Finite Group Databasebeta

← #14760682

Subgroups — #14760682

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622817C211yesmaximal, characteristic
2C4×#67004C211yesmaximal, characteristic
3C2×#10622643C211yesmaximal, characteristic, complemented
4#13077044C211yesmaximal, characteristic
5#13069530C211yesmaximal, characteristic, complemented
6#13069393C211yesmaximal, characteristic, complemented
7#13069274C211yesmaximal, characteristic, complemented
8#13069270C211yesmaximal, characteristic, complemented
9#13069133C211yesmaximal, characteristic
10#13069129C211yesmaximal, characteristic
11#13068673C211yesmaximal, characteristic
12#13068523C211yesmaximal, characteristic, complemented
13C4×#66888C211yesmaximal, characteristic, complemented
14C4×#66900C211yesmaximal, characteristic, complemented
15C4×C11×#137C211yesmaximal, characteristic
16C2×C11×#137C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67004C2211yescharacteristic
20C2×#67001C2211yescharacteristic
21C2×#67001C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#441—21no—
25C11×#440—21no—
26C4×C11×Q16—21no—
27C4×C11×SD16—21no—
28C11×#428C2211yescharacteristic
29C11×#419C2211yescharacteristic
30C11×#417C2211yescharacteristic
31C4×C11×M16C2211yescharacteristic
32#10622845C2211yescharacteristic
33C2×#66900C2211yescharacteristic
34C2×#66900C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622817C418yescomplemented
37C2×#66888C2211yescharacteristic
38C2×#66888C2211yescharacteristic
39C2×#66886C2211yescharacteristic
40C2×#66886C2211yescharacteristic
41#10622643—21no—
42#10622643—21no—
43#10622643—21no—
44#10622643—21no—
45#10622643—21no—
46C4×#4326—21no—
47#10622631—21no—
48C4×#4324—21no—
49#10622617C2211yescharacteristic
50#10622610—21no—
51#10622610—21no—
52#10622610C2211yescharacteristic
53#10622610C2211yescharacteristic
54#10622608C2211yescharacteristic
55C2×#66874C2211yescharacteristic
56C2×#66872C2211yescharacteristic
57C4×#4318—21no—
58C4×#4318C2211yescharacteristic
59C4×#4318C2211yescharacteristic
60C2×#66867—21no—
61C2×#66867C2211yescharacteristic
62#10622196C2211yescharacteristic
63#10622196C2211yescharacteristic
64#10622192C2211yescharacteristic
65#10622192C2211yescharacteristic
66#10622168C2211yescharacteristic
67#10622168C2211yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C11×#137—22no—
72C11×#137C2×C414yes—
73C2×C11×Q16—21no—
74C2×C11×SD16—21no—
75C2×C11×M16C2311yescharacteristic
76C2×C11×M16C2311yescharacteristic
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11D411yescharacteristic
82C4×Q8×C11D411yescharacteristic
83C4×D4×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11D411yescharacteristic
86C4×D4×C11D411yescharacteristic
87C11×#117—21no—
88C11×#117C2311yescharacteristic
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94#67004—22no—
95#67004C2×C414yes—
96#67001—22no—
97#67001—22no—
98#67001—22no—
99#67001C2×C414yes—
100C2×#4326—21no—
101C2×#4326—21no—
102C2×#4326—21no—
103C2×#4326—22no—
104C2×#4326C2×C414yescomplemented
105C2×#4324—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C2×#4318—21no—
110C2×#4318—21no—
111C2×#4318C2311yescharacteristic
112C2×#4318C2311yescharacteristic
113C2×#4318C2311yescharacteristic
114C2×#4318C2311yescharacteristic
115C22×C11⋊C8—21no—
116C22×C11⋊C8—21no—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C4×Dic22—21no—
120C4×Dic22—21no—
121C4×Dic22—21no—
122C4×Dic22—21no—
123C11×#107—21no—
124C11×#106—21no—
