Finite Group Databasebeta

← #14770646

Subgroups — #14770646

Order 2816.

1054 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×#10623115C211yesmaximal, characteristic
2#13071573C211yesmaximal, characteristic, complemented
3#13069546C211yesmaximal, characteristic
4#13069546C211yesmaximal, characteristic
5#13069538C211yesmaximal, characteristic, complemented
6#13069436C211yesmaximal, characteristic, complemented
7#13069432C211yesmaximal, characteristic
8#13069427C211yesmaximal, characteristic
9#13068632C211yesmaximal, characteristic, complemented
10#13068627C211yesmaximal, characteristic
11#13068622C211yesmaximal, characteristic, complemented
12#13068447C211yesmaximal, characteristic, complemented
13#13068442C211yesmaximal, characteristic
14C4×#66880C211yesmaximal, characteristic, complemented
15C2×C11×#446C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999—21no—
18#10623115—24no—
19#10623115C418yescomplemented
20C2×#66951—21no—
21C2×#66951—21no—
22C2×#66945—21no—
23C2×#66928C2211yescharacteristic
24C2×#66928C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C11×#446—24no—
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C2×C11×#97C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36#10622843—21no—
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×#66880C2211yescharacteristic
45C2×#66880C2211yescharacteristic
46C2×#66880C2211yescharacteristic
47C2×#66880C2211yescharacteristic
48C2×#66880C2211yescharacteristic
49#10622594—21no—
50#10622594—21no—
51C4⋊C4×Dic11—21no—
52#10622549C2211yescharacteristic
53#10622549C2211yescharacteristic
54#10622548C2211yescharacteristic
55C4×C4⋊Dic11C2211yescharacteristic
56C4×C4⋊Dic11C2211yescharacteristic
57C4×C4⋊Dic11C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62C22×Q8×C11D411yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×Q8×C11C2×C414yes—
72C4×Q8×C11D414yes—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79#66999—28no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101#66951—28no—
102#66951—28no—
103#66945—28no—
104#66928—22no—
105#66928—22no—
106#66928C2×C414yes—
107#66928C2×C414yes—
108C4×D44—22no—
109C4×D44C2×C414yes—
110#66922—22no—
111#66922C2×C414yes—
112C4×Dic22—22no—
113C4×Dic22—22no—
114C4×Dic22C2×C414yes—
115C4×Dic22C2×C414yes—
116C11×C4⋊C8—22no—
117C11×C4⋊C8—22no—
118C11×C4⋊C8—22no—
119C11×#97—22no—
120C11×#97—22no—
121C4×C8×C11—22no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129#66885—22no—
130#66885—22no—
131#66885—41no—
132#66885—41no—
133#66880—22no—
134#66880—22no—
135#66880—22no—
136#66880—22no—
137#66880—41no—
138#66880—41no—
139#66880—41no—
140#66880—41no—
141#22548—111nomaximal, Sylow
142C23×D11—21no—
143C2×Q8×C11—41no—
144C2×Q8×C11—41no—
145C2×Q8×C11C22⋊C414yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44C22×C412yes—
166C2×C4×D11—24no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22C22×C412yes—
180C2×Dic22C22×C412yes—
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×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11#4112yes—
193C11×C4⋊C4C22⋊C414yes—
194C11×C4⋊C4C22⋊C414yes—
195C11×C4⋊C4C22⋊C414yes—
196C42×C11C22×C412yes—
197C42×C11C22×C412yes—
198C42×C11C22×C412yes—
199C42×C11C2×D412yes—
200C42×C11C2×D412yes—
201C42×C11C2×D412yes—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—24no—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—24no—
207C4⋊Dic11—24no—
208C4⋊Dic11—24no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—42no—
218C4⋊Dic11—81no—
219C4⋊Dic11C22×C412yes—
220C4⋊Dic11#4112yes—
221Dic11⋊C4—24no—
222Dic11⋊C4—24no—
