Finite Group Databasebeta

← #15751181

Subgroups — #15751181

Order 3328.

436 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117395C211yesmaximal, characteristic
2#13114688C211yesmaximal, characteristic
3#13114688C211yesmaximal, characteristic
4#13112660C211yesmaximal, characteristic
5#13112659C211yesmaximal, characteristic
6#13112658C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic
8C2×#88144C411yescharacteristic
9C13×#389C2211yescharacteristic
10C2×#88055—21no—
11C2×#88055—21no—
12C2×#88054—21no—
13C2×#88054—21no—
14#11718639—21no—
15#11718638C411yescharacteristic
16C4⋊C4×Dic13—21no—
17C4⋊C4×Dic13C411yescharacteristic
18C4⋊C4×Dic13C411yescharacteristic
19C42×Dic13C2211yescharacteristic
20#11718589C2211yescharacteristic
21#11718314—21no—
22#11718310—21no—
23C13×#336C2211yescharacteristic
24C13×#336C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C22×#1055—21no—
47C22×#1055—21no—
48#88144—22no—
49#88144—22no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88055—42no—
57#88055—42no—
58#88054—24no—
59#88054—24no—
60#7636—131nomaximal, Sylow
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C2×C8×C13—22no—
73C2×C8×C13—22no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4M1612yes—
83C42×C13—41no—
84C4⋊Dic13—24no—
85C4⋊Dic13—21no—
86C4⋊Dic13—41no—
87C4⋊Dic13M1612yes—
88#6101—24no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—22no—
98C4×Dic13—22no—
99C4×Dic13—22no—
100C4×Dic13—42no—
101C4×Dic13—42no—
102C2×#1055—22no—
103C2×#1055—22no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108C4×#125—131no—
109#1767—131no—
110#1767—131no—
111#1271—131no—
112#1271—131no—
113#1271—131no—
114#1271D1311yescharacteristic
115C23×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—22no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13C2×M1611yescharacteristic
129C2×C4×C13C2×M1611yescharacteristic
130C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×C4×C13#13711yescharacteristic
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—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13#10112yes—
150C2×Dic13#10412yes—
151C2×Dic13#10412yes—
152C8×C13—42no—
153C8×C13—42no—
154#1055—42no—
155#1055—42no—
156C2×#125—131no—
157C2×C4⋊C8—261no—
158C2×C4⋊C8—261no—
159C2×#97—261no—
160C2×#97—261no—
161#389—131no—
162#389C2×D1311yescharacteristic
163#387—261no—
164#387—261no—
165#382—131no—
166C4×C4⋊C4—131no—
167C4×C4⋊C4—131no—
168C4×C4⋊C4—261no—
169C4×C4⋊C4—261no—
170C43—131no—
171#336—131no—
172#336—131no—
173#336C2×D1311yescharacteristic
174#336C2×D1311yescharacteristic
175C22×C13#40711yescharacteristic
176C22×C13#41011yescharacteristic
177C22×C13C2×#10111yescharacteristic
178C22×C13#41711yescharacteristic
179C22×C13#41711yescharacteristic
180C22×C13C2×#10411yescharacteristic
181C22×C13C2×#10411yescharacteristic
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—42no—
189C4×C13—81no—
190Dic13—41no—
191Dic13—41no—
192Dic13—41no—
193Dic13—42no—
194Dic13—81no—
195Dic13#33014yes—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—261no—
199C22×C8—261no—
200#125—262no—
201#125—262no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C4×D1311yescharacteristic
209C2×C4⋊C4C4×D1311yescharacteristic
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—131no—
215C2×C42—131no—
216C2×C42—261no—
217C2×C42—261no—
218C2×C42C22×D1311yescharacteristic
219C4⋊C8—264no—
220C4⋊C8—264no—
221#97—522no—
222#97—522no—
223#95—21no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228#95—261no—
229C2×C13#146711yescharacteristic
230C2×C13#148911yescharacteristic
231C2×C13#148911yescharacteristic
232C2×C13#150911yescharacteristic
233C2×C13#150911yescharacteristic
234C2×C13C2×#33011yescharacteristic
235C2×C13#156111yescharacteristic
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—22no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—262no—
254C2×C8—262no—
255C2×C8—521no—
256C2×C8—521no—
257C2×C8—521no—
258C2×C8—521no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—132no—
264C4⋊C4—264no—
265C4⋊C4—264no—
266C4⋊C4—261no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4#609412yes—
271C42—41no—
272C42—262no—
273C42—262no—
274C42—262no—
275C42—261no—
276C42—261no—
277C42—261no—
278C42—261no—
279C42—261no—
280C42—261no—
281C42—522no—
282C42—522no—
283C13#763611yescharacteristic, complemented, Sylow
284C23C22⋊C4×D1311yescharacteristic
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—132no—
298C2×C4—132no—
299C2×C4—132no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—262no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4C2×#609411yescharacteristic
316C2×C4M16×D1311yescharacteristic
317C2×C4#8816511yescharacteristic
318C2×C4#8816811yescharacteristic
319C2×C4#8816911yescharacteristic
320C2×C4#8817211yescharacteristic
321C8—42no—
322C8—42no—
323C8—522no—
324C8—522no—
325C22#1171838711yescharacteristic
326C22#1171840111yescharacteristic
327C22D13×#10111yescharacteristic
328C22#1171843211yescharacteristic
329C22#1171846411yescharacteristic
330C22D13×#10411yescharacteristic
331C22D13×#10411yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—42no—
339C4—81no—
340C4—134no—
341C4—521no—
342C4—521no—
343C4—522no—
344C4—521no—
345C4—1041no—
346C2#1311317811yescharacteristic
347C2#1311327211yescharacteristic
348C2#1311327411yescharacteristic
349C2#1311335811yescharacteristic
350C2#1311336011yescharacteristic
351C2D13×#33011yescharacteristic
352C2#1311357211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1271D13
hypocenterC13#7636
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
283. C13#7636semidirect

Maximal subgroups

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

subgroupindex
#131173952
#131146882
#131126602
#131126592
#131126582
C13×#12712
#763613