Finite Group Databasebeta

← #14765078

Subgroups — #14765078

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×#10622663C211yesmaximal, characteristic
2#13071200C211yesmaximal, characteristic
3#13069486C211yesmaximal, characteristic, complemented
4#13069476C211yesmaximal, characteristic, complemented
5#13069305C211yesmaximal, characteristic, complemented
6#13069291C211yesmaximal, characteristic, complemented
7#13069257C211yesmaximal, characteristic, complemented
8#13069250C211yesmaximal, characteristic, complemented
9#13068957C211yesmaximal, characteristic, complemented
10#13068957C211yesmaximal, characteristic, complemented
11#13068929C211yesmaximal, characteristic
12#13068813C211yesmaximal, characteristic
13#13068550C211yesmaximal, characteristic
14#13068382C211yesmaximal, characteristic
15C11×#2323C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#389—21no—
25C11×#389C2211yescharacteristic
26C11×#388—21no—
27C11×#388—21no—
28C11×#387—21no—
29C11×#380C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622663C418yescomplemented
36#10622587—21no—
37#10622587—21no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622556—21no—
47#10622556—21no—
48#10622542C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622542C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×Dic22—41no—
66C22×Dic22—41no—
67C22×Dic22—41no—
68C22×Dic22—41no—
69C22×Dic22C2×C414yes—
70C22×Dic22C2311yescharacteristic
71C22×Dic22C2311yescharacteristic
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8C2×C414yes—
74C4×Q8×C11—41no—
75C4×Q8×C11—41no—
76C11×#117—41no—
77C11×#117—41no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D411yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—21no—
95C2×#4326—41no—
96C2×#4326—41no—
97C2×#4326—41no—
98C2×#4326—41no—
99C2×#4326C2×C414yes—
100C2×#4326C2×C414yes—
101#66979—41no—
102#66979—41no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4×Dic11—21no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115#66899—41no—
116#66899—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—
125C22⋊(C11⋊C8)—22no—
126C22⋊(C11⋊C8)C2×C414yes—
127#66874—41no—
128#66874—41no—
129#66874—41no—
130#66874—41no—
131#66874C2×C414yes—
132#66874C2×C414yes—
133#66872—41no—
134#66871—41no—
135#66867—41no—
136C4×C11⋊C8—41no—
137#22054—111nomaximal, Sylow
138C24×C11C2×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×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—24no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—42no—
167C22×Dic11—42no—
168C2×Dic22—24no—
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×Dic22—44no—
180C2×Dic22—44no—
181C2×Dic22—42no—
182C2×Dic22—42no—
183C2×Dic22—44no—
184C2×Dic22—44no—
185C2×Dic22C22×C412yes—
186C2×Dic22C22×C412yes—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4—81no—
197C11×C4⋊C4C22×C412yes—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—41no—
200C11×C22⋊C4—41no—
201C11×C22⋊C4—81no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—42no—
207C42×C11—81no—
208C22⋊Dic11—42no—
209#4326—44no—
210#4326—44no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4×Dic11—42no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8C22×C412yes—
227C2×C11⋊C8C22×C412yes—
228C2×#451—111no—
229#2323D1111yescharacteristic
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#1854—111no—
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
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—41no—
254Q8×C11—41no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
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×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11C4×D412yes—
286C2×C4×C11C23×C411yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—48no—
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—41no—
304C2×Dic11—41no—
305Dic22—22no—
306Dic22—22no—
307Dic22—22no—
308Dic22—22no—
309Dic22—48no—
310Dic22—41no—
311Dic22—41no—
312Dic22—41no—
313Dic22—41no—
314C11⋊C8—22no—
315C11⋊C8—22no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C23×Q8—111no—
319C22×Q16—111no—
320C22×Q16—111no—
321C2×C22⋊Q8C2×D1111yescharacteristic
322C2×C4×Q8C2×D1111yescharacteristic
323C2×#117—111no—
324C2×#117C2×D1111yescharacteristic
325#451—118no—
326C2×#107—111no—
327C2×#106—111no—
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⋊C8—111no—
338C2×#97—111no—
339C2×C4×C8—111no—
340#391—111no—
341#391—111no—
342#391—111no—
343#391—111no—
344#391—221no—
345#391—221no—
346#391C2×D1111yescharacteristic
347#389—21no—
348#389C2×D1111yescharacteristic
349#388—21no—
350#388—21no—
351#387—21no—
352#381—221no—
353#381—221no—
