Finite Group Databasebeta

← #14772128

Subgroups — #14772128

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622323C211yesmaximal, characteristic
2C2×#10622323C211yesmaximal, characteristic
3C2×C4×#4314C211yesmaximal, characteristic
4#13071536C211yesmaximal, characteristic, complemented
5C4⋊C4×D44C211yesmaximal, characteristic
6#13069354C211yesmaximal, characteristic, complemented
7#13069349C211yesmaximal, characteristic, complemented
8#13068887C211yesmaximal, characteristic, complemented
9#13068880C211yesmaximal, characteristic
10#13068873C211yesmaximal, characteristic, complemented
11#13068866C211yesmaximal, characteristic
12#13068784C211yesmaximal, characteristic, complemented
13#13068627C211yesmaximal, characteristic
14#13068622C211yesmaximal, characteristic, complemented
15C11×#1771C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×C4⋊C4×D11—21no—
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40#10622600—21no—
41#10622585—21no—
42#10622585—21no—
43#10622549C2211yescharacteristic
44#10622548C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622323—24no—
50#10622323C418yescomplemented
51C4×#4314—24no—
52#10622281—21no—
53#10622281—21no—
54#10622263—21no—
55#10622262—21no—
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
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⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×#4314C2×C414yes—
98C2×#4314D414yes—
99C2×#4314Q814yes—
100C4⋊C4×D11—44no—
101C4×D44—22no—
102C4×D44—22no—
103C4×D44—22no—
104C4×D44—41no—
105C4×D44—41no—
106C4×D44C2×C414yes—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—41no—
111C4×Dic22—41no—
112C4×Dic22C2×C414yescomplemented
113C11×C4⋊C8—22no—
114C11×#97—22no—
115C11×#97C2×C414yescomplemented
116C4×C8×C11—22no—
117C11×#95D411yescharacteristic
118C11×#95D411yescharacteristic
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66885—22no—
126#66885—22no—
127#66885C2×C414yes—
128#66882—22no—
129#66882—41no—
130#66882C2×C414yescomplemented
131#66881—22no—
132#66881—41no—
133#66880—22no—
134#66880—22no—
135#66880C2×C414yescomplemented
136#22677—111nomaximal, Sylow
137C23×D11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C22×C412yes—
156C2×D44C2×D412yes—
157C2×D44C2×Q812yes—
158C2×C4×D11—24no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C2×Dic22C2×D412yes—
172C2×Dic22C2×Q812yes—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11C22×C412yes—
182C2×C8×C11C22×C412yes—
183C2×C8×C11C2×D412yes—
184C2×C8×C11C2×Q812yes—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—41no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11C22×C412yes—
192C42×C11#4112yes—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C4⋊Dic11—81no—
208C4⋊Dic11C22×C412yes—
209C4⋊Dic11C22×C412yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217C4×Dic11—24no—
218C4×Dic11—42no—
219C4×Dic11—42no—
220#4314C4⋊C4116yescomplemented
221C2×#440—111no—
222C2×#440—111no—
223C2×C4×SD16—111no—
224#2351—111no—
225D4×C4⋊C4—111no—
226#1943—111no—
227#1942—111no—
228#1865—111no—
229#1864—111no—
230#1863—111no—
231#1862—111no—
232#1847—111no—
233#1804—111no—
234#1803—111no—
235#1771D1111yescharacteristic, complemented
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
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×C11—21no—
259C2×C4×C11C4×D412yes—
260C2×C4×C11C4×D412yes—
261C2×C4×C11AGL(1,ℤ/8)12yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×Q811yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
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—
288C2×Dic11—41no—
289D44—22no—
290D44—22no—
291D44—22no—
292D44C2×C4⋊C414yes—
293C4×D11—48no—
294C4×D11—84no—
295C4×D11—84no—
296Dic22—22no—
297Dic22—22no—
298Dic22—22no—
299Dic22C2×C4⋊C414yescomplemented
300C8×C11—22no—
301C8×C11—41no—
302C8×C11—41no—
303C8×C11C2×C4⋊C414yescomplemented
304C22×SD16—111no—
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8—111no—
308C2×C4×D4—111no—
309C2×C4×D4—111no—
310C2×C4×D4—111no—
311C22×C4⋊C4—221no—
312#440—118no—
313#440—224no—
314C4×SD16—224no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#107—111no—
318C2×#106—111no—
319C2×#106—111no—
320C2×C4⋊C8C2×D1111yescharacteristic
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#97C2×D1111yescharacteristic
328C2×#97C2×D1111yescharacteristic
329C2×C4×C8C2×D1111yescharacteristic
330#389—111no—
331#389—111no—
332#389—111no—
333#389—111no—
334#389—221no—
335#389—221no—
336#385—221no—
337#385—221no—
338#384—111no—
339#382—111no—
340#382—221no—
341#380—221no—
342C4×C4⋊C4—221no—
343C4×C4⋊C4C2×D1111yescharacteristic
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#336C2×D1111yescharacteristic
349#336C2×D1111yescharacteristic
350C22×C11C2×C4×D411yescharacteristic
351C22×C11D4211yescharacteristic
352C22×C11D4×Q811yescharacteristic
353C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57711yescharacteristic
356C22×C11#57811yescharacteristic
357C2×D11—24no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—22no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11C22×C4⋊C411yescharacteristic
