Finite Group Databasebeta

← #14724632

Subgroups — #14724632

Order 2816.

544 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079198C211yesmaximal, characteristic
2#13077710C211yesmaximal, characteristic
3#13067487C212yesmaximal, complemented
4#13067485C212yesmaximal, complemented
5#13067466C212yesmaximal, complemented
6#13067464C212yesmaximal, complemented
7#13067377C211yesmaximal, characteristic
8#13067089C211yesmaximal, characteristic
9#13067088C211yesmaximal, characteristic
10#13066909C211yesmaximal, characteristic
11C11×#2985C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13#10623001C2211yescharacteristic
14C11×#446—22no—
15C11×#446C2212yes—
16C8×Q8×C11C2212yes—
17C11×#433—22no—
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622706C411yescharacteristic
21#10622705C411yescharacteristic
22#10622694C411yescharacteristic
23#10622691C411yescharacteristic
24#10622664C412yes—
25#10622664C412yes—
26C4×#4326C2212yes—
27C4×#4326C2212yes—
28#10622539C2211yescharacteristic
29#10622538C2211yescharacteristic
30C2×C4×C11⋊C8C2211yescharacteristic
31#10622441—22no—
32#10622333—22no—
33#10622292C2212yes—
34C8×Dic22C2212yes—
35Q8⋊(C11⋊C8)C2212yes—
36Q8⋊(C11⋊C8)C2212yes—
37#10622122C2212yes—
38#10622122C2212yes—
39#10622118C2212yes—
40#10622117C2212yes—
41#10622093C2211yescharacteristic
42#10622093C2211yescharacteristic
43#10622092C2211yescharacteristic
44#10622092C2211yescharacteristic
45C11×C4⋊Q8C2×C411yescharacteristic
46C11×C4⋊Q8C2×C411yescharacteristic
47C11×#125—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8C2×C412yes—
50C4×Q8×C11—21no—
51C4×Q8×C11C2312yes—
52C11×#117—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4326C2×C412yes—
55C2×#4326C2×C412yes—
56#66979—21no—
57#66977—21no—
58#66977C2×C412yes—
59C22×C11⋊C8C2×C411yescharacteristic
60C22×C11⋊C8C2×C411yescharacteristic
61#66923—21no—
62#66922C2×C411yescharacteristic
63#66922C2×C411yescharacteristic
64C4×Dic22—21no—
65C4×Dic22C2312yes—
66C11×C4⋊C8—22no—
67C11×C4⋊C8—22no—
68C11×C4⋊C8D412yes—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8—21no—
71C11×C22⋊C8D412yes—
72C11×#97—22no—
73C11×#97—21no—
74C4×C8×C11—22no—
75C4×C8×C11C2311yescharacteristic
76C4×C8×C11C2311yescharacteristic
77#66899C2×C412yes—
78#66899C2×C412yes—
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—21no—
81#66879—22no—
82Dic11⋊C8—22no—
83Dic11⋊C8—22no—
84C8×Dic11—22no—
85#66874C2×C412yes—
86#66874C2×C412yes—
87#66871C2×C412yes—
88#66871C2×C412yes—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)C2312yes—
91#66867—21no—
92C4×C11⋊C8C2×C411yescharacteristic
93C4×C11⋊C8C2×C411yescharacteristic
94C4×C11⋊C8C2311yescharacteristic
95C4×C11⋊C8C2311yescharacteristic
96C4×C11⋊C8C2311yescharacteristic
97C4×C11⋊C8C2311yescharacteristic
98#17991—111nomaximal, Sylow
99C2×Q8×C11—21no—
100C2×Q8×C11C22×C412yes—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C2×Dic22—21no—
105C2×Dic22C22×C412yes—
106C2×C8×C11—22no—
107C2×C8×C11C2×D412yes—
108C2×C8×C11C2×D412yes—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4C22×C412yes—
115C11×C22⋊C4—22no—
116C42×C11—22no—
117C42×C11C22×C411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11C2411yescharacteristic
121C22⋊Dic11—22no—
122#4326—42no—
123#4326—42no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11C22×C412yes—
128Dic11⋊C4—22no—
129Dic11⋊C4—22no—
130C4×Dic11—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8C22×C411yescharacteristic
137C2×C11⋊C8C22×C411yescharacteristic
138C2×C11⋊C8C22×C411yescharacteristic
139C2×C11⋊C8C22×C411yescharacteristic
140#3170—111no—
141#2985—111no—
142#2985D1111yescharacteristic
143#1587—112no—
144#1587—112no—
145#1584—112no—
146#1584—112no—
147#1568—111no—
148#1497—111no—
149#1497—111no—
150#1452—111no—
151C23×C11C4×D411yescharacteristic
152Q8×C11—22no—
153Q8×C11—22no—
154Q8×C11—81no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C2×Dic11—22no—
168C2×Dic11—22no—
169Dic22—22no—
170Dic22—22no—
171Dic22—81no—
172C8×C11—22no—
173C8×C11—22no—
174C8×C11—42no—
175C11⋊C8—21no—
176C11⋊C8—21no—
177C11⋊C8—21no—
178C11⋊C8—21no—
179C11⋊C8—41no—
180C11⋊C8—41no—
181C11⋊C8—42no—
182#533—111no—
183#533C2×D1111yescharacteristic
184#500—111no—
185#494—111no—
186#487—111no—
