Finite Group Databasebeta

← #14647667

Subgroups — #14647667

Order 2816.

440 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077729C211yesmaximal, characteristic
2#13068767C211yesmaximal, characteristic, complemented
3C4×#66889C211yesmaximal, characteristic
4#13067001C211yesmaximal, characteristic
5#13066467C211yesmaximal, characteristic, complemented
6#13066448C211yesmaximal, characteristic, complemented
7C11×#1565C211yesmaximal, characteristic, complemented
8C4×#4339C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12C2×#66889C411yescharacteristic
13C2×#66889C411yescharacteristic
14C2×Dic11⋊C8—22no—
15C42×Dic11C2211yescharacteristic
16#10622538C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18#10622450—21no—
19#10622448—21no—
20#10622343—22no—
21#10622301—21no—
22#10622292—21no—
23C11×#335—21no—
24C11×#334—21no—
25#10622193C411yescharacteristic
26#10622193C411yescharacteristic
27#10622122—21no—
28#10622121—21no—
29C2×#4339C2×C411yescharacteristic
30C2×C11×M16C2×C411yescharacteristic
31C2×C11×M16C2×C411yescharacteristic
32C22×C8×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C4×C22⋊D11—21no—
35C4×C22⋊D11—21no—
36#66979C2×C411yescharacteristic
37C2×C4×Dic11—21no—
38C2×C4×Dic11—21no—
39C2×C4×Dic11C2×C411yescharacteristic
40C2×C4×Dic11C2×C411yescharacteristic
41C22×C11⋊C8D412yes—
42C2×#4313—22no—
43C4×D44D411yescharacteristic
44C4×D44Q811yescharacteristic
45#66925—21no—
46C42×D11—21no—
47C4×Dic22D411yescharacteristic
48C4×Dic22Q811yescharacteristic
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8D411yescharacteristic
52C11×C4⋊C8D411yescharacteristic
53C11×C22⋊C8—21no—
54C11×#97—21no—
55C4×C8×C11—21no—
56C4×C8×C11—21no—
57C22⋊(C11⋊C8)—21no—
58#66889—22no—
59#66889—22no—
60(C2×D11)⋊C8—22no—
61#66879—22no—
62Dic11⋊C8—22no—
63Dic11⋊C8—44no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4×C11⋊C8—21no—
68#8841—111nomaximal, Sylow
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C2×C22⋊D11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75#4339—21no—
76#4339—21no—
77#4339—21no—
78#4339—21no—
79C2×D44C4⋊C411yescharacteristic
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×Dic22C4⋊C411yescharacteristic
84C11×M16—21no—
85C11×M16—21no—
86C11×M16—21no—
87C11×M16M1612yescomplemented
88C2×C8×C11—21no—
89C2×C8×C11—21no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11—42no—
93C2×C8×C11—41no—
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11C2×Q811yescharacteristic
97C42×C11#4111yescharacteristic
98C22⋊Dic11—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101C4⋊Dic11C4⋊C411yescharacteristic
102C4⋊Dic11C4⋊C411yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105C4×Dic11—22no—
106C4×Dic11—22no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—42no—
114C4×Dic11M1612yescomplemented
115C2×C11⋊C8—22no—
116C2×C11⋊C8—42no—
117C2×C11⋊C8—41no—
118#4313—82no—
119#2989—111no—
120#1842—111no—
121C4×#104—111no—
122#1565D1111yescharacteristic, complemented
123#1477—111no—
124#1283—111no—
125#1276—111no—
126C23×C11C4×D411yescharacteristic
127C22×D11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—41no—
131C2×C4×C11C2×C4⋊C411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11C22⋊Q811yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×C4×C11C2×M1611yescharacteristic
138C2×C4×C11C2×M1611yescharacteristic
139C2×C4×C11#13111yescharacteristic
140C2×C4×C11#13111yescharacteristic
141C22⋊D11—41no—
142C22⋊D11—41no—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152D44—21no—
153D44—21no—
154C4×D11—41no—
155C4×D11—41no—
156C4×D11—41no—
157C4×D11—41no—
158C4×D11—81no—
159Dic22—21no—
160Dic22—21no—
161C8×C11—22no—
162C8×C11—41no—
163C8×C11—41no—
164C8×C11—41no—
165C8×C11—81no—
166C11⋊C8—42no—
167C11⋊C8—81no—
168C4×#41—111no—
169#446—221no—
170#436—221no—
171#435—222no—
172#432—221no—
173#431—111no—
174#431C2×D1111yescharacteristic
175#423—221no—
176C2×C4⋊C8—111no—
177C2×C4⋊C8—222no—
178C2×C4⋊C8C2×D1111yescharacteristic
179C2×#104—111no—
180C2×#104—111no—
181C4×M16C2×D1111yescharacteristic
182C43—111no—
183#339—111no—
184#339—111no—
185#335—21no—
186#334—21no—
