Finite Group Databasebeta

← #14648552

Subgroups — #14648552

Order 2816.

692 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C211yesmaximal, characteristic
2#13071567C211yesmaximal, characteristic, complemented
3#13069544C211yesmaximal, characteristic, complemented
4C2×#10622097C211yesmaximal, characteristic, complemented
5#13066499C211yesmaximal, characteristic, complemented
6#13066456C211yesmaximal, characteristic, complemented
7C11×#1957C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C22×#4323—21no—
10C2×#66945—21no—
11C2×C4×D44C2211yescharacteristic
12C2×C11×#102—22no—
13C2×C4×C8×C11C2211yescharacteristic
14C11×#384C2211yescharacteristic
15C2×#66896—21no—
16C2×#66896—21no—
17C2×#66896—21no—
18#10622685—22no—
19#10622685C414yescomplemented
20#10622603—22no—
21#10622601—21no—
22#10622600—21no—
23C4⋊C4×Dic11—21no—
24C4×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622097—22no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×C8×C11—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127C2×C412yes—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D412yes—
41C2×C42×C11C2311yescharacteristic
42C2×#4323—24no—
43C2×#4323—42no—
44C2×#4323—42no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—22no—
48C2×C4⋊Dic11D411yescharacteristic
49C2×C4⋊Dic11D411yescharacteristic
50C2×C4⋊Dic11D411yescharacteristic
51C2×C4×Dic11—22no—
52C2×C4×Dic11—21no—
53C22×C11⋊C8—21no—
54C22×C11⋊C8—21no—
55#66945—42no—
56#66945—42no—
57C4×D44—21no—
58C4×D44—21no—
59C4×D44C2×C412yes—
60C4×D44D412yes—
61C11×#102—44no—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64#66896—24no—
65#66896—42no—
66#66896—42no—
67C11⋊#95—22no—
68C11⋊#95—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)C2×C412yes—
73#8980—111nomaximal, Sylow
74C24×C11—41no—
75C23×D11—21no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C22×C4×C11—22no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44C22⋊C412yes—
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C2×C4×D11—41no—
110C2×C4×D11—41no—
111C2×C8×C11—22no—
112C2×C8×C11—41no—
113C2×C8×C11—41no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C42×C11C22×C411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11#4111yescharacteristic
123#4323—48no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—22no—
126(C2×D11)⋊C4—44no—
127(C2×D11)⋊C4—82no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11C22⋊C412yes—
133C4⋊Dic11D812yescomplemented
134C4×Dic11—44no—
135C4×Dic11—41no—
136C4×Dic11—41no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×#459—111no—
144#2354—111no—
145#1982—111no—
146#1957D1111yescharacteristic, complemented
147C2×D4⋊C8—111no—
148#1296—111no—
149#1279—111no—
150C23×C11—42no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11—81no—
155C23×C11—81no—
156C23×C11—81no—
157C23×C11#12011yescharacteristic
158C22×D11—22no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C22×D11—41no—
164C22×D11—41no—
165D4×C11—44no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—42no—
169D4×C11—42no—
170D4×C11—82no—
171D4×C11—81no—
172D4×C11—81no—
173D4×C11—81no—
174D4×C11—81no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C2×C22⋊C411yescharacteristic
181C2×C4×C11C4×D411yescharacteristic
182C2×C4×C11C4×D411yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12311yescharacteristic
186C2×C4×C11C2×D811yescharacteristic
187C2×C4×C11#13511yescharacteristic
188C2×C4×C11#13511yescharacteristic
189C2×C4×C11#13511yescharacteristic
190C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203D44—22no—
204D44—22no—
205D44—41no—
206D44—41no—
207C4×D11—42no—
208C4×D11—42no—
209C4×D11—42no—
210C4×D11—42no—
211C8×C11—42no—
212C11⋊C8—42no—
213C11⋊C8—81no—
214C22×D8—221no—
215C2×#127C2×D1111yescharacteristic
216C2×C4×D4—111no—
217C2×#117—221no—
218#459—114no—
219#459—222no—
220C2×C4⋊C8—111no—
221C2×C4⋊C8—111no—
222C2×#102—22no—
223C2×#102—221no—
224C2×#102—221no—
225C2×#102—221no—
226C2×C4×C8C2×D1111yescharacteristic
227#390—221no—
228#388—222no—
229#384C2×D1111yescharacteristic
230#380—221no—
231C4×C4⋊C4—111no—
232C4×C4⋊C4—221no—
233D4⋊C8—222no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11—82no—
237C22×C11—161no—
238C22×C11—161no—
239C22×C11—161no—
240C22×C11—161no—
241C22×C11#38611yescharacteristic
242C22×C11#44711yescharacteristic
243C22×C11#44911yescharacteristic
244C22×C11#44911yescharacteristic
245C22×C11#44911yescharacteristic
246C22×C11#45311yescharacteristic
247C22×C11#45411yescharacteristic
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—82no—
258C4×C11#41611yescharacteristic
259C4×C11#41811yescharacteristic
260C4×C11C4×D811yescharacteristic
261C4×C11#44211yescharacteristic
262C4×C11#45911yescharacteristic
