Finite Group Databasebeta

← #14792592

Subgroups — #14792592

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622841C211yesmaximal, characteristic
2C2×#10622333C211yesmaximal, characteristic
3#13074415C211yesmaximal, characteristic
4#13071202C211yesmaximal, characteristic
5#13070007C211yesmaximal, characteristic, complemented
6#13069993C211yesmaximal, characteristic, complemented
7#13069937C211yesmaximal, characteristic, complemented
8#13069937C211yesmaximal, characteristic, complemented
9#13069484C211yesmaximal, characteristic, complemented
10#13069474C211yesmaximal, characteristic, complemented
11#13069308C211yesmaximal, characteristic, complemented
12#13069294C211yesmaximal, characteristic, complemented
13#13068926C211yesmaximal, characteristic
14#13068813C211yesmaximal, characteristic
15C11×#1787C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C22×#4326C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622843—21no—
29#10622843—21no—
30#10622843C2211yescharacteristic
31#10622843C2211yescharacteristic
32#10622843C2211yescharacteristic
33#10622843C2211yescharacteristic
34#10622841—24no—
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37#10622824—21no—
38#10622824—21no—
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×C8×Dic11C2211yescharacteristic
46#10622598C2211yescharacteristic
47#10622598C2211yescharacteristic
48#10622587C2211yescharacteristic
49#10622587C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52#10622566—21no—
53#10622566—21no—
54#10622333—24no—
55#10622274—21no—
56#10622272—21no—
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—22no—
62C22×Q8×C11—22no—
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—41no—
67C22×Q8×C11—41no—
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D411yescharacteristic
81C2×C22⋊Dic11D411yescharacteristic
82C2×#4326—22no—
83C2×#4326—22no—
84C2×#4326—22no—
85C2×#4326—22no—
86C2×#4326—41no—
87C2×#4326—41no—
88#66979—22no—
89#66979—22no—
90#66979—41no—
91#66979—41no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—22no—
100#66977—22no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—41no—
110C11×#103—41no—
111C11×C22⋊C8—22no—
112C11×#95—21no—
113#66899—22no—
114#66899—22no—
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—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C22⋊(C11⋊C8)D414yes—
130#66880—41no—
131#66880—41no—
132#66879—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136#66872—41no—
137#66871—41no—
138#24514—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C2×Q8×C11—24no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—44no—
152C2×Q8×C11—44no—
153C2×Q8×C11—44no—
154C2×Q8×C11—44no—
155C2×Q8×C11—42no—
156C2×Q8×C11—42no—
157C2×Q8×C11#4112yes—
158C2×Q8×C11#4112yes—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—24no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—42no—
169C22×C4×C11—42no—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11#4112yes—
173C22×C4×C11C2411yescharacteristic
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—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—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C22⋊C4—81no—
199C22⋊Dic11—22no—
200C22⋊Dic11—22no—
201C22⋊Dic11—42no—
202C22⋊Dic11—42no—
203#4326—44no—
204#4326—44no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—81no—
214C4⋊Dic11—81no—
215Dic11⋊C4—42no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—42no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8C2×D412yes—
226C2×C11⋊C8C2×D412yes—
227C2×#451—111no—
228C2×#433—111no—
229#2625—111no—
230#2310—111no—
231#2068—111no—
232#2066—111no—
233#2056—111no—
234#2056—111no—
235#1971—111no—
236#1969—111no—
237#1935—111no—
238#1933—111no—
239#1873—111no—
240#1854—111no—
241#1787D1111yescharacteristic
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11#12112yes—
249C23×C11C22×D411yescharacteristic
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—48no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—41no—
258Q8×C11—41no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—48no—
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×C11—41no—
278C2×C4×C11#12112yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—41no—
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×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309Dic22—41no—
310Dic22—41no—
311Dic22—41no—
312Dic22—41no—
313C8×C11—41no—
314C8×C11—41no—
315C11⋊C8—22no—
316C11⋊C8—22no—
317C23×Q8C2×D1111yescharacteristic
318C22×Q16—111no—
319C22×Q16—111no—
320C2×C22⋊Q8—111no—
321C2×#117—111no—
322C2×#117—111no—
323#451—224no—
324#433—224no—
325C2×#107—111no—
326C2×#106—111no—
327C2×C4⋊C8—111no—
328C2×C4⋊C8—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103C2×D1111yescharacteristic
334C2×#103C2×D1111yescharacteristic
335C2×#103C2×D1111yescharacteristic
336C2×#103C2×D1111yescharacteristic
337C2×C22⋊C8—111no—
338C2×C22⋊C8C2×D1111yescharacteristic
339C2×#97—111no—
340C2×C4×C8—111no—
341#400—221no—
342#398—221no—
343#397—221no—
344#397—221no—
345#391—111no—
346#391—111no—
347#391—111no—
