Finite Group Databasebeta

← #14724505

Subgroups — #14724505

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077592C212yesmaximal, complemented
2#13067467C212yesmaximal, complemented
3#13067460C212yesmaximal, complemented
4#13067453C212yesmaximal, complemented
5#13067446C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067076C212yesmaximal, complemented
8C2×#10622092C211yesmaximal, characteristic, complemented
9C11×#3168C211yesmaximal, characteristic
10C11×#529C2212yes—
11C11×#499C411yescharacteristic
12C11×#495C411yescharacteristic
13C11×#488C412yes—
14C11×#467C411yescharacteristic
15C11×#466C411yescharacteristic
16C11×#465C412yes—
17C4×C11×Q16C2211yescharacteristic
18C4×C11×SD16C2212yes—
19C4×C11×D8C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21#10622637C2212yes—
22Q8×C11⋊C8C2212yes—
23#10622625C2212yes—
24#10622624—22no—
25D4×C11⋊C8—22no—
26D4×C11⋊C8C2212yes—
27#10622613—22no—
28#10622610—22no—
29#10622539C2212yes—
30C2×C4×C11⋊C8C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32Q8⋊(C11⋊C8)C2212yes—
33Q8⋊(C11⋊C8)C2212yes—
34D4⋊(C11⋊C8)C2212yes—
35D4⋊(C11⋊C8)C2212yes—
36#10622096C2212yes—
37#10622095C2211yescharacteristic
38#10622095C2211yescharacteristic
39#10622092C2212yes—
40#10622092C2212yes—
41C2×C11×Q16C2×C411yescharacteristic
42C2×C11×SD16C2×C412yes—
43C2×C11×D8C2×C411yescharacteristic
44C22×C8×C11C2×C411yescharacteristic
45C22×C8×C11C2×C411yescharacteristic
46C11×#126—22no—
47C11×#125C2×C412yes—
48C11×#124C2×C412yes—
49C11×#123—22no—
50C11×C22⋊Q8C2×C412yes—
51C11×#121C2×C412yes—
52C4×Q8×C11C2312yes—
53C4×D4×C11—22no—
54C4×D4×C11C2312yes—
55C11×#117—22no—
56C2×C42×C11C2311yescharacteristic
57C2×#4318—22no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—22no—
60C22×C11⋊C8D412yes—
61C11×#107C2×C411yescharacteristic
62C11×#107C2×C411yescharacteristic
63C11×#106C2×C412yes—
64C11×#103C2×C412yes—
65C11×#103C2×C412yes—
66C11×#102C2×C412yes—
67C11×#102C2×C412yes—
68C4×C8×C11C2×C411yescharacteristic
69C4×C8×C11C2×C411yescharacteristic
70C4×C8×C11C2311yescharacteristic
71C4×C8×C11C2311yescharacteristic
72C22⋊(C11⋊C8)—22no—
73C22⋊(C11⋊C8)—22no—
74C22⋊(C11⋊C8)—22no—
75C4⋊(C11⋊C8)—22no—
76C4⋊(C11⋊C8)—22no—
77C4⋊(C11⋊C8)C2312yes—
78C4⋊(C11⋊C8)C2312yes—
79#66867—22no—
80#66867—22no—
81C4×C11⋊C8—21no—
82C4×C11⋊C8—22no—
83C4×C11⋊C8D411yescharacteristic
84C4×C11⋊C8D411yescharacteristic
85C4×C11⋊C8C2312yes—
86C4×C11⋊C8C2312yes—
87#17978—111nomaximal, Sylow
88C2×Q8×C11C22×C412yes—
89C2×D4×C11—22no—
90C2×D4×C11C22×C412yes—
91C22×C4×C11—22no—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C11×Q16—41no—
96C11×SD16—42no—
97C11×D8—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11C22×C411yescharacteristic
101C2×C8×C11C22×C411yescharacteristic
102C2×C8×C11C22×C411yescharacteristic
103C2×C8×C11C22×C411yescharacteristic
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4C22×C412yes—
109C11×C4⋊C4C22×C412yes—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—22no—
114C11×C22⋊C4—22no—
115C42×C11—22no—
116C42×C11C22×C411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4318—44no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—42no—
126C2×C11⋊C8—44no—
127C2×C11⋊C8C2×D412yes—
128C2×C11⋊C8C2×D412yes—
129#3168D1111yescharacteristic
130#2966—112no—
131#1584—112no—
132#1583—112no—
133#1582—112no—
134#1581—112no—
135#1568—111no—
136#1494—112no—
137C2×#322—111no—
138C23×C11—22no—
139C23×C11C4×D411yescharacteristic
140Q8×C11—22no—
141Q8×C11—22no—
142D4×C11—22no—
143D4×C11—22no—
144D4×C11—44no—
145C2×C4×C11—22no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C23×C411yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C2×#4111yescharacteristic
160C8×C11—21no—
161C8×C11—21no—
162C8×C11—21no—
163C8×C11—21no—
164C11⋊C8—22no—
165C11⋊C8—42no—
166C11⋊C8—42no—
167C11⋊C8—42no—
168C11⋊C8#13514yes—
169#529C2×D1112yes—
170#499Dic1111yescharacteristic
171#495Dic1111yescharacteristic
172#488Dic1112yes—
173#467Dic1111yescharacteristic
174#466Dic1111yescharacteristic
175#465Dic1112yes—
176#446—112no—
177C8×Q8—112no—
178C4×Q16C2×D1111yescharacteristic
179C4×SD16C2×D1112yes—
180C4×D8C2×D1111yescharacteristic
181#436—112no—
182#435—222no—
183C8×D4—112no—
184C8×D4—222no—
