Finite Group Databasebeta

← #14725073

Subgroups — #14725073

Order 2816.

656 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
1#13078612C211yesmaximal, characteristic
2#13077650C211yesmaximal, characteristic, complemented
3#13067528C211yesmaximal, characteristic, complemented
4#13067499C211yesmaximal, characteristic, complemented
5#13067480C211yesmaximal, characteristic, complemented
6#13067478C211yesmaximal, characteristic, complemented
7#13067445C211yesmaximal, characteristic, complemented
8#13067443C211yesmaximal, characteristic, complemented
9#13067438C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067394C211yesmaximal, characteristic, complemented
12#13067085C211yesmaximal, characteristic, complemented
13#13067006C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2979C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#436—21no—
19C11×#436C2211yescharacteristic, complemented
20C11×#436C2211yescharacteristic, complemented
21C8×D4×C11—21no—
22C8×D4×C11C2211yescharacteristic, complemented
23C8×D4×C11C2211yescharacteristic, complemented
24C11×#431C2211yescharacteristic
25C11×#431C2211yescharacteristic
26C11×#408—21no—
27C11×#408—21no—
28#10622700C411yescharacteristic
29#10622700C411yescharacteristic
30#10622685C411yescharacteristic
31#10622685C411yescharacteristic
32#10622649C411yescharacteristic
33#10622649C411yescharacteristic
34#10622646C411yescharacteristic
35#10622646C411yescharacteristic
36C4×#4323C2211yescharacteristic
37C4×#4323C2211yescharacteristic
38C4×#4323C2211yescharacteristic
39C4×#4323C2211yescharacteristic
40#10622539C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622449—21no—
44#10622449—21no—
45#10622339—21no—
46D11×C22⋊C8—21no—
47#10622301C2211yescharacteristic
48#10622301C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C8×D44C2211yescharacteristic
51D4⋊(C11⋊C8)C2211yescharacteristic, complemented
52D4⋊(C11⋊C8)C2211yescharacteristic, complemented
53D4⋊(C11⋊C8)C2211yescharacteristic, complemented
54D4⋊(C11⋊C8)C2211yescharacteristic, complemented
55#10622121C2211yescharacteristic
56#10622121C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622117C2211yescharacteristic, complemented
62#10622117C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C22×D44C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C11×C4⋊Q8C2×C411yescharacteristic
75C11×#127C2×C411yescharacteristic
76C11×#124—21no—
77C11×#121—21no—
78C11×#121C2×C411yescharacteristic
79C11×#121C2×C411yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11C2311yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4323C2×C411yescharacteristic
85C2×#4323C2×C411yescharacteristic
86C2×#4323C2×C411yescharacteristic
87C2×#4323C2×C411yescharacteristic
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11C2×C411yescharacteristic
90C2×#4313—21no—
91C2×#4313—21no—
92C2×C8×D11—21no—
93C2×C8×D11—21no—
94C4×D44—21no—
95C4×D44—21no—
96C4×D44C2×C411yescharacteristic
97C4×D44C2×C411yescharacteristic
98C4×D44C2311yescharacteristic
99C4×D44C2311yescharacteristic
100C11×C4⋊C8D411yescharacteristic
101C11×C4⋊C8D411yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66896C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)C2×C411yescharacteristic
121C22⋊(C11⋊C8)C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126#66873C2×C411yescharacteristic
127#66873C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66871C2×C411yescharacteristic
131#66871C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18026—111nomaximal, Sylow
145C23×D11—21no—
146C11×#41—81no—
147C11×#41—81no—
148C2×Q8×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11C22×C411yescharacteristic
154C2×D4×C11C22×C411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×Dic11—21no—
161C2×D44—22no—
162C2×D44—21no—
163C2×D44—41no—
164C2×D44C22×C411yescharacteristic
165C2×D44C22×C411yescharacteristic
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—81no—
171C2×C4×D11—81no—
172C11×M16—81no—
173C11×M16—81no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—81no—
177C2×C8×C11—81no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C11×C4⋊C4—21no—
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C4⋊C4C22×C411yescharacteristic
