Finite Group Databasebeta

← #14760697

Subgroups — #14760697

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622754C211yesmaximal, characteristic
2C4×#67004C211yesmaximal, characteristic, complemented
3C4×#67002C211yesmaximal, characteristic
4C2×#10622323C211yesmaximal, characteristic, complemented
5#13069519C211yesmaximal, characteristic, complemented
6#13069401C211yesmaximal, characteristic, complemented
7#13069278C211yesmaximal, characteristic, complemented
8#13069271C211yesmaximal, characteristic, complemented
9#13069131C211yesmaximal, characteristic, complemented
10#13069124C211yesmaximal, characteristic
11#13068680C211yesmaximal, characteristic, complemented
12#13068522C211yesmaximal, characteristic, complemented
13C4×#66888C211yesmaximal, characteristic, complemented
14C4×#66887C211yesmaximal, characteristic, complemented
15C11×#2875C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C2×#67004C2211yescharacteristic
20C2×#67002C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#405—21no—
25C11×#405—21no—
26C11×#405C2211yescharacteristic
27C11×#405C2211yescharacteristic
28C4×C11×M16—21no—
29C4×C11×M16C2211yescharacteristic
30C2×C11×#97—21no—
31C2×C11×#97C2211yescharacteristic
32#10622845C2211yescharacteristic
33#10622845C2211yescharacteristic
34#10622754C418yescomplemented
35C2×#66888C2211yescharacteristic
36C2×#66888C2211yescharacteristic
37C2×#66887C2211yescharacteristic
38C2×#66887C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66883C2211yescharacteristic
41C2×#66883C2211yescharacteristic
42C2×#66882C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44#10622643—21no—
45C4×#4326—21no—
46#10622639—21no—
47C4×#4325—21no—
48#10622631—21no—
49C4×#4324—21no—
50#10622627—21no—
51C4×#4323—21no—
52#10622617C2211yescharacteristic
53#10622614C2211yescharacteristic
54#10622608C2211yescharacteristic
55#10622608C2211yescharacteristic
56C4×#4318C2211yescharacteristic
57C4×#4318C2211yescharacteristic
58#10622323—21no—
59#10622323—21no—
60#10622323—21no—
61#10622323—21no—
62#10622192C2211yescharacteristic
63#10622192C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622192C2211yescharacteristic
66#10622190C2211yescharacteristic
67#10622190C2211yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×Dic22C2311yescharacteristic
72C11×#131—22no—
73C11×#131—22no—
74C11×#131—22no—
75C11×#131C2×C414yescomplemented
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C22×C8×C11—21no—
81C22×C8×C11—21no—
82C22×C8×C11C2311yescharacteristic
83C22×C8×C11C2311yescharacteristic
84C4×Q8×C11D411yescharacteristic
85C4×Q8×C11D411yescharacteristic
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11D411yescharacteristic
89C4×D4×C11D411yescharacteristic
90C11×#117—21no—
91C11×#117C2311yescharacteristic
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94#67004—22no—
95#67004C2×C414yescomplemented
96#67002—22no—
97#67002C2×C414yes—
98C2×#4326—21no—
99C2×#4325—21no—
100C2×#4324—21no—
101C2×#4323—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×#4318C2311yescharacteristic
108C2×#4318C2311yescharacteristic
109C2×#4318C2311yescharacteristic
110C2×#4318C2311yescharacteristic
111C2×#4314—21no—
112C2×#4314—21no—
113C2×#4314—22no—
114C2×#4314C2×C414yescomplemented
115C4×D44—21no—
116C4×D44—21no—
117C4×D44—21no—
118C4×D44—21no—
119C4×Dic22—21no—
120C4×Dic22—21no—
121C4×Dic22—21no—
122C4×Dic22—21no—
123C11×#97—21no—
124C11×#97—21no—
125C11×#97—21no—
126C11×#97D411yescharacteristic
127C11×#97D411yescharacteristic
128C11×#97D411yescharacteristic
129C11×#97D411yescharacteristic
130C4×C8×C11—21no—
131C4×C8×C11—21no—
132C4×C8×C11—21no—
133#66899—21no—
134#66899—21no—
135#66896—21no—
136#66896—21no—
137#66888—22no—
138#66888C2×C414yescomplemented
139#66887—22no—
