Finite Group Databasebeta

← #14736834

Subgroups — #14736834

Order 2816.

778 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#13079739C211yesmaximal, characteristic, complemented
2#13079534C211yesmaximal, characteristic
3C2×#10622689C211yesmaximal, characteristic, complemented
4#13077327C211yesmaximal, characteristic, complemented
5#13068080C214yesmaximal, complemented
6#13067956C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067289C211yesmaximal, characteristic, complemented
9C11×#1545C211yesmaximal, characteristic, complemented
10C2×C11×#127C2211yescharacteristic
11C22×#4324—21no—
12C22×#4324—21no—
13C2×#66960—21no—
14#10623008C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C11×#423C2211yescharacteristic
18#10622830—22no—
19#10622742—21no—
20#10622689—21no—
21#10622689—21no—
22#10622689C2212yes—
23#10622689C2212yes—
24#10622686—21no—
25#10622685C2214yes—
26#10622683—21no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622459C2214yescomplemented
30#10622451—21no—
31#10622451C2212yescomplemented
32#10622447—21no—
33#10622447C2212yescomplemented
34#10622349—22no—
35#10622307—21no—
36#10622295—21no—
37C11×#331C2214yes—
38#10622120C2214yescomplemented
39#10622118C2212yescomplemented
40#10622117C2212yescomplemented
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C2×#4339—21no—
45C22×Dic22—21no—
46C2×C11×M16—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127—21no—
50C11×#127C2312yes—
51C2×C42×C11C2311yescharacteristic
52C2×#4324—22no—
53C2×#4324—22no—
54C2×#4324—22no—
55C2×#4324—22no—
56C2×#4324—44no—
57C2×#4324—44no—
58C2×#4323—24no—
59#66983—21no—
60#66983D412yes—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C22×C11⋊C8D411yescharacteristic
64C22×C11⋊C8D411yescharacteristic
65#66960—44no—
66C2×#4313—22no—
67C2×C8×D11—22no—
68#66928—21no—
69#66927D411yescharacteristic
70C4×D44—21no—
71C4×D44C2312yes—
72#66922—21no—
73#66922—21no—
74#66922—21no—
75#66922D411yescharacteristic
76#66922C2312yes—
77C11×C4⋊C8—21no—
78C11×C4⋊C8C2312yes—
79C11×C4⋊C8C2312yes—
80C11×C22⋊C8—21no—
81C4×C8×C11—21no—
82#66896—24no—
83C22⋊(C11⋊C8)—21no—
84#66885—24no—
85(C2×D11)⋊C8—22no—
86(C2×D11)⋊C8—22no—
87#66882—24no—
88C4⋊(C11⋊C8)C2312yes—
89C4×C11⋊C8—21no—
90C4×C11⋊C8D411yescharacteristic
91C4×C11⋊C8D411yescharacteristic
92C4×C11⋊C8C2311yescharacteristic
93C4×C11⋊C8C2311yescharacteristic
94#19186—111nomaximal, Sylow
95C24×C11—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×C22⋊D11—22no—
110C22×Dic11—41no—
111#4339—42no—
112#4339—42no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44C2×D412yes—
116C2×C4×D11—22no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—41no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C11×M16—42no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C42×C11C2×D411yescharacteristic
126C42×C11C2×D411yescharacteristic
127C42×C11#4111yescharacteristic
128C42×C11C2411yescharacteristic
129#4324—44no—
130#4324—44no—
131#4324—44no—
132#4324—44no—
133#4323—84no—
134(C2×D11)⋊C4—22no—
135(C2×D11)⋊C4—22no—
136C4⋊Dic11—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11—41no—
140C4⋊Dic11—41no—
