Finite Group Databasebeta

← #14813924

Subgroups — #14813924

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622775C211yesmaximal, characteristic
2#13072386C211yesmaximal, characteristic, complemented
3#13071521C211yesmaximal, characteristic
4#13070165C211yesmaximal, characteristic, complemented
5#13070115C211yesmaximal, characteristic, complemented
6#13070037C211yesmaximal, characteristic, complemented
7#13069860C211yesmaximal, characteristic, complemented
8#13069292C211yesmaximal, characteristic, complemented
9#13069173C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic
11#13068950C211yesmaximal, characteristic
12#13068948C211yesmaximal, characteristic
13#13068870C211yesmaximal, characteristic, complemented
14#13068861C211yesmaximal, characteristic
15C2×C4×C11×SD16C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C4×C11×SD16—24no—
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622823—21no—
33C2×C11⋊#95—21no—
34#10622775—24no—
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38#10622595—21no—
39#10622593—21no—
40#10622590C2211yescharacteristic
41#10622587C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622559—21no—
47#10622555—21no—
48#10622546—21no—
49#10622546—21no—
50C4×Dic11⋊C4C2211yescharacteristic
51#10622542C2211yescharacteristic
52#10622541C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22C2311yescharacteristic
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16D414yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×Q8×C11—22no—
73C4×Q8×C11—41no—
74C4×D4×C11—22no—
75C4×D4×C11—41no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84#66997—22no—
85#66997—41no—
86D4×Dic11—22no—
87D4×Dic11—22no—
88D4×Dic11—22no—
89D4×Dic11—41no—
90C2×#4324—22no—
91C2×#4324—22no—
92C2×#4324—22no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4D411yescharacteristic
102C2×Dic11⋊C4D411yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C11×#106—22no—
108C11×#103—22no—
109C11×#102—22no—
110C4×C8×C11—22no—
111#66899—22no—
112#66899—22no—
113#66896—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⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127#66880—22no—
128#66880—22no—
129Dic11⋊C8—22no—
130#66874—41no—
131#66871—41no—
132#26170—111nomaximal, Sylow
133C24×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11C2×D412yes—
144C2×D4×C11#4112yes—
145C2×D4×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—24no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—81no—
163C22×Dic11—81no—
164C22×Dic11—81no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C11×SD16—28no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11C2×D412yes—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—42no—
187C11×C22⋊C4—42no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—42no—
191C22⋊Dic11—24no—
192C22⋊Dic11—42no—
193#4324—44no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—81no—
206Dic11⋊C4—81no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×#461—111no—
218C2×C4×SD16D1111yescharacteristic
219#2446—111no—
220#2349—111no—
221#2097—111no—
222#2088—111no—
223#2074—111no—
224#2043—111no—
225#1933—111no—
226#1916—111no—
227#1877—111no—
228#1877—111no—
229#1877—111no—
230#1863—111no—
231#1862—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C22×D411yescharacteristic
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—41no—
243Q8×C11—41no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11#12314yes—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
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×C11—84no—
263C2×C4×C11#13712yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—84no—
294C2×Dic11—84no—
295C2×Dic11#13512yes—
296Dic22—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300C8×C11—22no—
301C8×C11—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×SD16—111no—
305C22×SD16C2×D1111yescharacteristic
306C2×C4⋊Q8—111no—
307C2×C4×Q8C2×D1111yescharacteristic
308C2×C4×D4—111no—
309C2×C4×D4—111no—
310C2×C4×D4C2×D1111yescharacteristic
311#461—224no—
312C4×SD16—24no—
313C2×#107—111no—
314C2×#106C2×D1111yescharacteristic
315C2×C4⋊C8—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103C2×D1111yescharacteristic
322C2×#102—111no—
323C2×#102C2×D1111yescharacteristic
324C2×C4×C8C2×D1111yescharacteristic
325#400—221no—
326#398—221no—
327#391—111no—
328#391—111no—
329#391—111no—
330#389—111no—
331#389—111no—
332#389—111no—
333#387—221no—
334#387—221no—
335#385—221no—
336#385—221no—
337#382—111no—
338#380—221no—
339C4×C4⋊C4—111no—
340C2×#95—221no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#336—111no—
346#336—111no—
347#336—111no—
348#336—111no—
349C22×C11—24no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11#52511yescharacteristic
