Finite Group Databasebeta

← #14802166

Subgroups — #14802166

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622616C211yesmaximal, characteristic
2C2×#10622747C211yesmaximal, characteristic
3#13073065C211yesmaximal, characteristic, complemented
4#13071632C211yesmaximal, characteristic
5#13070091C211yesmaximal, characteristic, complemented
6#13070033C211yesmaximal, characteristic, complemented
7#13069998C211yesmaximal, characteristic, complemented
8#13069935C211yesmaximal, characteristic, complemented
9#13069387C211yesmaximal, characteristic, complemented
10#13069255C211yesmaximal, characteristic, complemented
11#13068951C211yesmaximal, characteristic, complemented
12#13068923C211yesmaximal, characteristic, complemented
13#13068799C211yesmaximal, characteristic, complemented
14#13068615C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C2×#66977C2211yescharacteristic
22C22×#4314C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24#10622826—21no—
25C4×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27#10622747—24no—
28C2×#66885C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622616—24no—
34#10622603—21no—
35#10622602—21no—
36#10622601C2211yescharacteristic
37#10622590C2211yescharacteristic
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622587C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622565—21no—
50#10622565—21no—
51#10622546—21no—
52#10622546—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16—41no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#117—22no—
73C11×#117—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—41no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86#66983—22no—
87#66983D414yes—
88C4×C22⋊D11—44no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—22no—
96#66977—22no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×#4314—22no—
107C2×#4314—22no—
108C2×#4314—41no—
109#66946—22no—
110#66946—41no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121C22⋊(C11⋊C8)—22no—
122#66885—22no—
123#66882—22no—
124#66880—22no—
125Dic11⋊C8—22no—
126Dic11⋊C8—41no—
127#66874—22no—
128#66874—41no—
129#66873—22no—
130#66873—22no—
131#66872—22no—
132#66871—22no—
133#25216—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C23×D11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—42no—
153C2×C22⋊D11—42no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44C2×D412yes—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C11×M16—44no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11#4112yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4#4112yes—
192C11×C22⋊C4—42no—
193C42×C11—42no—
194C22⋊Dic11—22no—
195C22⋊Dic11—41no—
196C22⋊Dic11—42no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—81no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C2×D412yes—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—42no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220#4314—44no—
221C2×#482—111no—
222C2×#468—111no—
223#2499—111no—
224#2361—111no—
225#2083—111no—
226#2073—111no—
227#2066—111no—
228#2055—111no—
229#1949—111no—
230#1928—111no—
231#1877—111no—
232#1872—111no—
233#1851—111no—
234#1802—111no—
235#1736D1111yescharacteristic, complemented
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11#12112yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
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—84no—
270C2×C4×C11#12112yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C22⋊D11—48no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11AGL(1,ℤ/8)12yes—
299D44—22no—
300D44—22no—
301D44—41no—
302D44—41no—
303C4×D11—84no—
304Dic22—41no—
305Dic22—41no—
306Dic22—41no—
307Dic22—41no—
308C8×C11—22no—
309C8×C11—41no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C22×SD16—111no—
313C22×M16C2×D1111yescharacteristic
314C2×C22⋊Q8—111no—
315C2×#121—111no—
316C2×C4×D4—111no—
317C2×C4×D4—221no—
318C2×#117C2×D1111yescharacteristic
319C22×C4⋊C4C2×D1111yescharacteristic
320#482—224no—
321#468—224no—
322C2×#107—111no—
323C2×#107—111no—
324C2×#106—111no—
325C2×C4⋊C8—111no—
326C2×C4⋊C8—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×C22⋊C8—111no—
334#397—221no—
335#397—221no—
336#391—111no—
337#391—111no—
338#390—111no—
339#389—111no—
340#388—221no—
341#387—221no—
342#387—221no—
343#386—221no—
344#385—221no—
