Finite Group Databasebeta

← #14802074

Subgroups — #14802074

Order 2816.

884 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×#10622335C211yesmaximal, characteristic, complemented
2C2×#10622727C211yesmaximal, characteristic
3#13073108C211yesmaximal, characteristic
4#13071619C211yesmaximal, characteristic, complemented
5#13070099C211yesmaximal, characteristic, complemented
6#13070036C211yesmaximal, characteristic, complemented
7#13070003C211yesmaximal, characteristic, complemented
8#13069934C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069237C211yesmaximal, characteristic, complemented
11#13068970C211yesmaximal, characteristic, complemented
12#13068931C211yesmaximal, characteristic
13#13068632C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622727—24no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622571—21no—
38#10622571—21no—
39#10622559—21no—
40C22⋊C4×Dic11—21no—
41#10622552C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622549C2211yescharacteristic
44#10622549C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622335—24no—
49#10622287—21no—
50#10622287—21no—
51#10622268—21no—
52#10622260—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×D44C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11—22no—
68C22×C8×C11—22no—
69C22×C8×C11—41no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79#66983—22no—
80#66983—22no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98#66977—22no—
99#66977D414yes—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×#4314—22no—
106C2×#4314—22no—
107C2×#4314—41no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C11×C4⋊C8—22no—
111C11×C4⋊C8—41no—
112C11×C22⋊C8—22no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66885—22no—
124#66885—22no—
125#66885—41no—
126#66882—22no—
127#66882—22no—
128#66881—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#25210—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—42no—
148C2×C22⋊D11—42no—
149C2×C22⋊D11—42no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—81no—
161C22×Dic11—81no—
162C22×Dic11—81no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22C2×D412yes—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—44no—
187C2×C8×C11#4112yes—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—24no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197(C2×D11)⋊C4—81no—
198(C2×D11)⋊C4—81no—
199(C2×D11)⋊C4—81no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—42no—
211C4⋊Dic11—42no—
212C4⋊Dic11C2×D412yes—
213C4⋊Dic11#4112yes—
214Dic11⋊C4—24no—
215Dic11⋊C4—42no—
216Dic11⋊C4—81no—
217C4×Dic11—42no—
218C4×Dic11—81no—
219#4314—44no—
220C2×#484—111no—
221C2×#465—111no—
222#2504—111no—
223#2360—111no—
224#2085—111no—
225#2074—111no—
226#2067—111no—
227#2055—111no—
228#1949—111no—
229#1925—111no—
230#1880—111no—
231#1874—111no—
232#1850D1111yescharacteristic, complemented
233#1805—111no—
234C2×#340—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11#12112yes—
240C23×C11#13512yes—
241C23×C11#13712yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
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#12112yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C22⋊D11—84no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—84no—
298C2×Dic11—84no—
299D44—41no—
300D44—41no—
301D44—41no—
302D44—41no—
303Dic22—22no—
304Dic22—22no—
305Dic22—41no—
306Dic22—41no—
307C8×C11—22no—
308C8×C11—41no—
309C8×C11—41no—
310C8×C11—41no—
311C22×SD16—111no—
312C23×C8C2×D1111yescharacteristic
313C2×C22⋊Q8—111no—
314C2×#121—111no—
315C2×C4×Q8—111no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4—111no—
318#484—224no—
319#465—224no—
320C2×#107—111no—
321C2×#107—111no—
322C2×#106—111no—
323C2×C4⋊C8C2×D1111yescharacteristic
324C2×C4⋊C8C2×D1111yescharacteristic
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×C22⋊C8C2×D1111yescharacteristic
332#397—221no—
333#397—221no—
334#391—111no—
335#390—111no—
336#390—111no—
337#389—111no—
338#389—221no—
339#387—221no—
340#386—221no—
341#386—221no—
342#385—221no—
343#382—111no—
344#382—111no—
345C4×C4⋊C4—111no—
346C4×C22⋊C4—221no—
347C4×C22⋊C4C2×D1111yescharacteristic
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#336C2×D1111yescharacteristic
355#336C2×D1111yescharacteristic
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11#46414yes—
363C22×C11C2×#12111yescharacteristic
364C22×C11#54611yescharacteristic
365C22×C11#54711yescharacteristic
366C22×C11C2×#13511yescharacteristic
367C22×C11C2×#13711yescharacteristic
368C22×C11#57611yescharacteristic
369C22×C11#57711yescharacteristic
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11—81no—
377C4×C11—22no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11#52911yescharacteristic
383C4×C11#53911yescharacteristic
