Finite Group Databasebeta

← #14723052

Subgroups — #14723052

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077582C211yesmaximal, characteristic
2#13077277C212yesmaximal
3#13067403C212yesmaximal, complemented
4#13067398C212yesmaximal, complemented
5#13067394C212yesmaximal, complemented
6#13067382C212yesmaximal, complemented
7#13067379C211yesmaximal, characteristic, complemented
8#13067367C212yesmaximal, complemented
9C11×#1564C211yesmaximal, characteristic, complemented
10C4×#4339C2211yescharacteristic
11C11×#431C2212yes—
12C2×C4×C8×C11C2211yescharacteristic
13#10622724C412yes—
14#10622724C412yes—
15#10622539C2212yes—
16#10622538C2211yescharacteristic
17#10622450C2212yes—
18#10622448C2212yes—
19#10622446C2212yes—
20D11×C4⋊C8C2212yes—
21#10622340—22no—
22#10622333—22no—
23#10622303—22no—
24#10622302—22no—
25#10622301C411yescharacteristic
26#10622301C411yescharacteristic
27C4×#4313C2212yes—
28#10622298C2212yes—
29#10622292C411yescharacteristic
30#10622292C411yescharacteristic
31C11×#335C2211yescharacteristic
32C11×#335C2211yescharacteristic
33C11×#334C2212yes—
34#10622118C2212yes—
35#10622118C2212yes—
36#10622117C2212yes—
37#10622117C2212yes—
38#10622096C2211yescharacteristic
39#10622096C2211yescharacteristic
40#10622095C2212yes—
41C2×#4339D411yescharacteristic
42C22×C8×C11C2×C411yescharacteristic
43C22×C8×C11C2×C411yescharacteristic
44C2×C42×C11C2311yescharacteristic
45C4×C22⋊D11C2×C412yes—
46C4×C22⋊D11Q812yes—
47#66979D411yescharacteristic
48C2×#4313—22no—
49C2×#4313C2×C412yes—
50C2×#4313C2×C412yes—
51C2×C8×D11—22no—
52C4×D44C2×C411yescharacteristic
53C4×D44Q811yescharacteristic
54#66925D412yes—
55C42×D11C2312yes—
56C4×Dic22C2×C411yescharacteristic
57C4×Dic22Q811yescharacteristic
58C11×C4⋊C8C2312yes—
59C11×C4⋊C8C2312yes—
60C11×C22⋊C8—22no—
61C4×C8×C11—22no—
62C4×C8×C11C2×C411yescharacteristic
63C4×C8×C11C2×C411yescharacteristic
64C4×C8×C11C2311yescharacteristic
65C4×C8×C11C2311yescharacteristic
66C22⋊(C11⋊C8)—22no—
67C22⋊(C11⋊C8)C2×C412yes—
68(C2×D11)⋊C8—22no—
69(C2×D11)⋊C8—22no—
70(C2×D11)⋊C8C2×C412yes—
71(C2×D11)⋊C8C2×C412yes—
72#66879—22no—
73#66879C2×C412yes—
74#66879C2×C412yes—
75Dic11⋊C8—22no—
76Dic11⋊C8—22no—
77Dic11⋊C8C2×C412yes—
78Dic11⋊C8C2×C412yes—
79C8×Dic11—22no—
80C4⋊(C11⋊C8)C2×C411yescharacteristic
81C4⋊(C11⋊C8)C2×C411yescharacteristic
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84#66867—22no—
85C4×C11⋊C8C2312yes—
86#17833—111nomaximal, Sylow
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×Q811yescharacteristic
90C2×C22⋊D11C4⋊C412yes—
91#4339—41no—
92#4339—41no—
93C2×D44C4⋊C411yescharacteristic
94C2×C4×D11C22×C412yes—
95C2×C4×D11C2×D412yes—
96C2×C4×D11C2×Q812yes—
97C2×Dic22C4⋊C411yescharacteristic
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C2×C8×C11C22×C411yescharacteristic
103C2×C8×C11C22×C411yescharacteristic
104C2×C8×C11C22×C411yescharacteristic
105C2×C8×C11C22×C411yescharacteristic
