Finite Group Databasebeta

← #15773411

Subgroups — #15773411

Order 3328.

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

normal subgroups only

This group has 436 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#13120534C211yesmaximal, characteristic
2#13114569C211yesmaximal, characteristic
3#13112861C212yesmaximal
4#13112837C212yesmaximal
5C13×#1464C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×#88180—21no—
8C2×#88124C411yescharacteristic, complemented
9C13×#432—21no—
10#11718871—21no—
11#11718647C411yescharacteristic, complemented
12#11718644C411yescharacteristic, complemented
13#11718633—21no—
14#11718614C2211yescharacteristic
15#11718610C2211yescharacteristic
16#11718606—21no—
17#11718594—21no—
18#11718593C411yescharacteristic, complemented
19C13×#324—21no—
20C13×#323C2212yes—
21#11718118—21no—
22#11718118C2212yes—
23C23×C4×C13D411yescharacteristic
24C13×#117—41no—
25C13×#117—41no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C22⋊C4D411yescharacteristic
29C2×C13×C22⋊C4C2311yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C22⋊Dic13—22no—
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35#88180—24no—
36#88180—42no—
37C2×C4⋊Dic13—41no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13—41no—
46#88124—41no—
47#88124—41no—
48C13×C4⋊C8—41no—
49C13×C22⋊C8—22no—
50C13×#97—41no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071C2×C411yescharacteristic
57#88071C2×C411yescharacteristic
58#11760—131nomaximal, Sylow
59C24×C13C2×D411yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—42no—
76C2×C8×C13—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13—21no—
85C22⋊Dic13—24no—
86C22⋊Dic13—42no—
87C22⋊Dic13—42no—
88C22⋊Dic13—41no—
89C22⋊Dic13—41no—
90C4⋊Dic13—44no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93#6101—42no—
94#6101—42no—
95#6101—41no—
96#6101—41no—
97#6101—42no—
98C4×Dic13—42no—
99C4×Dic13—44no—
100#2611—131no—
101#1740—131no—
102#1464D1311yescharacteristic
103#1352—132no—
104#1344—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13AGL(1,ℤ/8)11yescharacteristic
111C23×C13#13711yescharacteristic
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
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—21no—
123C2×C4×C13—21no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13#10412yes—
131C2×Dic13—22no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—44no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—82no—
145C2×Dic13—82no—
146C8×C13—82no—
147C2×#125—131no—
148C2×#117—261no—
149C2×#117C2×D1311yescharacteristic
150#432—21no—
151#400—131no—
152#399—131no—
153#398—131no—
154#397—131no—
155#389—261no—
156#388—261no—
157#387—261no—
158#385—261no—
159#376—131no—
160#342—132no—
161#342—261no—
162#324—21no—
163#323C2×D1312yes—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—81no—
173C22×C13C2×#9911yescharacteristic
174C22×C13#41711yescharacteristic
175C22×C13C2×#10411yescharacteristic
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183Dic13—42no—
184Dic13—81no—
185Dic13—84no—
186Dic13—81no—
187Dic13—81no—
188C23×C4D5211yescharacteristic
189#125—521no—
190#125—521no—
191#117—41no—
192#117—41no—
193#117—264no—
194#117—522no—
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—521no—
202C2×C4⋊C4C4×D1311yescharacteristic
203C2×C4⋊C4C22⋊D1311yescharacteristic
204C2×C22⋊C4—262no—
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C22⋊C4D5211yescharacteristic
208C2×C22⋊C4C22×D1311yescharacteristic
209C2×C42—261no—
210C2×C42—521no—
211C2×C42C4×D1311yescharacteristic
212C2×C42C22⋊D1311yescharacteristic
213C4⋊C8—41no—
214C22⋊C8—22no—
215#97—41no—
216#95—131no—
217#95—131no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223C2×C13—21no—
224C2×C13—21no—
225C2×C13—41no—
226C2×C13—41no—
227C2×C13#150411yescharacteristic
228C2×C13#212311yescharacteristic
229C2×C13#212611yescharacteristic
230C24C2×D5211yescharacteristic
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—522no—
241C22×C4#610311yescharacteristic
242C22×C4#610311yescharacteristic
243C22×C4#610311yescharacteristic
244C22×C4#610311yescharacteristic
245C22×C4C2×C4×D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247C2×C8—42no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C4⋊C4—522no—
253C4⋊C4—524no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—264no—
261C22⋊C4—522no—
262C22⋊C4—522no—
263C22⋊C4—521no—
264C22⋊C4—521no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—524no—
270C42—522no—
271C13#1176011yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#8816211yescharacteristic
277C23#8816311yescharacteristic
278C23C2×#610311yescharacteristic
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—262no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—524no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—1042no—
309C2×C4—1042no—
310C2×C4#8804611yescharacteristic
311C2×C4#8804611yescharacteristic
312C2×C4#8806512yes—
313C8—82no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22C2×#8804611yescharacteristic
324C22#1171879411yescharacteristic
325C22C2×#8806511yescharacteristic
326C4—22no—
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—522no—
334C4—1041no—
335C4—1044no—
336C4—1041no—
337C4—1041no—
338C2—21no—
339C2—21no—
340C2—41no—
341C2—41no—
342C2#1311334111yescharacteristic
343C2#1311649111yescharacteristic
344C2#1311649911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1464C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1464D13
hypocenterC13#11760
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
8. C2×#88124C4semidirect
11. #11718647C4semidirect
12. #11718644C4semidirect
18. #11718593C4semidirect
271. C13#11760semidirect

Maximal subgroups

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

subgroupindex
#131205342
#131145692
#131128612
#131128372
C13×#14642
#1176013