Finite Group Databasebeta

← #14813792

Subgroups — #14813792

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622667C211yesmaximal, characteristic
2C2×C4×#4324C211yesmaximal, characteristic
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13070159C211yesmaximal, characteristic, complemented
5#13070118C211yesmaximal, characteristic, complemented
6#13070019C211yesmaximal, characteristic
7#13069852C211yesmaximal, characteristic
8#13069295C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068974C211yesmaximal, characteristic
11#13068960C211yesmaximal, characteristic, complemented
12#13068960C211yesmaximal, characteristic, complemented
13#13068883C211yesmaximal, characteristic, complemented
14#13068877C211yesmaximal, characteristic
15C11×#2447C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#397—21no—
24C11×#397—21no—
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#385—21no—
30C11×#381—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622667—24no—
39C4×#4324—24no—
40#10622589—21no—
41C4⋊C4×Dic11—21no—
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622260—21no—
52#10622260—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×Dic22C2311yescharacteristic
65C11×#124—22no—
66C11×#124—41no—
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83C2×#4326—22no—
84C2×#4326—22no—
85C2×#4324—22no—
86C2×#4324—22no—
87C2×#4324D414yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C4×Dic22—22no—
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C4×Dic22—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118#66899—22no—
119#66899—22no—
120#66899—41no—
121#66896—22no—
122#66896—22no—
123#66896—22no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126#66874—22no—
127#66874—22no—
128#66872—22no—
129#66872—41no—
130C4⋊(C11⋊C8)—22no—
131C4×C11⋊C8—22no—
132#26161—111nomaximal, Sylow
133C24×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22C2×D412yes—
167C2×Dic22#4112yes—
168C2×Dic22#4112yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—81no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—81no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187#4326—44no—
188#4324—28no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—42no—
195C4⋊Dic11—81no—
196C4⋊Dic11#4112yes—
197Dic11⋊C4—24no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201Dic11⋊C4—81no—
202C4×Dic11—24no—
203C4×Dic11—42no—
204C4×Dic11—42no—
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⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×#464—111no—
218C2×C4×SD16—111no—
219#2447D1111yescharacteristic
220Q8×C4⋊C4—111no—
221#2096—111no—
222#2088—111no—
223#2071—111no—
224#2042—111no—
225#1933—111no—
226#1916—111no—
227#1880—111no—
228#1878—111no—
229#1878—111no—
230#1865—111no—
231#1864—111no—
232C23×C11—22no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C22×D411yescharacteristic
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—41no—
247D4×C11—41no—
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—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
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—41no—
273C2×C4×C11—84no—
274C2×C4×C11#13512yes—
275C2×C4×C11#13712yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C112−1+411yescharacteristic
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294Dic22—22no—
295Dic22—22no—
296Dic22—22no—
297Dic22#12314yes—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C22×Q16—111no—
303C22×SD16—111no—
304C2×#124C2×D1111yescharacteristic
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8—111no—
308C2×C4×D4C2×D1111yescharacteristic
309#464—224no—
310C4×SD16—224no—
311C2×#106—111no—
312C2×#106—111no—
313C2×C4⋊C8—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×C4×C8—111no—
323#397—21no—
324#397—21no—
325#391C2×D1111yescharacteristic
326#391C2×D1111yescharacteristic
327#390C2×D1111yescharacteristic
328#389—111no—
329#389—111no—
330#389—221no—
331#389—221no—
332#389C2×D1111yescharacteristic
333#385—21no—
334#384—111no—
335#384—221no—
336#381—21no—
337C4×C4⋊C4—221no—
338C4×C4⋊C4C2×D1111yescharacteristic
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#336—111no—
344#336—111no—
345#336—111no—
346#336—111no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11#52511yescharacteristic
355C22×C11D4211yescharacteristic
356C22×C11#54811yescharacteristic
357C22×C11C2×#13511yescharacteristic
358C22×C11C2×#13711yescharacteristic
359C22×C11#57711yescharacteristic
360C22×C11#57711yescharacteristic
361C4×C11—22no—
