Finite Group Databasebeta

← #14760314

Subgroups — #14760314

Order 2816.

954 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×#10622664C211yesmaximal, characteristic
2C2×#10622403C211yesmaximal, characteristic, complemented
3C2×#10622735C211yesmaximal, characteristic
4#13071300C211yesmaximal, characteristic
5#13071294C211yesmaximal, characteristic
6#13069474C211yesmaximal, characteristic, complemented
7#13069348C211yesmaximal, characteristic, complemented
8#13069307C211yesmaximal, characteristic, complemented
9#13069303C211yesmaximal, characteristic, complemented
10#13069049C211yesmaximal, characteristic
11#13068643C211yesmaximal, characteristic
12#13068508C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1894C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622735—24no—
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622664C418yescomplemented
38#10622598—21no—
39#10622598C2211yescharacteristic
40#10622594—21no—
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622587C2211yescharacteristic
44#10622586C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622564—21no—
50#10622564—21no—
51#10622558—21no—
52#10622557—21no—
53#10622403—24no—
54#10622268—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8C2×C414yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D411yescharacteristic
81C2×C22⋊Dic11D411yescharacteristic
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84C2×#4326—22no—
85C2×#4326—22no—
86C2×#4326C2×C414yes—
87#66979—22no—
88#66979—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96#66977—22no—
97#66977C2×C414yes—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8—22no—
108C22×C11⋊C8—22no—
109C22×C11⋊C8C2×C414yes—
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112#66940—22no—
113#66940—22no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#95—21no—
117#66899C2×C414yes—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66880—22no—
128#66880—22no—
129#66879—22no—
130#66879—22no—
131C8×Dic11—22no—
132C8×Dic11D414yes—
133#66874C2×C414yes—
134#66871—22no—
135#66871—22no—
136#66871C2×C414yes—
137#21525—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C11×M16—28no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D412yes—
177C2×C8×C11#4112yes—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—81no—
187C22⋊Dic11—22no—
188C22⋊Dic11—22no—
189C22⋊Dic11—24no—
190C22⋊Dic11—81no—
191#4326—28no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11C22×C412yes—
202Dic11⋊C4—24no—
203Dic11⋊C4—42no—
204Dic11⋊C4—81no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—81no—
210C4×Dic11—81no—
211C4×Dic11C2×D412yes—
212C4×Dic11#4112yes—
213C2×C11⋊C8—28no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C22×C412yes—
217C2×C11⋊C8C22×C412yes—
218C2×C11⋊C8C2×D412yes—
219C2×C11⋊C8#4112yes—
220C2×#467—111no—
221C2×C4×Q16—111no—
222C2×#405—111no—
223#2323—111no—
224#2323—111no—
225#1969—111no—
226#1942—111no—
227#1935—111no—
228#1935—111no—
229#1894—111no—
230#1894D1111yescharacteristic
231#1808—111no—
232C4×#107—111no—
233#1763—111no—
234#1763—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11C4×D412yes—
242C23×C11C22×D411yescharacteristic
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—41no—
246Q8×C11—41no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
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—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11C4×D412yes—
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
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—41no—
294C2×Dic11#12112yes—
295C2×Dic11#12112yes—
296Dic22—22no—
297Dic22—22no—
298Dic22—41no—
299Dic22—41no—
300C8×C11—22no—
301C8×C11—22no—
302C11⋊C8—22no—
303C11⋊C8C4×D414yes—
304C22×Q16—111no—
305C22×M16C2×D1111yescharacteristic
306C23×C8—111no—
307C2×C22⋊Q8—111no—
308C2×C22⋊Q8C2×D1111yescharacteristic
309C2×C4×Q8—111no—
310C2×C4×Q8—111no—
311C2×#117—111no—
312#467—118no—
313C4×Q16—224no—
314C2×#107—111no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103C2×D1111yescharacteristic
322C2×#103C2×D1111yescharacteristic
323#405—224no—
324C2×#97—111no—
325C2×#97—111no—
326C2×C4×C8—111no—
327C2×C4×C8—111no—
328#391—111no—
329#391—111no—
330#389—111no—
331#389—111no—
332#389—221no—
333#389—221no—
334#388—221no—
335#388—221no—
336#388—221no—
337#388—221no—
338#387—221no—
339#387—221no—
340#380—111no—
341#380C2×D1111yescharacteristic
342C4×C4⋊C4—111no—
343C4×C4⋊C4—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11C2×C4×D411yescharacteristic
358C22×C11C2×#12111yescharacteristic
359C22×C11#53211yescharacteristic
360C22×C11#57611yescharacteristic
361C22×C11#57811yescharacteristic
362C22×C11#57811yescharacteristic
