Finite Group Databasebeta

← #14787721

Subgroups — #14787721

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×#10623094C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic, complemented
4#13069796C212yesmaximal, complemented
5#13069616C212yesmaximal, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic, complemented
8#13068925C212yesmaximal, complemented
9#13068814C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
12C22×C11×SD16C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66999C2212yes—
16C2×#66991C2212yes—
17C2×#66983—21no—
18C2×#66979—21no—
19#10623094—24no—
20#10623094—24no—
21C2×#66945C2212yes—
22C2×#66938—22no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C4×C11×SD16—24no—
26C2×C11×#106C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C2×#66899C2212yes—
31C2×#66896C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34#10622634—24no—
35#10622607—22no—
36#10622600C2212yes—
37C2×#66871C2212yes—
38#10622552—21no—
39#10622548C2211yescharacteristic
40#10622541—21no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—22no—
49C22×D44D411yescharacteristic
50C22×C4×D11C2312yes—
51C22×Dic22—21no—
52C2×C11×SD16—22no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11D414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68#66999—24no—
69#66999—42no—
70#66991—24no—
71#66991—24no—
72#66983—28no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4D412yes—
77#66979—28no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11D411yescharacteristic
82C2×C4⋊Dic11C2312yes—
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—22no—
86C22×C11⋊C8C2312yes—
87#66945—24no—
88#66945—24no—
89#66938—216no—
90C4×D44—22no—
91C4×D44—22no—
92#66922—22no—
93#66922D414yes—
94C11×#106—22no—
95C11×#103—22no—
96C11×#102—22no—
97C4×C8×C11—22no—
98#66899—24no—
99#66896—42no—
100C11⋊#95—22no—
101(C2×D11)⋊C8—24no—
102(C2×D11)⋊C8—42no—
103#66871—24no—
104C4⋊(C11⋊C8)—22no—
105#24121—111nomaximal, Sylow
106C24×C11—21no—
107C23×D11C2×D412yes—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11#4112yes—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11C2×D412yes—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—28no—
130C2×C22⋊D11—82no—
131C2×C22⋊D11—82no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11C2×D412yes—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×Dic22—24no—
145C2×Dic22—81no—
146C2×Dic22—81no—
147C11×SD16—28no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11#4112yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4C2×D412yes—
159C11×C22⋊C4—24no—
160C42×C11—42no—
161C42×C11C2×D412yes—
162C42×C11C2×D412yes—
163C22⋊Dic11—28no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—82no—
168C4⋊Dic11—24no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—42no—
174C4⋊Dic11—81no—
175C4⋊Dic11C2×D414yes—
176Dic11⋊C4—44no—
177C4×Dic11—28no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×#555—111no—
182C2×#477—111no—
183C2×C4×SD16D1111yescharacteristic, complemented
184#2538—111no—
185#2033—112no—
186#2000—112no—
187#1990—111no—
188#1954—111no—
189#1873—112no—
190#1854—112no—
191#1802—111no—
192C23×C11—22no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11C22×D411yescharacteristic
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11—41no—
210Q8×C11—41no—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—41no—
214D4×C11—41no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—48no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11#12012yes—
228C2×C4×C11#12012yes—
229C2×C4×C11#13512yes—
230C2×C4×C11#13712yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C22⋊D11—88no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247D44—44no—
248C4×D11—42no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—42no—
252Dic22—84no—
253C8×C11—22no—
254C8×C11—41no—
255C11⋊C8—42no—
256C22×SD16C2×D1111yescharacteristic
257#555—224no—
258#555—224no—
259C2×C4⋊Q8—111no—
260C2×#124—222no—
261C2×C22⋊Q8—112no—
262C2×#121—112no—
263C2×#121—221no—
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×D4—111no—
266C2×C4×D4C2×D1111yescharacteristic
267C2×#117—112no—
268C2×#117—221no—
269#477—224no—
270C4×SD16—24no—
271C2×#107—112no—
272C2×#106C2×D1111yescharacteristic
273C2×C4⋊C8—111no—
274C2×#103—112no—
275C2×#103C2×D1111yescharacteristic
276C2×#102—112no—
277C2×#102C2×D1111yescharacteristic
278C2×C22⋊C8—112no—
279C2×C22⋊C8—112no—
280C2×C4×C8C2×D1111yescharacteristic
281#396—222no—
282#390—221no—
283#389—221no—
284#384—111no—
285#380—112no—
286#340—112no—
287#340—112no—
288#340—112no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11C2×#12011yescharacteristic
297C22×C11#54611yescharacteristic
298C22×C11#54711yescharacteristic
299C22×C11C2×#13511yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C22×C11#57611yescharacteristic
