Finite Group Databasebeta

← #14765082

Subgroups — #14765082

Order 2816.

920 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×#10622352C211yesmaximal, characteristic
2#13071294C211yesmaximal, characteristic
3#13071200C211yesmaximal, characteristic
4#13069485C211yesmaximal, characteristic, complemented
5#13069475C211yesmaximal, characteristic, complemented
6#13069304C211yesmaximal, characteristic, complemented
7#13069290C211yesmaximal, characteristic, complemented
8#13069256C211yesmaximal, characteristic, complemented
9#13069249C211yesmaximal, characteristic, complemented
10#13068958C211yesmaximal, characteristic, complemented
11#13068958C211yesmaximal, characteristic, complemented
12#13068928C211yesmaximal, characteristic
13#13068550C211yesmaximal, characteristic
14#13068384C211yesmaximal, characteristic
15C11×#1854C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C22×Dic44C2211yescharacteristic
21C22×Dic44C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622587C2211yescharacteristic
34#10622587C2211yescharacteristic
35#10622587C2211yescharacteristic
36#10622587C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45#10622558—21no—
46#10622557—21no—
47#10622556—21no—
48#10622556—21no—
49#10622542—21no—
50#10622542—21no—
51#10622352C418yescomplemented
52#10622268—21no—
53#10622260—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×Dic22—21no—
63C22×Dic22—22no—
64C22×Dic22—41no—
65C22×Dic22—41no—
66C22×Dic22—41no—
67C22×Dic22—41no—
68C22×Dic22C2×C414yes—
69C22×Dic22C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#117—41no—
75C11×#117—41no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86#66979—41no—
87#66979—41no—
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91#66977—22no—
92#66977C2×C414yes—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C2×Dic44—41no—
103C2×Dic44—41no—
104C2×Dic44—41no—
105C2×Dic44—41no—
106C2×Dic44C2×C414yes—
107C2×Dic44C2×C414yes—
108#66940—41no—
109#66940—41no—
110C11×#107—41no—
111C11×#106—41no—
112C11×C22⋊C8C2×C414yes—
113C11×#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C22⋊(C11⋊C8)—22no—
127#66880C2×C414yes—
128#66880C2×C414yes—
129#66879—41no—
130C8×Dic11—41no—
131#66874—41no—
132#66874—41no—
133#66874—41no—
134#66874—41no—
135#66874—41no—
136#66874—41no—
137#22054—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—24no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C2×Dic22—24no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
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—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—44no—
179C2×Dic22—44no—
180C2×Dic22—42no—
181C2×Dic22—42no—
182C2×Dic22—44no—
183C2×Dic22—44no—
184C2×Dic22C22×C412yes—
185C2×Dic22C22×C412yes—
186C2×Dic22C22×C412yes—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11C22×C412yes—
192C2×C8×C11C22×C412yes—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—81no—
203C42×C11—42no—
204C22⋊Dic11—24no—
205C22⋊Dic11—41no—
206C22⋊Dic11—41no—
207C4⋊Dic11—21no—
208C4⋊Dic11—41no—
209C4⋊Dic11—41no—
210C4⋊Dic11C22×C412yes—
211Dic11⋊C4—24no—
212Dic11⋊C4—42no—
213Dic11⋊C4—81no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—42no—
219C4×Dic11—81no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226Dic44—44no—
227Dic44—44no—
228C2×#451—111no—
229#2323—111no—
230#2310—111no—
231#1971—111no—
232#1969—111no—
233#1935—111no—
234#1933—111no—
235#1928—111no—
236#1927—111no—
237#1878—111no—
238#1878—111no—
239#1873—111no—
240#1854D1111yescharacteristic
241#1787—111no—
242#1750—111no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11C4×D412yes—
250C23×C11C22×D411yescharacteristic
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11C4×D412yes—
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—48no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301Dic22—22no—
302Dic22—22no—
303Dic22—22no—
304Dic22—22no—
305Dic22—22no—
306Dic22—22no—
307Dic22—48no—
308Dic22—41no—
309Dic22—41no—
310Dic22—41no—
311Dic22—41no—
312Dic22—41no—
313Dic22—41no—
314C8×C11—22no—
315C8×C11—22no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C23×Q8—111no—
319C22×Q16—111no—
320C22×Q16—111no—
321C2×C22⋊Q8—111no—
322C2×C4×Q8—111no—
323C2×#117—111no—
324C2×#117C2×D1111yescharacteristic
325#451—118no—
326C2×#107C2×D1111yescharacteristic
327C2×#106C2×D1111yescharacteristic
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×C22⋊C8—111no—
337C2×C22⋊C8C2×D1111yescharacteristic
338C2×#97—111no—
339C2×C4×C8—111no—
340#391—111no—
341#391—111no—
342#391—111no—
343#391—111no—
344#391—111no—
345#391—221no—
346#391—221no—
347#389—111no—
348#389—221no—
349#388—221no—
350#388—221no—
351#387—221no—
352#381—221no—
353#381—221no—
354#380C2×D1111yescharacteristic
355C4×C4⋊C4—111no—
356#340—111no—
357#340—111no—
358#340C2×D1111yescharacteristic
359#340C2×D1111yescharacteristic
360#336—111no—
361#336—111no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11C2×C4×D411yescharacteristic
370C22×C11#53411yescharacteristic
