Finite Group Databasebeta

← #14823701

Subgroups — #14823701

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622702C211yesmaximal, characteristic
2C2×#10622643C211yesmaximal, characteristic, complemented
3#13072414C211yesmaximal, characteristic
4#13069987C211yesmaximal, characteristic
5#13069946C211yesmaximal, characteristic, complemented
6#13069938C211yesmaximal, characteristic, complemented
7#13069709C211yesmaximal, characteristic
8#13069473C211yesmaximal, characteristic
9#13069312C211yesmaximal, characteristic
10#13069309C211yesmaximal, characteristic, complemented
11#13069291C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic
13#13068883C211yesmaximal, characteristic, complemented
14#13068485C211yesmaximal, characteristic, complemented
15C11×#2451C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66928C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#398—21no—
23C11×#395—21no—
24C11×#391—21no—
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#387—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622702—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×#66872C2211yescharacteristic
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×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—41no—
67C4×Q8×C11—22no—
68C4×Q8×C11—41no—
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#66872—41no—
128C4⋊(C11⋊C8)—22no—
129#66867—22no—
130#66867—22no—
131C4×C11⋊C8—22no—
132#26846—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—42no—
140C2×Q8×C11—42no—
141C2×Q8×C11—81no—
142C2×Q8×C11#4112yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22C2×D412yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—81no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4C2×D412yes—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—42no—
188#4326—28no—
189#4325—44no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200Dic11⋊C4—42no—
201Dic11⋊C4—81no—
202C4×Dic11—42no—
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⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D412yes—
213C2×C11⋊C8#4112yes—
214C2×C11⋊C8#4112yes—
215C2×#489—111no—
216C2×#441—111no—
217#2451D1111yescharacteristic, complemented
218#2448—111no—
219#2065—111no—
220#2058—111no—
221#2056—111no—
222#2015—111no—
223#1968—111no—
224#1936—111no—
225#1935—111no—
226#1933—111no—
227#1880—111no—
228#1865—111no—
229#1770—111no—
230C23×C11C22×D411yescharacteristic
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—84no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
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—21no—
261C2×C4×C11—21no—
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×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11#13712yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×Dic11—22no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288D44—41no—
289D44—41no—
290D44—41no—
291D44—41no—
292Dic22—22no—
293Dic22—22no—
294Dic22—41no—
295Dic22—41no—
296C11⋊C8—22no—
297C11⋊C8—22no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C22×Q16—111no—
301C22×SD16—111no—
302C2×C4⋊Q8C2×D1111yescharacteristic
303C2×#124—111no—
304C2×C4×Q8—111no—
305C2×C4×Q8C2×D1111yescharacteristic
306#489—224no—
307#441—224no—
308C2×#106—111no—
309C2×#106—111no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#97—111no—
320C2×#97—111no—
321C2×C4×C8—111no—
322#399—221no—
323#398—21no—
324#397—221no—
325#395—21no—
326#391—21no—
327#391—111no—
328#391C2×D1111yescharacteristic
329#391C2×D1111yescharacteristic
330#390—111no—
331#390—111no—
332#389—111no—
333#389C2×D1111yescharacteristic
334#389C2×D1111yescharacteristic
335#388—221no—
336#388—221no—
337#387—21no—
338C4×C4⋊C4C2×D1111yescharacteristic
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#336—111no—
344#336—111no—
345C22×C11#53211yescharacteristic
346C22×C11D4211yescharacteristic
347C22×C11#54811yescharacteristic
348C22×C11C2×#13711yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57711yescharacteristic
351C22×C11#57711yescharacteristic
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C4×C11—22no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11#52511yescharacteristic
370C4×C11#54211yescharacteristic
371C4×C11#54711yescharacteristic
372C4×C11#55111yescharacteristic
373Dic11—42no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—21no—
377C22×Q8—111no—
378C22×Q8C22×D1111yescharacteristic
379C22×D4—111no—
380C2×Q16—222no—
381C2×Q16—222no—
382C2×Q16—222no—
383C2×SD16—222no—
384C2×SD16—222no—
385C2×SD16—441no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—111no—
390C4⋊Q8—22no—
391C4⋊Q8—41no—
392#124—222no—
393#124—441no—
394C4×Q8—22no—
395C4×Q8—41no—
396C4×Q8—222no—
397C4×Q8—441no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22⋊D1111yescharacteristic
407C2×C4⋊C4C22⋊D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C42—21no—
418C2×C42—221no—
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422#106—222no—
423#106—441no—
424C4⋊C8—222no—
425#103—114no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—222no—
430#102—222no—
431#102—222no—
432#102—222no—
433#97—222no—
434#97—222no—
435C4×C8—222no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95C22⋊D1111yescharacteristic
446#95C22⋊D1111yescharacteristic
447C2×C11#246111yescharacteristic
448C2×C11#317311yescharacteristic
449C2×C11#318111yescharacteristic
450C2×C11#327511yescharacteristic
451C2×C11#327811yescharacteristic
452C2×C11#336911yescharacteristic
453C2×C11#337111yescharacteristic
454D11—161no—
455C24—221no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—81no—
464C2×Q8—112no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8#434312yes—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C23×D1111yescharacteristic
491Q16—228no—
492SD16—444no—
493C2×C8—112no—
494C2×C8—112no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—442no—
521C4⋊C4—881no—
522C4⋊C4D4×D1112yes—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—42no—
536C42—442no—
537C11#2684611yescharacteristic, complemented, Sylow
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23C22×C22⋊D1111yescharacteristic
546Q8—22no—
547Q8—22no—
548Q8—41no—
549Q8—41no—
550Q8—84no—
551Q8—222no—
552Q8—222no—
553Q8—441no—
554Q8—441no—
555D4—441no—
556D4—441no—
557D4—441no—
558D4—441no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—222no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4#6699512yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4#6703711yescharacteristic
600C2×C4C2×#434311yescharacteristic
601C2×C4#6704011yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C8—222no—
605C8—222no—
606C8—222no—
607C8—441no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22D4×C22⋊D1111yescharacteristic
616C22C2×#6699511yescharacteristic
617C22#1062334811yescharacteristic
618C22#1062335311yescharacteristic
619C22#1062336311yescharacteristic
620C22#1062336711yescharacteristic
621C22#1062336811yescharacteristic
622C4—22no—
623C4—41no—
624C4—41no—
625C4—42no—
626C4—41no—
627C4—42no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4—81no—
632C4—442no—
633C4—881no—
634C4—881no—
635C4#1062315811yescharacteristic
636C4#1062316211yescharacteristic
637C4#1062316811yescharacteristic
638C4#1062317111yescharacteristic
639C2—1761no—
640C2#1307259011yescharacteristic
641C2#1307922711yescharacteristic
642C2#1307931911yescharacteristic
643C2#1308024311yescharacteristic
644C2#1308027811yescharacteristic
645C2#1308135611yescharacteristic
646C2#1308138411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2451C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2451D11
hypocenterC11#26846
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2451

Complements

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

NH ≅ G/Ntype
2. C2×#10622643C2semidirect
5. #13069946C2semidirect
6. #13069938C2semidirect
10. #13069309C2semidirect
11. #13069291C2semidirect
13. #13068883C2semidirect
14. #13068485C2semidirect
15. C11×#2451C2semidirect
217. #2451D11semidirect
537. C11#26846semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
C2×#106226432
#130724142
#130699872
#130699462
#130699382
#130697092
#130694732
#130693122
#130693092
#130692912
#130689712
#130688832
#130684852
C11×#24512
#2684611