371C4×C11#52011yescharacteristic
372C4×C11#54711yescharacteristic
373C4×C11#55411yescharacteristic
374Dic11—24no—
375Dic11—42no—
376Dic11—42no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380Dic11—81no—
381C22×Q8—111no—
382C22×D4—111no—
383C23×C4—221no—
384C23×C4—221no—
385C23×C4—221no—
386C2×SD16—114no—
387C2×SD16—114no—
388C2×SD16—114no—
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C22×C8C22×D1111yescharacteristic
393C4×Q8—114no—
394C4×Q8—222no—
395C4×Q8—222no—
396C4×Q8—222no—
397C4×Q8—441no—
398C4×Q8—441no—
399C4×D4—114no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4—222no—
403C4×D4—441no—
404C4×D4—441no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
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—444no—
421C2×C4⋊C4D4411yescharacteristic
422C2×C4⋊C4D4411yescharacteristic
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432#107—114no—
433#107—222no—
434#107—441no—
435#106—222no—
436#106—441no—
437C4⋊C8—22no—
438#103—114no—
439#103—222no—
440#103—222no—
441#102—114no—
442#102—222no—
443#102—222no—
444#97—22no—
445#97C4×D1114yescomplemented
446C4×C8—22no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95D4411yescharacteristic
454#95D4411yescharacteristic
455C2×C11D4×C4⋊C411yescharacteristic
456C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
457C2×C11#294711yescharacteristic
458C2×C11#326511yescharacteristic
459C2×C11#326911yescharacteristic
460C2×C11#338611yescharacteristic
461C2×C11#338811yescharacteristic
462D11—44no—
463C24—221no—
464C2×Q8—112no—
465C2×Q8—112no—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×D4—112no—
471C2×D4—112no—
472C2×D4—112no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—224no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—881no—
491C22×C4—881no—
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×D4411yescharacteristic
494C22×C4C2×D4411yescharacteristic
495C22×C4C2×D4411yescharacteristic
496C22×C4C2×D4411yescharacteristic
497C22×C4C2×D4411yescharacteristic
498C22×C4C23×D1111yescharacteristic
499SD16—1116no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8C2×C4×D1112yes—
509C2×C8C2×C4×D1112yes—
510C2×C8D4×D1112yes—
511C2×C8Q8×D1112yes—
512C4⋊C4—22no—
513C4⋊C4—41no—
514C4⋊C4—112no—
515C4⋊C4—112no—
516C4⋊C4—224no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—881no—
535C22⋊C4—224no—
536C22⋊C4—442no—
537C22⋊C4—442no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—224no—
543C42—442no—
544C42—442no—
545C42C2×C4×D1112yes—
546C42#433912yes—
547C11#2267711yescharacteristic, complemented, Sylow
548C23—222no—
549C23—222no—
550C23—222no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23C22×D4411yescharacteristic
556Q8—114no—
557Q8—222no—
558Q8—222no—
559Q8—222no—
560D4—114no—
561D4—222no—
562D4—222no—
563D4—222no—
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—21no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—448no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
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—884no—
602C2×C4—884no—
603C2×C4C4×D4412yes—
604C2×C4C4×D4412yes—
605C2×C4#6696112yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4C2×Q8×D1111yescharacteristic
610C2×C4#6704211yescharacteristic
611C2×C4#6704311yescharacteristic
612C8—22no—
613C8—41no—
614C8—41no—
615C8C4⋊C4×D1114yescomplemented
616C22—224no—
617C22—442no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—442no—
622C22—442no—
623C22C2×C4×D4411yescharacteristic
624C22D4×D4411yescharacteristic
625C22Q8×D4411yescharacteristic
626C22C2×#6696111yescharacteristic
627C22#1062327911yescharacteristic
628C22#1062328211yescharacteristic
629C22#1062328411yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—224no—
637C4—442no—
638C4—442no—
639C4—881no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4C2×C4⋊C4×D1111yescharacteristic
644C4#1062305411yescharacteristic
645C4#1062308211yescharacteristic
646C4#1062311011yescharacteristic
647C2—444no—
648C2C4⋊C4×D4411yescharacteristic
649C2C4×#6696111yescharacteristic
650C2#1307746111yescharacteristic
651C2#1308011611yescharacteristic
652C2#1308017611yescharacteristic
653C2#1308153911yescharacteristic
654C2#1308156311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1771C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1771D11
hypocenterC11#22677
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. #13071536C2semidirect
6. #13069354C2semidirect
7. #13069349C2semidirect
8. #13068887C2semidirect
10. #13068873C2semidirect
12. #13068784C2semidirect
14. #13068622C2semidirect
15. C11×#1771C2semidirect
50. #10622323C4semidirect
112. C4×Dic22C2×C4semidirect
115. C11×#97C2×C4semidirect
130. #66882C2×C4semidirect
135. #66880C2×C4semidirect
220. #4314C4⋊C4semidirect
235. #1771D11semidirect
299. Dic22C2×C4⋊C4semidirect
303. C8×C11C2×C4⋊C4semidirect
445. #97C4×D11semidirect
547. C11#22677semidirect
615. C8C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106223232
C2×C4×#43142
#130715362
C4⋊C4×D442
#130693542
#130693492
#130688872
#130688802
#130688732
#130688662
#130687842
#130686272
#130686222
C11×#17712
#2267711