Finite Group Databasebeta

← #14772136

Subgroups — #14772136

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622631C211yesmaximal, characteristic
2C2×#10622370C211yesmaximal, characteristic
3C2×#10622371C211yesmaximal, characteristic
4#13071530C211yesmaximal, characteristic, complemented
5#13071521C211yesmaximal, characteristic
6#13069351C211yesmaximal, characteristic, complemented
7#13069348C211yesmaximal, characteristic, complemented
8#13068887C211yesmaximal, characteristic, complemented
9#13068879C211yesmaximal, characteristic
10#13068867C211yesmaximal, characteristic, complemented
11#13068783C211yesmaximal, characteristic, complemented
12#13068630C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic
14#13068489C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622823—21no—
29C2×C11⋊#95—21no—
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622631—24no—
37#10622598C2211yescharacteristic
38#10622590C2211yescharacteristic
39#10622589—21no—
40#10622589C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622585—21no—
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622559—21no—
48#10622555—21no—
49C4×Dic11⋊C4C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52#10622371—24no—
53#10622370C418yescomplemented
54#10622262—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×D4×C11—22no—
70C4×D4×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11—41no—
82D4×Dic11C2×C414yes—
83C2×#4324C2×C414yes—
84C2×#4324D414yes—
85C2×#4324Q814yes—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
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⋊C4D411yescharacteristic
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66940—22no—
107#66940—22no—
108#66940—41no—
109#66940C2×C414yescomplemented
110C4×Dic22—22no—
111C4×Dic22—41no—
112C11×#107—41no—
113C11×#102—22no—
114C11×#102C2×C414yes—
115C11×#95—21no—
116#66896—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66881—41no—
125#66880—22no—
126#66880C2×C414yescomplemented
127#66879C2×C414yescomplemented
128Dic11⋊C8—22no—
129C8×Dic11—22no—
130#66874—22no—
131#66872—22no—
132#66871—22no—
133#66871C2×C414yescomplemented
134#66867—22no—
135#22678—111nomaximal, Sylow
136C24×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11C22×C412yes—
141C2×D4×C11C2×D412yes—
142C2×D4×C11C2×Q812yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—24no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—81no—
160C22×Dic11—81no—
161C22×Dic11—81no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22C22×C412yes—
170C2×Dic22C2×D412yes—
171C2×Dic22C2×Q812yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C22×C412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—42no—
186C42×C11—21no—
187C42×C11—21no—
188C22⋊Dic11—24no—
189C22⋊Dic11—42no—
190#4324C4⋊C4116yescomplemented
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—81no—
197C4⋊Dic11C22×C412yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—22no—
200Dic11⋊C4—41no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—81no—
205Dic11⋊C4—81no—
206Dic11⋊C4—81no—
207C4×Dic11—24no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C4×Dic11C22×C412yes—
213C4×Dic11#4112yes—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C22×C412yes—
218C2×C11⋊C8C2×D412yes—
219C2×C11⋊C8C2×Q812yes—
220C2×#440—111no—
221C2×#440—111no—
222C2×C4×SD16—111no—
223Q8×C4⋊C4—111no—
224#2349—111no—
225#1943—111no—
226#1942—111no—
227#1865—111no—
228#1864—111no—
229#1863—111no—
230#1862D1111yescharacteristic
231#1847—111no—
232#1805—111no—
233#1802—111no—
234#1771—111no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C22×D411yescharacteristic
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11C2×C4⋊C414yes—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×Q811yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
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—84no—
291C2×Dic11—84no—
292C2×Dic11C4×D412yes—
293C2×Dic11C4×D412yes—
294C2×Dic11#13712yes—
295Dic22—22no—
296Dic22—22no—
297Dic22—22no—
298Dic22C2×C4⋊C414yes—
299C8×C11—22no—
300C8×C11—41no—
301C11⋊C8—41no—
302C11⋊C8C2×C4⋊C414yes—
303C22×SD16—111no—
304C2×C4×Q8—111no—
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×D4—111no—
308C2×C4×D4—111no—
309C2×C4×D4C2×D1111yescharacteristic
310#440—118no—
311#440—224no—
312C4×SD16—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#107C2×D1111yescharacteristic
316C2×#106—111no—
317C2×#106—111no—
318C2×C4⋊C8—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#102—111no—
323C2×#102C2×D1111yescharacteristic
324C2×#102C2×D1111yescharacteristic
325C2×#97—111no—
326C2×#97—111no—
327C2×C4×C8—111no—
328#389—111no—
329#389—111no—
330#389—111no—
331#389—221no—
332#389—221no—
333#389C2×D1111yescharacteristic
334#385—221no—
335#385—221no—
336#384—111no—
337#384—221no—
338#382—111no—
339#380—221no—
340C4×C4⋊C4—111no—
341C4×C4⋊C4—221no—
342C2×#95—221no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340C2×D1111yescharacteristic
347#336—111no—
348#336C2×D1111yescharacteristic
349C22×C11—24no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11C2×C4×D411yescharacteristic
357C22×C11D4211yescharacteristic
358C22×C11D4×Q811yescharacteristic
