Finite Group Databasebeta

← #14827043

Subgroups — #14827043

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073202C211yesmaximal, characteristic, complemented
2#13071685C211yesmaximal, characteristic, complemented
3#13070148C211yesmaximal, characteristic, complemented
4#13069927C211yesmaximal, characteristic
5#13069858C211yesmaximal, characteristic, complemented
6#13069696C211yesmaximal, characteristic
7#13069470C211yesmaximal, characteristic, complemented
8#13069251C211yesmaximal, characteristic, complemented
9#13069244C211yesmaximal, characteristic, complemented
10#13069202C211yesmaximal, characteristic, complemented
11#13068970C211yesmaximal, characteristic, complemented
12#13068963C211yesmaximal, characteristic
13#13068622C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×D88C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66951—21no—
19C2×#66928C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35#10622607—21no—
36#10622603—21no—
37#10622602—21no—
38#10622552C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622548C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622287—21no—
48#10622283—21no—
49#10622282—21no—
50#10622279—21no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×D88—22no—
96C2×D88—41no—
97C2×D88—41no—
98C2×#4314—22no—
99C2×#4314—22no—
100C2×#4314—41no—
101#66951—44no—
102#66928—22no—
103#66928—22no—
104C4×D44—22no—
105C4×D44—41no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C11×C4⋊C8—41no—
109C4×C8×C11—41no—
110C11×#95D411yescharacteristic
111C11×#95D411yescharacteristic
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66885—22no—
118#66885—22no—
119#66885—22no—
120#66885—41no—
121#66885—41no—
122#66881—22no—
123#66881—41no—
124#66880—22no—
125#66880—41no—
126#66880—41no—
127#27071—111nomaximal, Sylow
128C23×D11—21no—
129C23×D11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44#4112yes—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22#4112yes—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11#4112yes—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
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—
194(C2×D11)⋊C4—81no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205C4⋊Dic11—81no—
206C4⋊Dic11#4112yes—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212D88—44no—
213#4314—44no—
214#2512—111no—
215#2367—111no—
216#2094—111no—
217#2054—111no—
218#2042—111no—
219#2012—111no—
220#1968—111no—
221#1927—111no—
222#1926—111no—
223#1920—111no—
224#1916D1111yescharacteristic, complemented
225#1880—111no—
226#1879—111no—
227#1803—111no—
228C4×#102—111no—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
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—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#13512yes—
261C2×C4×C11AGL(1,ℤ/8)12yes—
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286D44—22no—
287D44—22no—
288D44—41no—
289D44—41no—
290D44—41no—
291D44—41no—
292D44—41no—
293D44—41no—
294C4×D11—84no—
295Dic22—22no—
296Dic22—22no—
297Dic22—41no—
298Dic22—41no—
299C8×C11—22no—
300C8×C11—41no—
301C8×C11—41no—
302C8×C11—41no—
303C22×SD16—111no—
304C22×D8—111no—
305C2×#126—221no—
306C2×#124—111no—
307C2×C4×Q8—111no—
308C2×C4×D4—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×C4×C8C2×D1111yescharacteristic
321#397—221no—
322#396—221no—
323#391—111no—
324#390—111no—
325#390—111no—
326#390—111no—
327#390—111no—
328#389—111no—
329#388—221no—
330#388—221no—
331#388—221no—
332#385—221no—
333#384—111no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4C2×D1111yescharacteristic
337C4×C22⋊C4—221no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336C2×D1111yescharacteristic
343#336C2×D1111yescharacteristic
344#336C2×D1111yescharacteristic
345#336C2×D1111yescharacteristic
346C22×C11#52511yescharacteristic
347C22×C11#54611yescharacteristic
348C22×C11#55011yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C11#57711yescharacteristic
352C22×C11#57711yescharacteristic
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11#52911yescharacteristic
374C4×C11#53811yescharacteristic
375C4×C11#55111yescharacteristic
376C4×C11#55311yescharacteristic
377Dic11—42no—
378Dic11—42no—
379Dic11—81no—
380Dic11—81no—
381Dic11—81no—
382Dic11—81no—
383C22×Q8—111no—
384C22×D4—111no—
385C22×D4—111no—
