Finite Group Databasebeta

← #14783512

Subgroups — #14783512

Order 2816.

776 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67002C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3#13077267C211yesmaximal, characteristic, complemented
4#13070124C211yesmaximal, characteristic, complemented
5#13070059C211yesmaximal, characteristic, complemented
6#13069983C211yesmaximal, characteristic, complemented
7#13069973C211yesmaximal, characteristic, complemented
8#13069912C211yesmaximal, characteristic, complemented
9#13069906C211yesmaximal, characteristic
10#13069876C211yesmaximal, characteristic, complemented
11#13069727C211yesmaximal, characteristic
12#13068523C211yesmaximal, characteristic, complemented
13C4×#66900C211yesmaximal, characteristic, complemented
14C4×#66887C211yesmaximal, characteristic, complemented
15C4×C11×#137C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67002C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C11×#441—21no—
23C11×#440—21no—
24C4×C11×Q16—21no—
25C4×C11×SD16—21no—
26C11×#428C2211yescharacteristic
27C11×#419C2211yescharacteristic
28C11×#417C2211yescharacteristic
29C4×C11×M16C2211yescharacteristic
30#10622847C2211yescharacteristic
31#10622847C2211yescharacteristic
32#10622845C2211yescharacteristic
33C2×#66900C2211yescharacteristic
34C2×#66900C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66887C2211yescharacteristic
37C2×#66887C2211yescharacteristic
38C2×#66886C2211yescharacteristic
39C2×#66886C2211yescharacteristic
40#10622639—21no—
41#10622639—22no—
42#10622639—22no—
43C4×#4325—21no—
44#10622627—21no—
45C4×#4323—21no—
46#10622614C2211yescharacteristic
47#10622613—22no—
48#10622612C2211yescharacteristic
49#10622612C2211yescharacteristic
50#10622608C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622539—22no—
54C4×#4318C2211yescharacteristic
55C4×#4318C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622196C2211yescharacteristic
58#10622196C2211yescharacteristic
59#10622192C2211yescharacteristic
60#10622192C2211yescharacteristic
61#10622168C2211yescharacteristic
62#10622168C2211yescharacteristic
63C2×C11×#41C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C11×#137—22no—
68C11×#137—22no—
69C2×C11×Q16—21no—
70C2×C11×SD16—21no—
71C2×C11×M16C2311yescharacteristic
72C2×C11×M16C2311yescharacteristic
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11D411yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11D411yescharacteristic
82C4×D4×C11D411yescharacteristic
83C11×#117—21no—
84C11×#117C2311yescharacteristic
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90#67002—22no—
91#67002—22no—
92C2×#4325—21no—
93C2×#4325—22no—
94C2×#4325—22no—
95C2×#4325—22no—
96C2×#4323—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×#4318C2311yescharacteristic
100C2×#4318C2311yescharacteristic
101C2×#4318C2311yescharacteristic
102C2×#4318C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C4×D44—21no—
106C4×D44—21no—
107C4×D44—21no—
108C4×D44—21no—
109C11×#107—21no—
110C11×#106—21no—
111C11×#103—21no—
112C11×#103—21no—
113C11×#103—21no—
114C11×#102—21no—
115C11×#97—21no—
116C4×C8×C11—21no—
117#66900—22no—
118#66900—22no—
119#66899—21no—
120#66899—22no—
121#66896—21no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—22no—
124#66887—22no—
125#66887—22no—
126#66886—22no—
127#66886—22no—
128#66873—21no—
129#66873—21no—
130#66873—22no—
131#66872—21no—
132#66871—21no—
133#66871—22no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—22no—
136#66867—21no—
137#66867—21no—
138#66867D412yes—
139#66867D412yes—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142#23721—111nomaximal, Sylow
143C23×D11—21no—
144C11×#41—21no—
145C11×#41—21no—
146C11×#41—21no—
147C11×#41—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×Q8×C11#4112yes—
155C2×D4×C11—21no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11#4111yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44#4112yes—
172C2×C4×D11—41no—
173C2×C4×D11—41no—
174C2×C4×D11—82no—
175C11×Q16—24no—
176C11×SD16—24no—
177C11×M16—21no—
