Finite Group Databasebeta

← #14813875

Subgroups — #14813875

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622454C211yesmaximal, characteristic
2C2×C4×#4314C211yesmaximal, characteristic
3#13072392C211yesmaximal, characteristic, complemented
4C4⋊C4×D44C211yesmaximal, characteristic
5#13070158C211yesmaximal, characteristic, complemented
6#13070114C211yesmaximal, characteristic, complemented
7#13070026C211yesmaximal, characteristic, complemented
8#13069863C211yesmaximal, characteristic, complemented
9#13069292C211yesmaximal, characteristic, complemented
10#13068949C211yesmaximal, characteristic
11#13068949C211yesmaximal, characteristic
12#13068949C211yesmaximal, characteristic
13#13068887C211yesmaximal, characteristic, complemented
14#13068880C211yesmaximal, characteristic
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×C4⋊C4×D11—21no—
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622600—21no—
38#10622597—21no—
39#10622594—21no—
40#10622548C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622542C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622454—24no—
48C4×#4314—24no—
49#10622281—21no—
50#10622281—21no—
51#10622273—21no—
52#10622268—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×#4314—22no—
94C2×#4314—22no—
95C2×#4314—22no—
96C2×#4314—22no—
97C2×#4314—22no—
98C2×#4314D414yes—
99C4⋊C4×D11—44no—
100C4×D44—22no—
101C4×D44—22no—
102C4×D44—22no—
103C4×D44—22no—
104C4×D44—41no—
105C4×D44—41no—
106#66922—22no—
107#66922—41no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C11×C4⋊C8—22no—
111C4×C8×C11—22no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66885—22no—
124#66885—22no—
125#66881—22no—
126#66881—41no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#66880—41no—
133#26166—111nomaximal, Sylow
134C23×D11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44C2×D412yes—
153C2×D44#4112yes—
154C2×D44#4112yes—
155C2×C4×D11—24no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22C2×D412yes—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11C2×D412yes—
188C11×C4⋊C4—41no—
189C11×C4⋊C4SD1614yescomplemented
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209C4⋊Dic11—42no—
210C4⋊Dic11—42no—
211C4⋊Dic11—81no—
212C4⋊Dic11#4112yes—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217C4×Dic11—42no—
218#4314—28no—
219#4314—44no—
220C2×#461—111no—
221C2×C4×SD16—111no—
222#2446—111no—
223D4×C4⋊C4—111no—
224#2096—111no—
225#2088—111no—
226#2072—111no—
227#2043—111no—
228#1933—111no—
229#1916D1111yescharacteristic, complemented
230#1877—111no—
231#1877—111no—
232#1877—111no—
233#1865—111no—
234#1864—111no—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C2×C4×C11—21no—
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×C11C2×SD1612yes—
259C2×C4×C11C2×SD1612yes—
260C2×C4×C11C2×SD1612yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—41no—
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—
286C2×Dic11—41no—
287C2×Dic11—41no—
288D44—22no—
289D44—22no—
290D44—22no—
291D44#12314yes—
292C4×D11—48no—
293C4×D11—84no—
294C4×D11—84no—
295Dic22—22no—
296Dic22—22no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303C8×C11—22no—
304C8×C11—41no—
305C8×C11—41no—
306C8×C11—41no—
307C22×SD16—111no—
308C22×SD16—111no—
309C2×C4⋊Q8—111no—
310C2×C4×Q8—111no—
311C2×C4×D4—111no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C22×C4⋊C4—221no—
315#461—224no—
316C4×SD16—224no—
317C2×#106—111no—
318C2×#106—111no—
319C2×C4⋊C8C2×D1111yescharacteristic
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×C4×C8C2×D1111yescharacteristic
329#400—221no—
330#398—221no—
331#391—111no—
332#391—111no—
333#391—111no—
334#389—111no—
335#389—111no—
336#389—111no—
337#387—221no—
338#387—221no—
339#385—221no—
340#385—221no—
341#384—111no—
342#380—221no—
343C4×C4⋊C4C2×D1111yescharacteristic
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#336C2×D1111yescharacteristic
349#336C2×D1111yescharacteristic
350#336C2×D1111yescharacteristic
351#336C2×D1111yescharacteristic
352C22×C11#52511yescharacteristic
353C22×C11D4211yescharacteristic
354C22×C11#54811yescharacteristic
355C22×C11C22×SD1611yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57811yescharacteristic
359C2×D11—24no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—42no—
366C4×C11—22no—
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11C2×#12311yescharacteristic
373C4×C11#53911yescharacteristic
374C4×C11#54711yescharacteristic
375C4×C11#55311yescharacteristic
