Finite Group Databasebeta

← #14725808

Subgroups — #14725808

Order 2816.

644 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic
2#13077681C211yesmaximal, characteristic, complemented
3#13077679C211yesmaximal, characteristic, complemented
4#13067528C211yesmaximal, characteristic, complemented
5#13067527C211yesmaximal, characteristic, complemented
6#13067447C211yesmaximal, characteristic, complemented
7#13067446C211yesmaximal, characteristic, complemented
8#13067444C211yesmaximal, characteristic, complemented
9#13067438C211yesmaximal, characteristic, complemented
10#13067437C211yesmaximal, characteristic, complemented
11#13067363C211yesmaximal, characteristic, complemented
12#13067031C211yesmaximal, characteristic, complemented
13#13067031C211yesmaximal, characteristic, complemented
14#13066904C211yesmaximal, characteristic, complemented
15C11×#1581C211yesmaximal, characteristic, complemented
16#10623079C2211yescharacteristic
17#10623079C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622770C411yescharacteristic
22#10622764C411yescharacteristic
23#10622742—21no—
24#10622741—21no—
25#10622723—21no—
26C8×C22⋊D11—21no—
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622496C411yescharacteristic
32#10622487C411yescharacteristic
33#10622451C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622446C2211yescharacteristic
36#10622446C2211yescharacteristic
37#10622388C411yescharacteristic
38#10622388C411yescharacteristic
39#10622373C411yescharacteristic
40#10622373C411yescharacteristic
41#10622342—21no—
42#10622340—21no—
43#10622340—21no—
44(C22⋊D11)⋊C8—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4339—21no—
68C2×#4339—21no—
69C2×C11×D8C2×C411yescharacteristic
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66993C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77#66991C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C2×#4323C2×C411yescharacteristic
80C4×C22⋊D11—21no—
81C4×C22⋊D11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C2×D88C2×C411yescharacteristic
85C2×#4313—21no—
86C2×#4313—21no—
87C2×#4313—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90C2×C8×D11C2×C411yescharacteristic
91C2×C8×D11C2×C411yescharacteristic
92#66948C2×C411yescharacteristic
93#66948C2×C411yescharacteristic
94#66941C2×C411yescharacteristic
95#66941C2×C411yescharacteristic
96#66938—21no—
97#66938—21no—
98#66937—21no—
99#66937—21no—
100C4×D44C2311yescharacteristic
101C4×D44C2311yescharacteristic
102C42×D11C2311yescharacteristic
103C11×#107C2×C411yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66896C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8D411yescharacteristic
126(C2×D11)⋊C8D411yescharacteristic
127#66882C2×C411yescharacteristic
128#66879—21no—
129Dic11⋊C8D411yescharacteristic
130Dic11⋊C8D411yescharacteristic
131C8×Dic11—21no—
132C8×Dic11—21no—
133C8×Dic11C2×C411yescharacteristic
134C8×Dic11C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138#66871C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18091—111nomaximal, Sylow
145C2×D4×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C2×C22⋊D11—21no—
155#4339—81no—
156#4339—81no—
157#4339—81no—
158#4339—81no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44C22×C411yescharacteristic
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11C22×C411yescharacteristic
166C2×C4×D11C2×D411yescharacteristic
167C2×C4×D11#4111yescharacteristic
168C2×Dic22—21no—
169C2×Dic22—21no—
170C11×D8—41no—
171C11×M16—81no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—81no—
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186C22⋊Dic11—21no—
187#4323—22no—
188#4323—22no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11C22×C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200#4318—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209D88—41no—
