Finite Group Databasebeta

← #15765485

Subgroups — #15765485

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic
2C2×#11718744C211yesmaximal, characteristic
3#13115630C211yesmaximal, characteristic
4C2×#11718139C211yesmaximal, characteristic, complemented
5C2×#11718139C211yesmaximal, characteristic, complemented
6#13112671C211yesmaximal, characteristic, complemented
7C2×C13×#487C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C22×#6106—21no—
11C2×C4×D52C2211yescharacteristic
12C13×#487—22no—
13C13×#487—22no—
14C2×C13×#103—22no—
15C2×C4×C8×C13C2211yescharacteristic
16C2×#88075—21no—
17C2×#88060—22no—
18#11718748—22no—
19#11718748—22no—
20#11718744—22no—
21#11718744—22no—
22C2×#88049—21no—
23C2×#88047—21no—
24C2×C4⋊#1055C2211yescharacteristic
25C2×C4⋊#1055C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718139—22no—
28#11718139—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×D52D411yescharacteristic
32C22×C4×D13—21no—
33C22×C8×C13D412yes—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8D412yes—
41C13×C4⋊Q8D412yes—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6106—24no—
48C2×#6106—42no—
49C2×#6106—42no—
50C2×#6103—21no—
51C2×C4⋊Dic13D411yescharacteristic
52C22×#1055—21no—
53C22×#1055—21no—
54C22×#1055—21no—
55C4×D52—21no—
56C4×D52—21no—
57C4×D52—21no—
58C4×D52—21no—
59C13×#103—28no—
60C4×C8×C13—21no—
61C4×C8×C13—21no—
62#88075—24no—
63#88060—44no—
64#88049—24no—
65#88047—24no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055—21no—
70C4⋊#1055D412yes—
71C4⋊#1055D412yes—
72#10270—131nomaximal, Sylow
73C23×D13—21no—
74C2×Q8×C13—22no—
75C2×Q8×C13—22no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C2×Q8×C13—41no—
79C2×Q8×C13—42no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—42no—
83C2×Q8×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13#4111yescharacteristic
89C22×Dic13—21no—
90C2×D52—21no—
91C2×D52—21no—
92C2×D52—21no—
93C2×D52—21no—
94C2×D52—21no—
95C2×D52SD1612yes—
96C2×C4×D13—41no—
97C2×C4×D13—41no—
98C2×C4×D13—42no—
99C2×C4×D13—42no—
100C2×C8×C13—22no—
101C2×C8×C13—22no—
102C2×C8×C13—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—22no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—41no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C42×C13C2×D411yescharacteristic
112C42×C13C2×D411yescharacteristic
113C42×C13C2×D411yescharacteristic
114C42×C13C2×D411yescharacteristic
115#6106—48no—
116#6103—41no—
117#6103—41no—
118C4⋊Dic13—21no—
119C4⋊Dic13—21no—
120C2×#1055—22no—
121C2×#1055—22no—
122C2×#1055—41no—
123C2×#1055—41no—
124C2×#1055—41no—
125C2×#1055—41no—
126C2×#1055—41no—
127C2×#1055—42no—
128C2×#487D1311yescharacteristic, complemented
129C2×#474—131no—
130C2×#461—131no—
131#1954—131no—
132C2×#332—131no—
133C2×#332—131no—
134#1277—131no—
135C23×C13#12111yescharacteristic
136C22×D13—22no—
137C22×D13—41no—
138C22×D13—42no—
139C22×D13—41no—
140C22×D13—42no—
141Q8×C13—44no—
142Q8×C13—42no—
143Q8×C13—42no—
144Q8×C13—81no—
145Q8×C13—81no—
146Q8×C13—81no—
147Q8×C13—81no—
148C2×C4×C13—22no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—82no—
152C2×C4×C13—81no—
153C2×C4×C13—81no—
154C2×C4×C13#12011yescharacteristic
155C2×C4×C13#12011yescharacteristic
156C2×C4×C13#12011yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13#12711yescharacteristic
160C2×C4×C13C2×SD1611yescharacteristic
161C2×C4×C13#13511yescharacteristic
162C2×C4×C13#13512yes—
163C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C13AGL(1,ℤ/8)12yes—
165C2×C4×C13#13711yescharacteristic
166C2×Dic13—41no—
167C2×Dic13—42no—
168D52—22no—
169D52—22no—
170D52—41no—
171D52—41no—
172C4×D13—82no—
173C4×D13—81no—
174C4×D13—81no—
175C8×C13—42no—
176#1055—42no—
177#1055—42no—
178#1055—81no—
179C22×SD16—261no—
180C2×C4⋊Q8C2×D1311yescharacteristic
181C2×C4⋊Q8C2×D1311yescharacteristic
182C2×C4×D4—131no—
183#487—22no—
184#487—22no—
185#474—262no—
186#474—262no—
187#461—262no—
188#461—262no—
189C2×#107—261no—
190C2×C4⋊C8—131no—
191C2×C4⋊C8—131no—
192C2×C4⋊C8—131no—
193C2×#103—22no—
194C2×#103—261no—
195C2×#102—261no—
196C2×C22⋊C8—262no—
197C2×C4×C8C2×D1311yescharacteristic
198#332—262no—
199#332—262no—
200C22×C13#39211yescharacteristic
201C22×C13#46312yes—
