Finite Group Databasebeta

← #14802016

Subgroups — #14802016

Order 2816.

858 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×#10622583C211yesmaximal, characteristic
2C2×#10622729C211yesmaximal, characteristic
3#13073090C211yesmaximal, characteristic
4#13071621C211yesmaximal, characteristic
5#13070091C211yesmaximal, characteristic, complemented
6#13070028C211yesmaximal, characteristic, complemented
7#13070012C211yesmaximal, characteristic, complemented
8#13069940C211yesmaximal, characteristic, complemented
9#13069373C211yesmaximal, characteristic, complemented
10#13069255C211yesmaximal, characteristic, complemented
11#13068958C211yesmaximal, characteristic, complemented
12#13068923C211yesmaximal, characteristic
13#13068794C211yesmaximal, characteristic
14#13068620C211yesmaximal, characteristic, complemented
15C2×C11×#340C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×Dic44C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23#10622823—21no—
24#10622823—21no—
25#10622823—21no—
26C4×C22⋊Dic11—21no—
27C4×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622729—24no—
30C2×#66882C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622593—21no—
36#10622593—21no—
37#10622591—21no—
38#10622589C2211yescharacteristic
39#10622589C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41#10622587C2211yescharacteristic
42#10622587C2211yescharacteristic
43#10622587C2211yescharacteristic
44#10622586C2211yescharacteristic
45#10622585—21no—
46#10622583—24no—
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87#66977—22no—
88#66977—22no—
89#66977—22no—
90#66977D414yes—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C2×Dic44—22no—
106C2×Dic44—22no—
107C2×Dic44—41no—
108#66940—22no—
109#66940—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120C22⋊(C11⋊C8)—22no—
121#66882—22no—
122#66880—22no—
123#66880—22no—
124Dic11⋊C8—22no—
125Dic11⋊C8—41no—
126#66874—22no—
127#66874—22no—
128#66874—22no—
129#66874—41no—
130#66871—22no—
131#66871—22no—
132#25206—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—81no—
146C22×C4×C11—81no—
147C22×C4×C11—81no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C2×D412yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—44no—
178C2×C8×C11#4112yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4#4112yes—
189C22⋊Dic11—24no—
190C22⋊Dic11—22no—
191C22⋊Dic11—42no—
192C22⋊Dic11Q1614yescomplemented
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2×D412yes—
197Dic11⋊C4—24no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201Dic11⋊C4—81no—
202Dic11⋊C4—81no—
203Dic11⋊C4—81no—
204Dic11⋊C4—81no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C4×Dic11—81no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217Dic44—44no—
218C2×#484—111no—
219C2×#467—111no—
220#2502—111no—
221#2360—111no—
222#2083—111no—
223#2072—111no—
224#2068—111no—
225#2056—111no—
226#1947—111no—
227#1928—111no—
228#1878—111no—
229#1872—111no—
230#1850—111no—
231#1803—111no—
232C2×#340D1111yescharacteristic
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11#12112yes—
238C23×C11C2×Q1612yes—
239C23×C11#13712yes—
240C23×C11C22×D411yescharacteristic
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—84no—
260C2×C4×C11—84no—
261C2×C4×C11#12112yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—41no—
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×Dic11C2×Q1612yes—
291C2×Dic11C2×Q1612yes—
292Dic22—22no—
293Dic22—22no—
294Dic22—41no—
295Dic22—41no—
296Dic22—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300C8×C11—22no—
301C8×C11—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×Q16—111no—
305C23×C8C2×D1111yescharacteristic
306C2×C22⋊Q8—111no—
307C2×C22⋊Q8—111no—
308C2×C4×Q8—111no—
309C22×C4⋊C4C2×D1111yescharacteristic
310C22×C4⋊C4C2×D1111yescharacteristic
311#484—224no—
312#467—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#107—111no—
316C2×C4⋊C8—111no—
317C2×C4⋊C8—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×C22⋊C8—111no—
325#398—221no—
326#398—221no—
327#391—111no—
328#391—111no—
329#391—111no—
330#389—111no—
331#389—221no—
332#387—221no—
333#385—221no—
334#385—221no—
335#385—221no—
336#384—111no—
337#384—111no—
338C4×C4⋊C4—111no—
339C4×C22⋊C4—111no—
340C4×C22⋊C4—221no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#340C2×D1111yescharacteristic
346#340C2×D1111yescharacteristic
347#336—111no—
348#336—111no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11#46214yes—
356C22×C11C2×#12111yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11#54711yescharacteristic
359C22×C11C22×Q1611yescharacteristic
