Finite Group Databasebeta

← #101×C22⋊D11 #14769140

Subgroups — #101×C22⋊D11 #14769140

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C22⋊D11C211yesmaximal, characteristic
2M16×C22⋊D11C212yesmaximal
3C2×D11×#101C211yesmaximal, characteristic, complemented
4#13069458C212yesmaximal, complemented
5#13069084C212yesmaximal, complemented
6#13069081C212yesmaximal, complemented
7#13068610C211yesmaximal, characteristic, complemented
8#13068540C211yesmaximal, characteristic, complemented
9#13068538C211yesmaximal, characteristic, complemented
10#101×Dic11C211yesmaximal, characteristic, complemented
11C22×C11×#101C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×Q8×D11C2211yescharacteristic
14C22×C11×M16C2212yes—
15Q8×C22⋊D11—22no—
16Q8×C22⋊D11—22no—
17Q8×C22⋊D11—22no—
18Q8×C22⋊D11—22no—
19C2×#66999C412yes—
20C2×#66999C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×#66997C412yes—
23C2×#66997C2211yescharacteristic
24C2×C4×C22⋊D11C412yes—
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66977C412yes—
27C2×#66977C2211yescharacteristic
28C2×M16×D11C2212yes—
29C2×C11×#101—24no—
30C2×C11×#101C2212yes—
31C2×C11×#101C2211yescharacteristic
32C2×C11×#101C2211yescharacteristic
33C2×#66900C2211yescharacteristic
34C2×#66900C2211yescharacteristic
35C2×#66900C2212yes—
36#10622820C2212yes—
37C2×#66888C2212yes—
38C2×#66888C2212yes—
39#10622741—22no—
40#10622740—22no—
41#10622739C2212yes—
42#10622731C2212yes—
43M16×Dic11C2212yes—
44#10622724—22no—
45C8×C22⋊D11—22no—
46D11×#101—24no—
47#10622192C2212yes—
48#10622192C2212yes—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11—42no—
54C22×Q8×C11C2×C412yes—
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C23×C4×C11C2×C412yes—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11C2×C411yescharacteristic
60C2×Q8×D11—22no—
61C2×Q8×D11—22no—
62C2×Q8×D11—22no—
63C2×Q8×D11—22no—
64C2×Q8×D11—42no—
65C22×C4×D11C2×C412yes—
66C22×C4×D11C2311yescharacteristic
67C22×Dic22C2×C412yes—
68C22×Dic22C2311yescharacteristic
69C2×C11×M16—22no—
70C2×C11×M16—24no—
71C2×C11×M16—42no—
72C2×C11×M16C2312yes—
73C2×C11×M16C2312yes—
74C22×C8×C11—22no—
75C2×C22⋊Dic11C2×C412yes—
76C2×C22⋊Dic11C2×C411yescharacteristic
77#66999—22no—
78#66999—22no—
79#66999—24no—
80#66999—24no—
81Q8×Dic11—22no—
82Q8×Dic11—22no—
83#66997—24no—
84#66997—24no—
85#66997—22no—
86#66997—22no—
87C4×C22⋊D11—22no—
88C4×C22⋊D11—22no—
89C4×C22⋊D11—22no—
90C4×C22⋊D11—22no—
91C4×C22⋊D11D412yes—
92C4×C22⋊D11D412yes—
93C4×C22⋊D11D412yes—
94C4×C22⋊D11D412yes—
95C2×(C2×D11)⋊C4C2×C412yes—
96C2×(C2×D11)⋊C4C2×C411yescharacteristic
97C2×C4⋊Dic11C2×C412yes—
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—22no—
100#66977—22no—
101#66977—24no—
102#66977—24no—
103C2×Dic11⋊C4C2×C412yes—
104C2×Dic11⋊C4C2×C412yes—
105C2×Dic11⋊C4C2×C412yes—
106C2×Dic11⋊C4C2×C412yes—
107C2×Dic11⋊C4C2×C411yescharacteristic
108C2×C4×Dic11C2×C412yes—
109C2×C4×Dic11C2311yescharacteristic
110C2×#4318C2312yes—
111C2×#4318C2312yes—
112M16×D11—24no—
113M16×D11—42no—
114C2×#4313—22no—
115C2×C8×D11—22no—
116C11×#101—22no—
117C11×#101—24no—
118C11×#101D414yescomplemented
119#66900—22no—
120#66900—22no—
121#66900—42no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—22no—
124#66888—24no—
125#66888—42no—
126(C2×D11)⋊C8—22no—
127(C2×D11)⋊C8—22no—
128#66879—22no—
129Dic11⋊C8—22no—
130Dic11⋊C8—22no—
131C8×Dic11—22no—
132D4×#101—111nomaximal, Sylow
