Finite Group Databasebeta

← #14725081

Subgroups — #14725081

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#13078617C211yesmaximal, characteristic
2#13077682C211yesmaximal, characteristic, complemented
3#13077650C211yesmaximal, characteristic, complemented
4#13067531C211yesmaximal, characteristic, complemented
5#13067502C211yesmaximal, characteristic, complemented
6#13067482C211yesmaximal, characteristic, complemented
7#13067482C211yesmaximal, characteristic, complemented
8#13067447C211yesmaximal, characteristic, complemented
9#13067447C211yesmaximal, characteristic, complemented
10#13067441C211yesmaximal, characteristic, complemented
11C8×D88C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067086C211yesmaximal, characteristic, complemented
14#13067008C211yesmaximal, characteristic, complemented
15C11×#1454C211yesmaximal, characteristic, complemented
16#10623008C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622459C411yescharacteristic
24#10622459C411yescharacteristic
25#10622456C411yescharacteristic
26#10622456C411yescharacteristic
27#10622451—21no—
28#10622449—21no—
29#10622449—21no—
30#10622447—21no—
31#10622349C411yescharacteristic
32#10622349C411yescharacteristic
33#10622345C411yescharacteristic
34#10622345C411yescharacteristic
35#10622340—21no—
36#10622340—21no—
37#10622339—21no—
38D11×C22⋊C8—21no—
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic
41C4×D88C2211yescharacteristic
42C4×D88C2211yescharacteristic
43#10622301C2211yescharacteristic
44#10622301C2211yescharacteristic
45#10622301C2211yescharacteristic, complemented
46#10622301C2211yescharacteristic, complemented
47C8×D44C2211yescharacteristic
48C8×D44C2211yescharacteristic
49C8×D44C2211yescharacteristic, complemented
50C8×D44C2211yescharacteristic, complemented
51C11×#322C2211yescharacteristic, complemented
52C11×#322C2211yescharacteristic, complemented
53C11×#322C2211yescharacteristic, complemented
54C82×C11C2211yescharacteristic, complemented
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622097C2211yescharacteristic
58#10622097C2211yescharacteristic
59#10622097C2211yescharacteristic, complemented
60#10622097C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic, complemented
62#10622097C2211yescharacteristic, complemented
63#10622096C2211yescharacteristic, complemented
64#10622096C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622095C2211yescharacteristic, complemented
67C2×#4339—21no—
68C22×D44C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C42×C11C2311yescharacteristic
71#66983—21no—
72#66983C2×C411yescharacteristic
73#66983C2×C411yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×D88C2×C411yescharacteristic
77C2×D88C2×C411yescharacteristic
78C2×D88C2×C411yescharacteristic
79C2×D88C2×C411yescharacteristic
80C2×#4313—21no—
81C2×#4313—21no—
82C2×#4313—21no—
83C2×#4313—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88#66928—21no—
89#66927C2×C411yescharacteristic
90C4×D44—21no—
91C4×D44—21no—
92C4×D44—21no—
93C4×D44C2×C411yescharacteristic
94C4×D44C2×C411yescharacteristic
95C4×D44C2311yescharacteristic
96C4×D44C2311yescharacteristic
97C4×D44C2311yescharacteristic
98C4×D44C2311yescharacteristic
99#66922C2×C411yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2×C411yescharacteristic
102C11×C4⋊C8C2×C411yescharacteristic
103C11×C4⋊C8D411yescharacteristic
104C11×C4⋊C8D411yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8C2×C411yescharacteristic
107C11×C22⋊C8C2×C411yescharacteristic
108C11×C22⋊C8D411yescharacteristic
109C11×C22⋊C8D411yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C22⋊(C11⋊C8)—21no—
117C22⋊(C11⋊C8)—21no—
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122#66885C2×C411yescharacteristic
123#66885C2×C411yescharacteristic
124#66885C2×C411yescharacteristic
125#66885C2×C411yescharacteristic
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8—21no—
129(C2×D11)⋊C8—21no—
130(C2×D11)⋊C8—21no—
131(C2×D11)⋊C8—21no—
132(C2×D11)⋊C8—21no—
133(C2×D11)⋊C8—21no—
134#66882C2×C411yescharacteristic
135#66882C2×C411yescharacteristic
