Finite Group Databasebeta

← #14813780

Subgroups — #14813780

Order 2816.

908 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×#10622629C211yesmaximal, characteristic
2C2×C4×#4323C211yesmaximal, characteristic
3#13072403C211yesmaximal, characteristic, complemented
4#13070167C211yesmaximal, characteristic, complemented
5#13070107C211yesmaximal, characteristic, complemented
6#13070030C211yesmaximal, characteristic, complemented
7#13069857C211yesmaximal, characteristic, complemented
8#13069291C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, characteristic
11#13068950C211yesmaximal, characteristic, complemented
12#13068950C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic, complemented
14#13068876C211yesmaximal, characteristic, complemented
15C11×#2349C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66928C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#385—21no—
26C11×#385—21no—
27C11×#382C2211yescharacteristic
28C11×#380—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×C11×#95—21no—
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622629—24no—
34C4×#4323—24no—
35#10622606—21no—
36#10622602—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622288—21no—
52#10622277—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22C2311yescharacteristic
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—41no—
73C4×D4×C11—41no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4324—22no—
88C2×#4324—22no—
89C2×#4324—22no—
90C2×#4323—22no—
91C2×#4323—22no—
92C2×#4323D414yes—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66928—22no—
106#66928—41no—
107C4×D44—22no—
108C4×D44—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115#66896—22no—
116#66896—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66874—22no—
123#66874—22no—
124#66874—41no—
125#66873—22no—
126#66873—22no—
127#66873—22no—
128#66872—41no—
129#66871—22no—
130C4⋊(C11⋊C8)—22no—
131C4×C11⋊C8—22no—
132#26160—111nomaximal, Sylow
133C24×C11—21no—
134C23×D11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11C2×D412yes—
139C2×D4×C11#4112yes—
140C2×D4×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11—81no—
151C22×C4×C11—81no—
152C22×C4×C11—81no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44C2×D412yes—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—81no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—81no—
186C11×C4⋊C4—81no—
187C11×C4⋊C4#4112yes—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197#4324—44no—
198#4323—28no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—81no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208Dic11⋊C4—81no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C2×D412yes—
221C2×#463—111no—
222C2×C4×D8—111no—
223#2447—111no—
224#2349D1111yescharacteristic, complemented
225#2097—111no—
226#2086—111no—
227#2073—111no—
228#2042—111no—
229#1933—111no—
230#1916—111no—
231#1879—111no—
232#1877—111no—
233#1877—111no—
234#1864—111no—
235#1864—111no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11#12314yes—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
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—41no—
274C2×C4×C11—41no—
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—84no—
282C2×C4×C11—84no—
283C2×C4×C11—84no—
284C2×C4×C11#13512yes—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C112−1+411yescharacteristic
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×Dic11—41no—
300D44—22no—
301D44—22no—
302D44—41no—
303D44—41no—
304C4×D11—84no—
305Dic22—41no—
306Dic22—41no—
307Dic22—41no—
308Dic22—41no—
309C11⋊C8—22no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C22×SD16—111no—
314C22×D8—111no—
315C2×#124—111no—
316C2×C4×D4—111no—
317C2×C4×D4C2×D1111yescharacteristic
318C2×C4×D4C2×D1111yescharacteristic
319C2×C4×D4C2×D1111yescharacteristic
320#463—224no—
321C4×D8—224no—
322C2×#107—111no—
323C2×#106—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×C4×C8—111no—
334#397—221no—
335#397—221no—
336#391—111no—
337#391—111no—
338#390—111no—
339#389—111no—
340#389C2×D1111yescharacteristic
341#389C2×D1111yescharacteristic
342#385—21no—
343#385—21no—
344#385—221no—
345#382C2×D1111yescharacteristic
346#381—221no—
347#380—21no—
348C4×C4⋊C4C2×D1111yescharacteristic
349C2×#95—21no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#336—111no—
355#336—111no—
356#336—111no—
357#336—111no—
358C22×C11—24no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11#52511yescharacteristic
366C22×C11D4211yescharacteristic
367C22×C11#54811yescharacteristic
368C22×C11C2×#13511yescharacteristic
369C22×C11#57511yescharacteristic
370C22×C11#57611yescharacteristic
371C22×C11#57711yescharacteristic
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11C2×#12311yescharacteristic
389C4×C11#53911yescharacteristic
390C4×C11#54711yescharacteristic
391C4×C11#55311yescharacteristic
