Finite Group Databasebeta

← #15766767

Subgroups — #15766767

Order 3328.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718503C211yesmaximal, characteristic
2#13115797C211yesmaximal, characteristic, complemented
3#13115630C211yesmaximal, characteristic
4#13114837C211yesmaximal, characteristic
5C2×#11718073C211yesmaximal, characteristic, complemented
6#13112720C211yesmaximal, characteristic, complemented
7C2×C13×#334C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C13C2211yescharacteristic
13C2×#88061—21no—
14C2×#88061—21no—
15C2×#88060—21no—
16C2×#88060—21no—
17C2×#88057—21no—
18#11718596C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20#11718503—22no—
21#11718503—22no—
22C13×#334—22no—
23#11718143—21no—
24#11718143—21no—
25#11718143—21no—
26#11718073—22no—
27C22×D52D411yescharacteristic
28C22×C4×D13—21no—
29C22×Dic26—21no—
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×#6103—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C22×#1055—21no—
43C4×D52—21no—
44C4×D52—21no—
45C4×D52—21no—
46C4×D52—21no—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50#88123D412yes—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8D412yes—
55C4×C8×C13—21no—
56C4×C8×C13—21no—
57#88061—24no—
58#88061—42no—
59#88060—42no—
60#88060—42no—
61#88057—24no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64#10480—131nomaximal, Sylow
65C23×D13—21no—
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13#4111yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—41no—
71C22×Dic13—41no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52SD1612yes—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×Dic26—22no—
85C2×Dic26—41no—
86C2×Dic26—81no—
87C2×Dic26—81no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—22no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13—41no—
97C2×C8×C13—41no—
98C2×C8×C13—41no—
99C2×C8×C13SD1612yes—
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13#4111yescharacteristic
103C42×C13#4111yescharacteristic
104#6103—41no—
105#6103—41no—
106C4⋊Dic13—22no—
107C4⋊Dic13—21no—
108C4⋊Dic13—22no—
109C4⋊Dic13—21no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4⋊Dic13—41no—
113C4⋊Dic13—41no—
114C4⋊Dic13—41no—
115C4⋊Dic13—41no—
116C4⋊Dic13—81no—
117C2×#1055—41no—
118C2×#1055—41no—
119C2×#1055—41no—
120C2×#476—131no—
121#1990—131no—
122#1954—131no—
123#1802—131no—
124C2×#334D1311yescharacteristic, complemented
125C2×#333—131no—
126#1296—131no—
127C23×C13#12111yescharacteristic
128C22×D13—22no—
129C22×D13—41no—
130C22×D13—41no—
131C22×D13—41no—
132C22×D13—41no—
133C22×D13—41no—
134C22×D13—41no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12311yescharacteristic
141C2×C4×C13#12311yescharacteristic
142C2×C4×C13#12411yescharacteristic
143C2×C4×C13C2×SD1611yescharacteristic
144C2×C4×C13C2×SD1611yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×C4×C13#13511yescharacteristic
147C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C13#13711yescharacteristic
149C2×C4×C13#13711yescharacteristic
150C2×C4×C13#13711yescharacteristic
151C2×Dic13—42no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—81no—
156C2×Dic13—81no—
157C2×Dic13—81no—
158C2×Dic13—81no—
159C2×Dic13—81no—
160D52—22no—
161D52—22no—
162D52—41no—
163D52—41no—
164C4×D13—81no—
165C4×D13—81no—
166C4×D13—81no—
167C4×D13—81no—
168Dic26—82no—
169Dic26—82no—
170C8×C13—22no—
171C8×C13—42no—
172C8×C13—41no—
173C8×C13—81no—
174#1055—81no—
175C2×C4⋊Q8—131no—
176C2×C4×D4—131no—
177#476—262no—
178#476—262no—
179C2×#106—261no—
180C2×C4⋊C8—131no—
181C2×C4⋊C8C2×D1311yescharacteristic
182C2×C4⋊C8C2×D1311yescharacteristic
183C2×#102—261no—
184C2×#102—261no—
185C2×C22⋊C8—261no—
186C2×C22⋊C8—261no—
187C2×C4×C8C2×D1311yescharacteristic
188#384—131no—
189#340—261no—
190#340—261no—
191#340—261no—
192#334—22no—
193#333—262no—
194C22×C13#39411yescharacteristic
195C22×C13#46111yescharacteristic
196C22×C13#46311yescharacteristic
197C22×C13#46511yescharacteristic
198C22×C13#47011yescharacteristic
199C22×C13#47111yescharacteristic
200C22×C13#47211yescharacteristic
201C2×D13—42no—
202C2×D13—42no—
203C2×D13—42no—
204C2×D13—81no—
205C2×D13—81no—
206C2×D13—81no—
207C2×D13—81no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13#44811yescharacteristic
211C4×C13#45211yescharacteristic
212C4×C13#46011yescharacteristic
213C4×C13#46411yescharacteristic
214C4×C13#46511yescharacteristic
215C4×C13#46811yescharacteristic
216C4×C13#48311yescharacteristic
217C4×C13#48511yescharacteristic
218Dic13—82no—
