Finite Group Databasebeta

← #14797701

Subgroups — #14797701

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622663C211yesmaximal, characteristic
2C2×#10622403C211yesmaximal, characteristic, complemented
3#13072137C211yesmaximal, characteristic
4#13071448C211yesmaximal, characteristic
5#13070151C211yesmaximal, characteristic, complemented
6#13070047C211yesmaximal, characteristic
7#13069937C211yesmaximal, characteristic, complemented
8#13069290C211yesmaximal, characteristic, complemented
9#13069225C211yesmaximal, characteristic
10#13068955C211yesmaximal, characteristic, complemented
11#13068954C211yesmaximal, characteristic, complemented
12#13068867C211yesmaximal, characteristic, complemented
13#13068620C211yesmaximal, characteristic, complemented
14#13068552C211yesmaximal, characteristic
15C11×#2036C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622825C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622663—24no—
39#10622596—21no—
40#10622591—21no—
41#10622589C2211yescharacteristic
42#10622587C2211yescharacteristic
43#10622587C2211yescharacteristic
44#10622586C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622562—21no—
49#10622557—21no—
50#10622555—21no—
51C22⋊C4×Dic11—21no—
52#10622403—24no—
53#10622259—21no—
54#10622259—21no—
55C11×#340C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×Dic22—21no—
65C22×Dic22—22no—
66C22×Dic22—22no—
67C22×Dic22—22no—
68C22×Dic22—22no—
69C22×Dic22—41no—
70C22×Dic22—41no—
71C22×Dic22C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86Q8×Dic11—22no—
87Q8×Dic11—41no—
88C2×#4326—22no—
89C2×#4326—22no—
90C2×#4326—22no—
91C2×#4326—22no—
92C2×#4326—41no—
93C2×#4326D414yes—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66940—22no—
110#66940—22no—
111#66940—41no—
112#66940—41no—
113C11×#107—41no—
114C11×#103—22no—
115C11×#103—41no—
116C11×C22⋊C8—41no—
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—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128C22⋊(C11⋊C8)—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#66880—41no—
133Dic11⋊C8—41no—
134C8×Dic11—22no—
135#66874—22no—
136#66874—22no—
137#66871—22no—
138#24906—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—24no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C2×Dic22—24no—
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—42no—
179C2×Dic22—42no—
180C2×Dic22—44no—
181C2×Dic22—44no—
182C2×Dic22—44no—
183C2×Dic22—44no—
184C2×Dic22C2×D412yes—
185C2×Dic22#4112yes—
186C2×Dic22#4112yes—
187C2×Dic22#4112yes—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—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—42no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—42no—
203C22⋊Dic11—41no—
204C22⋊Dic11—81no—
205C22⋊Dic11Q1614yescomplemented
206#4326—28no—
207#4326—44no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—81no—
217Dic11⋊C4—81no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—42no—
223C4×Dic11—42no—
224C4×Dic11—42no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8C2×D412yes—
231C2×#451—111no—
232C2×C4×Q16—111no—
233#2423—111no—
234Q8×C22⋊C4—111no—
235#2095—111no—
236#2076—111no—
237#2056—111no—
238#2036D1111yescharacteristic
239#1933—111no—
240#1923—111no—
241#1878—111no—
242#1878—111no—
243#1863—111no—
244#1803—111no—
245#1787—111no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11C2×Q1612yes—
253C23×C11C22×D411yescharacteristic
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
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×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—41no—
276C2×C4×C11—41no—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—48no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11C2×Q1612yes—
307C2×Dic11C2×Q1612yes—
308Dic22—22no—
309Dic22—22no—
310Dic22—22no—
311Dic22—22no—
312Dic22—22no—
313Dic22—48no—
314Dic22—41no—
315Dic22—41no—
316Dic22#12314yes—
317C8×C11—41no—
318C8×C11—41no—
319C11⋊C8—22no—
320C11⋊C8—41no—
321C23×Q8—111no—
322C22×Q16—111no—
323C22×Q16—111no—
324C2×C22⋊Q8C2×D1111yescharacteristic
325C2×C4×Q8—111no—
326C2×C4×Q8—111no—
327C2×C4×Q8—111no—
328#451—224no—
329C4×Q16—224no—
330C2×#107—111no—
331C2×#107C2×D1111yescharacteristic
332C2×C4⋊C8—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103C2×D1111yescharacteristic
340C2×#103C2×D1111yescharacteristic
341C2×C22⋊C8—111no—
342C2×C22⋊C8C2×D1111yescharacteristic
343C2×C4×C8—111no—
344#399—221no—
345#398—221no—
346#391—111no—
347#391—111no—
348#391—111no—
349#391—221no—
350#391—221no—
351#389—111no—
352#388—221no—
353#387—221no—
354#384—111no—
355#380—111no—
356#380—221no—
357#380C2×D1111yescharacteristic
358C4×C22⋊C4—111no—
359C4×C22⋊C4—221no—
360#340—111no—
361#340—111no—
362#340—111no—
363#340C2×D1111yescharacteristic
364#336—111no—
365#336—111no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11#52511yescharacteristic
374C22×C11D4211yescharacteristic
375C22×C11#54611yescharacteristic
376C22×C11C22×Q1611yescharacteristic
377C22×C11#57511yescharacteristic
378C22×C11#57711yescharacteristic