202C22×C13#46511yescharacteristic
203C22×C13#46811yescharacteristic
204C22×C13#47312yes—
205C2×D13—44no—
206C2×D13—42no—
207C2×D13—82no—
208C2×D13—81no—
209C2×D13—81no—
210C4×C13—21no—
211C4×C13—21no—
212C4×C13—82no—
213C4×C13—82no—
214C4×C13#44811yescharacteristic
215C4×C13#44911yescharacteristic
216C4×C13#44912yes—
217C4×C13#45011yescharacteristic
218C4×C13#45211yescharacteristic
219C4×C13#49511yescharacteristic
220C4×C13#49611yescharacteristic
221Dic13—81no—
222C22×Q8—21no—
223C22×Q8—21no—
224C22×D4—131no—
225C23×C4—261no—
226C2×SD16—264no—
227C2×SD16—522no—
228C2×SD16—522no—
229C22×C8—261no—
230C22×C8—261no—
231C22×C8—261no—
232C22×C8C22⋊D1312yes—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—21no—
238C4⋊Q8—21no—
239C4⋊Q8C22⋊D1312yes—
240C4⋊Q8C22⋊D1312yes—
241C4×D4—261no—
242C4×D4—261no—
243C4×D4—261no—
244C4×D4—261no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—131no—
250C2×C22⋊C4—261no—
251C2×C42C22×D1311yescharacteristic
252#107—264no—
253C4⋊C8—132no—
254C4⋊C8—132no—
255C4⋊C8—261no—
256C4⋊C8—261no—
257C4⋊C8—261no—
258C4⋊C8—261no—
259#103—28no—
260#103—264no—
261#102—264no—
262C22⋊C8—524no—
263C4×C8—21no—
264C4×C8—21no—
265C2×C13#167912yes—
266C2×C13#169912yes—
267C2×C13#200011yescharacteristic
268C2×C13#201211yescharacteristic
269C2×C13#202011yescharacteristic
270D13—82no—
271C24—261no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×D4—132no—
283C2×D4—261no—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—261no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—261no—
291C22×C4—521no—
292C22×C4—522no—
293C22×C4—522no—
294C22×C4—521no—
295C22×C4D4×D1311yescharacteristic
296C22×C4#612911yescharacteristic
297C22×C4C2×C22⋊D1311yescharacteristic
298SD16—528no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—262no—
303C2×C8—262no—
304C2×C8—521no—
305C2×C8—521no—
306C2×C8—521no—
307C2×C8—521no—
308C2×C8—521no—
309C2×C8—522no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—261no—
319C4⋊C4—261no—
320C22⋊C4—521no—
321C22⋊C4—521no—
322C42D4×D1311yescharacteristic
323C42D4×D1311yescharacteristic
324C42C2×C22⋊D1311yescharacteristic
325C42C2×C22⋊D1311yescharacteristic
326C13#1027011yescharacteristic, complemented, Sylow
327C23—262no—
328C23—522no—
329C23—521no—
330C23—522no—
331C23—521no—
332C23#8819211yescharacteristic
333Q8—42no—
334Q8—42no—
335Q8—44no—
336Q8—81no—
337Q8—81no—
338Q8—81no—
339Q8—81no—
340D4—262no—
341D4—262no—
342D4—521no—
343D4—521no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—522no—
351C2×C4—521no—
352C2×C4—1041no—
353C2×C4—1041no—
354C2×C4—1042no—
355C2×C4SD16×D1311yescharacteristic
356C2×C4#8816811yescharacteristic
357C2×C4#8816911yescharacteristic
358C2×C4#8817011yescharacteristic
359C2×C4#8819111yescharacteristic
360C2×C4#8819111yescharacteristic
361C2×C4#8819311yescharacteristic
362C2×C4#8819311yescharacteristic
363C2×C4#8819411yescharacteristic
364C2×C4#8820312yes—
365C2×C4#8820412yes—
366C2×C4#8820711yescharacteristic
367C8—42no—
368C8—522no—
369C8—522no—
370C8—1041no—
371C22—524no—
372C22—522no—
373C22—1041no—
374C22—1042no—
375C22—1041no—
376C22#1171871812yes—
377C22#1171883211yescharacteristic
378C22#1171883511yescharacteristic
379C22#1171885312yes—
380C22#1171888411yescharacteristic
381C4—21no—
382C4—21no—
383C4—82no—
384C4—82no—
385C4—1041no—
386C4#1171871911yescharacteristic
387C4#1171872011yescharacteristic
388C4#1171883011yescharacteristic
389C4#1171883111yescharacteristic
390C4#1171883311yescharacteristic
391C4#1171883411yescharacteristic
392C4#1171889912yes—
393C2—1042no—
394C2#1311425612yes—
395C2#1311438012yes—
396C2#1311583611yescharacteristic
397C2#1311591311yescharacteristic
398C2#1311595511yescharacteristic
subgroupG/H
centerC23#88192
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#487C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#487D13
hypocenterC13#10270
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. C2×#11718139C2semidirect
5. C2×#11718139C2semidirect
6. #13112671C2semidirect
7. C2×C13×#487C2semidirect
128. C2×#487D13semidirect
326. C13#10270semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
C2×#117187442
#131156302
C2×#117181392
#131126712
C2×C13×#4872
#1027013