Finite Group Databasebeta

← #15765952

Subgroups — #15765952

Order 3328.

416 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120075C211yesmaximal, characteristic
2#13115784C211yesmaximal, characteristic
3#13115783C211yesmaximal, characteristic
4#13115638C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic
6#13112676C211yesmaximal, characteristic
7C13×#1279C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C13C2211yescharacteristic
11C4×C13×C4⋊C4C2211yescharacteristic
12C2×#88056—22no—
13#11718638—21no—
14#11718634—21no—
15#11718597—21no—
16#11718596C2211yescharacteristic
17C4×C4⋊Dic13C2211yescharacteristic
18#11718589—21no—
19C2×C4⋊#1055C2211yescharacteristic
20#11718321—22no—
21#11718143—21no—
22#11718143—21no—
23#11718121—21no—
24#11718121—21no—
25C22×Dic26—21no—
26C22×C8×C13—21no—
27C22×C8×C13—21no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C42×C13—21no—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D412yes—
39C2×#6101—22no—
40C2×C4×Dic13—21no—
41C22×#1055—21no—
42#88123—21no—
43#88123—21no—
44#88123—21no—
45#88123Q812yes—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C4×C8×C13—21no—
49C4×C8×C13—21no—
50C13×#95—21no—
51#88071—22no—
52#88071—22no—
53#88071—22no—
54#88071—21no—
55#88056—44no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58#10352—131nomaximal, Sylow
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—22no—
67C22×Dic13—41no—
68C2×Dic26—22no—
69C2×Dic26—42no—
70C2×Dic26—42no—
71C2×Dic26—41no—
72C2×C8×C13—22no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C42×C13—41no—
83C42×C13—41no—
84C42×C13C2×Q811yescharacteristic
85C42×C13#4111yescharacteristic
86C42×C13#4111yescharacteristic
87C42×C13#4111yescharacteristic
88C4⋊Dic13—22no—
89C4⋊Dic13—22no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—42no—
101#6101—82no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107#2571—131no—
108#1987—131no—
109#1987—131no—
110#1956—131no—
111#1296—131no—
112#1279—131no—
113#1279D1311yescharacteristic
114C23×C13#12011yescharacteristic
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13C22⋊Q811yescharacteristic
124C2×C4×C13C22⋊Q811yescharacteristic
125C2×C4×C13C22⋊Q811yescharacteristic
126C2×C4×C13#12411yescharacteristic
127C2×C4×C13#12411yescharacteristic
128C2×C4×C13#12411yescharacteristic
129C2×C4×C13#13511yescharacteristic
130C2×C4×C13#13511yescharacteristic
131C2×C4×C13#13511yescharacteristic
132C2×C4×C13#13511yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×C4×C13#13711yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×Dic13—42no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—41no—
145C2×Dic13—42no—
146C2×Dic13—41no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149Dic26—44no—
150Dic26—82no—
151C8×C13—42no—
152C8×C13—81no—
153#1055—81no—
154C2×C4⋊Q8—131no—
155C2×C4⋊C8—131no—
156C2×C4⋊C8C2×D1311yescharacteristic
157C2×#103—262no—
158C2×C4×C8C2×D1311yescharacteristic
159#400—262no—
160#389—261no—
161#389—261no—
162#384—131no—
163#382—261no—
164#382—261no—
165C4×C4⋊C4—131no—
166C4×C4⋊C4C2×D1311yescharacteristic
167#340—261no—
168#340—261no—
169#340—261no—
170#340—261no—
171C22×C13#39311yescharacteristic
172C22×C13#45211yescharacteristic
173C22×C13#45211yescharacteristic
174C22×C13#45211yescharacteristic
175C22×C13#45211yescharacteristic
176C22×C13#45311yescharacteristic
177C22×C13#45411yescharacteristic
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13#47911yescharacteristic
183C4×C13#47911yescharacteristic
184C4×C13#47911yescharacteristic
185C4×C13#47911yescharacteristic
186C4×C13#48811yescharacteristic
187C4×C13#48811yescharacteristic
188C4×C13#49111yescharacteristic
