Finite Group Databasebeta

← #15779987

Subgroups — #15779987

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88068C211yesmaximal, characteristic
2C2×#11718533C211yesmaximal, characteristic
3C2×#11718101C211yesmaximal, characteristic
4#13115698C211yesmaximal, characteristic, complemented
5#13112927C211yesmaximal, characteristic, complemented
6#13112913C211yesmaximal, characteristic, complemented
7C2×C13×#358C211yesmaximal, characteristic, complemented
8C22×C13×Q16C2211yescharacteristic
9C22×D104C2211yescharacteristic
10C2×#88147—21no—
11C22×C13×C16C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13#11718891—21no—
14C2×#88075—21no—
15C2×#88068—22no—
16C2×#88068—22no—
17C2×#88068C414yescomplemented
18C2×#88058C2211yescharacteristic
19C2×C8×Dic13C2211yescharacteristic
20C22×#6090C2211yescharacteristic
21C2×#88049—21no—
22#11718533—22no—
23#11718533—22no—
24C13×#358—22no—
25#11718101—22no—
26C22×Q8×C13—21no—
27C22×D52—21no—
28C22×C4×D13—41no—
29C2×C13×Q16—21no—
30C2×C13×Q16—21no—
31C2×C13×Q16—21no—
32C2×C13×Q16—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16C2×C412yescomplemented
35C22×C8×C13C2311yescharacteristic
36C2×C13×C4⋊C4—21no—
37C2×#6103—41no—
38C2×C4⋊Dic13—21no—
39C2×C4×Dic13D411yescharacteristic
40C22×#1055D411yescharacteristic
41C2×D104—21no—
42C2×D104—21no—
43C2×D104—21no—
44C2×D104C2×C412yes—
45C2×D104D412yes—
46C2×D104D412yes—
47#88147—24no—
48#88147—42no—
49C2×C13×C16—21no—
50C2×C13×C16—21no—
51C2×C13×C16—21no—
52C13×#107—21no—
53C13×#107D412yes—
54#88075—42no—
55#88071—41no—
56#88071—41no—
57#88068—28no—
58#88058—21no—
59#88058—21no—
60C8×Dic13—21no—
61C8×Dic13—21no—
62C2×#6090—21no—
63C2×#6090—21no—
64C2×#6090C2×C412yescomplemented
65#88049—24no—
66#13014—131nomaximal, Sylow
67C23×D13—41no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—41no—
78C22×Dic13D811yescharacteristic
79C22×Dic13D811yescharacteristic
80C2×D52—22no—
81C2×D52—22no—
82C2×D52—22no—
83C2×D52—41no—
84C2×D52—41no—
85C2×D52—41no—
86C2×C4×D13—44no—
87C2×C4×D13—82no—
88C2×C4×D13—82no—
89C13×Q16—22no—
90C13×Q16—22no—
91C13×Q16—41no—
92C13×Q16—41no—
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—41no—
101#6103—44no—
102C4⋊Dic13—41no—
103C4⋊Dic13—41no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055—21no—
109D104—22no—
110D104—22no—
111D104—22no—
112D104C22⋊C414yes—
113C13×C16—41no—
114#6090—22no—
115C22×SD32—131no—
116C2×C4×D8—131no—
117C2×#358D1311yescharacteristic, complemented
118C2×#357—131no—
119#1969—131no—
120#1380—131no—
121#1374—131no—
122C23×C13C2×D811yescharacteristic
123C22×D13—42no—
124C22×D13—42no—
125C22×D13—42no—
126C22×D13—81no—
127C22×D13—81no—
128C22×D13—81no—
129C22×D13—81no—
130Q8×C13—42no—
131Q8×C13—42no—
132Q8×C13—81no—
133Q8×C13—81no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13—81no—
140C2×C4×C13C4×D411yescharacteristic
141C2×C4×C13#12011yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#13511yescharacteristic
144C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—81no—
152C2×Dic13—81no—
153C2×Dic13—81no—
154C2×Dic13SD3212yescomplemented
155D52—24no—
156D52—42no—
157D52—42no—
158D52—42no—
159C4×D13—88no—
160C8×C13C2×C22⋊C411yescharacteristic
161C8×C13C4×D411yescharacteristic
162C8×C13#12111yescharacteristic
163C8×C13#12311yescharacteristic
164#1055—41no—
165C22×Q16C2×D1311yescharacteristic
166C22×D8—131no—
167C2×C4×D4—261no—
168C2×SD32—134no—
169C2×SD32—262no—
170C2×SD32—262no—
171C22×C16—131no—
172C22×C16C2×D1311yescharacteristic
173C4×D8—262no—
174C4×D8—262no—
175C2×#107—131no—
176C2×#107C2×D1311yescharacteristic
177C2×#103—261no—
178C2×#102—261no—
179C2×C4×C8—131no—
180#391—261no—
181#358—22no—
182#357—262no—
183C22×C13C4×D811yescharacteristic
184C22×C13#44711yescharacteristic
185C22×C13#45911yescharacteristic
186C22×C13C2×SD3211yescharacteristic
187C22×C13#50811yescharacteristic
188C22×C13#50911yescharacteristic
189C22×C13#51011yescharacteristic
190C2×D13—44no—
191C2×D13—82no—
192C2×D13—82no—
193C2×D13—82no—
194C2×D13—82no—
195C2×D13—82no—
196C2×D13—82no—
197C4×C13—82no—
198C4×C13—82no—
199C4×C13#38611yescharacteristic
200C4×C13#44211yescharacteristic
201C4×C13#44911yescharacteristic
202C4×C13#46311yescharacteristic
