Finite Group Databasebeta

← #15778887

Subgroups — #15778887

Order 3328.

540 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718131C212yesmaximal
2#13114828C211yesmaximal, characteristic
3#13114824C211yesmaximal, characteristic
4#13112954C212yesmaximal
5C4×C13×#123C211yesmaximal, characteristic
6C2×C13×#123C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C22×C42×C13C411yescharacteristic, complemented
9C13×#388—21no—
10C13×#387—21no—
11C13×#386C2211yescharacteristic
12C13×#385C411yescharacteristic, complemented
13C13×#381C411yescharacteristic, complemented
14C4×C13×C4⋊C4—21no—
15C4×C13×C22⋊C4—21no—
16C4×C13×C22⋊C4C411yescharacteristic, complemented
17C2×#88074C2212yes—
18C2×#88073C2212yes—
19#11718873—21no—
20#11718585—21no—
21#11718131—24no—
22#11718122—21no—
23#11718118—21no—
24C22×D4×C13C2311yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C13×#123—21no—
30C13×#123—21no—
31C13×#123D412yes—
32C13×#123Q812yes—
33C4×D4×C13—41no—
34C4×D4×C13—41no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C42×C13—21no—
45C2×C42×C13—21no—
46C2×C42×C13—21no—
47C2×C42×C13—41no—
48C2×C42×C13—41no—
49C2×C42×C13D411yescharacteristic
50C2×C22⋊Dic13—22no—
51C2×C4⋊Dic13—41no—
52C2×#6099—22no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95—21no—
56C13×#95—21no—
57C13×#95—21no—
58#88074—22no—
59#88074—22no—
60#88073—22no—
61#88073—22no—
62#88071—41no—
63C4⋊#1055—41no—
64C4⋊#1055—41no—
65#12794—131nomaximal, Sylow
66C24×C13C22×C411yescharacteristic
67C24×C13C2×D411yescharacteristic
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13C2×D411yescharacteristic
71C2×D4×C13C2×Q811yescharacteristic
72C2×D4×C13#4111yescharacteristic
73C2×D4×C13#4111yescharacteristic
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—42no—
84C22×C4×C13—42no—
85C22×C4×C13—42no—
86C22×C4×C13—41no—
87C22×C4×C13—41no—
88C22×C4×C13—41no—
89C22×C4×C13C22⋊C411yescharacteristic
90C22×C4×C13C22⋊C411yescharacteristic
91C22×C4×C13C22⋊C411yescharacteristic
92C22×C4×C13C22⋊C411yescharacteristic
93C22×C4×C13C4⋊C412yescomplemented
94C22×C4×C13C2×D411yescharacteristic
95C22×Dic13—42no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—42no—
100C13×C22⋊C4—21no—
101C13×C22⋊C4—22no—
102C13×C22⋊C4—22no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C13×C22⋊C4—42no—
106C13×C22⋊C4—41no—
107C13×C22⋊C4C4⋊C412yescomplemented
108C42×C13—21no—
109C42×C13—21no—
110C42×C13—42no—
111C42×C13—42no—
112C42×C13—41no—
113C42×C13—41no—
114C22⋊Dic13—42no—
115C22⋊Dic13—42no—
116C4⋊Dic13—82no—
117#6099—42no—
118#6099—42no—
119C2×#1055—42no—
120C4×#123D1311yescharacteristic
121C2×#352—132no—
122#1800—131no—
123#1799—131no—
124#1390—132no—
125C23×C13—21no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13—21no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13C2×C4⋊C411yescharacteristic
135C23×C13#11711yescharacteristic
136C23×C13#12111yescharacteristic
137C23×C13C22⋊Q811yescharacteristic
138D4×C13—41no—
139D4×C13—41no—
140D4×C13—41no—
141D4×C13—41no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—42no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—41no—
156C2×C4×C13—42no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—41no—
160C2×C4×C13—42no—
161C2×C4×C13—42no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—42no—
166C2×C4×C13—42no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—41no—
170C2×C4×C13—81no—
171C2×C4×C13#9911yescharacteristic
172C2×C4×C13#9911yescharacteristic
173C2×C4×C13#12111yescharacteristic
174C2×C4×C13C22⋊Q811yescharacteristic
175C2×Dic13—82no—
176C2×Dic13—82no—
177C2×Dic13—82no—
178#1055—82no—
179C2×#123C2×D1311yescharacteristic
180C2×C4×D4C2×D1311yescharacteristic
181C22×C42Dic1311yescharacteristic, complemented
182#423—261no—
183C2×#100—132no—
184C2×#99—132no—
185#388—21no—
186#387—21no—
187#386C2×D1311yescharacteristic
188#385Dic1311yescharacteristic, complemented
189#381Dic1311yescharacteristic, complemented
190#380—261no—
191C4×C4⋊C4—21no—
192C4×C22⋊C4—21no—
193C4×C22⋊C4Dic1311yescharacteristic, complemented
194#352—264no—
195#343—261no—
196#342—261no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13—21no—
200C22×C13—21no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—41no—