362C4×C11—22no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11—81no—
370C4×C11C2×#12311yescharacteristic
371C4×C11#53911yescharacteristic
372C4×C11#54711yescharacteristic
373C4×C11#55311yescharacteristic
374Dic11—24no—
375Dic11—42no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8—111no—
379C22×Q8C22×D1111yescharacteristic
380C22×D4C22×D1111yescharacteristic
381C23×C4—21no—
382C2×Q16—222no—
383C2×Q16—222no—
384C2×Q16—222no—
385C2×SD16—114no—
386C2×SD16—222no—
387C2×SD16—222no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392#124—22no—
393#124—41no—
394C4×Q8—222no—
395C4×Q8—222no—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×Q8—441no—
399C4×Q8—441no—
400C4×D4—22no—
401C4×D4—41no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4C22⋊D1111yescharacteristic
414C2×C4⋊C4C22⋊D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1111yescharacteristic
427C2×C42C22×D1111yescharacteristic
428#106—222no—
429#106—441no—
430C4⋊C8—222no—
431#103—222no—
432#103—222no—
433#103—222no—
434#103—222no—
435#103—441no—
436#102—222no—
437#102—222no—
438#102—222no—
439C4×C8—222no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—221no—
446#95—221no—
447#95C22⋊D1111yescharacteristic
448#95C22⋊D1111yescharacteristic
449C2×C11—82no—
450C2×C11#244311yescharacteristic
451C2×C11#310811yescharacteristic
452C2×C11#312511yescharacteristic
453C2×C11#326611yescharacteristic
454C2×C11#328411yescharacteristic
455C2×C11#336511yescharacteristic
456C2×C11#336911yescharacteristic
457C24—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—112no—
465C2×Q8—112no—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4D4×D1112yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493Q16—444no—
494SD16—228no—
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—
505C2×C8—221no—
506C2×C8—221no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—81no—
514C4⋊C4—112no—
515C4⋊C4—224no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—881no—
525C4⋊C4—881no—
526C4⋊C4—881no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—81no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—224no—
539C42—442no—
540C42—442no—
541C11#2616111yescharacteristic, complemented, Sylow
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23C22×C22⋊D1111yescharacteristic
550Q8—41no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—114no—
555Q8—222no—
556Q8—222no—
557Q8—222no—
558D4—22no—
559D4—22no—
560D4—41no—
561D4—41no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
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—84no—
588C2×C4—222no—
589C2×C4—222no—
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#6700312yes—
601C2×C4#6700412yes—
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4#6703711yescharacteristic
604C2×C4#41×D1111yescharacteristic
605C2×C4#41×D1111yescharacteristic
606C2×C4#41×D1111yescharacteristic
607C2×C4#6704311yescharacteristic
608C8—222no—
609C8—441no—
610C8—441no—
611C8—441no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22D4×C22⋊D1111yescharacteristic
620C22C2×#6700311yescharacteristic
621C22C2×#6700411yescharacteristic
622C22#1062335911yescharacteristic
623C22#1062336211yescharacteristic
624C22#1062336711yescharacteristic
625C22#1062336811yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—41no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—224no—
636C4—442no—
637C4—881no—
638C4—881no—
639C4D11×#12311yescharacteristic
640C4#1062318611yescharacteristic
641C4#1062319111yescharacteristic
642C4#1062319211yescharacteristic
643C2—82no—
644C2#1307234811yescharacteristic
645C2#1307869211yescharacteristic
646C2#1307888711yescharacteristic
647C2#1308012211yescharacteristic
648C2#1308034211yescharacteristic
649C2#1308130811yescharacteristic
650C2#1308135211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2447C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2447D11
hypocenterC11#26161
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2447

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×Dic22C2semidirect
4. #13070159C2semidirect
5. #13070118C2semidirect
8. #13069295C2semidirect
9. #13069175C2semidirect
11. #13068960C2semidirect
12. #13068960C2semidirect
13. #13068883C2semidirect
541. C11#26161semidirect

Maximal subgroups

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

subgroupindex
C2×#106226672
C2×C4×#43242
C4⋊C4×Dic222
#130701592
#130701182
#130700192
#130698522
#130692952
#130691752
#130689742
#130689602
#130688832
#130688772
C11×#24472
#2616111