Finite Group Databasebeta

← #15761791

Subgroups — #15761791

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#6104C211yesmaximal, characteristic
2#13115630C211yesmaximal, characteristic, complemented
3C2×#11718072C211yesmaximal, characteristic, complemented
4C2×D4⋊#1055C211yesmaximal, characteristic, complemented
5C2×#11718075C211yesmaximal, characteristic, complemented
6C2×#11718046C211yesmaximal, characteristic, complemented
7C13×#1954C211yesmaximal, characteristic, complemented
8C2×C4×D4×C13C2211yescharacteristic
9C22×#6104C411yescharacteristic
10C2×C4×D52C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C22⋊C8—22no—
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88072C411yescharacteristic
15C2×#88060—22no—
16C4×#6104—22no—
17C4×#6104—22no—
18C2×#88049C411yescharacteristic
19C2×#88047C411yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23D4⋊#1055—22no—
24#11718075—22no—
25#11718072—22no—
26#11718046—22no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13—21no—
29C22×D52C2×C411yescharacteristic
30C22×C4×D13—21no—
31C22×C8×C13—21no—
32C22×C8×C13D412yes—
33C4×D4×C13—21no—
34C4×D4×C13—21no—
35C4×D4×C13—21no—
36C4×D4×C13—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C42×C13C2311yescharacteristic
40C2×#6104—22no—
41C2×#6104—22no—
42C2×#6104C814yescomplemented
43C2×#6103—21no—
44C2×C4⋊Dic13C2×C411yescharacteristic
45C22×#1055—21no—
46C22×#1055—21no—
47C22×#1055C2×C411yescharacteristic
48C22×#1055C2×C411yescharacteristic
49C4×D52—21no—
50C4×D52—21no—
51C4×D52—21no—
52C4×D52—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55C13×C22⋊C8—44no—
56C4×C8×C13—21no—
57C4×C8×C13—21no—
58#88072—22no—
59#88060—44no—
60#88049—22no—
61#88047—22no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4×#1055—21no—
65C4×#1055D412yes—
66C4×#1055D412yes—
67C4×#1055D412yes—
68#9659—131nomaximal, Sylow
69C24×C13—21no—
70C23×D13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13—21no—
76C2×D4×C13C2×C812yes—
77C22×C4×C13—21no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13#4111yescharacteristic
85C22×Dic13—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×D52—21no—
91C2×D52C2×C812yes—
92C2×C4×D13—41no—
93C2×C4×D13—41no—
94C2×C4×D13—42no—
95C2×C4×D13—42no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—22no—
99C2×C8×C13—41no—
100C2×C8×C13—42no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C22⋊C4—41no—
104C13×C22⋊C4—41no—
105C42×C13C2×D411yescharacteristic
106C42×C13C2×D411yescharacteristic
107C42×C13C2×D411yescharacteristic
108C42×C13#4111yescharacteristic
109#6104—28no—
110#6103—41no—
111#6103—41no—
112C4⋊Dic13—21no—
113C4⋊Dic13—21no—
114C2×#1055—21no—
115C2×#1055—21no—
116C2×#1055—22no—
117C2×#1055—42no—
118C2×#1055—41no—
119C2×#1055—42no—
120C2×#1055C22⋊C412yes—
121C2×#1055C22⋊C412yes—
122C2×#1055C2×C812yes—
123C2×#1055M1612yes—
124C2×C4×D8—131no—
125#1954—131no—
126#1954D1311yescharacteristic, complemented
127C2×#334—131no—
128C2×D4⋊C8—131no—
129C2×D4⋊C8—131no—
130C2×#322—131no—
131C23×C13—22no—
132C23×C13—41no—
133C23×C13—41no—
134C23×C13—42no—
135C23×C13—42no—