379C22×C11#57811yescharacteristic
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11C2×#12311yescharacteristic
386C4×C11#53811yescharacteristic
387C4×C11#54611yescharacteristic
388C4×C11#55111yescharacteristic
389Dic11—24no—
390Dic11—22no—
391Dic11—22no—
392Dic11—42no—
393Dic11—41no—
394Dic11—41no—
395Dic11—81no—
396Dic11—81no—
397C22×Q8—111no—
398C22×Q8—111no—
399C22×Q8—222no—
400C22×Q8—222no—
401C22×Q8—222no—
402C22×Q8—222no—
403C22×Q8—221no—
404C22×Q8—441no—
405C22×Q8—441no—
406C22×Q8C22×D1111yescharacteristic
407C23×C4—221no—
408C23×C4C22×D1111yescharacteristic
409C2×Q16—114no—
410C2×Q16—222no—
411C2×Q16—222no—
412C2×Q16—222no—
413C2×Q16—222no—
414C2×Q16—441no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C22⋊Q8—22no—
420C22⋊Q8—41no—
421C4×Q8—222no—
422C4×Q8—222no—
423C4×Q8—222no—
424C4×Q8—441no—
425C4×Q8—441no—
426C4×Q8—441no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
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⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—111no—
442C2×C22⋊C4—111no—
443C2×C22⋊C4—221no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—221no—
447C2×C42—221no—
448C2×C42—221no—
449#107—41no—
450#107—222no—
451C4⋊C8—441no—
452#103—22no—
453#103—41no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—222no—
458#103—222no—
459#103—441no—
460C22⋊C8—41no—
461C22⋊C8—222no—
462C4×C8—222no—
463#95—21no—
464#95—111no—
465#95—111no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474C2×C11—42no—
475C2×C11#241811yescharacteristic
476C2×C11#310411yescharacteristic
477C2×C11#312111yescharacteristic
478C2×C11#327111yescharacteristic
479C2×C11D4×Q1611yescharacteristic
480C2×C11#329911yescharacteristic
481C2×C11#332711yescharacteristic
482C24D4×D1111yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—112no—
489C2×Q8—112no—
490C2×Q8—112no—
491C2×Q8—112no—
492C2×Q8—224no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8—221no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—442no—
502C2×Q8—442no—
503C2×Q8—444no—
504C2×Q8—444no—
505C2×Q8—444no—
506C2×Q8—444no—
507C2×Q8D4×D1112yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—111no—
522C22×C4—221no—
523C22×C4—224no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—442no—
528C22×C4—442no—
529C22×C4D4×D1111yescharacteristic
530C22×C4C23×D1111yescharacteristic
531Q16—228no—
532Q16—444no—
533C2×C8—21no—
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—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4—442no—
560C4⋊C4—881no—
561C4⋊C4—881no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—114no—
565C22⋊C4—441no—
566C22⋊C4—881no—
567C42—221no—
568C42—221no—
569C42—221no—
570C42—221no—
571C42—442no—
572C42—442no—
573C42—442no—
574C11#2490611yescharacteristic, complemented, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23Q16×D1112yes—
582C23C2×D4×D1111yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—41no—
586Q8—41no—
587Q8—114no—
588Q8—222no—
589Q8—222no—
590Q8—222no—
591Q8—222no—
592Q8—222no—
593Q8—448no—
594Q8—441no—
595Q8—441no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
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—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—222no—
631C2×C4—448no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4#6703711yescharacteristic
642C2×C4#6703711yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#41×D1111yescharacteristic
645C2×C4#41×D1111yescharacteristic
646C8—41no—
647C8—41no—
648C8—222no—
649C8—441no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22#1062312111yescharacteristic
658C22#1062314111yescharacteristic
659C22#1062318711yescharacteristic
660C22C2×Q16×D1111yescharacteristic
661C22#1062330111yescharacteristic
662C22#1062330411yescharacteristic
663C22#1062331011yescharacteristic
664C4—41no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—222no—
670C4—222no—
671C4—224no—
672C4—441no—
673C4—441no—
674C4—442no—
675C4—881no—
676C4—881no—
677C4#1062314111yescharacteristic
678C4#1062314411yescharacteristic
679C4D11×#12311yescharacteristic
680C4#1062321011yescharacteristic
681C2—42no—
682C2#1307207111yescharacteristic
683C2#1307865211yescharacteristic
684C2#1307884811yescharacteristic
685C2#1308019911yescharacteristic
686C2#1308036111yescharacteristic
687C2#1308048711yescharacteristic
688C2#1308089011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2036C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2036D11
hypocenterC11#24906
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
2. C2×#10622403C2semidirect
5. #13070151C2semidirect
7. #13069937C2semidirect
8. #13069290C2semidirect
10. #13068955C2semidirect
11. #13068954C2semidirect
12. #13068867C2semidirect
13. #13068620C2semidirect
205. C22⋊Dic11Q16semidirect
574. C11#24906semidirect

Maximal subgroups

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

subgroupindex
C2×#106226632
C2×#106224032
#130721372
#130714482
#130701512
#130700472
#130699372
#130692902
#130692252
#130689552
#130689542
#130688672
#130686202
#130685522
C11×#20362
#2490611