136#66882C2×C411yescharacteristic
137#66882C2×C411yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#18026—111nomaximal, Sylow
145C23×D11—21no—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152#4339—81no—
153#4339—81no—
154C2×D44—22no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—41no—
159C2×D44C22×C411yescharacteristic
160C2×D44C22×C411yescharacteristic
161C2×D44C22×C411yescharacteristic
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×Dic22—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C42×C11C22×C411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C22×C411yescharacteristic
197C4⋊Dic11C22×C411yescharacteristic
198C4⋊Dic11C22×C411yescharacteristic
199C4⋊Dic11C22×C411yescharacteristic
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204D88—22no—
205D88—22no—
206D88—41no—
207D88—41no—
208#4313—81no—
209#4313—81no—
210#4313—81no—
211#4313—81no—
212C8×D11—81no—
213C8×D11—81no—
214C8×D11—81no—
215C8×D11—81no—
216#3100—111no—
217#2979—111no—
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#1454D1111yescharacteristic, complemented
231C23×C11C4×D411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—81no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—81no—
251C22⋊D11—81no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—81no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—21no—
261D44—21no—
262D44—21no—
263D44—21no—
264D44—42no—
265D44—42no—
266D44—81no—
267D44#13112yes—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—41no—
276C4×D11—81no—
277C4×D11—81no—
278Dic22—81no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—21no—
285C8×C11—21no—
286C8×C11—21no—
287C8×C11—41no—
288C8×C11—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293#532—111no—
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—111no—
308#436—111no—
309#436—111no—
310#436—111no—
311#436—221no—
312#435—221no—
313#435—221no—
314C8×D4—111no—
315C8×D4—111no—
316C8×D4—111no—
317C8×D4—111no—
318C8×D4—221no—
319#432—111no—
320#431—111no—
321#431C2×D1111yescharacteristic
322#431C2×D1111yescharacteristic
323#431C2×D1111yescharacteristic
324#408—221no—
325#408—221no—
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#322C2×D1111yescharacteristic, complemented
341#322C2×D1111yescharacteristic, complemented
342#322C2×D1111yescharacteristic, complemented
343C82C2×D1111yescharacteristic, complemented
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11C2×C4×D411yescharacteristic
348C2×D11—22no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—41no—
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×C11C2×#13111yescharacteristic
366C4×C11#56811yescharacteristic
367C4×C11#57611yescharacteristic
368C4×C11#57611yescharacteristic
369Dic11—41no—
370Dic11—41no—
371Dic11—41no—
372Dic11—41no—
373C2×#41—221no—
374C22×D4—111no—
375C23×C4—221no—
376C2×D8—111no—
377C2×D8—111no—
378C2×D8—111no—
379C2×D8—111no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16—221no—
383C2×M16—221no—
384C22×C8—221no—
385C22×C8—221no—
386C22×C8—221no—
387C22×C8—221no—
388C4⋊Q8—111no—
389#127—111no—
390#124—221no—
391#121—111no—
392#121—111no—
393#121—221no—
394C4×D4—111no—
395C4×D4—111no—
396C4×D4—111no—
397C4×D4—111no—
398C4×D4—111no—
399C4×D4—111no—
400C4×D4—221no—
401C4×D4—221no—
402C4×D4—221no—
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—21no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8C4×D1111yescharacteristic
416C4⋊C8C4×D1111yescharacteristic
417C4⋊C8D4411yescharacteristic
418C4⋊C8D4411yescharacteristic
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—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438C22⋊C8C4×D1111yescharacteristic
439C22⋊C8C4×D1111yescharacteristic
440C22⋊C8D4411yescharacteristic
441C22⋊C8D4411yescharacteristic
442#97—221no—
443C4×C8—221no—
444C4×C8C22×D1111yescharacteristic
445C4×C8C22×D1111yescharacteristic
446C4×C8C22×D1111yescharacteristic
447C4×C8C22×D1111yescharacteristic
448C4×C8C22×D1111yescharacteristic
449C4×C8C22×D1111yescharacteristic
450C2×C11—41no—
451C2×C11#293311yescharacteristic
452C2×C11#294811yescharacteristic
