Finite Group Databasebeta

← #14772120

Subgroups — #14772120

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×#10622502C211yesmaximal, characteristic
3C2×#10622465C211yesmaximal, characteristic
4#13071533C211yesmaximal, characteristic, complemented
5#13071516C211yesmaximal, characteristic
6#13069352C211yesmaximal, characteristic, complemented
7#13069347C211yesmaximal, characteristic, complemented
8#13068881C211yesmaximal, characteristic, complemented
9#13068874C211yesmaximal, characteristic
10#13068867C211yesmaximal, characteristic, complemented
11#13068860C211yesmaximal, characteristic
12#13068623C211yesmaximal, characteristic
13#13068618C211yesmaximal, characteristic, complemented
14#13068488C211yesmaximal, characteristic, complemented
15C11×#1847C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×C4⋊C4×D11—21no—
20C2×#66940C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×#106C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C11×#384C2211yescharacteristic
30C11×#382C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622602—21no—
37#10622602—21no—
38#10622600—21no—
39#10622586C2211yescharacteristic
40#10622586C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622502—24no—
50#10622465—24no—
51#10622323C418yescomplemented
52#10622263—21no—
53#10622262—21no—
54#10622260—21no—
55#10622260—21no—
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×#4314C2×C414yes—
98C2×#4314D414yes—
99C2×#4314Q814yes—
100#66946—22no—
101#66946—22no—
102#66946—41no—
103#66946—41no—
104C4⋊C4×D11—44no—
105#66940—22no—
106#66940—22no—
107#66940—41no—
108#66940—41no—
109C4×D44—22no—
110C4×D44C2×C414yes—
111C4×Dic22—22no—
112C4×Dic22C2×C414yescomplemented
113C11×#107—22no—
114C11×#107—41no—
115C11×#106—22no—
116C11×#106—41no—
117C11×#97C2×C414yescomplemented
118C11×#95—21no—
119C11×#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126#66885C2×C414yes—
127#66882C2×C414yescomplemented
128#66880C2×C414yescomplemented
129#66879—22no—
130C8×Dic11—22no—
131#66874—22no—
132#66874—22no—
133#66873—22no—
134#66873—22no—
135C4⋊(C11⋊C8)—22no—
136#22677—111nomaximal, Sylow
137C23×D11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
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×C11C22×C412yes—
176C2×C8×C11C22×C412yes—
177C2×C8×C11C2×D412yes—
178C2×C8×C11C2×Q812yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—81no—
189C42×C11C22×C412yes—
190C42×C11#4112yes—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194C4⋊Dic11—22no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—41no—
198C4⋊Dic11C22×C412yes—
199C4⋊Dic11C22×C412yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207C4×Dic11—24no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—42no—
213C4×Dic11—42no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
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#1847D1111yescharacteristic, complemented
233#1804—111no—
234#1803—111no—
235#1771—111no—
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—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11C4×D412yes—
261C2×C4×C11C4×D412yes—
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—21no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11AGL(1,ℤ/8)12yes—
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×C11C2×C4⋊C414yescomplemented
302C11⋊C8—41no—
303C11⋊C8—41no—
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×#107C2×D1111yescharacteristic
317C2×#107C2×D1111yescharacteristic
318C2×#106C2×D1111yescharacteristic
319C2×#106C2×D1111yescharacteristic
320C2×C4⋊C8—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#97—111no—
328C2×#97C2×D1111yescharacteristic
329C2×C4×C8—111no—
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#384C2×D1111yescharacteristic
339#382—221no—
340#382C2×D1111yescharacteristic
341#380—221no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—221no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#336—111no—
349#336—111no—
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—81no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11—81no—
370C4×C11C22×C4⋊C411yescharacteristic
371C4×C11#52011yescharacteristic
