Finite Group Databasebeta

← #14804205

Subgroups — #14804205

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079016C211yesmaximal, characteristic
2C2×#10622442C211yesmaximal, characteristic, complemented
3#13078084C211yesmaximal, characteristic
4#13070061C211yesmaximal, characteristic, complemented
5#13070056C211yesmaximal, characteristic, complemented
6#13069914C211yesmaximal, characteristic, complemented
7#13069914C211yesmaximal, characteristic, complemented
8#13069609C211yesmaximal, characteristic, complemented
9#13069392C211yesmaximal, characteristic, complemented
10#13069131C211yesmaximal, characteristic, complemented
11#13069131C211yesmaximal, characteristic, complemented
12#13068680C211yesmaximal, characteristic, complemented
13#13068675C211yesmaximal, characteristic, complemented
14C4×#66888C211yesmaximal, characteristic, complemented
15C11×#2935C211yesmaximal, characteristic
16C2×C11×#131C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C2×#67004C2211yescharacteristic
20C2×#67004C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#436—21no—
24C11×#435—21no—
25C11×#435—21no—
26C8×D4×C11—21no—
27C2×C11×C4⋊C8C2211yescharacteristic
28C11×#408C2211yescharacteristic
29C11×#408C2211yescharacteristic
30C4×C11×M16C2211yescharacteristic
31#10622845C2211yescharacteristic
32#10622845C2211yescharacteristic
33#10622845C2211yescharacteristic
34#10622845C2211yescharacteristic
35#10622845C2211yescharacteristic
36#10622845C2211yescharacteristic
37C2×#66888C2211yescharacteristic
38C2×#66888C2211yescharacteristic
39C2×#66883C2211yescharacteristic
40C2×#66883C2211yescharacteristic
41C2×#66882C2211yescharacteristic
42C2×#66881C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×#66880C2211yescharacteristic
45#10622703—21no—
46#10622695—21no—
47#10622688—21no—
48#10622684—21no—
49#10622669—21no—
50#10622669—21no—
51#10622667—21no—
52#10622667—21no—
53#10622537C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622442—21no—
56#10622442—21no—
57#10622442—21no—
58#10622442—21no—
59#10622192C2211yescharacteristic
60#10622192C2211yescharacteristic
61#10622192C2211yescharacteristic
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622190C2211yescharacteristic
66#10622190C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C22×Dic22C2311yescharacteristic
70C11×#131—22no—
71C11×#131—22no—
72C11×#131—41no—
73C11×#131—41no—
74C2×C11×M16—21no—
75C2×C11×M16—21no—
76C2×C11×M16C2311yescharacteristic
77C2×C11×M16C2311yescharacteristic
78C22×C8×C11—21no—
79C22×C8×C11—21no—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C11×C4⋊Q8D411yescharacteristic
83C11×#127D411yescharacteristic
84C11×#124D411yescharacteristic
85C11×#124D411yescharacteristic
86C11×#121—21no—
87C11×#121—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C2×C42×C11C2311yescharacteristic
91#67004—22no—
92#67004—22no—
93#67004—41no—
94#67004—41no—
95C2×#4326—21no—
96C2×#4326—21no—
97C2×#4324—21no—
98C2×#4324—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C2×#4318C2311yescharacteristic
107C2×#4318C2311yescharacteristic
108C2×#4318C2311yescharacteristic
109C2×#4318C2311yescharacteristic
110#66923—21no—
111#66923—21no—
112#66923—21no—
113#66923—21no—
114C4×Dic22—21no—
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—21no—
118C11×C4⋊C8D411yescharacteristic
119C11×C4⋊C8D411yescharacteristic
120C11×C4⋊C8D411yescharacteristic