141C4⋊Dic11C2×D412yes—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8D814yescomplemented
145C2×C11⋊C8C2×D411yescharacteristic
146C2×C11⋊C8C2×D411yescharacteristic
147C2×C11⋊C8C2×D411yescharacteristic
148C2×C11⋊C8C2×D411yescharacteristic
149#4313—44no—
150C8×D11—44no—
151#3226—111no—
152#3205—111no—
153C2×#492—111no—
154#2931—111no—
155#1685—114no—
156#1665—114no—
157#1564—111no—
158#1546—111no—
159#1545D1111yescharacteristic, complemented
160C23×C11—42no—
161C23×C11—82no—
162C23×C11—82no—
163C23×C11—82no—
164C23×C11#12111yescharacteristic
165C22×D11—22no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—44no—
169D4×C11—82no—
170D4×C11—82no—
171D4×C11—82no—
172D4×C11—82no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11C2×D812yes—
179C2×C4×C11AGL(1,ℤ/8)12yes—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C22⋊D11—44no—
184C2×Dic11—22no—
185C2×Dic11—42no—
186C2×Dic11—82no—
187D44—24no—
188D44—42no—
189D44—42no—
190C4×D11—42no—
191C4×D11—42no—
192Dic22—42no—
193Dic22—42no—
194Dic22—42no—
195Dic22—82no—
196C8×C11—42no—
197C8×C11—42no—
198C11⋊C8—21no—
199C11⋊C8—21no—
200C11⋊C8—42no—
201C11⋊C8C2×D812yes—
202C11⋊C8C2×D812yes—
203C22×SD16—221no—
204C22×SD16—221no—
205C2×#131—221no—
206#532—111no—
207C2×C4⋊Q8—111no—
208C2×#127C2×D1111yescharacteristic
209#500—221no—
210#493—221no—
211#492—112no—
212#492—112no—
213#492—221no—
214#492—221no—
215#486—221no—
216#486—221no—
217#480—222no—
218#474—114no—
219#459—114no—
220#447—222no—
221#436—112no—
222#436—221no—
223C8×D4—112no—
224C8×D4—221no—
225#431—111no—
226#431C2×D1111yescharacteristic
227#423C2×D1111yescharacteristic
228#408—221no—
229C2×C4×C8—111no—
230#335—112no—
231#334—112no—
232#332—114no—
233#331C2×D1114yes—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—82no—
237C22×C11—82no—
238C22×C11—82no—
239C22×C11—164no—
240C22×C11#45912yes—
241C22×C11C2×#12111yescharacteristic
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—42no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11#45912yes—
248C4×C11#47112yes—
249C4×C11C22×D811yescharacteristic
250C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C4×C11#57712yes—
252Dic11—42no—
253Dic11—82no—
254C2×#41—221no—
255C22×Q8—221no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C2×SD16—222no—
260C2×SD16—222no—
261C2×SD16—222no—
262C2×SD16—222no—
263C2×SD16—444no—
264C2×SD16—444no—
265C2×D8—224no—
266#131—444no—
267C2×M16—21no—
268C2×M16—222no—
269C22×C8—111no—
270C22×C8—111no—
271C22×C8—222no—
272C4⋊Q8—111no—
273C4⋊Q8—112no—
274C4⋊Q8—221no—
275C4⋊Q8—221no—
276C4⋊Q8—221no—
277#127—21no—
278#127—21no—
279#127—21no—
280#127—111no—
281#127C22×D1112yes—
282#124—221no—
283#121—112no—
284#121—221no—
285C4×D4—112no—
286C4×D4—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C42C22×D1111yescharacteristic
290#107—224no—
291C4⋊C8—21no—
292C4⋊C8—112no—
293C4⋊C8C22×D1112yes—
294C4⋊C8C22×D1112yes—
295#102—224no—
296#102—224no—
297C22⋊C8—21no—
298C22⋊C8—222no—
299C22⋊C8—222no—
300C22⋊C8—221no—
301C4×C8—21no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8—111no—
305C4×C8—111no—
306C4×C8—221no—
307C2×C11—22no—
308C2×C11—162no—
309C2×C11C2×#45911yescharacteristic
310C2×C11#305711yescharacteristic
