Finite Group Databasebeta

← #14736979

Subgroups — #14736979

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079559C211yesmaximal, characteristic, complemented
2#13079557C211yesmaximal, characteristic, complemented
3C2×#10622686C211yesmaximal, characteristic
4#13077546C211yesmaximal, characteristic, complemented
5#13068099C214yesmaximal, complemented
6#13067975C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067285C211yesmaximal, characteristic, complemented
9C11×#1545C211yesmaximal, characteristic, complemented
10C2×C11×#127C2211yescharacteristic
11C22×#4323—21no—
12C22×#4323—21no—
13C2×#66927C2211yescharacteristic
14#10623001C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17#10622831—22no—
18#10622735—21no—
19#10622732—21no—
20#10622689—21no—
21#10622688C2214yescomplemented
22#10622686—21no—
23#10622686—21no—
24#10622686C2212yes—
25#10622686C2212yes—
26#10622683—21no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622461C2214yescomplemented
30#10622444—21no—
31#10622444C2212yescomplemented
32#10622443—21no—
33#10622443C2212yescomplemented
34#10622344—22no—
35#10622307—21no—
36#10622306—21no—
37C11×#331C2214yescomplemented
38#10622123C2214yescomplemented
39#10622118C2212yescomplemented
40#10622117C2212yescomplemented
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44—21no—
47C2×C11×M16—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127—21no—
51C11×#127C2312yes—
52C2×C42×C11C2311yescharacteristic
53C2×#4324—24no—
54C2×#4323—22no—
55C2×#4323—22no—
56C2×#4323—22no—
57C2×#4323—22no—
58C2×#4323—44no—
59C2×#4323—44no—
60#66979—21no—
61#66977—21no—
62#66977D412yes—
63C22×C11⋊C8D411yescharacteristic
64C22×C11⋊C8D411yescharacteristic
65C2×#4314—24no—
66#66927—21no—
67#66927—21no—
68#66927—21no—
69#66927C2312yes—
70#66923—21no—
71#66922D411yescharacteristic
72#66922D411yescharacteristic
73C4×Dic22—21no—
74C4×Dic22C2312yes—
75C11×C4⋊C8—21no—
76C11×C4⋊C8C2312yes—
77C11×C4⋊C8C2312yes—
78C11×C22⋊C8—21no—
79C4×C8×C11—21no—
80#66896—24no—
81C22⋊(C11⋊C8)—21no—
82#66885—24no—
83#66879—22no—
84Dic11⋊C8—22no—
85Dic11⋊C8—22no—
86C8×Dic11—22no—
87C4⋊(C11⋊C8)C2312yes—
88C4×C11⋊C8—21no—
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8D411yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93#19203—111nomaximal, Sylow
94C24×C11—41no—
95C23×D11—41no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C2×D4×C11—82no—
105C2×D4×C11—82no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—41no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—42no—
116C2×D44—42no—
117C2×D44—82no—
118C2×D44—82no—
119C2×Dic22—21no—
120C2×Dic22C2×D412yes—
121C11×M16—42no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128C22⋊Dic11—22no—
129#4324—84no—
130#4323—44no—
131#4323—44no—
132#4323—44no—
133#4323—44no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11C2×D412yes—
138Dic11⋊C4—22no—
139Dic11⋊C4—22no—
140C4×Dic11—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8SD1614yescomplemented
144C2×C11⋊C8C2×D411yescharacteristic
145C2×C11⋊C8C2×D411yescharacteristic
146C2×C11⋊C8C2×D411yescharacteristic
147C2×C11⋊C8C2×D411yescharacteristic
148#4314—84no—
149#3208—111no—
150#3208—111no—
151C2×#493—111no—
152#2960—111no—
153#1688—114no—
154#1668—114no—
155#1564—111no—
156#1545—111no—
157#1545D1111yescharacteristic, complemented
158C23×C11—42no—
159C23×C11—82no—
160C23×C11—82no—
161C23×C11—82no—
162C23×C11#12111yescharacteristic
163C22×D11—42no—
164C22×D11—82no—
165C22×D11—82no—
166C22×D11—82no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—44no—
170D4×C11—82no—
171D4×C11—82no—
172D4×C11—82no—
173D4×C11—82no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11C2×SD1612yes—
180C2×C4×C11AGL(1,ℤ/8)12yes—
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×Dic11—22no—
185C2×Dic11—22no—
186D44—42no—
187D44—42no—
188D44—44no—
189D44—82no—
190D44—82no—
191D44—82no—
192D44—82no—
193Dic22—24no—
194Dic22—42no—
195C8×C11—42no—
196C8×C11—42no—
197C11⋊C8—21no—
198C11⋊C8—21no—
199C11⋊C8—42no—
200C11⋊C8C2×SD1612yes—
201C11⋊C8C2×SD1612yes—
202C22×D8—221no—
203C22×D8—221no—
204#533—111no—
205C2×#127—111no—
206C2×#127C2×D1111yescharacteristic
207#493—112no—
208#493—112no—
209#493—221no—
210#493—221no—
211#492—221no—
212#492—221no—
213#486—221no—
214#486—221no—
215#460—114no—
216#460—114no—
217#450—222no—
218#450—222no—
219#446—112no—
220#446—221no—
221C8×Q8—112no—
222C8×Q8—221no—
223#431—111no—
224#431C2×D1111yescharacteristic
225#424—221no—
226#423C2×D1111yescharacteristic
227#405—221no—
228C2×C4×C8—111no—
229#335—112no—
230#334—112no—
231#331—114no—
232#331C2×D1114yescomplemented
