Finite Group Databasebeta

← #14736912

Subgroups — #14736912

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079746C211yesmaximal, characteristic, complemented
2#13079534C211yesmaximal, characteristic
3C2×#10622683C211yesmaximal, characteristic, complemented
4#13077327C211yesmaximal, characteristic, complemented
5#13068148C214yesmaximal, complemented
6#13068024C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067298C211yesmaximal, characteristic, complemented
9C11×#1545C211yesmaximal, characteristic, complemented
10C2×C11×#127C2211yescharacteristic
11C2×#66960—21no—
12#10623008C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622830—22no—
17C2×#66896—21no—
18C2×#66896—21no—
19#10622742—21no—
20#10622686—21no—
21#10622685C2214yes—
22#10622683—21no—
23#10622683—21no—
24#10622683—21no—
25#10622683C2212yes—
26#10622683C2212yes—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622455C2214yescomplemented
30#10622451—21no—
31#10622451C2212yescomplemented
32#10622447—21no—
33#10622447C2212yescomplemented
34#10622348—22no—
35#10622307—21no—
36#10622293—21no—
37C11×#331C2214yes—
38#10622119C2214yescomplemented
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×#4323—24no—
53#66983—21no—
54#66983D412yes—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59#66960—44no—
60C2×#4313—22no—
61C2×C8×D11—22no—
62#66928—21no—
63#66927D411yescharacteristic
64C4×D44—21no—
65C4×D44C2312yes—
66#66922—21no—
67#66922—21no—
68#66922—21no—
69#66922D411yescharacteristic
70#66922C2312yes—
71C11×C4⋊C8—21no—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C22⋊C8—21no—
75C4×C8×C11—21no—
76#66896—24no—
77#66896—22no—
78#66896—22no—
79#66896—22no—
80#66896—22no—
81C22⋊(C11⋊C8)—21no—
82#66885—24no—
83(C2×D11)⋊C8—22no—
84(C2×D11)⋊C8—22no—
85#66881—24no—
86C4⋊(C11⋊C8)C2312yes—
87C4×C11⋊C8—21no—
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92#19196—111nomaximal, Sylow
93C24×C11—41no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—82no—
103C2×D4×C11—82no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C2×C22⋊D11—22no—
108C22×Dic11—41no—
109#4339—42no—
110#4339—42no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44C2×D412yes—
114C2×C4×D11—22no—
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—41no—
118C2×Dic22—82no—
119C11×M16—42no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C42×C11#4111yescharacteristic
125C42×C11C2411yescharacteristic
126#4323—84no—
127(C2×D11)⋊C4—22no—
128(C2×D11)⋊C4—22no—
129C4⋊Dic11—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C4⋊Dic11C2×D412yes—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8C2×D411yescharacteristic
139C2×C11⋊C8C2×D411yescharacteristic
140C2×C11⋊C8C2×D411yescharacteristic
141C2×C11⋊C8C2×D411yescharacteristic
142#4313—44no—
143C8×D11—44no—
144#3227—111no—
145#3205—111no—
146C2×#486—111no—
147#2931—111no—
148#1697—114no—
149#1677—114no—
150#1564—111no—
151#1548—111no—
152#1545D1111yescharacteristic, complemented
153C23×C11—42no—
154C23×C11—82no—
155C23×C11—82no—
156C23×C11—82no—
157C23×C11#12111yescharacteristic
158C22×D11—22no—
159D4×C11—42no—
160D4×C11—42no—
161D4×C11—44no—
162D4×C11—82no—
163D4×C11—82no—
164D4×C11—82no—
165D4×C11—82no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#13512yes—
172C2×C4×C11AGL(1,ℤ/8)12yes—
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C22⋊D11—44no—
177C2×Dic11—22no—
178C2×Dic11—42no—
179C2×Dic11—82no—
180D44—24no—
181D44—42no—
182D44—42no—
183C4×D11—42no—
184C4×D11—42no—
185Dic22—42no—
186Dic22—82no—
187Dic22—82no—
188C8×C11—42no—
189C8×C11—42no—
190C11⋊C8—21no—
191C11⋊C8—21no—
192C11⋊C8—21no—
193C11⋊C8—21no—
194C11⋊C8—42no—
195C2×#131—221no—
196#532—111no—
197C2×C4⋊Q8—111no—
198C2×#127C2×D1111yescharacteristic
199#498—221no—
200#493—221no—
201#486—112no—
202#486—112no—
203#486—221no—
204#486—221no—
205#486—221no—
206#486—221no—
207#481—222no—
208#476—114no—
209#459—114no—
210#447—222no—
211#436—112no—
212#436—221no—
213C8×D4—112no—
214C8×D4—221no—
215#431—111no—
216#431C2×D1111yescharacteristic
217#423C2×D1111yescharacteristic
218C2×#102—221no—
219C2×#102—221no—
220#408—221no—
221C2×C4×C8—111no—
222#335—112no—
223#334—112no—
224#333—114no—
225#331C2×D1114yes—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—82no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—164no—
