22⋊D1311yescharacteristic
230SD32—268no—
231C2×C16—132no—
232C2×C16—261no—
233C2×C16—261no—
234C2×C16—261no—
235C2×C16—261no—
236C2×C16—261no—
237#107—21no—
238#107—261no—
239#107—261no—
240#107C22⋊D1312yes—
241#103—24no—
242#102—522no—
243C4×C8—21no—
244C4×C8—21no—
245C2×C13#187911yescharacteristic
246C2×C13C4×SD3211yescharacteristic
247C2×C13#217511yescharacteristic
248C2×C13#218511yescharacteristic
249C2×C13#218611yescharacteristic
250C2×C13#220711yescharacteristic
251C2×C13#221111yescharacteristic
252D13—162no—
253C24—521no—
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×D4—262no—
261C2×D4—521no—
262C2×D4—521no—
263C2×D4—521no—
264C2×D4—521no—
265C2×D4—521no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—521no—
269C22×C4#610411yescharacteristic
270C22×C4#610411yescharacteristic
271C22×C4C2×C22⋊D1311yescharacteristic
272Q16—22no—
273Q16—22no—
274Q16—22no—
275Q16#610314yescomplemented
276D8—262no—
277D8—262no—
278D8—521no—
279D8—521no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8C2×C4×D1311yescharacteristic
284C2×C8C2×D5211yescharacteristic
285C2×C8#612711yescharacteristic
286C2×C8#612711yescharacteristic
287C2×C8C2×C22⋊D1311yescharacteristic
288C2×C8C2×C22⋊D1311yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—44no—
291C4⋊C4—41no—
292C4⋊C4—521no—
293C4⋊C4—521no—
294C22⋊C4—1042no—
295C22⋊C4—1042no—
296C42—21no—
297C42—21no—
298C42—44no—
299C16—262no—
300C16—521no—
301C13#1301311yescharacteristic, complemented, Sylow
302C23—522no—
303C23—1041no—
304C23—1041no—
305C23—1041no—
306C23—1041no—
307C23—1041no—
308C23—1041no—
309C23C2×#610411yescharacteristic
310Q8—24no—
311Q8—42no—
312Q8—42no—
313Q8—42no—
314D4—522no—
315D4—522no—
316D4—1041no—
317D4—1041no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—1041no—
330C2×C4—1041no—
331C2×C4—1041no—
332C2×C4#8806812yescomplemented
333C2×C4C4×C22⋊D1311yescharacteristic
334C2×C4#8818411yescharacteristic
335C2×C4#8818611yescharacteristic
336C2×C4#8820311yescharacteristic
337C2×C4#8820411yescharacteristic
338C2×C4#8820711yescharacteristic
339C8—41no—
340C8C2×#610311yescharacteristic
341C8C4×C22⋊D1311yescharacteristic
342C8#8818311yescharacteristic
343C8#8818411yescharacteristic
344C22—1042no—
345C22—1042no—
346C22—1042no—
347C22—2081no—
348C22—2081no—
349C22—2081no—
350C22—2081no—
351C22C4×#610411yescharacteristic
352C22#1171867611yescharacteristic
353C22C2×#8806811yescharacteristic
354C22#1171884011yescharacteristic
355C22#1171885411yescharacteristic
356C22#1171885511yescharacteristic
357C22#1171887811yescharacteristic
358C4—22no—
359C4—44no—
360C4—41no—
361C4—82no—
362C4—2081no—
363C4#1171867511yescharacteristic
364C4#1171867711yescharacteristic
365C4#1171887411yescharacteristic
366C4#1171889911yescharacteristic
367C2—2082no—
368C2#1311518411yescharacteristic
369C2C4×#8806811yescharacteristic
370C2#1311669811yescharacteristic
371C2#1311675311yescharacteristic
372C2#1311675911yescharacteristic
373C2#1311687611yescharacteristic
374C2#1311689811yescharacteristic
subgroupG/H
centerC23C2×#6104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C4×C13×Q16C2
socleC23×C13C2×D8
prime radicalC22×D104C22
cosocleC22×C8×C13C23
hypercenterC2×C4×Q16D13
hypocenterC13#13013
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#11718156C2semidirect
5. #13112927C2semidirect
6. #13112914C2semidirect
7. C2×C4×C13×Q16C2semidirect
18. C2×#88068C4semidirect
89. C13×Q16C22⋊C4semidirect
116. C2×C4×Q16D13semidirect
145. C2×C4×C13SD32semidirect
275. Q16#6103semidirect
301. C13#13013semidirect
332. C2×C4#88068semidirect

Maximal subgroups

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

subgroupindex
C22×#880682
C2×#117181562
C2×#117180832
#131157022
#131129272
#131129142
C2×C4×C13×Q162
#1301313