178C11×M16—21no—
179C11×M16—21no—
180C11×M16#4112yes—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4—41no—
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—41no—
198C42×C11—41no—
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202C42×C11C2×D411yescharacteristic
203#4325—28no—
204#4325—24no—
205#4323—24no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—41no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210#4318—21no—
211#4318—21no—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318#4112yes—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8C2×D412yes—
227C2×C11⋊C8C2×D412yes—
228C4×#137D1111yescharacteristic, complemented
229C4×AGL(1,ℤ/8)—111no—
230C2×#440—111no—
231#2923—111no—
232#2089—111no—
233#2078—111no—
234#2064—111no—
235#2063—111no—
236#2052—111no—
237#2051—111no—
238#2046—111no—
239#2019—111no—
240#1778—111no—
241C4×#101—111no—
242C4×#100—111no—
243C23×C11—21no—
244C23×C11C2×#4111yescharacteristic
245C22×D11—22no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—81no—
249C22×D11—81no—
250Q8×C11—22no—
251Q8×C11—21no—
252Q8×C11—22no—
253Q8×C11—21no—
254Q8×C11—41no—
255Q8×C11—41no—
256D4×C11—21no—
257D4×C11—21no—
258D4×C11—41no—
259D4×C11—41no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—81no—
272C2×C4×C11—81no—
273C2×C4×C11—81no—
274C2×C4×C11#12111yescharacteristic
275C2×C4×C11#12111yescharacteristic
276C2×C4×C11#12111yescharacteristic
277C2×C4×C11#12111yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×Dic11—41no—
285C2×Dic11—81no—
286D44—22no—
287D44—22no—
288D44—41no—
289D44—41no—
290C4×D11—82no—
291C4×D11—82no—
292C8×C11—22no—
293C8×C11—41no—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C2×#137C2×D1111yescharacteristic
301C2×AGL(1,ℤ/8)—111no—
302C22×SD16—111no—
303C4×#41C2×D1111yescharacteristic
304C2×C4×Q8C2×D1111yescharacteristic
305C2×C4×D4—111no—
306#442—221no—
307#441—21no—
308#440—21no—
309#440—222no—
310#440—222no—
311#440—221no—
312C4×Q16—21no—
313C4×SD16—21no—
314C4×SD16—221no—
315C4×D8—221no—
316#433—222no—
317#432—222no—
318C2×#108—111no—
319C2×#108—111no—
320#428—111no—
321#428C2×D1111yescharacteristic
322C2×#107—111no—
323#424—111no—
324#424—111no—
325#419C2×D1111yescharacteristic
326#418—111no—
327#417—111no—
328#417C2×D1111yescharacteristic
329C2×#103—111no—
330C2×#102—111no—
331C2×#101—111no—
332C2×#101—111no—
333C2×#100—111no—
334C2×#100—111no—
335#408—111no—
336#408—111no—
337C4×M16—111no—
338C4×M16—111no—
339C4×M16C2×D1111yescharacteristic
340C2×#97—111no—
341#343—111no—
342#343—111no—
343#343—111no—
344#343—111no—
345#341—111no—
346#341—111no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11C2×#12111yescharacteristic
353C22×C11#52911yescharacteristic
354C22×C11#52911yescharacteristic
355C2×D11—42no—
356C2×D11—82no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—82no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—41no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—81no—
369C4×C11#52511yescharacteristic
370C4×C11#52511yescharacteristic
371C4×C11#52511yescharacteristic
372C4×C11#53211yescharacteristic
373Dic11—81no—
374C2×#41C22×D1111yescharacteristic
375C22×Q8C22×D1111yescharacteristic
376C22×D4—111no—
377C23×C4—221no—
378#137—22no—
379#137—22no—
380AGL(1,ℤ/8)—222no—
381AGL(1,ℤ/8)—222no—
382C2×Q16—21no—
383C2×SD16—21no—
384C2×SD16—222no—
385C2×SD16—222no—
386C2×SD16—222no—
387C2×SD16—221no—
388C2×D8—221no—
389C2×M16—111no—
390C2×M16—111no—
391C2×M16—111no—
392C2×M16—111no—
393C2×M16C22×D1111yescharacteristic
394C2×M16C22×D1111yescharacteristic
395C22×C8—111no—
396C22×C8—111no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8C22⋊D1111yescharacteristic
402C4×Q8C22⋊D1111yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—221no—
406C4×D4—221no—
407C4×D4—221no—
408C4×D4—221no—
409C4×D4C22⋊D1111yescharacteristic
410C4×D4C22⋊D1111yescharacteristic
411#117—21no—
412#117C22×D1111yescharacteristic
413C2×C4⋊C4—21no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—221no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42C22×D1111yescharacteristic