232C22×C11#46312yes—
233C22×C11C2×#12111yescharacteristic
234C2×D11—42no—
235C2×D11—42no—
236C2×D11—42no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11#46312yes—
240C4×C11#47212yes—
241C4×C11C2×#13511yescharacteristic
242C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C4×C11#57712yes—
244Dic11—42no—
245Dic11—82no—
246C2×#41—221no—
247C22×Q8—221no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C2×D8—224no—
252#131—444no—
253C2×M16—21no—
254C2×M16—222no—
255C22×C8—111no—
256C22×C8—111no—
257C22×C8—222no—
258C4⋊Q8—111no—
259C4⋊Q8—112no—
260C4⋊Q8—221no—
261C4⋊Q8—221no—
262C4⋊Q8—221no—
263#127—21no—
264#127—21no—
265#127—21no—
266#127—111no—
267#127C22×D1112yes—
268#124—221no—
269#121—112no—
270#121—221no—
271C4×D4—112no—
272C4×D4—221no—
273C2×C4⋊C4—221no—
274C2×C4⋊C4—221no—
275C2×C42C22×D1111yescharacteristic
276#106—224no—
277C4⋊C8—21no—
278C4⋊C8—112no—
279C4⋊C8C22×D1112yes—
280C4⋊C8C22×D1112yes—
281#102—224no—
282#102—224no—
283#102—222no—
284#102—222no—
285#102—222no—
286#102—222no—
287C22⋊C8—21no—
288C22⋊C8—222no—
289C22⋊C8—222no—
290C22⋊C8—221no—
291C4×C8—21no—
292C4×C8—111no—
293C4×C8—111no—
294C4×C8—111no—
295C4×C8—111no—
296C4×C8—221no—
297C2×C11—22no—
298C2×C11—162no—
299C2×C11C2×#46311yescharacteristic
300C2×C11#305711yescharacteristic
301C2×C11C2×#47211yescharacteristic
302D11—82no—
303C24—41no—
304#41—442no—
305#41—442no—
306C2×Q8—221no—
307C2×Q8—222no—
308C2×Q8—441no—
309C2×Q8—882no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—42no—
317C2×D4—42no—
318C2×D4—82no—
319C2×D4—82no—
320C2×D4—112no—
321C2×D4—222no—
322C2×D4—221no—
323C2×D4—221no—
324C22×C4—222no—
325C22×C4—441no—
326C22×C4#433911yescharacteristic
327C22×C4D4×D1111yescharacteristic
328C22×C4D4×D1111yescharacteristic
329D8—884no—
330M16—42no—
331M16—444no—
332C2×C8—22no—
333C2×C8—22no—
334C2×C8—111no—
335C2×C8—111no—
336C2×C8—111no—
337C2×C8—111no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—444no—
342C4⋊C4—112no—
343C4⋊C4—221no—
344C4⋊C4—222no—
345C4⋊C4—222no—
346C4⋊C4—441no—
347C4⋊C4—441no—
348C22⋊C4—222no—
349C22⋊C4—222no—
350C42#433911yescharacteristic
351C42D4×D1111yescharacteristic
352C42D4×D1111yescharacteristic
353C42C23×D1111yescharacteristic
354C11#1919611yescharacteristic, complemented, Sylow
355C23—42no—
356C23—82no—
357C23—82no—
358C23—82no—
359C23—222no—
360C23#6693711yescharacteristic
361Q8—442no—
362Q8—882no—
363Q8—882no—
364D4—42no—
365D4—42no—
366D4—44no—
367D4—82no—
368D4—82no—
369D4—82no—
370D4—82no—
371D4—224no—
372D4—444no—
373D4—442no—
374D4—442no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—222no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—882no—
382C2×C4#6693711yescharacteristic
383C2×C4#6693711yescharacteristic
384C2×C4#6693711yescharacteristic
385C2×C4#6696412yes—
386C2×C4#6696912yes—
387C2×C4C2×#433911yescharacteristic
388C2×C4C2×D4×D1111yescharacteristic
389C2×C4C2×D4×D1111yescharacteristic
390C8—42no—
391C8—42no—
392C8—221no—
393C8—221no—
394C8—221no—
395C8—221no—
396C8—442no—
397C22—21no—
398C22—21no—
399C22—82no—
400C22—82no—
401C22—82no—
402C22—164no—
403C22—442no—
404C22—442no—
405C22—442no—
406C22#1062240012yes—
407C22C2×#6693711yescharacteristic
408C4—21no—
409C4—21no—
410C4—442no—
411C4—882no—
412C4#1062236212yes—
413C4#1062240012yes—
414C4C2×#6696411yescharacteristic
415C4C2×#6696911yescharacteristic
416C4#1062330612yes—
417C2—22no—
418C2—162no—
419C2—882no—
420C2C2×#1062240011yescharacteristic
421C2#1307825411yescharacteristic
422C2C2×#1062236211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1545C2
socleC22×C11C2×#121
prime radical#13079534C2
hypercenter#1545D11
hypocenterC11#19196
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. #13079746C2semidirect
3. C2×#10622683C2semidirect
4. #13077327C2semidirect
5. #13068148C2semidirect
6. #13068024C2semidirect
7. #13067362C2semidirect
8. #13067298C2semidirect
9. C11×#1545C2semidirect
29. #10622455C22semidirect
31. #10622451C22semidirect
33. #10622447C22semidirect
38. #10622119C22semidirect
39. #10622118C22semidirect
40. #10622117C22semidirect
152. #1545D11semidirect
354. C11#19196semidirect

Maximal subgroups

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

subgroupindex
#130797462
#130795342
C2×#106226832
#130773272
#130681482
#130680242
#130673622
#130672982
C11×#15452
#1919611