363C22×C11#57811yescharacteristic
364C4×C11—22no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11C2×C4×D411yescharacteristic
370C4×C11C4×#4111yescharacteristic
371C4×C11#52511yescharacteristic
372C4×C11#52911yescharacteristic
373Dic11—22no—
374Dic11—22no—
375Dic11—42no—
376Dic11—41no—
377Dic11—41no—
378Dic11—42no—
379Dic11—81no—
380Dic11—81no—
381C22×Q8—111no—
382C22×Q8C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C2×Q16—114no—
385C2×Q16—222no—
386C2×Q16—222no—
387C2×M16—22no—
388C2×M16—22no—
389C2×M16—22no—
390C22×C8—111no—
391C22×C8—114no—
392C22×C8—111no—
393C22×C8—222no—
394C22×C8—222no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C22⋊Q8—22no—
398C22⋊Q8—114no—
399C22⋊Q8—222no—
400C22⋊Q8C4×D1114yes—
401C4×Q8—222no—
402C4×Q8—222no—
403C4×Q8—222no—
404C4×Q8—222no—
405#117—222no—
406#117—222no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
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—21no—
423C2×C22⋊C4—111no—
424C2×C22⋊C4—111no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42—221no—
433#107—114no—
434#107—222no—
435#107—222no—
436#103—22no—
437#103—22no—
438#103—114no—
439#103—114no—
440#103—222no—
441#103—222no—
442#97—222no—
443#97—222no—
444C4×C8—114no—
445C4×C8—222no—
446#95—21no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—42no—
457C2×C11C4×#12111yescharacteristic
458C2×C11#295011yescharacteristic
459C2×C11#295111yescharacteristic
460C2×C11#305911yescharacteristic
461C2×C11#306111yescharacteristic
462C2×C11#317511yescharacteristic
463C2×C11#317711yescharacteristic
464C24D4×D1111yescharacteristic
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—112no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8C2×C4×D1112yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4C2×C4×D1112yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4#434112yes—
496C22×C4C23×D1111yescharacteristic
497Q16—228no—
498M16—28no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—112no—
506C2×C8—112no—
507C2×C8—228no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8D4×D1112yes—
511C2×C8#434112yes—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—112no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—224no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C4⋊C4—881no—
530C4⋊C4—881no—
531C4⋊C4C2×C4×D1112yes—
532C22⋊C4—24no—
533C22⋊C4—81no—
534C22⋊C4—222no—
535C22⋊C4—222no—
536C22⋊C4—224no—
537C22⋊C4—881no—
538C42—112no—
539C42—112no—
540C42—221no—
541C42—221no—
542C42—442no—
543C42—442no—
544C42—881no—
545C42—881no—
546C11#2152511yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23(C22⋊D11)⋊C412yes—
554C23C2×D4×D1111yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—222no—
560Q8—222no—
561Q8—441no—
562Q8—441no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
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—41no—
580C2×C4—41no—
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(C22⋊D11)⋊C412yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×D4×D1111yescharacteristic
608C2×C4C2×#434111yescharacteristic
609C2×C4C2×#434111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C8—22no—
613C8—22no—
614C8—114no—
615C8—222no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22C2×(C22⋊D11)⋊C411yescharacteristic
624C22#1062312711yescharacteristic
625C22D11×#12111yescharacteristic
626C22#1062330511yescharacteristic
627C22#1062331011yescharacteristic
628C22#1062331011yescharacteristic
629C22#1062331011yescharacteristic
630C4—22no—
631C4—42no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—222no—
636C4—222no—
637C4—441no—
638C4—442no—
639C4—442no—
640C4—441no—
641C4—881no—
642C4—881no—
643C4C4×#434111yescharacteristic
644C4C4×D4×D1111yescharacteristic
645C4#1062311711yescharacteristic
646C4#1062318011yescharacteristic
647C2—42no—
648C2#1307112611yescharacteristic
649C2#1307748011yescharacteristic
650C2#1307748711yescharacteristic
651C2#1307826911yescharacteristic
652C2#1307828411yescharacteristic
653C2#1307925011yescharacteristic
654C2#1307927011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1894D11
hypocenterC11#21525
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
2. C2×#10622403C2semidirect
6. #13069474C2semidirect
7. #13069348C2semidirect
8. #13069307C2semidirect
9. #13069303C2semidirect
12. #13068508C2semidirect
13. #13068448C2semidirect
14. #13068445C2semidirect
37. #10622664C4semidirect
546. C11#21525semidirect

Maximal subgroups

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

subgroupindex
C2×#106226642
C2×#106224032
C2×#106227352
#130713002
#130712942
#130694742
#130693482
#130693072
#130693032
#130690492
#130686432
#130685082
#130684482
#130684452
C11×#18942
#2152511