384C4×C11#54611yescharacteristic
385C4×C11#54711yescharacteristic
386Dic11—42no—
387Dic11—42no—
388Dic11—42no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393C22×Q8—111no—
394C22×D4—111no—
395C22×D4—221no—
396C23×C4—221no—
397C23×C4—221no—
398C23×C4C22×D1111yescharacteristic
399C2×SD16—222no—
400C2×SD16—222no—
401C2×SD16—441no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—41no—
405C22×C8C22×D1111yescharacteristic
406C22×C8C22×D1111yescharacteristic
407C22×C8C22×D1111yescharacteristic
408C22×C8C22×D1111yescharacteristic
409C22⋊Q8—114no—
410C22⋊Q8—222no—
411#121—222no—
412#121—222no—
413C4×Q8—222no—
414C4×Q8—441no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—222no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—441no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4D4411yescharacteristic
437C2×C22⋊C4D4411yescharacteristic
438C2×C42—221no—
439C2×C42—221no—
440C2×C42C22×D1111yescharacteristic
441C2×C42C22×D1111yescharacteristic
442#107—222no—
443#107—222no—
444#106—222no—
445C4⋊C8—22no—
446C4⋊C8—41no—
447#103—222no—
448#103—222no—
449#103—222no—
450#102—222no—
451#102—222no—
452#102—441no—
453C22⋊C8—22no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95D4411yescharacteristic
463#95D4411yescharacteristic
464C2×C11—24no—
465C2×C11#242511yescharacteristic
466C2×C11C2×#46411yescharacteristic
467C2×C11#304511yescharacteristic
468C2×C11#329711yescharacteristic
469C2×C11#332011yescharacteristic
470C2×C11#333711yescharacteristic
471C2×C11#334611yescharacteristic
472D11—161no—
473C24—221no—
474C24C2×D4411yescharacteristic
475C2×Q8—112no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—442no—
488C2×D4—442no—
489C2×D4—442no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—881no—
505C22×C4—881no—
506C22×C4—881no—
507C22×C4C2×D4411yescharacteristic
508C22×C4C2×D4411yescharacteristic
509C22×C4C2×D4411yescharacteristic
510C22×C4C2×D4411yescharacteristic
511C22×C4C2×D4411yescharacteristic
512C22×C4D4×D1112yes—
513C22×C4#434312yes—
514C22×C4C23×D1111yescharacteristic
515SD16—444no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—44no—
528C2×C8#434112yes—
529C4⋊C4—112no—
530C4⋊C4—112no—
531C4⋊C4—224no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—881no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—224no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—442no—
559C42—881no—
560C11#2521011yescharacteristic, complemented, Sylow
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23#6694812yes—
573C23#6695712yes—
574C23#6696212yes—
575C23C22×D4411yescharacteristic
576Q8—222no—
577Q8—222no—
578Q8—441no—
579Q8—441no—
580D4—441no—
581D4—441no—
582D4—441no—
583D4—441no—
584D4—884no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—884no—
625C2×C4—884no—
626C2×C4#6694812yes—
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#6703711yescharacteristic
630C2×C4C2×#434311yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#6704311yescharacteristic
633C8—22no—
634C8—41no—
635C8—41no—
636C8—41no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—881no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22—881no—
648C22—881no—
649C22—881no—
650C22#1062245814yes—
651C22C2×#6694811yescharacteristic
652C22#1062308511yescharacteristic
653C22#1062308611yescharacteristic
654C22C2×#6695711yescharacteristic
655C22C2×#6696211yescharacteristic
656C22#1062328211yescharacteristic
657C22#1062328311yescharacteristic
658C4—22no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—442no—
664C4—442no—
665C4—442no—
666C4—881no—
667C4—881no—
668C4—881no—
669C4—881no—
670C4#1062312211yescharacteristic
671C4#1062315511yescharacteristic
672C4#1062317611yescharacteristic
673C4#1062318611yescharacteristic
674C2—24no—
675C2—1761no—
676C2#1307216511yescharacteristic
677C2C2×#1062245811yescharacteristic
678C2#1307815711yescharacteristic
679C2#1308046811yescharacteristic
680C2#1308078911yescharacteristic
681C2#1308099711yescharacteristic
682C2#1308110311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1850D11
hypocenterC11#25210
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#10622335C2semidirect
4. #13071619C2semidirect
5. #13070099C2semidirect
6. #13070036C2semidirect
7. #13070003C2semidirect
8. #13069934C2semidirect
9. #13069386C2semidirect
10. #13069237C2semidirect
11. #13068970C2semidirect
13. #13068632C2semidirect
14. C2×#10622189C2semidirect
15. C11×#1850C2semidirect
232. #1850D11semidirect
560. C11#25210semidirect

Maximal subgroups

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

subgroupindex
C2×#106223352
C2×#106227272
#130731082
#130716192
#130700992
#130700362
#130700032
#130699342
#130693862
#130692372
#130689702
#130689312
#130686322
C2×#106221892
C11×#18502
#2521011