Finite Group Databasebeta

← #15779974

Subgroups — #15779974

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88066C211yesmaximal, characteristic
2C2×D8×Dic13C211yesmaximal, characteristic, complemented
3C2×#11718101C211yesmaximal, characteristic, complemented
4#13115700C211yesmaximal, characteristic, complemented
5#13112927C211yesmaximal, characteristic, complemented
6#13112913C211yesmaximal, characteristic, complemented
7C2×C13×#357C211yesmaximal, characteristic, complemented
8C22×C13×D8C2211yescharacteristic
9C2×D4×Dic13—21no—
10C22×D104C2211yescharacteristic
11C22×C13×C16C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×#88072—21no—
14D8×Dic13—22no—
15D8×Dic13—22no—
16C2×#88066—22no—
17C2×#88066—22no—
18C2×#88066C414yescomplemented
19C2×#88058C2211yescharacteristic
20C2×C8×Dic13C2211yescharacteristic
21C22×#6090C2211yescharacteristic
22#11718649—21no—
23C2×#88049—21no—
24C13×#357—22no—
25#11718101—22no—
26C22×D4×C13—21no—
27C23×Dic13—41no—
28C22×D52—21no—
29C2×C13×D8—21no—
30C2×C13×D8—21no—
31C2×C13×D8—21no—
32C2×C13×D8C2×C412yes—
33C2×C13×D8D412yes—
34C2×C13×D8D412yes—
35C22×C8×C13C2311yescharacteristic
36C2×C13×C4⋊C4—21no—
37C2×C22⋊Dic13—41no—
38D4×Dic13—24no—
39D4×Dic13—42no—
40C2×#6103—41no—
41C2×#6103—41no—
42C2×C4⋊Dic13—21no—
43C2×C4×Dic13D411yescharacteristic
44C22×#1055D411yescharacteristic
45C2×D104—21no—
46C2×D104—21no—
47C2×D104—21no—
48C2×D104—21no—
49C2×D104—21no—
50C2×D104C2×C412yescomplemented
51C2×C13×C16—21no—
52C2×C13×C16—21no—
53C2×C13×C16—21no—
54C13×#107—21no—
55C13×#107—21no—
56#88072—24no—
57#88066—28no—
58#88058—21no—
59#88058D412yes—
60C8×Dic13—21no—
61C8×Dic13—21no—
62C2×#6090—21no—
63C2×#6090—21no—
64C2×#6090C2×C412yescomplemented
65#88049—42no—
66#13012—131nomaximal, Sylow
67C24×C13—41no—
68C23×D13—41no—
69C2×D4×C13—22no—
70C2×D4×C13—22no—
71C2×D4×C13—22no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—44no—
78C22×Dic13—41no—
79C22×Dic13—82no—
80C22×Dic13—82no—
81C22×Dic13D811yescharacteristic
82C22×Dic13D811yescharacteristic
83C2×D52—22no—
84C2×D52—41no—
85C2×D52—41no—
86C2×D52—41no—
87C2×D52—41no—
88C2×D52—41no—
89C13×D8—22no—
90C13×D8—22no—
91C13×D8—22no—
92C13×D8C22⋊C414yescomplemented
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—41no—
100C13×C4⋊C4—41no—
101C22⋊Dic13—44no—
102#6103—82no—
103#6103—82no—
104C4⋊Dic13—22no—
105C4⋊Dic13—41no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—21no—
111D104—22no—
112D104—22no—
113D104—41no—
114D104—41no—
115C13×C16—41no—
116#6090—22no—
117C22×D16—131no—
118C2×C4×D8—131no—
119C2×#357—131no—
120C2×#357D1311yescharacteristic, complemented
121#1970—131no—
122#1380—131no—
123#1374—131no—
124C23×C13—42no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—81no—
128C23×C13—81no—
129C23×C13—81no—
130C23×C13—81no—
131C23×C13C2×D811yescharacteristic
132C22×D13—42no—
133C22×D13—81no—
134C22×D13—81no—
135C22×D13—81no—
136C22×D13—81no—
137C22×D13—81no—
138C22×D13—81no—
139D4×C13—24no—
140D4×C13—42no—
141D4×C13—42no—