357C22×C11D4211yescharacteristic
358C22×C11#54811yescharacteristic
359C22×C11C2×#13511yescharacteristic
360C22×C11C2×#13711yescharacteristic
361C22×C11#57711yescharacteristic
362C22×C11#57711yescharacteristic
363C4×C11—22no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11C2×#12311yescharacteristic
369C4×C11#53911yescharacteristic
370C4×C11#54711yescharacteristic
371C4×C11#55311yescharacteristic
372Dic11—22no—
373Dic11—41no—
374Dic11—41no—
375Dic11—42no—
376Dic11—41no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—111no—
381C22×Q8C22×D1111yescharacteristic
382C22×D4C22×D1111yescharacteristic
383C23×C4—21no—
384C23×C4—221no—
385C23×C4—221no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—222no—
389C2×SD16—222no—
390C2×SD16—222no—
391C2×SD16C22⋊D1114yes—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C4⋊Q8—222no—
397C4⋊Q8—441no—
398C4×Q8—22no—
399C4×Q8—41no—
400C4×D4—22no—
401C4×D4—41no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—441no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—21no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42C22×D1111yescharacteristic
426#107—441no—
427#106—22no—
428C4⋊C8—222no—
429#103—22no—
430#103—222no—
431#103—222no—
432#103—222no—
433#103—222no—
434#103—441no—
435#102—22no—
436#102—222no—
437C4×C8—22no—
438#95—111no—
439#95—111no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11—44no—
452C2×C11#244311yescharacteristic
453C2×C11#310711yescharacteristic
454C2×C11#312311yescharacteristic
455C2×C11#326611yescharacteristic
456C2×C11#328211yescharacteristic
457C2×C11#336011yescharacteristic
458C2×C11#337211yescharacteristic
459C24—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8C2×C22⋊D1112yes—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4#433912yes—
476C2×D4#433912yes—
477C2×D4C2×C22⋊D1112yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—81no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—221no—
489C22×C4—224no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—881no—
496C22×C4—881no—
497C22×C4—881no—
498C22×C4D4×D1111yescharacteristic
499C22×C4D4×D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501SD16—28no—
502SD16—444no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8C2×C22⋊D1112yes—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—112no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—881no—
532C4⋊C4—881no—
533C22⋊C4—42no—
534C22⋊C4—224no—
535C22⋊C4—442no—
536C42—21no—
537C42—21no—
538C42—42no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—221no—
543C11#2617011yescharacteristic, complemented, Sylow
544C23—22no—
545C23—22no—
546C23—22no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23C2×D4×D1111yescharacteristic
552Q8—22no—
553Q8—22no—
554Q8—41no—
555Q8—41no—
556Q8—441no—
557Q8—441no—
558Q8—441no—
559Q8—441no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4#6698214yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—84no—
579C2×C4—112no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—222no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—884no—
604C2×C4—884no—
605C2×C4#6696812yes—
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704311yescharacteristic
611C2×C4C22×C22⋊D1111yescharacteristic
612C8—22no—
613C8—41no—
614C8—441no—
615C8—441no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22#1062307811yescharacteristic
624C22#1062308311yescharacteristic
625C22C2×#6696811yescharacteristic
626C22#1062329311yescharacteristic
627C22D11×#13511yescharacteristic
628C22#1062330111yescharacteristic
629C22D4×C22⋊D1111yescharacteristic
630C4—22no—
631C4—42no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—222no—
636C4—441no—
637C4—441no—
638C4—442no—
639C4—441no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4#1062307111yescharacteristic
644C4#1062309511yescharacteristic
645C4C2×#6698211yescharacteristic
646C4#1062335511yescharacteristic
647C2—44no—
648C2#1307234511yescharacteristic
649C2#1307868311yescharacteristic
650C2#1307886511yescharacteristic
651C2#1308012611yescharacteristic
652C2#1308031711yescharacteristic
653C2#1308126611yescharacteristic
654C2#1308139511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×C4×SD16D11
hypocenterC11#26170
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. #13072386C2semidirect
4. #13070165C2semidirect
5. #13070115C2semidirect
6. #13070037C2semidirect
7. #13069860C2semidirect
8. #13069292C2semidirect
9. #13069173C2semidirect
13. #13068870C2semidirect
543. C11#26170semidirect

Maximal subgroups

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

subgroupindex
C2×#106227752
#130723862
#130715212
#130701652
#130701152
#130700372
#130698602
#130692922
#130691732
#130689522
#130689502
#130689482
#130688702
#130688612
C2×C4×C11×SD162
#2617011