136C23×C13C4×D411yescharacteristic
137C22×D13—22no—
138C22×D13—41no—
139C22×D13—41no—
140C22×D13—42no—
141C22×D13—42no—
142D4×C13—22no—
143D4×C13—22no—
144D4×C13—41no—
145D4×C13—41no—
146C2×C4×C13—22no—
147C2×C4×C13—41no—
148C2×C4×C13—42no—
149C2×C4×C13—82no—
150C2×C4×C13—81no—
151C2×C4×C13—81no—
152C2×C4×C13C2×C22⋊C411yescharacteristic
153C2×C4×C13C4×D411yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12411yescharacteristic
157C2×C4×C13#12711yescharacteristic
158C2×C4×C13C22×C811yescharacteristic
159C2×C4×C13C2×M1611yescharacteristic
160C2×C4×C13#13111yescharacteristic
161C2×C4×C13#13111yescharacteristic
162C2×C4×C13AGL(1,ℤ/8)12yes—
163C2×C4×C13AGL(1,ℤ/8)12yes—
164C2×Dic13—41no—
165C2×Dic13—42no—
166D52—22no—
167D52—22no—
168D52—41no—
169D52—41no—
170C4×D13—82no—
171C4×D13—81no—
172C4×D13—81no—
173C8×C13—42no—
174C8×C13—81no—
175#1055—22no—
176#1055—42no—
177#1055—81no—
178#1055C22⋊C814yescomplemented
179C22×D8—131no—
180C2×C4×D4—131no—
181C2×C4×D4C2×D1311yescharacteristic
182C4×D8—262no—
183C4×D8—262no—
184C2×#107—131no—
185C2×C4⋊C8—131no—
186C2×C4⋊C8C2×D1311yescharacteristic
187C2×#102—131no—
188C2×#102—131no—
189C2×C22⋊C8—22no—
190C2×C22⋊C8—262no—
191C2×C4×C8—131no—
192C2×C4×C8—131no—
193C2×C4×C8C2×D1311yescharacteristic
194#334—262no—
195D4⋊C8—262no—
196D4⋊C8—262no—
197#322—262no—
198C22×C13—44no—
199C22×C13—42no—
200C22×C13—82no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13#39011yescharacteristic
204C22×C13C8×D411yescharacteristic
205C22×C13#43611yescharacteristic
206C22×C13#44212yes—
207C22×C13#44412yes—
208C2×D13—44no—
209C2×D13—42no—
210C2×D13—82no—
211C2×D13—81no—
212C2×D13—81no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—81no—
216C4×C13C2×C22⋊C811yescharacteristic
217C4×C13#40811yescharacteristic
218C4×C13C8×D411yescharacteristic
219C4×C13#43611yescharacteristic
220C4×C13#46912yes—
221C4×C13#49611yescharacteristic
222C4×C13#49611yescharacteristic
223Dic13—81no—
224C22×D4—131no—
225C22×D4C4×D1311yescharacteristic
226C23×C4—21no—
227C23×C4—261no—
228C2×D8—134no—
229C2×D8—262no—
230C2×D8—262no—
231C22×C8—21no—
232C22×C8—131no—
233C22×C8—131no—
234C22×C8—261no—
235C22×C8—261no—
236C22×C8C22⋊D1312yes—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4—261no—
242C4×D4—261no—
243C4×D4—261no—
244C4×D4—261no—
245C2×C4⋊C4—131no—
246C2×C4⋊C4C4×D1311yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4—261no—
249C2×C42C22×D1311yescharacteristic
250#107—262no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—261no—
254C4⋊C8—261no—
255#102—262no—
256#102—262no—
257C22⋊C8—44no—
258C22⋊C8—524no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8—132no—
262C4×C8—132no—
263C4×C8—132no—
264C4×C8—261no—
265C2×C13—82no—
266C2×C13#158012yes—
267C2×C13#159412yes—
268C2×C13#195411yescharacteristic
269C2×C13#197211yescharacteristic
270C2×C13#197511yescharacteristic
271D13—82no—
272C24—21no—
273C24—261no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—132no—
280C2×D4—261no—
281C2×D4—261no—
282C2×D4—261no—
283C2×D4—261no—
284C2×D4—261no—
285C2×D4C8×D1312yes—