142D4×C13—42no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
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—21no—
153C2×Dic13—21no—
154C2×Dic13—21no—
155C2×Dic13—21no—
156C2×Dic13—21no—
157C2×Dic13—42no—
158C2×Dic13—88no—
159C2×Dic13—81no—
160C2×Dic13—81no—
161C2×Dic13D1612yescomplemented
162D52—42no—
163D52—42no—
164D52—81no—
165D52—81no—
166C8×C13C2×C22⋊C411yescharacteristic
167C8×C13C4×D411yescharacteristic
168C8×C13#12111yescharacteristic
169C8×C13#12311yescharacteristic
170#1055—41no—
171C22×D8—131no—
172C22×D8C2×D1311yescharacteristic
173C2×C4×D4—261no—
174C2×D16—134no—
175C2×D16—262no—
176C2×D16—262no—
177C22×C16—131no—
178C22×C16C2×D1311yescharacteristic
179C4×D8—262no—
180C4×D8—262no—
181C2×#107—131no—
182C2×#107C2×D1311yescharacteristic
183C2×#102—261no—
184C2×#102—261no—
185C2×C4×C8—131no—
186#390—261no—
187#357—22no—
188#357—262no—
189C22×C13—44no—
190C22×C13—82no—
191C22×C13—82no—
192C22×C13—82no—
193C22×C13—82no—
194C22×C13—82no—
195C22×C13—82no—
196C22×C13C4×D811yescharacteristic
197C22×C13#44711yescharacteristic
198C22×C13#45911yescharacteristic
199C22×C13C2×D1611yescharacteristic
200C22×C13#50811yescharacteristic
201C22×C13#50911yescharacteristic
202C22×C13#50911yescharacteristic
203C2×D13—82no—
204C2×D13—82no—
205C2×D13—82no—
206C2×D13—161no—
207C2×D13—161no—
208C2×D13—161no—
209C2×D13—161no—
210C4×C13—161no—
211C4×C13#38611yescharacteristic
212C4×C13#44211yescharacteristic
213C4×C13#44911yescharacteristic
214C4×C13#46311yescharacteristic
215Dic13—22no—
216Dic13—41no—
217Dic13—82no—
218C22×D4—21no—
219C22×D4—261no—
220C23×C4—521no—
221C2×D8—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—132no—
225C2×D8—261no—
226C2×D8—261no—
227C2×D8—261no—
228C2×D8—261no—
229C2×D8—261no—
230C2×D8C4×D1312yes—
231C2×D8D5212yes—
232C2×D8C22⋊D1312yes—
233C22×C8—131no—
234C22×C8C22×D1311yescharacteristic
235C4×D4—264no—
236C4×D4—522no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—261no—
239C2×C22⋊C4—521no—
240C2×C22⋊C4—521no—
241C2×C22⋊C4—521no—
242C2×C42—131no—
243D16—268no—
244C2×C16—21no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—132no—
248C2×C16—261no—
249C2×C16—261no—
250#107—21no—
251#107—21no—
252#107—132no—
253#107—261no—
254#102—264no—
255#102—522no—
256C4×C8—261no—
257C4×C8—261no—
258C2×C13—84no—
259C2×C13#187911yescharacteristic
260C2×C13C4×D1611yescharacteristic
261C2×C13#217711yescharacteristic
262C2×C13#218411yescharacteristic
263C2×C13#218611yescharacteristic
264C2×C13#220611yescharacteristic
265C2×C13#221011yescharacteristic
266D13—162no—
267C24—41no—
268C24—521no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—262no—
276C2×D4—521no—
277C2×D4—521no—
278C2×D4—521no—
279C2×D4—521no—
280C2×D4—521no—
281C22×C4—41no—
282C22×C4—131no—
283C22×C4—131no—
284C22×C4—524no—
285C22×C4—521no—
286C22×C4—1042no—
287C22×C4—1042no—
288C22×C4D4×D1311yescharacteristic
289D8—22no—
290D8—22no—
291D8—22no—
292D8—262no—
293D8—262no—
294D8—521no—
295D8—521no—
296D8#610314yescomplemented
