Finite Group Databasebeta

← #14804527

Subgroups — #14804527

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622420C212yesmaximal, complemented
2C2×#10622640C211yesmaximal, characteristic, complemented
3C2×C8×D44C211yesmaximal, characteristic, complemented
4#13073558C211yesmaximal, characteristic
5#13073534C211yesmaximal, characteristic, complemented
6#13069808C212yesmaximal, complemented
7#13069618C212yesmaximal, complemented
8#13069422C211yesmaximal, characteristic, complemented
9#13069379C211yesmaximal, characteristic, complemented
10#13069043C212yesmaximal, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2212yes—
14C22×#4325C2212yes—
15C22×C8×D11C2212yes—
16C2×#66948C2212yes—
17C2×#66948C2212yes—
18C2×#66927—21no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2212yes—
26C2×#66885C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28#10622640—24no—
29#10622607—22no—
30#10622600C2212yes—
31C2×#66873C2212yes—
32C2×#66872C2212yes—
33#10622552—21no—
34#10622552—21no—
35#10622548C2211yescharacteristic
36#10622541—21no—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622420—28no—
39C8×D44—24no—
40#10622284—22no—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43#10622167C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D44—21no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—21no—
49C22×D44D411yescharacteristic
50C22×D44C2312yes—
51C22×C4×D11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#66999—24no—
64#66999—42no—
65C2×#4325—24no—
66C2×#4325—24no—
67C2×#4325—42no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4D412yes—
73C2×C4⋊Dic11—21no—
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#66948—24no—
83#66948—24no—
84#66948—42no—
85#66948—42no—
86#66927—22no—
87#66927—22no—
88#66927—44no—
89C4×D44—22no—
90C4×D44—22no—
91C11×#103—22no—
92C11×#103D414yescomplemented
93C4×C8×C11—22no—
94C11×#95—21no—
95C11⋊#95—22no—
96#66885—24no—
97#66885—42no—
98(C2×D11)⋊C8—24no—
99#66873—24no—
100#66872—24no—
101C4⋊(C11⋊C8)D414yescomplemented
102#25387—111nomaximal, Sylow
103C23×D11—22no—
104C23×D11C2×D412yes—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11C2×D412yes—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11C2×D412yes—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—44no—
129C2×D44—44no—
130C2×D44—44no—
131C2×D44—44no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—42no—
135C2×D44—42no—
136C2×D44—81no—
137C2×D44—81no—
138C2×D44—82no—
139C2×D44—82no—
140C2×D44SD1614yescomplemented
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C2×D412yes—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4#4112yes—
160C42×C11—42no—
161C42×C11—42no—
162C42×C11C2×D412yes—
163C42×C11#4112yes—
164#4325—48no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—44no—
168(C2×D11)⋊C4—44no—
169(C2×D11)⋊C4—82no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—42no—
174C4⋊Dic11—81no—
175Dic11⋊C4—44no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8C2×D414yes—
179C8×D11—48no—
180C2×#465—112no—
181C2×#460—111no—
182C2×C8×D4—111no—
183#2541—111no—
184#2538—111no—
185#2034—112no—
186#2000—112no—
187#1957—111no—
188#1948—111no—
189#1893—112no—
190C4×#103D1111yescharacteristic, complemented
191C23×C11C22×D411yescharacteristic
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11C2×SD1614yes—
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—41no—
209Q8×C11—41no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11#12112yes—
225C2×C4×C11#12112yes—
226C2×C4×C11C2×SD1612yes—
227C2×C4×C11#13512yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240D44—28no—
241D44—42no—
242D44—42no—
243D44—42no—
244D44—42no—
245D44—84no—
246D44—88no—
247D44—88no—
248D44—84no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—42no—
253C8×C11—22no—
254C8×C11—41no—
255C11⋊C8—24no—
256C22×SD16—112no—
257C23×C8—112no—
258C2×#127—111no—
259C2×#127—221no—
260C2×C22⋊Q8—112no—
261C2×#121—112no—
262C2×#121—112no—
263C2×C4×Q8C2×D1111yescharacteristic
264C2×C4×D4—111no—
265#465—228no—
266#460—224no—
267C8×D4—224no—
268C2×#106—112no—
269C2×C4⋊C8—111no—
270C2×#103C2×D1111yescharacteristic
271C2×#103C2×D1111yescharacteristic
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—112no—
275C2×C22⋊C8—112no—
276C2×C4×C8C2×D1111yescharacteristic
277#396—222no—
278#392—222no—
279#390—221no—
280#390—221no—
281#389—221no—
282#384—111no—
283#380—112no—
284C4×C4⋊C4C2×D1111yescharacteristic
285#340—112no—
286#340C2×D1111yescharacteristic
287#340C2×D1111yescharacteristic
288C22×C11C2×#12111yescharacteristic
289C22×C11D4211yescharacteristic
290C22×C11#54611yescharacteristic
291C22×C11C22×SD1611yescharacteristic
292C22×C11C2×#13511yescharacteristic
293C22×C11#57611yescharacteristic
294C22×C11#57711yescharacteristic
295C2×D11—24no—
296C2×D11—24no—
297C2×D11—24no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—82no—
303C2×D11—82no—
304C2×D11—82no—
305C2×D11—82no—
306C2×D11—82no—
307C2×D11—82no—
308C2×D11—82no—
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—81no—
314C4×C11#46514yescomplemented