133C24×C11C22×C411yescharacteristic
134C23×D11C22×C411yescharacteristic
135C2×Q8×C11—24no—
136C2×Q8×C11—24no—
137C2×Q8×C11—22no—
138C2×Q8×C11—21no—
139C2×Q8×C11—22no—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—42no—
144C2×Q8×C11—44no—
145C2×Q8×C11—44no—
146C2×Q8×C11—44no—
147C2×Q8×C11—44no—
148C2×Q8×C11C2×D412yes—
149C2×Q8×C11#4112yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—24no—
156C22×C4×C11—42no—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C411yescharacteristic
159C22×C4×C11C22×C412yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—24no—
164C2×C22⋊D11C22⋊C411yescharacteristic
165C2×C22⋊D11C22⋊C411yescharacteristic
166C2×C22⋊D11C22⋊C411yescharacteristic
167C2×C22⋊D11C22⋊C411yescharacteristic
168C22×Dic11C22×C412yes—
169C22×Dic11C22×C411yescharacteristic
170C22×Dic11C22×C411yescharacteristic
171C22×Dic11C22×C412yes—
172C22×Dic11C22×C411yescharacteristic
173Q8×D11—44no—
174Q8×D11—44no—
175Q8×D11—44no—
176Q8×D11—44no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—24no—
180C2×C4×D11—21no—
181C2×C4×D11—21no—
182C2×C4×D11—22no—
183C2×C4×D11—42no—
184C2×C4×D11C2×D412yes—
185C2×C4×D11C2×D412yes—
186C2×Dic22—24no—
187C2×Dic22—24no—
188C2×Dic22—21no—
189C2×Dic22—22no—
190C2×Dic22—21no—
191C2×Dic22—22no—
192C2×Dic22—42no—
193C11×M16—22no—
194C11×M16—22no—
195C11×M16—22no—
196C11×M16—44no—
197C11×M16C2×D414yes—
198C2×C8×C11—22no—
199C2×C8×C11—22no—
200C2×C8×C11—44no—
201C22⋊Dic11—22no—
202C22⋊Dic11—22no—
203C22⋊Dic11C22⋊C412yes—
204C22⋊Dic11C22⋊C412yes—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207(C2×D11)⋊C4C22⋊C412yes—
208(C2×D11)⋊C4C22⋊C412yes—
209C4⋊Dic11—24no—
210C4⋊Dic11—22no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—24no—
216Dic11⋊C4C22⋊C412yes—
217Dic11⋊C4C22⋊C412yes—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11C2×D412yes—
221C4×Dic11C2×D412yes—
222#4318—22no—
223#4318—22no—
224#4318—22no—
225#4318—22no—
226C2×C11⋊C8—22no—
227C2×C11⋊C8—22no—
228#4313—44no—
229C8×D11—44no—
230C2×D4×Q8—111no—
231D4×M16—112no—
232C22×#101—111no—
233C22×#101D1111yescharacteristic, complemented
234#1966—112no—
235#1901—112no—
236#1901—112no—
237#1801—111no—
238#1784—111no—
239#1784—111no—
240C4×#101—111no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—22no—
244C23×C11—41no—
245C23×C11C2×C22⋊C411yescharacteristic
246C23×C11C2×C22⋊C411yescharacteristic
247C23×C11C23×C411yescharacteristic
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—22no—
251C22×D11—41no—
252C22×D11C2×C22⋊C411yescharacteristic
253C22×D11C2×C22⋊C411yescharacteristic
254Q8×C11—24no—
255Q8×C11—24no—
256Q8×C11—48no—
257Q8×C11—42no—
258Q8×C11—42no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—44no—
271C2×C4×C11—44no—
272C2×C4×C11C2×C22⋊C412yes—
273C2×C4×C11C4×D414yes—
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)12yes—
278C22⋊D11—22no—
279C22⋊D11—22no—
280C22⋊D11—22no—
281C22⋊D11#10114yesdirect product factor
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—41no—
290C2×Dic11—42no—
291C2×Dic11C2×C22⋊C411yescharacteristic
292C2×Dic11C2×C22⋊C412yes—
293C2×Dic11C2×C22⋊C412yes—
294C2×Dic11C2×C22⋊C411yescharacteristic
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—44no—
300C4×D11—44no—
301Dic22—48no—
302Dic22—42no—
303Dic22—42no—
304C8×C11—24no—
305C8×C11—42no—
306C11⋊C8—42no—
307C11⋊C8—42no—
308C23×Q8—111no—
309C23×Q8C2×D1111yescharacteristic
