Finite Group Databasebeta

← #14739151

Subgroups — #14739151

Order 2816.

576 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079775C211yesmaximal, characteristic
2#13078746C211yesmaximal, characteristic
3#13077697C211yesmaximal, characteristic
4#13068076C212yesmaximal, complemented
5#13068048C212yesmaximal, complemented
6#13068008C212yesmaximal, complemented
7#13068000C212yesmaximal, complemented
8#13067394C211yesmaximal, characteristic
9#13067326C211yesmaximal, characteristic
10#13067280C211yesmaximal, characteristic
11C11×#3104C211yesmaximal, characteristic
12C11×#533C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#484—21no—
16C11×#477C2212yes—
17C11×#462C2212yes—
18C11×#451—21no—
19C4×C11×Q16—22no—
20C11×#431C2211yescharacteristic
21#10622841—21no—
22#10622706C2211yescharacteristic
23#10622706C2211yescharacteristic
24#10622692C2211yescharacteristic
25#10622691C2211yescharacteristic
26#10622676—22no—
27#10622644C2212yes—
28#10622643—22no—
29Q8×C11⋊C8—22no—
30Q8×C11⋊C8C2212yes—
31Q8×C11⋊C8C2212yes—
32#10622633C2212yes—
33#10622609—22no—
34#10622584—21no—
35#10622539C2211yescharacteristic
36#10622538—22no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622185C2212yes—
40#10622184C2212yes—
41#10622124C2212yes—
42#10622120C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45C22×Q8×C11D411yescharacteristic
46C2×C11×Q16—22no—
47C11×C4⋊Q8C2311yescharacteristic
48C11×C4⋊Q8C2311yescharacteristic
49C11×#125—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8—21no—
52C4×Q8×C11—21no—
53C4×Q8×C11—21no—
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11D412yes—
57C4×Q8×C11C2312yes—
58C11×#117—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4326—22no—
64#66979—21no—
65#66977—21no—
66#66977—21no—
67#66923—21no—
68#66922C2311yescharacteristic
69#66922C2311yescharacteristic
70C4×Dic22—21no—
71C4×Dic22—21no—
72C11×#107—22no—
73C11×C4⋊C8C2312yes—
74C11×#103—22no—
75C11×#103—22no—
76C11×C22⋊C8—21no—
77C4×C8×C11—21no—
78#66899—22no—
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—21no—
81C22⋊(C11⋊C8)D412yes—
82#66874—22no—
83#66874—22no—
84#66874—22no—
85#66872—22no—
86#66872—22no—
87#66871—22no—
88C4⋊(C11⋊C8)—22no—
89C4⋊(C11⋊C8)—22no—
90C4⋊(C11⋊C8)D412yes—
91C4⋊(C11⋊C8)C2312yes—
92C4⋊(C11⋊C8)C2312yes—
93#66867—21no—
94C4×C11⋊C8—21no—
95C4×C11⋊C8—22no—
96C4×C11⋊C8—22no—
97C4×C11⋊C8C2311yescharacteristic
98C4×C11⋊C8C2311yescharacteristic
99#19407—111nomaximal, Sylow
100C2×Q8×C11—24no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11C2×D412yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×Dic22—21no—
111C2×Dic22—21no—
112C11×Q16—44no—
113C2×C8×C11—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4C2×D412yes—
124C11×C22⋊C4—41no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11—41no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132C22⋊Dic11—41no—
133#4326—44no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140C4×Dic11—41no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8C2×D412yes—
144C2×C11⋊C8C2×D412yes—
145#3231—111no—
146#3113—111no—
147#3104D1111yescharacteristic
148#2982—111no—
149#1684—112no—
150#1680—112no—
151#1674—112no—
152#1672—112no—
153#1572—111no—
154#1554—111no—
155#1544—111no—
156C23×C11#12111yescharacteristic
157Q8×C11—24no—
158Q8×C11—22no—
159Q8×C11—42no—
160Q8×C11—81no—
161Q8×C11#13514yes—
162C2×C4×C11—24no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×Dic11—41no—
178C2×Dic11—41no—
179Dic22—42no—
180Dic22—42no—
181C8×C11—42no—
182C11⋊C8—22no—
183C11⋊C8—22no—
184C11⋊C8—42no—
185C11⋊C8—42no—
186#533—111no—
187#533C2×D1111yescharacteristic
188C2×C4×Q8C2×D1111yescharacteristic
189#500—111no—
190#498—111no—
191#487—111no—
192#487—111no—
193#485—222no—
194#484—21no—
195#483—221no—
196#479—222no—
197#477C2×D1112yes—
198#475—112no—
