Finite Group Databasebeta

← #15758550

Subgroups — #15758550

Order 3328.

530 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718587C211yesmaximal, characteristic
2#13114598C211yesmaximal, characteristic
3C2×#11718135C212yesmaximal, complemented
4#13112717C212yesmaximal, complemented
5C13×#2851C211yesmaximal, characteristic
6C2×C13×#125C2211yescharacteristic
7C22×C42×C13C2211yescharacteristic
8C13×#389C411yescharacteristic
9C13×#389C411yescharacteristic
10C13×#387—21no—
11C13×#387—21no—
12C13×#385—21no—
13C13×#385—21no—
14C13×#382C2211yescharacteristic
15C13×#380C411yescharacteristic
16C13×#380C411yescharacteristic
17C2×C22⋊#1055—21no—
18C2×C22⋊#1055—21no—
19#11718587—24no—
20C2×C4⋊#1055—21no—
21C2×#88043C2212yes—
22C2×#88043C2212yes—
23#11718135—24no—
24#11718116—21no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×#125—22no—
29C13×#125—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C42×C13—22no—
41C2×C42×C13—22no—
42C2×C42×C13C2×C411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13C2311yescharacteristic
46C22×#1055—22no—
47C22×#1055—22no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C22⋊#1055—24no—
55C22⋊#1055—24no—
56C4⋊#1055—24no—
57#88043—22no—
58#88043—22no—
59#88043—22no—
60#88043D414yes—
61#9126—131nomaximal, Sylow
62C24×C13C22⋊C411yescharacteristic
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—41no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C42×C13—22no—
95C42×C13—21no—
96C42×C13—22no—
97C42×C13—21no—
98C42×C13C2×D412yes—
99C42×C13#4112yes—
100C2×#1055—24no—
101C2×#1055—24no—
102C2×#1055—42no—
103C2×#1055—42no—
104C2×#1055—42no—
105C2×#1055—42no—
106C2×#432—131no—
107#2851D1311yescharacteristic
108#1749—131no—
109C2×#330—132no—
110#1295—132no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13#10112yes—
118C23×C13C2×C22⋊C411yescharacteristic
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—44no—
134C2×C4×C13—44no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
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—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13#10412yes—
150C2×C4×C13C4×D412yes—
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13#12112yes—
153C2×C4×C13#12311yescharacteristic
154#1055—44no—
155#1055—44no—
156C2×#125C2×D1311yescharacteristic
157C22×C42C2×D1311yescharacteristic
158#432—264no—
159C2×C4⋊C8—261no—
160C2×C22⋊C8—261no—
161C2×C22⋊C8—261no—
162C2×#97—132no—
163C2×#97—132no—
164#389Dic1311yescharacteristic
165#389Dic1311yescharacteristic
166#387—21no—
167#387—21no—
168#385—21no—
169#385—21no—
170#382C2×D1311yescharacteristic
171#380Dic1311yescharacteristic
172#380Dic1311yescharacteristic
173#336—261no—
174#330—264no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13#38611yescharacteristic
183C22×C13C2×#10111yescharacteristic
184C22×C13#41311yescharacteristic
185C22×C13C2×#10411yescharacteristic
186C22×C13#42111yescharacteristic
187C22×C13#42111yescharacteristic
188C22×C13#42111yescharacteristic
189C4×C13—22no—
190C4×C13—22no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—22no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—81no—
197C4×C13—81no—
198C4×C13—81no—
199C4×C13—81no—
200C23×C4C2×Dic1311yescharacteristic
201C23×C4C22⋊D1311yescharacteristic
202C23×C4C22⋊D1311yescharacteristic
203C22×C8—262no—
204C22×C8—262no—
205#125—22no—
206#125—22no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C2×Dic1311yescharacteristic
212C2×C4⋊C4C2×Dic1311yescharacteristic
213C2×C4⋊C4C2×Dic1311yescharacteristic
214C2×C4⋊C4C2×Dic1311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42C2×Dic1311yescharacteristic
220C2×C42C22⋊D1311yescharacteristic
221C2×C42C22⋊D1311yescharacteristic
222C2×C42C22×D1311yescharacteristic
223C4⋊C8—264no—
224C22⋊C8—264no—
225C22⋊C8—264no—
226#97—134no—
227#97—262no—
228#97—262no—
229#97—262no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236C2×C13—42no—
237C2×C13#152911yescharacteristic
238C2×C13#153111yescharacteristic
239C2×C13#153411yescharacteristic
240C2×C13#153511yescharacteristic
241C2×C13#187111yescharacteristic
242C2×C13#189711yescharacteristic
243C2×C13#190111yescharacteristic
244C24C22⋊Dic1311yescharacteristic
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4C22⋊Dic1311yescharacteristic
260C22×C4C22⋊Dic1311yescharacteristic
261C22×C4C22⋊Dic1311yescharacteristic
262C22×C4C22×Dic1311yescharacteristic
263C22×C4C2×C22⋊D1311yescharacteristic
264C22×C4C2×C22⋊D1311yescharacteristic
265C2×C8—264no—
266C2×C8—264no—
267C2×C8—522no—
268C2×C8—522no—
269C2×C8—522no—
270C2×C8—522no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C42—22no—
283C42—21no—
284C42—21no—
285C42—22no—
286C42D4×D1312yes—
287C42#612912yes—
288C13#912611yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#8807612yes—
296C23C2×C22⋊Dic1311yescharacteristic
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—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4#8807712yes—
328C2×C4D4×Dic1312yes—
329C2×C4#8818911yescharacteristic
330C2×C4#8819111yescharacteristic
331C2×C4#8819312yes—
332C8—524no—
333C8—524no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22#1171888111yescharacteristic
342C22C2×#8807611yescharacteristic
343C22C2×#8807711yescharacteristic
344C22#1171889711yescharacteristic
345C22#1171889711yescharacteristic
346C22#1171889711yescharacteristic
347C22#1171889811yescharacteristic
348C4—22no—
349C4—22no—
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—81no—
359C2—42no—
360C2#1311344311yescharacteristic
361C2#1311345111yescharacteristic
362C2#1311346311yescharacteristic
363C2#1311346711yescharacteristic
364C2#1311513911yescharacteristic
365C2#1311528511yescharacteristic
366C2#1311530511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2851C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2851D13
hypocenterC13#9126
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. C2×#11718135C2semidirect
4. #13112717C2semidirect
288. C13#9126semidirect

Maximal subgroups

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

subgroupindex
C2×#117185872
#131145982
C2×#117181352
#131127172
C13×#28512
#912613