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C42×C11C22×C411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11#4111yescharacteristic
192C42×C11C2411yescharacteristic
193#4323—22no—
194#4323—22no—
195#4323—41no—
196#4323—41no—
197(C2×D11)⋊C4—21no—
198(C2×D11)⋊C4—21no—
199(C2×D11)⋊C4—21no—
200(C2×D11)⋊C4—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C22×C411yescharacteristic
203C4⋊Dic11C22×C411yescharacteristic
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C22×C411yescharacteristic
212#4313—81no—
213#4313—81no—
214C8×D11—81no—
215C8×D11—81no—
216#3100—111no—
217#2979D1111yescharacteristic, complemented
218#2974—111no—
219#1594—111no—
220#1589—111no—
221#1586—111no—
222#1586—111no—
223#1581—111no—
224#1581—111no—
225#1580—111no—
226C8×D8—111no—
227#1572—111no—
228#1496—111no—
229#1478—111no—
230#1454—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11C4×D411yescharacteristic
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—81no—
239Q8×C11—81no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—42no—
245D4×C11—81no—
246D4×C11—81no—
247D4×C11—81no—
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—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C4×D411yescharacteristic
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—81no—
268D44—21no—
269D44—21no—
270D44—21no—
271D44—42no—
272D44#13112yes—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—41no—
277C4×D11—81no—
278C4×D11—81no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—41no—
284C8×C11—41no—
285C11⋊C8—21no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293#532C2×D1111yescharacteristic
294C2×C4×D4—111no—
295#480—111no—
296#480—111no—
297#474—111no—
298#474—111no—
299#459—111no—
300#459—111no—
301#447—111no—
302#447—111no—
303C4×D8—111no—
304C4×D8—111no—
305C4×D8—111no—
306C4×D8—111no—
307#436—21no—
308#436—111no—
309#436—111no—
310#436C2×D1111yescharacteristic, complemented
311#436C2×D1111yescharacteristic, complemented
312#435—221no—
313#435—221no—
314C8×D4—21no—
315C8×D4—111no—
316C8×D4—111no—
317C8×D4C2×D1111yescharacteristic, complemented
318C8×D4C2×D1111yescharacteristic, complemented
319#432—111no—
320#431—111no—
321#431—111no—
322#431C2×D1111yescharacteristic
323#431C2×D1111yescharacteristic
324#408—21no—
325#408—21no—
326#407—221no—
327C2×C22⋊C8—221no—
328#335—111no—
329#335—111no—
330#334—111no—
331#334—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8—111no—
340#322—111no—
341#322—111no—
342#322—111no—
343C82—111no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11C2×C4×D411yescharacteristic
354C2×D11—22no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—84no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11C2×#13111yescharacteristic
368C4×C11#56811yescharacteristic
369C4×C11#57611yescharacteristic
370C4×C11#57611yescharacteristic
371Dic11—41no—
372Dic11—41no—
373C2×#41—21no—
374C22×D4—111no—
375C23×C4—221no—
376C2×D8—111no—
377C2×D8—111no—
378C2×D8—111no—
379C2×D8—111no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—221no—
383C2×M16—221no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—221no—
387C22×C8—221no—
388C4⋊Q8C4×D1111yescharacteristic
389#127C4×D1111yescharacteristic
390#124—21no—
391#121—21no—
392#121C4×D1111yescharacteristic
393#121C4×D1111yescharacteristic
394C4×D4—21no—
395C4×D4—111no—
396C4×D4—111no—
397C4×D4—111no—
398C4×D4—111no—
399C4×D4—221no—
400C4×D4—221no—
401C4×D4C22×D1111yescharacteristic
402C4×D4C22×D1111yescharacteristic
403C2×C4⋊C4—111no—
404C2×C22⋊C4—221no—
405C2×C42C22×D1111yescharacteristic
406#107—111no—
407#107—111no—
408#107—111no—
409#107—111no—
410C4⋊C8—111no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—221no—
415C4⋊C8C22⋊D1111yescharacteristic
416C4⋊C8C22⋊D1111yescharacteristic
417C4⋊C8C22×D1111yescharacteristic
418C4⋊C8C22×D1111yescharacteristic
419#102—111no—
420#102—111no—
421#102—111no—
422#102—111no—
423#102—111no—
424#102—111no—
425#102—111no—
426#102—111no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—111no—
433C22⋊C8—111no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438C22⋊C8—221no—
439C22⋊C8—221no—
