Finite Group Databasebeta

← #15751984

Subgroups — #15751984

Order 3328.

374 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 85 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#13121788C211yesmaximal, characteristic
2#13116395C211yesmaximal, characteristic
3#13116309C211yesmaximal, characteristic
4#13116307C211yesmaximal, characteristic
5#13112658C211yesmaximal, characteristic
6#13112658C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic
8C2×#88143—21no—
9C13×#389C2211yescharacteristic
10C2×#88058—21no—
11#11718646—21no—
12#11718644—21no—
13#11718644—21no—
14C2×#88047—21no—
15#11718596C2211yescharacteristic
16#11718589C2211yescharacteristic
17#11718589C2211yescharacteristic
18#11718322—21no—
19#11718314—21no—
20C13×#336C2211yescharacteristic
21C13×#336C2211yescharacteristic
22#11718143—21no—
23#11718143—21no—
24#11718143—21no—
25#11718121—21no—
26#11718116C2211yescharacteristic
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13D411yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×C4×Dic13—21no—
47C22×#1055—21no—
48#88143—42no—
49#88143—42no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88058—42no—
57#88047—42no—
58#7792—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—21no—
67C22×Dic13—21no—
68C22×Dic13—41no—
69C2×C8×C13—22no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4D812yes—
80C42×C13—41no—
81C4⋊Dic13—21no—
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—42no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C4⋊Dic13—42no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—81no—
93C4⋊Dic13Q1612yes—
94#6101—42no—
95#6101—42no—
96#6101—41no—
97#6101—41no—
98#6101—41no—
99#6101—41no—
100C4×Dic13—42no—
101C2×#1055—22no—
102C2×#1055—41no—
103C2×#1055—41no—
104#2726—131no—
105#2099—131no—
106#2083—131no—
107#2083—131no—
108#1271—131no—
109#1271—131no—
110#1271D1311yescharacteristic
111C23×C13#12011yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—22no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13C2×D811yescharacteristic
125C2×C4×C13C2×Q1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C13#13711yescharacteristic
130C2×Dic13—22no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145C8×C13—42no—
146C8×C13—81no—
147#1055—42no—
148C2×#125—261no—
149C2×#107—261no—
150C2×#107—261no—
151#398—261no—
152#398—261no—
153#398—261no—
154#389—131no—
155#389—131no—
156#389—261no—
157#389C2×D1311yescharacteristic
158#387—261no—
159#384—131no—
160#340—261no—
161#340—261no—
162#340—261no—
163#340—261no—
164#336—131no—
165#336C2×D1311yescharacteristic
166#336C2×D1311yescharacteristic
167C22×C13#44711yescharacteristic
168C22×C13#44911yescharacteristic
169C22×C13#45111yescharacteristic
170C22×C13#45411yescharacteristic
171C22×C13#45611yescharacteristic
172C22×C13#45611yescharacteristic
173C22×C13#45811yescharacteristic
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—42no—
181C4×C13—81no—
182Dic13—42no—
183Dic13—81no—
184Dic13—81no—
185Dic13—81no—
186Dic13—161no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—261no—
190#125—522no—
191#125—522no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4D5211yescharacteristic
207C2×C4⋊C4D5211yescharacteristic
208C2×C42—261no—
209C2×C42C22×D1311yescharacteristic
210#107—522no—
211#107—522no—
212#95—21no—
213#95—261no—
214#95—261no—
215#95—261no—
216#95—261no—
217#95—261no—
218C2×C13#160911yescharacteristic
219C2×C13#161011yescharacteristic
220C2×C13#161711yescharacteristic
221C2×C13#162511yescharacteristic
222C2×C13#164811yescharacteristic
223C2×C13#164911yescharacteristic
224C2×C13#166311yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—261no—
231C22×C4—521no—
232C22×C4C2×D5211yescharacteristic
233C22×C4D4×D1311yescharacteristic
234C22×C4D4×D1311yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—262no—
242C2×C8—521no—
243C2×C8—521no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—132no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C4⋊C4—522no—
257C4⋊C4—522no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—1041no—
267C4⋊C4D10412yes—
268C42—41no—
269C42—522no—
270C13#779211yescharacteristic, complemented, Sylow
271C23#8813611yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—262no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—1041no—
297C2×C4—1041no—
298C2×C4—1041no—
299C2×C4C2×D10411yescharacteristic
300C2×C4#8816211yescharacteristic
301C2×C4#8816511yescharacteristic
302C2×C4#8816911yescharacteristic
303C2×C4#8817011yescharacteristic
304C2×C4Q16×D1311yescharacteristic
305C8—42no—
306C8—81no—
307C8—522no—
308C22#1171839311yescharacteristic
309C22#1171840311yescharacteristic
310C22#1171841311yescharacteristic
311C22#1171844211yescharacteristic
312C22#1171846911yescharacteristic
313C22#1171848711yescharacteristic
314C22#1171848811yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—81no—
323C4—522no—
324C4—1041no—
325C4—1041no—
326C4—1041no—
327C4—2081no—
328C2#1311383411yescharacteristic
329C2#1311384111yescharacteristic
330C2#1311387911yescharacteristic
331C2#1311392711yescharacteristic
332C2#1311407911yescharacteristic
333C2#1311408711yescharacteristic
334C2#1311416611yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socle, prime radicalC23×C13#120
hypercenter#1271D13
hypocenterC13#7792
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
270. C13#7792semidirect

Maximal subgroups

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

subgroupindex
#131217882
#131163952
#131163092
#131163072
#131126582
C13×#12712
#779213