Finite Group Databasebeta

← #14814213

Subgroups — #14814213

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622798C211yesmaximal, characteristic
2C2×#10622797C211yesmaximal, characteristic, complemented
3#13072412C211yesmaximal, characteristic
4#13071537C211yesmaximal, characteristic, complemented
5#13070136C211yesmaximal, characteristic
6#13070116C211yesmaximal, characteristic, complemented
7#13070034C211yesmaximal, characteristic, complemented
8#13069854C211yesmaximal, characteristic
9#13069314C211yesmaximal, characteristic
10#13069181C211yesmaximal, characteristic, complemented
11#13068971C211yesmaximal, characteristic
12#13068969C211yesmaximal, characteristic
13#13068872C211yesmaximal, characteristic, complemented
14#13068872C211yesmaximal, characteristic, complemented
15C11×#1878C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622798—24no—
30#10622797—24no—
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622601C2211yescharacteristic
38#10622598—21no—
39#10622598—21no—
40#10622598C2211yescharacteristic
41#10622598C2211yescharacteristic
42#10622598C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44#10622552C2211yescharacteristic
45#10622549—21no—
46#10622549C2211yescharacteristic
47C4×C4⋊Dic11—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622290—21no—
50#10622287—21no—
51#10622283—21no—
52#10622283—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C2×C11×Q16—22no—
65C2×C11×Q16—22no—
66C2×C11×Q16D414yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#67000—22no—
77#67000—41no—
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80Q8×Dic11—22no—
81Q8×Dic11—41no—
82Q8×Dic11—41no—
83Q8×Dic11—41no—
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325—22no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11D411yescharacteristic
100C2×C4⋊Dic11D411yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C11×#103—22no—
112C11×#103—22no—
113C11×#95—21no—
114C11×#95—21no—
115#66899—22no—
116#66899—22no—
117#66899—22no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66885—22no—
126#66885—41no—
127#66882—41no—
128#66881—22no—
129#66879—22no—
130Dic11⋊C8—22no—
131#66873—22no—
132#26189—111nomaximal, Sylow
133C23×D11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11C2×D412yes—
144C2×Q8×C11#4112yes—
145C2×Q8×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C11×Q16—28no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D412yes—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4#4112yes—
178C42×C11—24no—
179C42×C11—21no—
180C42×C11—21no—
181#4325—44no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—81no—
187(C2×D11)⋊C4—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—41no—
195C4⋊Dic11—41no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11—42no—
201C4⋊Dic11—81no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×#464—111no—
216C2×#441—111no—
217#2448—111no—
218#2351—111no—
219#2092—111no—
220#2088—111no—
221#2074—111no—
222#2042—111no—
223#1936—111no—
224#1917—111no—
225#1880—111no—
226#1880—111no—
227#1878D1111yescharacteristic, complemented
228#1863—111no—
229#1863—111no—
230C23×C11C22×D411yescharacteristic
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11#12314yes—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291D44—41no—
292D44—41no—
293D44—41no—
294D44—41no—
295C8×C11—22no—
296C8×C11—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C22×Q16C2×D1111yescharacteristic
300C22×SD16—111no—
301C2×#124—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×Q8—111no—
305C2×C4×Q8C2×D1111yescharacteristic
306#464—224no—
307#441—224no—
308C2×#107—111no—
309C2×#106—111no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103C2×D1111yescharacteristic
315C2×#103C2×D1111yescharacteristic
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#97—111no—
320#399—221no—
321#397—221no—
322#391C2×D1111yescharacteristic
323#390—111no—
324#390—111no—
325#389—111no—
326#389—111no—
327#389—111no—
328#389—221no—
329#389—221no—
330#388—221no—
331#388—221no—
332#382—111no—
333#382—221no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—221no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340C2×D1111yescharacteristic
340#336—111no—
341#336—111no—
342#336—111no—
343#336C2×D1111yescharacteristic
344C22×C11#52511yescharacteristic
345C22×C11D4211yescharacteristic
346C22×C11#54811yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57811yescharacteristic