185#433—222no—
186#432—112no—
187#405—222no—
188C2×C4×C8—111no—
189C2×C4×C8—111no—
190C2×C4×C8C2×D1111yescharacteristic
191#335—112no—
192#334—111no—
193#334—111no—
194Q8⋊C8—112no—
195Q8⋊C8—112no—
196D4⋊C8—112no—
197D4⋊C8—112no—
198#322—112no—
199#322—112no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—42no—
203C22×C11—42no—
204C22×C11—42no—
205C22×C11#44412yes—
206C22×C11C2×C4×D411yescharacteristic
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—42no—
212C4×C11—42no—
213C4×C11—42no—
214C4×C11#56811yescharacteristic
215C4×C11#56811yescharacteristic
216C4×C11C2×#13512yes—
217C2×Q16C2×Dic1111yescharacteristic
218C2×SD16C2×Dic1112yes—
219C2×D8C2×Dic1111yescharacteristic
220C2×M16—222no—
221C22×C8—112no—
222C22×C8—222no—
223C22×C8—221no—
224C22×C8C2×Dic1111yescharacteristic
225C22×C8C2×Dic1111yescharacteristic
226#126—22no—
227#125C2×Dic1112yes—
228#124C2×Dic1112yes—
229#123—22no—
230C22⋊Q8C2×Dic1112yes—
231#121C2×Dic1112yes—
232C4×Q8C22×D1112yes—
233C4×D4—22no—
234C4×D4C22×D1112yes—
235#117—22no—
236C2×C42C22×D1111yescharacteristic
237#107C2×Dic1111yescharacteristic
238#107C2×Dic1111yescharacteristic
239#106C2×Dic1112yes—
240C4⋊C8—112no—
241C4⋊C8—112no—
242C4⋊C8—222no—
243C4⋊C8—222no—
244#103C2×Dic1112yes—
245#103C2×Dic1112yes—
246#102C2×Dic1112yes—
247#102C2×Dic1112yes—
248C22⋊C8—222no—
249C22⋊C8—222no—
250C22⋊C8—222no—
251#97—222no—
252#97—222no—
253C4×C8—111no—
254C4×C8—111no—
255C4×C8—112no—
256C4×C8—112no—
257C4×C8—222no—
258C4×C8—221no—
259C4×C8C2×Dic1111yescharacteristic
260C4×C8C2×Dic1111yescharacteristic
261C4×C8C22×D1111yescharacteristic
262C4×C8C22×D1111yescharacteristic
263C2×C11—22no—
264C2×C11—82no—
265C2×C11#293211yescharacteristic
266C2×C11C4×#13511yescharacteristic
267C2×C11C2×#44411yescharacteristic
268C2×Q8C22×Dic1112yes—
269C2×D4—22no—
270C2×D4C22×Dic1112yes—
271C22×C4—22no—
272C22×C4D4×D1111yescharacteristic
273C22×C4#434111yescharacteristic
274C22×C4C22×Dic1111yescharacteristic
275Q16—41no—
276SD16—42no—
277D8—41no—
278M16—444no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—112no—
282C2×C8—112no—
283C2×C8—224no—
284C2×C8—222no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—444no—
288C2×C8—442no—
289C2×C8C22×Dic1111yescharacteristic
290C2×C8C22×Dic1111yescharacteristic
291C2×C8C22×Dic1111yescharacteristic
292C2×C8C22×Dic1111yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4C22×Dic1112yes—
298C4⋊C4C22×Dic1112yes—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C42—22no—
305C42D4×D1111yescharacteristic
306C42#434111yescharacteristic
307C42C22×Dic1111yescharacteristic
308C42C23×D1111yescharacteristic
309C11#1797811yescharacteristic, complemented, Sylow
310C23—22no—
311C23D4×Dic1111yescharacteristic
312Q8—22no—
313Q8—22no—
314D4—22no—
315D4—22no—
316D4—44no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4D4×Dic1111yescharacteristic
327C2×C4D4×Dic1111yescharacteristic
328C2×C4D4×Dic1111yescharacteristic
329C2×C4C2×D4×D1111yescharacteristic
330C2×C4C2×#434111yescharacteristic
331C2×C4C23×Dic1111yescharacteristic
332C8—21no—
333C8—21no—
334C8—21no—
335C8—21no—
336C8—114no—
337C8—222no—
338C8—442no—
339C8—442no—
340C8—442no—
341C22—21no—
342C22—21no—
343C22—42no—
344C22—42no—
345C22—42no—
346C22#1062281012yes—
347C22C2×D4×Dic1111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—42no—
354C4—42no—
355C4D11×#13512yes—
356C4#1062335011yescharacteristic
357C4#1062335011yescharacteristic
358C2—22no—
359C2—82no—
360C2#1307733411yescharacteristic
361C2#135×Dic1111yescharacteristic
362C2C2×#1062281011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3168C2
socleC22×C11C2×C4×D4
prime radicalC11×#466C4
cosocleC42×C11C24
hypercenter#3168D11
hypocenterC11#17978
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13077592C2semidirect
2. #13067467C2semidirect
3. #13067460C2semidirect
4. #13067453C2semidirect
5. #13067446C2semidirect
6. #13067379C2semidirect
7. #13067076C2semidirect
8. C2×#10622092C2semidirect
309. C11#17978semidirect

Maximal subgroups

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

subgroupindex
#130775922
#130674672
#130674602
#130674532
#130674462
#130673792
#130670762
C2×#106220922
C11×#31682
#1797811