Finite Group Databasebeta

← #14723926

Subgroups — #14723926

Order 2816.

586 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#13078655C211yesmaximal, characteristic
2#13077710C211yesmaximal, characteristic
3#13067487C212yesmaximal, complemented
4#13067466C212yesmaximal, complemented
5#13067433C212yesmaximal, complemented
6C8×#4326C212yesmaximal, complemented
7#13067394C211yesmaximal, characteristic
8#13067063C211yesmaximal, characteristic
9#13067036C211yesmaximal, characteristic
10#13066911C211yesmaximal, characteristic
11C11×#2982C211yesmaximal, characteristic
12C2×C4×Q8×C11C2211yescharacteristic
13#10623001C2211yescharacteristic
14C8×Q8×C11—22no—
15C8×Q8×C11C2212yes—
16C8×Q8×C11C2212yes—
17C11×#431—22no—
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622841C412yes—
21#10622644C412yes—
22C4×#4326C2212yes—
23C4×#4326C2212yes—
24#10622634C412yes—
25#10622583C412yes—
26#10622539C2211yescharacteristic
27#10622538C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622441—22no—
30#10622333—22no—
31#10622292C2212yes—
32C8×Dic22C2212yes—
33Q8⋊(C11⋊C8)C2212yes—
34Q8⋊(C11⋊C8)C2212yes—
35#10622122C2212yes—
36#10622122C2212yes—
37#10622118C2212yes—
38#10622117C2212yes—
39#10622093C2211yescharacteristic
40#10622092C2211yescharacteristic
41#10622092C2211yescharacteristic
42C8×C11⋊C8C2211yescharacteristic
43C22×Q8×C11C2×C411yescharacteristic
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11C2×C412yes—
47C4×Q8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4326C2×C412yes—
53C2×#4326C2×C412yes—
54#66979—21no—
55#66977—21no—
56#66977C2×C412yes—
57C2×#4318—21no—
58#66923—21no—
59#66922C2×C411yescharacteristic
60#66922C2×C411yescharacteristic
61C4×Dic22—21no—
62C4×Dic22C2312yes—
63C11×C4⋊C8—22no—
64C11×C4⋊C8—22no—
65C11×C4⋊C8D412yes—
66C11×C4⋊C8C2312yes—
67C11×C22⋊C8—21no—
68C11×C22⋊C8D412yes—
69C4×C8×C11—22no—
70C4×C8×C11—22no—
71C4×C8×C11—21no—
72C4×C8×C11C2311yescharacteristic
73C4×C8×C11C2311yescharacteristic
74#66899C2×C412yes—
75#66899C2×C412yes—
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)C2×C412yes—
78#66879—22no—
79Dic11⋊C8—22no—
80Dic11⋊C8—22no—
81C8×Dic11—22no—
82#66874C2×C412yes—
83#66874C2×C412yes—
84#66871C2×C412yes—
85#66871C2×C412yes—
86C4⋊(C11⋊C8)C2×C412yes—
87C4⋊(C11⋊C8)C2312yes—
88#66867—21no—
89#66867—21no—
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93C4×C11⋊C8C2311yescharacteristic
94#17925—111nomaximal, Sylow
95C2×Q8×C11—24no—
96C2×Q8×C11—21no—
97C2×Q8×C11C22×C412yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C2×Dic22—21no—
104C2×Dic22C22×C412yes—
105C2×C8×C11—22no—
106C2×C8×C11C2×D412yes—
107C2×C8×C11C2×D412yes—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4C22×C412yes—
112C42×C11—22no—
113C42×C11—22no—
114C42×C11C22×C411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118C22⋊Dic11—22no—
119#4326—24no—
120#4326—24no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11C22×C412yes—
125Dic11⋊C4—22no—
126Dic11⋊C4—22no—
127C4×Dic11—22no—
128#4318—42no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8C22×C412yes—
133C2×C11⋊C8C22×C412yes—
134#3104—111no—
135#2985—111no—
136#2982D1111yescharacteristic
137#1587—112no—
138#1584—112no—
139#1579—112no—
140C8×Q16—112no—
141#1572—111no—
142#1491—111no—
143#1485—111no—
144#1453—111no—
145C23×C11C4×D411yescharacteristic
146Q8×C11—24no—
147Q8×C11—22no—
148Q8×C11#13114yes—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—81no—
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C2×Dic11—22no—
163C2×Dic11—22no—
164Dic22—22no—
165Dic22—22no—
166Dic22—81no—
167C8×C11—22no—
168C8×C11—22no—
169C8×C11—42no—
170C11⋊C8—22no—
171C11⋊C8—22no—
172C11⋊C8—22no—
173C11⋊C8—41no—
174C11⋊C8—42no—
175#533—111no—
176C2×C4×Q8C2×D1111yescharacteristic
177#484—112no—
178#477—112no—
179#462—112no—
180#451—112no—
181#446—112no—
182#446—222no—
183C8×Q8—22no—
184C8×Q8—112no—
185C8×Q8C2×D1112yes—
186C8×Q8C2×D1112yes—
187C4×Q16—112no—