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C4×C11—24no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—42no—
363C4×C11—81no—
364C4×C11C2×#12311yescharacteristic
365C4×C11#53911yescharacteristic
366C4×C11#54711yescharacteristic
367C4×C11#55311yescharacteristic
368Dic11—41no—
369Dic11—41no—
370Dic11—41no—
371Dic11—41no—
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375C22×Q8C22×D1111yescharacteristic
376C22×Q8C22×D1111yescharacteristic
377C22×D4—111no—
378C2×Q16—22no—
379C2×Q16—22no—
380C2×Q16D4414yes—
381C2×SD16—222no—
382C2×SD16—222no—
383C2×SD16—222no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8C22×D1111yescharacteristic
387C22×C8C22×D1111yescharacteristic
388#124—222no—
389#124—441no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—222no—
393C4×Q8—222no—
394C4×Q8—222no—
395C4×Q8—441no—
396C4×Q8—441no—
397C4×Q8—441no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—21no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—221no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425#107—441no—
426#106—222no—
427C4⋊C8—222no—
428#103—22no—
429#103—22no—
430#103—222no—
431#103—222no—
432#103—222no—
433#102—222no—
434#102—222no—
435#102—441no—
436#97—222no—
437#95—21no—
438#95—21no—
439#95—111no—
440#95—111no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446C2×C11#244311yescharacteristic
447C2×C11#311111yescharacteristic
448C2×C11#312111yescharacteristic
449C2×C11#327111yescharacteristic
450C2×C11#327711yescharacteristic
451C2×C11#337111yescharacteristic
452C2×C11#337711yescharacteristic
453D11—161no—
454C24—221no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8C2×D4412yes—
464C2×Q8C2×D4412yes—
465C2×Q8#434112yes—
466C2×Q8#434112yes—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487Q16—28no—
488SD16—444no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8C2×D4412yes—
501C4⋊C4—24no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—441no—
512C4⋊C4—441no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4#434112yes—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—442no—
524C22⋊C4—881no—
525C22⋊C4—881no—
526C42—24no—
527C42—21no—
528C42—21no—
529C42—221no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—442no—
534C42—442no—
535C42—442no—
536C11#2618911yescharacteristic, complemented, Sylow
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23C2×D4×D1111yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—22no—
548Q8—22no—
549Q8—22no—
550Q8—41no—
551Q8—41no—
552Q8#6693914yes—
553D4—441no—
554D4—441no—
555D4—441no—
556D4—441no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4C22×D4411yescharacteristic
597C2×C4C2×#434111yescharacteristic
598C2×C4C2×#434111yescharacteristic
599C2×C4C2×#434111yescharacteristic
600C2×C4#6704211yescharacteristic
601C2×C4#6704311yescharacteristic
602C8—22no—
603C8—41no—
604C8—441no—
605C8—441no—
606C22—881no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22D4×D4411yescharacteristic
614C22#1062311711yescharacteristic
615C22#1062312911yescharacteristic
616C22#1062329711yescharacteristic
617C22#1062329911yescharacteristic
618C22#1062330811yescharacteristic
619C22#1062330911yescharacteristic
620C4—24no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—42no—
625C4—81no—
626C4—441no—
627C4—441no—
628C4—441no—
629C4—441no—
630C4—881no—
631C4—881no—
632C4—881no—
633C4C2×#6693911yescharacteristic
634C4#1062308611yescharacteristic
635C4#1062314911yescharacteristic
636C4#1062319611yescharacteristic
637C2—1761no—
638C2#1307234911yescharacteristic
639C2#1307872611yescharacteristic
640C2#1307884611yescharacteristic
641C2#1308020311yescharacteristic
642C2#1308027211yescharacteristic
643C2#1308138811yescharacteristic
644C2#1308145111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1878D11
hypocenterC11#26189
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×#10622797C2semidirect
4. #13071537C2semidirect
6. #13070116C2semidirect
7. #13070034C2semidirect
10. #13069181C2semidirect
13. #13068872C2semidirect
14. #13068872C2semidirect
15. C11×#1878C2semidirect
227. #1878D11semidirect
536. C11#26189semidirect

Maximal subgroups

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

subgroupindex
C2×#106227982
C2×#106227972
#130724122
#130715372
#130701362
#130701162
#130700342
#130698542
#130693142
#130691812
#130689712
#130689692
#130688722
C11×#18782
#2618911