189C4×C13#49111yescharacteristic
190Dic13—82no—
191Dic13—81no—
192Dic13—81no—
193Dic13—82no—
194C22×Q8—261no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—261no—
198C4⋊Q8—132no—
199C4⋊Q8—261no—
200C4⋊Q8—261no—
201C4⋊Q8—261no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—132no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—262no—
210C2×C4⋊C4D5211yescharacteristic
211C2×C4⋊C4D5211yescharacteristic
212C2×C42—21no—
213C2×C42—261no—
214C2×C42C22×D1311yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—261no—
218C4⋊C8—261no—
219#103—524no—
220C4×C8—21no—
221C4×C8—21no—
222#95—21no—
223#95—262no—
224#95—262no—
225#95—262no—
226#95—261no—
227C2×C13#163011yescharacteristic
228C2×C13#163411yescharacteristic
229C2×C13#163811yescharacteristic
230C2×C13#163811yescharacteristic
231C2×C13#202611yescharacteristic
232C2×C13#202611yescharacteristic
233C2×C13#202711yescharacteristic
234C2×Q8—262no—
235C2×Q8—522no—
236C2×Q8—522no—
237C2×Q8—521no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—262no—
243C22×C4—521no—
244C22×C4C2×D5211yescharacteristic
245C22×C4D4×D1311yescharacteristic
246C22×C4D4×D1311yescharacteristic
247C2×C8—22no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—521no—
254C2×C8—521no—
255C2×C8—521no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—262no—
261C4⋊C4—262no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—522no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C4⋊C4—1042no—
274C42—41no—
275C42—41no—
276C42—521no—
277C42—521no—
278C42#612711yescharacteristic
279C42#612711yescharacteristic
280C42#612911yescharacteristic
281C42Q8×D1311yescharacteristic
282C13#1035211yescharacteristic, complemented, Sylow
283C23#8813611yescharacteristic
284Q8—524no—
285Q8—1042no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—522no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—522no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4#8812911yescharacteristic
307C2×C4#8813911yescharacteristic
308C2×C4#8813911yescharacteristic
309C2×C4#8815011yescharacteristic
310C2×C4#8815011yescharacteristic
311C2×C4#8815111yescharacteristic
312C2×C4#8815811yescharacteristic
313C2×C4#8815811yescharacteristic
314C2×C4#8816311yescharacteristic
315C2×C4#8816311yescharacteristic
316C2×C4#8816611yescharacteristic
317C2×C4#8816911yescharacteristic
318C2×C4#8817011yescharacteristic
319C2×C4#8817211yescharacteristic
320C8—42no—
321C8—81no—
322C8—1041no—
323C22#1171833411yescharacteristic
324C22#1171839411yescharacteristic
325C22#1171839411yescharacteristic
326C22#1171844411yescharacteristic
327C22#1171847111yescharacteristic
328C22#1171848311yescharacteristic
329C22#1171848811yescharacteristic
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—1042no—
335C4—1042no—
336C4—1041no—
337C4—1041no—
338C4#1171835811yescharacteristic
339C4#1171836411yescharacteristic
340C4#1171842911yescharacteristic
341C4#1171845811yescharacteristic
342C4#1171849011yescharacteristic
343C4#1171849011yescharacteristic
344C4#1171851811yescharacteristic
345C4#1171853811yescharacteristic
346C2#1311395911yescharacteristic
347C2#1311398311yescharacteristic
348C2#1311401011yescharacteristic
349C2#1311401111yescharacteristic
350C2#1311598611yescharacteristic
351C2#1311598811yescharacteristic
352C2#1311599111yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socle, prime radicalC23×C13#120
hypercenter#1279D13
hypocenterC13#10352
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
282. C13#10352semidirect

Maximal subgroups

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

subgroupindex
#131200752
#131157842
#131157832
#131156382
#131127202
#131126762
C13×#12792
#1035213