Finite Group Databasebeta

← #14823583

Subgroups — #14823583

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622413C211yesmaximal, characteristic
2#13072471C211yesmaximal, characteristic, complemented
3#13072408C211yesmaximal, characteristic
4#13069985C211yesmaximal, characteristic
5#13069956C211yesmaximal, characteristic, complemented
6#13069936C211yesmaximal, characteristic, complemented
7#13069707C211yesmaximal, characteristic
8#13069494C211yesmaximal, characteristic
9#13069313C211yesmaximal, characteristic
10#13069308C211yesmaximal, characteristic, complemented
11#13069289C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic
13#13068870C211yesmaximal, characteristic, complemented
14#13068492C211yesmaximal, characteristic, complemented
15C2×C11×#441C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C11×#441—24no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27#10622843C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622606—21no—
39#10622605—21no—
40#10622601C2211yescharacteristic
41#10622599—21no—
42#10622598C2211yescharacteristic
43#10622597—21no—
44#10622586C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622553—21no—
48#10622553—21no—
49#10622552C2211yescharacteristic
50#10622546—21no—
51C4×Dic11⋊C4C2211yescharacteristic
52#10622541—21no—
53#10622541C2211yescharacteristic
54#10622413—24no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C2×C11×Q16—22no—
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—41no—
72C4×Q8×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80#67000—22no—
81#67000—41no—
82C2×#4325—22no—
83C2×#4325—22no—
84C2×#4325—41no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66943—22no—
106#66943—41no—
107C11×#106—22no—
108C11×#103—22no—
109C11×#103D414yes—
110C11×#97—22no—
111#66899—22no—
112#66899—22no—
113#66899—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66885—22no—
126#66885—22no—
127#66879—22no—
128Dic11⋊C8—22no—
129C8×Dic11—22no—
130#66873—22no—
131#66871—41no—
132#26839—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×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C2×D412yes—
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×C11C2×D412yes—
172C2×C8×C11#4112yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4C2×D412yes—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—42no—
182C42×C11—42no—
183#4325—44no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—81no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8#4112yes—
213C2×#488—111no—
214C2×#441D1111yescharacteristic, complemented
215#2453—111no—
216#2448—111no—
217#2065—111no—
218#2059—111no—
219#2056—111no—
220#2015—111no—
221#1973—111no—
222#1936—111no—
223#1935—111no—
224#1933—111no—
225#1880—111no—
226#1863—111no—
227#1771—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—21no—
269C2×Dic11—21no—
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—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289D44—41no—
290D44—41no—
291D44—41no—
292D44—41no—
293C8×C11—22no—
294C8×C11—22no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C22×Q16C2×D1111yescharacteristic
298C22×SD16—111no—
299C2×#125—111no—
300C2×#124—111no—
301C2×C4×Q8C2×D1111yescharacteristic
302C2×C4×Q8C2×D1111yescharacteristic
303#488—224no—
304#441—24no—
305C2×#107—111no—
306C2×#106C2×D1111yescharacteristic
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103C2×D1111yescharacteristic
312C2×#103C2×D1111yescharacteristic
313C2×#102—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×#97—111no—
317C2×#97C2×D1111yescharacteristic
318C2×C4×C8—111no—
319#400—221no—
320#399—221no—
321#398—221no—
322#397—221no—
323#391—111no—
324#391—111no—
325#391—111no—
326#390—111no—
327#390—111no—
328#389—111no—
329#389—111no—
330#389—111no—
331#389—221no—
332#388—221no—
333#388—221no—
334#387—221no—
335C4×C4⋊C4—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#336—111no—
341#336—111no—
342C22×C11#53211yescharacteristic
343C22×C11D4211yescharacteristic
344C22×C11#54811yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57511yescharacteristic
347C22×C11#57711yescharacteristic
348C22×C11#57811yescharacteristic
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—81no—
362C4×C11#52511yescharacteristic
363C4×C11#54211yescharacteristic
364C4×C11#54711yescharacteristic
