Finite Group Databasebeta

← #15751157

Subgroups — #15751157

Order 3328.

434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 101 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#13117307C211yesmaximal, characteristic
2#13114688C211yesmaximal, characteristic
3#13114583C211yesmaximal, characteristic
4#13112661C211yesmaximal, characteristic
5#13112661C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic
8C2×#88141C411yescharacteristic
9C13×#389C2211yescharacteristic
10C2×#88055—21no—
11C2×#88055—21no—
12C2×#88054—21no—
13#11718646C411yescharacteristic
14#11718639—21no—
15C4⋊C4×Dic13—21no—
16C4⋊C4×Dic13C411yescharacteristic
17#11718635C411yescharacteristic
18C42×Dic13C2211yescharacteristic
19#11718590C2211yescharacteristic
20#11718316—21no—
21#11718309—21no—
22C13×#336C2211yescharacteristic
23C13×#336C2211yescharacteristic
24#11718142—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Dic26C2×C411yescharacteristic
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C22×#1055—21no—
46C22×#1055—21no—
47#88141—22no—
48#88141—22no—
49C13×#95—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88055—24no—
57#88055—42no—
58#88054—24no—
59#7630—131nomaximal, Sylow
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C411yescharacteristic
71C2×Dic26—21no—
72C2×Dic26—41no—
73C2×Dic26—41no—
74C2×Dic26M1612yes—
75C2×C8×C13—22no—
76C2×C8×C13—22no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4M1612yes—
86C42×C13—41no—
87C4⋊Dic13—42no—
88C4⋊Dic13—41no—
89#6101—24no—
90C4×Dic13—24no—
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—41no—
100C4×Dic13—42no—
101C2×#1055—22no—
102C2×#1055—22no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#1055—41no—
107#2295—131no—
108#1767—131no—
109#1745—131no—
110#1272—131no—
111#1272—131no—
112#1271—131no—
113#1271D1311yescharacteristic
114C23×C13C2×C22⋊C411yescharacteristic
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×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×C4×C13#13711yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—22no—
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#10412yes—
150C2×Dic13#10412yes—
151Dic26—42no—
152Dic26—42no—
153C8×C13—42no—
154C8×C13—42no—
155#1055—42no—
156#1055—42no—
157C2×C4×Q8—131no—
158C2×C4⋊C8—261no—
159C2×#97—261no—
160C2×#97—261no—
161#391—131no—
162#391—131no—
163#389—131no—
164#389C2×D1311yescharacteristic
165#387—261no—
166#387—261no—
167C4×C4⋊C4—131no—
168C4×C4⋊C4—261no—
169#376—261no—
170C43—131no—
171#336—131no—
172#336—131no—
173#336—261no—
174#336C2×D1311yescharacteristic
175#336C2×D1311yescharacteristic
176C22×C13#40711yescharacteristic
177C22×C13#41011yescharacteristic
178C22×C13#41311yescharacteristic
179C22×C13#41711yescharacteristic
180C22×C13#41911yescharacteristic
181C22×C13C2×#10411yescharacteristic
182C22×C13C2×#10411yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—42no—
190C4×C13—81no—
191Dic13—22no—
192Dic13—22no—
193Dic13—41no—
194Dic13—42no—
195Dic13—41no—
196Dic13—81no—
197C22×Q8—131no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—261no—
201C22×C8—261no—
202C4×Q8—262no—
203C4×Q8—262no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—131no—
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—
220#97—264no—
221#97—522no—
222#95—21no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228#95—261no—
229C2×C13#146411yescharacteristic
230C2×C13#148911yescharacteristic
231C2×C13#149111yescharacteristic
232C2×C13#150611yescharacteristic
233C2×C13#150911yescharacteristic
234C2×C13#152411yescharacteristic
235C2×C13#155911yescharacteristic
236C2×Q8—132no—
237C2×Q8—261no—
238C2×Q8—521no—
239C2×Q8—521no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4C2×C4×D1311yescharacteristic
249C22×C4D4×D1311yescharacteristic
250C22×C4D4×D1311yescharacteristic
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—262no—
258C2×C8—262no—
259C2×C8—521no—
260C2×C8—521no—
261C2×C8—521no—
262C2×C8—521no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—264no—
268C4⋊C4—521no—
269C4⋊C4—522no—
270C4⋊C4#609412yes—
271C42—41no—
272C42—262no—
273C42—262no—
274C42—264no—
275C42—261no—
276C42—261no—
277C42—261no—
278C42—261no—
279C42—261no—
280C42—261no—
281C42—521no—
282C42—522no—
283C13#763011yescharacteristic, complemented, Sylow
284C23C22⋊C4×D1311yescharacteristic
285Q8—522no—
286Q8—522no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—132no—
300C2×C4—132no—
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—261no—
310C2×C4—261no—
311C2×C4—262no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4C2×#609411yescharacteristic
318C2×C4M16×D1311yescharacteristic
319C2×C4#8816511yescharacteristic
320C2×C4#8816911yescharacteristic
321C2×C4#8816911yescharacteristic
322C2×C4#8817211yescharacteristic
323C8—42no—
324C8—42no—
325C8—522no—
326C8—522no—
327C22#1171838711yescharacteristic
328C22#1171840111yescharacteristic
329C22#1171841211yescharacteristic
330C22#1171843211yescharacteristic
331C22#1171846311yescharacteristic
332C22D13×#10411yescharacteristic
333C22D13×#10411yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—262no—
343C4—262no—
344C4—522no—
345C4—521no—
346C4—521no—
347C4—1041no—
348C2#1311316911yescharacteristic
349C2#1311327211yescharacteristic
350C2#1311328111yescharacteristic
351C2#1311334611yescharacteristic
352C2#1311335811yescharacteristic
353C2#1311342311yescharacteristic
354C2#1311356511yescharacteristic
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#7630
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#7630semidirect

Maximal subgroups

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

subgroupindex
#131173072
#131146882
#131145832
#131126612
#131126592
C13×#12712
#763013