Finite Group Databasebeta

← #14804514

Subgroups — #14804514

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622500C212yesmaximal, complemented
2C2×#10622462C211yesmaximal, characteristic, complemented
3C2×#10622447C211yesmaximal, characteristic
4#13073565C211yesmaximal, characteristic
5#13073539C211yesmaximal, characteristic
6#13069821C212yesmaximal, complemented
7#13069627C212yesmaximal, complemented
8#13069417C211yesmaximal, characteristic, complemented
9#13069038C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#1947C211yesmaximal, characteristic, complemented
12C22×Dic44C2212yes—
13C22×C8×D11C2212yes—
14C2×#66950C2212yes—
15C2×#66950C2212yes—
16C2×#66950C2212yes—
17C2×C4×D44C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×#107C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#384C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2212yes—
25C2×#66880C2212yes—
26#10622607—22no—
27#10622601—21no—
28#10622600C2212yes—
29#10622598—21no—
30C2×#66874C2211yescharacteristic
31C2×#66874C2212yes—
32C2×#66874C2212yes—
33C2×#66874C2211yescharacteristic
34#10622552—21no—
35#10622548—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622500—28no—
38#10622462—24no—
39#10622447—24no—
40#10622290—22no—
41C11×#340C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D44D411yescharacteristic
45C22×C4×D11C2312yes—
46C22×Dic22C2312yes—
47C22×Dic22C2311yescharacteristic
48C22×C8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4D412yes—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—21no—
69C2×C4×Dic11—21no—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C2×Dic44—24no—
73C2×Dic44—24no—
74C2×Dic44—42no—
75C2×C8×D11—24no—
76C2×C8×D11—24no—
77C2×C8×D11—42no—
78#66950—24no—
79#66950—24no—
80#66950—24no—
81#66950—42no—
82#66950—42no—
83#66950—42no—
84C4×D44—22no—
85C4×D44—22no—
86#66922—22no—
87#66922—22no—
88C4×Dic22—22no—
89C4×Dic22—22no—
90C11×#107—24no—
91C11×C4⋊C8D414yes—
92C11×#95—21no—
93C11⋊#95—22no—
94(C2×D11)⋊C8—24no—
95#66880—24no—
96#66874—22no—
97#66874—24no—
98#66874—42no—
99#66874D414yescomplemented
100C4×C11⋊C8—22no—
101#25386—111nomaximal, Sylow
102C23×D11C2×D412yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11C2×D412yes—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44Q1614yescomplemented
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×Dic22—21no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22C2×D412yes—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11C2×D414yes—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—81no—
143C11×C4⋊C4C2×D412yes—
144C11×C4⋊C4#4112yes—
145C42×C11—42no—
146C42×C11C2×D412yes—
147C42×C11#4112yes—
148(C2×D11)⋊C4—24no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—44no—
151(C2×D11)⋊C4—44no—
152(C2×D11)⋊C4—82no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—44no—
157C4⋊Dic11—44no—
158C4⋊Dic11—44no—
159C4⋊Dic11—42no—
160C4⋊Dic11—42no—
161Dic11⋊C4—42no—
162C4×Dic11—42no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8C2×D412yes—
169Dic44—48no—
170C8×D11—48no—
171C2×#467—112no—
172C2×#462—111no—
173C2×C8×D4—111no—
174#2542—111no—
175#2538—111no—
176#2036—112no—
177#2001—112no—
178#1956—111no—
179#1947D1111yescharacteristic, complemented
180#1892—112no—
181C4×#103—111no—
182C23×C11C22×D411yescharacteristic
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11—22no—
189C22×D11C2×Q1614yes—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11#12112yes—
202C2×C4×C11#12112yes—
203C2×C4×C11C2×Q1612yes—
204C2×C4×C11#13512yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223D44—28no—
224C4×D11—42no—
225C4×D11—42no—
226C4×D11—42no—
227C4×D11—42no—
228Dic22—22no—
229Dic22—22no—
230Dic22—41no—
231Dic22—41no—
232Dic22—42no—
233Dic22—42no—
234Dic22—42no—
235Dic22—42no—
236C8×C11—24no—
237C11⋊C8—22no—
238C11⋊C8—41no—
239C22×Q16—112no—
240C23×C8—112no—
241C2×C4⋊Q8—111no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—112no—
244C2×C22⋊Q8—112no—
245C2×C4×Q8—111no—
246C2×C4×D4—111no—
247#467—228no—
248#462—224no—
249C8×D4—224no—
250C2×#107C2×D1112yes—
251C2×C4⋊C8C2×D1111yescharacteristic
252C2×#103—111no—
253C2×#103—112no—
254C2×#103—112no—
255C2×#103—111no—
256C2×#103—112no—
257C2×C22⋊C8—112no—
258C2×C4×C8—111no—
259#399—222no—
260#396—222no—
261#390—221no—
262#390—221no—
263#389—221no—
264#384—221no—
265#384C2×D1111yescharacteristic
266#380—112no—
267C4×C4⋊C4C2×D1111yescharacteristic
268#340—111no—
269#340—111no—
270#340C2×D1112yes—
271C22×C11C2×#12111yescharacteristic
272C22×C11D4211yescharacteristic
273C22×C11#54611yescharacteristic
274C22×C11C22×Q1611yescharacteristic
275C22×C11C2×#13511yescharacteristic
276C22×C11#57711yescharacteristic
277C22×C11#57811yescharacteristic
278C2×D11—24no—
279C2×D11—24no—
