Finite Group Databasebeta

← #14725830

Subgroups — #14725830

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077776C212yesmaximal, complemented
2#13067530C211yesmaximal, characteristic, complemented
3#13067525C211yesmaximal, characteristic, complemented
4#13067460C212yesmaximal, complemented
5#13067453C212yesmaximal, complemented
6#13067440C211yesmaximal, characteristic, complemented
7#13067435C211yesmaximal, characteristic, complemented
8C2×#10622095C211yesmaximal, characteristic, complemented
9#13067029C212yesmaximal, complemented
10#13066905C211yesmaximal, characteristic, complemented
11C11×#3168C211yesmaximal, characteristic
12C11×#529C2212yes—
13C11×#499C411yescharacteristic
14C11×#495C411yescharacteristic
15C11×#488C412yes—
16C11×#467C411yescharacteristic
17C11×#466C411yescharacteristic
18C11×#465C412yes—
19C4×C11×Q16C2211yescharacteristic
20C4×C11×SD16C2212yes—
21C4×C11×D8C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23#10622637C2212yes—
24Q8×C11⋊C8C2212yes—
25#10622625C2212yes—
26#10622624—22no—
27D4×C11⋊C8—22no—
28D4×C11⋊C8C2212yes—
29#10622613—22no—
30#10622612—22no—
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2212yes—
33C4×#4318C2211yescharacteristic
34Q8⋊(C11⋊C8)C2212yes—
35Q8⋊(C11⋊C8)C2212yes—
36D4⋊(C11⋊C8)C2212yes—
37D4⋊(C11⋊C8)C2212yes—
38#10622095C2211yescharacteristic
39#10622095C2211yescharacteristic
40#10622095C2212yes—
41#10622093C2211yescharacteristic
42#10622093C2211yescharacteristic
43#10622092C2211yescharacteristic
44#10622092C2211yescharacteristic
45C2×C11×Q16C2×C411yescharacteristic
46C2×C11×SD16C2×C412yes—
47C2×C11×D8C2×C411yescharacteristic
48C22×C8×C11C2×C411yescharacteristic
49C22×C8×C11C2×C411yescharacteristic
50C11×#126—22no—
51C11×#125C2×C412yes—
52C11×#124C2×C412yes—
53C11×#123—22no—
54C11×C22⋊Q8C2×C412yes—
55C11×#121C2×C412yes—
56C4×Q8×C11C2312yes—
57C4×D4×C11—22no—
58C4×D4×C11C2312yes—
59C11×#117—22no—
60C2×C42×C11C2311yescharacteristic
61C2×#4318—21no—
62C2×#4318—22no—
63C22×C11⋊C8—22no—
64C22×C11⋊C8—22no—
65C11×#107C2×C411yescharacteristic
66C11×#107C2×C411yescharacteristic
67C11×#106C2×C412yes—
68C11×#103C2×C412yes—
69C11×#103C2×C412yes—
70C11×#102C2×C412yes—
71C11×#102C2×C412yes—
72C4×C8×C11C2×C411yescharacteristic
73C4×C8×C11C2×C411yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)D412yes—
79C4⋊(C11⋊C8)—22no—
80C4⋊(C11⋊C8)—22no—
81C4⋊(C11⋊C8)—22no—
82C4⋊(C11⋊C8)D412yes—
83C4⋊(C11⋊C8)C2312yes—
84C4⋊(C11⋊C8)C2312yes—
85#66867—21no—
86#66867—22no—
87C4×C11⋊C8—22no—
88C4×C11⋊C8C2311yescharacteristic
89C4×C11⋊C8C2311yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92#18093—111nomaximal, Sylow
93C2×Q8×C11C22×C412yes—
94C2×D4×C11—22no—
95C2×D4×C11C22×C412yes—
96C22×C4×C11—22no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C11×Q16—22no—
101C11×SD16—42no—
102C11×D8—22no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C2×C8×C11C22×C411yescharacteristic
106C2×C8×C11C22×C411yescharacteristic
107C2×C8×C11C22×C411yescharacteristic
108C2×C8×C11C22×C411yescharacteristic
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4C22×C412yes—
114C11×C4⋊C4C22×C412yes—
115C11×C22⋊C4—22no—
116C11×C22⋊C4—22no—
117C11×C22⋊C4—22no—
118C11×C22⋊C4—22no—
119C11×C22⋊C4—22no—
120C42×C11—22no—
121C42×C11C22×C411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11#4111yescharacteristic
124C42×C11C2411yescharacteristic
125#4318—42no—
126#4318—82no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—82no—
132C2×C11⋊C8—82no—
133C2×C11⋊C8C2×D412yes—
134C2×C11⋊C8C2×D412yes—
135#3168D1111yescharacteristic
136#2994—112no—
137#1594—111no—
138#1593—111no—
139#1583—112no—
140#1582—112no—
141#1580—111no—
142#1579—111no—
143C2×#334—111no—
144#1483—112no—
145#1451—111no—
146C23×C11—22no—
147C23×C11C4×D411yescharacteristic
148Q8×C11—22no—
149Q8×C11—22no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—44no—
153C2×C4×C11—22no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C4×D411yescharacteristic
165C2×C4×C11C23×C411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×C4×C11C2×#4111yescharacteristic
168C8×C11—21no—
169C8×C11—21no—
170C8×C11—21no—
171C8×C11#13112yes—
172C11⋊C8—22no—
173C11⋊C8—22no—
174C11⋊C8—41no—
175C11⋊C8—41no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178#529C2×D1112yes—
179#499Dic1111yescharacteristic
180#495Dic1111yescharacteristic
181#488Dic1112yes—
182#467Dic1111yescharacteristic
183#466Dic1111yescharacteristic