359C22×C11C2×#13711yescharacteristic
360C22×C11#57511yescharacteristic
361C22×C11#57611yescharacteristic
362C22×C11#57711yescharacteristic
363C4×C11—42no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11C22×C4⋊C411yescharacteristic
369C4×C11#52011yescharacteristic
370C4×C11#54711yescharacteristic
371C4×C11#55411yescharacteristic
372Dic11—24no—
373Dic11—22no—
374Dic11—22no—
375Dic11—22no—
376Dic11—42no—
377Dic11—41no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—111no—
381C22×D4C22×D1111yescharacteristic
382C23×C4—21no—
383C23×C4—221no—
384C23×C4—221no—
385C2×SD16—114no—
386C2×SD16—114no—
387C2×SD16—114no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C4×Q8—114no—
393C4×Q8—222no—
394C4×Q8—222no—
395C4×Q8—222no—
396C4×Q8—441no—
397C4×Q8—441no—
398C4×D4—22no—
399C4×D4—41no—
400C4×D4—114no—
401C4×D4—222no—
402C4×D4—222no—
403C4×D4—441no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
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⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430#107—41no—
431#107—114no—
432#107—222no—
433#106—222no—
434#106—441no—
435C4⋊C8—222no—
436#103—114no—
437#103—222no—
438#103—222no—
439#102—22no—
440#102—222no—
441#102C4×D1114yes—
442#97—114no—
443#97—222no—
444C4×C8—222no—
445#95—21no—
446#95—111no—
447#95—111no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453C2×C11—44no—
454C2×C11D4×C4⋊C411yescharacteristic
455C2×C11C4×#13711yescharacteristic
456C2×C11#294611yescharacteristic
457C2×C11#326611yescharacteristic
458C2×C11#326811yescharacteristic
459C2×C11#338511yescharacteristic
460C2×C11#338811yescharacteristic
461C24—21no—
462C2×Q8—112no—
463C2×Q8—112no—
464C2×Q8—112no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4C2×C4×D1112yes—
472C2×D4D4×D1112yes—
473C2×D4Q8×D1112yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—81no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—224no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4—881no—
493C22×C4—881no—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497SD16—1116no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—112no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8C2×C4×D1112yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—81no—
516C4⋊C4—112no—
517C4⋊C4—222no—
518C4⋊C4—224no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—441no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—881no—
529C4⋊C4—881no—
530C4⋊C4—881no—
531C4⋊C4—881no—
532C4⋊C4C2×C4×D1112yes—
533C22⋊C4—42no—
534C22⋊C4—224no—
535C22⋊C4—442no—
536C42—21no—
537C42—21no—
538C42—112no—
539C42—112no—
540C42—224no—
541C42—221no—
542C42—221no—
543C42—442no—
544C42—442no—
545C11#2267811yescharacteristic, complemented, Sylow
546C23—22no—
547C23—22no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23C2×D4×D1111yescharacteristic
554Q8—114no—
555Q8—222no—
556Q8—222no—
557Q8—222no—
558D4—22no—
559D4—22no—
560D4—22no—
561D4C4⋊C4×D1114yes—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
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—84no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—222no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—222no—
593C2×C4—221no—
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—884no—
603C2×C4—884no—
604C2×C4C22×C4×D1111yescharacteristic
605C2×C4C2×D4×D1111yescharacteristic
606C2×C4#6703711yescharacteristic
607C2×C4C2×Q8×D1111yescharacteristic
608C2×C4#41×D1111yescharacteristic
609C2×C4#6704311yescharacteristic
610C8—22no—
611C8—41no—
612C8—114no—
613C8—441no—
614C22—24no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22C4×D4×D1111yescharacteristic
622C22#1062312111yescharacteristic
623C22#1062316311yescharacteristic
624C22#1062328811yescharacteristic
625C22#1062330111yescharacteristic
626C22#1062330411yescharacteristic
627C22D11×#13711yescharacteristic
628C4—41no—
629C4—41no—
630C4—42no—
631C4—81no—
632C4—81no—
633C4—222no—
634C4—224no—
635C4—222no—
636C4—222no—
637C4—441no—
638C4—442no—
639C4—881no—
640C4—881no—
641C4C2×C4⋊C4×D1111yescharacteristic
642C4#1062307711yescharacteristic
643C4#1062316711yescharacteristic
644C4#1062318611yescharacteristic
645C2—44no—
646C2#1307151411yescharacteristic
647C2#1307743811yescharacteristic
648C2#1307744111yescharacteristic
649C2#1308012411yescharacteristic
650C2#1308015411yescharacteristic
651C2#1308152111yescharacteristic
652C2#1308155811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1862D11
hypocenterC11#22678
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
4. #13071530C2semidirect
6. #13069351C2semidirect
7. #13069348C2semidirect
8. #13068887C2semidirect
10. #13068867C2semidirect
11. #13068783C2semidirect
12. #13068630C2semidirect
14. #13068489C2semidirect
53. #10622370C4semidirect
109. #66940C2×C4semidirect
126. #66880C2×C4semidirect
127. #66879C2×C4semidirect
133. #66871C2×C4semidirect
190. #4324C4⋊C4semidirect
545. C11#22678semidirect

Maximal subgroups

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

subgroupindex
C2×#106226312
C2×#106223702
C2×#106223712
#130715302
#130715212
#130693512
#130693482
#130688872
#130688792
#130688672
#130687832
#130686302
#130686142
#130684892
C11×#18622
#2267811