440C22⋊C8C22⋊D1111yescharacteristic
441C22⋊C8C22⋊D1111yescharacteristic
442#97—221no—
443C4×C8—21no—
444C4×C8—111no—
445C4×C8—111no—
446C4×C8—111no—
447C4×C8—111no—
448C4×C8C22×D1111yescharacteristic
449C4×C8C22×D1111yescharacteristic
450C2×C11—41no—
451C2×C11—81no—
452C2×C11—81no—
453C2×C11#293311yescharacteristic
454C2×C11#294811yescharacteristic
455C2×C11#295511yescharacteristic
456D11—42no—
457D11—81no—
458C24—221no—
459#41—81no—
460#41—81no—
461C2×Q8—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—111no—
467C2×D4—111no—
468C2×D4—222no—
469C2×D4—221no—
470C2×D4—441no—
471C2×D4C2×C4×D1111yescharacteristic
472C2×D4C2×C4×D1111yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—881no—
481C22×C4—881no—
482C22×C4C2×C4×D1111yescharacteristic
483C22×C4#433911yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485D8—222no—
486D8—222no—
487D8—441no—
488D8—441no—
489M16—81no—
490M16—81no—
491M16—881no—
492M16—881no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—81no—
496C2×C8—81no—
497C2×C8—111no—
498C2×C8—111no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—881no—
506C2×C8—881no—
507C2×C8C2×C22⋊D1111yescharacteristic
508C2×C8C2×C22⋊D1111yescharacteristic
509C2×C8C2×C22⋊D1111yescharacteristic
510C2×C8C2×C22⋊D1111yescharacteristic
511C4⋊C4—21no—
512C4⋊C4—111no—
513C4⋊C4—111no—
514C4⋊C4—221no—
515C4⋊C4C2×C4×D1111yescharacteristic
516C4⋊C4C2×C4×D1111yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—221no—
522C22⋊C4—221no—
523C22⋊C4—221no—
524C22⋊C4—221no—
525C42C2×C4×D1111yescharacteristic
526C42#433911yescharacteristic
527C42C2×C22⋊D1111yescharacteristic
528C42C23×D1111yescharacteristic
529C11#1802611yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—221no—
533C23—221no—
534C23—442no—
535C23—442no—
536C23—881no—
537C23C4×C22⋊D1111yescharacteristic
538Q8—81no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—42no—
544D4—81no—
545D4—81no—
546D4—81no—
547D4—112no—
548D4—221no—
549D4—221no—
550D4—221no—
551D4—442no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—881no—
570C2×C4—881no—
571C2×C4—881no—
572C2×C4C4×C22⋊D1111yescharacteristic
573C2×C4C4×C22⋊D1111yescharacteristic
574C2×C4C4×C22⋊D1111yescharacteristic
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C2×#433911yescharacteristic
577C2×C4C22×C22⋊D1111yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—221no—
585C8—221no—
586C8—221no—
587C8—221no—
588C8—441no—
589C8—441no—
590C8—441no—
591C8—441no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—222no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22—441no—
606C22—441no—
607C22—884no—
608C22C2×C4×C22⋊D1111yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—441no—
616C4—441no—
617C4D11×#13111yescharacteristic
618C4#1062328111yescharacteristic
619C4#1062336611yescharacteristic
620C4#1062336611yescharacteristic
621C2—41no—
622C2—81no—
623C2—81no—
624C2—442no—
625C2—881no—
626C2#1307733811yescharacteristic
627C2#1307746611yescharacteristic
628C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2979C2
socleC22×C11C2×C4×D4
prime radical#13078612C2
cosocleC42×C11C24
hypercenter#2979D11
hypocenterC11#18026
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #13077650C2semidirect
3. #13067528C2semidirect
4. #13067499C2semidirect
5. #13067480C2semidirect
6. #13067478C2semidirect
7. #13067445C2semidirect
8. #13067443C2semidirect
9. #13067438C2semidirect
10. C8×#4323C2semidirect
11. #13067394C2semidirect
12. #13067085C2semidirect
13. #13067006C2semidirect
14. #13066916C2semidirect
15. C11×#2979C2semidirect
19. C11×#436C22semidirect
20. C11×#436C22semidirect
22. C8×D4×C11C22semidirect
23. C8×D4×C11C22semidirect
51. D4⋊(C11⋊C8)C22semidirect
52. D4⋊(C11⋊C8)C22semidirect
53. D4⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
217. #2979D11semidirect
310. #436C2×D11semidirect
311. #436C2×D11semidirect
317. C8×D4C2×D11semidirect
318. C8×D4C2×D11semidirect
529. C11#18026semidirect

Maximal subgroups

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

subgroupindex
#130786122
#130776502
#130675282
#130674992
#130674802
#130674782
#130674452
#130674432
#130674382
C8×#43232
#130673942
#130670852
#130670062
#130669162
C11×#29792
#1802611