348#391—111no—
349#391—111no—
350#391—111no—
351#391—221no—
352#391—221no—
353#389—111no—
354#389—111no—
355#381—221no—
356#381—221no—
357#380C2×D1111yescharacteristic
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11C2×#12111yescharacteristic
370C22×C11#52511yescharacteristic
371C22×C11#53511yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57811yescharacteristic
374C22×C11#57811yescharacteristic
375C22×C11#57811yescharacteristic
376C4×C11—22no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11#54611yescharacteristic
382C4×C11#54611yescharacteristic
383C4×C11#55111yescharacteristic
384C4×C11#55111yescharacteristic
385Dic11—41no—
386Dic11—41no—
387Dic11—41no—
388Dic11—41no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8—22no—
394C22×Q8—22no—
395C22×Q8—21no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—41no—
399C22×Q8—41no—
400C22×Q8—111no—
401C22×Q8C22×D1111yescharacteristic
402C22×Q8C22×D1111yescharacteristic
403C23×C4—21no—
404C23×C4C22×D1111yescharacteristic
405C2×Q16—222no—
406C2×Q16—222no—
407C2×Q16—222no—
408C2×Q16—222no—
409C2×Q16—441no—
410C2×Q16—441no—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C22⋊Q8—222no—
416C22⋊Q8—222no—
417#117—222no—
418#117—222no—
419#117—441no—
420#117—441no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
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×C22⋊C4—21no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—221no—
439#107—441no—
440#106—441no—
441C4⋊C8—222no—
442C4⋊C8—222no—
443#103—22no—
444#103—22no—
445#103—41no—
446#103—41no—
447#103—222no—
448#103—222no—
449#103—441no—
450#103—441no—
451C22⋊C8—22no—
452C22⋊C8—114no—
453#97—222no—
454C4×C8—222no—
455#95—21no—
456#95—221no—
457#95—221no—
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#241111yescharacteristic
472C2×C11#305911yescharacteristic
473C2×C11#306311yescharacteristic
474C2×C11#312111yescharacteristic
475C2×C11#312711yescharacteristic
476C2×C11#322311yescharacteristic
477C2×C11#322511yescharacteristic
478C24D4×D1111yescharacteristic
479C2×Q8—24no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—221no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—221no—
502C2×Q8#434112yes—
503C2×Q8#434112yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4#433912yes—
524C22×C4D4×D1111yescharacteristic
525C22×C4D4×D1112yes—
526C22×C4C23×D1111yescharacteristic
527Q16—444no—
528Q16—444no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—112no—
536C2×C8—112no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—222no—
546C4⋊C4—222no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—442no—
554C4⋊C4—881no—
555C4⋊C4—881no—
556C22⋊C4—81no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C42—221no—
562C42—221no—
563C42—221no—
564C42—221no—
565C42—442no—
566C11#2451411yescharacteristic, complemented, Sylow
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#6693712yes—
574C23C2×D4×D1111yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—22no—
578Q8—22no—
579Q8—48no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—441no—
585Q8—441no—
586Q8—441no—
587Q8—441no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—48no—
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—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
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—441no—
631C2×C4#6693712yes—
632C2×C4C2×#433911yescharacteristic
633C2×C4C2×D4×D1111yescharacteristic
634C2×C4C2×#434111yescharacteristic
635C2×C4C2×#434111yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4#6703711yescharacteristic
638C8—41no—
639C8—41no—
640C8—222no—
641C8—222no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×#6693711yescharacteristic
650C22#1062311711yescharacteristic
651C22#1062312311yescharacteristic
652C22#1062329311yescharacteristic
653C22#1062329711yescharacteristic
654C22#1062331011yescharacteristic
655C22#1062331011yescharacteristic
656C4—22no—
657C4—42no—
658C4—42no—
659C4—81no—
660C4—81no—
661C4—441no—
662C4—441no—
663C4—441no—
664C4—441no—
665C4—881no—
666C4—881no—
667C4—881no—
668C4—881no—
669C4#1062302611yescharacteristic
670C4#1062302611yescharacteristic
671C4#1062312211yescharacteristic
672C4#1062312211yescharacteristic
673C2—42no—
674C2#1307200311yescharacteristic
675C2#1307827011yescharacteristic
676C2#1307830511yescharacteristic
677C2#1307883811yescharacteristic
678C2#1307891011yescharacteristic
679C2#1307969511yescharacteristic
680C2#1307972311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1787D11
hypocenterC11#24514
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
5. #13070007C2semidirect
6. #13069993C2semidirect
7. #13069937C2semidirect
8. #13069937C2semidirect
9. #13069484C2semidirect
10. #13069474C2semidirect
11. #13069308C2semidirect
12. #13069294C2semidirect
566. C11#24514semidirect

Maximal subgroups

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

subgroupindex
C2×#106228412
C2×#106223332
#130744152
#130712022
#130700072
#130699932
#130699372
#130694842
#130694742
#130693082
#130692942
#130689262
#130688132
C11×#17872
#2451411