310C22×M16—112no—
311C22×M16C2×D1112yes—
312D4×Q8—222no—
313D4×Q8—222no—
314D4×Q8—222no—
315D4×Q8—222no—
316C2×C4⋊Q8—111no—
317C2×C4⋊Q8—112no—
318C2×C22⋊Q8—111no—
319C2×C22⋊Q8—112no—
320C2×C22⋊Q8—111no—
321C2×C22⋊Q8—112no—
322C2×C4×Q8—111no—
323C2×C4×D4—111no—
324C2×C4×D4—112no—
325#436—222no—
326#435—222no—
327#435—222no—
328C8×D4—222no—
329#423—112no—
330C2×#101—24no—
331C2×#101—111no—
332C2×#101—111no—
333C2×#101—112no—
334C2×#101—112no—
335C2×#101—112no—
336C2×#101—224no—
337C2×#101C2×D1111yescharacteristic
338C2×#101C2×D1112yes—
339C2×#101C2×D1111yescharacteristic
340#407—112no—
341#407—112no—
342C4×M16—112no—
343#343—112no—
344#343—112no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—21no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11C2×#10112yescomplemented
355C22×C11C22×C22⋊C411yescharacteristic
356C22×C11C2×C4×D411yescharacteristic
357C22×C11#51811yescharacteristic
358C2×D11—21no—
359C2×D11—21no—
360C2×D11—21no—
361C2×D11—21no—
362C2×D11—21no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11C2×#10112yescomplemented
366C4×C11—22no—
367C4×C11—24no—
368C4×C11—42no—
369C4×C11D4212yes—
370C4×C11#54612yes—
371Dic11—22no—
372Dic11—21no—
373Dic11—22no—
374Dic11—42no—
375Dic11—42no—
376Dic11C2×#10112yescomplemented
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—22no—
381C22×Q8—42no—
382C22×Q8—112no—
383C22×Q8—111no—
384C22×Q8—222no—
385C22×Q8—222no—
386C22×Q8—222no—
387C22×Q8—222no—
388C22×Q8—442no—
389C22×Q8C4×D1112yes—
390C22×Q8C22×D1111yescharacteristic
391C22×Q8C22×D1111yescharacteristic
392C22×D4—111no—
393C23×C4—111no—
394C23×C4—112no—
395C23×C4C4×D1112yes—
396C23×C4C22×D1111yescharacteristic
397C2×M16—22no—
398C2×M16—24no—
399C2×M16—42no—
400C2×M16—112no—
401C2×M16—112no—
402C2×M16—222no—
403C2×M16—224no—
404C2×M16—442no—
405C2×M16C22×D1112yes—
406C2×M16C22×D1112yes—
407C22×C8—22no—
408C22×C8—222no—
409C4⋊Q8—222no—
410C4⋊Q8—222no—
411C4⋊Q8—224no—
412C4⋊Q8—224no—
413C22⋊Q8—224no—
414C22⋊Q8—224no—
415C22⋊Q8—224no—
416C22⋊Q8—224no—
417C22⋊Q8—222no—
418C22⋊Q8—222no—
419C22⋊Q8—222no—
420C22⋊Q8—222no—
421C4×Q8—222no—
422C4×Q8—222no—
423C4×D4—112no—
424C4×D4—112no—
425C4×D4—112no—
426C4×D4—112no—
427C4×D4—222no—
428C4×D4—222no—
429C4×D4—222no—
430C4×D4—222no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—111no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—112no—
441C2×C22⋊C4—112no—
442C2×C42—111no—
443C2×C42—112no—
444C4⋊C8—222no—
445C4⋊C8—222no—
446#101—22no—
447#101—24no—
448#101—222no—
449#101—222no—
450#101—224no—
451#101—442no—
452#101—442no—
453#101C22⋊D1114yesdirect product factor
454C22⋊C8—222no—
455C22⋊C8—222no—
456C22⋊C8—222no—
457C22⋊C8—222no—
458#97—222no—
459C4×C8—222no—
460C2×C11—21no—
461C2×C11—21no—
462C2×C11—22no—
463C2×C11—41no—
464C2×C11D4×C22⋊C411yescharacteristic
465C2×C11C22×#10111yescharacteristic
466C2×C11#288911yescharacteristic
467D11—22no—
468D11—41no—
469C24—111no—
470C24C2×C4×D1111yescharacteristic
471C2×Q8—24no—
472C2×Q8—24no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—21no—
479C2×Q8—42no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—224no—
485C2×Q8—224no—
486C2×Q8—221no—
487C2×Q8—222no—
488C2×Q8—222no—
489C2×Q8—221no—
490C2×Q8—442no—
491C2×Q8—444no—
492C2×Q8—444no—
493C2×Q8—444no—
494C2×Q8—444no—
495C2×Q8#433912yes—
496C2×Q8C2×C22⋊D1112yes—
497C2×D4—111no—
498C2×D4—111no—
499C2×D4—111no—
500C2×D4—111no—
