Finite Group Databasebeta

← #14646523

Subgroups — #14646523

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66983C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic, complemented
3C2×#10622089C212yesmaximal
4#13066495C212yesmaximal, complemented
5C11×C4⋊#95C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66983C2211yescharacteristic
9C2×C4×C22⋊D11—21no—
10C2×C4×D44C411yescharacteristic, complemented
11C2×C11×#95—21no—
12C2×C11×#95C2212yes—
13#10622826—21no—
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622553—21no—
17#10622552C411yescharacteristic, complemented
18C4×(C2×D11)⋊C4—21no—
19C4×C4⋊Dic11C411yescharacteristic, complemented
20#10622541C411yescharacteristic, complemented
21C2×C4⋊(C11⋊C8)—21no—
22#10622162—21no—
23#10622089—24no—
24C23×C4×C11—22no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C2×C11×C4⋊C4—24no—
32C2×C11×C4⋊C4—42no—
33C2×C11×C4⋊C4—42no—
34C2×C42×C11—42no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C22⋊Dic11—21no—
40#66983—21no—
41#66983—21no—
42#66983D412yes—
43#66983Q812yes—
44C4×C22⋊D11—42no—
45C4×C22⋊D11—42no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×Dic11⋊C4—21no—
54C2×C4×Dic11—21no—
55C22×C11⋊C8—22no—
56C4×D44—42no—
57C11×#95—22no—
58C11×#95—22no—
59C11×#95—42no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C22⋊(C11⋊C8)—22no—
64C22⋊(C11⋊C8)—22no—
65C4⋊(C11⋊C8)—42no—
66#8577—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11D812yes—
89C22×C4×C11SD1612yes—
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×Q811yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—22no—
97C2×C22⋊D11—22no—
98C2×C22⋊D11—41no—
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C2×C22⋊D11—41no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C2×D44—21no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44C4⋊C412yescomplemented
109C2×C4×D11—42no—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C11×C4⋊C4—48no—
113C42×C11—22no—
114C42×C11—22no—
115C42×C11—41no—
116C42×C11—41no—
117C22⋊Dic11—41no—
118C22⋊Dic11—41no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—42no—
122(C2×D11)⋊C4—42no—
123(C2×D11)⋊C4—42no—
124C4⋊Dic11—21no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C4⋊Dic11C4⋊C412yescomplemented
128Dic11⋊C4—42no—
129C4×Dic11—42no—
130C2×C11⋊C8—42no—
131C2×C11⋊C8—42no—
132C2×C11⋊C8—42no—
133C4×#121—111no—
134#1797—111no—
135C2×#327—112no—
136C4⋊#95D1111yescharacteristic, complemented
137#1294—112no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11C2×C22⋊C411yescharacteristic
143C23×C11#12111yescharacteristic
144C23×C11C22⋊Q811yescharacteristic
145C23×C11C2×D811yescharacteristic
146C23×C11C2×SD1611yescharacteristic
147C23×C11AGL(1,ℤ/8)11yescharacteristic
148C23×C11#13711yescharacteristic
149C22×D11—22no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11—41no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—41no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—44no—
177C2×C4×C11—44no—
178C2×C4×C11—44no—
179C2×C4×C11—82no—
180C2×C4×C11—82no—
181C2×C4×C11—82no—
182C2×C4×C11—82no—
183C2×C4×C11#9912yes—
184C2×C4×C11#10212yes—
185C2×C4×C11#10212yes—
186C2×C4×C11#10412yes—
187C2×C4×C11C2×C4⋊C411yescharacteristic
188C2×C4×C11#11711yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11C22⋊Q811yescharacteristic
191C22⋊D11—42no—
192C22⋊D11—42no—
193C22⋊D11—42no—
194C22⋊D11—42no—
195C2×Dic11—22no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204D44—42no—
205D44—42no—
206C4×D11—84no—
207C11⋊C8—82no—
208C2×#121—111no—
209C2×C4×D4—111no—
210C2×C4×D4—221no—
211C22×C4⋊C4—21no—
212C22×C42C2×D1111yescharacteristic
213C2×C4⋊C8—221no—
214C2×C22⋊C8—112no—
215#390—111no—
216#389—111no—
217#388—221no—
218#386—221no—
219#380—111no—
220C4×C4⋊C4—111no—
221C4×C22⋊C4—221no—
222C2×#95—21no—
223C2×#95C2×D1112yes—
224#336—221no—
225#327—224no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11#38011yescharacteristic
239C22×C11C2×#9911yescharacteristic
240C22×C11#41011yescharacteristic
241C22×C11C2×#10211yescharacteristic
242C22×C11#41711yescharacteristic
243C22×C11C2×#10411yescharacteristic
244C22×C11#42111yescharacteristic
245C22×C11#45911yescharacteristic
246C22×C11#46111yescharacteristic
247C22×C11#47411yescharacteristic
248C22×C11#47611yescharacteristic
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—81no—
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—84no—
265Dic11—42no—
266Dic11—81no—
267Dic11—81no—
268C22×D4—111no—
269C22×D4—221no—
270C23×C4—22no—
271C23×C4—221no—