365C4×C11#55111yescharacteristic
366Dic11—41no—
367Dic11—41no—
368Dic11—41no—
369Dic11—41no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373C22×Q8C22×D1111yescharacteristic
374C22×Q8C22×D1111yescharacteristic
375C22×D4—111no—
376C2×Q16—22no—
377C2×Q16—22no—
378C2×Q16—22no—
379C2×SD16—222no—
380C2×SD16—222no—
381C2×SD16—441no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386#125—222no—
387#125—441no—
388#124—222no—
389#124—441no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—41no—
393C4×Q8—41no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42C22×D1111yescharacteristic
419#107—441no—
420#106—22no—
421C4⋊C8—222no—
422#103—22no—
423#103—222no—
424#103—222no—
425#103—222no—
426#103C22⋊D1114yes—
427#102—222no—
428#102—222no—
429#102—222no—
430#97—22no—
431#97—222no—
432C4×C8—222no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11#246111yescharacteristic
445C2×C11#317811yescharacteristic
446C2×C11#318311yescharacteristic
447C2×C11#326911yescharacteristic
448C2×C11#327111yescharacteristic
449C2×C11#337111yescharacteristic
450C2×C11#337711yescharacteristic
451D11—161no—
452C24—221no—
453C2×Q8—21no—
454C2×Q8—21no—
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×Q8#433912yes—
464C2×Q8C2×C22⋊D1112yes—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485Q16—28no—
486SD16—444no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—112no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8#433912yes—
498C2×C8C2×C22⋊D1112yes—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—441no—
511C4⋊C4—441no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—881no—
517C4⋊C4C2×C22⋊D1112yes—
518C22⋊C4—442no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—881no—
523C22⋊C4—881no—
524C42—21no—
525C42—21no—
526C42—42no—
527C42—42no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—221no—
532C11#2683911yescharacteristic, complemented, Sylow
533C23—441no—
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23C2×D4×D1111yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—22no—
544Q8—22no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549D4—441no—
550D4—441no—
551D4—441no—
552D4—441no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
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—221no—
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—221no—
582C2×C4—221no—
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×C4C2×#433911yescharacteristic
593C2×C4C2×#433911yescharacteristic
594C2×C4#6703711yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#6704311yescharacteristic
597C2×C4C22×C22⋊D1111yescharacteristic
598C8—22no—
599C8—22no—
600C8—222no—
601C8—441no—
602C22—881no—
603C22—881no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22—881no—
608C22—881no—
609C22#1062307911yescharacteristic
610C22#1062308311yescharacteristic
611C22#1062330811yescharacteristic
612C22#1062330811yescharacteristic
613C22#1062330911yescharacteristic
614C22#1062331011yescharacteristic
615C22D4×C22⋊D1111yescharacteristic
616C4—41no—
617C4—42no—
618C4—41no—
619C4—42no—
620C4—42no—
621C4—81no—
622C4—441no—
623C4—441no—
624C4—441no—
625C4—441no—
626C4—881no—
627C4—881no—
628C4—881no—
629C4#1062308711yescharacteristic
630C4#1062309211yescharacteristic
631C4#1062332211yescharacteristic
632C4#1062335511yescharacteristic
633C2—1761no—
634C2#1307257711yescharacteristic
635C2#1307929011yescharacteristic
636C2#1307934811yescharacteristic
637C2#1308016511yescharacteristic
638C2#1308019511yescharacteristic
639C2#1308138511yescharacteristic
640C2#1308146311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#441C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#441D11
hypocenterC11#26839
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
2. #13072471C2semidirect
5. #13069956C2semidirect
6. #13069936C2semidirect
10. #13069308C2semidirect
11. #13069289C2semidirect
13. #13068870C2semidirect
14. #13068492C2semidirect
15. C2×C11×#441C2semidirect
214. C2×#441D11semidirect
532. C11#26839semidirect

Maximal subgroups

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

subgroupindex
C2×#106224132
#130724712
#130724082
#130699852
#130699562
#130699362
#130697072
#130694942
#130693132
#130693082
#130692892
#130689712
#130688702
#130684922
C2×C11×#4412
#2683911