Finite Group Databasebeta

← #14810910

Subgroups — #14810910

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622464C211yesmaximal, characteristic, complemented
2C22×#66880C211yesmaximal, characteristic
3#13072318C211yesmaximal, characteristic
4C22⋊C4×Dic22C211yesmaximal, characteristic
5#13070158C211yesmaximal, characteristic, complemented
6#13069996C211yesmaximal, characteristic, complemented
7#13069996C211yesmaximal, characteristic, complemented
8#13069758C211yesmaximal, characteristic, complemented
9#13068887C211yesmaximal, characteristic, complemented
10#13068887C211yesmaximal, characteristic, complemented
11#13068811C211yesmaximal, characteristic
12#13068641C211yesmaximal, characteristic
13#13068622C211yesmaximal, characteristic, complemented
14#13068552C211yesmaximal, characteristic
15C11×#1850C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66931—21no—
20C2×#66922C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622825C2211yescharacteristic
28#10622825C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880—24no—
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42#10622563—21no—
43#10622555—21no—
44C22⋊C4×Dic11—21no—
45#10622548C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622464—24no—
51#10622274—21no—
52#10622269—21no—
53#10622259—21no—
54#10622259—21no—
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22—21no—
67C22×Dic22—22no—
68C22×Dic22—21no—
69C22×Dic22—41no—
70C22×Dic22—41no—
71C22×Dic22Q814yescomplemented
72C22×Dic22C2311yescharacteristic
73C22×Dic22C2311yescharacteristic
74C22×C8×C11—22no—
75C22×C8×C11—22no—
76C22×C8×C11—41no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105#66931—44no—
106#66922—22no—
107#66922—41no—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—41no—
111C4×Dic22—41no—
112C11×C4⋊C8—22no—
113C11×C4⋊C8—41no—
114C11×C22⋊C8—22no—
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66881—22no—
126#66881—22no—
127#66881—41no—
128#66881—41no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#66880—22no—
133#66880—22no—
134#66880—41no—
135#66880—41no—
136#66880D414yes—
137#25955—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×Q812yes—
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—24no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11—81no—
165C2×Dic22—28no—
166C2×Dic22—24no—
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×Dic22—44no—
176C2×Dic22—44no—
177C2×Dic22—44no—
178C2×Dic22—42no—
179C2×Dic22—42no—
180C2×Dic22—42no—
181C2×Dic22—42no—
182C2×Dic22—81no—
183C2×Dic22C2×D412yes—
184C2×Dic22C2×Q812yes—
185C2×Dic22C2×Q812yes—
186C2×Dic22#4112yes—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—44no—
199C2×C8×C11C2×D412yes—
200C11×C22⋊C4—22no—
201C11×C22⋊C4SD1614yes—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C22⋊Dic11—42no—
207C22⋊Dic11—42no—
208C4⋊Dic11—21no—
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—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—42no—
220C4⋊Dic11—42no—
221C4⋊Dic11—42no—
222C4⋊Dic11—81no—
223C4⋊Dic11C2×D412yes—
224Dic11⋊C4—42no—
225Dic11⋊C4—42no—
226Dic11⋊C4—42no—
227Dic11⋊C4—42no—
228C4×Dic11—42no—
229C4×Dic11—42no—
230C2×#475—111no—
231C22×#103—111no—
232#2440—111no—
233Q8×C22⋊C4—111no—
234#2096—111no—
235#2066—111no—
236#2066—111no—
237#2024—111no—
238#1865—111no—
239#1865—111no—
240#1853—111no—
241#1850D1111yescharacteristic
242#1807—111no—
243#1803—111no—
244#1787—111no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11C22⋊Q812yes—
250C23×C11C2×SD1612yes—
251C23×C11#13712yes—
252C23×C11C22×D411yescharacteristic
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—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11C22⋊Q812yes—
270C2×C4×C11C2×SD1612yes—
271C2×C4×C11C2×SD1612yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×Q811yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—48no—
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—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—84no—
304Dic22—22no—
305Dic22—22no—
306Dic22—22no—
307Dic22—22no—
308Dic22—22no—
309Dic22—48no—
310Dic22—41no—
311Dic22—41no—
312Dic22—84no—
313Dic22C22⋊Q814yescomplemented
314C8×C11—22no—
315C8×C11—41no—
316C8×C11—41no—
317C8×C11—41no—
318C23×Q8—111no—
319C23×C8C2×D1111yescharacteristic
320C2×C4⋊Q8—111no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C22×C4⋊C4—111no—
325#475—224no—
326C2×#106—111no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#106—111no—
330C2×C4⋊C8C2×D1111yescharacteristic
331C2×C4⋊C8C2×D1111yescharacteristic
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#103—224no—
341C2×C22⋊C8C2×D1111yescharacteristic
342#398—221no—
343#395—221no—
344#391—111no—
345#391—111no—
346#391—221no—
347#391—221no—
348#389—111no—
349#389—111no—
350#385—221no—
351#384—111no—
352#380—111no—
353#380—111no—
354#380—221no—
355C4×C22⋊C4—221no—
356C4×C22⋊C4C2×D1111yescharacteristic
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#336C2×D1111yescharacteristic
362#336C2×D1111yescharacteristic
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11#47514yescomplemented
370C22×C11C2×C22⋊Q811yescharacteristic
371C22×C11D4211yescharacteristic
372C22×C11#54611yescharacteristic
373C22×C11C22×SD1611yescharacteristic