106C42×C11C22×C411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×Q811yescharacteristic
109C42×C11C2411yescharacteristic
110C22⋊Dic11C4⋊C412yes—
111(C2×D11)⋊C4C4⋊C412yes—
112(C2×D11)⋊C4C4⋊C412yes—
113C4⋊Dic11C4⋊C411yescharacteristic
114C4⋊Dic11C4⋊C411yescharacteristic
115Dic11⋊C4C4⋊C412yes—
116Dic11⋊C4C4⋊C412yes—
117C4×Dic11C22×C412yes—
118C4×Dic11C2×D412yes—
119C4×Dic11C2×Q812yes—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8C22×C412yes—
123C2×C11⋊C8C22×C412yes—
124#4313—24no—
125#4313—42no—
126#4313—44no—
127C8×D11—44no—
128#2965—111no—
129#2925—112no—
130#1574—112no—
131#1573—112no—
132#1572—112no—
133#1569—112no—
134#1568—111no—
135#1565—112no—
136#1564D1111yescharacteristic, complemented
137C23×C11C2×C4⋊C411yescharacteristic
138C22×D11C2×C4⋊C412yes—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11C2×C4⋊C411yescharacteristic
145C2×C4×C11C2×C4⋊C411yescharacteristic
146C2×C4×C11C2×C4⋊C411yescharacteristic
147C2×C4×C11C23×C411yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C22×Q811yescharacteristic
150C22⋊D11—42no—
151C2×Dic11C2×C4⋊C412yes—
152C2×Dic11C2×C4⋊C412yes—
153C2×Dic11C2×C4⋊C412yes—
154D44—41no—
155C4×D11—22no—
156C4×D11—22no—
157C4×D11—22no—
158C4×D11—22no—
159C4×D11—42no—
160Dic22—41no—
161C8×C11—21no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11—42no—
165C8×C11—42no—
166C8×C11#13112yes—
167C11⋊C8—22no—
168C11⋊C8—22no—
169C11⋊C8—42no—
170C11⋊C8—42no—
171C4×#41—111no—
172#446—111no—
173#446—111no—
174#436—111no—
175#436—111no—
176#435—112no—
177#435—112no—
178#433—222no—
179#433—222no—
180#432—112no—
181#432—112no—
182#431—111no—
183#431—112no—
184#431—112no—
185#431C2×D1112yes—
186#423—112no—
187C2×C4⋊C8—112no—
188#408—222no—
189#405—222no—
190C4×M16—112no—
191C2×C4×C8C2×D1111yescharacteristic
192#335—112no—
193#335—112no—
194#335—111no—
195#335—111no—
196#335C2×D1111yescharacteristic
197#335C2×D1111yescharacteristic
198#334—112no—
199#334—112no—
200#334—112no—
201#334C2×D1112yes—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11C22×C4⋊C411yescharacteristic
206C2×D11—22no—
207C2×D11—22no—
208C2×D11—22no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11C2×#13111yescharacteristic
214C4×C11#56811yescharacteristic
215C4×C11#57511yescharacteristic
216C4×C11#57511yescharacteristic
217Dic11—22no—
218Dic11—22no—
219Dic11—22no—
220C2×#41—111no—
221C2×M16—112no—
222C2×M16—112no—
223C2×M16—222no—
224C22×C8—222no—
225C22×C8C4×D1111yescharacteristic
226C22×C8C4×D1111yescharacteristic
227C4×Q8—111no—
228C4×Q8—111no—
229C4×D4—112no—
230C4×D4—112no—
231C4×D4—111no—
232C4×D4—111no—
233#117—111no—
234#117—112no—
235C2×C42—112no—
236C2×C42C22×D1111yescharacteristic
237C4⋊C8—112no—
238C4⋊C8—112no—
239C4⋊C8—111no—
240C4⋊C8—111no—
241C4⋊C8—112no—
242C4⋊C8—112no—
243C4⋊C8—222no—
244C4⋊C8—222no—
245C4⋊C8C22×D1112yes—
246C4⋊C8C22×D1112yes—
247C22⋊C8—22no—
248C22⋊C8—112no—
249C22⋊C8—112no—
250C22⋊C8—112no—
251C22⋊C8—222no—
252C22⋊C8—222no—
253C22⋊C8—222no—
254#97—112no—
255#97—112no—