354#380C2×D1111yescharacteristic
355C4×C4⋊C4C2×D1111yescharacteristic
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
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—42no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11#51811yescharacteristic
386C4×C11#51811yescharacteristic
387C4×C11#53811yescharacteristic
388C4×C11#53811yescharacteristic
389Dic11—42no—
390Dic11—42no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8—114no—
394C22×Q8—111no—
395C22×Q8—111no—
396C22×Q8—222no—
397C22×Q8—221no—
398C22×Q8—441no—
399C22×Q8—441no—
400C22×Q8—441no—
401C22×Q8—441no—
402C22×Q8C22×D1111yescharacteristic
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×C8—111no—
414C22×C8—111no—
415C22⋊Q8—22no—
416C22⋊Q8C4×D1114yes—
417C4×Q8—41no—
418C4×Q8—41no—
419#117—41no—
420#117—41no—
421#117—441no—
422#117—441no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4C22⋊D1111yescharacteristic
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—221no—
436C2×C22⋊C4C22⋊D1111yescharacteristic
437C2×C22⋊C4C22⋊D1111yescharacteristic
438C2×C42—21no—
439C2×C42—21no—
440C2×C42—221no—
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1111yescharacteristic
443#107—441no—
444#106—441no—
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—114no—
454C22⋊C8—222no—
455#97—441no—
456C4×C8—441no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
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
478C24C2×C22⋊D1111yescharacteristic
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—112no—
485C2×Q8—112no—
486C2×Q8—224no—
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—444no—
498C2×Q8—444no—
499C2×Q8—442no—
500C2×Q8—442no—
501C2×Q8—444no—
502C2×Q8—444no—
503C2×Q8C2×C4×D1112yes—
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—224no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4C2×C4×D1112yes—
520C22×C4#433912yes—
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527Q16—444no—
528Q16—444no—
529C2×C8—112no—
530C2×C8—112no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C4⋊C4—24no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—42no—
550C4⋊C4—81no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4C2×C4×D1112yes—
556C22⋊C4—24no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—81no—
560C22⋊C4—442no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—81no—
567C42—442no—
568C11#2205411yescharacteristic, complemented, Sylow
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23C4×C22⋊D1112yes—
576C23C22×C22⋊D1111yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581Q8—222no—
582Q8—222no—
583Q8—222no—
584Q8—222no—
585Q8—448no—
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—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—448no—
623C2×C4—441no—
624C2×C4—441no—
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×C4C4×C22⋊D1112yes—
634C2×C4C22×C4×D1111yescharacteristic
635C2×C4C2×#433911yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4#6703711yescharacteristic
638C2×C4#6704211yescharacteristic
639C2×C4#6704211yescharacteristic
640C8—222no—
641C8—222no—
642C8—441no—
643C8—441no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×C4×C22⋊D1111yescharacteristic
652C22#1062333511yescharacteristic
653C22#1062336111yescharacteristic
654C22#1062336711yescharacteristic
655C22#1062336911yescharacteristic
656C22#1062336911yescharacteristic
657C22#1062336911yescharacteristic
658C4—22no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—41no—
665C4—81no—
666C4—81no—
667C4—442no—
668C4—442no—
669C4—881no—
670C4—881no—
671C4#1062307611yescharacteristic
672C4#1062307611yescharacteristic
673C4#1062309111yescharacteristic
674C4#1062309111yescharacteristic
675C2—42no—
676C2#1307127011yescharacteristic
677C2#1307745511yescharacteristic
678C2#1307748211yescharacteristic
679C2#1307949211yescharacteristic
680C2#1307950711yescharacteristic
681C2#1307969311yescharacteristic
682C2#1307971911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2323C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2323D11
hypocenterC11#22054
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
3. #13069486C2semidirect
4. #13069476C2semidirect
5. #13069305C2semidirect
6. #13069291C2semidirect
7. #13069257C2semidirect
8. #13069250C2semidirect
9. #13068957C2semidirect
10. #13068957C2semidirect
35. #10622663C4semidirect
568. C11#22054semidirect

Maximal subgroups

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

subgroupindex
C2×#106226632
#130712002
#130694862
#130694762
#130693052
#130692912
#130692572
#130692502
#130689572
#130689292
#130688132
#130685502
#130683822
C11×#23232
#2205411