Finite Group Databasebeta

← #15765514

Subgroups — #15765514

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718753C211yesmaximal, characteristic, complemented
2C2×#11718507C211yesmaximal, characteristic
3C2×#11718748C211yesmaximal, characteristic
4#13115629C211yesmaximal, characteristic
5C2×#11718074C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C2×C13×#332C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C22×#6107—22no—
10C2×C4×D52C2211yescharacteristic
11C2×#88123C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×#88061—21no—
15C2×#88060—22no—
16C2×#88058—21no—
17#11718753—22no—
18#11718753—22no—
19#11718748—22no—
20#11718748—22no—
21C2×#88049—21no—
22C2×#88047—21no—
23C2×C4⋊#1055C2211yescharacteristic
24C2×C4×#1055C2211yescharacteristic
25#11718507—22no—
26#11718507—22no—
27C13×#332—22no—
28#11718074—22no—
29C22×Q8×C13—21no—
30C22×D52D411yescharacteristic
31C22×C4×D13—21no—
32C22×Dic26—21no—
33C22×C8×C13—21no—
34C22×C8×C13—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8D412yes—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C42×C13C2311yescharacteristic
42C2×#6107—28no—
43C2×#6107—44no—
44C2×#6107—44no—
45C2×#6103—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13D411yescharacteristic
49C22×#1055—21no—
50C22×#1055D412yes—
51C4×D52—21no—
52C4×D52—21no—
53C4×D52—21no—
54C4×D52—21no—
55#88123—21no—
56#88123—21no—
57#88123—21no—
58#88123D412yes—
59C13×C4⋊C8—21no—
60C13×C4⋊C8—21no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8D412yes—
63#88061—24no—
64#88060—44no—
65#88058—24no—
66#88049—24no—
67#88047—24no—
68C4⋊#1055—21no—
69C4⋊#1055D412yes—
70C4×#1055—21no—
71C4×#1055—21no—
72#10274—131nomaximal, Sylow
73C23×D13—21no—
74C2×Q8×C13—22no—
75C2×Q8×C13—41no—
76C2×Q8×C13—42no—
77C2×Q8×C13—42no—
78C22×C4×C13—41no—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×Dic13—21no—
83C22×Dic13—41no—
84C2×D52—21no—
85C2×D52—21no—
86C2×D52—21no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52Q1612yescomplemented
90C2×C4×D13—41no—
91C2×C4×D13—41no—
92C2×C4×D13—42no—
93C2×C4×D13—42no—
94C2×Dic26—22no—
95C2×Dic26—42no—
96C2×Dic26—42no—
97C2×Dic26—41no—
98C2×C8×C13—22no—
99C2×C8×C13—41no—
100C2×C8×C13—41no—
101C2×C8×C13—41no—
102C2×C8×C13—42no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C42×C13C2×D411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13C2×D411yescharacteristic
111#6107—416no—
112#6103—41no—
113#6103—41no—
114C4⋊Dic13—22no—
115C4⋊Dic13—21no—
116C4⋊Dic13—21no—
117C4⋊Dic13—22no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120C2×#1055—22no—
121C2×#1055—22no—
122C2×#1055—22no—
123C2×#1055—41no—
124C2×#1055—41no—
125C2×#1055D814yes—
126C2×#494—131no—
127C2×#474—131no—
128C2×#474—131no—
129#1954—131no—
130C2×#332—131no—
131C2×#332D1311yescharacteristic, complemented
132#1277—131no—
133C23×C13#12111yescharacteristic
134C22×D13—22no—
135C22×D13—41no—
136C22×D13—42no—
137C22×D13—41no—
138C22×D13—42no—
139Q8×C13—44no—
140Q8×C13—81no—
141Q8×C13—81no—
142C2×C4×C13—22no—
143C2×C4×C13—42no—
144C2×C4×C13—82no—
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13#12011yescharacteristic
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12711yescharacteristic
151C2×C4×C13C2×D812yes—
152C2×C4×C13C2×Q1611yescharacteristic
153C2×C4×C13#13511yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)12yes—
155C2×C4×C13#13711yescharacteristic
156C2×C4×C13#13711yescharacteristic
157C2×Dic13—42no—
158C2×Dic13—41no—
159C2×Dic13—42no—
160C2×Dic13—82no—
161D52—22no—
162D52—22no—
163D52—41no—
164D52—41no—
165C4×D13—82no—
166C4×D13—81no—
167C4×D13—81no—
168Dic26—44no—
169Dic26—81no—
170Dic26—81no—
171C8×C13—42no—
172C8×C13—81no—
173#1055—24no—
174#1055—42no—
175C22×Q16—262no—
176C2×C4⋊Q8—131no—
177C2×C4⋊Q8C2×D1311yescharacteristic
178C2×C4×D4—131no—
179#494—262no—
180#494—262no—
181#474—262no—
182#474—262no—
183#474—262no—
184#474—262no—
185C2×#107—261no—
186C2×#107—261no—
187C2×C4⋊C8—131no—
188C2×C4⋊C8C2×D1311yescharacteristic
189C2×C4⋊C8C2×D1311yescharacteristic
190C2×#102—261no—
191C2×#102—261no—
192C2×C22⋊C8—262no—
193C2×C4×C8—131no—
194#332—22no—
195#332—262no—
196C22×C13#39211yescharacteristic
197C22×C13#45912yes—
198C22×C13#46711yescharacteristic
199C22×C13#47011yescharacteristic
200C22×C13#47312yes—
201C2×D13—44no—
202C2×D13—42no—