297C2×C8—261no—
298C2×C8—261no—
299C2×C8—261no—
300C2×C8C2×C4×D1311yescharacteristic
301C2×C8C2×D5211yescharacteristic
302C2×C8D4×D1311yescharacteristic
303C2×C8#612911yescharacteristic
304C2×C8#612911yescharacteristic
305C2×C8C2×C22⋊D1311yescharacteristic
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—262no—
309C4⋊C4—521no—
310C22⋊C4—524no—
311C22⋊C4—1042no—
312C22⋊C4—1042no—
313C42—261no—
314C42—261no—
315C16—41no—
316C16—262no—
317C13#1301211yescharacteristic, complemented, Sylow
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—522no—
326C23—1041no—
327C23—1041no—
328C23—1041no—
329C23—1041no—
330C23—1041no—
331C23—1041no—
332C23D8×D1311yescharacteristic
333D4—24no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—522no—
338D4—522no—
339D4—1041no—
340D4—1041no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—132no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—261no—
350C2×C4—522no—
351C2×C4—1048no—
352C2×C4—1041no—
353C2×C4—1041no—
354C2×C4#8813511yescharacteristic
355C2×C4#8813611yescharacteristic
356C2×C4#8816511yescharacteristic
357C2×C4#8816811yescharacteristic
358C2×C4#8817011yescharacteristic
359C2×C4#8819311yescharacteristic
360C8—521no—
361C8#8813511yescharacteristic
362C8#8814011yescharacteristic
363C8C2×#610311yescharacteristic
364C8#8819311yescharacteristic
365C22—44no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—1042no—
373C22—1042no—
374C22—1042no—
375C22—2081no—
376C22—2081no—
377C22—2081no—
378C22—2081no—
379C22#1171841711yescharacteristic
380C22#1171843411yescharacteristic
381C22D13×D1611yescharacteristic
382C22#1171857211yescharacteristic
383C22#1171857511yescharacteristic
384C22#1171857711yescharacteristic
385C22#1171881111yescharacteristic
386C4—161no—
387C4—262no—
388C4—521no—
389C4—1042no—
390C4#1171844211yescharacteristic
391C4#1171844611yescharacteristic
392C4#1171861911yescharacteristic
393C4#1171882611yescharacteristic
394C2—84no—
395C2—2082no—
396C2#1311518211yescharacteristic
397C2#1311668011yescharacteristic
398C2#1311670911yescharacteristic
399C2#1311674911yescharacteristic
400C2#1311676011yescharacteristic
401C2#1311686911yescharacteristic
402C2#1311689311yescharacteristic
subgroupG/H
centerC23D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#357C2
socleC23×C13C2×D8
prime radicalC22×#88066C2
cosocleC22×C8×C13C23
hypercenterC2×#357D13
hypocenterC13#13012
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×D8×Dic13C2semidirect
3. C2×#11718101C2semidirect
4. #13115700C2semidirect
5. #13112927C2semidirect
6. #13112913C2semidirect
7. C2×C13×#357C2semidirect
18. C2×#88066C4semidirect
50. C2×D104C2×C4semidirect
64. C2×#6090C2×C4semidirect
92. C13×D8C22⋊C4semidirect
120. C2×#357D13semidirect
161. C2×Dic13D16semidirect
296. D8#6103semidirect
317. C13#13012semidirect

Maximal subgroups

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

subgroupindex
C22×#880662
C2×D8×Dic132
C2×#117181012
#131157002
#131129272
#131129132
C2×C13×#3572
#1301213