Finite Group Databasebeta

← #15779871

Subgroups — #15779871

Order 3328.

530 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
1C2×#11718548C211yesmaximal, characteristic
2C2×#11718541C211yesmaximal, characteristic
3C2×#11718095C211yesmaximal, characteristic, complemented
4C2×#11718084C211yesmaximal, characteristic, complemented
5C2×#11718099C211yesmaximal, characteristic
6#13112927C211yesmaximal, characteristic, complemented
7C13×#1380C211yesmaximal, characteristic, complemented
8C22×Dic52C2211yescharacteristic
9C22×C8×D13C2211yescharacteristic
10C2×#88151—21no—
11C2×#88146—21no—
12C22×C13×C16C2211yescharacteristic
13C2×C13×#107C2211yescharacteristic
14C2×C13×#107C2211yescharacteristic
15C2×#88058C2211yescharacteristic
16C22×#6090C2211yescharacteristic
17C2×#88050—21no—
18C2×#88048—21no—
19#11718548—22no—
20#11718548C414yescomplemented
21#11718541—22no—
22#11718541—22no—
23#11718099—22no—
24#11718095—22no—
25#11718084—22no—
26C22×C4×D13D411yescharacteristic
27C22×Dic26—21no—
28C22×C8×C13C2311yescharacteristic
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×#6103—41no—
32C2×#6103—41no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—41no—
35C2×C4×Dic13—41no—
36C22×#1055D411yescharacteristic
37C2×Dic52—21no—
38C2×Dic52—21no—
39C2×Dic52—21no—
40C2×Dic52—21no—
41C2×Dic52—21no—
42C2×Dic52C2×C412yes—
43C2×C8×D13—21no—
44C2×C8×D13—21no—
45C2×C8×D13—21no—
46C2×C8×D13—21no—
47C2×C8×D13C2×C412yes—
48C2×C8×D13D412yes—
49#88151—24no—
50#88151—42no—
51#88146—24no—
52#88146—42no—
53C2×C13×C16—21no—
54C2×C13×C16—21no—
55C2×C13×C16—21no—
56C13×#107—21no—
57C13×#107—21no—
58C13×#107C2×C412yes—
59C13×#107D412yes—
60#88058—21no—
61#88058D412yes—
62C2×#6090—21no—
63C2×#6090—21no—
64C2×#6090—21no—
65#88050—24no—
66#88048—24no—
67#12994—131nomaximal, Sylow
68C23×D13D811yescharacteristic
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—41no—
73C22×Dic13—41no—
74C22×Dic13D811yescharacteristic
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13C22⋊C412yes—
80C2×C4×D13SD1612yes—
81C2×Dic26—22no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×Dic26—41no—
87C2×C8×C13C22×C411yescharacteristic
88C2×C8×C13C2×D411yescharacteristic
89C2×C8×C13C2×D411yescharacteristic
90C2×C8×C13C2×D411yescharacteristic
91C2×C8×C13#4111yescharacteristic
92C2×C8×C13#4111yescharacteristic
93C13×C4⋊C4—22no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97#6103—44no—
98#6103—44no—
99C4⋊Dic13—22no—
100C4⋊Dic13—41no—
101C4⋊Dic13—44no—
102C4×Dic13—44no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055C22⋊C412yes—
106Dic52—22no—
107Dic52—22no—
108Dic52—41no—
109Dic52—41no—
110C8×D13—22no—
111C8×D13—22no—
112C8×D13—22no—
113C8×D13—22no—
114C13×C16—41no—
115#6090—41no—
116C2×#467—131no—
117C2×#427—131no—
118C2×#358—131no—
119C2×#358—131no—
120C2×C22⋊C16—131no—
121#1380—131no—
122#1380D1311yescharacteristic, complemented
123C23×C13C2×D811yescharacteristic
124C22×D13—21no—
125C22×D13—21no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13#10212yes—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13C2×C22⋊C411yescharacteristic
138C2×C4×C13#12011yescharacteristic
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13C2×SD1611yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151C2×Dic13#10212yes—
152C4×D13—22no—
153C4×D13—22no—
154C4×D13—22no—
155C4×D13—22no—
156Dic26—42no—
157Dic26—42no—
158Dic26—81no—
159Dic26—81no—
160C8×C13C4×D411yescharacteristic
161C8×C13C4×D411yescharacteristic
162C8×C13#12111yescharacteristic
163C8×C13#12111yescharacteristic
164#1055—22no—
165C22×Q16—131no—
166C23×C8—131no—
167C2×C22⋊Q8—261no—
168C2×#117—261no—
169C22×C16—131no—
170C22×C16C2×D1311yescharacteristic
171#467—134no—
172#467—262no—
173#427—262no—
174#427—262no—
175C2×#107—131no—
176C2×#107C2×D1311yescharacteristic
177C2×#107C2×D1311yescharacteristic
178C2×#106—261no—
179C2×#103—261no—
180#358—262no—
181#358—262no—
182C22⋊C16—262no—
183C22×C13C2×#10211yescharacteristic
184C22×C13#44711yescharacteristic
185C22×C13#48011yescharacteristic
186C22×C13#50811yescharacteristic
187C22×C13#50811yescharacteristic
188C22×C13#51011yescharacteristic
189C22×C13#51011yescharacteristic
190C2×D13—22no—
191C2×D13—22no—
192C2×D13—22no—
193C2×D13—41no—
194C2×D13—41no—
195C2×D13—41no—
196C2×D13—41no—
197C4×C13—82no—
198C4×C13—82no—