376Dic11—42no—
377Dic11—42no—
378Dic11—81no—
379Dic11—81no—
380Dic11—81no—
381Dic11—81no—
382Dic11—81no—
383C22×Q8—111no—
384C22×Q8—111no—
385C22×D4—111no—
386C23×C4—221no—
387C23×C4—221no—
388C23×C4—221no—
389C2×SD16—114no—
390C2×SD16—222no—
391C2×SD16—222no—
392C2×SD16—222no—
393C2×SD16—222no—
394C2×SD16—222no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C4⋊Q8—222no—
400C4⋊Q8—441no—
401C4×Q8—222no—
402C4×Q8—441no—
403C4×D4—222no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—222no—
407C4×D4—441no—
408C4×D4—441no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—444no—
423C2×C4⋊C4D4411yescharacteristic
424C2×C4⋊C4D4411yescharacteristic
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432#106—222no—
433#106—441no—
434C4⋊C8—22no—
435#103—222no—
436#103—222no—
437#103—222no—
438#103—222no—
439#103—222no—
440#103—441no—
441#102—222no—
442#102—222no—
443C4×C8—22no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95D4411yescharacteristic
454#95D4411yescharacteristic
455C2×C11#244311yescharacteristic
456C2×C11#310111yescharacteristic
457C2×C11#312011yescharacteristic
458C2×C11#326911yescharacteristic
459C2×C11D4×SD1611yescharacteristic
460C2×C11#335911yescharacteristic
461C2×C11#337611yescharacteristic
462D11—44no—
463C24—221no—
464C2×Q8—112no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×D4—112no—
477C2×D4—112no—
478C2×D4—112no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C22×C4—224no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—881no—
497C22×C4—881no—
498C22×C4C2×D4411yescharacteristic
499C22×C4C2×D4411yescharacteristic
500C22×C4C2×D4411yescharacteristic
501C22×C4C2×D4411yescharacteristic
502C22×C4C2×D4411yescharacteristic
503C22×C4C2×D4411yescharacteristic
504C22×C4C23×D1111yescharacteristic
505SD16—228no—
506SD16—444no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8D4×D1112yes—
519C4⋊C4—41no—
520C4⋊C4—112no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—881no—
538C4⋊C4#431414yescomplemented
539C22⋊C4—224no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—442no—
549C11#2616611yescharacteristic, complemented, Sylow
550C23—222no—
551C23—222no—
552C23—222no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23C22×D4411yescharacteristic
558Q8—222no—
559Q8—222no—
560Q8—441no—
561Q8—441no—
562Q8—441no—
563Q8—441no—
564Q8—441no—
565Q8—441no—
566D4—114no—
567D4—222no—
568D4—222no—
569D4—222no—
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—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—448no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
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—884no—
608C2×C4—884no—
609C2×C4C2×#431412yes—
610C2×C4C2×#431412yes—
611C2×C4C2×#431412yes—
612C2×C4C2×D4×D1111yescharacteristic
613C2×C4#6704011yescharacteristic
614C2×C4#41×D1111yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#6704211yescharacteristic
618C8—22no—
619C8—41no—
620C8—41no—
621C8—41no—
622C22—224no—
623C22—442no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22—442no—
628C22—442no—
629C22#1062305511yescharacteristic
630C22D4×D4411yescharacteristic
631C22#1062310711yescharacteristic
632C22C22×#431411yescharacteristic
633C22#1062327911yescharacteristic
634C22#1062328211yescharacteristic
635C22#1062328411yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—442no—
643C4—442no—
644C4—881no—
645C4—881no—
646C4—881no—
647C4—881no—
648C4—881no—
649C4#1062316211yescharacteristic
650C4D11×#12311yescharacteristic
651C4#1062322311yescharacteristic
652C4#1062324011yescharacteristic
653C2—444no—
654C2#1307235611yescharacteristic
655C2#1307862511yescharacteristic
656C2#1307883211yescharacteristic
657C2#1308017611yescharacteristic
658C2D4×#431411yescharacteristic
659C2#1308125911yescharacteristic
660C2#1308144511yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1916D11
hypocenterC11#26166
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
3. #13072392C2semidirect
5. #13070158C2semidirect
6. #13070114C2semidirect
7. #13070026C2semidirect
8. #13069863C2semidirect
9. #13069292C2semidirect
13. #13068887C2semidirect
15. C11×#1916C2semidirect
189. C11×C4⋊C4SD16semidirect
229. #1916D11semidirect
538. C4⋊C4#4314semidirect
549. C11#26166semidirect

Maximal subgroups

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

subgroupindex
C2×#106224542
C2×C4×#43142
#130723922
C4⋊C4×D442
#130701582
#130701142
#130700262
#130698632
#130692922
#130689492
#130688872
#130688802
C11×#19162
#2616611