204C22×C13—41no—
205C22×C13—41no—
206C22×C13—41no—
207C22×C13—42no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13—81no—
213C22×C13#38011yescharacteristic
214C22×C13C2×#9911yescharacteristic
215C22×C13#41011yescharacteristic
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—42no—
220C4×C13—42no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13—42no—
225C4×C13—81no—
226C4×C13#35212yescomplemented
227Dic13—162no—
228C22×D4C22×D1311yescharacteristic
229C23×C4C2×Dic1311yescharacteristic
230C23×C4C2×Dic1311yescharacteristic
231C23×C4C2×Dic1311yescharacteristic
232C23×C4C22⋊D1311yescharacteristic
233C2×M16—262no—
234#123—21no—
235#123—21no—
236#123Dic2612yes—
237#123D5212yes—
238C4×D4—41no—
239C4×D4—41no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—521no—
243C2×C4⋊C4C22⋊D1311yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—262no—
247C2×C22⋊C4C2×Dic1311yescharacteristic
248C2×C22⋊C4C2×Dic1311yescharacteristic
249C2×C22⋊C4C2×Dic1311yescharacteristic
250C2×C22⋊C4C22⋊D1311yescharacteristic
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42—41no—
255C2×C42—41no—
256C2×C42C22⋊D1311yescharacteristic
257C4⋊C8—521no—
258C4⋊C8—521no—
259#100—262no—
260#100—262no—
261#99—262no—
262#99—262no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—521no—
269C2×C13—21no—
270C2×C13—21no—
271C2×C13—41no—
272C2×C13—41no—
273C2×C13—41no—
274C2×C13—41no—
275C2×C13#179911yescharacteristic
276C2×C13C2×#35211yescharacteristic
277C2×C13#212011yescharacteristic
278C24C22×Dic1311yescharacteristic
279C24C2×C22⋊D1311yescharacteristic
280C2×D4—41no—
281C2×D4—41no—
282C2×D4C2×Dic2611yescharacteristic
283C2×D4C2×D5211yescharacteristic
284C2×D4#612711yescharacteristic
285C2×D4#612711yescharacteristic
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—522no—
302C22×C4C4⋊Dic1312yescomplemented
303C22×C4C22⋊Dic1311yescharacteristic
304C22×C4C22⋊Dic1311yescharacteristic
305C22×C4C22⋊Dic1311yescharacteristic
306C22×C4C22⋊Dic1311yescharacteristic
307C22×C4C2×C22⋊D1311yescharacteristic
308M16—522no—
309M16—522no—
310C2×C8—522no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—1042no—
316C22⋊C4—22no—
317C22⋊C4—21no—
318C22⋊C4—22no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—42no—
322C22⋊C4—41no—
323C22⋊C4—522no—
324C22⋊C4—522no—
325C22⋊C4C4⋊Dic1312yescomplemented
326C42—21no—
327C42—21no—
328C42—42no—
329C42—42no—
330C42—41no—
331C42—41no—
332C13#1279411yescharacteristic, complemented, Sylow
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23#8817811yescharacteristic
342C23C2×C4⋊Dic1311yescharacteristic
343C23#8818011yescharacteristic
344C23#8818411yescharacteristic
345C23C2×C22⋊Dic1311yescharacteristic
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—1042no—
380C2×C4—1042no—
381C2×C4—1042no—
382C2×C4#8807411yescharacteristic
383C2×C4#8807411yescharacteristic
384C2×C4#8817811yescharacteristic
385C2×C4#8818411yescharacteristic
386C8—1042no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22#1171887311yescharacteristic
404C22C2×#8807411yescharacteristic
405C22#1171890111yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—42no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—42no—
414C4—42no—
415C4—81no—
416C4—2082no—
417C4#1171813112yescomplemented
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—41no—
423C2—41no—
424C2#1311482411yescharacteristic
425C2C2×#1171813111yescharacteristic
426C2#1311647711yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC4×C13×#123C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#123D13
hypocenterC13#12794
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
8. C22×C42×C13C4semidirect
12. C13×#385C4semidirect
13. C13×#381C4semidirect
16. C4×C13×C22⋊C4C4semidirect
93. C22×C4×C13C4⋊C4semidirect
107. C13×C22⋊C4C4⋊C4semidirect
181. C22×C42Dic13semidirect
188. #385Dic13semidirect
189. #381Dic13semidirect
193. C4×C22⋊C4Dic13semidirect
226. C4×C13#352semidirect
302. C22×C4C4⋊Dic13semidirect
325. C22⋊C4C4⋊Dic13semidirect
332. C13#12794semidirect
417. C4#11718131semidirect

Maximal subgroups

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

subgroupindex
C2×#117181312
#131148282
#131148242
#131129542
C4×C13×#1232
#1279413