311C2×C11C2×#47111yescharacteristic
312D11—82no—
313C24—41no—
314#41—442no—
315#41—442no—
316C2×Q8—221no—
317C2×Q8—222no—
318C2×Q8—441no—
319C2×Q8—442no—
320C2×Q8—442no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—82no—
330C2×D4—82no—
331C2×D4—112no—
332C2×D4—222no—
333C2×D4—221no—
334C2×D4—221no—
335C22×C4—222no—
336C22×C4—441no—
337C22×C4#433911yescharacteristic
338C22×C4D4×D1111yescharacteristic
339C22×C4D4×D1111yescharacteristic
340SD16—444no—
341SD16—444no—
342SD16—444no—
343SD16—444no—
344D8—884no—
345M16—42no—
346M16—444no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—114no—
350C2×C8—111no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8—111no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—444no—
357C4⋊C4—112no—
358C4⋊C4—221no—
359C4⋊C4—222no—
360C4⋊C4—222no—
361C4⋊C4—441no—
362C4⋊C4—441no—
363C22⋊C4—222no—
364C22⋊C4—222no—
365C42#433911yescharacteristic
366C42D4×D1111yescharacteristic
367C42D4×D1111yescharacteristic
368C42C23×D1111yescharacteristic
369C11#1918611yescharacteristic, complemented, Sylow
370C23—42no—
371C23—82no—
372C23—82no—
373C23—82no—
374C23—222no—
375C23#6693711yescharacteristic
376Q8—442no—
377Q8—442no—
378Q8—442no—
379Q8—882no—
380D4—42no—
381D4—42no—
382D4—44no—
383D4—82no—
384D4—82no—
385D4—82no—
386D4—82no—
387D4—224no—
388D4—444no—
389D4—442no—
390D4—442no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—222no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—882no—
398C2×C4#6693711yescharacteristic
399C2×C4#6693711yescharacteristic
400C2×C4#6693711yescharacteristic
401C2×C4D8×D1112yes—
402C2×C4#6696712yes—
403C2×C4C2×#433911yescharacteristic
404C2×C4C2×D4×D1111yescharacteristic
405C2×C4C2×D4×D1111yescharacteristic
406C8—42no—
407C8—42no—
408C8—112no—
409C8—112no—
410C8—221no—
411C8—221no—
412C8—442no—
413C22—21no—
414C22—21no—
415C22—82no—
416C22—82no—
417C22—82no—
418C22—164no—
419C22—442no—
420C22—442no—
421C22—442no—
422C22#1062239912yes—
423C22C2×#6693711yescharacteristic
424C4—21no—
425C4—21no—
426C4—442no—
427C4—882no—
428C4#1062236112yes—
429C4#1062239912yes—
430C4C2×D8×D1111yescharacteristic
431C4C2×#6696711yescharacteristic
432C4#1062330612yes—
433C2—22no—
434C2—162no—
435C2—882no—
436C2C2×#1062239911yescharacteristic
437C2#1307825411yescharacteristic
438C2C2×#1062236111yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1545C2
socleC22×C11C2×#121
prime radical#13079534C2
hypercenter#1545D11
hypocenterC11#19186
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. #13079739C2semidirect
3. C2×#10622689C2semidirect
4. #13077327C2semidirect
5. #13068080C2semidirect
6. #13067956C2semidirect
7. #13067362C2semidirect
8. #13067289C2semidirect
9. C11×#1545C2semidirect
29. #10622459C22semidirect
31. #10622451C22semidirect
33. #10622447C22semidirect
38. #10622120C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
144. C2×C11⋊C8D8semidirect
159. #1545D11semidirect
369. C11#19186semidirect

Maximal subgroups

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

subgroupindex
#130797392
#130795342
C2×#106226892
#130773272
#130680802
#130679562
#130673622
#130672892
C11×#15452
#1918611