372C4×C11#54711yescharacteristic
373C4×C11#55411yescharacteristic
374Dic11—24no—
375Dic11—22no—
376Dic11—42no—
377Dic11—42no—
378Dic11—41no—
379Dic11—41no—
380Dic11—41no—
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×C8—111no—
390C22×C8—111no—
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—21no—
406C2×C4⋊C4—21no—
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—444no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432#107—22no—
433#107—41no—
434#107—114no—
435#106—22no—
436#106—41no—
437C4⋊C8—222no—
438#103—114no—
439#103—222no—
440#103—222no—
441#102—114no—
442#102—222no—
443#102—222no—
444#97—222no—
445#97C4×D1114yescomplemented
446C4×C8—222no—
447#95—21no—
448#95—21no—
449#95—111no—
450#95—111no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
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—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—224no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—881no—
495C22×C4—881no—
496C22×C4D4×D1111yescharacteristic
497C22×C4D4×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499SD16—1116no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8C2×C4×D1112yes—
509C2×C8C2×C4×D1112yes—
510C2×C8D4×D1112yes—
511C2×C8Q8×D1112yes—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—81no—
522C4⋊C4—112no—
523C4⋊C4—112no—
524C4⋊C4—222no—
525C4⋊C4—224no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—441no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C22⋊C4—224no—
536C22⋊C4—442no—
537C22⋊C4—442no—
538C42—224no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—221no—
543C42—442no—
544C42—442no—
545C42C2×C4×D1112yes—
546C42#434312yes—
547C11#2267711yescharacteristic, complemented, Sylow
548C23—222no—
549C23—222no—
550C23—222no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23C2×D4×D1111yescharacteristic
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—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—112no—
581C2×C4—221no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—448no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—884no—
603C2×C4—884no—
604C2×C4#6694612yes—
605C2×C4#6694612yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×D4×D1111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4C2×Q8×D1111yescharacteristic
610C2×C4C2×#434311yescharacteristic
611C2×C4#6704011yescharacteristic
612C8—22no—
613C8—441no—
614C8—441no—
615C8C4⋊C4×D1114yescomplemented
616C22—224no—
617C22—442no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—442no—
622C22—442no—
623C22C2×#6694611yescharacteristic
624C22#1062324811yescharacteristic
625C22#1062325811yescharacteristic
626C22D11×AGL(1,ℤ/8)11yescharacteristic
627C22#1062330611yescharacteristic
628C22#1062330811yescharacteristic
629C22#1062331011yescharacteristic
630C4—22no—
631C4—22no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—222no—
637C4—224no—
638C4—441no—
639C4—441no—
640C4—441no—
641C4—442no—
642C4—442no—
643C4C2×C4⋊C4×D1111yescharacteristic
644C4#1062303511yescharacteristic
645C4#1062325711yescharacteristic
646C4#1062326111yescharacteristic
647C2—444no—
648C2#1307151611yescharacteristic
649C2#1307742311yescharacteristic
650C2#1307745711yescharacteristic
651C2#1308011011yescharacteristic
652C2#1308017011yescharacteristic
653C2#1308153411yescharacteristic
654C2#1308156011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1847C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1847D11
hypocenterC11#22677
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
4. #13071533C2semidirect
6. #13069352C2semidirect
7. #13069347C2semidirect
8. #13068881C2semidirect
10. #13068867C2semidirect
13. #13068618C2semidirect
14. #13068488C2semidirect
15. C11×#1847C2semidirect
51. #10622323C4semidirect
112. C4×Dic22C2×C4semidirect
117. C11×#97C2×C4semidirect
127. #66882C2×C4semidirect
128. #66880C2×C4semidirect
220. #4314C4⋊C4semidirect
232. #1847D11semidirect
299. Dic22C2×C4⋊C4semidirect
301. 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×#106225022
C2×#106224652
#130715332
#130715162
#130693522
#130693472
#130688812
#130688742
#130688672
#130688602
#130686232
#130686182
#130684882
C11×#18472
#2267711