Finite Group Databasebeta

← #15752203

Subgroups — #15752203

Order 3328.

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

normal subgroups only

This group has 358 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#13116398C211yesmaximal, characteristic
3#13116398C211yesmaximal, characteristic
4#13112660C211yesmaximal, characteristic
5#13112660C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#2100C211yesmaximal, characteristic
8C2×#88143—21no—
9C13×#389C2211yescharacteristic
10C13×#384C2211yescharacteristic
11#11718646—21no—
12#11718644—21no—
13#11718644—21no—
14#11718589C2211yescharacteristic
15#11718589C2211yescharacteristic
16#11718322—21no—
17#11718314—21no—
18C13×#340—21no—
19C13×#340—21no—
20C13×#336C2211yescharacteristic
21#11718121—21no—
22#11718121—21no—
23#11718121—21no—
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×C8×C13—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×C4⋊Dic13D411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C22×#1055—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#7827—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—41no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×C8×C13—41no—
68C2×C8×C13—41no—
69C2×C8×C13—41no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C13×C4⋊C4—42no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4SD1612yes—
78C42×C13—41no—
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13—42no—
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85C4⋊Dic13—81no—
86C4⋊Dic13Q1612yes—
87#6101—42no—
88#6101—42no—
89#6101—41no—
90#6101—41no—
91#6101—41no—
92#6101—41no—
93C4×Dic13—42no—
94C2×#1055—41no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100#2726—131no—
101#2100—131no—
102#2100—131no—
103#2100D1311yescharacteristic
104#1271—131no—
105#1271—131no—
106#1271—131no—
107C23×C13#12011yescharacteristic
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13—81no—
123C2×C4×C13C2×SD1611yescharacteristic
124C2×C4×C13C2×Q1611yescharacteristic
125C2×C4×C13#13511yescharacteristic
126C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C13#13711yescharacteristic
128C2×C4×C13#13711yescharacteristic
129C2×Dic13—22no—
130C2×Dic13—41no—
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—
141C8×C13—81no—
142#1055—81no—
143#1055—81no—
144C2×#125—261no—
145#398—261no—
146#398—261no—
147#398—261no—
148#389—131no—
149#389—131no—
150#389—261no—
151#389C2×D1311yescharacteristic
152#387—261no—
153#384C2×D1311yescharacteristic
154#340—21no—
155#340—21no—
156#340—261no—
157#340—261no—
158#340—261no—
159#340—261no—
160#336—131no—
161#336—131no—
162#336C2×D1311yescharacteristic
163C22×C13#45011yescharacteristic
164C22×C13#45111yescharacteristic
165C22×C13#45211yescharacteristic
166C22×C13#45411yescharacteristic
167C22×C13#45411yescharacteristic
168C22×C13#45411yescharacteristic
169C22×C13#45811yescharacteristic
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—42no—
177C4×C13—81no—
178C4×C13—161no—
179Dic13—42no—
180Dic13—81no—
181Dic13—81no—
182Dic13—81no—
183C22×C8—21no—
184C22×C8—261no—
185C22×C8—261no—
186#125—522no—
187#125—522no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4C22⋊D1311yescharacteristic
203C2×C4⋊C4C22⋊D1311yescharacteristic
204C2×C42—261no—
205C2×C42C22×D1311yescharacteristic
206#95—21no—
207#95—261no—
208#95—261no—
209#95—261no—
210#95—261no—
211#95—261no—
212C2×C13#161511yescharacteristic
213C2×C13#161611yescharacteristic
214C2×C13#161711yescharacteristic
215C2×C13#163511yescharacteristic
216C2×C13#163611yescharacteristic
217C2×C13#163711yescharacteristic
218C2×C13#165811yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—261no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4D4×D1311yescharacteristic
227C22×C4D4×D1311yescharacteristic
228C22×C4C2×C22⋊D1311yescharacteristic
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—521no—
233C2×C8—521no—
234C2×C8—521no—
235C2×C8—521no—
236C2×C8—521no—
237C2×C8—521no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—132no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—521no—
250C4⋊C4—521no—
251C4⋊C4—522no—
252C4⋊C4—522no—
253C4⋊C4—522no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—1041no—
259C4⋊C4#610612yes—
260C42—41no—
261C42—522no—
262C13#782711yescharacteristic, complemented, Sylow
263C23#8819111yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—262no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4#8816911yescharacteristic
292C2×C4#8817011yescharacteristic
293C2×C4Q16×D1311yescharacteristic
294C2×C4#8817211yescharacteristic
295C2×C4C2×#610611yescharacteristic
296C2×C4#8820311yescharacteristic
297C8—81no—
298C8—1041no—
299C8—1041no—
300C22#1171870711yescharacteristic
301C22#1171871411yescharacteristic
302C22#1171872311yescharacteristic
303C22#1171883411yescharacteristic
304C22#1171884711yescharacteristic
305C22#1171886211yescharacteristic
306C22#1171886211yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—161no—
316C4—522no—
317C4—1041no—
318C4—1041no—
319C4—1041no—
320C2#1311386411yescharacteristic
321C2#1311387211yescharacteristic
322C2#1311387611yescharacteristic
323C2#1311398511yescharacteristic
324C2#1311399111yescharacteristic
325C2#1311399911yescharacteristic
326C2#1311413711yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2100C2
socle, prime radicalC23×C13#120
hypercenter#2100D13
hypocenterC13#7827
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
262. C13#7827semidirect

Maximal subgroups

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

subgroupindex
#131217882
#131163982
#131126602
#131126592
C13×#21002
#782713