Finite Group Databasebeta

← #14653113

Subgroups — #14653113

Order 2816.

406 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079126C211yesmaximal, characteristic
2#13068481C211yesmaximal, characteristic
3#13067362C211yesmaximal, characteristic
4#13067116C211yesmaximal, characteristic
5#13067115C211yesmaximal, characteristic
6#13067018C211yesmaximal, characteristic
7C11×#1481C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C8×Dic11—21no—
13#10622692C411yescharacteristic, complemented
14#10622692C411yescharacteristic, complemented
15#10622691C411yescharacteristic, complemented
16#10622691C411yescharacteristic, complemented
17#10622677—21no—
18#10622677—21no—
19#10622611—21no—
20#10622611—21no—
21C4×C4⋊Dic11C2211yescharacteristic
22#10622538C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24C11×Q8⋊C8—22no—
25#10622188—21no—
26#10622176—22no—
27#10622122—22no—
28#10622118—21no—
29#10622117—21no—
30#10622105—22no—
31C22×C8×C11—21no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×C4⋊Q8C2×C411yescharacteristic
34C11×#125—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C11×#117—21no—
40C2×C42×C11C2311yescharacteristic
41#66979—21no—
42C2×C4⋊Dic11—21no—
43#66977—21no—
44#66977—21no—
45C2×C4×Dic11—21no—
46C22×C11⋊C8D411yescharacteristic
47C22×C11⋊C8D411yescharacteristic
48#66923—21no—
49#66922C2×C411yescharacteristic
50#66922C2×C411yescharacteristic
51C4×Dic22—21no—
52C4×Dic22—21no—
53C11×C4⋊C8—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8D412yes—
56C11×C22⋊C8—21no—
57C4×C8×C11—21no—
58C11⋊#95D412yes—
59C22⋊(C11⋊C8)—21no—
60C8×Dic11—42no—
61#66872—21no—
62#66872—21no—
63#66872—21no—
64#66872—21no—
65#66871—21no—
66#66871—21no—
67#66871—21no—
68#66871—21no—
69C4⋊(C11⋊C8)—21no—
70C4×C11⋊C8—21no—
71C4×C11⋊C8C2×C411yescharacteristic
72C4×C11⋊C8C2×C411yescharacteristic
73C4×C11⋊C8D411yescharacteristic
74C4×C11⋊C8D411yescharacteristic
75#9749—111nomaximal, Sylow
76C2×Q8×C11—21no—
77C2×Q8×C11—21no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—22no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×C8×C11—22no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—41no—
95C42×C11—41no—
96C42×C11C22×C411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100C22⋊Dic11—41no—
101C4⋊Dic11—24no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109C4×Dic11—41no—
110C4×Dic11—41no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8C22⋊C411yescharacteristic
115C2×C11⋊C8C22⋊C411yescharacteristic
116C2×C11⋊C8C22⋊C411yescharacteristic
117C2×C11⋊C8C22⋊C411yescharacteristic
118C2×C11⋊C8SD1612yes—
119C2×C11⋊C8Q1612yes—
120#3160—111no—
121C8×C4⋊C4—111no—
122#1564—111no—
123#1503—111no—
124#1503—111no—
125#1481—111no—
126#1481D1111yescharacteristic
127C23×C11#12111yescharacteristic
128Q8×C11—42no—
129Q8×C11—81no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11C2×C22⋊C411yescharacteristic
135C2×C4×C11C4×D411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12411yescharacteristic
139C2×C4×C11#12711yescharacteristic
140C2×C4×C11C2×SD1611yescharacteristic
141C2×C4×C11C2×Q1611yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C2×Dic11—24no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149Dic22—42no—
150Dic22—81no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155C11⋊C8—81no—
156C11⋊C8#10312yes—
157C11⋊C8#10312yes—
158#533—111no—
159#533C2×D1111yescharacteristic
160#500—111no—
161#500—111no—
162#499—221no—
163#499—221no—
164#498—111no—
165#498—111no—
166#431—111no—
167#431C2×D1111yescharacteristic
168#427—221no—
169#427—221no—
170C2×C4⋊C8C2×D1111yescharacteristic
171C2×C4×C8—111no—
172C2×C4×C8—221no—
173C4×C4⋊C4—111no—
174#336—221no—
175#335—221no—
176#334—221no—
177#328—222no—
178#328—222no—
179Q8⋊C8—22no—
