Finite Group Databasebeta

← #15760584

Subgroups — #15760584

Order 3328.

486 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 107 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#13123921C211yesmaximal, characteristic, complemented
2#13113460C212yesmaximal
3#13113180C211yesmaximal, characteristic, complemented
4#13112692C212yesmaximal, complemented
5C13×#2545C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C411yescharacteristic
7C2×C13×#124C411yescharacteristic
8C2×C13×#124C2211yescharacteristic
9C2×C4×Q8×C13C2211yescharacteristic
10C13×#396—21no—
11C13×#396—21no—
12C13×#391C411yescharacteristic
13C13×#390C411yescharacteristic
14C13×#388—21no—
15C13×#388—21no—
16C4×C13×C4⋊C4C2211yescharacteristic
17#11718685—24no—
18#11718587—21no—
19#11718587C2212yes—
20#11718587C2212yes—
21#11718586—21no—
22#11718132—24no—
23#11718120—21no—
24#11718120—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×Q8×C13C2×C411yescharacteristic
27C22×D4×C13C2×C411yescharacteristic
28C13×C4⋊Q8—42no—
29C13×#124—22no—
30C13×#124—22no—
31C13×#124—42no—
32C4×Q8×C13—22no—
33C4×Q8×C13—22no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C42×C13C2×C411yescharacteristic
47C2×C42×C13C2×C411yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×C42×C13D411yescharacteristic
50C2×C42×C13C2311yescharacteristic
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C22⋊#1055—22no—
55C22⋊#1055—22no—
56C4⋊#1055—22no—
57C4⋊#1055—22no—
58C4⋊#1055—22no—
59C4⋊#1055—22no—
60#88043—22no—
61#88043—22no—
62#88043D414yes—
63C4×#1055—22no—
64#9448—131nomaximal, Sylow
65C24×C13—21no—
66C2×Q8×C13—22no—
67C2×Q8×C13—22no—
68C2×Q8×C13—22no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×D4×C13—22no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—42no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—41no—
98C42×C13—21no—
99C42×C13—21no—
100C42×C13—21no—
101C42×C13—21no—
102C42×C13—41no—
103C42×C13—41no—
104C42×C13C2×D412yes—
105C42×C13#4112yes—
106C2×#1055—24no—
107C2×#1055—42no—
108#2983—131no—
109#2545D1311yescharacteristic
110#1533—132no—
111#1467—131no—
112#1285—132no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13C2×C22⋊C411yescharacteristic
121Q8×C13—44no—
122Q8×C13—82no—
123D4×C13—82no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—22no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
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—41no—
145C2×C4×C13—41no—
146C2×C4×C13#10012yes—
147C2×C4×C13C4×D412yes—
148C2×C4×C13#12011yescharacteristic
149C2×C4×C13#12112yes—
150C2×C4×C13#12311yescharacteristic
151#1055—44no—
152#1055—82no—
153C2×C4⋊Q8Dic1311yescharacteristic
154C2×#124Dic1311yescharacteristic
155C2×#124C2×D1311yescharacteristic
156C2×C4×Q8C2×D1311yescharacteristic
157#446—264no—
158#432—132no—
159#432—132no—
160#432—261no—
161#431—261no—
162#396—21no—
163#396—21no—
164#391Dic1311yescharacteristic
165#390Dic1311yescharacteristic
166#388—21no—
167#388—21no—
168C4×C4⋊C4C2×D1311yescharacteristic
169#329—264no—
170#324—261no—
171#324—261no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13#38611yescharacteristic
182C22×C13C2×#10011yescharacteristic
183C22×C13#41311yescharacteristic
184C4×C13—22no—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—42no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—81no—
194C4×C13—81no—
195C22×Q8C2×Dic1311yescharacteristic
196C22×Q8C2×Dic1311yescharacteristic
197C22×D4C2×Dic1311yescharacteristic
198C4⋊Q8—42no—
199#124—22no—
200#124—22no—
201#124—42no—
202C4×Q8—22no—
203C4×Q8—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×Dic1311yescharacteristic
208C2×C4⋊C4C22⋊D1311yescharacteristic
209C2×C4⋊C4C22⋊D1311yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C42C2×Dic1311yescharacteristic
217C2×C42C2×Dic1311yescharacteristic
218C2×C42C22⋊D1311yescharacteristic
219C2×C42C22⋊D1311yescharacteristic
220C2×C42C22×D1311yescharacteristic
221C4⋊C8—262no—
222C4⋊C8—262no—
223C4⋊C8—262no—
224C4⋊C8—262no—
225C22⋊C8—262no—
226C22⋊C8—262no—
227#97—134no—
228#97—262no—
229#97—262no—
230C4×C8—262no—
231#95—21no—
232#95—21no—
233#95—21no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—161no—
237C2×C13#188411yescharacteristic
238C2×C13#190011yescharacteristic
239C2×C13#191211yescharacteristic
240C24—21no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×D4—22no—
248C2×D4—41no—
249C2×D4—41no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22⋊Dic1311yescharacteristic
255C22×C4C22⋊Dic1311yescharacteristic
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22×Dic1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260C2×C8—264no—
261C2×C8—522no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—42no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—41no—
280C42—41no—
281C42D4×D1312yes—
282C42#612912yes—
283C13#944811yescharacteristic, complemented, Sylow
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23C2×C22⋊Dic1311yescharacteristic
292Q8—44no—
293Q8—82no—
294D4—82no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
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#8807312yes—
318C2×C4D4×Dic1312yes—
319C2×C4#8818911yescharacteristic
320C2×C4#8819111yescharacteristic
321C2×C4#8819312yes—
322C8—524no—
323C8—1042no—
324C22—21no—
325C22—21no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22C2×#8807311yescharacteristic
334C22#1171888111yescharacteristic
335C22#1171889811yescharacteristic
336C4—22no—
337C4—22no—
338C4—22no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C2—21no—
348C2—21no—
349C2—161no—
350C2#1311522011yescharacteristic
351C2#1311530011yescharacteristic
352C2#1311537411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2545C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2545D13
hypocenterC13#9448
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2545

Complements

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

NH ≅ G/Ntype
1. #13123921C2semidirect
3. #13113180C2semidirect
4. #13112692C2semidirect
283. C13#9448semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131134602
#131131802
#131126922
C13×#25452
#944813