203C2×D13—82no—
204C2×D13—81no—
205C2×D13—81no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—82no—
209C4×C13#44712yes—
210C4×C13#45111yescharacteristic
211C4×C13#45111yescharacteristic
212C4×C13#45211yescharacteristic
213C4×C13#45211yescharacteristic
214C4×C13#49311yescharacteristic
215C4×C13#49611yescharacteristic
216Dic13—82no—
217Dic13—81no—
218C22×Q8—21no—
219C22×Q8—261no—
220C22×D4—131no—
221C23×C4—261no—
222C2×Q16—268no—
223C2×Q16—524no—
224C2×Q16—524no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—132no—
228C22×C8—261no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—132no—
233C4⋊Q8—261no—
234C4⋊Q8—261no—
235C4⋊Q8—261no—
236C4⋊Q8D5212yes—
237C4×D4—261no—
238C4×D4—261no—
239C4×D4—261no—
240C4×D4—261no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—131no—
244C2×C4⋊C4—261no—
245C2×C4⋊C4—261no—
246C2×C22⋊C4—261no—
247C2×C42C22×D1311yescharacteristic
248#107—264no—
249#107—264no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—132no—
254C4⋊C8—261no—
255C4⋊C8C22⋊D1312yes—
256#102—264no—
257#102—264no—
258C22⋊C8—524no—
259C4×C8—261no—
260C4×C8—261no—
261C2×C13#166912yes—
262C2×C13#168912yes—
263C2×C13#200111yescharacteristic
264C2×C13#201111yescharacteristic
265C2×C13#202011yescharacteristic
266D13—82no—
267C24—261no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—262no—
273C2×Q8—521no—
274C2×Q8—522no—
275C2×Q8—522no—
276C2×D4—132no—
277C2×D4—261no—
278C2×D4—261no—
279C2×D4—261no—
280C2×D4—261no—
281C2×D4—261no—
282C22×C4—41no—
283C22×C4—261no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4—522no—
287C22×C4—522no—
288C22×C4—521no—
289C22×C4#612711yescharacteristic
290C22×C4D4×D1311yescharacteristic
291C22×C4D4×D1311yescharacteristic
292Q16—5216no—
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—42no—
297C2×C8—41no—
298C2×C8—134no—
299C2×C8—262no—
300C2×C8—262no—
301C2×C8—262no—
302C2×C8—521no—
303C2×C8—521no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—261no—
309C4⋊C4—262no—
310C4⋊C4—262no—
311C4⋊C4—261no—
312C4⋊C4—521no—
313C4⋊C4—521no—
314C22⋊C4—521no—
315C22⋊C4—521no—
316C42C2×D5211yescharacteristic
317C42D4×D1311yescharacteristic
318C42D4×D1311yescharacteristic
319C42C2×C22⋊D1311yescharacteristic
320C13#1027411yescharacteristic, complemented, Sylow
321C23—262no—
322C23—522no—
323C23—522no—
324C23—521no—
325C23—521no—
326C23#8813811yescharacteristic
327Q8—44no—
328Q8—81no—
329Q8—81no—
330Q8—524no—
331Q8—1041no—
332Q8—1041no—
333D4—262no—
334D4—262no—
335D4—521no—
336D4—521no—
337C2×C4—22no—
338C2×C4—42no—
339C2×C4—82no—
340C2×C4—522no—
341C2×C4—521no—
342C2×C4—522no—
343C2×C4—1042no—
344C2×C4—1042no—
345C2×C4—1041no—
346C2×C4—1041no—
347C2×C4#8813611yescharacteristic
348C2×C4#8813611yescharacteristic
349C2×C4#8813811yescharacteristic
350C2×C4D8×D1312yes—
351C2×C4#8816812yes—
352C2×C4#8816911yescharacteristic
353C2×C4#8817011yescharacteristic
354C2×C4Q16×D1311yescharacteristic
355C2×C4#8817211yescharacteristic
356C2×C4#8818411yescharacteristic
357C2×C4#8819111yescharacteristic
358C2×C4#8819411yescharacteristic
359C8—42no—
360C8—81no—
361C8—264no—
362C8—522no—
363C22—524no—
364C22—522no—
365C22—1041no—
366C22—1041no—
367C22—1042no—
368C22#1171841612yes—
369C22#1171844712yes—
370C22#1171847411yescharacteristic
371C22#1171847711yescharacteristic
372C22#1171862111yescharacteristic
373C4—21no—
374C4—21no—
375C4—82no—
376C4—1041no—
377C4—1042no—
378C4#1171843412yes—
379C4#1171846911yescharacteristic
380C4#1171847111yescharacteristic
381C4#1171881211yescharacteristic
382C4#1171883411yescharacteristic
383C4#1171883711yescharacteristic
384C4#1171884711yescharacteristic
385C2—1042no—
386C2#1311420012yes—
387C2#1311432412yes—
388C2#1311584511yescharacteristic
389C2#1311590811yescharacteristic
390C2#1311595611yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socleC23×C13#121
prime radicalC22×D52D4
hypercenterC2×#332D13
hypocenterC13#10274
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#11718753C2semidirect
5. C2×#11718074C2semidirect
6. #13112670C2semidirect
7. C2×C13×#332C2semidirect
89. C2×D52Q16semidirect
131. C2×#332D13semidirect
320. C13#10274semidirect

Maximal subgroups

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

subgroupindex
C2×#117187532
C2×#117185072
C2×#117187482
#131156292
C2×#117180742
#131126702
C2×C13×#3322
#1027413