199#462—112no—
200#462C2×D1112yes—
201#451—21no—
202#451—221no—
203C8×Q8—112no—
204C8×Q8—112no—
205C8×Q8—222no—
206#441—222no—
207C4×Q16—22no—
208#432—111no—
209#431—111no—
210#431—111no—
211#431—222no—
212#431C2×D1111yescharacteristic
213#335—112no—
214#334—112no—
215#333—112no—
216#332—112no—
217#332—112no—
218#332—112no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11C2×#12111yescharacteristic
223C4×C11—21no—
224C4×C11—24no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—42no—
229C4×C11—81no—
230C4×C11—81no—
231C4×C11C2×#13512yes—
232C4×C11#57812yes—
233Dic11—81no—
234Dic11—81no—
235C22×Q8C22⋊D1111yescharacteristic
236C2×Q16—22no—
237C2×Q16—222no—
238C4⋊Q8—111no—
239C4⋊Q8—111no—
240C4⋊Q8C22×D1111yescharacteristic
241C4⋊Q8C22×D1111yescharacteristic
242#125—21no—
243#125—221no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—221no—
247C22⋊Q8—221no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8—221no—
253C4×Q8—221no—
254C4×Q8C22⋊D1112yes—
255C4×Q8C22×D1112yes—
256#117—21no—
257#117—221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4C22⋊D1111yescharacteristic
260C2×C42—21no—
261C2×C42C22×D1111yescharacteristic
262#107—22no—
263#107—222no—
264#106—222no—
265#106—222no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—112no—
269C4⋊C8—222no—
270C4⋊C8—222no—
271C4⋊C8C22×D1112yes—
272#103—22no—
273#103—22no—
274#103—222no—
275#103—222no—
276#103—222no—
277#103—222no—
278C22⋊C8—21no—
279C22⋊C8—112no—
280C22⋊C8—221no—
281C22⋊C8—221no—
282#97—221no—
283C4×C8—21no—
284C4×C8—111no—
285C4×C8—111no—
286C4×C8—222no—
287C4×C8—222no—
288C4×C8—221no—
289C2×C11—41no—
290C2×C11#304411yescharacteristic
291C2×C11#305011yescharacteristic
292C2×C11#306911yescharacteristic
293C2×Q8—24no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—221no—
298C2×Q8—221no—
299C2×Q8C2×C22⋊D1112yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4D4×D1111yescharacteristic
303C22×C4#434111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305Q16—44no—
306Q16—444no—
307C2×C8—22no—
308C2×C8—112no—
309C2×C8—112no—
310C2×C8—222no—
311C2×C8—222no—
312C4⋊C4—22no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C4⋊C4C2×C22⋊D1112yes—
328C22⋊C4—41no—
329C22⋊C4—441no—
330C42—22no—
331C42—22no—
332C42—41no—
333C42—441no—
334C42D4×D1111yescharacteristic
335C42#434111yescharacteristic
336C42C2×C22⋊D1111yescharacteristic
337C42C23×D1111yescharacteristic
338C11#1940711yescharacteristic, complemented, Sylow
339C23#6699211yescharacteristic
340Q8—24no—
341Q8—22no—
342Q8—42no—
343Q8—81no—
344Q8—442no—
345Q8—442no—
346Q8#6700314yes—
347C2×C4—24no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4#6699211yescharacteristic
359C2×C4#6699211yescharacteristic
360C2×C4#6699211yescharacteristic
361C2×C4C2×D4×D1111yescharacteristic
362C2×C4C2×#434111yescharacteristic
363C2×C4C22×C22⋊D1111yescharacteristic
364C8—42no—
365C8—222no—
366C8—222no—
367C8—442no—
368C8—442no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22C2×#6699211yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—24no—
377C4—21no—
378C4—42no—
379C4—81no—
380C4—81no—
381C4—881no—
382C4—881no—
383C4#1062329712yes—
384C4C2×#6700312yes—
385C2—41no—
386C2#1307814311yescharacteristic
387C2#1307819411yescharacteristic
388C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3104C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#3104D11
hypocenterC11#19407
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
4. #13068076C2semidirect
5. #13068048C2semidirect
6. #13068008C2semidirect
7. #13068000C2semidirect
338. C11#19407semidirect

Maximal subgroups

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

subgroupindex
#130797752
#130787462
#130776972
#130680762
#130680482
#130680082
#130680002
#130673942
#130673262
#130672802
C11×#31042
#1940711