501C2×D4—224no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—42no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—221no—
519C22×C4—222no—
520C22×C4—221no—
521C22×C4—224no—
522C22×C4—442no—
523C22×C4C2×C4×D1112yes—
524C22×C4C2×C4×D1111yescharacteristic
525C22×C4C2×C4×D1112yes—
526C22×C4D4×D1112yes—
527C22×C4D4×D1112yes—
528C22×C4C23×D1111yescharacteristic
529M16—22no—
530M16—22no—
531M16—22no—
532M16—44no—
533M16—222no—
534M16—222no—
535M16—222no—
536M16—222no—
537M16—444no—
538M16C2×C22⋊D1114yes—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—44no—
542C2×C8—222no—
543C2×C8—222no—
544C2×C8—444no—
545C4⋊C4—112no—
546C4⋊C4—112no—
547C4⋊C4—222no—
548C4⋊C4—222no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—224no—
552C4⋊C4—224no—
553C4⋊C4—222no—
554C22⋊C4—112no—
555C22⋊C4—112no—
556C22⋊C4—112no—
557C22⋊C4—112no—
558C22⋊C4—222no—
559C22⋊C4—222no—
560C22⋊C4—222no—
561C22⋊C4—222no—
562C42—112no—
563C42—112no—
564C42—222no—
565C42—222no—
566C11D4×#10111yescharacteristic, complemented, Sylow
567C23—21no—
568C23—21no—
569C23—22no—
570C23—41no—
571C23—111no—
572C23—111no—
573C23—222no—
574C23—221no—
575C23—221no—
576C23—441no—
577C23C22⋊C4×D1111yescharacteristic
578C23C22⋊C4×D1111yescharacteristic
579C23C22×C4×D1111yescharacteristic
580Q8—24no—
581Q8—24no—
582Q8—48no—
583Q8—42no—
584Q8—42no—
585Q8—448no—
586Q8—442no—
587Q8—442no—
588D4—114no—
589D4—222no—
590D4—222no—
591D4—222no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—111no—
606C2×C4—111no—
607C2×C4—112no—
608C2×C4—112no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—444no—
621C2×C4—444no—
622C2×C4—441no—
623C2×C4—442no—
624C2×C4C22⋊C4×D1112yes—
625C2×C4C4×C22⋊D1114yes—
626C2×C4C2×#433911yescharacteristic
627C2×C4C2×D4×D1112yes—
628C2×C4#6703712yes—
629C2×C4C22×C22⋊D1111yescharacteristic
630C8—24no—
631C8—42no—
632C8—442no—
633C8—442no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—42no—
642C22—42no—
643C22—112no—
644C22—221no—
645C22—221no—
646C22—221no—
647C22—221no—
648C22—221no—
649C22—442no—
650C22—442no—
651C22D11×#10112yescomplemented
652C22C2×C22⋊C4×D1111yescharacteristic
653C22#1062301711yescharacteristic
654C22C2×C4×C22⋊D1111yescharacteristic
655C4—22no—
656C4—24no—
657C4—42no—
658C4—112no—
659C4—222no—
660C4—221no—
661C4—222no—
662C4—442no—
663C4—442no—
664C4#1062302112yes—
665C4D4×C22⋊D1112yes—
666C2—21no—
667C2—21no—
668C2—22no—
669C2—41no—
670C2—222no—
671C2—441no—
672C2C22⋊C4×C22⋊D1111yescharacteristic
673C2C2×D11×#10111yescharacteristic
674C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#101C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenterC22×#101D11
hypocenterC11D4×#101
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
3. C2×D11×#101C2semidirect
4. #13069458C2semidirect
5. #13069084C2semidirect
6. #13069081C2semidirect
7. #13068610C2semidirect
8. #13068540C2semidirect
9. #13068538C2semidirect
10. #101×Dic11C2semidirect
11. C22×C11×#101C2semidirect
118. C11×#101D4semidirect
233. C22×#101D11semidirect
281. C22⋊D11#101direct (N × H)
354. C22×C11C2×#101semidirect
365. C2×D11C2×#101semidirect
376. Dic11C2×#101semidirect
453. #101C22⋊D11direct (N × H)
566. C11D4×#101semidirect
651. C22D11×#101semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D112
M16×C22⋊D112
C2×D11×#1012
#130694582
#130690842
#130690812
#130686102
#130685402
#130685382
#101×Dic112
C22×C11×#1012
D4×#10111