272C23×C4C22⋊D1111yescharacteristic
273C23×C4C22⋊D1111yescharacteristic
274C23×C4C22×D1111yescharacteristic
275C22×C8—222no—
276#121—112no—
277#121—112no—
278#121—221no—
279#121—221no—
280C4×D4—442no—
281C4×D4—442no—
282C4×D4—442no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—221no—
290C2×C22⋊C4—221no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—221no—
295C2×C42—42no—
296C2×C42—221no—
297C2×C42C4×D1111yescharacteristic
298C2×C42C4×D1111yescharacteristic
299C2×C42D4411yescharacteristic
300C2×C42D4411yescharacteristic
301C4⋊C8—442no—
302C22⋊C8—222no—
303C22⋊C8—222no—
304#95—22no—
305#95—22no—
306#95—42no—
307#95—221no—
308#95—221no—
309#95—221no—
310C2×C11—21no—
311C2×C11—21no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11#150211yescharacteristic
315C2×C11#150411yescharacteristic
316C2×C11#151211yescharacteristic
317C2×C11#151911yescharacteristic
318C2×C11#179911yescharacteristic
319C2×C11#180211yescharacteristic
320C2×C11#180611yescharacteristic
321D11—82no—
322C24—221no—
323C24C2×C22⋊D1111yescharacteristic
324C2×D4—112no—
325C2×D4—222no—
326C2×D4—222no—
327C2×D4—221no—
328C2×D4—441no—
329C2×D4—441no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—441no—
333C2×D4—441no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—442no—
353C22×C4—442no—
354C22×C4—442no—
355C22×C4(C2×D11)⋊C411yescharacteristic
356C22×C4(C2×D11)⋊C411yescharacteristic
357C22×C4(C2×D11)⋊C411yescharacteristic
358C22×C4(C2×D11)⋊C411yescharacteristic
359C22×C4#432312yes—
360C22×C4#432512yes—
361C22×C4C2×C4×D1111yescharacteristic
362C22×C4C2×D4411yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4#434111yescharacteristic
365C22×C4Q8×D1111yescharacteristic
366C22×C4#434311yescharacteristic
367C2×C8—442no—
368C2×C8—442no—
369C2×C8—442no—
370C4⋊C4—48no—
371C4⋊C4—112no—
372C4⋊C4—221no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—442no—
376C22⋊C4—222no—
377C22⋊C4—222no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C22⋊C4—442no—
381C22⋊C4—442no—
382C22⋊C4—442no—
383C42—22no—
384C42—22no—
385C42—41no—
386C42—41no—
387C42—442no—
388C11#857711yescharacteristic, complemented, Sylow
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—222no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23C2×(C2×D11)⋊C411yescharacteristic
401C23C2×#432311yescharacteristic
402C23#6698511yescharacteristic
403C23#6699111yescharacteristic
404C23C2×#432511yescharacteristic
405C23#6699511yescharacteristic
406C23#6699911yescharacteristic
407D4—442no—
408D4—442no—
409D4—442no—
410D4—442no—
411D4—442no—
412D4—442no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—44no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—222no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—884no—
450C2×C4#6686912yes—
451C2×C4#6687012yes—
452C2×C4#6687312yes—
453C2×C4#6687312yes—
454C2×C4C4⋊C4×D1111yescharacteristic
455C2×C4#6694511yescharacteristic
456C2×C4#6694811yescharacteristic
457C2×C4#6695011yescharacteristic
458C8—882no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—442no—
472C22—442no—
473C22—442no—
474C22—881no—
475C22—881no—
476C22—881no—
477C22—881no—
478C22C2×#6686911yescharacteristic
479C22C2×#6687011yescharacteristic
480C22C2×#6687311yescharacteristic
481C22#1062257911yescharacteristic
482C22#1062260011yescharacteristic
483C22#1062261811yescharacteristic
484C22#1062261911yescharacteristic
485C22#1062268511yescharacteristic
486C22#1062269611yescharacteristic
487C22#1062269711yescharacteristic
488C22#1062270011yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—84no—
498C4—442no—
499C4—881no—
500C4—881no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—882no—
506C2#1306711011yescharacteristic
507C2#1306711811yescharacteristic
508C2#1306715211yescharacteristic
509C2#1306718311yescharacteristic
510C2#1306860111yescharacteristic
511C2#1306861311yescharacteristic
512C2#1306863711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×C4⋊#95C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenterC4⋊#95D11
hypocenterC11#8577
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. #13068596C2semidirect
4. #13066495C2semidirect
5. C11×C4⋊#95C2semidirect
10. C2×C4×D44C4semidirect
17. #10622552C4semidirect
19. C4×C4⋊Dic11C4semidirect
20. #10622541C4semidirect
108. C2×D44C4⋊C4semidirect
127. C4⋊Dic11C4⋊C4semidirect
136. C4⋊#95D11semidirect
388. C11#8577semidirect

Maximal subgroups

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

subgroupindex
C4×#669832
#130685962
C2×#106220892
#130664952
C11×C4⋊#952
#857711