420#108—222no—
421#108—222no—
422#107—21no—
423#107—222no—
424#107—221no—
425#106—21no—
426#106—221no—
427C4⋊C8—222no—
428C4⋊C8—222no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103—222no—
433#103—221no—
434#102—21no—
435#102—222no—
436#102—221no—
437#102—221no—
438#102—221no—
439#101—222no—
440#101—222no—
441#100—222no—
442#100—222no—
443C22⋊C8—222no—
444C22⋊C8—222no—
445#97—21no—
446#97—112no—
447#97—112no—
448#97—221no—
449#97—221no—
450C4×C8—21no—
451C4×C8—221no—
452C4×C8—221no—
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—81no—
456C2×C11#239211yescharacteristic
457C2×C11#306811yescharacteristic
458C2×C11#306911yescharacteristic
459D11—82no—
460C24—221no—
461#41—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8#433912yes—
471C2×Q8C2×C22⋊D1111yescharacteristic
472C2×D4—21no—
473C2×D4—112no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4C2×C22⋊D1111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—221no—
486C22×C4—441no—
487C22×C4—441no—
488C22×C4—882no—
489C22×C4#434111yescharacteristic
490C22×C4#434111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492Q16—24no—
493SD16—24no—
494SD16—228no—
495SD16—224no—
496D8—224no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—112no—
501M16—221no—
502M16—221no—
503M16—221no—
504M16—221no—
505M16—221no—
506M16—221no—
507M16—221no—
508M16#433912yes—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—112no—
512C2×C8—112no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4C2×C22⋊D1111yescharacteristic
530C4⋊C4C2×C22⋊D1111yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—441no—
535C22⋊C4—441no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—41no—
540C42—41no—
541C42D4×D1111yescharacteristic
542C42D4×D1111yescharacteristic
543C42C2×C22⋊D1111yescharacteristic
544C42C2×C22⋊D1111yescharacteristic
545C11#2372111yescharacteristic, complemented, Sylow
546C23—21no—
547C23—222no—
548C23—441no—
549C23—441no—
550C23—881no—
551C23—881no—
552C23C2×#434111yescharacteristic
553Q8—22no—
554Q8—21no—
555Q8—22no—
556Q8—21no—
557Q8—41no—
558Q8—41no—
559D4—21no—
560D4—21no—
561D4—41no—
562D4—41no—
563D4—222no—
564D4—222no—
565D4—441no—
566D4—441no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—441no—
582C2×C4—882no—
583C2×C4—882no—
584C2×C4—881no—
585C2×C4#6699211yescharacteristic
586C2×C4#6699211yescharacteristic
587C2×C4#6699211yescharacteristic
588C2×C4#6699211yescharacteristic
589C2×C4C2×#433911yescharacteristic
590C2×C4C2×#433911yescharacteristic
591C2×C4C2×D4×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4C22×C22⋊D1111yescharacteristic
595C8—22no—
596C8—41no—
597C8—222no—
598C8—222no—
599C8—222no—
600C8—441no—
601C8—441no—
602C8—441no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—442no—
609C22—882no—
610C22—882no—
611C22—881no—
612C22—881no—
613C22#1062306911yescharacteristic
614C22#1062308811yescharacteristic
615C22C2×#6699211yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—81no—
625C4—881no—
626C4#1062307811yescharacteristic
627C4#1062307911yescharacteristic
628C4#1062332211yescharacteristic
629C4#1062335911yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—882no—
634C2#1307185811yescharacteristic
635C2#1307834611yescharacteristic
636C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#137C2
socleC22×C11C2×#121
prime radicalC2×#67002C22
hypercenterC4×#137D11
hypocenterC11#23721
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
3. #13077267C2semidirect
4. #13070124C2semidirect
5. #13070059C2semidirect
6. #13069983C2semidirect
7. #13069973C2semidirect
8. #13069912C2semidirect
10. #13069876C2semidirect
12. #13068523C2semidirect
13. C4×#66900C2semidirect
14. C4×#66887C2semidirect
15. C4×C11×#137C2semidirect
228. C4×#137D11semidirect
545. C11#23721semidirect

Maximal subgroups

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

subgroupindex
C4×#670022
C2×#106226392
#130772672
#130701242
#130700592
#130699832
#130699732
#130699122
#130699062
#130698762
#130697272
#130685232
C4×#669002
C4×#668872
C4×C11×#1372
#2372111