199C4×C13#38611yescharacteristic
200C4×C13#41711yescharacteristic
201C4×C13#44811yescharacteristic
202C4×C13#48111yescharacteristic
203Dic13—22no—
204Dic13—82no—
205Dic13—82no—
206C22×Q8—261no—
207C23×C4—131no—
208C2×Q16—132no—
209C2×Q16—261no—
210C2×Q16—261no—
211C2×Q16—261no—
212C2×Q16—261no—
213C2×Q16—261no—
214C22×C8—131no—
215C22×C8—132no—
216C22×C8—132no—
217C22×C8—261no—
218C22×C8—261no—
219C22×C8—261no—
220C22×C8—261no—
221C22×C8C22×D1311yescharacteristic
222C22⋊Q8—264no—
223C22⋊Q8—522no—
224#117—264no—
225#117—522no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4—521no—
230C2×C22⋊C4—521no—
231C2×C22⋊C4—521no—
232C2×C42—521no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16—261no—
237C2×C16—261no—
238C2×C16—261no—
239#107—21no—
240#107—21no—
241#107—132no—
242#107—261no—
243#107C4×D1312yes—
244#107D5212yes—
245#106—264no—
246#103—264no—
247C2×C13#187411yescharacteristic
248C2×C13#213811yescharacteristic
249C2×C13#214111yescharacteristic
250C2×C13#218911yescharacteristic
251C2×C13#218911yescharacteristic
252C2×C13#223711yescharacteristic
253C2×C13#223711yescharacteristic
254D13—42no—
255C24—131no—
256C2×Q8—262no—
257C2×Q8—521no—
258C2×Q8—521no—
259C2×Q8—521no—
260C2×Q8—521no—
261C2×Q8—521no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—131no—
265C22×C4—132no—
266C22×C4—132no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4—261no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4D4×D1311yescharacteristic
274Q16—262no—
275Q16—262no—
276Q16—521no—
277Q16—521no—
278C2×C8—132no—
279C2×C8—261no—
280C2×C8—261no—
281C2×C8—262no—
282C2×C8—262no—
283C2×C8—262no—
284C2×C8—262no—
285C2×C8C2×C4×D1311yescharacteristic
286C2×C8C2×D5211yescharacteristic
287C2×C8#612711yescharacteristic
288C2×C8D4×D1311yescharacteristic
289C2×C8D4×D1311yescharacteristic
290C2×C8#613111yescharacteristic
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—262no—
296C4⋊C4—524no—
297C4⋊C4—521no—
298C22⋊C4—524no—
299C22⋊C4—524no—
300C42—524no—
301C16—41no—
302C16—521no—
303C13#1299411yescharacteristic, complemented, Sylow
304C23—132no—
305C23—261no—
306C23—261no—
307C23—261no—
308C23—261no—
309C23—261no—
310C23—261no—
311C23D8×D1311yescharacteristic
312Q8—522no—
313Q8—522no—
314Q8—1041no—
315Q8—1041no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—132no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—262no—
326C2×C4—262no—
327C2×C4—262no—
328C2×C4—262no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—1041no—
332C2×C4—1041no—
333C2×C4—1041no—
334C2×C4—1041no—
335C2×C4C22⋊C4×D1311yescharacteristic
336C2×C4#8813611yescharacteristic
337C2×C4#8814811yescharacteristic
338C2×C4SD16×D1311yescharacteristic
339C2×C4#8816811yescharacteristic
340C2×C4#8817211yescharacteristic
341C8—262no—
342C8C4×D5211yescharacteristic
343C8#8813811yescharacteristic
344C8#8814711yescharacteristic
345C8#8814911yescharacteristic
346C22—262no—
347C22—262no—
348C22—262no—
349C22—521no—
350C22—521no—
351C22—521no—
352C22—521no—
353C22D13×#10211yescharacteristic
354C22#1171843411yescharacteristic
355C22#1171854311yescharacteristic
356C22#1171857311yescharacteristic
357C22#1171857611yescharacteristic
358C22#1171857711yescharacteristic
359C22#1171857911yescharacteristic
360C4—82no—
361C4—82no—
362C4—262no—
363C4—1042no—
364C4—1042no—
365C4#1171832611yescharacteristic
366C4#1171846411yescharacteristic
367C4#1171846711yescharacteristic
368C4#1171852411yescharacteristic
369C2—522no—
370C2#1311515211yescharacteristic
371C2#1311654011yescharacteristic
372C2#1311655411yescharacteristic
373C2#1311677711yescharacteristic
374C2#1311677911yescharacteristic
375C2#1311704611yescharacteristic
376C2#1311704711yescharacteristic
subgroupG/H
centerC23D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1380C2
socleC23×C13C2×D8
prime radicalC23×D13D8
cosocleC22×C8×C13C23
hypercenter#1380D13
hypocenterC13#12994
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#11718095C2semidirect
4. C2×#11718084C2semidirect
6. #13112927C2semidirect
7. C13×#1380C2semidirect
20. #11718548C4semidirect
122. #1380D13semidirect
303. C13#12994semidirect

Maximal subgroups

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

subgroupindex
C2×#117185482
C2×#117185412
C2×#117180952
C2×#117180842
C2×#117180992
#131129272
C13×#13802
#1299413