Finite Group Databasebeta

← #15779866

Subgroups — #15779866

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718548C211yesmaximal, characteristic
2C2×D13×#107C211yesmaximal, 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×C4⋊C4×D13—21no—
12C22×C13×C16C2211yescharacteristic
13C2×C13×#107C2211yescharacteristic
14C2×C13×#107C2211yescharacteristic
15C2×#88058C2211yescharacteristic
16C22×#6090C2211yescharacteristic
17C2×#88050—21no—
18C2×#88047—21no—
19#11718548—22no—
20#11718548C414yescomplemented
21D13×#107—22no—
22D13×#107—22no—
23#11718099—22no—
24#11718095—22no—
25#11718084—22no—
26C22×C4×D13—41no—
27C22×C4×D13D411yescharacteristic
28C22×Dic26—21no—
29C22×C8×C13C2311yescharacteristic
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×#6103—41no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—41no—
35C2×#6101—41no—
36C22×#1055D411yescharacteristic
37C2×Dic52—21no—
38C2×Dic52—21no—
39C2×Dic52—21no—
40C2×Dic52—21no—
41C2×Dic52—21no—
42C2×Dic52C2×C412yescomplemented
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—
51C4⋊C4×D13—24no—
52C4⋊C4×D13—42no—
53C2×C13×C16—21no—
54C2×C13×C16—21no—
55C2×C13×C16—21no—
56C13×#107—21no—
57C13×#107—21no—
58C13×#107C2×C412yescomplemented
59C13×#107D412yes—
60#88058—21no—
61#88058D412yes—
62C2×#6090—21no—
63C2×#6090—21no—
64C2×#6090—21no—
65#88050—24no—
66#88047—24no—
67#12993—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×D13—44no—
80C2×C4×D13—82no—
81C2×C4×D13—82no—
82C2×C4×D13C22⋊C412yes—
83C2×C4×D13SD1612yes—
84C2×Dic26—22no—
85C2×Dic26—41no—
86C2×Dic26—41no—
87C2×Dic26—41no—
88C2×Dic26—41no—
89C2×Dic26—41no—
90C2×C8×C13C22×C411yescharacteristic
91C2×C8×C13C2×D411yescharacteristic
92C2×C8×C13C2×D411yescharacteristic
93C2×C8×C13C2×D411yescharacteristic
94C2×C8×C13#4111yescharacteristic
95C2×C8×C13#4111yescharacteristic
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100#6103—44no—
101C4⋊Dic13—22no—
102C4⋊Dic13—41no—
103C4⋊Dic13—44no—
104#6101—44no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055C22⋊C412yes—
108Dic52—22no—
109Dic52—22no—
110Dic52—41no—
111Dic52—41no—
112C8×D13—22no—
113C8×D13—22no—
114C8×D13—22no—
115C8×D13—22no—
116C13×C16—41no—
117#6090—41no—
118C2×#467—131no—
119C22×#107—131no—
120C2×#358—131no—
121C2×#358—131no—
122C2×C22⋊C16—131no—
123#1380—131no—
124#1380D1311yescharacteristic, complemented
125C23×C13C2×D811yescharacteristic
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—21no—
129C22×D13—21no—
130C22×D13#10212yes—
131C22×D13SD3212yes—
132C22×D13Q3212yes—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13C2×C22⋊C411yescharacteristic
140C2×C4×C13#12011yescharacteristic
141C2×C4×C13#12311yescharacteristic
142C2×C4×C13C2×SD1611yescharacteristic
143C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C13#13711yescharacteristic
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151C2×Dic13—81no—
152C2×Dic13—81no—
153C2×Dic13#10212yes—
154C4×D13—22no—
155C4×D13—22no—
156C4×D13—22no—
157C4×D13—22no—
158C4×D13—88no—
159Dic26—42no—
160Dic26—42no—
161Dic26—81no—
162Dic26—81no—
163C8×C13C4×D411yescharacteristic
164C8×C13C4×D411yescharacteristic
165C8×C13#12111yescharacteristic
166C8×C13#12111yescharacteristic
167#1055—22no—
168C22×Q16—131no—
169C23×C8—131no—
170C2×C22⋊Q8—261no—
171C22×C4⋊C4—261no—
172C22×C16—131no—
173C22×C16C2×D1311yescharacteristic
174#467—134no—
175#467—262no—
176C2×#107—131no—
177C2×#107—262no—
178C2×#107—261no—
179C2×#107—262no—
180C2×#107C2×D1311yescharacteristic
181C2×#107C2×D1311yescharacteristic
182C2×#103—261no—
183#358—262no—
184#358—262no—
185C22⋊C16—262no—
186C22×C13C2×#10211yescharacteristic
187C22×C13#44711yescharacteristic
188C22×C13#48011yescharacteristic
189C22×C13C2×SD3211yescharacteristic
190C22×C13C2×Q3211yescharacteristic
191C22×C13#50911yescharacteristic
192C22×C13#51011yescharacteristic
193C2×D13—22no—
194C2×D13—22no—
195C2×D13—22no—
196C2×D13—22no—
197C2×D13—22no—
198C2×D13—22no—
199C2×D13#35814yescomplemented
200C4×C13—82no—
201C4×C13—82no—
202C4×C13#38611yescharacteristic
203C4×C13#41711yescharacteristic
204C4×C13#44811yescharacteristic
205C4×C13#48111yescharacteristic