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11—164no—
239C22×C11#46012yes—
240C22×C11C2×#12111yescharacteristic
241C2×D11—82no—
242C2×D11—82no—
243C2×D11—82no—
244C2×D11—164no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11#46012yes—
248C4×C11#47212yes—
249C4×C11C22×SD1611yescharacteristic
250C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C4×C11#57612yes—
252Dic11—42no—
253Dic11—42no—
254C22×D4—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—221no—
258C22×D4—221no—
259C22×D4—221no—
260C2×SD16—224no—
261C2×SD16—224no—
262C2×D8—222no—
263C2×D8—222no—
264C2×D8—222no—
265C2×D8—222no—
266C2×D8—444no—
267C2×D8—444no—
268C2×M16—21no—
269C22×C8—111no—
270C22×C8—111no—
271C4⋊Q8—111no—
272C4⋊Q8—111no—
273#127—21no—
274#127—21no—
275#127—21no—
276#127—112no—
277#127—221no—
278#127—221no—
279#127—221no—
280#127C22×D1112yes—
281#125—221no—
282C22⋊Q8—112no—
283C22⋊Q8—221no—
284C4×Q8—112no—
285C4×Q8—221no—
286#117—221no—
287C2×C42C22×D1111yescharacteristic
288C4⋊C8—21no—
289C4⋊C8—112no—
290C4⋊C8—222no—
291C4⋊C8—222no—
292C4⋊C8C22×D1112yes—
293C4⋊C8C22×D1112yes—
294#102—224no—
295#102—224no—
296C22⋊C8—21no—
297C22⋊C8—221no—
298#97—222no—
299C4×C8—21no—
300C4×C8—111no—
301C4×C8—111no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8—222no—
305C4×C8—221no—
306C2×C11—22no—
307C2×C11—162no—
308C2×C11C2×#46011yescharacteristic
309C2×C11#305811yescharacteristic
310C2×C11C2×#47211yescharacteristic
311D11—162no—
312C24—41no—
313C24—441no—
314C2×Q8—112no—
315C2×Q8—221no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—42no—
323C2×D4—42no—
324C2×D4—82no—
325C2×D4—82no—
326C2×D4—222no—
327C2×D4—222no—
328C2×D4—222no—
329C2×D4—441no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—442no—
333C2×D4—442no—
334C2×D4—882no—
335C2×D4—882no—
336C22×C4#433911yescharacteristic
337C22×C4D4×D1111yescharacteristic
338C22×C4D4×D1111yescharacteristic
339SD16—884no—
340SD16—884no—
341D8—444no—
342D8—444no—
343D8—444no—
344D8—444no—
345M16—42no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—114no—
349C2×C8—111no—
350C2×C8—111no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—222no—
354C2×C8—222no—
355C4⋊C4—112no—
356C4⋊C4—221no—
357C4⋊C4—221no—
358C4⋊C4—222no—
359C4⋊C4—221no—
360C4⋊C4—222no—
361C22⋊C4—222no—
362C42—222no—
363C42#433911yescharacteristic
364C42D4×D1111yescharacteristic
365C42D4×D1111yescharacteristic
366C42C23×D1111yescharacteristic
367C11#1920311yescharacteristic, complemented, Sylow
368C23—42no—
369C23—82no—
370C23—82no—
371C23—82no—
372C23—442no—
373C23—882no—
374C23—882no—
375C23—882no—
376C23#6693711yescharacteristic
377Q8—224no—
378Q8—442no—
379D4—42no—
380D4—42no—
381D4—44no—
382D4—82no—
383D4—82no—
384D4—82no—
385D4—82no—
386D4—442no—
387D4—442no—
388D4—444no—
389D4—882no—
390D4—882no—
391D4—882no—
392D4—882no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4#6693711yescharacteristic
398C2×C4#6693711yescharacteristic
399C2×C4#6693711yescharacteristic
400C2×C4#6696412yes—
401C2×C4SD16×D1112yes—
402C2×C4C2×#433911yescharacteristic
403C2×C4C2×D4×D1111yescharacteristic
404C2×C4C2×D4×D1111yescharacteristic
405C8—42no—
406C8—42no—
407C8—112no—
408C8—112no—
409C8—221no—
410C8—221no—
411C8—442no—
412C22—21no—
413C22—21no—
414C22—82no—
415C22—82no—
416C22—82no—
417C22—164no—
418C22—882no—
419C22—882no—
420C22—882no—
421C22—1764no—
422C22#1062237512yes—
423C22C2×#6693711yescharacteristic
424C4—21no—
425C4—21no—
426C4—442no—
427C4—442no—
428C4#1062236212yes—
429C4#1062237512yes—
430C4C2×#6696411yescharacteristic
431C4C2×SD16×D1111yescharacteristic
432C4#1062330512yes—
433C2—22no—
434C2—162no—
435C2—1762no—
436C2C2×#1062237511yescharacteristic
437C2#1307826311yescharacteristic
438C2C2×#1062236211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1545C2
socleC22×C11C2×#121
prime radicalC2×#10622686C2
hypercenter#1545D11
hypocenterC11#19203
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
1. #13079559C2semidirect
2. #13079557C2semidirect
4. #13077546C2semidirect
5. #13068099C2semidirect
6. #13067975C2semidirect
7. #13067362C2semidirect
8. #13067285C2semidirect
9. C11×#1545C2semidirect
21. #10622688C22semidirect
29. #10622461C22semidirect
31. #10622444C22semidirect
33. #10622443C22semidirect
37. C11×#331C22semidirect
38. #10622123C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
143. C2×C11⋊C8SD16semidirect
157. #1545D11semidirect
232. #331C2×D11semidirect
367. C11#19203semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130795572
C2×#106226862
#130775462
#130680992
#130679752
#130673622
#130672852
C11×#15452
#1920311