140#66887C2×C414yescomplemented
141#66885—21no—
142#66885—21no—
143#66883—22no—
144#66883C2×C414yescomplemented
145#66882—21no—
146#66882—21no—
147#66880—21no—
148#66880—21no—
149#66874—21no—
150#66874—21no—
151#66873—21no—
152#66873—21no—
153#66872—21no—
154#66872—21no—
155#66871—21no—
156#66871—21no—
157#66867—21no—
158#66867—21no—
159C4×C11⋊C8—21no—
160C4×C11⋊C8—21no—
161#21557—111nomaximal, Sylow
162C23×D11—21no—
163C11×#41—21no—
164C11×#41—21no—
165C11×#41C22×C412yes—
166C11×#41#4112yes—
167C2×Q8×C11C2×D411yescharacteristic
168C2×D4×C11—21no—
169C2×D4×C11C2×D411yescharacteristic
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11#4111yescharacteristic
174C22×C4×C11#4111yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44C22×C412yes—
185C2×C4×D11—41no—
186C2×C4×D11—41no—
187C2×C4×D11—82no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22C22×C412yes—
194C11×M16—24no—
195C11×M16—24no—
196C11×M16—21no—
197C11×M16—21no—
198C11×M16C22×C412yes—
199C11×M16#4112yes—
200C2×C8×C11—24no—
201C2×C8×C11—24no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11C22×C412yes—
207C2×C8×C11C2×D411yescharacteristic
208C2×C8×C11C2×D411yescharacteristic
209C2×C8×C11C2×D411yescharacteristic
210C2×C8×C11C2×D411yescharacteristic
211C2×C8×C11#4112yes—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4C2×D411yescharacteristic
215C11×C4⋊C4C2×D411yescharacteristic
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11C2×D411yescharacteristic
223C42×C11C2×D411yescharacteristic
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226#4326—24no—
227#4325—24no—
228#4324—24no—
229#4323—24no—
230(C2×D11)⋊C4—41no—
231(C2×D11)⋊C4—41no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236Dic11⋊C4—41no—
237Dic11⋊C4—41no—
238C4×Dic11—41no—
239C4×Dic11—41no—
240#4318—21no—
241#4318—21no—
242#4318—21no—
243#4318—21no—
244#4318—21no—
245#4318—21no—
246#4318C22×C412yes—
247#4318C22×C412yes—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252#4314—24no—
253#4314—24no—
254C2×#471—111no—
255C4×#137—111no—
256C4×AGL(1,ℤ/8)—111no—
257C2×#440—111no—
258#2875D1111yescharacteristic, complemented
259#1977—111no—
260#1952—111no—
261#1931—111no—
262#1930—111no—
263#1908—111no—
264#1907—111no—
265#1816—111no—
266#1778—111no—
267C4×#101—111no—
268C4×#100—111no—
269C23×C11—21no—
270C23×C11C2×#4111yescharacteristic
271C22×D11—22no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—81no—
275C22×D11—81no—
276Q8×C11—21no—
277Q8×C11C4×D412yes—
278D4×C11—22no—
279D4×C11—22no—
280D4×C11—21no—
281D4×C11C4×D412yes—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—81no—
290C2×C4×C11—81no—
291C2×C4×C11#12111yescharacteristic
292C2×C4×C11#12111yescharacteristic
293C2×C4×C11#12111yescharacteristic
294C2×C4×C11#12111yescharacteristic
295C2×C4×C11C23×C411yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C2×#4111yescharacteristic
299C2×C4×C11C2×#4111yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×Dic11—22no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—81no—
307C2×Dic11—81no—
308D44—22no—
309D44—22no—
310D44—41no—
311D44—41no—
312C4×D11—82no—
313C4×D11—82no—
314Dic22—22no—
315Dic22—22no—
316Dic22—41no—
317Dic22—41no—
318C8×C11—22no—
319C8×C11—21no—
320C8×C11—22no—
321C8×C11—21no—
322C8×C11C4×D412yes—
323C8×C11C4×D412yes—
324C11⋊C8—22no—
325C11⋊C8—22no—
326C11⋊C8—41no—
327C11⋊C8—41no—
328C2×#137—111no—
329C2×AGL(1,ℤ/8)—111no—
330C22×SD16—111no—
331C2×#131C2×D1111yescharacteristic
332C2×#131C2×D1111yescharacteristic
333C4×#41C2×D1111yescharacteristic
334C2×C4×Q8—111no—
335C2×C4×D4—111no—
336#471—118no—
337#442—221no—
338#441—221no—
339#440—221no—
340#440—221no—
341#440—221no—
342#440—221no—
343#440—221no—
344#440—221no—
345C4×Q16—221no—
346C4×SD16—221no—
347C4×SD16—221no—
348C4×D8—221no—
