Finite Group Databasebeta

← #14646520

Subgroups — #14646520

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071144C211yesmaximal, characteristic
2#13068594C211yesmaximal, characteristic
3C2×#10622105C211yesmaximal, characteristic
4C2×#10622090C211yesmaximal, characteristic
5#13066842C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C2×#66977C2211yescharacteristic
9C22×C4×Dic11C2211yescharacteristic
10C2×#66940C411yescharacteristic, complemented
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×Dic11⋊C8—21no—
19C4⋊C4×Dic11C411yescharacteristic, complemented
20#10622587C411yescharacteristic, complemented
21#10622586C411yescharacteristic, complemented
22#10622559—21no—
23C22⋊C4×Dic11—21no—
24#10622265—21no—
25#10622262—21no—
26#10622188—21no—
27#10622105—22no—
28#10622090—22no—
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C23×Dic11D411yescharacteristic
34C22×Dic22C2×C411yescharacteristic
35C22×C8×C11—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C22⋊Dic11—21no—
40C2×C4⋊Dic11C2×C411yescharacteristic
41#66977—21no—
42#66977—21no—
43#66977D412yes—
44#66977Q812yes—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—42no—
51C2×C4×Dic11C2×C411yescharacteristic
52C2×C4×Dic11C2×C411yescharacteristic
53C2×C4×Dic11D411yescharacteristic
54C2×C4×Dic11D411yescharacteristic
55C22×C11⋊C8—21no—
56#66940—42no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11⋊#95—24no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—42no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72Dic11⋊C8—42no—
73#8576—111nomaximal, Sylow
74C24×C11C2×D411yescharacteristic
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×Q811yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11C22⋊C411yescharacteristic
110C22×Dic11C22⋊C411yescharacteristic
111C22×Dic11C22⋊C411yescharacteristic
112C22×Dic11C22⋊C411yescharacteristic
113C2×Dic22—21no—
114C2×Dic22—41no—
115C2×Dic22—41no—
116C2×Dic22C4⋊C412yes—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C11×C4⋊C4—41no—
121C11×C4⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C22⋊Dic11—22no—
125C22⋊Dic11—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11C4⋊C412yes—
128Dic11⋊C4—22no—
129Dic11⋊C4—22no—
130Dic11⋊C4—42no—
131Dic11⋊C4—42no—
132C4×Dic11—22no—
133C4×Dic11—22no—
134C4×Dic11—41no—
135C4×Dic11—41no—
136C4×Dic11—42no—
137C4×Dic11—42no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8—41no—
140C2×C11⋊C8—41no—
141C4×C22⋊Q8—111no—
142#1797—111no—
143C2×#328—111no—
144C2×#328—111no—
145#1434—111no—
146#1294—111no—
147#1294D1111yescharacteristic
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11C2×C22⋊C411yescharacteristic
153C23×C11#12111yescharacteristic
154C23×C11C22⋊Q811yescharacteristic
155C23×C11#13511yescharacteristic
156C23×C11#13511yescharacteristic
157C23×C11#13711yescharacteristic
158C23×C11#13711yescharacteristic
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—81no—
177C2×C4×C11—81no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11C2×C4⋊C411yescharacteristic
181C2×C4×C11#11711yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C22⋊Q811yescharacteristic
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209C2×Dic11—81no—
210C2×Dic11—81no—
211C2×Dic11#9912yes—
212C2×Dic11#10412yes—
213Dic22—42no—
214Dic22—42no—
215C8×C11—81no—
216C11⋊C8—81no—
217C2×C22⋊Q8—111no—
218C2×C4×Q8—111no—
219C22×C42—111no—
220C2×C4⋊C8—221no—
221C2×C22⋊C8—111no—
222C2×C22⋊C8C2×D1111yescharacteristic
223#391—111no—
224#389—111no—
225#387—221no—
226#385—221no—
227#380C2×D1111yescharacteristic
228C4×C4⋊C4—111no—
229C4×C4⋊C4—221no—
230C4×C22⋊C4—221no—
231C2×#95—111no—
232C2×#95—221no—
233C2×#95—221no—
234C2×#95C2×D1111yescharacteristic
235#336—221no—
236#328—222no—
237#328—222no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11#38011yescharacteristic
251C22×C11C2×#9911yescharacteristic
252C22×C11#41011yescharacteristic
253C22×C11#41611yescharacteristic
254C22×C11#41911yescharacteristic
255C22×C11C2×#10411yescharacteristic
256C22×C11#42111yescharacteristic
257C22×C11#46411yescharacteristic
258C22×C11#46411yescharacteristic
