Finite Group Databasebeta

← #14804516

Subgroups — #14804516

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×#10622426C212yesmaximal, complemented
2C2×#10622644C211yesmaximal, characteristic, complemented
3C2×C8×D44C211yesmaximal, characteristic
4#13073565C211yesmaximal, characteristic
5#13073534C211yesmaximal, characteristic
6#13069822C212yesmaximal, complemented
7#13069625C212yesmaximal, complemented
8#13069418C211yesmaximal, characteristic, complemented
9#13069374C211yesmaximal, characteristic, complemented
10#13069038C212yesmaximal, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2212yes—
14C22×#4326C2212yes—
15C22×C8×D11C2212yes—
16C2×#66950C2212yes—
17C2×#66950C2212yes—
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2212yes—
25C2×#66880C2212yes—
26C2×#66880C2212yes—
27#10622644—24no—
28#10622607—22no—
29#10622600C2212yes—
30C2×#66874C2212yes—
31C2×#66871C2212yes—
32#10622552—21no—
33#10622552—21no—
34#10622548—21no—
35#10622548C2211yescharacteristic
36#10622541—21no—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622426—28no—
39C8×D44—24no—
40#10622290—22no—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43#10622167C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D44D411yescharacteristic
46C22×C4×D11C2312yes—
47C22×Dic22C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59#66999—24no—
60#66999—42no—
61C2×#4326—24no—
62C2×#4326—24no—
63C2×#4326—42no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4D412yes—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—22no—
78C22×C11⋊C8C2312yes—
79C2×C8×D11—24no—
80C2×C8×D11—24no—
81C2×C8×D11—42no—
82#66950—24no—
83#66950—24no—
84#66950—42no—
85#66950—42no—
86C4×D44—22no—
87C4×D44—22no—
88#66922—22no—
89#66922—22no—
90C11×#103—22no—
91C11×#103D414yescomplemented
92C4×C8×C11—22no—
93C11×#95—21no—
94C11⋊#95—22no—
95(C2×D11)⋊C8—24no—
96#66880—24no—
97#66880—42no—
98#66874—24no—
99#66871—24no—
100C4⋊(C11⋊C8)D414yes—
101#25386—111nomaximal, Sylow
102C23×D11C2×D412yes—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11C2×D412yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11C2×D412yes—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44Q1614yescomplemented
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11C2×D412yes—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4C2×D412yes—
146C11×C4⋊C4#4112yes—
147C42×C11—42no—
148C42×C11—42no—
149C42×C11C2×D412yes—
150C42×C11#4112yes—
151#4326—48no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—44no—
154(C2×D11)⋊C4—44no—
155(C2×D11)⋊C4—44no—
156(C2×D11)⋊C4—82no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11—44no—
161C4⋊Dic11—44no—
162C4⋊Dic11—42no—
163C4⋊Dic11—42no—
164C4⋊Dic11—42no—
165C4⋊Dic11—81no—
166Dic11⋊C4—44no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8C2×D414yes—
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#1947—111no—
180#1892—112no—
181C4×#103D1111yescharacteristic, complemented
182C23×C11C22×D411yescharacteristic
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11—22no—
189C22×D11C2×Q1614yes—
190Q8×C11—22no—
191Q8×C11—22no—
192Q8×C11—41no—
193Q8×C11—41no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11#12112yes—
209C2×C4×C11#12112yes—
210C2×C4×C11C2×Q1612yes—
211C2×C4×C11#13512yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227D44—28no—
228C4×D11—42no—
229C4×D11—42no—
230C4×D11—42no—
231C4×D11—42no—
232Dic22—42no—
233Dic22—42no—
234Dic22—42no—
235Dic22—42no—
236C8×C11—22no—
237C8×C11—41no—
238C11⋊C8—24no—
239C22×Q16—112no—
240C23×C8—112no—
241C2×C4⋊Q8—111no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—112no—
244C2×C22⋊Q8—112no—
245C2×C4×Q8C2×D1111yescharacteristic
246C2×C4×D4—111no—
247#467—228no—
248#462—224no—
249C8×D4—224no—
250C2×#107—112no—
251C2×C4⋊C8—111no—
252C2×#103—112no—
253C2×#103—112no—
254C2×#103—112no—
255C2×#103C2×D1111yescharacteristic
256C2×#103C2×D1111yescharacteristic
257C2×C22⋊C8—112no—
258C2×C4×C8C2×D1111yescharacteristic
259#399—222no—
260#396—222no—
261#390—221no—
262#390—221no—
263#389—221no—
264#384—111no—
265#384—221no—
266#380—112no—
267C4×C4⋊C4C2×D1111yescharacteristic
268#340—112no—
269#340C2×D1111yescharacteristic
270#340C2×D1111yescharacteristic