360C22×C11C2×#13711yescharacteristic
361C22×C11#57611yescharacteristic
362C22×C11#57711yescharacteristic
363C4×C11—22no—
364C4×C11—42no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11#52911yescharacteristic
369C4×C11#53911yescharacteristic
370C4×C11#54611yescharacteristic
371C4×C11#54711yescharacteristic
372Dic11—22no—
373Dic11—22no—
374Dic11—41no—
375Dic11—42no—
376Dic11—42no—
377Dic11—41no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—111no—
381C22×Q8—111no—
382C23×C4—21no—
383C23×C4—21no—
384C23×C4C22×D1111yescharacteristic
385C2×Q16—222no—
386C2×Q16—222no—
387C2×Q16—441no—
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—41no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C22⋊Q8—114no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399C4×Q8—222no—
400C4×Q8—441no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—41no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
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×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—111no—
422C2×C22⋊C4—111no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—221no—
428C2×C42—221no—
429#107—222no—
430#107—222no—
431#107—222no—
432C4⋊C8—222no—
433C4⋊C8—441no—
434#103—222no—
435#103—222no—
436#103—222no—
437#103—222no—
438#103—222no—
439#103—441no—
440C22⋊C8—222no—
441#95—111no—
442#95—111no—
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—24no—
452C2×C11#242511yescharacteristic
453C2×C11C2×#46211yescharacteristic
454C2×C11#304511yescharacteristic
455C2×C11#329911yescharacteristic
456C2×C11#331411yescharacteristic
457C2×C11#333811yescharacteristic
458C2×C11#334411yescharacteristic
459C24D4×D1111yescharacteristic
460C2×Q8—112no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4#433912yes—
495C22×C4D4×D1111yescharacteristic
496C22×C4D4×D1112yes—
497C22×C4C23×D1111yescharacteristic
498Q16—444no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—44no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8#433912yes—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—112no—
522C4⋊C4—224no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—881no—
529C4⋊C4—881no—
530C4⋊C4—881no—
531C4⋊C4—881no—
532C4⋊C4—881no—
533C4⋊C4#433912yes—
534C22⋊C4—114no—
535C22⋊C4—224no—
536C22⋊C4—222no—
537C22⋊C4—442no—
538C42—221no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—442no—
543C42—881no—
544C11#2520611yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23#6693712yes—
550C23#6696812yes—
551C23Q16×D1112yes—
552C23C2×D4×D1111yescharacteristic
553Q8—222no—
554Q8—222no—
555Q8—441no—
556Q8—441no—
557Q8—441no—
558Q8—441no—
559Q8—441no—
560Q8—441no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
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—41no—
579C2×C4—84no—
580C2×C4—84no—
581C2×C4—112no—
582C2×C4—112no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
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—441no—
604C2×C4—441no—
605C2×C4#6693712yes—
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4#6704011yescharacteristic
612C8—22no—
613C8—41no—
614C8—441no—
615C8—441no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22#1062240614yes—
623C22C2×#6693711yescharacteristic
624C22#1062302111yescharacteristic
625C22#1062303811yescharacteristic
626C22#1062328811yescharacteristic
627C22C2×#6696811yescharacteristic
628C22#1062329311yescharacteristic
629C22C2×Q16×D1111yescharacteristic
630C4—22no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—222no—
636C4—222no—
637C4—442no—
638C4—441no—
639C4—442no—
640C4—441no—
641C4—881no—
642C4—881no—
643C4#1062301011yescharacteristic
644C4#1062302111yescharacteristic
645C4#1062303811yescharacteristic
646C4#1062304611yescharacteristic
647C2—24no—
648C2#1307216711yescharacteristic
649C2C2×#1062240611yescharacteristic
650C2#1307816011yescharacteristic
651C2#1308048811yescharacteristic
652C2#1308069311yescharacteristic
653C2#1308100611yescharacteristic
654C2#1308106711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#340D11
hypocenterC11#25206
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
5. #13070091C2semidirect
6. #13070028C2semidirect
7. #13070012C2semidirect
8. #13069940C2semidirect
9. #13069373C2semidirect
10. #13069255C2semidirect
11. #13068958C2semidirect
14. #13068620C2semidirect
192. C22⋊Dic11Q16semidirect
544. C11#25206semidirect

Maximal subgroups

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

subgroupindex
C2×#106225832
C2×#106227292
#130730902
#130716212
#130700912
#130700282
#130700122
#130699402
#130693732
#130692552
#130689582
#130689232
#130687942
#130686202
C2×C11×#3402
#2520611