349C2×#108—111no—
350C2×#108—111no—
351#428—111no—
352#428—111no—
353C2×#107—111no—
354#419—111no—
355#418—111no—
356#417—111no—
357#417—111no—
358C2×#103—111no—
359C2×#102—111no—
360C2×#101—111no—
361C2×#101—111no—
362C2×#100—111no—
363C2×#100—111no—
364#405—21no—
365#405—21no—
366#405C2×D1111yescharacteristic
367#405C2×D1111yescharacteristic
368C4×M16—21no—
369C4×M16—111no—
370C4×M16—111no—
371C4×M16C2×D1111yescharacteristic
372C2×#97—21no—
373C2×#97C2×D1111yescharacteristic
374#343—111no—
375#343—111no—
376#343—111no—
377#343—111no—
378#341—111no—
379#341—111no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—22no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11C4×#4111yescharacteristic
386C22×C11C2×#12111yescharacteristic
387C22×C11#52911yescharacteristic
388C2×D11—42no—
389C2×D11—82no—
390C2×D11—81no—
391C2×D11—81no—
392C2×D11—82no—
393C4×C11—22no—
394C4×C11—21no—
395C4×C11—21no—
396C4×C11—21no—
397C4×C11—21no—
398C4×C11—41no—
399C4×C11—41no—
400C4×C11C2×C4×D411yescharacteristic
401C4×C11C2×C4×D411yescharacteristic
402C4×C11#52511yescharacteristic
403C4×C11#53211yescharacteristic
404Dic11—42no—
405Dic11—81no—
406Dic11—81no—
407C2×#41C22×D1111yescharacteristic
408C22×Q8—111no—
409C22×D4—111no—
410C23×C4—221no—
411#137—114no—
412#137—222no—
413AGL(1,ℤ/8)—114no—
414AGL(1,ℤ/8)—222no—
415C2×Q16—221no—
416C2×SD16—114no—
417C2×SD16—221no—
418C2×SD16—221no—
419C2×SD16—222no—
420C2×SD16—221no—
421C2×SD16—221no—
422C2×D8—221no—
423#131—22no—
424#131—22no—
425#131—22no—
426#131C4×D1114yescomplemented
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—111no—
430C2×M16—111no—
431C2×M16—111no—
432C2×M16—111no—
433C2×M16C22×D1111yescharacteristic
434C2×M16C22×D1111yescharacteristic
435C22×C8—21no—
436C22×C8—21no—
437C22×C8C22×D1111yescharacteristic
438C22×C8C22×D1111yescharacteristic
439C4×Q8—221no—
440C4×Q8—221no—
441C4×Q8—221no—
442C4×Q8—221no—
443C4×Q8D4411yescharacteristic
444C4×Q8D4411yescharacteristic
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—221no—
448C4×D4—221no—
449C4×D4—221no—
450C4×D4—221no—
451C4×D4D4411yescharacteristic
452C4×D4D4411yescharacteristic
453#117—21no—
454#117C22×D1111yescharacteristic
455C2×C4⋊C4—111no—
456C2×C4⋊C4—111no—
457C2×C4⋊C4—221no—
458C2×C22⋊C4—221no—
459C2×C42—21no—
460C2×C42—221no—
461C2×C42C22×D1111yescharacteristic
462#108—114no—
463#108—222no—
464#107—221no—
465#107—221no—
466#107—221no—
467#107—221no—
468#106—221no—
469#106—221no—
470#103—221no—
471#103—221no—
472#103—221no—
473#103—221no—
474#103—221no—
475#103—221no—
476#102—221no—
477#102—221no—
478#102—221no—
479#102—221no—
480#102—221no—
481#102—221no—
482#101—114no—
483#101—222no—
484#100—114no—
485#100—222no—
486#97—21no—
487#97—21no—
488#97—21no—
489#97—221no—
490#97—221no—
491#97C22⋊D1111yescharacteristic
492#97C22⋊D1111yescharacteristic
493#97C22⋊D1111yescharacteristic
494#97C22⋊D1111yescharacteristic
495C4×C8—21no—
496C4×C8—21no—
497C4×C8—21no—
498C4×C8—221no—
499C4×C8—221no—
500C2×C11—21no—
501C2×C11—21no—
502C2×C11—42no—
503C2×C11C4×#12111yescharacteristic
504C2×C11#306811yescharacteristic
505C2×C11#306911yescharacteristic
506D11—82no—
507C24—221no—
508#41—21no—
509#41—21no—
510#41C2×C4×D1112yes—
511#41#433912yes—
512C2×Q8—112no—
513C2×Q8—221no—
514C2×Q8—221no—
515C2×Q8—221no—
516C2×Q8—221no—
517C2×Q8—221no—
518C2×Q8C2×D4411yescharacteristic
519C2×D4—21no—
520C2×D4—112no—
521C2×D4—221no—
522C2×D4—221no—
523C2×D4—221no—
524C2×D4—221no—
525C2×D4—221no—
526C2×D4C2×D4411yescharacteristic
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—441no—
534C22×C4—441no—
535C22×C4—882no—
536C22×C4#433911yescharacteristic
537C22×C4#433911yescharacteristic
538C22×C4C23×D1111yescharacteristic
539Q16—224no—
540SD16—224no—
541SD16—224no—
542SD16—224no—
543SD16—224no—