187#487—111no—
188#467—112no—
189#467—112no—
190#446—22no—
191#446—112no—
192#446—222no—
193#446C2×D1112yes—
194C8×Q8—112no—
195C8×Q8C2×D1112yes—
196C4×Q16—112no—
197C4×Q16—112no—
198#433—22no—
199#433—222no—
200#432—111no—
201#432C2×D1111yescharacteristic
202#431—111no—
203#431C2×D1111yescharacteristic
204C2×C4×C8—111no—
205#335—112no—
206#334—112no—
207Q8⋊C8—112no—
208Q8⋊C8—112no—
209Q8⋊C8—112no—
210Q8⋊C8—112no—
211#322—111no—
212#322—111no—
213#322—111no—
214#322—111no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11C2×C4×D411yescharacteristic
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—42no—
224C4×C11—42no—
225C4×C11#56811yescharacteristic
226C4×C11#56811yescharacteristic
227C4×C11#57812yes—
228Dic11—42no—
229Dic11—42no—
230C2×Q16—112no—
231C2×Q16—112no—
232C22×C8—111no—
233C22×C8—111no—
234C4⋊Q8—111no—
235C4⋊Q8—111no—
236C4⋊Q8C4×D1111yescharacteristic
237C4⋊Q8C4×D1111yescharacteristic
238#125—21no—
239#125—221no—
240C22⋊Q8—21no—
241C22⋊Q8—112no—
242C22⋊Q8—221no—
243C22⋊Q8C4×D1112yes—
244C4×Q8—21no—
245C4×Q8—112no—
246C4×Q8—221no—
247C4×Q8C22×D1112yes—
248#117—21no—
249#117—221no—
250C2×C42C22×D1111yescharacteristic
251#107—112no—
252#107—112no—
253C4⋊C8—22no—
254C4⋊C8—22no—
255C4⋊C8—112no—
256C4⋊C8—222no—
257C4⋊C8—222no—
258C4⋊C8—221no—
259C4⋊C8C22⋊D1112yes—
260C4⋊C8C22×D1112yes—
261#103—112no—
262#103—112no—
263#103—112no—
264#103—112no—
265C22⋊C8—21no—
266C22⋊C8—221no—
267C22⋊C8—221no—
268C22⋊C8C22⋊D1112yes—
269#97—22no—
270#97—21no—
271#97—222no—
272#97—221no—
273C4×C8—22no—
274C4×C8—111no—
275C4×C8—111no—
276C4×C8—111no—
277C4×C8—111no—
278C4×C8—111no—
279C4×C8—111no—
280C4×C8—222no—
281C4×C8C22×D1111yescharacteristic
282C4×C8C22×D1111yescharacteristic
283C2×C11—41no—
284C2×C11#293211yescharacteristic
285C2×C11#295011yescharacteristic
286C2×C11#295711yescharacteristic
287C2×Q8—21no—
288C2×Q8—112no—
289C2×Q8—221no—
290C2×Q8C2×C4×D1112yes—
291C22×C4C2×C4×D1111yescharacteristic
292C22×C4#433911yescharacteristic
293C22×C4C2×C22⋊D1111yescharacteristic
294Q16—442no—
295Q16—442no—
296C2×C8—22no—
297C2×C8—111no—
298C2×C8—111no—
299C2×C8—111no—
300C2×C8—111no—
301C2×C8—221no—
302C2×C8—221no—
303C2×C8—222no—
304C2×C8—441no—
305C2×C8—441no—
306C2×C8C2×C22⋊D1112yes—
307C2×C8C2×C22⋊D1112yes—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—22no—
313C4⋊C4—112no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—222no—
317C4⋊C4—221no—
318C4⋊C4—222no—
319C4⋊C4C2×C4×D1112yes—
320C22⋊C4—22no—
321C22⋊C4—222no—
322C42—22no—
323C42—222no—
324C42C2×C4×D1111yescharacteristic
325C42#433911yescharacteristic
326C42C2×C22⋊D1111yescharacteristic
327C42C23×D1111yescharacteristic
328C11#1799111yescharacteristic, complemented, Sylow
329C23C4×C22⋊D1111yescharacteristic
330Q8—22no—
331Q8—22no—
332Q8—81no—
333Q8—222no—
334Q8—222no—
335Q8—881no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—222no—
343C2×C4—222no—
344C2×C4C4×C22⋊D1111yescharacteristic
345C2×C4C4×C22⋊D1111yescharacteristic
346C2×C4C4×C22⋊D1111yescharacteristic
347C2×C4C22×C4×D1111yescharacteristic
348C2×C4C2×#433911yescharacteristic
349C2×C4C22×C22⋊D1111yescharacteristic
350C8—22no—
351C8—22no—
352C8—42no—
353C8—221no—
354C8—221no—
355C8—221no—
356C8—221no—
357C8—441no—
358C8—441no—
359C8—442no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22C2×C4×C22⋊D1111yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—42no—
370C4—442no—
371C4—442no—
372C4#1062328111yescharacteristic
373C4#1062328111yescharacteristic
374C4#1062336912yes—
375C2—41no—
376C2#1307733211yescharacteristic
377C2#1307748211yescharacteristic
378C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2985C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#2985D11
hypocenterC11#17991
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2985

Complements

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

NH ≅ G/Ntype
3. #13067487C2semidirect
4. #13067485C2semidirect
5. #13067466C2semidirect
6. #13067464C2semidirect
328. C11#17991semidirect

Maximal subgroups

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

subgroupindex
#130791982
#130777102
#130674872
#130674852
#130674662
#130674642
#130673772
#130670892
#130670882
#130669092
C11×#29852
#1799111