121C11×C4⋊C8D411yescharacteristic
122C11×C22⋊C8—21no—
123C11×C22⋊C8—21no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—21no—
126C11×#97—21no—
127C4×C8×C11—21no—
128#66899—21no—
129#66899—21no—
130#66899—21no—
131#66899—21no—
132#66899—21no—
133#66899—21no—
134#66896—21no—
135#66896—21no—
136#66896—21no—
137#66896—21no—
138#66896—21no—
139#66896—21no—
140#66888—22no—
141#66888—22no—
142#66883—41no—
143#66883—41no—
144#66882—21no—
145#66882—21no—
146#66881—21no—
147#66881—21no—
148#66880—21no—
149#66880—21no—
150#66880—21no—
151#66880—21no—
152C4⋊(C11⋊C8)—21no—
153C4⋊(C11⋊C8)—21no—
154#66867—21no—
155C4×C11⋊C8—21no—
156#25363—111nomaximal, Sylow
157C11×#41—21no—
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C11×#41—21no—
162C11×#41—21no—
163C11×#41—21no—
164C11×#41—21no—
165C2×Q8×C11C2×D411yescharacteristic
166C2×Q8×C11C2×D411yescharacteristic
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11C2×D411yescharacteristic
172C2×D4×C11C2×D411yescharacteristic
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11#4111yescharacteristic
176C22×C4×C11#4111yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22#4112yes—
188C11×M16—21no—
189C11×M16—21no—
190C11×M16—21no—
191C11×M16—42no—
192C11×M16—42no—
193C11×M16#4112yes—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—42no—
201C2×C8×C11—42no—
202C2×C8×C11C2×D411yescharacteristic
203C2×C8×C11C2×D411yescharacteristic
204C2×C8×C11C2×D411yescharacteristic
205C2×C8×C11C2×D411yescharacteristic
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C42×C11C2×D411yescharacteristic
213C42×C11C2×D411yescharacteristic
214C42×C11C2×D411yescharacteristic
215C42×C11C2×D411yescharacteristic
216#4326—42no—
217#4326—42no—
218#4324—42no—
219#4324—42no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226Dic11⋊C4—41no—
227Dic11⋊C4—41no—
228Dic11⋊C4—41no—
229Dic11⋊C4—41no—
230Dic11⋊C4—41no—
231Dic11⋊C4—41no—
232C4×Dic11—41no—
233C4×Dic11—41no—
234#4318—21no—
235#4318—21no—
236#4318—21no—
237#4318—21no—
238#4318—21no—
239#4318—21no—
240#4318—21no—
241#4318—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246#3142—111no—
247C2×#479—111no—
248#3037—111no—
249#2935D1111yescharacteristic
250#2079—111no—
251#2078—111no—
252#2052—111no—
253#2052—111no—
254#1998—111no—
255#1950—111no—
256#1908—111no—
257#1908—111no—
258#1816—111no—
259#1815—111no—
260C4×#101—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11C2×#4111yescharacteristic
264Q8×C11—21no—
265Q8×C11—21no—
266Q8×C11—21no—
267Q8×C11—21no—
268D4×C11—21no—
269D4×C11—21no—
270D4×C11—21no—
271D4×C11—21no—
272D4×C11—42no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11—81no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11#12111yescharacteristic
287C2×C4×C11#12111yescharacteristic
288C2×C4×C11#12111yescharacteristic
289C2×C4×C11#12111yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C2×C4×C112−1+411yescharacteristic
296C2×Dic11—22no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—81no—
303C2×Dic11—81no—
304C2×Dic11—81no—
305Dic22—22no—
306Dic22—22no—
307Dic22—41no—
308Dic22—41no—
309C8×C11—21no—
310C8×C11—21no—
311C8×C11—21no—
312C8×C11—21no—
313C8×C11—22no—
314C8×C11—41no—
315C11⋊C8—41no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C2×#137—111no—
320C2×#137—111no—
321C2×#131C2×D1111yescharacteristic
322C2×#131C2×D1111yescharacteristic
323#532C2×D1111yescharacteristic