187Q8⋊C8—221no—
188D4⋊C8—221no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11#38511yescharacteristic
192C22×C11#43511yescharacteristic
193C22×C11#43611yescharacteristic
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11#42311yescharacteristic
201C4×C11#42411yescharacteristic
202C4×C11#43511yescharacteristic
203C4×C11#43611yescharacteristic
204C4×C11#45311yescharacteristic
205C4×C11#45611yescharacteristic
206Dic11—24no—
207Dic11—42no—
208Dic11—41no—
209Dic11—41no—
210Dic11—41no—
211C2×#41—111no—
212C2×M16—222no—
213C2×M16C4×D1111yescharacteristic
214C2×M16C4×D1111yescharacteristic
215C22×C8—21no—
216C22×C8—112no—
217C4×Q8—111no—
218C4×Q8—111no—
219C4×D4—111no—
220C4×D4—111no—
221C4×D4—221no—
222C4×D4—221no—
223#117—111no—
224#117—221no—
225C2×C42—111no—
226C2×C42—111no—
227C2×C42—221no—
228C2×C42—221no—
229C2×C42—221no—
230C2×C42C22×D1111yescharacteristic
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8—222no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237C4⋊C8—444no—
238C4⋊C8C22⋊D1111yescharacteristic
239C4⋊C8C22⋊D1111yescharacteristic
240#104—222no—
241#104—222no—
242C22⋊C8—21no—
243C22⋊C8—222no—
244C22⋊C8—221no—
245#97—21no—
246#97—222no—
247C4×C8—21no—
248C4×C8—21no—
249C4×C8—221no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11#185111yescharacteristic
253C2×C11#185911yescharacteristic
254C2×C11#186111yescharacteristic
255D11—81no—
256#41—221no—
257#41—221no—
258#41—221no—
259#41—221no—
260C2×Q8—111no—
261C2×D4—111no—
262C2×D4—221no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—221no—
268C22×C4C2×C4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C22×C4#434311yescharacteristic
271M16—21no—
272M16—21no—
273M16—21no—
274M16—882no—
275M16#431312yescomplemented
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—42no—
281C2×C8—41no—
282C2×C8—222no—
283C2×C8—442no—
284C2×C8—441no—
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C42—112no—
293C42—222no—
294C42—222no—
295C42—221no—
296C42—221no—
297C42—221no—
298C42—221no—
299C42—221no—
300C42—221no—
301C42—442no—
302C42#433911yescharacteristic
303C42D4×D1111yescharacteristic
304C42Q8×D1111yescharacteristic
305C42C2×C22⋊D1111yescharacteristic
306C11#884111yescharacteristic, complemented, Sylow
307C23—221no—
308C23#6694611yescharacteristic
309Q8—221no—
310Q8—221no—
311D4—221no—
312D4—221no—
313D4—441no—
314D4—441no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—881no—
332C2×C4C4⋊C4×D1111yescharacteristic
333C2×C4#6694711yescharacteristic
334C2×C4#6694911yescharacteristic
335C2×C4C2×#431311yescharacteristic
336C2×C4#6695411yescharacteristic
337C2×C4M16×D1111yescharacteristic
338C2×C4#6696011yescharacteristic
339C2×C4C4×C22⋊D1111yescharacteristic
340C2×C4#6699011yescharacteristic
341C2×C4#6699911yescharacteristic
342C8—22no—
343C8—41no—
344C8—41no—
345C8—41no—
346C8—81no—
347C8—442no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22—441no—
352C22—441no—
353C22—441no—
354C22#1062244911yescharacteristic
355C22#1062245111yescharacteristic
356C22#1062260211yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—224no—
361C4—442no—
362C4—441no—
363C4—441no—
364C4—441no—
365C4#1062245011yescharacteristic
366C4#1062245211yescharacteristic
367C4#1062272411yescharacteristic
368C4#1062274111yescharacteristic
369C4#1062281111yescharacteristic
370C4#1062281811yescharacteristic
371C2—21no—
372C2—21no—
373C2—881no—
374C2#1306879711yescharacteristic
375C2#1306883911yescharacteristic
376C2#1306885311yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1565C2
socleC22×C11#385
prime radicalC2×#4339C2×C4
cosocleC2×C42×C11C23
hypercenter#1565D11
hypocenterC11#8841
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
2. #13068767C2semidirect
5. #13066467C2semidirect
6. #13066448C2semidirect
7. C11×#1565C2semidirect
87. C11×M16M16semidirect
114. C4×Dic11M16semidirect
122. #1565D11semidirect
275. M16#4313semidirect
306. C11#8841semidirect

Maximal subgroups

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

subgroupindex
#130777292
#130687672
C4×#668892
#130670012
#130664672
#130664482
C11×#15652
#884111