125C11×#103—21no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#102—21no—
129C11×#97—21no—
130C4×C8×C11—21no—
131#66900—22no—
132#66900C2×C414yescomplemented
133#66899—21no—
134#66899—21no—
135#66899—21no—
136#66896—21no—
137#66888—22no—
138#66888C2×C414yescomplemented
139#66886—22no—
140#66886C2×C414yescomplemented
141#66874—21no—
142#66874—21no—
143#66874—21no—
144#66874—21no—
145#66872—21no—
146#66872—21no—
147#66872—21no—
148#66871—21no—
149#66867—21no—
150#66867—21no—
151#66867—21no—
152#66867—21no—
153#66867D411yescharacteristic
154#66867D411yescharacteristic
155#66867D411yescharacteristic
156#66867D411yescharacteristic
157C4×C11⋊C8—21no—
158C4×C11⋊C8—21no—
159C4×C11⋊C8—21no—
160C4×C11⋊C8—21no—
161#21556—111nomaximal, Sylow
162C11×#41—21no—
163C11×#41—21no—
164C11×#41C22×C412yes—
165C11×#41#4112yes—
166C2×Q8×C11—21no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11C22×C412yes—
172C2×Q8×C11C2×D411yescharacteristic
173C2×D4×C11—21no—
174C2×D4×C11C2×D411yescharacteristic
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11#4111yescharacteristic
181C22×C4×C11#4111yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C22×Dic11—21no—
184C22×Dic11—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22C22×C412yes—
191C11×Q16—24no—
192C11×SD16—24no—
193C11×M16—21no—
194C11×M16—21no—
195C11×M16—21no—
196C11×M16C22×C412yes—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—41no—
204C11×C4⋊C4—41no—
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—41no—
214C42×C11—41no—
215C42×C11C2×D411yescharacteristic
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219#4326—24no—
220#4326—24no—
221#4326—24no—
222#4324—24no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225Dic11⋊C4—41no—
226Dic11⋊C4—41no—
227C4×Dic11—41no—
228C4×Dic11—41no—
229#4318—24no—
230#4318—24no—
231#4318—21no—
232#4318—21no—
233#4318—21no—
234#4318—21no—
235#4318—21no—
236#4318C22×C412yes—
237#4318C22×C412yes—
238#4318#4112yes—
239C2×C11⋊C8—24no—
240C2×C11⋊C8—24no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8C22×C412yes—
248C2×C11⋊C8C2×D411yescharacteristic
249C2×C11⋊C8C2×D411yescharacteristic
250C2×C11⋊C8C2×D411yescharacteristic
251C2×C11⋊C8C2×D411yescharacteristic
252C2×C11⋊C8#4112yes—
253C2×#473—111no—
254C4×#137—111no—
255C4×#137D1111yescharacteristic
256C2×#441—111no—
257#2875—111no—
258#1979—111no—
259#1951—111no—
260#1930—111no—
261#1930—111no—
262#1908—111no—
263#1908—111no—
264#1815—111no—
265#1778—111no—
266C4×#101—111no—
267C4×#101—111no—
268C23×C11—21no—
269C23×C11C2×#4111yescharacteristic
270Q8×C11—21no—
271Q8×C11—22no—
272Q8×C11—22no—
273Q8×C11—41no—
274Q8×C11—41no—
275Q8×C11C4×D412yes—
276D4×C11—22no—
277D4×C11—22no—
278D4×C11—21no—
279D4×C11C4×D412yes—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—81no—
292C2×C4×C11—81no—
293C2×C4×C11—81no—
294C2×C4×C11#12111yescharacteristic
295C2×C4×C11#12111yescharacteristic
296C2×C4×C11#12111yescharacteristic
297C2×C4×C11#12111yescharacteristic
298C2×C4×C11C23×C411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C2×#4111yescharacteristic
302C2×C4×C11C2×#4111yescharacteristic
303C2×C4×C11C2×#4111yescharacteristic
304C2×Dic11—22no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—81no—
309Dic22—22no—
310Dic22—22no—
311Dic22—41no—
312Dic22—41no—
313C8×C11—22no—
314C8×C11—41no—
315C11⋊C8—22no—
316C11⋊C8—22no—
317C11⋊C8—21no—
318C11⋊C8—22no—
319C11⋊C8—21no—
320C11⋊C8—41no—
321C11⋊C8C4×D412yes—
322C11⋊C8C4×D412yes—
323C2×#137—111no—
324C2×#137C2×D1111yescharacteristic
