Finite Group Databasebeta

← #15773431

Subgroups — #15773431

Order 3328.

446 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 87 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#13119123C211yesmaximal, characteristic
2C2×#11718122C211yesmaximal, characteristic
3#13112864C212yesmaximal, complemented
4#13112843C212yesmaximal, complemented
5C13×#1463C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88180C411yescharacteristic
8C22×#6099—21no—
9C13×#407—21no—
10#11718872—21no—
11#11718872C411yescharacteristic
12#11718871—21no—
13#11718647C411yescharacteristic
14#11718647C2211yescharacteristic
15#11718644C411yescharacteristic
16#11718644C2211yescharacteristic
17#11718639—21no—
18#11718639—21no—
19C13×#324—21no—
20C13×#324C2212yes—
21#11718122—21no—
22#11718122C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C2×C13×M16—41no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35#88180—41no—
36#88180—41no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×#6099—24no—
43C2×#6099—22no—
44C2×#6099—41no—
45C2×#6099—42no—
46C22×#1055—41no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—41no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071C2×C411yescharacteristic
57#88071C2×C411yescharacteristic
58#11764—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C13×M16—82no—
82C2×C8×C13—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C22⋊Dic13—42no—
88C22⋊Dic13—41no—
89C22⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92#6101—42no—
93#6101—41no—
94#6101—41no—
95C4×Dic13—42no—
96#6099—24no—
97#6099—44no—
98#6099—42no—
99C2×#1055—44no—
100C2×#1055—42no—
101#2484—131no—
102C2×#343—131no—
103#1463D1311yescharacteristic
104#1353—132no—
105#1346—132no—
106C23×C13—22no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—41no—
110C23×C13#9911yescharacteristic
111C23×C13#9911yescharacteristic
112C23×C13C2×C22⋊C411yescharacteristic
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
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—21no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—81no—
133C2×C4×C13#10412yes—
134C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C13#13711yescharacteristic
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—42no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C8×C13—82no—
148#1055—44no—
149C22×M16—261no—
150C2×#117—131no—
151C22×C4⋊C4C2×D1311yescharacteristic
152#407—21no—
153#400—131no—
154#400—131no—
155#398—131no—
156#398—131no—
157#387—261no—
158#387—261no—
159#385—261no—
160#381—131no—
161#381—261no—
162#343—132no—
163#343—261no—
164#324—21no—
165#324C2×D1312yes—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—42no—
174C22×C13—42no—
175C22×C13#35212yes—
176C22×C13C2×#9911yescharacteristic
177C22×C13#41711yescharacteristic
178C22×C13C2×#10411yescharacteristic
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—21no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186Dic13—81no—
187Dic13—81no—
188Dic13—81no—
189Dic13—81no—
190C23×C4C4×D1311yescharacteristic
191C23×C4D5211yescharacteristic
192C23×C4C22⋊D1311yescharacteristic
193C2×M16—41no—
194C2×M16—264no—
195C2×M16—262no—
196C2×M16—521no—
197C2×M16—522no—
198C22×C8—521no—
199#117—521no—
200#117—521no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4—41no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4C4×D1311yescharacteristic
208C2×C4⋊C4D5211yescharacteristic
209C2×C4⋊C4C22⋊D1311yescharacteristic
210C2×C4⋊C4C22×D1311yescharacteristic
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C42—261no—
214C22⋊C8—22no—
215C22⋊C8—41no—
216#95—131no—
217#95—131no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223#95—261no—
224#95—261no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—22no—
228C2×C13—41no—
229C2×C13#150411yescharacteristic
230C2×C13C2×#35211yescharacteristic
231C2×C13#213311yescharacteristic
232C24#610311yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4#610311yescharacteristic
249C22×C4#610311yescharacteristic
250C22×C4#610311yescharacteristic
251C22×C4C2×C4×D1311yescharacteristic
252C22×C4C2×D5211yescharacteristic
253C22×C4C2×C22⋊D1311yescharacteristic
254M16—82no—
255M16—264no—
256M16—524no—
257M16—522no—
258C2×C8—42no—
259C2×C8—524no—
260C2×C8—522no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C4⋊C4—522no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C22⋊C4—522no—
271C22⋊C4—521no—
272C22⋊C4—521no—
273C42—522no—
274C13#1176411yescharacteristic, complemented, Sylow
275C23—21no—
276C23—21no—
277C23—22no—
278C23—41no—
279C23#8804611yescharacteristic
280C23#8804611yescharacteristic
281C23C2×#610311yescharacteristic
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—522no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4#8806512yes—
314C2×C4#8816211yescharacteristic
315C2×C4#8816311yescharacteristic
316C8—82no—
317C8—524no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22#1171806412yes—
328C22C2×#8804611yescharacteristic
329C22#1171879411yescharacteristic
330C22C2×#8806511yescharacteristic
331C4—21no—
332C4—22no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—1041no—
339C4—1041no—
340C4—1041no—
341C4—1041no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—41no—
346C2#1311334111yescharacteristic
347C2C2×#1171806411yescharacteristic
348C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1463C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1463D13
hypocenterC13#11764
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #13112864C2semidirect
4. #13112843C2semidirect
274. C13#11764semidirect

Maximal subgroups

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

subgroupindex
#131191232
C2×#117181222
#131128642
#131128432
C13×#14632
#1176413