324C2×#125—111no—
325C2×C4×Q8—111no—
326#491—221no—
327#490—221no—
328#488—221no—
329#488—221no—
330#479—221no—
331#479—221no—
332#479—221no—
333#479—221no—
334#464—221no—
335#464—221no—
336#462—221no—
337#460—221no—
338#436—21no—
339#435—21no—
340#435—21no—
341C8×D4—21no—
342C2×#108—111no—
343C2×#108—111no—
344C2×#107—111no—
345C2×#106—111no—
346#423—111no—
347C2×C4⋊C8C2×D1111yescharacteristic
348#417—111no—
349#417—111no—
350#417—111no—
351#417—111no—
352#417—111no—
353#417—111no—
354C2×#103—111no—
355C2×#103—111no—
356C2×#101—111no—
357C2×#101—111no—
358#408C2×D1111yescharacteristic
359#408C2×D1111yescharacteristic
360C4×M16—111no—
361C4×M16C2×D1111yescharacteristic
362#343—111no—
363#343—111no—
364#343—111no—
365#343—111no—
366#343—111no—
367#343—111no—
368#341—111no—
369#341—111no—
370C22×C11—21no—
371C22×C11—21no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11C2×#12111yescharacteristic
379C22×C11#52911yescharacteristic
380C22×C11#54211yescharacteristic
381C4×C11—21no—
382C4×C11—21no—
383C4×C11—21no—
384C4×C11—21no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11#54611yescharacteristic
388C4×C11#54611yescharacteristic
389C4×C11#54711yescharacteristic
390C4×C11#54811yescharacteristic
391Dic11—42no—
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C2×#41C22×D1111yescharacteristic
396C2×#41C22×D1111yescharacteristic
397C22×Q8—111no—
398#137—222no—
399#137—222no—
400#137—441no—
401#137—441no—
402C2×Q16—221no—
403C2×Q16—221no—
404C2×SD16—221no—
405C2×SD16—221no—
406#131—22no—
407#131—22no—
408#131—41no—
409#131—41no—
410C2×M16—21no—
411C2×M16—21no—
412C2×M16—111no—
413C2×M16—111no—
414C2×M16—111no—
415C2×M16—111no—
416C2×M16C22×D1111yescharacteristic
417C2×M16C22×D1111yescharacteristic
418C22×C8—21no—
419C22×C8—21no—
420C22×C8C22×D1111yescharacteristic
421C22×C8C22×D1111yescharacteristic
422C4⋊Q8D4411yescharacteristic
423#127D4411yescharacteristic
424#125—221no—
425#125—221no—
426#125—221no—
427#125—221no—
428#124D4411yescharacteristic
429#124D4411yescharacteristic
430#121—21no—
431#121—21no—
432C4×Q8—221no—
433C4×Q8—221no—
434C4×Q8—221no—
435C4×Q8—221no—
436C4×D4—21no—
437C4×D4—21no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4—221no—
443C2×C4⋊C4—221no—
444C2×C42—221no—
445C2×C42C22×D1111yescharacteristic
446#108—441no—
447#108—441no—
448#107—221no—
449#107—221no—
450#106—221no—
451#106—221no—
452C4⋊C8—221no—
453C4⋊C8—221no—
454C4⋊C8C22⋊D1111yescharacteristic
455C4⋊C8C22⋊D1111yescharacteristic
456C4⋊C8C22⋊D1111yescharacteristic
457C4⋊C8C22⋊D1111yescharacteristic
458#103—221no—
459#103—221no—
460#103—221no—
461#103—221no—
462#103—221no—
463#103—221no—
464#103—221no—
465#103—221no—
466#103—221no—
467#103—221no—
468#102—221no—
469#102—221no—
470#102—221no—
471#102—221no—
472#102—221no—
473#102—221no—
474#101—222no—
475#101—222no—
476C22⋊C8—21no—
477C22⋊C8—21no—
478C22⋊C8—21no—
479C22⋊C8—21no—
480#97—21no—
481#97—221no—
482C4×C8—21no—
483C4×C8—221no—
484C2×C11—21no—
485C2×C11—21no—
486C2×C11—81no—
487C2×C11—81no—
488C2×C11#242711yescharacteristic
489C2×C11#306711yescharacteristic
490C2×C11#306911yescharacteristic
491#41—21no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499C2×Q8—112no—
500C2×Q8—221no—
501C2×Q8—221no—
502C2×Q8—221no—
503C2×Q8—221no—
504C2×Q8—221no—
505C2×Q8C2×D4411yescharacteristic
506C2×Q8C2×D4411yescharacteristic
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4C2×D4411yescharacteristic
