Finite Group Databasebeta

← #14657568

Subgroups — #14657568

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C211yesmaximal, characteristic
2#13069423C211yesmaximal, characteristic, complemented
3#13069409C211yesmaximal, characteristic, complemented
4#13068617C211yesmaximal, characteristic, complemented
5C2×#10622118C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C22×#4323—21no—
10C2×C4×D44C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×#66896—21no—
14C2×#66896—21no—
15C2×#66896—21no—
16C2×#66885—21no—
17C2×(C2×D11)⋊C8—21no—
18C2×(C2×D11)⋊C8—21no—
19#10622685—22no—
20#10622685—22no—
21#10622548C2211yescharacteristic
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C2×C4×C11⋊C8C2211yescharacteristic
24C11×#331—22no—
25#10622189—21no—
26#10622118—22no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D44D411yescharacteristic
31C22×C4×D11—21no—
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127D412yes—
38C2×C42×C11C2311yescharacteristic
39C2×#4323—24no—
40C2×#4323—42no—
41C2×#4323—42no—
42C2×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11D411yescharacteristic
47C22×C11⋊C8—21no—
48C22×C11⋊C8D411yescharacteristic
49C22×C11⋊C8D411yescharacteristic
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58#66896—24no—
59#66896—42no—
60#66896—42no—
61#66885—42no—
62(C2×D11)⋊C8—42no—
63(C2×D11)⋊C8—42no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68#10473—111nomaximal, Sylow
69C24×C11—41no—
70C23×D11—21no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—81no—
86C2×D4×C11—81no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—41no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44SD1612yes—
98C2×C4×D11—41no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114#4323—48no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—81no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—21no—
126C2×C11⋊C8—21no—
127C2×C11⋊C8—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—41no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8D812yescomplemented
133C2×#459—111no—
134#1957—111no—
135#1954—111no—
136#1802—111no—
137C2×#334—111no—
138C2×#331D1111yescharacteristic, complemented
139#1296—111no—
140C23×C11—42no—
141C23×C11—81no—
142C23×C11—81no—
143C23×C11—81no—
144C23×C11—81no—
145C23×C11—81no—
146C23×C11—81no—
147C23×C11#12111yescharacteristic
148C22×D11—22no—
149C22×D11—41no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—41no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—42no—
158D4×C11—42no—
159D4×C11—82no—
160D4×C11—82no—
161D4×C11—81no—
162D4×C11—81no—
163D4×C11—81no—
164D4×C11—81no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C2×C4×C11#12311yescharacteristic
172C2×C4×C11#12411yescharacteristic
173C2×C4×C11C2×D811yescharacteristic
174C2×C4×C11C2×SD1611yescharacteristic
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11#13511yescharacteristic
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186C2×Dic11—81no—
187D44—22no—
188D44—22no—
189D44—41no—
190D44—41no—
191C4×D11—81no—
192C4×D11—81no—
193C4×D11—81no—
194C4×D11—81no—
195C8×C11—81no—
196C8×C11—81no—
197C11⋊C8—22no—
198C11⋊C8—42no—
199C11⋊C8—41no—
200C22×D8—221no—
201C2×#127C2×D1111yescharacteristic
202C2×C4×D4—111no—
203#459—222no—
204#459—222no—
205C2×C4⋊C8—111no—
206C2×C4⋊C8C2×D1111yescharacteristic
207C2×C4⋊C8C2×D1111yescharacteristic
208C2×#102—221no—
209C2×#102—221no—
210C2×#102—221no—
211C2×#102—221no—
212C2×C22⋊C8—221no—
213C2×C22⋊C8—221no—
214C2×C4×C8—111no—
215#384—111no—
216#340—221no—
217#334—222no—
218#331—22no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11—161no—
223C22×C11—161no—
224C22×C11—161no—
225C22×C11—161no—
226C22×C11#39411yescharacteristic
227C22×C11#45911yescharacteristic
228C22×C11#46311yescharacteristic
229C22×C11#46511yescharacteristic
230C22×C11#46911yescharacteristic
231C22×C11#47111yescharacteristic
232C22×C11#47211yescharacteristic
233C2×D11—42no—
234C2×D11—42no—
235C2×D11—42no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C2×D11—81no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11#44911yescharacteristic
243C4×C11#45011yescharacteristic
244C4×C11#45911yescharacteristic
245C4×C11#46311yescharacteristic
246C4×C11#46611yescharacteristic
247C4×C11#46911yescharacteristic
248C4×C11#48111yescharacteristic
249C4×C11#48211yescharacteristic
250Dic11—81no—
251Dic11—161no—
252C22×D4—21no—
253C22×D4—21no—
254C22×D4—21no—
255C22×D4—111no—
256C23×C4—221no—
257C2×D8—224no—
258C2×D8—442no—