223C4×Dic11—24no—
224C4×Dic11—24no—
225C4×Dic11—42no—
226C4×Dic11—81no—
227C4×Dic11—81no—
228C2×#556—111no—
229C2×#446D1111yescharacteristic, complemented
230#2355—111no—
231#1983—111no—
232#1983—111no—
233#1981—111no—
234#1960—111no—
235#1959—111no—
236#1958—111no—
237#1805—111no—
238#1804—111no—
239#1803—111no—
240#1763—111no—
241#1762—111no—
242C4×#103—111no—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251Q8×C11—44no—
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×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C2×C22⋊C412yes—
267C2×C4×C11C2×C22⋊C412yes—
268C2×C4×C11C2×C22⋊C412yes—
269C2×C4×C11C2×C22⋊C412yes—
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
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—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297D44—22no—
298D44—22no—
299D44—41no—
300D44—41no—
301C4×D11—48no—
302Dic22—22no—
303Dic22—22no—
304Dic22—22no—
305Dic22—22no—
306Dic22—41no—
307Dic22—41no—
308Dic22—41no—
309Dic22—41no—
310C8×C11—22no—
311C8×C11—41no—
312C8×C11—41no—
313C8×C11—41no—
314#556—118no—
315#556—224no—
316C2×C4⋊Q8—111no—
317C2×#126—221no—
318C2×#126—221no—
319C2×#124—111no—
320C2×#124—111no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C2×C4×Q8C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×#117—221no—
327#446—24no—
328C2×C4⋊C8C2×D1111yescharacteristic
329C2×C4⋊C8C2×D1111yescharacteristic
330C2×C4⋊C8C2×D1111yescharacteristic
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#102—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#97C2×D1111yescharacteristic
344C2×#97C2×D1111yescharacteristic
345C2×C4×C8C2×D1111yescharacteristic
346#391—221no—
347#387—221no—
348#387—221no—
349#384—111no—
350#382—111no—
351#382—111no—
352C4×C4⋊C4—111no—
353C4×C4⋊C4—111no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4—221no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360C22×C11C22×C22⋊C411yescharacteristic
361C22×C11#54811yescharacteristic
362C22×C11#55011yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57511yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57811yescharacteristic
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—22no—
380C4×C11C4×#4111yescharacteristic
381C4×C11#52011yescharacteristic
382C4×C11#54811yescharacteristic
383C4×C11#55011yescharacteristic
384Dic11—42no—
385Dic11—42no—
386Dic11—42no—
387Dic11—42no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—111no—
392C22×Q8—111no—
393C22×Q8D4411yescharacteristic
394C22×D4—111no—
395C23×C4—221no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C4⋊Q8—114no—
401C4⋊Q8—222no—
402#126—228no—
403#126—228no—
404#124—114no—
405#124—114no—
406#124—222no—
407#124—222no—
408C22⋊Q8—228no—
409C4×Q8—114no—
410C4×Q8—114no—
411C4×Q8—222no—
412C4×Q8—222no—
413C4×Q8C4×D1114yes—
414C4×Q8C22⋊D1114yes—
415C4×D4—114no—
416C4×D4—222no—
417#117—228no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4D4411yescharacteristic
430C2×C4⋊C4D4411yescharacteristic
431C2×C4⋊C4D4411yescharacteristic
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42—221no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1111yescharacteristic
444C2×C42C22×D1111yescharacteristic
445C4⋊C8—22no—
446C4⋊C8—22no—
447C4⋊C8—22no—
448#103—222no—
449#103—222no—
450#103—222no—
451#103—222no—
452#103—441no—
453#103—441no—
454#103—441no—
455#103—441no—
456#102—222no—
457#102—222no—
458#102—441no—
459#102—441no—
460#97—22no—
461#97—22no—
462C4×C8—22no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11#234111yescharacteristic
471C2×C11#289611yescharacteristic