210#4313—42no—
211#4313—81no—
212#4313—81no—
213C8×D11—22no—
214C8×D11—41no—
215C8×D11—81no—
216C8×D11—81no—
217#3169—111no—
218#2979—111no—
219#2979—111no—
220#1594—111no—
221#1594—111no—
222#1581—111no—
223#1581—111no—
224#1581—111no—
225#1581D1111yescharacteristic, complemented
226#1580—111no—
227#1580—111no—
228#1564—111no—
229#1484—111no—
230#1484—111no—
231#1451—111no—
232C23×C11—21no—
233C23×C11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11C4×D411yescharacteristic
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C22⋊D11—42no—
251C22⋊D11—42no—
252C22⋊D11—81no—
253C22⋊D11—81no—
254C22⋊D11—81no—
255C22⋊D11—81no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11C4×D411yescharacteristic
259C2×Dic11C4×D411yescharacteristic
260C2×Dic11C4×D411yescharacteristic
261D44—21no—
262D44—21no—
263D44—21no—
264D44—21no—
265D44—81no—
266D44—81no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—21no—
271C4×D11—22no—
272C4×D11—41no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—41no—
276Dic22—81no—
277Dic22—81no—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11—41no—
285C11⋊C8—21no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8#13112yes—
292#532—111no—
293#532—111no—
294#500—111no—
295#493—111no—
296#486—111no—
297#486—111no—
298#466—111no—
299#466—111no—
300#466—111no—
301#466—111no—
302C4×D8—111no—
303C4×D8—111no—
304C4×D8—111no—
305C4×D8C2×D1111yescharacteristic
306#436—111no—
307#436—111no—
308#436—111no—
309#436—221no—
310#436—221no—
311#436C2×D1111yescharacteristic
312C8×D4—111no—
313C8×D4—111no—
314C8×D4—111no—
315C8×D4—221no—
316C8×D4—221no—
317C8×D4C2×D1111yescharacteristic
318#431—111no—
319#431—111no—
320#431—111no—
321#408—221no—
322#408—221no—
323#408—221no—
324#408—221no—
325C4×M16—111no—
326C2×C4×C8—111no—
327#335—111no—
328#335C2×D1111yescharacteristic
329#334—111no—
330#334—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8—111no—
334D4⋊C8—111no—
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8C2×D1111yescharacteristic
338D4⋊C8C2×D1111yescharacteristic
339#322—111no—
340#322—111no—
341#322—111no—
342#322C2×D1111yescharacteristic
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11C2×C4×D411yescharacteristic
350C2×D11—21no—
351C2×D11—21no—
352C2×D11—21no—
353C2×D11—41no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C4×C11—21no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11C2×#13111yescharacteristic
363C4×C11#56811yescharacteristic
364C4×C11#57611yescharacteristic
365C4×C11#57611yescharacteristic
366Dic11—21no—
367Dic11—21no—
368Dic11—41no—
369Dic11—41no—
370Dic11#44412yes—
371C2×#41—221no—
372C2×#41—221no—
373C2×D8—111no—
374C2×D8—111no—
375C2×D8—111no—
376C2×D8C4×D1111yescharacteristic
377C2×M16—21no—
378C2×M16—221no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—221no—
382C22×C8—21no—
383C22×C8—111no—
384C22×C8—111no—
385C22×C8—221no—
386C22×C8—221no—
387C22×C8—221no—
388C4⋊Q8—111no—
389C4⋊Q8—111no—
390#127—111no—
391#127—111no—
392#124—221no—
393#124—221no—
394#121—111no—
395#121—111no—
396#121—111no—
397#121—111no—
398#121—221no—
399#121—221no—
400C4×D4—111no—
401C4×D4—111no—
402C4×D4—221no—
403C4×D4—221no—
404C4×D4C22×D1111yescharacteristic
405C4×D4C22×D1111yescharacteristic
406C2×C42—111no—
407#107—111no—
408#107—111no—
409#107—111no—
410#107C4×D1111yescharacteristic
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—111no—
414C4⋊C8—111no—
415C4⋊C8C22×D1111yescharacteristic
416C4⋊C8C22×D1111yescharacteristic
417#102—111no—
418#102—111no—
419#102—111no—
420#102—111no—
421#102—111no—
422#102—111no—
423#102C4×D1111yescharacteristic
424#102C4×D1111yescharacteristic
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—111no—
