Finite Group Databasebeta

← #14644773

Subgroups — #14644773

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077310C211yesmaximal, characteristic
2C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
3#13067108C211yesmaximal, characteristic
4#13067105C211yesmaximal, characteristic
5#13066504C211yesmaximal, characteristic, complemented
6#13066502C211yesmaximal, characteristic, complemented
7C11×#1752C211yesmaximal, characteristic, complemented
8C23×C8×C11C2211yescharacteristic
9#10623322C2211yescharacteristic
10C2×#66954C411yescharacteristic, complemented
11C2×C11×C22⋊C8C2211yescharacteristic
12C2×C11×#97—21no—
13C4×C11×C22⋊C4C2211yescharacteristic
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622724—21no—
18#10622724—21no—
19#10622723C411yescharacteristic, complemented
20C8×C22⋊D11—21no—
21C8×C22⋊D11—21no—
22#10622715C411yescharacteristic, complemented
23#10622714C411yescharacteristic, complemented
24C2×C8×Dic11—21no—
25C11×#336—21no—
26#10622188—21no—
27#10622108C412yescomplemented
28#10622105C412yescomplemented
29#10622090C412yescomplemented
30#10622089C412yescomplemented
31C23×C4×C11C2311yescharacteristic
32C2×#4339C2×C411yescharacteristic
33C22×C8×C11—21no—
34C22×C8×C11—42no—
35C22×C8×C11C2×C411yescharacteristic
36C22×C8×C11C2×C411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C22×C8×C11D411yescharacteristic
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C42×C11—21no—
43#67006—21no—
44C2×C22⋊Dic11—21no—
45#66983C2×C411yescharacteristic
46#66983C2×C411yescharacteristic
47#66982—21no—
48C4×C22⋊D11—21no—
49C4×C22⋊D11—21no—
50#66979C2×C411yescharacteristic
51#66977C2×C411yescharacteristic
52#66977C2×C411yescharacteristic
53C2×C4×Dic11—21no—
54C2×#4318C2×C411yescharacteristic
55C2×#4318C2×C411yescharacteristic
56C22×C11⋊C8—21no—
57#66954—42no—
58C2×#4313—21no—
59C2×C8×D11—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8C2×C412yes—
62C11×#97—42no—
63C11×#95C2×C412yes—
64C11⋊#95C2×C412yes—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)C2×C412yes—
69(C2×D11)⋊C8—21no—
70(C2×D11)⋊C8—21no—
71#66879—21no—
72Dic11⋊C8—21no—
73Dic11⋊C8—21no—
74C8×Dic11—21no—
75C8×Dic11—42no—
76#8240—111nomaximal, Sylow
77C24×C11#4111yescharacteristic
78C22×C4×C11—22no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C2×C22⋊D11—21no—
88C2×C22⋊D11—21no—
89C2×C22⋊D11—21no—
90C22×Dic11—22no—
91#4339—41no—
92#4339—41no—
93C2×D44C4211yescharacteristic
94C2×C4×D11—21no—
95C2×Dic22C4211yescharacteristic
96C2×C8×C11—22no—
97C2×C8×C11—22no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C2×C8×C11C22⋊C411yescharacteristic
106C2×C8×C11C22⋊C411yescharacteristic
107C2×C8×C11C22⋊C411yescharacteristic
108C2×C8×C11C22⋊C411yescharacteristic
109C11×C22⋊C4—42no—
110C42×C11—41no—
111C42×C11—41no—
112C22⋊Dic11—24no—
113C22⋊Dic11—21no—
114C22⋊Dic11—21no—
115C22⋊Dic11—21no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—21no—
118C4⋊Dic11C4211yescharacteristic
119C4⋊Dic11C4211yescharacteristic
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122C4×Dic11—21no—
123C4×Dic11—41no—
124C4×Dic11—41no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132#4313—42no—
133C8×D11—42no—
134#2929—111no—
135#1752D1111yescharacteristic, complemented
136C8×C22⋊C4—111no—
137#1501—111no—
138#1501—111no—
139#1298—111no—
140#1297—111no—
141C23×C11—22no—
142C23×C11—22no—
143C23×C11—41no—
144C23×C11#11711yescharacteristic
145C23×C11C4×D411yescharacteristic
146C23×C11C4×D411yescharacteristic
147C22×D11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11C2×C4211yescharacteristic
161C2×C4×C11C2×C22⋊C411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C22⋊D11—42no—
165C22⋊D11—42no—
166C22⋊D11—42no—
167C2×Dic11—24no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173D44—41no—
174C4×D11—41no—
175C4×D11—41no—
176Dic22—41no—
177C8×C11—21no—
178C8×C11—21no—
179C8×C11—21no—
180C8×C11—42no—
181C8×C11#9912yes—
182C11⋊C8—42no—
183C11⋊C8—41no—
184C11⋊C8—41no—
185C2×#131—111no—
186C23×C8C2×D1111yescharacteristic
187#525—111no—
188#435—221no—
189#435—221no—
190C8×D4—221no—
191C8×D4—221no—
192#424—111no—
193#408—111no—
194#407—111no—
195C2×C22⋊C8—111no—
196C2×C22⋊C8C2×D1111yescharacteristic
197#405—111no—
198C2×#97—21no—
199C2×C4×C8—221no—
200C4×C22⋊C4—111no—
201C4×C22⋊C4C2×D1111yescharacteristic
202#336—21no—
203#336—221no—
204#328—112no—
205#328—112no—
206#327—112no—
