Finite Group Databasebeta

← #14756194

Subgroups — #14756194

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622474C211yesmaximal, characteristic
2C2×#10622415C211yesmaximal, characteristic
3C2×#10622415C211yesmaximal, characteristic
4D11×#391C211yesmaximal, characteristic
5C4×#66945C211yesmaximal, characteristic
6#13069259C211yesmaximal, characteristic, complemented
7#13069258C211yesmaximal, characteristic, complemented
8#13069255C211yesmaximal, characteristic, complemented
9#13069254C211yesmaximal, characteristic, complemented
10#13069253C211yesmaximal, characteristic, complemented
11#13069250C211yesmaximal, characteristic, complemented
12#13069249C211yesmaximal, characteristic, complemented
13#13068334C211yesmaximal, characteristic
14#13068308C211yesmaximal, characteristic
15C11×#1927C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622587C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C4×(C2×D11)⋊C4—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C42×Dic11—21no—
44#10622542C2211yescharacteristic
45#10622474—24no—
46#10622415—24no—
47#10622415C418yescomplemented
48#10622279—21no—
49D11×#95—21no—
50D11×#95—21no—
51#10622261—21no—
52#10622259—21no—
53#10622259—21no—
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C2×Q8×D11—22no—
64C2×Q8×D11—22no—
65C2×Q8×D11—22no—
66C2×Q8×D11—22no—
67C2×Q8×D11—22no—
68C2×Q8×D11C2×C414yes—
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11D411yescharacteristic
72C22×C4×D11D411yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×Dic22—21no—
75C22×Dic22C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×#4313—22no—
100C2×#4313—22no—
101C2×#4313—22no—
102C2×#4313—22no—
103C2×#4313—22no—
104C2×#4313C2×C414yes—
105#66945—22no—
106#66945—22no—
107#66945C2×C414yes—
108#66945D414yes—
109C4⋊C4×D11—22no—
110C4⋊C4×D11—22no—
111C42×D11—22no—
112C42×D11—22no—
113C11×#106—22no—
114C11×#103—22no—
115C11×#103C2×C414yescomplemented
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119#66899—22no—
120#66899C2×C414yescomplemented
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130#66882—22no—
131#66880—22no—
132#66880C2×C414yescomplemented
133#66874—22no—
134#66874C2×C414yescomplemented
135#66872—22no—
136#66871—22no—
137#21061—111nomaximal, Sylow
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159Q8×D11—28no—
160Q8×D11—28no—
161Q8×D11—44no—
162Q8×D11—44no—
163C2×C4×D11—22no—
164C2×C4×D11—24no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—41no—
169C2×C4×D11—41no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11C22×C412yes—
176C2×C4×D11C2×D412yes—
177C2×C4×D11#4112yes—
178C2×C4×D11#4112yes—
179C2×C4×D11#4112yes—
180C2×C4×D11#4112yes—
181C2×Dic22—24no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—42no—
188C2×Dic22—42no—
189C2×Dic22C22×C412yes—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11C22×C412yes—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4C22×C412yes—
201C11×C4⋊C4C2×D412yes—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—42no—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—24no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11C22×C412yes—
212C4⋊Dic11C2×D412yes—
213Dic11⋊C4—42no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—42no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8C22×C412yes—
229#4313—28no—
230#4313—44no—
231C2×#428—111no—
232C2×#419—111no—
233C2×#419—111no—
234C2×#391—111no—
235C4×#117—111no—
236#1928—111no—
237#1928—111no—
238#1928—111no—
239#1928—111no—
240#1927—111no—
241#1927—111no—
242#1927—111no—
243#1927D1111yescharacteristic, complemented
244#1736—111no—
245#1728—111no—
246C23×C11C22×D411yescharacteristic