203Dic13—22no—
204Dic13—41no—
205Dic13—161no—
206C22×Q8—21no—
207C22×D4—261no—
208C23×C4—521no—
209C2×Q16—21no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16C4×D1312yescomplemented
215C2×D8—132no—
216C2×D8—132no—
217C2×D8—132no—
218C2×D8—261no—
219C2×D8—261no—
220C2×D8—261no—
221C22×C8—131no—
222C22×C8C22×D1311yescharacteristic
223C4×D4—264no—
224C4×D4—522no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—261no—
227C2×C22⋊C4—521no—
228C2×C42—131no—
229SD32—268no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—132no—
234C2×C16—261no—
235C2×C16—261no—
236#107—21no—
237#107—261no—
238#107—261no—
239#107C22⋊D1312yes—
240#103—522no—
241#102—264no—
242C4×C8—261no—
243C4×C8—261no—
244#95—521no—
245#95—521no—
246C2×C13#187911yescharacteristic
247C2×C13C4×SD3211yescharacteristic
248C2×C13#217511yescharacteristic
249C2×C13#218711yescharacteristic
250C2×C13#218911yescharacteristic
251C2×C13#220811yescharacteristic
252C2×C13#221011yescharacteristic
253D13—84no—
254C24—521no—
255C2×Q8—22no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×D4—262no—
262C2×D4—262no—
263C2×D4—262no—
264C2×D4—521no—
265C2×D4—521no—
266C2×D4—521no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—524no—
272C22×C4—521no—
273C22×C4—1042no—
274C22×C4—1042no—
275C22×C4D4×D1311yescharacteristic
276Q16—22no—
277Q16—22no—
278Q16—41no—
279Q16—41no—
280D8—134no—
281D8—262no—
282D8—262no—
283D8—262no—
284C2×C8—261no—
285C2×C8—261no—
286C2×C8—261no—
287C2×C8C2×C4×D1311yescharacteristic
288C2×C8#612711yescharacteristic
289C2×C8D4×D1311yescharacteristic
290C2×C8D4×D1311yescharacteristic
291C2×C8#612911yescharacteristic
292C2×C8C2×C22⋊D1311yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—41no—
295C4⋊C4—521no—
296C4⋊C4—521no—
297C22⋊C4—524no—
298C42—261no—
299C42—261no—
300C16—41no—
301C16—262no—
302C13#1301411yescharacteristic, complemented, Sylow
303C23—522no—
304C23—522no—
305C23—522no—
306C23—1041no—
307C23—1041no—
308C23—1041no—
309C23—1041no—
310C23D8×D1311yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—81no—
314Q8—81no—
315D4—264no—
316D4—522no—
317D4—522no—
318D4—522no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—132no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—1048no—
332C2×C4—1041no—
333C2×C4—1041no—
334C2×C4—1041no—
335C2×C4#8813511yescharacteristic
336C2×C4#8813811yescharacteristic
337C2×C4#8816511yescharacteristic
338C2×C4#8816811yescharacteristic
339C2×C4#8817011yescharacteristic
340C2×C4#8819111yescharacteristic
341C8—521no—
342C8C22⋊C4×D1311yescharacteristic
343C8#8813711yescharacteristic
344C8C4×C22⋊D1311yescharacteristic
345C8#8819211yescharacteristic
346C22—524no—
347C22—1042no—
348C22—1042no—
349C22—1042no—
350C22—1042no—
351C22—1042no—
352C22—1042no—
353C22#1171841711yescharacteristic
354C22#1171844711yescharacteristic
355C22D13×SD3211yescharacteristic
356C22#1171857511yescharacteristic
357C22#1171857911yescharacteristic
358C22#1171858011yescharacteristic
359C22#1171881711yescharacteristic
360C4—82no—
361C4—82no—
362C4—262no—
363C4—521no—
364C4—2081no—
365C4#1171844611yescharacteristic
366C4#1171844811yescharacteristic
367C4#1171861711yescharacteristic
368C4#1171883311yescharacteristic
369C2—1044no—
370C2#1311518111yescharacteristic
371C2#1311668511yescharacteristic
372C2#1311670311yescharacteristic
373C2#1311676311yescharacteristic
374C2#1311677511yescharacteristic
375C2#1311688011yescharacteristic
376C2#1311689411yescharacteristic
subgroupG/H
centerC23D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#358C2
socleC23×C13C2×D8
prime radicalC22×D104C22
cosocleC22×C8×C13C23
hypercenterC2×#358D13
hypocenterC13#13014
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
4. #13115698C2semidirect
5. #13112927C2semidirect
6. #13112913C2semidirect
7. C2×C13×#358C2semidirect
17. C2×#88068C4semidirect
34. C2×C13×Q16C2×C4semidirect
64. C2×#6090C2×C4semidirect
117. C2×#358D13semidirect
154. C2×Dic13SD32semidirect
214. C2×Q16C4×D13semidirect
302. C13#13014semidirect

Maximal subgroups

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

subgroupindex
C22×#880682
C2×#117185332
C2×#117181012
#131156982
#131129272
#131129132
C2×C13×#3582
#1301413