188C4×Q16—112no—
189#433—222no—
190#432—111no—
191#431—22no—
192#431—111no—
193#431C2×D1111yescharacteristic
194#431C2×D1111yescharacteristic
195C4×M16—111no—
196#335—112no—
197#334—112no—
198Q8⋊C8—112no—
199Q8⋊C8—112no—
200Q8⋊C8—112no—
201Q8⋊C8—112no—
202#322—111no—
203#322—111no—
204#322—111no—
205C82—111no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11C2×C4×D411yescharacteristic
210C4×C11—24no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11C2×#13112yes—
217C4×C11#57812yes—
218Dic11—42no—
219Dic11—42no—
220C22×Q8C4×D1111yescharacteristic
221C2×Q16—112no—
222C2×Q16—112no—
223C2×M16—221no—
224C4⋊Q8—111no—
225C4⋊Q8—111no—
226#125—221no—
227C22⋊Q8—112no—
228C22⋊Q8—221no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—112no—
232C4×Q8—221no—
233C4×Q8C4×D1112yes—
234C4×Q8C22×D1112yes—
235#117—221no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C4×D1111yescharacteristic
238C2×C42—21no—
239C2×C42C22×D1111yescharacteristic
240#107—112no—
241#107—112no—
242C4⋊C8—22no—
243C4⋊C8—22no—
244C4⋊C8—112no—
245C4⋊C8—112no—
246C4⋊C8—222no—
247C4⋊C8—222no—
248C4⋊C8C22⋊D1112yes—
249C4⋊C8C22×D1112yes—
250#103—112no—
251#103—112no—
252#103—112no—
253#103—112no—
254C22⋊C8—21no—
255C22⋊C8—112no—
256C22⋊C8—221no—
257C22⋊C8C22⋊D1112yes—
258#97—222no—
259#97—221no—
260#97—221no—
261C4×C8—22no—
262C4×C8—22no—
263C4×C8—21no—
264C4×C8—111no—
265C4×C8—111no—
266C4×C8—111no—
267C4×C8—111no—
268C4×C8—222no—
269C4×C8C22×D1111yescharacteristic
270C4×C8C22×D1111yescharacteristic
271C2×C11—41no—
272C2×C11#292911yescharacteristic
273C2×C11#295011yescharacteristic
274C2×C11#295611yescharacteristic
275C2×Q8—24no—
276C2×Q8—21no—
277C2×Q8—112no—
278C2×Q8—221no—
279C2×Q8C2×C4×D1112yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4C2×C4×D1111yescharacteristic
283C22×C4#433911yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285Q16—224no—
286Q16—224no—
287M16—442no—
288C2×C8—22no—
289C2×C8—112no—
290C2×C8—112no—
291C2×C8—221no—
292C2×C8—221no—
293C2×C8—222no—
294C2×C8C2×C22⋊D1112yes—
295C2×C8C2×C22⋊D1112yes—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—112no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C4⋊C4—221no—
304C4⋊C4—222no—
305C4⋊C4C2×C4×D1112yes—
306C22⋊C4—222no—
307C42—22no—
308C42—22no—
309C42—222no—
310C42C2×C4×D1111yescharacteristic
311C42#433911yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C42C23×D1111yescharacteristic
314C11#1792511yescharacteristic, complemented, Sylow
315C23C4×C22⋊D1111yescharacteristic
316Q8—24no—
317Q8—22no—
318Q8—222no—
319Q8—222no—
320Q8—881no—
321Q8#6695414yes—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—81no—
329C2×C4—222no—
330C2×C4—222no—
331C2×C4C4×C22⋊D1111yescharacteristic
332C2×C4C4×C22⋊D1111yescharacteristic
333C2×C4C4×C22⋊D1111yescharacteristic
334C2×C4C22×C4×D1111yescharacteristic
335C2×C4C2×#433911yescharacteristic
336C2×C4C22×C22⋊D1111yescharacteristic
337C8—22no—
338C8—22no—
339C8—42no—
340C8—222no—
341C8—222no—
342C8—222no—
343C8—441no—
344C8—442no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22C2×C4×C22⋊D1111yescharacteristic
349C4—21no—
350C4—21no—
351C4—24no—
352C4—21no—
353C4—21no—
354C4—42no—
355C4—442no—
356C4—442no—
357C4C2×#6695412yes—
358C4#1062336912yes—
359C2—41no—
360C2#1307731011yescharacteristic
361C2#1307748211yescharacteristic
362C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2982C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#2982D11
hypocenterC11#17925
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2982

Complements

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

NH ≅ G/Ntype
3. #13067487C2semidirect
4. #13067466C2semidirect
5. #13067433C2semidirect
6. C8×#4326C2semidirect
314. C11#17925semidirect

Maximal subgroups

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

subgroupindex
#130786552
#130777102
#130674872
#130674662
#130674332
C8×#43262
#130673942
#130670632
#130670362
#130669112
C11×#29822
#1792511