Finite Group Databasebeta

← #14776265

Subgroups — #14776265

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×#10622406C211yesmaximal, characteristic
2C2×#10622329C211yesmaximal, characteristic
3C2×#10622403C211yesmaximal, characteristic
4#13071673C211yesmaximal, characteristic
5#13071535C211yesmaximal, characteristic
6#13069434C211yesmaximal, characteristic
7#13069383C211yesmaximal, characteristic
8#13069293C211yesmaximal, characteristic
9#13068960C211yesmaximal, characteristic
10#13068958C211yesmaximal, characteristic
11#13068886C211yesmaximal, characteristic
12#13068869C211yesmaximal, characteristic
13#13068492C211yesmaximal, characteristic
14#13068445C211yesmaximal, characteristic
15C11×#1935C211yesmaximal, characteristic
16C2×Q8×Dic11C2211yescharacteristic
17C2×#66997C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×Dic44C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622590C2211yescharacteristic
38C4⋊C4×Dic11—21no—
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622585—21no—
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C4×Dic11⋊C4C2211yescharacteristic
47#10622406C418yescomplemented
48#10622403—24no—
49#10622329—24no—
50#10622268—21no—
51#10622265—21no—
52#10622263—21no—
53#10622262—21no—
54#10622260—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72Q8×Dic11—22no—
73Q8×Dic11—41no—
74#66997—22no—
75#66997C2×C414yes—
76C2×#4326—22no—
77C2×#4326—22no—
78C2×#4326C2×C414yes—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4D411yescharacteristic
90C2×Dic11⋊C4D411yescharacteristic
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×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×Dic44—22no—
102C2×Dic44—22no—
103C2×Dic44C2×C414yes—
104#66940—22no—
105#66940—22no—
106#66940—41no—
107#66940C2×C414yes—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—41no—
111C4×Dic22—41no—
112C11×#103—22no—
113C11×#103C2×C414yes—
114C11×#97—22no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118#66899—41no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127#66881—22no—
128#66880—22no—
129#66880D414yes—
130#66879—22no—
131Dic11⋊C8C2×C414yes—
132C8×Dic11—22no—
133#66874—22no—
134#66874—41no—
135#66874C2×C414yes—
136#66871—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×C11C22×C412yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22C22×C412yes—
168C2×Dic22C22×C412yes—
169C2×Dic22C2×D412yes—
170C2×Dic22#4112yes—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C22×C412yes—
176C2×C8×C11C2×D412yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4C22×C412yes—
184C42×C11—21no—
185C42×C11—21no—
186#4326—28no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—42no—
191C4⋊Dic11—42no—
192C4⋊Dic11C2×D412yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195Dic11⋊C4—24no—
196Dic11⋊C4—22no—
197Dic11⋊C4—41no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201C4×Dic11—24no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11C22×C412yes—
210C4×Dic11#4112yes—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C22×C412yes—
217Dic44—28no—
218C2×#462—111no—
219C2×#441—111no—
220C2×C4×Q16—111no—
221#2365—111no—
222#2351—111no—
223#1960—111no—
224#1949—111no—
225#1935D1111yescharacteristic
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—41no—
237Q8×C11—41no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
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×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11C4×D412yes—
284C2×Dic11C4×D412yes—
285C2×Dic11#13712yes—
286Dic22—22no—
287Dic22—22no—
288Dic22—22no—
289Dic22—22no—
290Dic22—22no—
291Dic22—41no—
292Dic22—41no—
293Dic22C4×D414yes—
294C8×C11—22no—
295C8×C11—22no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×Q16—111no—
299C22×Q16—111no—
300C2×C4⋊Q8—111no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×Q8—111no—
305C2×C4×Q8—111no—
306#462—118no—
307#441—224no—
308C4×Q16—224no—
309C2×#107—111no—
310C2×#106—111no—
311C2×C4⋊C8—111no—
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×#97C2×D1111yescharacteristic
322C2×C4×C8—111no—
323#391—111no—
324#391C2×D1111yescharacteristic
