Finite Group Databasebeta

← #15761938

Subgroups — #15761938

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114689C211yesmaximal, characteristic, complemented
2#13114585C211yesmaximal, characteristic, complemented
3C2×#11718135C212yesmaximal, complemented
4C2×#11718132C212yesmaximal
5C13×#2861C211yesmaximal, characteristic
6C2×C13×#125C2211yescharacteristic
7C2×C13×#124C2211yescharacteristic
8C13×#391C411yescharacteristic
9C13×#391C411yescharacteristic
10C13×#390C411yescharacteristic
11C13×#390C411yescharacteristic
12C13×#388—21no—
13C13×#388—21no—
14C13×#388—21no—
15C13×#388—21no—
16C43×C13C2211yescharacteristic
17C2×C4⋊#1055—21no—
18C2×#88043C2212yes—
19C2×#88043C2212yes—
20#11718135—24no—
21#11718132—24no—
22#11718116—21no—
23#11718116—21no—
24#11718116—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13C2×C411yescharacteristic
27C13×#125—22no—
28C13×#125—22no—
29C13×#124—22no—
30C13×#124—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
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⋊C4—21no—
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×C42×C13D411yescharacteristic
47C2×C42×C13C2311yescharacteristic
48C22×#1055—22no—
49C22×#1055—22no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C4⋊#1055—24no—
55#88043—22no—
56#88043—22no—
57#88043—22no—
58#88043D414yes—
59#9688—131nomaximal, Sylow
60C24×C13—21no—
61C2×Q8×C13—22no—
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C2×D4×C13—22no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C42×C13—22no—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13—41no—
93C42×C13—41no—
94C42×C13—41no—
95C42×C13C2×D412yes—
96C42×C13#4112yes—
97C2×#1055—24no—
98C2×#1055—24no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#1055—42no—
102C2×#1055—42no—
103#2861D1311yescharacteristic
104#1767—131no—
105#1745—131no—
106C2×#330—132no—
107C2×#329—132no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13C2×C22⋊C411yescharacteristic
116Q8×C13—82no—
117D4×C13—82no—
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—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
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#10412yes—
145C2×C4×C13C4×D412yes—
146C2×C4×C13#12112yes—
147C2×C4×C13#12411yescharacteristic
148C2×C4×C13#12711yescharacteristic
149#1055—44no—
150#1055—44no—
151C2×#125C2×D1311yescharacteristic
152C2×#124C2×D1311yescharacteristic
153C2×C4⋊C8—261no—
154C2×#97—132no—
155C2×#97—132no—
156#391Dic1311yescharacteristic
157#391Dic1311yescharacteristic
158#390Dic1311yescharacteristic
159#390Dic1311yescharacteristic
160#388—21no—
161#388—21no—
162#388—21no—
163#388—21no—
164C43C2×D1311yescharacteristic
165#336—261no—
166#336—261no—
167#336—261no—
168#330—264no—
169#329—264no—
170C22×C13—81no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13#39011yescharacteristic
178C22×C13#41311yescharacteristic
179C22×C13#41311yescharacteristic
180C22×C13C2×#10411yescharacteristic
181C22×C13#42111yescharacteristic
182C22×C13#42111yescharacteristic
183C22×C13#42111yescharacteristic
184C4×C13—22no—
185C4×C13—22no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—22no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13—81no—
195C22×Q8C2×Dic1311yescharacteristic
196C22×D4C2×Dic1311yescharacteristic
197C22×C8—262no—
198C22×C8—262no—
199#125—22no—
200#125—22no—
201#124—22no—
202#124—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic1311yescharacteristic
206C2×C4⋊C4C2×Dic1311yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42C2×Dic1311yescharacteristic
214C2×C42C2×Dic1311yescharacteristic
215C2×C42C22⋊D1311yescharacteristic
216C2×C42C22⋊D1311yescharacteristic
217C2×C42C22⋊D1311yescharacteristic
218C2×C42C22⋊D1311yescharacteristic
219C2×C42C22×D1311yescharacteristic
220C4⋊C8—264no—
221#97—134no—
222#97—262no—
223#97—262no—
224#97—262no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229C2×C13—161no—
230C2×C13#152911yescharacteristic
231C2×C13#153211yescharacteristic
232C2×C13#153511yescharacteristic
233C2×C13#153511yescharacteristic
234C2×C13#196311yescharacteristic
235C2×C13#196711yescharacteristic
236C2×C13#198011yescharacteristic
237C24—21no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×D4—22no—
242C2×D4—41no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4C22⋊Dic1311yescharacteristic
249C22×C4C22⋊Dic1311yescharacteristic
250C22×C4C22⋊Dic1311yescharacteristic
251C22×C4C22×Dic1311yescharacteristic
252C22×C4C2×C22⋊D1311yescharacteristic
253C22×C4C2×C22⋊D1311yescharacteristic
254C2×C8—264no—
255C2×C8—264no—
256C2×C8—522no—
257C2×C8—522no—
258C2×C8—522no—
259C2×C8—522no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C4⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—41no—
272C42—22no—
273C42—41no—
274C42—41no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42D4×D1312yes—
279C42#612912yes—
280C13#968811yescharacteristic, complemented, Sylow
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23C2×C22⋊Dic1311yescharacteristic
289Q8—82no—
290D4—82no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
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—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
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#8807712yes—
318C2×C4D4×Dic1312yes—
319C2×C4#8819011yescharacteristic
320C2×C4#8819212yes—
321C2×C4#8819411yescharacteristic
322C8—524no—
323C8—524no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22#1171888211yescharacteristic
332C22C2×#8807711yescharacteristic
333C22#1171889711yescharacteristic
334C22#1171889711yescharacteristic
335C22#1171889711yescharacteristic
336C22#1171889811yescharacteristic
337C22#1171889811yescharacteristic
338C4—22no—
339C4—22no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—161no—
350C2#1311344311yescharacteristic
351C2#1311345611yescharacteristic
352C2#1311346711yescharacteristic
353C2#1311346711yescharacteristic
354C2#1311566911yescharacteristic
355C2#1311568611yescharacteristic
356C2#1311575611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2861C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2861D13
hypocenterC13#9688
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #2861

Complements

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

NH ≅ G/Ntype
1. #13114689C2semidirect
2. #13114585C2semidirect
3. C2×#11718135C2semidirect
280. C13#9688semidirect

Maximal subgroups

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

subgroupindex
#131146892
#131145852
C2×#117181352
C2×#117181322
C13×#28612
#968813