280C2×D11—24no—
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C4×C11—22no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—82no—
289C4×C11#46714yescomplemented
290C4×C11#53211yescharacteristic
291C4×C11#54011yescharacteristic
292C4×C11D4211yescharacteristic
293C4×C11#55011yescharacteristic
294Dic11—42no—
295Dic11—42no—
296Dic11—82no—
297Dic11—81no—
298C22×Q8—111no—
299C22×Q8—112no—
300C22×D4—111no—
301C23×C4—112no—
302C2×Q16—224no—
303C2×Q16—224no—
304C2×Q16—442no—
305C22×C8—111no—
306C22×C8—111no—
307C22×C8—224no—
308C22×C8—224no—
309C22×C8—442no—
310C22×C8C22×D1112yes—
311C4⋊Q8—222no—
312C4⋊Q8—222no—
313C22⋊Q8—224no—
314C22⋊Q8—224no—
315C22⋊Q8—224no—
316C22⋊Q8—442no—
317C22⋊Q8—442no—
318C22⋊Q8—442no—
319C4×Q8—222no—
320C4×Q8—222no—
321C4×D4—222no—
322C4×D4—222no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22×D1112yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—112no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C42—21no—
342C2×C42—221no—
343C2×C42C22×D1111yescharacteristic
344#107—24no—
345C4⋊C8D4414yes—
346#103—114no—
347#103—224no—
348#103—224no—
349#103—222no—
350#103—442no—
351C22⋊C8—224no—
352C4×C8—222no—
353#95—21no—
354#95—222no—
355C2×C11#242811yescharacteristic
356C2×C11C2×#46711yescharacteristic
357C2×C11#306311yescharacteristic
358C2×C11#328411yescharacteristic
359C2×C11D4×Q1611yescharacteristic
360C2×C11#329911yescharacteristic
361C2×C11#330211yescharacteristic
362D11—44no—
363C24—112no—
364C2×Q8—112no—
365C2×Q8—221no—
366C2×Q8—221no—
367C2×Q8—222no—
368C2×Q8—222no—
369C2×Q8—221no—
370C2×Q8—221no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8—221no—
374C2×Q8—222no—
375C2×Q8—222no—
376C2×D4—114no—
377C2×D4—222no—
378C2×D4—222no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—112no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—221no—
391C22×C4—222no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395Q16—448no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—112no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—448no—
405C2×C8C2×D4414yes—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—42no—
411C4⋊C4—81no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—444no—
416C4⋊C4—444no—
417C4⋊C4—444no—
418C4⋊C4—442no—
419C4⋊C4—442no—
420C4⋊C4—442no—
421C4⋊C4D4×D1112yes—
422C4⋊C4#434312yes—
423C22⋊C4—224no—
424C22⋊C4—444no—
425C22⋊C4—444no—
426C22⋊C4—444no—
427C22⋊C4—882no—
428C42—42no—
429C42—442no—
430C42C2×D4412yes—
431C42#434312yes—
432C11#2538611yescharacteristic, complemented, Sylow
433C23—114no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23—222no—
438C23—222no—
439C23—222no—
440C23C2×D4×D1111yescharacteristic
441Q8—222no—
442Q8—222no—
443Q8—441no—
444Q8—441no—
445Q8—442no—
446Q8—442no—
447Q8—442no—
448Q8—442no—
449D4—228no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4#6694812yes—
478C2×C4#6694812yes—
479C2×C4#6696512yes—
480C2×C4Q16×D1112yes—
481C2×C4C22×D4411yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×#434311yescharacteristic
484C2×C4C2×#434311yescharacteristic
485C2×C4#6704211yescharacteristic
486C2×C4#6704211yescharacteristic
487C8—24no—
488C8—222no—
489C8—441no—
490C22—224no—
491C22—224no—
492C22—224no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22C2×#6694811yescharacteristic
498C22#1062314011yescharacteristic
499C22#1062316111yescharacteristic
500C22C2×#6696511yescharacteristic
501C22C2×Q16×D1111yescharacteristic
502C22#1062330611yescharacteristic
503C22#1062331011yescharacteristic
504C4—22no—
505C4—42no—
506C4—42no—
507C4—82no—
508C4—442no—
509C4—442no—
510C4—881no—
511C4—882no—
512C4#1062250014yescomplemented
513C4D4×D4411yescharacteristic
514C4#1062310811yescharacteristic
515C4#1062322911yescharacteristic
516C4#1062325611yescharacteristic
517C2—444no—
518C2#1307220211yescharacteristic
519C2C2×#1062250011yescharacteristic
520C2#1307830811yescharacteristic
521C2#1308034911yescharacteristic
522C2#1308036311yescharacteristic
523C2#1308048911yescharacteristic
524C2#1308053011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1947D11
hypocenterC11#25386
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
1. C2×#10622500C2semidirect
2. C2×#10622462C2semidirect
6. #13069821C2semidirect
7. #13069627C2semidirect
8. #13069417C2semidirect
9. #13069038C2semidirect
10. C4×#66874C2semidirect
11. C11×#1947C2semidirect
99. #66874D4semidirect
115. C2×D44Q16semidirect
179. #1947D11semidirect
289. C4×C11#467semidirect
432. C11#25386semidirect
512. C4#10622500semidirect

Maximal subgroups

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

subgroupindex
C2×#106225002
C2×#106224622
C2×#106224472
#130735652
#130735392
#130698212
#130696272
#130694172
#130690382
C4×#668742
C11×#19472
#2538611