180Q8⋊C8—222no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#39011yescharacteristic
184C22×C11#46111yescharacteristic
185C22×C11#46211yescharacteristic
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11C2×#10311yescharacteristic
192C4×C11#41911yescharacteristic
193C4×C11#44312yes—
194C4×C11#46111yescharacteristic
195C4×C11#46211yescharacteristic
196Dic11—44no—
197Dic11—81no—
198Dic11—81no—
199C22×C8—21no—
200C22×C8—111no—
201C22×C8—111no—
202C4⋊Q8—111no—
203C4⋊Q8—111no—
204C4⋊Q8C4×D1111yescharacteristic
205C4⋊Q8C4×D1111yescharacteristic
206#125—21no—
207#125—221no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—221no—
211C22⋊Q8—221no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—221no—
215C4×Q8—221no—
216#117—21no—
217#117—221no—
218C2×C4⋊C4—221no—
219C2×C42—221no—
220C2×C42C22×D1111yescharacteristic
221#107—221no—
222#107—221no—
223#107—221no—
224#107—221no—
225#106—221no—
226#106—221no—
227#106—221no—
228#106—221no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—221no—
232C4⋊C8C22⋊D1112yes—
233C22⋊C8—21no—
234C22⋊C8—221no—
235C4×C8—21no—
236C4×C8—111no—
237C4×C8—111no—
238C4×C8—111no—
239C4×C8—111no—
240C4×C8—221no—
241C4×C8—442no—
242#95—112no—
243C2×C11—21no—
244C2×C11—21no—
245C2×C11#197411yescharacteristic
246C2×C11#197611yescharacteristic
247C2×C11#198111yescharacteristic
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—221no—
251C2×Q8—221no—
252C22×C4—222no—
253C22×C4#433911yescharacteristic
254C22×C4D4×D1111yescharacteristic
255C22×C4D4×D1111yescharacteristic
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—111no—
261C2×C8—111no—
262C2×C8—112no—
263C2×C8—112no—
264C2×C8—111no—
265C2×C8—111no—
266C2×C8—221no—
267C2×C8—221no—
268C2×C8—441no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—224no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C22⋊C4—41no—
283C22⋊C4—441no—
284C42—41no—
285C42—441no—
286C42—441no—
287C42—441no—
288C42C2×C4×D1111yescharacteristic
289C42D4×D1111yescharacteristic
290C42#434111yescharacteristic
291C42C2×C22⋊D1111yescharacteristic
292C11#974911yescharacteristic, complemented, Sylow
293C23#6693711yescharacteristic
294Q8—42no—
295Q8—81no—
296Q8—442no—
297Q8—881no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—224no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4C22⋊C4×D1111yescharacteristic
308C2×C4(C22⋊D11)⋊C411yescharacteristic
309C2×C4#6693811yescharacteristic
310C2×C4SD16×D1111yescharacteristic
311C2×C4#6696811yescharacteristic
312C2×C4Q16×D1111yescharacteristic
313C2×C4#6697111yescharacteristic
314C2×C4C4×C22⋊D1111yescharacteristic
315C2×C4#6699211yescharacteristic
316C2×C4#6699311yescharacteristic
317C8—42no—
318C8—81no—
319C8—112no—
320C8—112no—
321C8—221no—
322C8—221no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22#1062240611yescharacteristic
327C22#1062243111yescharacteristic
328C22#1062257011yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—444no—
335C4—881no—
336C4—881no—
337C4D11×#10311yescharacteristic
338C4#1062241511yescharacteristic
339C4#1062275712yes—
340C4#1062277511yescharacteristic
341C4#1062279511yescharacteristic
342C2—21no—
343C2—21no—
344C2#1306950311yescharacteristic
345C2#1306951311yescharacteristic
346C2#1306953711yescharacteristic
subgroupG/H
centerC2×C4#66992
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1481C2
socleC22×C11#390
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1481D11
hypocenterC11#9749
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
13. #10622692C4semidirect
14. #10622692C4semidirect
15. #10622691C4semidirect
16. #10622691C4semidirect
292. C11#9749semidirect

Maximal subgroups

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

subgroupindex
#130791262
#130684812
#130673622
#130671162
#130671152
#130670182
C11×#14812
#974911