Finite Group Databasebeta

← #15764184

Subgroups — #15764184

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718739C211yesmaximal, characteristic, complemented
2C2×#11718748C211yesmaximal, characteristic
3#13119785C211yesmaximal, characteristic
4C2×#11718074C211yesmaximal, characteristic, complemented
5C2×#11718075C211yesmaximal, characteristic
6#13112677C211yesmaximal, characteristic, complemented
7C13×#1981C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88151—22no—
10C2×C4×D52C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×#103—22no—
14C4×C13×C4⋊C4C2211yescharacteristic
15#11718748—22no—
16#11718748—22no—
17#11718739—22no—
18#11718739—22no—
19C2×#88049—21no—
20C2×#88047—22no—
21C2×#88047—21no—
22#11718600—21no—
23#11718596—21no—
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4×#1055C2211yescharacteristic
26#11718338—22no—
27#11718075—22no—
28#11718074—22no—
29C22×Q8×C13—21no—
30C22×D52D411yescharacteristic
31C22×C4×D13—21no—
32C22×Dic26—21no—
33C22×C8×C13—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8D412yes—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4D412yes—
41C2×C42×C13—21no—
42C2×C42×C13C2311yescharacteristic
43C2×#6103—24no—
44C2×#6103—21no—
45C2×C4⋊Dic13—24no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13D412yes—
48C2×C4⋊Dic13D411yescharacteristic
49C22×#1055—21no—
50C22×#1055—21no—
51#88151—44no—
52#88151—44no—
53C4×D52—21no—
54C4×D52—21no—
55C4×D52—21no—
56C4×D52—21no—
57#88123—21no—
58#88123—21no—
59#88123—21no—
60#88123—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8—21no—
63C13×#103—44no—
64C13×#95—21no—
65#88049—24no—
66#88047—28no—
67#88047—24no—
68C4⋊#1055—21no—
69C4⋊#1055D412yes—
70C4×#1055—21no—
71C4×#1055D412yes—
72#10076—131nomaximal, Sylow
73C23×D13—21no—
74C2×Q8×C13—22no—
75C2×Q8×C13—41no—
76C2×Q8×C13—42no—
77C2×Q8×C13—42no—
78C22×C4×C13—22no—
79C22×C4×C13—41no—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×Dic13—21no—
84C22×Dic13—22no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×D52Q1612yes—
91C2×C4×D13—41no—
92C2×C4×D13—41no—
93C2×C4×D13—42no—
94C2×C4×D13—42no—
95C2×Dic26—41no—
96C2×Dic26—41no—
97C2×Dic26—42no—
98C2×Dic26—42no—
99C2×C8×C13—41no—
100C2×C8×C13—42no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4D814yes—
107C42×C13—41no—
108C42×C13—41no—
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111C42×C13C2×D411yescharacteristic
112C42×C13#4111yescharacteristic
113#6103—48no—
114#6103—41no—
115#6103—41no—
116C4⋊Dic13—22no—
117C4⋊Dic13—21no—
118C4⋊Dic13—22no—
119C4⋊Dic13—21no—
120C4⋊Dic13—48no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123C2×#1055—24no—
124C2×#1055—22no—
125C2×#1055—22no—
126C2×#1055—41no—
127C2×#1055—41no—
128C2×#500—131no—
129C2×#474—131no—
130#2542—131no—
131#1981D1311yescharacteristic, complemented
132C2×#332—131no—
133C2×D4⋊C8—131no—
134#1279—131no—
135C23×C13#12011yescharacteristic
136C22×D13—22no—
137C22×D13—41no—
138C22×D13—42no—
139C22×D13—41no—
140C22×D13—42no—
141Q8×C13—44no—
142Q8×C13—81no—
143Q8×C13—81no—
144C2×C4×C13—22no—
145C2×C4×C13—24no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—42no—
149C2×C4×C13—82no—
150C2×C4×C13#12011yescharacteristic
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13#12711yescharacteristic
156C2×C4×C13C2×D812yes—
157C2×C4×C13C2×Q1611yescharacteristic
158C2×C4×C13#13511yescharacteristic
159C2×C4×C13AGL(1,ℤ/8)12yes—
160C2×C4×C13#13711yescharacteristic
161C2×C4×C13#13711yescharacteristic
162C2×Dic13—42no—
163C2×Dic13—41no—
164C2×Dic13—42no—
165C2×Dic13—44no—
166D52—22no—
167D52—22no—
168D52—41no—
169D52—41no—
170C4×D13—82no—
171C4×D13—81no—
172C4×D13—81no—
173Dic26—82no—
174Dic26—81no—
175Dic26—81no—
176C8×C13—81no—
177#1055—24no—
178#1055—42no—
179C2×C4⋊Q8—131no—
180C2×C4⋊Q8C2×D1311yescharacteristic
181C2×C22⋊Q8—262no—
182C2×C4×D4—131no—
183#500—262no—
184#500—262no—
185#474—262no—
186#474—262no—
187C2×#107—262no—
188C2×#107—261no—
189C2×C4⋊C8—131no—
190C2×C4⋊C8C2×D1311yescharacteristic
191C2×#103—22no—
192C2×#102—261no—
193C2×C4×C8—131no—
194#399—262no—
195#390—261no—
196#384—261no—
197C4×C4⋊C4C2×D1311yescharacteristic
198#332—262no—
199D4⋊C8—262no—
200C22×C13#39211yescharacteristic
201C22×C13#44712yes—
202C22×C13#45111yescharacteristic
203C22×C13#45211yescharacteristic
204C22×C13#45612yes—
205C2×D13—44no—
206C2×D13—42no—
