Finite Group Databasebeta

← #14776270

Subgroups — #14776270

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622797C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic
3#13071676C211yesmaximal, characteristic
4#13071537C211yesmaximal, characteristic
5#13069437C211yesmaximal, characteristic
6#13069386C211yesmaximal, characteristic
7#13069308C211yesmaximal, characteristic
8#13069294C211yesmaximal, characteristic
9#13068959C211yesmaximal, characteristic
10#13068959C211yesmaximal, characteristic
11#13068886C211yesmaximal, characteristic
12#13068872C211yesmaximal, characteristic
13#13068493C211yesmaximal, characteristic
14#13068446C211yesmaximal, characteristic
15C2×C11×#462C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C11×#462C418yescomplemented
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622797—24no—
37Q16×Dic11—24no—
38C2×#66882C2211yescharacteristic
39C2×#66881C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42#10622598—21no—
43#10622598—21no—
44#10622598—21no—
45#10622598C2211yescharacteristic
46#10622598C2211yescharacteristic
47#10622594—21no—
48#10622594—21no—
49C4⋊C4×Dic11—21no—
50#10622549—21no—
51#10622549C2211yescharacteristic
52C4×C4⋊Dic11—21no—
53C4×C4⋊Dic11C2211yescharacteristic
54C4×C4⋊Dic11C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16—22no—
69C2×C11×Q16C2×C414yes—
70C2×C11×Q16C2×C414yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8C2×C414yes—
75C4×Q8×C11—22no—
76C4×Q8×C11C2×C414yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83Q8×Dic11—22no—
84Q8×Dic11—22no—
85Q8×Dic11—22no—
86Q8×Dic11—22no—
87Q8×Dic11—41no—
88Q8×Dic11—41no—
89Q8×Dic11—41no—
90Q8×Dic11—41no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11D411yescharacteristic
98C2×C4⋊Dic11D411yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×C4⋊C8C2×C414yes—
113C11×#103C2×C414yes—
114C11×#103C2×C414yes—
115#66899—22no—
116#66899—22no—
117#66899—22no—
118#66899—41no—
119#66899—41no—
120#66899D414yes—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95D411yescharacteristic
131C11⋊#95D411yescharacteristic
132#66882—22no—
133#66881—22no—
134#66879—22no—
135C8×Dic11—22no—
136#66867—22no—
137#23014—111nomaximal, Sylow
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C22×C412yes—
152C2×Q8×C11C22×C412yes—
153C2×Q8×C11C22×C412yes—
154C2×Q8×C11C2×D412yes—
155C2×Q8×C11#4112yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C11×Q16—28no—
172C11×Q16—28no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C22×C412yes—
178C2×C8×C11C22×C412yes—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C22×C412yes—
184C42×C11—24no—
185C42×C11C22×C412yes—
186C42×C11#4112yes—
187C4⋊Dic11—22no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—41no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11—42no—
201C4⋊Dic11—42no—
202C4⋊Dic11C2×D412yes—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C2×D412yes—
218C2×#462D1111yescharacteristic
219C2×#441—111no—
220C2×C4×Q16—111no—
221#2365—111no—
222#2351—111no—
223#1960—111no—
224#1949—111no—
225#1935—111no—
226#1933—111no—
227#1878—111no—
228#1878—111no—
229#1865—111no—
230#1863—111no—
231#1771—111no—
232#1763—111no—
233C23×C11C22×D411yescharacteristic
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11C4×D414yes—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
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×C11C4×D412yes—
263C2×C4×C11C4×D412yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
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—21no—
275C2×Dic11—22no—
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#13712yes—
294C8×C11—22no—
295C8×C11—22no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×Q16C2×D1111yescharacteristic
299C22×Q16C2×D1111yescharacteristic
300C2×C4⋊Q8C2×D1111yescharacteristic
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×Q8—111no—
305C2×C4×Q8C2×D1111yescharacteristic
306#462Dic1118yescomplemented
307#441—224no—
308C4×Q16—224no—
309C2×#107—111no—
310C2×#106—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#103C2×D1111yescharacteristic
320C2×#97—111no—
321C2×#97—111no—
322C2×C4×C8—111no—
323#391—111no—
324#391—111no—
325#389—111no—
326#389—111no—
327#389—221no—
328#389—221no—
329#389—221no—
330#387—221no—
331#387—221no—
332#382—111no—
333#382—221no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4—221no—
337C4×C4⋊C4—221no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336—111no—
343#336—111no—
344C22×C11C2×C4×D411yescharacteristic