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11C4×D412yes—
252C22×D11#12112yes—
253C22×D11#12312yes—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
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—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11#13712yes—
276C2×C4×C11C23×C411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
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×Dic11C4×D412yes—
300C2×Dic11#12112yes—
301C2×Dic11#12312yes—
302C2×Dic11#13712yes—
303C4×D11—44no—
304C4×D11—44no—
305C4×D11—48no—
306C4×D11—84no—
307C4×D11#11714yes—
308C4×D11C4×D414yes—
309C4×D11#12414yes—
310C4×D11#12614yes—
311Dic22—22no—
312Dic22—22no—
313Dic22—41no—
314Dic22—41no—
315Dic22—48no—
316C8×C11—22no—
317C8×C11—41no—
318C11⋊C8—22no—
319C11⋊C8—41no—
320C23×Q8—111no—
321C22×M16—111no—
322C22×M16—111no—
323C2×#117—111no—
324C2×#117—111no—
325C22×C4⋊C4—111no—
326C22×C42—111no—
327#428—224no—
328C2×#107—111no—
329C2×#107—111no—
330C2×#106—111no—
331C2×#106C2×D1111yescharacteristic
332#419—118no—
333#419—224no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#103C2×D1111yescharacteristic
341C2×#103C2×D1111yescharacteristic
342#391—111no—
343#391—111no—
344#391—111no—
345#391—221no—
346#391—221no—
347#391C2×D1111yescharacteristic
348C4×C4⋊C4—111no—
349C4×C4⋊C4—111no—
350C4×C4⋊C4—111no—
351C4×C4⋊C4C2×D1111yescharacteristic
352C4×C22⋊C4—221no—
353C4×C22⋊C4—221no—
354#376—221no—
355C2×#95—221no—
356C2×#95—221no—
357C43—221no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340C2×D1111yescharacteristic
362#336—111no—
363#336—111no—
364#336—111no—
365#336C2×D1111yescharacteristic
366C22×C11C2×C4×D411yescharacteristic
367C22×C11C2×#12111yescharacteristic
368C22×C11C2×#12311yescharacteristic
369C22×C11C2×#13711yescharacteristic
370C22×C11C2×#13711yescharacteristic
371C22×C11#57511yescharacteristic
372C22×C11#57511yescharacteristic
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11#38814yes—
380C4×C11—22no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—42no—
384C4×C11—42no—
385C4×C11—81no—
386C4×C11C2×#11711yescharacteristic
387C4×C11C2×C4×D411yescharacteristic
388C4×C11C2×#12411yescharacteristic
389C4×C11C2×#12611yescharacteristic
390Dic11—22no—
391Dic11—41no—
392Dic11—42no—
393Dic11—42no—
394Dic11—42no—
395Dic11—81no—
396Dic11#38814yes—
397C22×Q8—114no—
398C22×Q8—111no—
399C22×Q8—221no—
400C22×Q8—222no—
401C22×Q8—222no—
402C22×Q8—222no—
403C22×Q8—222no—
404C22×Q8—222no—
405C22×Q8C22×D1111yescharacteristic
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—111no—
409C23×C4—221no—
410C23×C4—221no—
411C2×M16—114no—
412C2×M16—222no—
413C2×M16—222no—
414C2×M16—222no—
415C2×M16—222no—
416C2×M16—222no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421#117—114no—
422#117—114no—
423#117—222no—
424#117—222no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C42—21no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—222no—
441C2×C42—222no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42—221no—
447C2×C42C22×D1111yescharacteristic
448#107—222no—
449#107—222no—
450#106—22no—
451#106—222no—
452#103—22no—
453#103—114no—
454#103—114no—
455#103—114no—
456#103—222no—
457#103—222no—
458#103—222no—
459#103C4×D1114yescomplemented
460#95—21no—
461#95—21no—
462#95—21no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472C2×C11C2×#38811yescharacteristic
473C2×C11C4×#13711yescharacteristic
474C2×C11C4×#13711yescharacteristic
475C2×C11#303911yescharacteristic
476C2×C11#304011yescharacteristic
477C2×C11#309511yescharacteristic
478C2×C11#309511yescharacteristic
479D11—24no—
480C24—111no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—112no—
487C2×Q8—224no—
488C2×Q8—228no—