302C22×C11#57711yescharacteristic
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C4×C11—22no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—81no—
314C4×C11#45214yes—
315C4×C11#52511yescharacteristic
316C4×C11#53711yescharacteristic
317C4×C11#54811yescharacteristic
318C4×C11#55011yescharacteristic
319Dic11—42no—
320Dic11—44no—
321Dic11—82no—
322C22×Q8—221no—
323C22×Q8C22×D1111yescharacteristic
324C22×D4—111no—
325C22×D4—222no—
326C22×D4C22×D1111yescharacteristic
327C23×C4—21no—
328C23×C4—112no—
329C2×SD16—22no—
330C2×SD16—22no—
331C2×SD16—22no—
332C22×C8—112no—
333C22×C8C22×D1111yescharacteristic
334C22×C8C22×D1111yescharacteristic
335C4⋊Q8—114no—
336C4⋊Q8—222no—
337#124—2216no—
338C22⋊Q8—224no—
339C22⋊Q8—442no—
340#121—224no—
341#121—228no—
342#121—224no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×D4—22no—
346C4×D4—222no—
347C4×D4—222no—
348C4×D4C22⋊D1114yes—
349#117—224no—
350#117—228no—
351#117—224no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C4⋊C4C22×D1111yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—112no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C42—21no—
369C2×C42—222no—
370C2×C42C22×D1111yescharacteristic
371#107—224no—
372#106—22no—
373C4⋊C8—222no—
374#103—22no—
375#103—224no—
376#102—22no—
377#102—442no—
378C22⋊C8—224no—
379C22⋊C8—442no—
380C4×C8—22no—
381#95—222no—
382C2×C11—82no—
383C2×C11#240711yescharacteristic
384C2×C11C2×#45211yescharacteristic
385C2×C11#301211yescharacteristic
386C2×C11#330511yescharacteristic
387C2×C11#332911yescharacteristic
388C2×C11#334011yescharacteristic
389C2×C11#335711yescharacteristic
390D11—82no—
391C24—21no—
392C24—112no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—224no—
399C2×Q8—881no—
400C2×Q8—881no—
401C2×Q8#433912yes—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—228no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—882no—
412C2×D4—882no—
413C2×D4C2×C22⋊D1112yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—112no—
421C22×C4—222no—
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—28no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8#433912yes—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—42no—
446C4⋊C4—114no—
447C4⋊C4—222no—
448C4⋊C4—224no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C4⋊C4—444no—
453C4⋊C4—442no—
454C4⋊C4—881no—
455C4⋊C4C2×C22⋊D1112yes—
456C22⋊C4—24no—
457C22⋊C4—228no—
458C22⋊C4—228no—
459C22⋊C4—224no—
460C22⋊C4—444no—
461C22⋊C4—882no—
462C42—42no—
463C42—228no—
464C42D4×D1112yes—
465C42C2×C22⋊D1112yes—
466C11#2412111yescharacteristic, complemented, Sylow
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—222no—
475C23—222no—
476C23—222no—
477C23—222no—
478C23—222no—
479C23—222no—
480C23—222no—
481C23C2×D4×D1111yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—884no—
487D4—22no—
488D4—22no—
489D4—41no—
490D4—41no—
491D4—444no—
492D4—888no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—48no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4#6696812yes—
519C2×C4#6696912yes—
520C2×C4#6699012yes—
521C2×C4#6699012yes—
522C2×C4C2×#433911yescharacteristic
523C2×C4C2×#433911yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4#6704211yescharacteristic
526C2×C4#6704311yescharacteristic
527C2×C4C22×C22⋊D1111yescharacteristic
528C8—22no—
529C8—41no—
530C8—442no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—442no—
539C22—442no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—442no—
544C22—442no—
545C22#1062308111yescharacteristic
546C22#1062308211yescharacteristic
547C22C2×#6696811yescharacteristic
548C22C2×#6696911yescharacteristic
549C22#1062330011yescharacteristic
550C22#1062330111yescharacteristic
551C22C2×#6699011yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—442no—
557C4—444no—
558C4—882no—
559C4#1062278614yes—
560C4#1062308311yescharacteristic
561C4#1062308411yescharacteristic
562C4#1062332211yescharacteristic
563C4#1062336411yescharacteristic
564C2—82no—
565C2—882no—
566C2#1307196111yescharacteristic
567C2C2×#1062278611yescharacteristic
568C2#1307791611yescharacteristic
569C2#1308056811yescharacteristic
570C2#1308091211yescharacteristic
571C2#1308103111yescharacteristic
572C2#1308124411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
hypercenterC2×C4×SD16D11
hypocenterC11#24121
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#10622634C2semidirect
3. #13073534C2semidirect
4. #13069796C2semidirect
5. #13069616C2semidirect
6. #13069577C2semidirect
7. #13069410C2semidirect
8. #13068925C2semidirect
9. #13068814C2semidirect
10. #13068616C2semidirect
11. C2×C4×C11×SD16C2semidirect
183. C2×C4×SD16D11semidirect
466. C11#24121semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106226342
#130735342
#130697962
#130696162
#130695772
#130694102
#130689252
#130688142
#130686162
C2×C4×C11×SD162
#2412111