184#465Dic1112yes—
185#446—112no—
186C8×Q8—112no—
187C4×Q16C2×D1111yescharacteristic
188C4×SD16C2×D1112yes—
189C4×D8C2×D1111yescharacteristic
190#436—112no—
191#435—222no—
192C8×D4—112no—
193C8×D4—222no—
194#433—222no—
195#431—111no—
196#424—222no—
197C2×C4⋊C8—112no—
198C4×M16—111no—
199C2×C4×C8C2×D1111yescharacteristic
200#334—111no—
201#334—112no—
202#334—111no—
203Q8⋊C8—112no—
204Q8⋊C8—112no—
205D4⋊C8—112no—
206D4⋊C8—112no—
207#322—111no—
208#322—111no—
209#322—111no—
210#322—111no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11#44412yes—
217C22×C11C2×C4×D411yescharacteristic
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—42no—
223C4×C11—42no—
224C4×C11—42no—
225C4×C11C2×#13111yescharacteristic
226C4×C11#56811yescharacteristic
227C4×C11#57712yes—
228C2×Q16C2×Dic1111yescharacteristic
229C2×SD16C2×Dic1112yes—
230C2×D8C2×Dic1111yescharacteristic
231C2×M16—222no—
232C2×M16—221no—
233C22×C8—222no—
234C22×C8—222no—
235C22×C8C2×Dic1111yescharacteristic
236C22×C8C2×Dic1111yescharacteristic
237#126—22no—
238#125C2×Dic1112yes—
239#124C2×Dic1112yes—
240#123—22no—
241C22⋊Q8C2×Dic1112yes—
242#121C2×Dic1112yes—
243C4×Q8C22×D1112yes—
244C4×D4—22no—
245C4×D4C22×D1112yes—
246#117—22no—
247C2×C42C22×D1111yescharacteristic
248#107C2×Dic1111yescharacteristic
249#107C2×Dic1111yescharacteristic
250#106C2×Dic1112yes—
251C4⋊C8—112no—
252C4⋊C8—112no—
253C4⋊C8—112no—
254C4⋊C8—222no—
255C4⋊C8—222no—
256C4⋊C8—222no—
257#103C2×Dic1112yes—
258#103C2×Dic1112yes—
259#102C2×Dic1112yes—
260#102C2×Dic1112yes—
261C22⋊C8—112no—
262C22⋊C8—222no—
263C22⋊C8—222no—
264#97—222no—
265#97—221no—
266C4×C8—111no—
267C4×C8—111no—
268C4×C8—111no—
269C4×C8—111no—
270C4×C8—222no—
271C4×C8C2×Dic1111yescharacteristic
272C4×C8C2×Dic1111yescharacteristic
273C4×C8C22×D1111yescharacteristic
274C4×C8C22×D1111yescharacteristic
275C2×C11—22no—
276C2×C11—82no—
277C2×C11#293511yescharacteristic
278C2×C11#295211yescharacteristic
279C2×C11C2×#44411yescharacteristic
280C2×Q8C22×Dic1112yes—
281C2×D4—22no—
282C2×D4C22×Dic1112yes—
283C22×C4—22no—
284C22×C4D4×D1111yescharacteristic
285C22×C4#434111yescharacteristic
286C22×C4C22×Dic1111yescharacteristic
287Q16—22no—
288SD16—42no—
289D8—22no—
290M16—442no—
291M16—882no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—112no—
295C2×C8—112no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8—221no—
299C2×C8—221no—
300C2×C8—882no—
301C2×C8—882no—
302C2×C8C22×Dic1111yescharacteristic
303C2×C8C22×Dic1111yescharacteristic
304C2×C8C22×Dic1111yescharacteristic
305C2×C8C22×Dic1111yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4C22×Dic1112yes—
311C4⋊C4C22×Dic1112yes—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C42—22no—
318C42D4×D1111yescharacteristic
319C42#434111yescharacteristic
320C42C22×Dic1111yescharacteristic
321C42C23×D1111yescharacteristic
322C11#1809311yescharacteristic, complemented, Sylow
323C23—22no—
324C23D4×Dic1111yescharacteristic
325Q8—22no—
326Q8—22no—
327D4—22no—
328D4—22no—
329D4—44no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4D4×Dic1111yescharacteristic
340C2×C4D4×Dic1111yescharacteristic
341C2×C4D4×Dic1111yescharacteristic
342C2×C4C2×D4×D1111yescharacteristic
343C2×C4C2×#434111yescharacteristic
344C2×C4C23×Dic1111yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—222no—
349C8—222no—
350C8—441no—
351C8—441no—
352C8—442no—
353C8—442no—
354C8#6700112yes—
355C22—21no—
356C22—21no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22#1062281012yes—
361C22C2×D4×Dic1111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—42no—
367C4—42no—
368C4—42no—
369C4#1062330112yes—
370C4C2×#6700111yescharacteristic
371C4#1062335011yescharacteristic
372C2—22no—
373C2—82no—
374C2#1307736011yescharacteristic
375C2#1307750011yescharacteristic
376C2C2×#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#18093
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. #13077776C2semidirect
2. #13067530C2semidirect
3. #13067525C2semidirect
4. #13067460C2semidirect
5. #13067453C2semidirect
6. #13067440C2semidirect
7. #13067435C2semidirect
8. C2×#10622095C2semidirect
9. #13067029C2semidirect
10. #13066905C2semidirect
322. C11#18093semidirect

Maximal subgroups

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

subgroupindex
#130777762
#130675302
#130675252
#130674602
#130674532
#130674402
#130674352
C2×#106220952
#130670292
#130669052
C11×#31682
#1809311