428C22⋊C8—111no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437#97—221no—
438C4×C8—111no—
439C4×C8—111no—
440C4×C8—111no—
441C4×C8—111no—
442C4×C8—111no—
443C4×C8—221no—
444C4×C8—221no—
445C4×C8C22×D1111yescharacteristic
446C4×C8C22×D1111yescharacteristic
447C4×C8C22×D1111yescharacteristic
448C2×C11—81no—
449C2×C11—81no—
450C2×C11#293511yescharacteristic
451C2×C11#294811yescharacteristic
452C2×C11C2×#44411yescharacteristic
453D11—41no—
454D11—81no—
455D11—81no—
456#41—881no—
457#41—881no—
458#41—881no—
459#41—881no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×D4—111no—
463C2×D4—111no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4C2×C4×D1111yescharacteristic
473C2×D4C2×C4×D1111yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—221no—
480C22×C4—221no—
481D8—41no—
482D8—222no—
483D8—222no—
484D8—441no—
485M16—81no—
486M16—442no—
487M16—881no—
488M16—881no—
489M16—881no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—81no—
494C2×C8—111no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—111no—
498C2×C8—222no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—441no—
503C2×C8—881no—
504C2×C8—881no—
505C2×C8—881no—
506C2×C8C2×C4×D1111yescharacteristic
507C2×C8C2×C4×D1111yescharacteristic
508C2×C8D4×D1111yescharacteristic
509C2×C8D4×D1111yescharacteristic
510C4⋊C4—111no—
511C4⋊C4—111no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4C2×C4×D1111yescharacteristic
515C4⋊C4C2×C4×D1111yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—221no—
519C22⋊C4—221no—
520C22⋊C4—221no—
521C22⋊C4—221no—
522C22⋊C4—221no—
523C22⋊C4—221no—
524C42—111no—
525C42—111no—
526C42—111no—
527C42C23×D1111yescharacteristic
528C11#1809111yescharacteristic, complemented, Sylow
529C23—21no—
530C23—21no—
531C23—111no—
532C23—221no—
533C23—221no—
534Q8—881no—
535Q8—881no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—221no—
541D4—221no—
542D4—221no—
543D4—221no—
544D4—442no—
545D4—442no—
546D4—881no—
547D4—881no—
548D4—881no—
549D4—881no—
550D4—881no—
551D4—881no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—111no—
559C2×C4—111no—
560C2×C4—111no—
561C2×C4—222no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C8—21no—
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—112no—
583C8—221no—
584C8—221no—
585C8—221no—
586C8—441no—
587C8—441no—
588C8—441no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—221no—
596C22—221no—
597C22—221no—
598C22—441no—
599C22—441no—
600C22—441no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22C4×D4×D1111yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—112no—
609C4—221no—
610C4—221no—
611C4—441no—
612C4—441no—
613C4#1062327611yescharacteristic
614C4D11×#13111yescharacteristic
615C4#1062328811yescharacteristic
616C4#1062330011yescharacteristic
617C2—81no—
618C2—81no—
619C2—441no—
620C2—881no—
621C2—881no—
622C2#1307735711yescharacteristic
623C2#1307746311yescharacteristic
624C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1581C2
socleC22×C11C2×C4×D4
prime radical#13079192C2
cosocleC42×C11C24
hypercenter#1581D11
hypocenterC11#18091
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #13077681C2semidirect
3. #13077679C2semidirect
4. #13067528C2semidirect
5. #13067527C2semidirect
6. #13067447C2semidirect
7. #13067446C2semidirect
8. #13067444C2semidirect
9. #13067438C2semidirect
10. #13067437C2semidirect
11. #13067363C2semidirect
12. #13067031C2semidirect
13. #13067031C2semidirect
14. #13066904C2semidirect
15. C11×#1581C2semidirect
225. #1581D11semidirect
528. C11#18091semidirect

Maximal subgroups

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

subgroupindex
#130791922
#130776812
#130776792
#130675282
#130675272
#130674472
#130674462
#130674442
#130674382
#130674372
#130673632
#130670312
#130669042
C11×#15812
#1809111