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8—111no—
396C22×D4—111no—
397C22×D4C22×D1111yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—221no—
402C2×SD16—222no—
403C2×SD16—222no—
404C2×SD16—222no—
405C2×D8—114no—
406C2×D8—222no—
407C2×D8—222no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8—111no—
411C22×C8—111no—
412#124—222no—
413#124—441no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—41no—
419C4×D4—41no—
420C4×D4—222no—
421C4×D4—441no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4C22⋊D1111yescharacteristic
428C2×C4⋊C4C22⋊D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42C22×D1111yescharacteristic
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1111yescharacteristic
443#107—222no—
444#106—441no—
445C4⋊C8—222no—
446#103—222no—
447#103—222no—
448#103—441no—
449#102—222no—
450#102—222no—
451#102—222no—
452#102—222no—
453#102—222no—
454C4×C8—222no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95C22⋊D1111yescharacteristic
465#95C22⋊D1111yescharacteristic
466C2×C11—44no—
467C2×C11#244311yescharacteristic
468C2×C11#310211yescharacteristic
469C2×C11#311811yescharacteristic
470C2×C11#326711yescharacteristic
471C2×C11#328011yescharacteristic
472C2×C11#336011yescharacteristic
473C2×C11#337011yescharacteristic
474D11—82no—
475C24—21no—
476C24—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—112no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4#433912yes—
493C2×D4D4×D1112yes—
494C2×D4#434312yes—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—881no—
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C2×C22⋊D1111yescharacteristic
517C22×C4C2×C22⋊D1111yescharacteristic
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520SD16—444no—
521D8—228no—
522C2×C8—112no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C4⋊C4—22no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—41no—
541C4⋊C4—81no—
542C4⋊C4—81no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—881no—
548C4⋊C4#433912yes—
549C22⋊C4—24no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—881no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C11#2616011yescharacteristic, complemented, Sylow
564C23—22no—
565C23—22no—
566C23—22no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—222no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23—441no—
578C23C22×C22⋊D1111yescharacteristic
579Q8—441no—
580Q8—441no—
581Q8—441no—
582Q8—441no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—222no—
587D4—222no—
588D4—441no—
589D4—441no—
590D4#6694714yes—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
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—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—84no—
618C2×C4—84no—
619C2×C4—84no—
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—884no—
630C2×C4#6700312yes—
631C2×C4C2×#433911yescharacteristic
632C2×C4C2×#433911yescharacteristic
633C2×C4C2×D4×D1111yescharacteristic
634C2×C4#6703711yescharacteristic
635C2×C4C2×#434311yescharacteristic
636C2×C4#6704011yescharacteristic
637C8—222no—
638C8—441no—
639C8—441no—
640C8—441no—
641C22—24no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—442no—
649C22—442no—
650C22—442no—
651C22—881no—
652C22—881no—
653C22—881no—
654C22—881no—
655C22#1062332211yescharacteristic
656C22D4×C22⋊D1111yescharacteristic
657C22#1062334811yescharacteristic
658C22C2×#6700311yescharacteristic
659C22#1062335311yescharacteristic
660C22#1062336611yescharacteristic
661C22#1062336711yescharacteristic
662C4—22no—
663C4—41no—
664C4—42no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—81no—
670C4—81no—
671C4—881no—
672C4—881no—
673C4—881no—
674C4C2×#6694711yescharacteristic
675C4#1062303811yescharacteristic
676C4#1062304511yescharacteristic
677C4#1062304611yescharacteristic
678C2—44no—
679C2—882no—
680C2#1307235111yescharacteristic
681C2#1307863411yescharacteristic
682C2#1307880011yescharacteristic
683C2#1308013711yescharacteristic
684C2#1308029711yescharacteristic
685C2#1308126511yescharacteristic
686C2#1308136911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2349C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2349D11
hypocenterC11#26160
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #13072403C2semidirect
4. #13070167C2semidirect
5. #13070107C2semidirect
6. #13070030C2semidirect
7. #13069857C2semidirect
8. #13069291C2semidirect
9. #13069175C2semidirect
11. #13068950C2semidirect
12. #13068950C2semidirect
13. #13068877C2semidirect
14. #13068876C2semidirect
15. C11×#2349C2semidirect
224. #2349D11semidirect
563. C11#26160semidirect

Maximal subgroups

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

subgroupindex
C2×#106226292
C2×C4×#43232
#130724032
#130701672
#130701072
#130700302
#130698572
#130692912
#130691752
#130689642
#130689502
#130688772
#130688762
C11×#23492
#2616011