325C22×Q16—111no—
326C2×#131—111no—
327C2×#131—111no—
328C4×#41C2×D1111yescharacteristic
329C2×C4×Q8—111no—
330C2×C4×Q8C2×D1111yescharacteristic
331#473—118no—
332#441—21no—
333#441—221no—
334#441—221no—
335#441—221no—
336#441—221no—
337#441—221no—
338#440—21no—
339#440—221no—
340C4×Q16—21no—
341C4×Q16—221no—
342C4×SD16—21no—
343C4×SD16—221no—
344C2×#108—111no—
345C2×#108—111no—
346#428—111no—
347#428C2×D1111yescharacteristic
348C2×#106—111no—
349#419—111no—
350#419C2×D1111yescharacteristic
351#417—111no—
352#417C2×D1111yescharacteristic
353C2×#103—111no—
354C2×#103—111no—
355C2×#101—111no—
356C2×#101—111no—
357C2×#101—111no—
358C2×#101—111no—
359#405—111no—
360#405—111no—
361#405—221no—
362#405—221no—
363C4×M16—111no—
364C4×M16—111no—
365C4×M16—221no—
366C4×M16C2×D1111yescharacteristic
367C2×#97—111no—
368C2×#97—221no—
369#343—111no—
370#343—111no—
371#343—111no—
372#343—111no—
373#341—111no—
374#341—111no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—22no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11C4×#4111yescharacteristic
381C22×C11C2×#12111yescharacteristic
382C22×C11#52911yescharacteristic
383C4×C11—22no—
384C4×C11—21no—
385C4×C11—21no—
386C4×C11—21no—
387C4×C11—21no—
388C4×C11—42no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11—81no—
392C4×C11C2×C4×D411yescharacteristic
393C4×C11C2×C4×D411yescharacteristic
394C4×C11#52511yescharacteristic
395C4×C11#53211yescharacteristic
396Dic11—42no—
397Dic11—81no—
398C2×#41C22×D1111yescharacteristic
399C22×Q8—111no—
400C22×Q8C22×D1111yescharacteristic
401#137—22no—
402#137—114no—
403#137—222no—
404#137C4×D1114yes—
405C2×Q16—21no—
406C2×Q16—114no—
407C2×Q16—222no—
408C2×Q16—221no—
409C2×Q16—221no—
410C2×Q16—221no—
411C2×SD16—21no—
412C2×SD16—221no—
413#131—114no—
414#131—222no—
415#131—222no—
416#131—222no—
417C2×M16—111no—
418C2×M16—111no—
419C2×M16—111no—
420C2×M16—111no—
421C2×M16—221no—
422C2×M16—221no—
423C2×M16C22×D1111yescharacteristic
424C2×M16C22×D1111yescharacteristic
425C22×C8—111no—
426C22×C8—111no—
427C22×C8—221no—
428C22×C8—221no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8—221no—
434C4×Q8—221no—
435C4×Q8—221no—
436C4×Q8—221no—
437C4×Q8C22⋊D1111yescharacteristic
438C4×Q8C22⋊D1111yescharacteristic
439C4×D4—21no—
440C4×D4—21no—
441C4×D4C22⋊D1111yescharacteristic
442C4×D4C22⋊D1111yescharacteristic
443#117—21no—
444#117C22×D1111yescharacteristic
445C2×C4⋊C4—21no—
446C2×C4⋊C4—111no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—221no—
452C2×C42C22×D1111yescharacteristic
453#108—114no—
454#108—222no—
455#107—21no—
456#107—221no—
457#106—21no—
458#106—221no—
459#106—221no—
460#106—221no—
461#103—21no—
462#103—21no—
463#103—21no—
464#103—221no—
465#103—221no—
466#103—221no—
467#103—221no—
468#103—221no—
469#103—221no—
470#103—221no—
471#102—21no—
472#102—221no—
473#101—114no—
474#101—114no—
475#101—222no—
476#101—222no—
477#97—21no—
478#97—111no—
479#97—111no—
480#97—111no—
481#97—111no—
482#97—221no—
483#97—221no—
484#97—221no—
485#97—221no—
486C4×C8—21no—
487C4×C8—221no—
488C4×C8—221no—
489C4×C8—221no—
490C4×C8—221no—
491C2×C11—21no—
492C2×C11—21no—
493C2×C11—42no—
494C2×C11C4×#12111yescharacteristic
495C2×C11#306911yescharacteristic
496C2×C11#306911yescharacteristic
497#41—21no—
498#41—21no—
499#41C2×C4×D1112yes—
500#41#433912yes—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—112no—
507C2×Q8—221no—
508C2×Q8—221no—
509C2×Q8—221no—
510C2×Q8—221no—
511C2×Q8—221no—
512C2×Q8C2×C4×D1112yes—
