Finite Group Databasebeta

← #14795168

Subgroups — #14795168

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622455C211yesmaximal, characteristic, complemented
2C2×#10622453C211yesmaximal, characteristic, complemented
3#13074440C211yesmaximal, characteristic, complemented
4#13071310C211yesmaximal, characteristic
5#13070051C211yesmaximal, characteristic, complemented
6#13070051C211yesmaximal, characteristic, complemented
7#13069807C211yesmaximal, characteristic
8#13069800C211yesmaximal, characteristic
9#13069568C211yesmaximal, characteristic, complemented
10#13069355C211yesmaximal, characteristic, complemented
11#13069345C211yesmaximal, characteristic, complemented
12#13069314C211yesmaximal, characteristic, complemented
13#13069300C211yesmaximal, characteristic, complemented
14#13068623C211yesmaximal, characteristic, complemented
15C11×#1949C211yesmaximal, characteristic, complemented
16C2×#66948C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×#66925C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C11×#382C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622601C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42#10622553—21no—
43#10622552—21no—
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622455—24no—
46#10622453—24no—
47#10622290—21no—
48#10622286—21no—
49#10622281—21no—
50#10622278—21no—
51#10622272—21no—
52#10622269—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×Dic22—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4D411yescharacteristic
91C2×Dic11⋊C4D411yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66948—22no—
96#66948—22no—
97C4×D44—22no—
98C4×D44—22no—
99#66925—22no—
100#66925—22no—
101#66922—22no—
102#66922—22no—
103C11×#107—22no—
104C11×#106—22no—
105C11×C4⋊C8D414yescomplemented
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115#66885—22no—
116#66885—22no—
117(C2×D11)⋊C8—22no—
118(C2×D11)⋊C8—22no—
119#66881—22no—
120#66881—22no—
121#66879—22no—
122C8×Dic11—22no—
123#66873—22no—
124#66873—22no—
125C4⋊(C11⋊C8)—22no—
126#24716—111nomaximal, Sylow
127C23×D11—21no—
128C23×D11C2×D411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×D44—24no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—81no—
149C2×D44—81no—
150C2×D44#4112yes—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—42no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×Dic22—42no—
161C2×Dic22—81no—
162C2×Dic22—81no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C2×D412yes—
168C2×C8×C11C2×D412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4#4112yes—
177C42×C11—81no—
178C42×C11C2×D412yes—
179C42×C11#4112yes—
180(C2×D11)⋊C4—24no—
181(C2×D11)⋊C4—22no—
182(C2×D11)⋊C4—22no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—81no—
185(C2×D11)⋊C4—81no—
186(C2×D11)⋊C4—81no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—42no—
196C4⋊Dic11—81no—
197C4⋊Dic11—81no—
198C4⋊Dic11—81no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×#476—111no—
210C2×#433—111no—
211#2628—111no—
212#2324—111no—
213#2077—111no—
214#2077—111no—
215#2034—111no—
216#2033—111no—
217#1988—111no—
218#1949D1111yescharacteristic, complemented
219#1943—111no—
220#1941—111no—
221#1936—111no—
222#1934—111no—
223#1804—111no—
224C23×C11C22×D411yescharacteristic
225C22×D11—21no—
226C22×D11—22no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11#12112yes—
256C2×C4×C11#12112yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281D44—22no—
282D44—22no—
283D44—41no—
284D44—41no—
285D44—84no—
286C4×D11—41no—
287C4×D11—41no—
288C4×D11—41no—
289C4×D11—41no—
290C4×D11—84no—
291Dic22—84no—
292C8×C11—22no—
293C8×C11—22no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C2×C4⋊Q8—111no—
297C2×#121—111no—
298C2×C4×D4—111no—
299C2×#117—111no—
300#476—224no—
301#433—224no—
302C2×#107C2×D1111yescharacteristic
303C2×#106—111no—
304C2×#106—111no—
305C2×#106C2×D1111yescharacteristic
306C2×C4⋊C8—111no—
307C2×C4⋊C8C2×D1111yescharacteristic
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×#97—111no—
315C2×C4×C8—111no—
316#400—221no—
317#399—221no—
318#395—221no—
319#393—221no—
320#390—111no—
321#390—221no—
322#389—111no—
323#389—111no—
324#389—111no—
325#388—221no—
326#386—221no—
327#385—221no—
328#382C2×D1111yescharacteristic
329#380—111no—
330#380—111no—
331#380—111no—
332C4×C4⋊C4C2×D1111yescharacteristic
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340C2×D1111yescharacteristic
340#340C2×D1111yescharacteristic
341C22×C11C2×#12111yescharacteristic
342C22×C11#52511yescharacteristic
343C22×C11#53611yescharacteristic
344C22×C11#57611yescharacteristic
345C22×C11#57711yescharacteristic
346C22×C11#57711yescharacteristic
347C22×C11#57711yescharacteristic
348C2×D11—41no—
349C2×D11—42no—
350C2×D11—41no—