219Dic13—81no—
220Dic13—161no—
221C22×Q8—261no—
222C22×D4—131no—
223C23×C4—261no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—261no—
227C22×C8D5211yescharacteristic
228C22×C8D5211yescharacteristic
229C4⋊Q8—132no—
230C4⋊Q8—261no—
231C4⋊Q8—261no—
232C4⋊Q8—261no—
233C4×D4—261no—
234C4×D4—261no—
235C4×D4—261no—
236C4×D4—261no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—261no—
239C2×C4⋊C4—261no—
240C2×C4⋊C4—261no—
241C2×C4⋊C4—261no—
242C2×C4⋊C4—261no—
243C2×C22⋊C4—261no—
244C2×C42C22×D1311yescharacteristic
245#106—264no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—261no—
250C4⋊C8—261no—
251C4⋊C8C22⋊D1312yes—
252#102—264no—
253#102—522no—
254C22⋊C8—522no—
255C22⋊C8—522no—
256C4×C8—21no—
257C4×C8—21no—
258C2×C13#167111yescharacteristic
259C2×C13#167711yescharacteristic
260C2×C13#169511yescharacteristic
261C2×C13#170311yescharacteristic
262C2×C13#203511yescharacteristic
263C2×C13#205111yescharacteristic
264C2×C13#205511yescharacteristic
265D13—82no—
266C24—261no—
267C2×Q8—262no—
268C2×Q8—521no—
269C2×Q8—1041no—
270C2×Q8—1041no—
271C2×D4—132no—
272C2×D4—261no—
273C2×D4—261no—
274C2×D4—261no—
275C2×D4—261no—
276C2×D4—261no—
277C22×C4—261no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4—521no—
281C22×C4—521no—
282C22×C4—521no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4C2×D5211yescharacteristic
287C22×C4D4×D1311yescharacteristic
288C22×C4#613111yescharacteristic
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—521no—
301C2×C8—521no—
302C2×C8—521no—
303C2×C8#609512yes—
304C4⋊C4—261no—
305C4⋊C4—262no—
306C4⋊C4—262no—
307C4⋊C4—261no—
308C4⋊C4—521no—
309C4⋊C4—521no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C4⋊C4—521no—
313C4⋊C4—521no—
314C4⋊C4—1041no—
315C22⋊C4—521no—
316C22⋊C4—521no—
317C42#612711yescharacteristic
318C42D4×D1311yescharacteristic
319C42#613111yescharacteristic
320C42C2×C22⋊D1311yescharacteristic
321C13#1048011yescharacteristic, complemented, Sylow
322C23—262no—
323C23—521no—
324C23—521no—
325C23—521no—
326C23—521no—
327C23—521no—
328C23—521no—
329C23#8814911yescharacteristic
330Q8—1042no—
331Q8—1042no—
332D4—262no—
333D4—262no—
334D4—521no—
335D4—521no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—521no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—522no—
342C2×C4—1041no—
343C2×C4—1041no—
344C2×C4—1041no—
345C2×C4—1041no—
346C2×C4—1041no—
347C2×C4—1041no—
348C2×C4—1041no—
349C2×C4—1041no—
350C2×C4—1041no—
351C2×C4#8814811yescharacteristic
352C2×C4#8814811yescharacteristic
353C2×C4#8814911yescharacteristic
354C2×C4C2×#609511yescharacteristic
355C2×C4#8815811yescharacteristic
356C2×C4#8816211yescharacteristic
357C2×C4#8816311yescharacteristic
358C2×C4SD16×D1311yescharacteristic
359C2×C4#8816911yescharacteristic
360C2×C4#8816911yescharacteristic
361C2×C4#8817011yescharacteristic
362C2×C4#8818411yescharacteristic
363C2×C4#8819111yescharacteristic
364C2×C4#8820111yescharacteristic
365C8—22no—
366C8—41no—
367C8—42no—
368C8—81no—
369C8—1041no—
370C22—522no—
371C22—522no—
372C22—522no—
373C22—1041no—
374C22—1041no—
375C22—1041no—
376C22—1041no—
377C22#1171850211yescharacteristic
378C22#1171850511yescharacteristic
379C22#1171852511yescharacteristic
380C22#1171852911yescharacteristic
381C22#1171855811yescharacteristic
382C22#1171855911yescharacteristic
383C22#1171865211yescharacteristic
384C4—21no—
385C4—21no—
386C4—1042no—
387C4—1041no—
388C4—2081no—
389C4#1171850611yescharacteristic
390C4#1171850911yescharacteristic
391C4#1171852311yescharacteristic
392C4#1171852811yescharacteristic
393C4#1171877511yescharacteristic
394C4#1171879511yescharacteristic
395C4#1171883111yescharacteristic
396C4#1171883411yescharacteristic
397C2—1042no—
398C2#1311421211yescharacteristic
399C2#1311424611yescharacteristic
400C2#1311436011yescharacteristic
401C2#1311441211yescharacteristic
402C2#1311603411yescharacteristic
403C2#1311613011yescharacteristic
404C2#1311615411yescharacteristic
subgroupG/H
centerC23#88149
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#334C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#334D13
hypocenterC13#10480
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #13115797C2semidirect
5. C2×#11718073C2semidirect
6. #13112720C2semidirect
7. C2×C13×#334C2semidirect
124. C2×#334D13semidirect
321. C13#10480semidirect

Maximal subgroups

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

subgroupindex
C2×#117185032
#131157972
#131156302
#131148372
C2×#117180732
#131127202
C2×C13×#3342
#1048013