263C4×C11#46311yescharacteristic
264C4×C11#48211yescharacteristic
265C4×C11#48211yescharacteristic
266Dic11—42no—
267Dic11—42no—
268Dic11—81no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—111no—
273C23×C4—221no—
274C2×D8—224no—
275C2×D8—442no—
276C2×D8—442no—
277C22×C8—21no—
278C22×C8—221no—
279C22×C8—221no—
280#127—21no—
281#127—21no—
282#127—21no—
283#127C4×D1112yes—
284C4×D4—112no—
285C4×D4—112no—
286C4×D4—221no—
287C4×D4—221no—
288#117—442no—
289#117—442no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4C22⋊D1112yes—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—222no—
299C2×C42—222no—
300C2×C42—221no—
301C2×C42C22×D1111yescharacteristic
302C4⋊C8—112no—
303C4⋊C8—221no—
304C4⋊C8—221no—
305C4⋊C8—221no—
306#102—44no—
307#102—224no—
308#102—442no—
309#102—442no—
310C4×C8—21no—
311C4×C8—21no—
312#95—222no—
313#95—221no—
314C2×C11—162no—
315C2×C11#162111yescharacteristic
316C2×C11#162411yescharacteristic
317C2×C11#162511yescharacteristic
318C2×C11#162811yescharacteristic
319C2×C11#187511yescharacteristic
320C2×C11#187911yescharacteristic
321C2×C11#188311yescharacteristic
322D11—82no—
323C24—41no—
324C24—221no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—112no—
342C2×D4—221no—
343C2×D4—221no—
344C2×D4—221no—
345C2×D4—221no—
346C2×D4—221no—
347C22×C4—22no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—221no—
353C22×C4—441no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4D4×D1111yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360D8—448no—
361C2×C8—22no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—222no—
365C2×C8—441no—
366C2×C8—441no—
367C2×C8—441no—
368C2×C8—441no—
369C2×C8—441no—
370C4⋊C4—42no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—112no—
376C4⋊C4—112no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C22⋊C4—222no—
382C22⋊C4—222no—
383C22⋊C4—444no—
384C22⋊C4—882no—
385C42—444no—
386C42—441no—
387C42—441no—
388C42C2×C4×D1111yescharacteristic
389C42#433911yescharacteristic
390C42D4×D1111yescharacteristic
391C42#434111yescharacteristic
392C11#898011yescharacteristic, complemented, Sylow
393C23—42no—
394C23—81no—
395C23—81no—
396C23—81no—
397C23—81no—
398C23—81no—
399C23—81no—
400C23—222no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23#6699011yescharacteristic
408D4—44no—
409D4—42no—
410D4—42no—
411D4—42no—
412D4—42no—
413D4—82no—
414D4—81no—
415D4—81no—
416D4—81no—
417D4—81no—
418D4—222no—
419D4—222no—
420D4—441no—
421D4—441no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4C22⋊C4×D1111yescharacteristic
441C2×C4(C22⋊D11)⋊C411yescharacteristic
442C2×C4#6693611yescharacteristic
443C2×C4#6693711yescharacteristic
444C2×C4D8×D1111yescharacteristic
445C2×C4#6696411yescharacteristic
446C2×C4#6696411yescharacteristic
447C2×C4#6696511yescharacteristic
448C2×C4#6696711yescharacteristic
449C2×C4#6696711yescharacteristic
450C2×C4#6696911yescharacteristic
451C2×C4#6696911yescharacteristic
452C2×C4C4×C22⋊D1111yescharacteristic
453C2×C4#6699111yescharacteristic
454C8—42no—
455C8—442no—
456C8—881no—
457C22—82no—
458C22—82no—
459C22—82no—
460C22—161no—
461C22—161no—
462C22—161no—
463C22—161no—
464C22—442no—
465C22—442no—
466C22—442no—
467C22—881no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22#1062256911yescharacteristic
472C22#1062267511yescharacteristic
473C22#1062269011yescharacteristic
474C22#1062276911yescharacteristic
475C22#1062277111yescharacteristic
476C22#1062278511yescharacteristic
477C22#1062278511yescharacteristic
478C4—21no—
479C4—21no—
480C4—82no—
481C4—442no—
482C4—442no—
483C4—881no—
484C4#1062236911yescharacteristic
485C4#1062238311yescharacteristic
486C4#1062238511yescharacteristic
487C4#1062239211yescharacteristic
488C4#1062239711yescharacteristic
489C4#1062239811yescharacteristic
490C4#1062239911yescharacteristic
491C4#1062240011yescharacteristic
492C2—162no—
493C2—882no—
494C2#1306767811yescharacteristic
495C2#1306769711yescharacteristic
496C2#1306770211yescharacteristic
497C2#1306772311yescharacteristic
498C2#1306893511yescharacteristic
499C2#1306896111yescharacteristic
500C2#1306899511yescharacteristic
subgroupG/H
centerC23#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1957C2
socleC23×C11#120
prime radicalC2×#10622685C2
cosocleC2×C42×C11C23
hypercenter#1957D11
hypocenterC11#8980
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13071567C2semidirect
3. #13069544C2semidirect
4. C2×#10622097C2semidirect
5. #13066499C2semidirect
6. #13066456C2semidirect
7. C11×#1957C2semidirect
19. #10622685C4semidirect
133. C4⋊Dic11D8semidirect
146. #1957D11semidirect
392. C11#8980semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
#130715672
#130695442
C2×#106220972
#130664992
#130664562
C11×#19572
#898011