Finite Group Databasebeta

← #14823596

Subgroups — #14823596

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622681C211yesmaximal, characteristic
2C2×#10622643C211yesmaximal, characteristic, complemented
3#13072414C211yesmaximal, characteristic
4#13069987C211yesmaximal, characteristic
5#13069951C211yesmaximal, characteristic, complemented
6#13069938C211yesmaximal, characteristic, complemented
7#13069709C211yesmaximal, characteristic
8#13069500C211yesmaximal, characteristic
9#13069312C211yesmaximal, characteristic
10#13069305C211yesmaximal, characteristic, complemented
11#13069295C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic
13#13068869C211yesmaximal, characteristic, complemented
14#13068491C211yesmaximal, characteristic, complemented
15C11×#2453C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66928C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#400—21no—
23C11×#398—21no—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#389—21no—
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#387—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622681—24no—
34#10622643—24no—
35#10622605—21no—
36#10622603—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622288—21no—
54#10622282—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C11×#125—22no—
65C11×#125—41no—
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83C2×#4326—22no—
84C2×#4326—22no—
85C2×#4325—22no—
86C2×#4325—22no—
87C2×#4325—41no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66928—22no—
104#66928—41no—
105C4×Dic22—22no—
106C4×Dic22—41no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115#66899—22no—
116#66899—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66874—22no—
121#66874—22no—
122#66874D414yes—
123#66873—22no—
124#66873—22no—
125#66873—22no—
126#66872—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129#66867—22no—
130#66867—22no—
131C4×C11⋊C8—22no—
132#26839—111nomaximal, Sylow
133C23×D11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C2×D412yes—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4C2×D412yes—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186#4326—28no—
187#4325—44no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—81no—
193(C2×D11)⋊C4—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200C4×Dic11—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×D412yes—
211C2×C11⋊C8#4112yes—
212C2×C11⋊C8#4112yes—
213C2×#488—111no—
214C2×#441—111no—
215#2453D1111yescharacteristic, complemented
216#2448—111no—
217#2065—111no—
218#2059—111no—
219#2056—111no—
220#2015—111no—
221#1973—111no—
222#1936—111no—
223#1935—111no—
224#1933—111no—
225#1880—111no—
226#1863—111no—
227#1771—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
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—22no—
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—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285D44—41no—
286D44—41no—
287D44—41no—
288D44—41no—
289Dic22—22no—
290Dic22—22no—
291Dic22—41no—
292Dic22—41no—
293C11⋊C8—22no—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C22×Q16—111no—
298C22×SD16—111no—
299C2×#125C2×D1111yescharacteristic
300C2×#124—111no—
301C2×C4×Q8—111no—
302C2×C4×Q8C2×D1111yescharacteristic
303#488—224no—
304#441—224no—
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×#97—111no—
317C2×#97—111no—
318C2×C4×C8—111no—
319#400—21no—
320#399—221no—
321#398—21no—
322#397—221no—
323#391—111no—
324#391C2×D1111yescharacteristic
325#391C2×D1111yescharacteristic
326#390—111no—
327#390—111no—
328#389—21no—
329#389—111no—
330#389C2×D1111yescharacteristic
331#389C2×D1111yescharacteristic
332#388—221no—
333#388—221no—
334#387—21no—
335C4×C4⋊C4C2×D1111yescharacteristic
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#336—111no—
341#336—111no—
342C22×C11#53211yescharacteristic
343C22×C11D4211yescharacteristic
344C22×C11#54811yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57511yescharacteristic
347C22×C11#57711yescharacteristic
348C22×C11#57811yescharacteristic
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11#52511yescharacteristic
367C4×C11#54211yescharacteristic
368C4×C11#54711yescharacteristic
369C4×C11#55111yescharacteristic
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373C22×Q8—111no—
374C22×Q8C22×D1111yescharacteristic
375C22×D4—111no—
376C2×Q16—222no—
377C2×Q16—222no—
378C2×Q16—222no—
379C2×SD16—222no—
380C2×SD16—222no—
381C2×SD16—441no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8—111no—
385C22×C8—111no—
386#125—22no—
387#125—41no—
388#124—222no—
389#124—441no—
390C4×Q8—22no—
391C4×Q8—41no—
392C4×Q8—222no—
393C4×Q8—441no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C22⋊D1111yescharacteristic
404C2×C4⋊C4C22⋊D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C42—21no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#107—441no—
420#106—222no—
421C4⋊C8—222no—
422#103—114no—
423#103—222no—
424#103—222no—
425#103—222no—
426#103—222no—
427#102—222no—
428#102—222no—
429#102—222no—
430#97—222no—
431#97—222no—
432C4×C8—222no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95C22⋊D1111yescharacteristic
443#95C22⋊D1111yescharacteristic
444C2×C11#246111yescharacteristic
445C2×C11#317811yescharacteristic
446C2×C11#318311yescharacteristic
447C2×C11#326911yescharacteristic
448C2×C11#327111yescharacteristic
449C2×C11#337111yescharacteristic
450C2×C11#337711yescharacteristic
451D11—161no—
452C24—221no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—112no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8#434312yes—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485Q16—228no—
486SD16—444no—
487C2×C8—112no—
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—442no—
516C4⋊C4—881no—
517C4⋊C4D4×D1112yes—
518C22⋊C4—442no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—881no—
523C22⋊C4—881no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—42no—
531C42—442no—
532C11#2683911yescharacteristic, complemented, Sylow
533C23—441no—
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23C22×C22⋊D1111yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—222no—
546Q8—222no—
547Q8—441no—
548Q8—441no—
549D4—441no—
550D4—441no—
551D4—441no—
552D4—441no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
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—41no—
582C2×C4—41no—
583C2×C4—222no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4#6703711yescharacteristic
594C2×C4C2×#434311yescharacteristic
595C2×C4#6704011yescharacteristic
596C2×C4#41×D1111yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C8—222no—
599C8—222no—
600C8—222no—
601C8—441no—
602C22—881no—
603C22—881no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22—881no—
608C22—881no—
609C22D4×C22⋊D1111yescharacteristic
610C22#1062334811yescharacteristic
611C22#1062335311yescharacteristic
612C22#1062335311yescharacteristic
613C22#1062336311yescharacteristic
614C22#1062336811yescharacteristic
615C22#1062336911yescharacteristic
616C4—41no—
617C4—41no—
618C4—41no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—442no—
627C4—881no—
628C4—881no—
629C4#1062315811yescharacteristic
630C4#1062316211yescharacteristic
631C4#1062316811yescharacteristic
632C4#1062317111yescharacteristic
633C2—1761no—
634C2#1307259011yescharacteristic
635C2#1307928611yescharacteristic
636C2#1307933911yescharacteristic
637C2#1308016711yescharacteristic
638C2#1308020211yescharacteristic
639C2#1308138411yescharacteristic
640C2#1308145811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2453C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2453D11
hypocenterC11#26839
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2453

Complements

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

NH ≅ G/Ntype
2. C2×#10622643C2semidirect
5. #13069951C2semidirect
6. #13069938C2semidirect
10. #13069305C2semidirect
11. #13069295C2semidirect
13. #13068869C2semidirect
14. #13068491C2semidirect
15. C11×#2453C2semidirect
215. #2453D11semidirect
532. C11#26839semidirect

Maximal subgroups

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

subgroupindex
C2×#106226812
C2×#106226432
#130724142
#130699872
#130699512
#130699382
#130697092
#130695002
#130693122
#130693052
#130692952
#130689712
#130688692
#130684912
C11×#24532
#2683911