206Dic13—22no—
207Dic13—82no—
208Dic13—82no—
209C22×Q8—261no—
210C23×C4—131no—
211C23×C4—521no—
212C2×Q16—132no—
213C2×Q16—261no—
214C2×Q16—261no—
215C2×Q16—261no—
216C2×Q16—261no—
217C2×Q16—261no—
218C22×C8—131no—
219C22×C8—132no—
220C22×C8—132no—
221C22×C8—261no—
222C22×C8—261no—
223C22×C8—261no—
224C22×C8—261no—
225C22×C8C22×D1311yescharacteristic
226C22⋊Q8—264no—
227C22⋊Q8—522no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—264no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4—522no—
233C2×C4⋊C4—521no—
234C2×C4⋊C4—521no—
235C2×C22⋊C4—521no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—261no—
240C2×C16—261no—
241C2×C16—261no—
242#107—21no—
243#107—21no—
244#107—132no—
245#107—264no—
246#107—261no—
247#107C4×D1312yescomplemented
248#107D5212yes—
249#103—264no—
250C2×C13#187411yescharacteristic
251C2×C13C2×#35811yescharacteristic
252C2×C13#213911yescharacteristic
253C2×C13#218711yescharacteristic
254C2×C13#218811yescharacteristic
255C2×C13#223511yescharacteristic
256C2×C13#223611yescharacteristic
257D13—24no—
258C24—131no—
259C2×Q8—262no—
260C2×Q8—521no—
261C2×Q8—521no—
262C2×Q8—521no—
263C2×Q8—521no—
264C2×Q8—521no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—131no—
268C22×C4—132no—
269C22×C4—132no—
270C22×C4—261no—
271C22×C4—261no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4—524no—
275C22×C4—521no—
276C22×C4—521no—
277C22×C4—1042no—
278C22×C4—1042no—
279C22×C4D4×D1311yescharacteristic
280Q16—262no—
281Q16—262no—
282Q16—521no—
283Q16—521no—
284C2×C8—132no—
285C2×C8—261no—
286C2×C8—261no—
287C2×C8—262no—
288C2×C8—262no—
289C2×C8—262no—
290C2×C8—262no—
291C2×C8C2×C4×D1311yescharacteristic
292C2×C8C2×D5211yescharacteristic
293C2×C8#612711yescharacteristic
294C2×C8D4×D1311yescharacteristic
295C2×C8D4×D1311yescharacteristic
296C2×C8#613111yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—262no—
302C4⋊C4—524no—
303C4⋊C4—524no—
304C4⋊C4—521no—
305C22⋊C4—524no—
306C16—41no—
307C16—521no—
308C13#1299311yescharacteristic, complemented, Sylow
309C23—132no—
310C23—132no—
311C23—132no—
312C23—261no—
313C23—261no—
314C23—261no—
315C23—261no—
316C23D8×D1311yescharacteristic
317Q8—522no—
318Q8—522no—
319Q8—1041no—
320Q8—1041no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—132no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—262no—
331C2×C4—262no—
332C2×C4—262no—
333C2×C4—262no—
334C2×C4—522no—
335C2×C4—522no—
336C2×C4—1048no—
337C2×C4—1041no—
338C2×C4—1041no—
339C2×C4—1041no—
340C2×C4—1041no—
341C2×C4C22⋊C4×D1311yescharacteristic
342C2×C4#8813611yescharacteristic
343C2×C4#8814811yescharacteristic
344C2×C4SD16×D1311yescharacteristic
345C2×C4#8816811yescharacteristic
346C2×C4#8817211yescharacteristic
347C8—262no—
348C8C4×D5211yescharacteristic
349C8#8813811yescharacteristic
350C8#8814711yescharacteristic
351C8#8814911yescharacteristic
352C22—134no—
353C22—262no—
354C22—262no—
355C22—262no—
356C22—262no—
357C22—262no—
358C22—262no—
359C22D13×#10211yescharacteristic
360C22#1171843411yescharacteristic
361C22#1171854311yescharacteristic
362C22#1171857211yescharacteristic
363C22D13×SD3211yescharacteristic
364C22#1171857611yescharacteristic
365C22D13×Q3211yescharacteristic
366C4—82no—
367C4—82no—
368C4—262no—
369C4—1042no—
370C4—1042no—
371C4#1171832611yescharacteristic
372C4#1171846411yescharacteristic
373C4#1171846711yescharacteristic
374C4#1171852411yescharacteristic
375C2—264no—
376C2#1311515211yescharacteristic
377C2D13×#35811yescharacteristic
378C2#1311654511yescharacteristic
379C2#1311676611yescharacteristic
380C2#1311677111yescharacteristic
381C2#1311703511yescharacteristic
382C2#1311704011yescharacteristic
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#12993
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
42. C2×Dic52C2×C4semidirect
58. C13×#107C2×C4semidirect
124. #1380D13semidirect
199. C2×D13#358semidirect
247. #107C4×D13semidirect
308. C13#12993semidirect

Maximal subgroups

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

subgroupindex
C2×#117185482
C2×D13×#1072
C2×#117180952
C2×#117180842
C2×#117180992
#131129272
C13×#13802
#1299313