Finite Group Databasebeta

← #15751069

Subgroups — #15751069

Order 3328.

408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117311C211yesmaximal, characteristic
2#13114978C211yesmaximal, characteristic
3#13114583C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic
5#13112660C211yesmaximal, characteristic
6#13112658C211yesmaximal, characteristic
7C13×#1272C211yesmaximal, characteristic
8C2×Q8×Dic13C411yescharacteristic
9C13×#391C2211yescharacteristic
10#11718891C411yescharacteristic
11C2×#88055—21no—
12C4⋊C4×Dic13C411yescharacteristic
13#11718634C411yescharacteristic
14C42×Dic13C2211yescharacteristic
15#11718589C2211yescharacteristic
16#11718315—21no—
17#11718314—21no—
18#11718310—21no—
19#11718309—21no—
20C13×#336C2211yescharacteristic
21C13×#336C2211yescharacteristic
22#11718142—21no—
23#11718142—21no—
24#11718142—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13C2×C411yescharacteristic
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32Q8×Dic13—22no—
33Q8×Dic13—22no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13C2×C411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C22×#1055—21no—
48C22×#1055—21no—
49C13×#95—21no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88055—24no—
57#7611—131nomaximal, Sylow
58C2×Q8×C13—21no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C2×Q8×C13M1612yes—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C22⋊C411yescharacteristic
73C2×C8×C13—22no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C13×C4⋊C4—41no—
80C42×C13—41no—
81C4⋊Dic13—24no—
82C4⋊Dic13—21no—
83C4⋊Dic13—41no—
84C4⋊Dic13M1612yes—
85#6101—42no—
86#6101—41no—
87#6101—41no—
88C4×Dic13—24no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—22no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98C4×Dic13—42no—
99C2×#1055—22no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105#2295—131no—
106#1839—131no—
107#1745—131no—
108#1272—131no—
109#1272D1311yescharacteristic
110#1271—131no—
111#1271—131no—
112C23×C13C2×C22⋊C411yescharacteristic
113Q8×C13—42no—
114Q8×C13—42no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13C2×M1611yescharacteristic
128C2×C4×C13C2×M1611yescharacteristic
129C2×C4×C13#13511yescharacteristic
130C2×C4×C13#13511yescharacteristic
131C2×C4×C13#13711yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—22no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13#10412yes—
151C8×C13—42no—
152C8×C13—81no—
153#1055—42no—
154#1055—81no—
155C2×C4×Q8—131no—
156C2×#97—261no—
157#391—131no—
158#391C2×D1311yescharacteristic
159#389—131no—
160#389—131no—
161#387—261no—
162#387—261no—
163C4×C4⋊C4—131no—
164C4×C4⋊C4—261no—
165#376—261no—
166C43—131no—
167#336—131no—
168#336—131no—
169#336—261no—
170#336—261no—
171#336—261no—
172#336C2×D1311yescharacteristic
173#336C2×D1311yescharacteristic
174C22×C13#40711yescharacteristic
175C22×C13#41011yescharacteristic
176C22×C13#41311yescharacteristic
177C22×C13#41611yescharacteristic
178C22×C13#41911yescharacteristic
179C22×C13C2×#10411yescharacteristic
180C22×C13#42111yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—42no—
188C4×C13—81no—
189Dic13—22no—
190Dic13—41no—
191Dic13—41no—
192Dic13—42no—
193Dic13—41no—
194Dic13—81no—
195C22×Q8C4×D1311yescharacteristic
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—261no—
199C22×C8—261no—
200C4×Q8—262no—
201C4×Q8—262no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4C4×D1311yescharacteristic
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—261no—
215C2×C42—261no—
216C2×C42C22×D1311yescharacteristic
217#97—264no—
218#95—21no—
219#95—21no—
220#95—261no—
221#95—261no—
222#95—261no—
223#95—261no—
224#95—261no—
225C2×C13#146411yescharacteristic
226C2×C13#148811yescharacteristic
227C2×C13#149111yescharacteristic
228C2×C13#150011yescharacteristic
229C2×C13#151511yescharacteristic
230C2×C13#152911yescharacteristic
231C2×C13#155411yescharacteristic
232C2×Q8—21no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8#609412yes—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—131no—
241C22×C4—131no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4C2×C4×D1311yescharacteristic
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—262no—
254C2×C8—521no—
255C2×C8—521no—
256C2×C8—521no—
257C2×C8—521no—
258C2×C8—521no—
259C4⋊C4—41no—
260C4⋊C4—132no—
261C4⋊C4—264no—
262C4⋊C4—261no—
263C4⋊C4—521no—
264C4⋊C4—522no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C42—41no—
268C42—262no—
269C42—264no—
270C42—261no—
271C42—261no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42—261no—
276C42—521no—
277C42—521no—
278C42—522no—
279C13#761111yescharacteristic, complemented, Sylow
280C23C22⋊C4×D1311yescharacteristic
281Q8—42no—
282Q8—42no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—132no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—262no—
307C2×C4—261no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4C2×#609411yescharacteristic
314C2×C4M16×D1311yescharacteristic
315C2×C4#8816911yescharacteristic
316C2×C4#8817011yescharacteristic
317C2×C4#8817211yescharacteristic
318C2×C4#8817311yescharacteristic
319C8—42no—
320C8—81no—
321C8—522no—
322C8—1041no—
323C22#1171838711yescharacteristic
324C22#1171840111yescharacteristic
325C22#1171840611yescharacteristic
326C22#1171846311yescharacteristic
327C22#1171846511yescharacteristic
328C22D13×#10411yescharacteristic
329C22#1171848211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4—81no—
338C4—262no—
339C4—521no—
340C4—521no—
341C4—522no—
342C4—521no—
343C4—1041no—
344C2#1311316711yescharacteristic
345C2#1311326911yescharacteristic
346C2#1311328111yescharacteristic
347C2#1311332111yescharacteristic
348C2#1311338511yescharacteristic
349C2#1311344011yescharacteristic
350C2#1311354511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1272D13
hypocenterC13#7611
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
279. C13#7611semidirect

Maximal subgroups

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

subgroupindex
#131173112
#131149782
#131145832
#131126622
#131126602
#131126582
C13×#12722
#761113