489C2×Q8—228no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×Q8—442no—
496C2×Q8—442no—
497C2×Q8—444no—
498C2×Q8—444no—
499C2×Q8C2×C4×D1112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—112no—
510C22×C4—112no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—224no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—222no—
521C22×C4—221no—
522C22×C4—441no—
523C22×C4—441no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4—442no—
529C22×C4D4×D1111yescharacteristic
530C22×C4D4×D1111yescharacteristic
531C22×C4C23×D1111yescharacteristic
532M16—228no—
533M16—444no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—112no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8C2×C4×D1112yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—112no—
551C4⋊C4—112no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—442no—
557C4⋊C4C2×C4×D1112yes—
558C4⋊C4D4×D1112yes—
559C22⋊C4—224no—
560C22⋊C4—224no—
561C42—21no—
562C42—21no—
563C42—42no—
564C42—222no—
565C42—222no—
566C42—224no—
567C42—224no—
568C42—221no—
569C42—221no—
570C42—442no—
571C42—442no—
572C42—442no—
573C11#2106111yescharacteristic, complemented, Sylow
574C23—112no—
575C23—112no—
576C23—112no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23—221no—
581C23C2×D4×D1111yescharacteristic
582Q8—22no—
583Q8—22no—
584Q8—41no—
585Q8—41no—
586Q8—222no—
587Q8—222no—
588Q8—448no—
589Q8—441no—
590Q8—441no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—112no—
609C2×C4—112no—
610C2×C4—112no—
611C2×C4—114no—
612C2×C4—114no—
613C2×C4—114no—
614C2×C4—114no—
615C2×C4—112no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—221no—
624C2×C4—444no—
625C2×C4—444no—
626C2×C4—448no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—884no—
637C2×C4#6696812yes—
638C2×C4C22×C4×D1111yescharacteristic
639C2×C4C2×D4×D1111yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C8—22no—
645C8—41no—
646C8—222no—
647C8—441no—
648C22—114no—
649C22—222no—
650C22—222no—
651C22—222no—
652C22—222no—
653C22—222no—
654C22—222no—
655C22C4×D4×D1111yescharacteristic
656C22D11×#12111yescharacteristic
657C22D11×#12311yescharacteristic
658C22C2×#6696811yescharacteristic
659C22#1062329911yescharacteristic
660C22D11×#13711yescharacteristic
661C22#1062330811yescharacteristic
662C4—22no—
663C4—41no—
664C4—42no—
665C4—42no—
666C4—42no—
667C4—81no—
668C4—114no—
669C4—222no—
670C4—441no—
671C4—442no—
672C4—442no—
673C4—442no—
674C4—881no—
675C4D11×#11711yescharacteristic
676C4C4×D4×D1111yescharacteristic
677C4D11×#12411yescharacteristic
678C4D11×#12611yescharacteristic
679C2—224no—
680C2D11×#38811yescharacteristic
681C2C4×#6696811yescharacteristic
682C2#1307743211yescharacteristic
683C2#1307809811yescharacteristic
684C2#1307810711yescharacteristic
685C2#1307855911yescharacteristic
686C2#1307856311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1927C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1927D11
hypocenterC11#21061
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
6. #13069259C2semidirect
7. #13069258C2semidirect
8. #13069255C2semidirect
9. #13069254C2semidirect
10. #13069253C2semidirect
11. #13069250C2semidirect
12. #13069249C2semidirect
15. C11×#1927C2semidirect
47. #10622415C4semidirect
115. C11×#103C2×C4semidirect
120. #66899C2×C4semidirect
132. #66880C2×C4semidirect
134. #66874C2×C4semidirect
243. #1927D11semidirect
459. #103C4×D11semidirect
573. C11#21061semidirect

Maximal subgroups

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

subgroupindex
C2×#106224742
C2×#106224152
D11×#3912
C4×#669452
#130692592
#130692582
#130692552
#130692542
#130692532
#130692502
#130692492
#130683342
#130683082
C11×#19272
#2106111