Finite Group Databasebeta

← #15772606

Subgroups — #15772606

Order 3328.

426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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#13113177C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112784C212yesmaximal, complemented
4#13112784C212yesmaximal, complemented
5C13×#2579C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic
8C13×#398—21no—
9C13×#396—21no—
10C13×#387—21no—
11C13×#386C411yescharacteristic
12C13×#386C411yescharacteristic
13C13×#385—21no—
14C13×#385C2211yescharacteristic
15C13×#385C2211yescharacteristic
16C13×#380C411yescharacteristic
17C2×C22⋊#1055—21no—
18#11718587—21no—
19#11718120—21no—
20#11718117—21no—
21#11718117C2212yes—
22#11718117C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4—41no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C2×C42×C13D411yescharacteristic
45C22×#1055—41no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53C22⋊#1055—41no—
54C4⋊#1055—41no—
55#88043—41no—
56#11578—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C24×C13C22×C411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—41no—
62C22×C4×C13—21no—
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—21no—
70C22×C4×C13—42no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13—81no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C13×C4⋊C4—41no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—81no—
87C13×C4⋊C4—81no—
88C13×C22⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—81no—
94C42×C13—21no—
95C42×C13—21no—
96C2×#1055—42no—
97C2×#1055—42no—
98C2×#1055—82no—
99#2579D1311yescharacteristic
100#1466—131no—
101#1459—131no—
102#1326—132no—
103#1326—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13#10112yes—
113C23×C13C2×C22⋊C411yescharacteristic
114C23×C13#13112yes—
115D4×C13—44no—
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—41no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
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—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—82no—
145C2×C4×C13#9911yescharacteristic
146C2×C4×C13#9911yescharacteristic
147#1055—82no—
148#1055—82no—
149C2×C4×D4C2×D1311yescharacteristic
150C22×C4⋊C4Dic1311yescharacteristic
151#432—261no—
152C2×C22⋊C8—261no—
153#398—21no—
154#396—21no—
155#387—21no—
156#386Dic1311yescharacteristic
157#386Dic1311yescharacteristic
158#385—21no—
159#385C2×D1311yescharacteristic
160#385C2×D1311yescharacteristic
161#380Dic1311yescharacteristic
162#324—261no—
163#323—132no—
164#323—132no—
165#323—261no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—42no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—81no—
178C22×C13#40811yescharacteristic
179C22×C13C2×#9911yescharacteristic
180C22×C13C2×#10111yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—42no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191C22×D4C2×Dic1311yescharacteristic
192C23×C4C2×Dic1311yescharacteristic
193C23×C4C2×Dic1311yescharacteristic
194C23×C4C2×Dic1311yescharacteristic
195C23×C4C22⋊D1311yescharacteristic
196C22×C8—521no—
197C4×D4—41no—
198C4×D4—41no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4—41no—
206C2×C4⋊C4C22⋊D1311yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4C2×Dic1311yescharacteristic
210C2×C22⋊C4C2×Dic1311yescharacteristic
211C2×C22⋊C4C22⋊D1311yescharacteristic
212C2×C22⋊C4C22×D1311yescharacteristic
213C2×C42C22⋊D1311yescharacteristic
214C4⋊C8—521no—
215C22⋊C8—262no—
216C22⋊C8—262no—
217C22⋊C8—521no—
218#97—521no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13—42no—
227C2×C13—42no—
228C2×C13#147211yescharacteristic
229C2×C13#212011yescharacteristic
230C2×C13#212111yescharacteristic
231C24C22⋊Dic1311yescharacteristic
232C24C22×Dic1311yescharacteristic
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—41no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—42no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4C22⋊Dic1311yescharacteristic
251C22×C4C22⋊Dic1311yescharacteristic
252C22×C4C22⋊Dic1311yescharacteristic
253C22×C4C2×C22⋊D1311yescharacteristic
254C22×C4C2×C22⋊D1311yescharacteristic
255C2×C8—522no—
256C2×C8—522no—
257C2×C8—1042no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—81no—
271C42—21no—
272C42—21no—
273C13#1157811yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#8807612yes—
283C23#8820212yes—
284C23C2×C22⋊Dic1311yescharacteristic
285D4—44no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—82no—
315C2×C4#8807411yescharacteristic
316C2×C4#8807411yescharacteristic
317C8—1042no—
318C8—1042no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22C2×#8807411yescharacteristic
332C22C2×#8807611yescharacteristic
333C22#1171889511yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—42no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2#1311320011yescharacteristic
349C2#1311647711yescharacteristic
350C2#1311648211yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2579C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenter#2579D13
hypocenterC13#11578
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2579

Complements

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

NH ≅ G/Ntype
3. #13112784C2semidirect
4. #13112784C2semidirect
273. C13#11578semidirect

Maximal subgroups

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

subgroupindex
#131131772
#131131542
#131127842
C13×#25792
#1157813