315C4×C11#53211yescharacteristic
316C4×C11#54011yescharacteristic
317C4×C11D4211yescharacteristic
318C4×C11#55011yescharacteristic
319Dic11—42no—
320Dic11—82no—
321C22×Q8C22×D1111yescharacteristic
322C22×D4—111no—
323C22×D4—112no—
324C22×D4—222no—
325C22×D4—222no—
326C22×D4—221no—
327C22×D4—221no—
328C23×C4—112no—
329C2×SD16—224no—
330C2×SD16—224no—
331C2×SD16—442no—
332C22×C8—112no—
333C22×C8—224no—
334C22×C8—224no—
335C22×C8—442no—
336C22×C8C22×D1111yescharacteristic
337C22×C8C22×D1111yescharacteristic
338#127—222no—
339#127—222no—
340#127—444no—
341C22⋊Q8—224no—
342C22⋊Q8—442no—
343#121—224no—
344#121—224no—
345#121—442no—
346#121—442no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×D4—222no—
350C4×D4—222no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C22⋊C4—112no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4—222no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42C22×D1111yescharacteristic
368#106—224no—
369C4⋊C8—114no—
370#103—22no—
371#103D4414yescomplemented
372#102—224no—
373#102—224no—
374#102—442no—
375C22⋊C8—224no—
376C4×C8—22no—
377#95—21no—
378#95—222no—
379C2×C11#242811yescharacteristic
380C2×C11C2×#46511yescharacteristic
381C2×C11#306211yescharacteristic
382C2×C11D4×SD1611yescharacteristic
383C2×C11#328711yescharacteristic
384C2×C11#329511yescharacteristic
385C2×C11#330411yescharacteristic
386D11—44no—
387D11—162no—
388C24—112no—
389C24—222no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8C2×D4412yes—
396C2×D4—114no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—444no—
406C2×D4—444no—
407C2×D4—444no—
408C2×D4—444no—
409C2×D4—442no—
410C2×D4—442no—
411C2×D4—442no—
412C2×D4—442no—
413C2×D4—881no—
414C2×D4—881no—
415C2×D4—882no—
416C2×D4—882no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—112no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4C23×D1111yescharacteristic
432SD16—448no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—114no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—448no—
442C2×C8C2×D4412yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—42no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—444no—
452C4⋊C4—442no—
453C4⋊C4—881no—
454C4⋊C4C2×D4412yes—
455C4⋊C4#433912yes—
456C22⋊C4—224no—
457C22⋊C4—444no—
458C22⋊C4—444no—
459C22⋊C4—444no—
460C22⋊C4—882no—
461C42—42no—
462C42—42no—
463C42#433912yes—
464C42D4×D1112yes—
465C11#2538711yescharacteristic, complemented, Sylow
466C23—114no—
467C23—222no—
468C23—222no—
469C23—222no—
470C23—222no—
471C23—222no—
472C23—222no—
473C23—442no—
474C23—442no—
475C23—442no—
476C23—442no—
477C23—442no—
478C23—442no—
479C23—442no—
480C23C2×D4×D1111yescharacteristic
481Q8—22no—
482Q8—22no—
483Q8—41no—
484Q8—41no—
485D4—228no—
486D4—442no—
487D4—442no—
488D4—442no—
489D4—442no—
490D4—884no—
491D4—888no—
492D4—888no—
493D4—884no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4#6693712yes—
519C2×C4#6693712yes—
520C2×C4SD16×D1112yes—
521C2×C4#6697212yes—
522C2×C4C22×D4411yescharacteristic
523C2×C4C2×#433911yescharacteristic
524C2×C4C2×#433911yescharacteristic
525C2×C4C2×D4×D1111yescharacteristic
526C2×C4#6704211yescharacteristic
527C2×C4#6704211yescharacteristic
528C8—22no—
529C8—41no—
530C8—224no—
531C22—224no—
532C22—224no—
533C22—224no—
534C22—442no—
535C22—442no—
536C22—442no—
537C22—442no—
538C22—882no—
539C22—882no—
540C22—882no—
541C22—882no—
542C22—882no—
543C22—882no—
544C22—882no—
545C22C2×#6693711yescharacteristic
546C22D4×D4411yescharacteristic
547C22#1062308111yescharacteristic
548C22C2×SD16×D1111yescharacteristic
549C22C2×#6697211yescharacteristic
550C22#1062330011yescharacteristic
551C22#1062330111yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—42no—
556C4—81no—
557C4—442no—
558C4—882no—
559C4#1062242014yescomplemented
560C4#1062300811yescharacteristic
561C4#1062306611yescharacteristic
562C4D4×D4411yescharacteristic
563C4#1062308411yescharacteristic
564C2—444no—
565C2—1762no—
566C2#1307220411yescharacteristic
567C2C2×#1062242011yescharacteristic
568C2#1307829911yescharacteristic
569C2SD16×D4411yescharacteristic
570C2#1308037511yescharacteristic
571C2#1308044211yescharacteristic
572C2#1308055711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radical#13073558C2
hypercenterC4×#103D11
hypocenterC11#25387
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×#10622420C2semidirect
2. C2×#10622640C2semidirect
3. C2×C8×D44C2semidirect
5. #13073534C2semidirect
6. #13069808C2semidirect
7. #13069618C2semidirect
8. #13069422C2semidirect
9. #13069379C2semidirect
10. #13069043C2semidirect
11. C4×C11×#103C2semidirect
92. C11×#103D4semidirect
101. C4⋊(C11⋊C8)D4semidirect
140. C2×D44SD16semidirect
190. C4×#103D11semidirect
314. C4×C11#465semidirect
371. #103D44semidirect
465. C11#25387semidirect
559. C4#10622420semidirect

Maximal subgroups

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

subgroupindex
C2×#106224202
C2×#106226402
C2×C8×D442
#130735582
#130735342
#130698082
#130696182
#130694222
#130693792
#130690432
C4×C11×#1032
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