472C2×C11#289811yescharacteristic
473C2×C11#337611yescharacteristic
474C2×C11#337711yescharacteristic
475C2×C11#340111yescharacteristic
476C2×C11#340211yescharacteristic
477D11—82no—
478C24—221no—
479C2×Q8—41no—
480C2×Q8—41no—
481C2×Q8—112no—
482C2×Q8—112no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8(C2×D11)⋊C414yes—
494C2×D4—112no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—224no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4C2×D4411yescharacteristic
511C22×C4C2×D4411yescharacteristic
512C22×C4C2×D4411yescharacteristic
513C22×C4C2×D4411yescharacteristic
514C22×C4C2×D4411yescharacteristic
515C22×C4C2×D4411yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8#434312yes—
529C4⋊C4—112no—
530C4⋊C4—112no—
531C4⋊C4—224no—
532C4⋊C4—224no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—442no—
544C4⋊C4—881no—
545C4⋊C4(C2×D11)⋊C414yes—
546C4⋊C4(C2×D11)⋊C414yes—
547C4⋊C4(C2×D11)⋊C414yes—
548C22⋊C4—224no—
549C22⋊C4—224no—
550C22⋊C4—224no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C42—224no—
554C42—224no—
555C42—442no—
556C42—881no—
557C42—881no—
558C42C2×C4×D1112yes—
559C42C2×C4×D1112yes—
560C42C2×C4×D1112yes—
561C42C2×C22⋊D1112yes—
562C42C2×C22⋊D1112yes—
563C42C2×C22⋊D1112yes—
564C11#2254811yescharacteristic, complemented, Sylow
565C23—222no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23C22×D4411yescharacteristic
573Q8—44no—
574Q8—222no—
575Q8—222no—
576Q8—222no—
577Q8—222no—
578Q8—441no—
579Q8—441no—
580Q8—441no—
581Q8—441no—
582D4—222no—
583D4—222no—
584D4—441no—
585D4—441no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—448no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4C2×(C2×D11)⋊C412yes—
621C2×C4C2×(C2×D11)⋊C412yes—
622C2×C4C2×(C2×D11)⋊C412yes—
623C2×C4C2×(C2×D11)⋊C412yes—
624C2×C4C2×(C2×D11)⋊C412yes—
625C2×C4C2×(C2×D11)⋊C412yes—
626C2×C4C22×C4×D1111yescharacteristic
627C2×C4C2×#434311yescharacteristic
628C2×C4#6704011yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#6704211yescharacteristic
631C2×C4C22×C22⋊D1111yescharacteristic
632C8—22no—
633C8—41no—
634C8—41no—
635C8—41no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22#1062310711yescharacteristic
644C22#1062310811yescharacteristic
645C22#1062327911yescharacteristic
646C22#1062327911yescharacteristic
647C22#1062328211yescharacteristic
648C22#1062328411yescharacteristic
649C22C22×(C2×D11)⋊C411yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—442no—
657C4—442no—
658C4—442no—
659C4—442no—
660C4—881no—
661C4—881no—
662C4—881no—
663C4C4×#434311yescharacteristic
664C4#1062310511yescharacteristic
665C4#1062334811yescharacteristic
666C4#1062336511yescharacteristic
667C2—882no—
668C2#1307145411yescharacteristic
669C2#1307713611yescharacteristic
670C2#1307715011yescharacteristic
671C2#1308144511yescharacteristic
672C2#1308146011yescharacteristic
673C2#1308168411yescharacteristic
674C2#1308169711yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#446C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC2×#446D11
hypocenterC11#22548
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13071573C2semidirect
5. #13069538C2semidirect
6. #13069436C2semidirect
9. #13068632C2semidirect
11. #13068622C2semidirect
12. #13068447C2semidirect
14. C4×#66880C2semidirect
15. C2×C11×#446C2semidirect
19. #10623115C4semidirect
229. C2×#446D11semidirect
564. C11#22548semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
#130715732
#130695462
#130695382
#130694362
#130694322
#130694272
#130686322
#130686272
#130686222
#130684472
#130684422
C4×#668802
C2×C11×#4462
#2254811