Finite Group Databasebeta

← #15760640

Subgroups — #15760640

Order 3328.

512 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 93 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#13119322C211yesmaximal, characteristic
2#13117437C211yesmaximal, characteristic
3#13114914C211yesmaximal, characteristic
4#13113369C211yesmaximal, characteristic
5#13112690C211yesmaximal, characteristic
6#13112688C211yesmaximal, characteristic
7C13×#1511C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C4⋊Dic13C2211yescharacteristic
10C13×#407C2211yescharacteristic
11C13×#381C2211yescharacteristic
12#11718891C412yescomplemented
13#11718872C2211yescharacteristic
14C4×C22⋊Dic13C2211yescharacteristic
15#11718868C2211yescharacteristic
16#11718647—22no—
17#11718638C412yescomplemented
18#11718604—21no—
19#11718604—21no—
20#11718603—21no—
21C22⋊C4×Dic13—21no—
22#11718315—22no—
23#11718314—22no—
24C13×#328—22no—
25#11718146—22no—
26#11718130—22no—
27C22×Q8×C13C2×C411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C23×Dic13D411yescharacteristic
30C23×Dic13D411yescharacteristic
31C2×C13×M16—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C13×C22⋊Q8—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C22⋊Dic13—21no—
41C2×C22⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13C2×C412yes—
47C2×C4⋊Dic13D412yes—
48C2×#6101—22no—
49C2×C4×Dic13—22no—
50C2×C4×Dic13C2×C412yes—
51C2×#6099—21no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8—21no—
54C13×#95—21no—
55C13×#95D412yes—
56#88071—22no—
57#88071—22no—
58#88071—21no—
59#88071—21no—
60#88071—22no—
61#88071—22no—
62#88071—22no—
63#88071—22no—
64#88071D412yes—
65C22⋊#1055—21no—
66C22⋊#1055—21no—
67#9460—131nomaximal, Sylow
68C24×C13C2×D411yescharacteristic
69C2×Q8×C13—21no—
70C2×Q8×C13—21no—
71C2×Q8×C13—42no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—22no—
75C22×C4×C13—42no—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—21no—
86C22×Dic13—22no—
87C22×Dic13—22no—
88C22×Dic13—42no—
89C22×Dic13—42no—
90C22×Dic13C22⋊C412yes—
91C22×Dic13C22⋊C412yes—
92C13×M16—42no—
93C2×C8×C13—41no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C22⋊C4—42no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C22⋊Dic13—42no—
102C22⋊Dic13—42no—
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4⋊Dic13—22no—
106C4⋊Dic13—22no—
107#6101—82no—
108C4×Dic13—42no—
109C4×Dic13—82no—
110#6099—42no—
111C2×#1055—41no—
112#2503—131no—
113#2313—131no—
114#1821—131no—
115#1511—131no—
116#1511D1311yescharacteristic
117#1284—131no—
118#1284—131no—
119C23×C13—22no—
120C23×C13—22no—
121C23×C13—41no—
122C23×C13C2×C22⋊C411yescharacteristic
123C23×C13#12011yescharacteristic
124C23×C13#12311yescharacteristic
125Q8×C13—81no—
126Q8×C13—81no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13C4×D411yescharacteristic
141C2×C4×C13C4×D411yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13—42no—
151C2×Dic13—42no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13—42no—
156C2×Dic13—81no—
157C2×Dic13—81no—
158C8×C13—81no—
159#1055—81no—
160C2×C22⋊Q8C2×D1311yescharacteristic
161C22×C4⋊C4—131no—
162#407—131no—
163#407C2×D1311yescharacteristic
164#400—262no—
165#391—132no—
166#387—262no—
167#387—262no—
168#382—132no—
169#381—131no—
170#381—261no—
171#381—261no—
172#381C2×D1311yescharacteristic
173#380—261no—
174C4×C22⋊C4—131no—
175C4×C22⋊C4—261no—
176#343—262no—
177#328—22no—
178#328—262no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—44no—
187C22×C13#38611yescharacteristic
188C22×C13#41012yes—
189C22×C13#45512yes—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—82no—
195C4×C13—81no—
196C4×C13—81no—
197Dic13—42no—
198Dic13—42no—
199Dic13—82no—
200Dic13—82no—
201C22×Q8C4×D1311yescharacteristic
202C23×C4—131no—
203C23×C4—131no—
204C23×C4C22×D1311yescharacteristic
205C2×M16—21no—
206C2×M16—261no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—132no—
213C2×C4⋊C4—132no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—262no—
219C2×C4⋊C4C4×D1311yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—261no—
223C2×C22⋊C4—261no—
224C2×C42—132no—
225C2×C42—262no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8—261no—
229C22⋊C8—261no—
230#95—21no—
231#95—132no—
232#95—262no—
233#95—262no—
234#95—262no—
235#95—262no—
236#95—262no—
237#95—262no—
238#95—261no—
239#95—261no—
240#95C22⋊D1312yes—
241C2×C13—22no—
242C2×C13—22no—
243C2×C13—41no—
244C2×C13#188511yescharacteristic
245C2×C13#189911yescharacteristic
246C2×C13#191211yescharacteristic
247C24D4×D1311yescharacteristic
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—42no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—42no—
255C22×C4—132no—
256C22×C4—132no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—262no—
262C22×C4—262no—
263C22×C4—522no—
264C22×C4—522no—
265C22×C4C2×C4×D1311yescharacteristic
266C22×C4#612711yescharacteristic
267C22×C4D4×D1311yescharacteristic
268C22×C4D4×D1311yescharacteristic
269C22×C4#612911yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271M16—42no—
272M16—522no—
273C2×C8—41no—
274C2×C8—521no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C4⋊C4—262no—
283C4⋊C4—1042no—
284C22⋊C4—42no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—522no—
288C22⋊C4—522no—
289C42—522no—
290C42—1042no—
291C13#946011yescharacteristic, complemented, Sylow
292C23—22no—
293C23—22no—
294C23—41no—
295C23C22⋊C4×D1311yescharacteristic
296C23#8813711yescharacteristic
297C23#8819111yescharacteristic
298Q8—81no—
299Q8—81no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—262no—
314C2×C4—262no—
315C2×C4—522no—
316C2×C4—522no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4—522no—
322C2×C4—522no—
323C2×C4—522no—
324C2×C4—522no—
325C2×C4—1041no—
326C2×C4—1041no—
327C2×C4#8813511yescharacteristic
328C2×C4#8813811yescharacteristic
329C2×C4C4×C22⋊D1311yescharacteristic
330C2×C4#8819211yescharacteristic
331C8—81no—
332C8—1041no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—44no—
341C22#1171840112yes—
342C22#1171861711yescharacteristic
343C22#1171886312yes—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—81no—
350C4—81no—
351C4—522no—
352C4—522no—
353C4—1042no—
354C4—1042no—
355C2—22no—
356C2—22no—
357C2—41no—
358C2#1311522111yescharacteristic
359C2#1311529111yescharacteristic
360C2#1311537011yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1511C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1511D13
hypocenterC13#9460
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
12. #11718891C4semidirect
17. #11718638C4semidirect
291. C13#9460semidirect

Maximal subgroups

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

subgroupindex
#131193222
#131174372
#131149142
#131133692
#131126902
#131126882
C13×#15112
#946013