386C23×C4—221no—
387C2×SD16—222no—
388C2×SD16—222no—
389C2×SD16—441no—
390C2×D8—222no—
391C2×D8—441no—
392C2×D8—441no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397#126—444no—
398#124—222no—
399#124—222no—
400C4×Q8—222no—
401C4×Q8—441no—
402C4×D4—222no—
403C4×D4—441no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4D4411yescharacteristic
414C2×C4⋊C4D4411yescharacteristic
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432#106—222no—
433#106—441no—
434C4⋊C8—41no—
435#103—222no—
436#103—441no—
437#103—441no—
438#102—222no—
439#102—222no—
440#102—222no—
441#102—441no—
442#102—441no—
443C4×C8—41no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95D4411yescharacteristic
450#95D4411yescharacteristic
451C2×C11#246711yescharacteristic
452C2×C11#310611yescharacteristic
453C2×C11#312511yescharacteristic
454C2×C11#330111yescharacteristic
455C2×C11#330611yescharacteristic
456C2×C11#339411yescharacteristic
457C2×C11#339711yescharacteristic
458D11—82no—
459D11—161no—
460C24—221no—
461C24—221no—
462C2×Q8—112no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×D4—112no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—881no—
489C22×C4C2×D4411yescharacteristic
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×D4411yescharacteristic
494C22×C4C2×D4411yescharacteristic
495C22×C4C23×D1111yescharacteristic
496SD16—444no—
497D8—444no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8#434312yes—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—112no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—881no—
526C22⋊C4—224no—
527C22⋊C4—224no—
528C22⋊C4—442no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—881no—
535C22⋊C4—881no—
536C22⋊C4—881no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—442no—
544C42—442no—
545C42—881no—
546C11#2707111yescharacteristic, complemented, Sylow
547C23—222no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23C22×D4411yescharacteristic
562Q8—222no—
563Q8—222no—
564Q8—441no—
565Q8—441no—
566D4—222no—
567D4—222no—
568D4—441no—
569D4—441no—
570D4—441no—
571D4—441no—
572D4—441no—
573D4—441no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
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—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—884no—
609C2×C4#6695712yes—
610C2×C4#6696112yes—
611C2×C4#6703711yescharacteristic
612C2×C4C2×#434311yescharacteristic
613C2×C4#41×D1111yescharacteristic
614C2×C4#41×D1111yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#6704211yescharacteristic
617C8—22no—
618C8—41no—
619C8—41no—
620C8—41no—
621C22—442no—
622C22—442no—
623C22—442no—
624C22—881no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22—881no—
629C22—881no—
630C22—881no—
631C22—881no—
632C22—881no—
633C22—881no—
634C22—881no—
635C22#1062305511yescharacteristic
636C22#1062308511yescharacteristic
637C22#1062310811yescharacteristic
638C22C2×#6695711yescharacteristic
639C22C2×#6696111yescharacteristic
640C22#1062328211yescharacteristic
641C22#1062328211yescharacteristic
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—442no—
649C4—442no—
650C4—881no—
651C4—881no—
652C4—881no—
653C4—881no—
654C4#1062316811yescharacteristic
655C4#1062318811yescharacteristic
656C4#1062322211yescharacteristic
657C4#1062324011yescharacteristic
658C2—882no—
659C2—1761no—
660C2#1307266511yescharacteristic
661C2#1307867711yescharacteristic
662C2#1307889511yescharacteristic
663C2#1308052011yescharacteristic
664C2#1308057911yescharacteristic
665C2#1308161411yescharacteristic
666C2#1308163811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenter#1916D11
hypocenterC11#27071
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. #13073202C2semidirect
2. #13071685C2semidirect
3. #13070148C2semidirect
5. #13069858C2semidirect
7. #13069470C2semidirect
8. #13069251C2semidirect
9. #13069244C2semidirect
10. #13069202C2semidirect
11. #13068970C2semidirect
13. #13068622C2semidirect
14. C4×#66885C2semidirect
15. C11×#1916C2semidirect
224. #1916D11semidirect
546. C11#27071semidirect

Maximal subgroups

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

subgroupindex
#130732022
#130716852
#130701482
#130699272
#130698582
#130696962
#130694702
#130692512
#130692442
#130692022
#130689702
#130689632
#130686222
C4×#668852
C11×#19162
#2707111