512C2×D4C2×D4411yescharacteristic
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4#433911yescharacteristic
520C22×C4#433911yescharacteristic
521C22×C4C23×D1111yescharacteristic
522Q16—442no—
523Q16—442no—
524SD16—442no—
525SD16—442no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—42no—
530M16—42no—
531M16—221no—
532M16—221no—
533M16—221no—
534M16—221no—
535M16—221no—
536M16—221no—
537M16—221no—
538M16—221no—
539M16#434112yes—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—42no—
547C2×C8—42no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8C2×C22⋊D1111yescharacteristic
553C2×C8C2×C22⋊D1111yescharacteristic
554C2×C8C2×C22⋊D1111yescharacteristic
555C2×C8C2×C22⋊D1111yescharacteristic
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—441no—
565C4⋊C4—441no—
566C4⋊C4—441no—
567C4⋊C4—441no—
568C4⋊C4—441no—
569C4⋊C4—441no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C42—441no—
575C42—441no—
576C42C2×D4411yescharacteristic
577C42C2×D4411yescharacteristic
578C42C2×C22⋊D1111yescharacteristic
579C42C2×C22⋊D1111yescharacteristic
580C11#2536311yescharacteristic, complemented, Sylow
581C23—21no—
582C23—21no—
583C23C2×#433911yescharacteristic
584Q8—21no—
585Q8—21no—
586Q8—21no—
587Q8—21no—
588Q8—222no—
589Q8—222no—
590Q8—441no—
591Q8—441no—
592D4—21no—
593D4—21no—
594D4—21no—
595D4—21no—
596D4—42no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—81no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—222no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—881no—
617C2×C4—881no—
618C2×C4—881no—
619C2×C4#6698311yescharacteristic
620C2×C4#6698311yescharacteristic
621C2×C4#6698311yescharacteristic
622C2×C4#6698311yescharacteristic
623C2×C4C22×D4411yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4#6703711yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C2×C4#6704311yescharacteristic
628C2×C4C22×C22⋊D1111yescharacteristic
629C8—21no—
630C8—21no—
631C8—21no—
632C8—21no—
633C8—22no—
634C8—41no—
635C8—441no—
636C8—441no—
637C8—441no—
638C8—441no—
639C22—21no—
640C22—21no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22#1062308811yescharacteristic
648C22#1062309211yescharacteristic
649C22C2×#6698311yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—41no—
655C4—41no—
656C4—442no—
657C4—881no—
658C4—881no—
659C4—881no—
660C4#1062308511yescharacteristic
661C4#1062308611yescharacteristic
662C4#1062333711yescharacteristic
663C4#1062336211yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—81no—
668C2#1307218711yescharacteristic
669C2#1307833611yescharacteristic
670C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2935C2
socleC22×C11C2×#121
prime radicalC11×#532C22
hypercenter#2935D11
hypocenterC11#25363
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. C2×#10622442C2semidirect
4. #13070061C2semidirect
5. #13070056C2semidirect
6. #13069914C2semidirect
7. #13069914C2semidirect
8. #13069609C2semidirect
9. #13069392C2semidirect
10. #13069131C2semidirect
11. #13069131C2semidirect
12. #13068680C2semidirect
13. #13068675C2semidirect
14. C4×#66888C2semidirect
580. C11#25363semidirect

Maximal subgroups

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

subgroupindex
#130790162
C2×#106224422
#130780842
#130700612
#130700562
#130699142
#130696092
#130693922
#130691312
#130686802
#130686752
C4×#668882
C11×#29352
#2536311