544D8—224no—
545M16—24no—
546M16—21no—
547M16—21no—
548M16—24no—
549M16—112no—
550M16—112no—
551M16—221no—
552M16—221no—
553M16—221no—
554M16—221no—
555M16—221no—
556M16—221no—
557M16C2×C4×D1112yes—
558M16#433912yes—
559C2×C8—24no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—24no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8C2×C4×D1112yes—
570C2×C8#433912yes—
571C2×C8C2×C22⋊D1111yescharacteristic
572C2×C8C2×C22⋊D1111yescharacteristic
573C2×C8C2×C22⋊D1111yescharacteristic
574C2×C8C2×C22⋊D1111yescharacteristic
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4—441no—
582C4⋊C4—441no—
583C4⋊C4C2×D4411yescharacteristic
584C4⋊C4C2×D4411yescharacteristic
585C22⋊C4—21no—
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—441no—
589C22⋊C4—441no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—441no—
594C42—441no—
595C42C2×D4411yescharacteristic
596C42C2×D4411yescharacteristic
597C42C2×C22⋊D1111yescharacteristic
598C42C2×C22⋊D1111yescharacteristic
599C11#2155711yescharacteristic, complemented, Sylow
600C23—21no—
601C23—222no—
602C23—441no—
603C23—441no—
604C23—881no—
605C23—881no—
606C23C2×#433911yescharacteristic
607Q8—21no—
608Q8—222no—
609Q8—222no—
610Q8—441no—
611Q8—441no—
612Q8C4×D4412yes—
613D4—22no—
614D4—22no—
615D4—21no—
616D4—222no—
617D4—222no—
618D4—441no—
619D4—441no—
620D4C4×D4412yes—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—81no—
629C2×C4—81no—
630C2×C4—222no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—882no—
636C2×C4—882no—
637C2×C4—881no—
638C2×C4—881no—
639C2×C4#6698311yescharacteristic
640C2×C4#6698311yescharacteristic
641C2×C4#6698311yescharacteristic
642C2×C4#6698311yescharacteristic
643C2×C4C22×C4×D1111yescharacteristic
644C2×C4C22×D4411yescharacteristic
645C2×C4C2×#433911yescharacteristic
646C2×C4C2×#433911yescharacteristic
647C2×C4C2×#433911yescharacteristic
648C2×C4C22×C22⋊D1111yescharacteristic
649C8—22no—
650C8—21no—
651C8—22no—
652C8—21no—
653C8—222no—
654C8—222no—
655C8—441no—
656C8—441no—
657C8C4×C22⋊D1112yes—
658C8C4×C22⋊D1112yes—
659C22—21no—
660C22—21no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—442no—
665C22—882no—
666C22—882no—
667C22—881no—
668C22—881no—
669C22C4×#433911yescharacteristic
670C22#1062301011yescharacteristic
671C22C2×#6698311yescharacteristic
672C4—22no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—41no—
678C4—41no—
679C4—442no—
680C4—881no—
681C4—881no—
682C4C2×C4×D4411yescharacteristic
683C4#1062300811yescharacteristic
684C4C2×C4×C22⋊D1111yescharacteristic
685C4#1062332211yescharacteristic
686C2—21no—
687C2—21no—
688C2—42no—
689C2—882no—
690C2C4×#6698311yescharacteristic
691C2#1307834411yescharacteristic
692C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2875C2
socleC22×C11C2×#121
prime radicalC2×#67002C22
cosocleC22×C4×C11C24
hypercenter#2875D11
hypocenterC11#21557
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. C4×#67004C2semidirect
4. C2×#10622323C2semidirect
5. #13069519C2semidirect
6. #13069401C2semidirect
7. #13069278C2semidirect
8. #13069271C2semidirect
9. #13069131C2semidirect
11. #13068680C2semidirect
12. #13068522C2semidirect
13. C4×#66888C2semidirect
14. C4×#66887C2semidirect
15. C11×#2875C2semidirect
34. #10622754C4semidirect
75. C11×#131C2×C4semidirect
95. #67004C2×C4semidirect
114. C2×#4314C2×C4semidirect
138. #66888C2×C4semidirect
140. #66887C2×C4semidirect
144. #66883C2×C4semidirect
258. #2875D11semidirect
426. #131C4×D11semidirect
599. C11#21557semidirect

Maximal subgroups

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

subgroupindex
C2×#106227542
C4×#670042
C4×#670022
C2×#106223232
#130695192
#130694012
#130692782
#130692712
#130691312
#130691242
#130686802
#130685222
C4×#668882
C4×#668872
C11×#28752
#2155711