374C22×C11C2×#13711yescharacteristic
375C22×C11#57711yescharacteristic
376C22×C11#57811yescharacteristic
377C4×C11—22no—
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11C2×C22⋊Q811yescharacteristic
383C4×C11#54311yescharacteristic
384C4×C11#54611yescharacteristic
385C4×C11#55111yescharacteristic
386Dic11—24no—
387Dic11—42no—
388Dic11—42no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393Dic11—81no—
394C22×Q8—114no—
395C22×Q8—111no—
396C22×Q8—111no—
397C22×Q8—222no—
398C22×Q8—222no—
399C22×Q8—221no—
400C22×Q8—221no—
401C22×Q8—222no—
402C22×Q8—441no—
403C22×Q8—441no—
404C23×C4—221no—
405C23×C4—221no—
406C23×C4C22×D1111yescharacteristic
407C22×C8—22no—
408C22×C8—22no—
409C22×C8—41no—
410C22×C8C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412C22×C8C22×D1111yescharacteristic
413C22×C8C22×D1111yescharacteristic
414C4⋊Q8—222no—
415C4⋊Q8—441no—
416C22⋊Q8—444no—
417C4×Q8—222no—
418C4×Q8—222no—
419C4×Q8—441no—
420C4×Q8—441no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—441no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4D4411yescharacteristic
440C2×C22⋊C4D4411yescharacteristic
441C2×C42—221no—
442C2×C42—221no—
443C2×C42C22×D1111yescharacteristic
444C2×C42C22×D1111yescharacteristic
445#106—222no—
446#106—222no—
447#106—441no—
448#106—441no—
449C4⋊C8—22no—
450C4⋊C8—41no—
451#103—114no—
452#103—222no—
453#103—222no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—441no—
458#103—441no—
459C22⋊C8—22no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95D4411yescharacteristic
469#95D4411yescharacteristic
470C2×C11—24no—
471C2×C11#243711yescharacteristic
472C2×C11C2×#47511yescharacteristic
473C2×C11#308211yescharacteristic
474C2×C11#327011yescharacteristic
475C2×C11D4×SD1611yescharacteristic
476C2×C11#329811yescharacteristic
477C2×C11#331611yescharacteristic
478C24C2×D4411yescharacteristic
479C2×Q8—112no—
480C2×Q8—112no—
481C2×Q8—112no—
482C2×Q8—112no—
483C2×Q8—228no—
484C2×Q8—224no—
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—442no—
494C2×Q8—442no—
495C2×Q8—442no—
496C2×Q8—444no—
497C2×Q8—444no—
498C2×Q8—444no—
499C2×Q8—442no—
500C2×Q8—881no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—221no—
506C22×C4—224no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—881no—
519C22×C4C2×D4411yescharacteristic
520C22×C4C2×D4411yescharacteristic
521C22×C4C2×D4411yescharacteristic
522C22×C4C2×D4411yescharacteristic
523C22×C4C2×D4411yescharacteristic
524C22×C4#434112yes—
525C22×C4Q8×D1112yes—
526C22×C4C23×D1111yescharacteristic
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—44no—
539C2×C8D4×D1112yes—
540C4⋊C4—112no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4—881no—
560C22⋊C4—22no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4#431414yes—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—442no—
569C42—442no—
570C11#2595511yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23#6695012yes—
576C23C2×#431412yes—
577C23#6696212yes—
578C23C22×D4411yescharacteristic
579Q8—114no—
580Q8—222no—
581Q8—222no—
582Q8—222no—
583Q8—222no—
584Q8—222no—
585Q8—448no—
586Q8—441no—
587Q8—441no—
588Q8—884no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—448no—
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×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—884no—
631C2×C4#6695012yes—
632C2×C4C2×#431412yes—
633C2×C4C2×#431412yes—
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4C2×#434111yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4C2×Q8×D1111yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#6704211yescharacteristic
640C8—22no—
641C8—41no—
642C8—41no—
643C8—41no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22#1062246414yescomplemented
651C22C2×#6695011yescharacteristic
652C22D4×D4411yescharacteristic
653C22#1062308511yescharacteristic
654C22C22×#431411yescharacteristic
655C22C2×#6696211yescharacteristic
656C22#1062328211yescharacteristic
657C22#1062328411yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—41no—
662C4—41no—
663C4—224no—
664C4—442no—
665C4—442no—
666C4—881no—
667C4—881no—
668C4—881no—
669C4—881no—
670C4—881no—
671C4#1062312211yescharacteristic
672C4D11×C22⋊Q811yescharacteristic
673C4#1062316511yescharacteristic
674C4#1062318911yescharacteristic
675C2—24no—
676C2#1307228011yescharacteristic
677C2C2×#1062246411yescharacteristic
678C2#1307845911yescharacteristic
679C2#1308019111yescharacteristic
680C2D4×#431411yescharacteristic
681C2#1308048211yescharacteristic
682C2#1308072911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1850D11
hypocenterC11#25955
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#10622464C2semidirect
5. #13070158C2semidirect
6. #13069996C2semidirect
7. #13069996C2semidirect
8. #13069758C2semidirect
9. #13068887C2semidirect
10. #13068887C2semidirect
13. #13068622C2semidirect
71. C22×Dic22Q8semidirect
313. Dic22C22⋊Q8semidirect
369. C22×C11#475semidirect
570. C11#25955semidirect
650. C22#10622464semidirect

Maximal subgroups

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

subgroupindex
C2×#106224642
C22×#668802
#130723182
C22⋊C4×Dic222
#130701582
#130699962
#130697582
#130688872
#130688112
#130686412
#130686222
#130685522
C11×#18502
#2595511