325#389—111no—
326#389—221no—
327#389—221no—
328#389—221no—
329#389C2×D1111yescharacteristic
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#340C2×D1111yescharacteristic
341#340C2×D1111yescharacteristic
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—42no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11C2×C4×D411yescharacteristic
358C4×C11#52011yescharacteristic
359C4×C11#54711yescharacteristic
360C4×C11#55311yescharacteristic
361Dic11—24no—
362Dic11—22no—
363Dic11—22no—
364Dic11—22no—
365Dic11—42no—
366Dic11—41no—
367Dic11—42no—
368Dic11—81no—
369C22×Q8—111no—
370C22×Q8—111no—
371C22×Q8C22×D1111yescharacteristic
372C2×Q16—114no—
373C2×Q16—114no—
374C2×Q16—222no—
375C2×Q16—222no—
376C2×Q16—222no—
377C2×Q16—222no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—114no—
383C4⋊Q8—222no—
384C4×Q8—114no—
385C4×Q8—222no—
386C4×Q8—222no—
387C4×Q8—222no—
388C4×Q8—222no—
389C4×Q8—222no—
390C4×Q8—441no—
391C4×Q8—441no—
392C4×Q8—441no—
393C4×Q8—441no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—221no—
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⋊C8—114no—
422#103—22no—
423#103—114no—
424#103—114no—
425#103—222no—
426#103—222no—
427#103—441no—
428#103—441no—
429#103C4×D1114yes—
430#97—22no—
431#97—222no—
432C4×C8—222no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—111no—
437#95—111no—
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—112no—
457C2×Q8—112no—
458C2×Q8—112no—
459C2×Q8—112no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8C2×C4×D1112yes—
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—228no—
485Q16—228no—
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×C8C2×C4×D1112yes—
497C2×C8D4×D1112yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—112no—
505C4⋊C4—222no—
506C4⋊C4—224no—
507C4⋊C4—224no—
508C4⋊C4—224no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—441no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4C2×C4×D1112yes—
519C42—21no—
520C42—21no—
521C42—112no—
522C42—112no—
523C42—224no—
524C42—221no—
525C42—221no—
526C42—442no—
527C42—442no—
528C42—442no—
529C42—442no—
530C42—442no—
531C11#2301411yescharacteristic, complemented, Sylow
532C23C2×D4×D1111yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—41no—
536Q8—41no—
537Q8—114no—
538Q8—222no—
539Q8—222no—
540Q8—222no—
541Q8—222no—
542Q8—222no—
543Q8—441no—
544Q8—441no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—222no—
572C2×C4—221no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—222no—
578C2×C4—221no—
579C2×C4—222no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4C22×C4×D1111yescharacteristic
588C2×C4C2×D4×D1111yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#6704211yescharacteristic
592C2×C4#6704311yescharacteristic
593C8—22no—
594C8—22no—
595C8—222no—
596C8—441no—
597C22C4×D4×D1111yescharacteristic
598C22#1062314011yescharacteristic
599C22#1062320811yescharacteristic
600C22#1062330411yescharacteristic
601C22D11×#13711yescharacteristic
602C22#1062331011yescharacteristic
603C22#1062331011yescharacteristic
604C4—42no—
605C4—41no—
606C4—41no—
607C4—42no—
608C4—81no—
609C4—81no—
610C4—224no—
611C4—222no—
612C4—222no—
613C4—222no—
614C4—442no—
615C4—441no—
616C4—442no—
617C4—881no—
618C4#1062305411yescharacteristic
619C4C4×D4×D1111yescharacteristic
620C4#1062318611yescharacteristic
621C4#1062324011yescharacteristic
622C2#1307162911yescharacteristic
623C2#1307743811yescharacteristic
624C2#1307748111yescharacteristic
625C2#1308017811yescharacteristic
626C2#1308019311yescharacteristic
627C2#1308141611yescharacteristic
628C2#1308145711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1935C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1935D11
hypocenterC11#23014
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
47. #10622406C4semidirect
531. C11#23014semidirect

Maximal subgroups

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

subgroupindex
C2×#106224062
C2×#106223292
C2×#106224032
#130716732
#130715352
#130694342
#130693832
#130692932
#130689602
#130689582
#130688862
#130688692
#130684922
#130684452
C11×#19352
#2301411