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—42no—
289C4×C11—81no—
290C4×C11#46714yescomplemented
291C4×C11#53211yescharacteristic
292C4×C11#54011yescharacteristic
293C4×C11D4211yescharacteristic
294C4×C11#55011yescharacteristic
295Dic11—42no—
296Dic11—82no—
297Dic11—82no—
298C22×Q8—112no—
299C22×Q8C22×D1111yescharacteristic
300C22×D4—111no—
301C23×C4—112no—
302C2×Q16—224no—
303C2×Q16—224no—
304C2×Q16—442no—
305C22×C8—112no—
306C22×C8—224no—
307C22×C8—224no—
308C22×C8—442no—
309C22×C8C22×D1111yescharacteristic
310C22×C8C22×D1111yescharacteristic
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—22no—
320C4×Q8—22no—
321C4×D4—222no—
322C4×D4—222no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4C22×D1111yescharacteristic
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—21no—
343C2×C42C22×D1111yescharacteristic
344#107—224no—
345C4⋊C8—114no—
346#103—22no—
347#103—224no—
348#103—224no—
349#103—442no—
350#103D4414yescomplemented
351C22⋊C8—224no—
352C4×C8—22no—
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—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8—222no—
374C2×Q8—222no—
375C2×Q8C2×D4412yes—
376C2×D4—114no—
377C2×D4—222no—
378C2×D4—222no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—112no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395Q16—448no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—114no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—448no—
405C2×C8C2×D4412yes—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—42no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—444no—
415C4⋊C4—444no—
416C4⋊C4—444no—
417C4⋊C4—442no—
418C4⋊C4—442no—
419C4⋊C4—442no—
420C4⋊C4—881no—
421C4⋊C4C2×D4412yes—
422C4⋊C4#433912yes—
423C22⋊C4—224no—
424C22⋊C4—444no—
425C22⋊C4—444no—
426C22⋊C4—444no—
427C22⋊C4—882no—
428C42—42no—
429C42—42no—
430C42#433912yes—
431C42D4×D1112yes—
432C11#2538611yescharacteristic, complemented, Sylow
433C23—114no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23—222no—
438C23—222no—
439C23—222no—
440C23C2×D4×D1111yescharacteristic
441Q8—22no—
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8—442no—
446Q8—442no—
447Q8—442no—
448Q8—442no—
449D4—228no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4#6693712yes—
478C2×C4#6693712yes—
479C2×C4#6696912yes—
480C2×C4Q16×D1112yes—
481C2×C4C22×D4411yescharacteristic
482C2×C4C2×#433911yescharacteristic
483C2×C4C2×#433911yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4#6704211yescharacteristic
486C2×C4#6704211yescharacteristic
487C8—22no—
488C8—41no—
489C8—224no—
490C22—224no—
491C22—224no—
492C22—224no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22C2×#6693711yescharacteristic
498C22D4×D4411yescharacteristic
499C22#1062308111yescharacteristic
500C22C2×#6696911yescharacteristic
501C22C2×Q16×D1111yescharacteristic
502C22#1062330111yescharacteristic
503C22#1062330211yescharacteristic
504C4—22no—
505C4—42no—
506C4—42no—
507C4—42no—
508C4—81no—
509C4—442no—
510C4—882no—
511C4—882no—
512C4#1062242614yescomplemented
513C4#1062300811yescharacteristic
514C4#1062306611yescharacteristic
515C4D4×D4411yescharacteristic
516C4#1062308411yescharacteristic
517C2—444no—
518C2#1307220411yescharacteristic
519C2C2×#1062242611yescharacteristic
520C2#1307831011yescharacteristic
521C2#1308034711yescharacteristic
522C2Q16×D4411yescharacteristic
523C2#1308049411yescharacteristic
524C2#1308053511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC4×#103D11
hypocenterC11#25386
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
1. C2×#10622426C2semidirect
2. C2×#10622644C2semidirect
6. #13069822C2semidirect
7. #13069625C2semidirect
8. #13069418C2semidirect
9. #13069374C2semidirect
10. #13069038C2semidirect
11. C4×C11×#103C2semidirect
91. C11×#103D4semidirect
121. C2×D44Q16semidirect
181. C4×#103D11semidirect
290. C4×C11#467semidirect
350. #103D44semidirect
432. C11#25386semidirect
512. C4#10622426semidirect

Maximal subgroups

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

subgroupindex
C2×#106224262
C2×#106226442
C2×C8×D442
#130735652
#130735342
#130698222
#130696252
#130694182
#130693742
#130690382
C4×C11×#1032
#2538611