207C2×D13—82no—
208C2×D13—81no—
209C2×D13—81no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—44no—
213C4×C13—82no—
214C4×C13#45111yescharacteristic
215C4×C13#45211yescharacteristic
216C4×C13#45912yes—
217C4×C13#46711yescharacteristic
218C4×C13#47011yescharacteristic
219C4×C13#49311yescharacteristic
220C4×C13#49611yescharacteristic
221Dic13—82no—
222Dic13—81no—
223C22×Q8—21no—
224C22×Q8—261no—
225C22×D4—131no—
226C23×C4—261no—
227C22×C8—21no—
228C22×C8—261no—
229C22×C8—261no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—261no—
234C4⋊Q8—261no—
235C4⋊Q8—261no—
236C4⋊Q8—261no—
237C4⋊Q8D5212yes—
238C22⋊Q8—524no—
239C22⋊Q8—524no—
240C4×D4—261no—
241C4×D4—261no—
242C4×D4—261no—
243C4×D4—261no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—131no—
247C2×C4⋊C4—132no—
248C2×C4⋊C4—264no—
249C2×C4⋊C4—261no—
250C2×C4⋊C4C22⋊D1312yes—
251C2×C22⋊C4—264no—
252C2×C22⋊C4—261no—
253C2×C42—21no—
254C2×C42C22×D1311yescharacteristic
255#107—264no—
256#107—268no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—132no—
260C4⋊C8—261no—
261#103—44no—
262#102—264no—
263C4×C8—132no—
264C4×C8—261no—
265#95—21no—
266C2×C13#164712yes—
267C2×C13#164912yes—
268C2×C13#200111yescharacteristic
269C2×C13#200511yescharacteristic
270C2×C13#201111yescharacteristic
271D13—82no—
272C24—261no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—521no—
278C2×Q8—522no—
279C2×Q8—521no—
280C2×Q8—522no—
281C2×D4—132no—
282C2×D4—261no—
283C2×D4—261no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—262no—
290C22×C4—261no—
291C22×C4—521no—
292C22×C4—522no—
293C22×C4—521no—
294C22×C4—522no—
295C22×C4D4×D1311yescharacteristic
296C22×C4D4×D1311yescharacteristic
297C22×C4C2×C22⋊D1311yescharacteristic
298C2×C8—42no—
299C2×C8—41no—
300C2×C8—264no—
301C2×C8—262no—
302C2×C8—262no—
303C2×C8—521no—
304C2×C8—521no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—261no—
311C4⋊C4—262no—
312C4⋊C4—261no—
313C4⋊C4—262no—
314C4⋊C4—528no—
315C4⋊C4—521no—
316C4⋊C4—521no—
317C4⋊C4#610414yes—
318C22⋊C4—528no—
319C22⋊C4—521no—
320C22⋊C4—521no—
321C42—41no—
322C42—41no—
323C42C2×D5211yescharacteristic
324C42#612711yescharacteristic
325C42D4×D1311yescharacteristic
326C42D4×D1311yescharacteristic
327C13#1007611yescharacteristic, complemented, Sylow
328C23—262no—
329C23—522no—
330C23—521no—
331C23—522no—
332C23—521no—
333C23#8819111yescharacteristic
334Q8—44no—
335Q8—81no—
336Q8—81no—
337Q8—1042no—
338Q8—1041no—
339Q8—1041no—
340D4—262no—
341D4—262no—
342D4—521no—
343D4—521no—
344C2×C4—22no—
345C2×C4—24no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—82no—
350C2×C4—524no—
351C2×C4—522no—
352C2×C4—521no—
353C2×C4—522no—
354C2×C4—1042no—
355C2×C4—1041no—
356C2×C4—1041no—
357C2×C4#8813611yescharacteristic
358C2×C4#8813611yescharacteristic
359C2×C4#8813811yescharacteristic
360C2×C4#8813811yescharacteristic
361C2×C4#8816911yescharacteristic
362C2×C4#8817011yescharacteristic
363C2×C4Q16×D1311yescharacteristic
364C2×C4#8817211yescharacteristic
365C2×C4#8818411yescharacteristic
366C2×C4C2×#610412yes—
367C2×C4#8819411yescharacteristic
368C2×C4#8820312yes—
369C8—81no—
370C8—264no—
371C8—522no—
372C22—522no—
373C22—524no—
374C22—1041no—
375C22—1042no—
376C22—1041no—
377C22#1171862111yescharacteristic
378C22#1171869712yes—
379C22#1171883411yescharacteristic
380C22#1171884711yescharacteristic
381C22#1171886612yes—
382C4—21no—
383C4—21no—
384C4—44no—
385C4—82no—
386C4—1041no—
387C4—1042no—
388C4#1171846911yescharacteristic
389C4#1171847111yescharacteristic
390C4#1171847411yescharacteristic
391C4#1171847711yescharacteristic
392C4#1171867612yes—
393C4#1171871911yescharacteristic
394C4#1171873411yescharacteristic
395C2—1042no—
396C2#1311406912yes—
397C2#1311408312yes—
398C2#1311584511yescharacteristic
399C2#1311587311yescharacteristic
400C2#1311590611yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1981C2
socleC23×C13#120
prime radicalC22×D52D4
hypercenter#1981D13
hypocenterC13#10076
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
1. C2×#11718739C2semidirect
4. C2×#11718074C2semidirect
6. #13112677C2semidirect
7. C13×#1981C2semidirect
131. #1981D13semidirect
327. C13#10076semidirect

Maximal subgroups

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

subgroupindex
C2×#117187392
C2×#117187482
#131197852
C2×#117180742
C2×#117180752
#131126772
C13×#19812
#1007613