286C22×C4—21no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—261no—
292C22×C4—522no—
293C22×C4—521no—
294C22×C4—521no—
295C22×C4—522no—
296C22×C4C2×C4×D1311yescharacteristic
297C22×C4#612711yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299D8—268no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—42no—
304C2×C8—41no—
305C2×C8—132no—
306C2×C8—132no—
307C2×C8—132no—
308C2×C8—132no—
309C2×C8—261no—
310C2×C8—261no—
311C2×C8—262no—
312C2×C8—522no—
313C2×C8—521no—
314C2×C8—522no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—261no—
318C4⋊C4—261no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—521no—
322C22⋊C4—521no—
323C42D4×D1311yescharacteristic
324C42D4×D1311yescharacteristic
325C42D4×D1311yescharacteristic
326C42#612911yescharacteristic
327C13#965911yescharacteristic, complemented, Sylow
328C23—22no—
329C23—42no—
330C23—41no—
331C23—42no—
332C23—41no—
333C23—262no—
334C23—522no—
335C23—521no—
336C23—522no—
337C23—521no—
338C23C4×C22⋊D1311yescharacteristic
339D4—22no—
340D4—22no—
341D4—41no—
342D4—41no—
343D4—262no—
344D4—262no—
345D4—521no—
346D4—521no—
347C2×C4—22no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—82no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—522no—
354C2×C4—521no—
355C2×C4—1042no—
356C2×C4—1041no—
357C2×C4—1041no—
358C2×C4C22⋊C4×D1311yescharacteristic
359C2×C4#8813511yescharacteristic
360C2×C4#8813811yescharacteristic
361C2×C4#8813911yescharacteristic
362C2×C4C2×C8×D1311yescharacteristic
363C2×C4#8815511yescharacteristic
364C2×C4M16×D1311yescharacteristic
365C2×C4#8816111yescharacteristic
366C2×C4#8818612yes—
367C2×C4#8819311yescharacteristic
368C2×C4#8819411yescharacteristic
369C2×C4#8820312yes—
370C8—42no—
371C8—81no—
372C8—134no—
373C8—262no—
374C8—522no—
375C8—1041no—
376C22—44no—
377C22—42no—
378C22—81no—
379C22—81no—
380C22—82no—
381C22—524no—
382C22—522no—
383C22—1041no—
384C22—1041no—
385C22—1042no—
386C22#1171861811yescharacteristic
387C22#1171867512yes—
388C22C8×C22⋊D1311yescharacteristic
389C22#1171878911yescharacteristic
390C22#1171880612yes—
391C4—21no—
392C4—21no—
393C4—81no—
394C4—1041no—
395C4D13×C22⋊C811yescharacteristic
396C4#1171838611yescharacteristic
397C4#1171838811yescharacteristic
398C4#1171839011yescharacteristic
399C4#1171870012yes—
400C4#1171871911yescharacteristic
401C4#1171873511yescharacteristic
402C2—82no—
403C2—1042no—
404C2#1311365812yes—
405C2#1311374812yes—
406C2#1311562811yescharacteristic
407C2#1311571111yescharacteristic
408C2#1311572811yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1954C2
socleC23×C13C4×D4
prime radicalC22×#6104C4
cosocleC2×C42×C13C23
hypercenter#1954D13
hypocenterC13#9659
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. #13115630C2semidirect
3. C2×#11718072C2semidirect
4. C2×D4⋊#1055C2semidirect
5. C2×#11718075C2semidirect
6. C2×#11718046C2semidirect
7. C13×#1954C2semidirect
42. C2×#6104C8semidirect
126. #1954D13semidirect
178. #1055C22⋊C8semidirect
327. C13#9659semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#61042
#131156302
C2×#117180722
C2×D4⋊#10552
C2×#117180752
C2×#117180462
C13×#19542
#965913