207#327—112no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—44no—
216C22×C11C4×C22⋊C411yescharacteristic
217C22×C11#44312yes—
218C22×C11#44412yes—
219C2×D11—41no—
220C2×D11—41no—
221C2×D11—41no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—82no—
226C4×C11C2×#9911yescharacteristic
227C4×C11#41011yescharacteristic
228Dic11—44no—
229Dic11—41no—
230Dic11—41no—
231Dic11—41no—
232C2×#41—111no—
233C23×C4C22×D1111yescharacteristic
234#131—442no—
235C2×M16—111no—
236C2×M16—111no—
237C2×M16—221no—
238C22×C8—21no—
239C22×C8—42no—
240C22×C8—221no—
241C22×C8—221no—
242C22×C8C4×D1111yescharacteristic
243C22×C8C4×D1111yescharacteristic
244C22×C8D4411yescharacteristic
245C22×C8D4411yescharacteristic
246C22×C8C22⋊D1111yescharacteristic
247C22×C8C22⋊D1111yescharacteristic
248#123—221no—
249C22⋊Q8—111no—
250C22⋊Q8—111no—
251#121—111no—
252#121—111no—
253#120—221no—
254C4×D4—221no—
255C4×D4—221no—
256#117—111no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—221no—
259C2×C42—21no—
260C2×C42—221no—
261C4⋊C8—221no—
262C4⋊C8—221no—
263C22⋊C8—21no—
264C22⋊C8—112no—
265C22⋊C8—221no—
266C22⋊C8—221no—
267C22⋊C8—221no—
268C22⋊C8—221no—
269C22⋊C8—221no—
270C22⋊C8C4×D1112yes—
271#97—42no—
272#97—221no—
273C4×C8—221no—
274C4×C8—442no—
275#95—112no—
276#95C4×D1112yes—
277C2×C11—22no—
278C2×C11—22no—
279C2×C11—41no—
280C2×C11C4×#9911yescharacteristic
281C2×C11#176411yescharacteristic
282C2×C11#176511yescharacteristic
283D11—81no—
284C24#433911yescharacteristic
285#41—441no—
286#41—441no—
287C2×Q8—111no—
288C2×D4—111no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—221no—
292C22×C4—22no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—222no—
296C22×C4—221no—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4C2×C4×D1111yescharacteristic
300C22×C4C2×D4411yescharacteristic
301C22×C4#433911yescharacteristic
302C22×C4C2×C22⋊D1111yescharacteristic
303M16—442no—
304M16—441no—
305M16—441no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—222no—
316C2×C8—221no—
317C2×C8—221no—
318C2×C8—442no—
319C2×C8—441no—
320C2×C8—441no—
321C2×C8(C2×D11)⋊C411yescharacteristic
322C2×C8(C2×D11)⋊C411yescharacteristic
323C2×C8(C2×D11)⋊C411yescharacteristic
324C2×C8(C2×D11)⋊C411yescharacteristic
325C4⋊C4—111no—
326C4⋊C4—111no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C22⋊C4—42no—
330C22⋊C4—224no—
331C22⋊C4—221no—
332C22⋊C4—221no—
333C22⋊C4—221no—
334C22⋊C4—221no—
335C22⋊C4—221no—
336C42—41no—
337C42—41no—
338C42—221no—
339C42—441no—
340C42—441no—
341C11#824011yescharacteristic, complemented, Sylow
342C23—22no—
343C23—22no—
344C23—41no—
345C23—221no—
346C23#6692511yescharacteristic
347C23C4×D4411yescharacteristic
348C23C4×C22⋊D1111yescharacteristic
349Q8—441no—
350D4—441no—
351D4—442no—
352D4—442no—
353D4—442no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—224no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4C42×D1111yescharacteristic
375C2×C4C4×D4411yescharacteristic
376C2×C4C2×(C2×D11)⋊C411yescharacteristic
377C2×C4C4×C22⋊D1111yescharacteristic
378C8—21no—
379C8—21no—
380C8—21no—
381C8—42no—
382C8—442no—
383C8—441no—
384C8—441no—
385C8#6687012yes—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—441no—
395C22—441no—
396C22—441no—
397C22#1062233012yes—
398C22C4×(C2×D11)⋊C411yescharacteristic
399C22#1062275712yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—82no—
404C4—444no—
405C4—441no—
406C4—441no—
407C4—441no—
408C4C2×#6687011yescharacteristic
409C4#1062261911yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—881no—
414C2C4×#6687011yescharacteristic
415C2#1306845511yescharacteristic
416C2#1306846011yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D11)⋊C4
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1752C2
socleC22×C11C4×C22⋊C4
prime radical#10623322C22
cosocleC23×C4×C11C23
hypercenter#1752D11
hypocenterC11#8240
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C8×C22⋊Dic11C2semidirect
5. #13066504C2semidirect
6. #13066502C2semidirect
7. C11×#1752C2semidirect
10. C2×#66954C4semidirect
19. #10622723C4semidirect
22. #10622715C4semidirect
23. #10622714C4semidirect
27. #10622108C4semidirect
28. #10622105C4semidirect
29. #10622090C4semidirect
30. #10622089C4semidirect
135. #1752D11semidirect
341. C11#8240semidirect

Maximal subgroups

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

subgroupindex
#130773102
C8×C22⋊Dic112
#130671082
#130671052
#130665042
#130665022
C11×#17522
#824011