259C22×C11#47911yescharacteristic
260C22×C11#47911yescharacteristic
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—82no—
266C4×C11—81no—
267C4×C11—81no—
268Dic11—22no—
269Dic11—22no—
270Dic11—42no—
271Dic11—42no—
272Dic11—41no—
273Dic11—41no—
274Dic11—82no—
275C22×Q8—111no—
276C23×C4—21no—
277C23×C4—111no—
278C23×C4—111no—
279C23×C4—221no—
280C23×C4C22×D1111yescharacteristic
281C22×C8—21no—
282C22×C8—221no—
283C22⋊Q8—112no—
284C22⋊Q8—112no—
285C22⋊Q8—221no—
286C22⋊Q8—221no—
287C4×Q8—442no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4C4×D1111yescharacteristic
293C2×C4⋊C4C4×D1111yescharacteristic
294C2×C22⋊C4—21no—
295C2×C22⋊C4—221no—
296C2×C42—111no—
297C2×C42—111no—
298C2×C42—111no—
299C2×C42—111no—
300C2×C42—221no—
301C2×C42—221no—
302C2×C42—442no—
303C4⋊C8—442no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—221no—
307C22⋊C8—221no—
308#95—21no—
309#95—21no—
310#95—21no—
311#95—221no—
312#95—221no—
313#95—221no—
314#95—221no—
315#95—224no—
316#95—221no—
317#95—221no—
318#95—442no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11#150111yescharacteristic
324C2×C11#150611yescharacteristic
325C2×C11#151111yescharacteristic
326C2×C11#152111yescharacteristic
327C2×C11#179911yescharacteristic
328C2×C11#180511yescharacteristic
329C2×C11#180611yescharacteristic
330C24D4×D1111yescharacteristic
331C2×Q8—112no—
332C2×Q8—221no—
333C2×Q8—441no—
334C2×Q8—441no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—111no—
347C22×C4—111no—
348C22×C4—111no—
349C22×C4—111no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4C2×C4×D1111yescharacteristic
368C22×C4#433911yescharacteristic
369C22×C4#433911yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4D4×D1111yescharacteristic
372C22×C4Q8×D1111yescharacteristic
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—441no—
377C2×C8—441no—
378C2×C8—441no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—112no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—442no—
386C4⋊C4—442no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—222no—
390C22⋊C4—222no—
391C42—222no—
392C42—222no—
393C42—441no—
394C42—441no—
395C42—442no—
396C42—442no—
397C11#857611yescharacteristic, complemented, Sylow
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23C22⋊C4×D1111yescharacteristic
403C23#6693711yescharacteristic
404C23#6694911yescharacteristic
405C23#6696511yescharacteristic
406C23#6696811yescharacteristic
407C23#6696911yescharacteristic
408C23#6697111yescharacteristic
409Q8—442no—
410Q8—442no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—112no—
433C2×C4—112no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4—881no—
460C2×C4—881no—
461C2×C4#6692511yescharacteristic
462C2×C4#6693711yescharacteristic
463C2×C4C4⋊C4×D1111yescharacteristic
464C2×C4#6694911yescharacteristic
465C8—81no—
466C8—881no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22#1062228011yescharacteristic
480C22#1062235311yescharacteristic
481C22D11×#9911yescharacteristic
482C22#1062238011yescharacteristic
483C22#1062238511yescharacteristic
484C22#1062241111yescharacteristic
485C22#1062241511yescharacteristic
486C22D11×#10411yescharacteristic
487C22#1062243411yescharacteristic
488C22#1062247011yescharacteristic
489C22#1062249011yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—82no—
495C4—81no—
496C4—81no—
497C4—222no—
498C4—222no—
499C4—442no—
500C4—442no—
501C4—441no—
502C4—441no—
503C4—882no—
504C2—21no—
505C2—21no—
506C2—21no—
507C2—21no—
508C2#1306710411yescharacteristic
509C2#1306712611yescharacteristic
510C2#1306714711yescharacteristic
511C2#1306719011yescharacteristic
512C2#1306860311yescharacteristic
513C2#1306863011yescharacteristic
514C2#1306863511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#8576
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
10. C2×#66940C4semidirect
19. C4⋊C4×Dic11C4semidirect
20. #10622587C4semidirect
21. #10622586C4semidirect
397. C11#8576semidirect

Maximal subgroups

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

subgroupindex
#130711442
#130685942
C2×#106221052
C2×#106220902
#130668422
#130664942
C11×#12942
#857611