Finite Group Databasebeta

← #15752056

Subgroups — #15752056

Order 3328.

338 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 83 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#13116394C211yesmaximal, characteristic
2#13116312C211yesmaximal, characteristic
3#13116307C211yesmaximal, characteristic
4#13112659C211yesmaximal, characteristic
5#13112659C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#2810C211yesmaximal, characteristic
8C13×#400—21no—
9C13×#400—21no—
10C13×#400—21no—
11C13×#389C2211yescharacteristic
12C13×#389C2211yescharacteristic
13C13×#389C2211yescharacteristic
14C13×#387—21no—
15C13×#387—21no—
16C13×#387—21no—
17C2×#88048—21no—
18C2×#88047—21no—
19#11718596C2211yescharacteristic
20#11718121—21no—
21#11718121—21no—
22#11718121—21no—
23#11718121—21no—
24#11718116C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C22×#1055—21no—
42C22×#1055—21no—
43C22×#1055—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54#88048—42no—
55#88047—42no—
56#7803—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—41no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C42×C13—41no—
83C42×C13—81no—
84C4⋊Dic13—42no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C2×#1055—22no—
90C2×#1055—22no—
91C2×#1055—41no—
92C2×#1055—41no—
93C2×#1055—41no—
94C2×#1055—41no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98#2810D1311yescharacteristic
99#2099—131no—
100#2084—131no—
101#2083—131no—
102#1271—131no—
103#1271—131no—
104#1271—131no—
105C23×C13#12011yescharacteristic
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
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×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13#13511yescharacteristic
131C2×C4×C13#13511yescharacteristic
132C2×C4×C13#13511yescharacteristic
133C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C13#13711yescharacteristic
136C2×Dic13—81no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139#1055—42no—
140#1055—42no—
141#1055—81no—
142C2×#107—261no—
143C2×#106—261no—
144#400—21no—
145#400—21no—
146#400—21no—
147#389C2×D1311yescharacteristic
148#389C2×D1311yescharacteristic
149#389C2×D1311yescharacteristic
150#387—21no—
151#387—21no—
152#387—21no—
153#384—131no—
154#340—261no—
155#340—261no—
156#340—261no—
157#340—261no—
158#336—131no—
159#336—131no—
160#336—131no—
161C22×C13#44911yescharacteristic
162C22×C13#44911yescharacteristic
163C22×C13#45211yescharacteristic
164C22×C13#45411yescharacteristic
165C22×C13#45611yescharacteristic
166C22×C13#45611yescharacteristic
167C22×C13#45811yescharacteristic
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—81no—
175C4×C13—81no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13—81no—
179C4×C13—81no—
180Dic13—161no—
181C22×C8—261no—
182C22×C8—261no—
183C22×C8—261no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4C22⋊D1311yescharacteristic
191C2×C4⋊C4C22⋊D1311yescharacteristic
192C2×C4⋊C4C22⋊D1311yescharacteristic
193C2×C4⋊C4C22⋊D1311yescharacteristic
194C2×C4⋊C4C22⋊D1311yescharacteristic
195C2×C4⋊C4C22⋊D1311yescharacteristic
196C2×C42—21no—
197C2×C42C22×D1311yescharacteristic
198#107—522no—
199#106—522no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210C2×C13#160911yescharacteristic
211C2×C13#160911yescharacteristic
212C2×C13#161511yescharacteristic
213C2×C13#162811yescharacteristic
214C2×C13#165011yescharacteristic
215C2×C13#165211yescharacteristic
216C2×C13#166311yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—521no—
224C22×C4C2×C22⋊D1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226C22×C4C2×C22⋊D1311yescharacteristic
227C2×C8—262no—
228C2×C8—262no—
229C2×C8—521no—
230C2×C8—521no—
231C2×C8—521no—
232C2×C8—521no—
233C2×C8—521no—
234C2×C8—521no—
235C2×C8—521no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—522no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C42—41no—
257C42—81no—
258C13#780311yescharacteristic, complemented, Sylow
259C23#8820711yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—1041no—
285C2×C4—1041no—
286C2×C4—1041no—
287C2×C4#8820311yescharacteristic
288C2×C4#8820311yescharacteristic
289C2×C4#8820411yescharacteristic
290C2×C4#8820411yescharacteristic
291C2×C4#8820411yescharacteristic
292C2×C4#8820511yescharacteristic
293C8—522no—
294C8—522no—
295C8—1041no—
296C22#1171889911yescharacteristic
297C22#1171889911yescharacteristic
298C22#1171890011yescharacteristic
299C22#1171890411yescharacteristic
300C22#1171890611yescharacteristic
301C22#1171890711yescharacteristic
302C22#1171890711yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—2081no—
316C2#1311383311yescharacteristic
317C2#1311383311yescharacteristic
318C2#1311386711yescharacteristic
319C2#1311394611yescharacteristic
320C2#1311409211yescharacteristic
321C2#1311410611yescharacteristic
322C2#1311416411yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2810C2
socle, prime radicalC23×C13#120
hypercenter#2810D13
hypocenterC13#7803
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2810

Complements

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

NH ≅ G/Ntype
258. C13#7803semidirect

Maximal subgroups

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

subgroupindex
#131163942
#131163122
#131163072
#131126592
C13×#28102
#780313