453C2×C11#295511yescharacteristic
454D11—42no—
455D11—81no—
456D11—81no—
457D11—81no—
458C24—221no—
459#41—881no—
460#41—881no—
461C2×Q8—221no—
462C2×D4—111no—
463C2×D4—111no—
464C2×D4—111no—
465C2×D4—111no—
466C2×D4—222no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—441no—
473C22×C4—221no—
474C22×C4—221no—
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×C4C2×D4411yescharacteristic
484C22×C4#433911yescharacteristic
485D8—222no—
486D8—222no—
487D8—441no—
488D8—441no—
489M16—881no—
490M16—881no—
491M16—881no—
492M16—881no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—881no—
500C2×C8—881no—
501C2×C8—881no—
502C2×C8—881no—
503C2×C8C2×C4×D1111yescharacteristic
504C2×C8C2×C4×D1111yescharacteristic
505C2×C8C2×C4×D1111yescharacteristic
506C2×C8C2×C4×D1111yescharacteristic
507C2×C8C2×D4411yescharacteristic
508C2×C8C2×D4411yescharacteristic
509C2×C8C2×D4411yescharacteristic
510C2×C8C2×D4411yescharacteristic
511C4⋊C4—111no—
512C4⋊C4—111no—
513C4⋊C4—111no—
514C4⋊C4—111no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C22⋊C4—221no—
518C22⋊C4—221no—
519C22⋊C4—221no—
520C22⋊C4—221no—
521C22⋊C4—221no—
522C22⋊C4—221no—
523C22⋊C4—221no—
524C22⋊C4—221no—
525C42C2×C4×D1111yescharacteristic
526C42C2×D4411yescharacteristic
527C42#433911yescharacteristic
528C42C23×D1111yescharacteristic
529C11#1802611yescharacteristic, complemented, Sylow
530C23—221no—
531C23—221no—
532C23—221no—
533C23—221no—
534C23—442no—
535C23—442no—
536C23—881no—
537C23C4×D4411yescharacteristic
538Q8—881no—
539D4—112no—
540D4—221no—
541D4—221no—
542D4—221no—
543D4—221no—
544D4—221no—
545D4—221no—
546D4—221no—
547D4—442no—
548D4—442no—
549D4—881no—
550D4—881no—
551D4—881no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—881no—
570C2×C4—881no—
571C2×C4—881no—
572C2×C4C4×D4411yescharacteristic
573C2×C4C4×D4411yescharacteristic
574C2×C4C4×D4411yescharacteristic
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C22×D4411yescharacteristic
577C2×C4C2×#433911yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—441no—
589C8—441no—
590C8—441no—
591C8—441no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—222no—
596C22—441no—
597C22—441no—
598C22—441no—
599C22—441no—
600C22—441no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22—441no—
606C22—441no—
607C22—884no—
608C22C2×C4×D4411yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—441no—
614C4—441no—
615C4—441no—
616C4—441no—
617C4D11×#13111yescharacteristic
618C4#1062328111yescharacteristic
619C4#1062328311yescharacteristic
620C4#1062328311yescharacteristic
621C2—41no—
622C2—442no—
623C2—881no—
624C2—881no—
625C2—881no—
626C2#1307734411yescharacteristic
627C2#1307746911yescharacteristic
628C2#1307752011yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1454C2
socleC22×C11C2×C4×D4
prime radical#13078617C2
cosocleC42×C11C24
hypercenter#1454D11
hypocenterC11#18026
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #13077682C2semidirect
3. #13077650C2semidirect
4. #13067531C2semidirect
5. #13067502C2semidirect
6. #13067482C2semidirect
7. #13067482C2semidirect
8. #13067447C2semidirect
9. #13067447C2semidirect
10. #13067441C2semidirect
11. C8×D88C2semidirect
12. #13067396C2semidirect
13. #13067086C2semidirect
14. #13067008C2semidirect
15. C11×#1454C2semidirect
45. #10622301C22semidirect
46. #10622301C22semidirect
49. C8×D44C22semidirect
50. C8×D44C22semidirect
51. C11×#322C22semidirect
52. C11×#322C22semidirect
53. C11×#322C22semidirect
54. C82×C11C22semidirect
59. #10622097C22semidirect
60. #10622097C22semidirect
61. #10622097C22semidirect
62. #10622097C22semidirect
63. #10622096C22semidirect
64. #10622096C22semidirect
65. #10622095C22semidirect
66. #10622095C22semidirect
230. #1454D11semidirect
340. #322C2×D11semidirect
341. #322C2×D11semidirect
342. #322C2×D11semidirect
343. C82C2×D11semidirect
529. C11#18026semidirect

Maximal subgroups

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

subgroupindex
#130786172
#130776822
#130776502
#130675312
#130675022
#130674822
#130674472
#130674412
C8×D882
#130673962
#130670862
#130670082
C11×#14542
#1802611