351C2×D11—42no—
352C2×D11—41no—
353C2×D11—42no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C4×C11—22no—
363C4×C11—22no—
364C4×C11—42no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11#54711yescharacteristic
369C4×C11#54811yescharacteristic
370C4×C11#55211yescharacteristic
371C4×C11#55611yescharacteristic
372Dic11—41no—
373Dic11—41no—
374Dic11—41no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8—221no—
379C22×D4—111no—
380C22×D4—221no—
381C23×C4—111no—
382C23×C4—221no—
383C22×C8—111no—
384C22×C8—111no—
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387C4⋊Q8—222no—
388C4⋊Q8—222no—
389#121—222no—
390#121—222no—
391C4×D4—222no—
392C4×D4—222no—
393#117—222no—
394#117—222no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—111no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C42—21no—
418C2×C42—111no—
419C2×C42C22×D1111yescharacteristic
420#107—22no—
421#106—22no—
422#106—222no—
423#106—222no—
424C4⋊C8—222no—
425C4⋊C8D4414yescomplemented
426#102—222no—
427#102—222no—
428#102—222no—
429#102—222no—
430C22⋊C8—222no—
431C22⋊C8—222no—
432#97—222no—
433C4×C8—222no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443C2×C11#241511yescharacteristic
444C2×C11#305711yescharacteristic
445C2×C11#306211yescharacteristic
446C2×C11#311811yescharacteristic
447C2×C11#312511yescharacteristic
448C2×C11#324111yescharacteristic
449C2×C11#324411yescharacteristic
450D11—81no—
451D11—82no—
452C24—111no—
453C24—221no—
454C2×Q8—442no—
455C2×Q8—881no—
456C2×Q8—881no—
457C2×D4—112no—
458C2×D4—224no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—881no—
465C2×D4—881no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—442no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4D4×D1111yescharacteristic
486C22×C4D4×D1111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8C2×D4412yes—
499C2×C8C2×D4412yes—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—442no—
516C4⋊C4—881no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4#434112yes—
520C22⋊C4—224no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4—442no—
524C22⋊C4—881no—
525C22⋊C4—881no—
526C22⋊C4—881no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C42—81no—
530C42—221no—
531C42—221no—
532C42C2×D4412yes—
533C42#434312yes—
534C11#2471611yescharacteristic, complemented, Sylow
535C23—221no—
536C23—221no—
537C23—221no—
538C23—221no—
539C23—221no—
540C23—222no—
541C23—221no—
542C23—221no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23C2×D4×D1111yescharacteristic
550Q8—884no—
551D4—222no—
552D4—222no—
553D4—441no—
554D4—441no—
555D4—884no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—884no—
595C2×C4#6694812yes—
596C2×C4#6694812yes—
597C2×C4C22×D4411yescharacteristic
598C2×C4C2×#434111yescharacteristic
599C2×C4C2×#434311yescharacteristic
600C2×C4#6704011yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#6704311yescharacteristic
603C8—22no—
604C8—22no—
605C8—441no—
606C8—441no—
607C22—441no—
608C22—442no—
609C22—441no—
610C22—441no—
611C22—441no—
612C22—442no—
613C22—441no—
614C22—441no—
615C22—442no—
616C22—441no—
617C22—881no—
618C22—881no—
619C22—881no—
620C22—881no—
621C22C2×#6694811yescharacteristic
622C22#1062313711yescharacteristic
623C22#1062315911yescharacteristic
624C22#1062330111yescharacteristic
625C22#1062330111yescharacteristic
626C22#1062330511yescharacteristic
627C22#1062330911yescharacteristic
628C4—22no—
629C4—22no—
630C4—42no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—441no—
635C4—441no—
636C4—441no—
637C4—881no—
638C4—881no—
639C4—881no—
640C4#1062308611yescharacteristic
641C4#1062310711yescharacteristic
642C4#1062322511yescharacteristic
643C4#1062326311yescharacteristic
644C2—881no—
645C2—882no—
646C2#1307204311yescharacteristic
647C2#1307825611yescharacteristic
648C2#1307829711yescharacteristic
649C2#1307879911yescharacteristic
650C2#1307889211yescharacteristic
651C2#1307987411yescharacteristic
652C2#1307992111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1949D11
hypocenterC11#24716
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
1. C2×#10622455C2semidirect
2. C2×#10622453C2semidirect
3. #13074440C2semidirect
5. #13070051C2semidirect
6. #13070051C2semidirect
9. #13069568C2semidirect
10. #13069355C2semidirect
11. #13069345C2semidirect
12. #13069314C2semidirect
13. #13069300C2semidirect
14. #13068623C2semidirect
15. C11×#1949C2semidirect
105. C11×C4⋊C8D4semidirect
218. #1949D11semidirect
425. C4⋊C8D44semidirect
534. C11#24716semidirect

Maximal subgroups

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

subgroupindex
C2×#106224552
C2×#106224532
#130744402
#130713102
#130700512
#130698072
#130698002
#130695682
#130693552
#130693452
#130693142
#130693002
#130686232
C11×#19492
#2471611