345C22×C11D4211yescharacteristic
346C22×C11#54811yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57811yescharacteristic
350C22×C11#57811yescharacteristic
351C4×C11—24no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11C2×C4×D411yescharacteristic
358C4×C11#52011yescharacteristic
359C4×C11#54711yescharacteristic
360C4×C11#55311yescharacteristic
361Dic11—22no—
362Dic11—41no—
363Dic11—41no—
364Dic11—42no—
365Dic11—41no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C22×Q8C22×D1111yescharacteristic
370C22×Q8C22×D1111yescharacteristic
371C22×Q8C22×D1111yescharacteristic
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16C2×Dic1114yes—
377C2×Q16C2×Dic1114yes—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—22no—
383C4⋊Q8C2×Dic1114yes—
384C4×Q8—22no—
385C4×Q8—222no—
386C4×Q8—222no—
387C4×Q8—222no—
388C4×Q8—222no—
389C4×Q8—441no—
390C4×Q8—441no—
391C4×Q8—441no—
392C4×Q8—441no—
393C4×Q8C2×Dic1114yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C42—21no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#107—222no—
420#106—222no—
421C4⋊C8C2×Dic1114yes—
422#103—114no—
423#103—222no—
424#103—222no—
425#103—222no—
426#103—441no—
427#103—441no—
428#103C2×Dic1114yes—
429#103C2×Dic1114yes—
430#97—222no—
431#97—222no—
432C4×C8—222no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11#236111yescharacteristic
445C2×C11C4×#13711yescharacteristic
446C2×C11#295011yescharacteristic
447C2×C11#326911yescharacteristic
448C2×C11#327011yescharacteristic
449C2×C11#337411yescharacteristic
450C2×C11#337711yescharacteristic
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8D4×D1112yes—
465C2×Q8#434112yes—
466C2×Q8C22×Dic1112yes—
467C2×Q8C22×Dic1112yes—
468C2×Q8C22×Dic1112yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4D4×D1111yescharacteristic
482C22×C4D4×D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484Q16—28no—
485Q16—28no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—112no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8C22×Dic1112yes—
497C2×C8C22×Dic1112yes—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—21no—
502C4⋊C4—112no—
503C4⋊C4—222no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—441no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4C22×Dic1112yes—
519C42—24no—
520C42—221no—
521C42—221no—
522C42—221no—
523C42—221no—
524C42—442no—
525C42—442no—
526C42—442no—
527C42—442no—
528C42—442no—
529C42#434112yes—
530C42C22×Dic1112yes—
531C11#2301411yescharacteristic, complemented, Sylow
532C23C2×D4×D1111yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—22no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
544Q8D4×Dic1114yes—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—112no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—222no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4D4×Dic1112yes—
586C2×C4D4×Dic1112yes—
587C2×C4C2×D4×D1111yescharacteristic
588C2×C4C2×#434111yescharacteristic
589C2×C4C2×#434111yescharacteristic
590C2×C4#6704211yescharacteristic
591C2×C4#6704311yescharacteristic
592C2×C4C23×Dic1111yescharacteristic
593C8—22no—
594C8—22no—
595C8—222no—
596C8—441no—
597C22#1062312911yescharacteristic
598C22#1062314011yescharacteristic
599C22#1062329711yescharacteristic
600C22#1062329711yescharacteristic
601C22D11×#13711yescharacteristic
602C22#1062330811yescharacteristic
603C22C2×D4×Dic1111yescharacteristic
604C4—24no—
605C4—22no—
606C4—22no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—222no—
611C4—441no—
612C4—441no—
613C4—442no—
614C4—441no—
615C4—881no—
616C4—881no—
617C4—881no—
618C4#1062314211yescharacteristic
619C4#1062314911yescharacteristic
620C4C2×D4×Dic1111yescharacteristic
621C4#1062335811yescharacteristic
622C2#1307163611yescharacteristic
623C2#137×Dic1111yescharacteristic
624C2#1307748411yescharacteristic
625C2#1308016611yescharacteristic
626C2#1308019211yescharacteristic
627C2#1308141411yescharacteristic
628C2#1308145111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#462C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#462D11
hypocenterC11#23014
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
24. C11×#462C4semidirect
306. #462Dic11semidirect
531. C11#23014semidirect

Maximal subgroups

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

subgroupindex
C2×#106227972
C2×Q16×Dic112
#130716762
#130715372
#130694372
#130693862
#130693082
#130692942
#130689592
#130688862
#130688722
#130684932
#130684462
C2×C11×#4622
#2301411