513C2×Q8C2×C22⋊D1111yescharacteristic
514C2×D4—21no—
515C2×D4C2×C22⋊D1111yescharacteristic
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4#434111yescharacteristic
524C22×C4#434111yescharacteristic
525C22×C4C23×D1111yescharacteristic
526Q16—24no—
527Q16—224no—
528Q16—224no—
529Q16—224no—
530SD16—24no—
531SD16—224no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—112no—
536M16—112no—
537M16—112no—
538M16—224no—
539M16—224no—
540M16—221no—
541M16—221no—
542M16—221no—
543M16—221no—
544M16—221no—
545M16C2×C4×D1112yes—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—112no—
549C2×C8—111no—
550C2×C8—111no—
551C2×C8—112no—
552C2×C8—111no—
553C2×C8—111no—
554C2×C8—224no—
555C2×C8—224no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—221no—
569C4⋊C4—221no—
570C4⋊C4—441no—
571C4⋊C4—441no—
572C4⋊C4C2×C22⋊D1111yescharacteristic
573C4⋊C4C2×C22⋊D1111yescharacteristic
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—41no—
581C42—41no—
582C42—441no—
583C42—441no—
584C42D4×D1111yescharacteristic
585C42D4×D1111yescharacteristic
586C42C2×C22⋊D1111yescharacteristic
587C42C2×C22⋊D1111yescharacteristic
588C11#2155611yescharacteristic, complemented, Sylow
589C23—21no—
590C23C2×#434111yescharacteristic
591Q8—21no—
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—222no—
597Q8—222no—
598Q8—441no—
599Q8—441no—
600Q8C4×C22⋊D1112yes—
601D4—22no—
602D4—22no—
603D4—21no—
604D4C4×C22⋊D1112yes—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—81no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—222no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—881no—
624C2×C4#6699211yescharacteristic
625C2×C4#6699211yescharacteristic
626C2×C4#6699211yescharacteristic
627C2×C4#6699211yescharacteristic
628C2×C4C22×C4×D1111yescharacteristic
629C2×C4C2×#433911yescharacteristic
630C2×C4C2×D4×D1111yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#41×D1111yescharacteristic
633C2×C4C22×C22⋊D1111yescharacteristic
634C8—22no—
635C8—41no—
636C8—112no—
637C8—112no—
638C8—222no—
639C8—222no—
640C8—221no—
641C8—221no—
642C8—222no—
643C8—441no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22C4×#434111yescharacteristic
650C22#1062306911yescharacteristic
651C22C2×#6699211yescharacteristic
652C4—22no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4—81no—
661C4—442no—
662C4—881no—
663C4C4×D4×D1111yescharacteristic
664C4#1062307811yescharacteristic
665C4C2×C4×C22⋊D1111yescharacteristic
666C4#1062336311yescharacteristic
667C2—21no—
668C2—21no—
669C2—42no—
670C2C4×#6699211yescharacteristic
671C2#1307835011yescharacteristic
672C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#137C2
socleC22×C11C2×#121
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenterC4×#137D11
hypocenterC11#21556
LCSG ▷ C2×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
3. C2×#10622643C2semidirect
5. #13069530C2semidirect
6. #13069393C2semidirect
7. #13069274C2semidirect
8. #13069270C2semidirect
12. #13068523C2semidirect
13. C4×#66888C2semidirect
14. C4×#66900C2semidirect
36. #10622817C4semidirect
104. C2×#4326C2×C4semidirect
132. #66900C2×C4semidirect
138. #66888C2×C4semidirect
140. #66886C2×C4semidirect
588. C11#21556semidirect

Maximal subgroups

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

subgroupindex
C2×#106228172
C4×#670042
C2×#106226432
#130770442
#130695302
#130693932
#130692742
#130692702
#130691332
#130691292
#130686732
#130685232
C4×#668882
C4×#669002
C4×C11×#1372
#2155611