256#97—222no—
257#97—222no—
258C4×C8—22no—
259C4×C8—112no—
260C4×C8—222no—
261C4×C8C4×D1111yescharacteristic
262C4×C8C4×D1111yescharacteristic
263C4×C8C22×D1111yescharacteristic
264C4×C8C22×D1111yescharacteristic
265C2×C11—41no—
266C2×C11#290611yescharacteristic
267C2×C11#291111yescharacteristic
268C2×C11#291611yescharacteristic
269D11—42no—
270#41—441no—
271#41—441no—
272C2×Q8—111no—
273C2×D4—112no—
274C2×D4—111no—
275C22×C4—112no—
276C22×C4—112no—
277C22×C4—112no—
278C22×C4C2×C4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C22×C4Q8×D1111yescharacteristic
281M16—224no—
282M16—442no—
283M16—444no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—112no—
289C2×C8—112no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—444no—
293C2×C8C2×C4×D1111yescharacteristic
294C2×C8C2×C4×D1111yescharacteristic
295C2×C8C2×C4×D1111yescharacteristic
296C2×C8C2×C4×D1111yescharacteristic
297C4⋊C4—112no—
298C4⋊C4—112no—
299C4⋊C4—111no—
300C4⋊C4—111no—
301C22⋊C4—112no—
302C22⋊C4—112no—
303C22⋊C4—112no—
304C42—112no—
305C42—112no—
306C42—112no—
307C42C2×C4×D1111yescharacteristic
308C42D4×D1111yescharacteristic
309C42Q8×D1111yescharacteristic
310C42C23×D1111yescharacteristic
311C11#1783311yescharacteristic, complemented, Sylow
312C23—112no—
313C23C4⋊C4×D1111yescharacteristic
314Q8—441no—
315D4—441no—
316D4—442no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—112no—
323C2×C4—112no—
324C2×C4—112no—
325C2×C4—222no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—442no—
330C2×C4C4⋊C4×D1111yescharacteristic
331C2×C4C4⋊C4×D1111yescharacteristic
332C2×C4C4⋊C4×D1111yescharacteristic
333C2×C4C22×C4×D1111yescharacteristic
334C2×C4C2×D4×D1111yescharacteristic
335C2×C4C2×Q8×D1111yescharacteristic
336C8—21no—
337C8—21no—
338C8—21no—
339C8—42no—
340C8—42no—
341C8—222no—
342C8—222no—
343C8—442no—
344C8—442no—
345C8#6695412yes—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—222no—
350C22—222no—
351C22—222no—
352C22C2×C4⋊C4×D1111yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—222no—
358C4—222no—
359C4—222no—
360C4C2×#6695411yescharacteristic
361C4#1062327611yescharacteristic
362C4#1062329911yescharacteristic
363C4#1062329911yescharacteristic
364C2—41no—
365C2—442no—
366C2#1307718111yescharacteristic
367C2#1307720411yescharacteristic
368C2#1307722411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1564C2
socleC22×C11C22×C4⋊C4
prime radicalC2×#4339D4
cosocleC42×C11C24
hypercenter#1564D11
hypocenterC11#17833
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
3. #13067403C2semidirect
4. #13067398C2semidirect
5. #13067394C2semidirect
6. #13067382C2semidirect
7. #13067379C2semidirect
8. #13067367C2semidirect
9. C11×#1564C2semidirect
136. #1564D11semidirect
311. C11#17833semidirect

Maximal subgroups

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

subgroupindex
#130775822
#130772772
#130674032
#130673982
#130673942
#130673822
#130673792
#130673672
C11×#15642
#1783311