371C22×C11#53511yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57811yescharacteristic
374C22×C11#57811yescharacteristic
375C22×C11#57811yescharacteristic
376C4×C11—22no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11#51811yescharacteristic
382C4×C11#51811yescharacteristic
383C4×C11#53811yescharacteristic
384C4×C11#53811yescharacteristic
385Dic11—42no—
386Dic11—42no—
387Dic11—42no—
388Dic11—41no—
389Dic11—41no—
390Dic11—41no—
391Dic11—41no—
392Dic11—42no—
393C22×Q8—114no—
394C22×Q8—111no—
395C22×Q8—111no—
396C22×Q8—111no—
397C22×Q8—221no—
398C22×Q8—222no—
399C22×Q8—441no—
400C22×Q8—441no—
401C22×Q8—441no—
402C22×Q8—441no—
403C23×C4—221no—
404C23×C4C22×D1111yescharacteristic
405C2×Q16—114no—
406C2×Q16—114no—
407C2×Q16—441no—
408C2×Q16—441no—
409C2×Q16—441no—
410C2×Q16—441no—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C22⋊Q8—114no—
416C22⋊Q8—222no—
417C4×Q8—441no—
418C4×Q8—441no—
419#117—41no—
420#117—41no—
421#117—441no—
422#117—441no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—221no—
438C2×C42—21no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—221no—
442C2×C42—221no—
443#107—41no—
444#106—41no—
445#103—114no—
446#103—114no—
447#103—441no—
448#103—441no—
449#103—441no—
450#103—441no—
451#103—441no—
452#103—441no—
453C22⋊C8—222no—
454C22⋊C8C4×D1114yes—
455#97—441no—
456C4×C8—441no—
457#95—21no—
458#95—221no—
459#95—221no—
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#95—221no—
469#95—221no—
470C2×C11—42no—
471C2×C11#232111yescharacteristic
472C2×C11#294711yescharacteristic
473C2×C11#295011yescharacteristic
474C2×C11#320111yescharacteristic
475C2×C11#320211yescharacteristic
476C2×C11#322311yescharacteristic
477C2×C11#322511yescharacteristic
478C24D4×D1111yescharacteristic
479C2×Q8—112no—
480C2×Q8—112no—
481C2×Q8—112no—
482C2×Q8—224no—
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—221no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8—221no—
497C2×Q8—221no—
498C2×Q8—444no—
499C2×Q8—444no—
500C2×Q8—442no—
501C2×Q8—442no—
502C2×Q8—444no—
503C2×Q8—444no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—224no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—442no—
522C22×C4—442no—
523C22×C4C2×C4×D1112yes—
524C22×C4D4×D1111yescharacteristic
525C22×C4#434312yes—
526C22×C4C23×D1111yescharacteristic
527Q16—444no—
528Q16—444no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8C2×C4×D1112yes—
540C2×C8C2×C4×D1112yes—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—112no—
550C4⋊C4—224no—
551C4⋊C4—221no—
552C4⋊C4—441no—
553C4⋊C4—441no—
554C4⋊C4—442no—
555C4⋊C4—881no—
556C22⋊C4—42no—
557C22⋊C4—81no—
558C22⋊C4—224no—
559C22⋊C4—441no—
560C22⋊C4—441no—
561C42—42no—
562C42—221no—
563C42—221no—
564C42—221no—
565C42—221no—
566C42—442no—
567C42—881no—
568C11#2205411yescharacteristic, complemented, Sylow
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23#6694612yes—
576C23C2×D4×D1111yescharacteristic
577Q8—222no—
578Q8—222no—
579Q8—222no—
580Q8—222no—
581Q8—222no—
582Q8—222no—
583Q8—448no—
584Q8—441no—
585Q8—441no—
586Q8—441no—
587Q8—441no—
588Q8—441no—
589Q8—441no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
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—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—448no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4#6694612yes—
634C2×C4C22×C4×D1111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4C2×#434311yescharacteristic
638C2×C4#6704211yescharacteristic
639C2×C4#6704211yescharacteristic
640C8—22no—
641C8—22no—
642C8—441no—
643C8—441no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×#6694611yescharacteristic
652C22#1062312311yescharacteristic
653C22#1062318411yescharacteristic
654C22#1062330211yescharacteristic
655C22#1062330211yescharacteristic
656C22#1062330611yescharacteristic
657C22#1062331011yescharacteristic
658C4—22no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—442no—
664C4—442no—
665C4—442no—
666C4—441no—
667C4—441no—
668C4—442no—
669C4—441no—
670C4—441no—
671C4#1062307611yescharacteristic
672C4#1062307611yescharacteristic
673C4#1062317511yescharacteristic
674C4#1062317511yescharacteristic
675C2—42no—
676C2#1307127311yescharacteristic
677C2#1307745711yescharacteristic
678C2#1307748311yescharacteristic
679C2#1307949611yescharacteristic
680C2#1307951011yescharacteristic
681C2#1307969711yescharacteristic
682C2#1307972111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1854D11
hypocenterC11#22054
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #13069485C2semidirect
5. #13069475C2semidirect
6. #13069304C2semidirect
7. #13069290C2semidirect
8. #13069256C2semidirect
9. #13069249C2semidirect
10. #13068958C2semidirect
11. #13068958C2semidirect
51. #10622352C4semidirect
568. C11#22054semidirect

Maximal subgroups

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

subgroupindex
C2×#106223522
#130712942
#130712002
#130694852
#130694752
#130693042
#130692902
#130692562
#130692492
#130689582
#130689282
#130685502
#130683842
C11×#18542
#2205411