Finite Group Databasebeta

← #15773817

Subgroups — #15773817

Order 3328.

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

normal subgroups only

This group has 432 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#13114919C211yesmaximal, characteristic, complemented
2#13113150C211yesmaximal, characteristic, complemented
3#13112863C212yesmaximal, complemented
4#13112839C212yesmaximal, complemented
5C13×#2598C211yesmaximal, characteristic
6C2×C4×D4×C13C411yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C13×#400C2211yescharacteristic
9C13×#399C411yescharacteristic
10C13×#394C2211yescharacteristic
11C13×#392C411yescharacteristic
12C13×#388—21no—
13C13×#386—21no—
14C13×#386—21no—
15C13×#385—21no—
16C13×#383C411yescharacteristic
17#11718868—21no—
18#11718586—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120C2212yes—
22#11718117—21no—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13—21no—
26C23×C4×C13D411yescharacteristic
27C4×D4×C13—41no—
28C4×D4×C13—41no—
29C13×#117—41no—
30C13×#117—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×#6099—22no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51C22⋊#1055—22no—
52C22⋊#1055—41no—
53C22⋊#1055—41no—
54C4⋊#1055—41no—
55C4×#1055—41no—
56#11847—131nomaximal, Sylow
57C24×C13—21no—
58C24×C13C22⋊C411yescharacteristic
59C2×D4×C13—41no—
60C2×D4×C13—42no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—81no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—41no—
71C22×C4×C13—42no—
72C22×C4×C13—81no—
73C22×C4×C13—81no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—81no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—81no—
91C13×C22⋊C4—81no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—21no—
96#6099—42no—
97#6099—42no—
98C2×#1055—42no—
99C2×#1055—42no—
100#2598D1311yescharacteristic
101#1822—131no—
102#1458—131no—
103#1353—132no—
104#1345—132no—
105C23×C13—22no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13C2×C22⋊C411yescharacteristic
118D4×C13—42no—
119D4×C13—42no—
120D4×C13—84no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—84no—
145C2×C4×C13#9911yescharacteristic
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13#13512yes—
148#1055—82no—
149#1055—82no—
150C2×C4×D4Dic1311yescharacteristic
151C2×#117C2×D1311yescharacteristic
152#431—261no—
153#407—261no—
154#400C2×D1311yescharacteristic
155#399Dic1311yescharacteristic
156#394C2×D1311yescharacteristic
157#392Dic1311yescharacteristic
158#388—21no—
159#386—21no—
160#386—21no—
161#385—21no—
162#383Dic1311yescharacteristic
163#343—132no—
164#343—261no—
165#324—132no—
166#323—261no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—42no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—42no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13C2×#9911yescharacteristic
182C22×C13#41611yescharacteristic
183C22×C13#42111yescharacteristic
184C4×C13—22no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13—81no—
194C22×D4—21no—
195C22×D4C2×Dic1311yescharacteristic
196C23×C4—21no—
197C23×C4C22⋊D1311yescharacteristic
198C2×M16—262no—
199C4×D4—41no—
200C4×D4—41no—
201#117—41no—
202#117—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×Dic1311yescharacteristic
205C2×C4⋊C4C22⋊D1311yescharacteristic
206C2×C4⋊C4C22×D1311yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4C2×Dic1311yescharacteristic
213C2×C22⋊C4C22⋊D1311yescharacteristic
214C2×C42C2×Dic1311yescharacteristic
215C2×C42C22⋊D1311yescharacteristic
216C4⋊C8—521no—
217C22⋊C8—262no—
218C22⋊C8—521no—
219C22⋊C8—521no—
220C4×C8—521no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C2×Dic1311yescharacteristic
226#95C2×Dic1311yescharacteristic
227C2×C13—21no—
228C2×C13—21no—
229C2×C13—81no—
230C2×C13—82no—
231C2×C13#151611yescharacteristic
232C2×C13#212011yescharacteristic
233C2×C13#213411yescharacteristic
234C24—21no—
235C24C22⋊Dic1311yescharacteristic
236C2×D4—41no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—42no—
240C2×D4—81no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—41no—
248C22×C4—42no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4C22⋊Dic1311yescharacteristic
252C22×C4C22⋊Dic1311yescharacteristic
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22×Dic1311yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257M16—522no—
258M16—522no—
259C2×C8—522no—
260C2×C8—522no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—42no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—81no—
272C22⋊C4—81no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42—21no—
277C13#1184711yescharacteristic, complemented, Sylow
278C23—22no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23C2×C22⋊Dic1311yescharacteristic
291D4—42no—
292D4—42no—
293D4—84no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—84no—
318C2×C4#8807411yescharacteristic
319C2×C4#8807411yescharacteristic
320C2×C4#8820412yes—
321C8—1042no—
322C8—1042no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22C2×#8807411yescharacteristic
338C22#1171889411yescharacteristic
339C22#1171889711yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—81no—
348C4—81no—
349C4—81no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—82no—
354C2#1311339211yescharacteristic
355C2#1311647711yescharacteristic
356C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2598C2
socleC22×C13C2×#99
prime radicalC13×#392C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2598D13
hypocenterC13#11847
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2598

Complements

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

NH ≅ G/Ntype
1. #13114919C2semidirect
2. #13113150C2semidirect
3. #13112863C2semidirect
4. #13112839C2semidirect
277. C13#11847semidirect

Maximal subgroups

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

subgroupindex
#131149192
#131131502
#131128632
#131128392
C13×#25982
#1184713