259C2×D8—442no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—111no—
263C22×C8—111no—
264C22×C8—221no—
265#127—21no—
266#127—21no—
267#127—21no—
268#127C22⋊D1112yes—
269C4×D4—221no—
270C4×D4—221no—
271C4×D4—221no—
272C4×D4—221no—
273C2×C4⋊C4—111no—
274C2×C4⋊C4—221no—
275C2×C4⋊C4—221no—
276C2×C4⋊C4—221no—
277C2×C22⋊C4—221no—
278C2×C42C22×D1111yescharacteristic
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—112no—
284C4⋊C8—221no—
285#102—224no—
286#102—442no—
287#102—442no—
288#102—442no—
289C22⋊C8—442no—
290C22⋊C8—442no—
291C4×C8—221no—
292C4×C8—221no—
293C2×C11—162no—
294C2×C11#166511yescharacteristic
295C2×C11#167711yescharacteristic
296C2×C11#168711yescharacteristic
297C2×C11#170111yescharacteristic
298C2×C11#203411yescharacteristic
299C2×C11#205111yescharacteristic
300C2×C11#205411yescharacteristic
301D11—82no—
302C24—41no—
303C24—221no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—81no—
319C2×D4—81no—
320C2×D4—112no—
321C2×D4—221no—
322C2×D4—221no—
323C2×D4—221no—
324C2×D4—221no—
325C2×D4—221no—
326C22×C4—221no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4—441no—
330C22×C4—441no—
331C22×C4—441no—
332C22×C4—441no—
333C22×C4—441no—
334C22×C4#433911yescharacteristic
335C22×C4D4×D1111yescharacteristic
336C22×C4D4×D1111yescharacteristic
337D8—448no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—112no—
345C2×C8—221no—
346C2×C8—221no—
347C2×C8—221no—
348C2×C8—221no—
349C2×C8—221no—
350C2×C8—222no—
351C2×C8—441no—
352C2×C8—441no—
353C4⋊C4—221no—
354C4⋊C4—221no—
355C4⋊C4—441no—
356C4⋊C4—441no—
357C4⋊C4—441no—
358C4⋊C4—441no—
359C4⋊C4—881no—
360C22⋊C4—441no—
361C22⋊C4—441no—
362C42#433911yescharacteristic
363C42D4×D1111yescharacteristic
364C42#434111yescharacteristic
365C42C2×C22⋊D1111yescharacteristic
366C11#1047311yescharacteristic, complemented, Sylow
367C23—42no—
368C23—81no—
369C23—81no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23—81no—
374C23—222no—
375C23—441no—
376C23—441no—
377C23—441no—
378C23—441no—
379C23—441no—
380C23—441no—
381C23#6693711yescharacteristic
382D4—42no—
383D4—42no—
384D4—42no—
385D4—42no—
386D4—82no—
387D4—82no—
388D4—81no—
389D4—81no—
390D4—81no—
391D4—81no—
392D4—222no—
393D4—222no—
394D4—441no—
395D4—441no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—881no—
402C2×C4—881no—
403C2×C4—881no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4#6693611yescharacteristic
409C2×C4#6693711yescharacteristic
410C2×C4#6693811yescharacteristic
411C2×C4D8×D1111yescharacteristic
412C2×C4#6696411yescharacteristic
413C2×C4#6696411yescharacteristic
414C2×C4#6696511yescharacteristic
415C2×C4SD16×D1111yescharacteristic
416C2×C4#6696711yescharacteristic
417C2×C4#6696711yescharacteristic
418C2×C4#6696911yescharacteristic
419C2×C4#6698211yescharacteristic
420C2×C4#6699011yescharacteristic
421C2×C4#6699211yescharacteristic
422C8—81no—
423C8—81no—
424C8—222no—
425C8—442no—
426C8—441no—
427C22—82no—
428C22—82no—
429C22—82no—
430C22—161no—
431C22—161no—
432C22—161no—
433C22—161no—
434C22—442no—
435C22—442no—
436C22—442no—
437C22—881no—
438C22—881no—
439C22—881no—
440C22—881no—
441C22#1062236111yescharacteristic
442C22#1062236211yescharacteristic
443C22#1062239111yescharacteristic
444C22#1062239511yescharacteristic
445C22#1062239911yescharacteristic
446C22#1062240011yescharacteristic
447C22#1062257211yescharacteristic
448C4—21no—
449C4—21no—
450C4—881no—
451C4—1761no—
452C4#1062238811yescharacteristic
453C4#1062239011yescharacteristic
454C4#1062239511yescharacteristic
455C4#1062239711yescharacteristic
456C4#1062276311yescharacteristic
457C4#1062277111yescharacteristic
458C4#1062277811yescharacteristic
459C4#1062278211yescharacteristic
460C2—162no—
461C2—882no—
462C2#1306795611yescharacteristic
463C2#1306802411yescharacteristic
464C2#1306809411yescharacteristic
465C2#1306817611yescharacteristic
466C2#1306980311yescharacteristic
467C2#1306990811yescharacteristic
468C2#1306992511yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11#121
prime radicalC2×#10622685C2
hypercenterC2×#331D11
hypocenterC11#10473
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. #13069423C2semidirect
3. #13069409C2semidirect
4. #13068617C2semidirect
5. C2×#10622118C2semidirect
6. #13066500C2semidirect
7. C2×C11×#331C2semidirect
132. C2×C11⋊C8D8semidirect
138. C2×#331D11semidirect
366. C11#10473semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
#130694232
#130694092
#130686172
C2×#106221182
#130665002
C2×C11×#3312
#1047311