345#384—111no—
346#382—111no—
347C4×C4⋊C4—111no—
348C4×C22⋊C4—111no—
349#340—111no—
350#340—111no—
351#340C2×D1111yescharacteristic
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354#340C2×D1111yescharacteristic
355#336—111no—
356#336—111no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11C2×#12111yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11#54711yescharacteristic
367C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57811yescharacteristic
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C4×C11—22no—
379C4×C11—42no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11#52911yescharacteristic
384C4×C11#53911yescharacteristic
385C4×C11#54611yescharacteristic
386C4×C11#54711yescharacteristic
387Dic11—22no—
388Dic11—41no—
389Dic11—41no—
390Dic11—42no—
391Dic11—41no—
392Dic11—81no—
393Dic11—81no—
394C22×Q8—111no—
395C22×D4—111no—
396C22×D4—221no—
397C23×C4—21no—
398C23×C4—221no—
399C23×C4C22×D1111yescharacteristic
400C2×SD16—222no—
401C2×SD16—222no—
402C2×SD16—441no—
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—41no—
406C22×C8—111no—
407C22×C8—111no—
408C22×C8C22×D1111yescharacteristic
409C22×C8C22×D1111yescharacteristic
410C22⋊Q8—222no—
411C22⋊Q8—222no—
412#121—114no—
413#121—222no—
414C4×D4—222no—
415C4×D4—441no—
416C4×D4—444no—
417#117—22no—
418#117—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—21no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—221no—
444#107—222no—
445#107—222no—
446#106—222no—
447C4⋊C8—222no—
448C4⋊C8—441no—
449#103—222no—
450#103—222no—
451#103—441no—
452#102—222no—
453#102—222no—
454#102—222no—
455C22⋊C8—222no—
456#95—111no—
457#95—111no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11—42no—
467C2×C11#242511yescharacteristic
468C2×C11#303611yescharacteristic
469C2×C11#304611yescharacteristic
470C2×C11#331011yescharacteristic
471C2×C11#332711yescharacteristic
472C2×C11#335011yescharacteristic
473C2×C11#335311yescharacteristic
474D11—82no—
475C24—221no—
476C24D4×D1111yescharacteristic
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×D4—112no—
484C2×D4—224no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—442no—
491C2×D4—442no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—81no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—881no—
513C22×C4#433912yes—
514C22×C4D4×D1111yescharacteristic
515C22×C4D4×D1112yes—
516C22×C4C23×D1111yescharacteristic
517SD16—444no—
518M16—44no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8#433912yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—112no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4#433912yes—
548C22⋊C4—42no—
549C22⋊C4—222no—
550C22⋊C4—224no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C22⋊C4—441no—
554C22⋊C4—442no—
555C22⋊C4—881no—
556C42—42no—
557C42—221no—
558C42—221no—
559C42—221no—
560C42—221no—
561C42—442no—
562C11#2521611yescharacteristic, complemented, Sylow
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—222no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23#6693712yes—
577C23C2×D4×D1111yescharacteristic
578Q8—441no—
579Q8—441no—
580Q8—441no—
581Q8—441no—
582D4—222no—
583D4—222no—
584D4—448no—
585D4—441no—
586D4—441no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
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—84no—
606C2×C4—112no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—222no—
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—884no—
628C2×C4#6693712yes—
629C2×C4C2×#433911yescharacteristic
630C2×C4C2×#433911yescharacteristic
631C2×C4C2×#433911yescharacteristic
632C2×C4C2×D4×D1111yescharacteristic
633C2×C4#6703711yescharacteristic
634C2×C4#6704011yescharacteristic
635C8—22no—
636C8—41no—
637C8—441no—
638C8—441no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—442no—
647C22—442no—
648C22—442no—
649C22—881no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22C2×#6693711yescharacteristic
654C22#1062302111yescharacteristic
655C22#1062303811yescharacteristic
656C22D11×AGL(1,ℤ/8)11yescharacteristic
657C22#1062330611yescharacteristic
658C22#1062330811yescharacteristic
659C22#1062331011yescharacteristic
660C4—22no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—222no—
666C4—441no—
667C4—442no—
668C4—441no—
669C4—441no—
670C4—881no—
671C4—881no—
672C4#1062301011yescharacteristic
673C4#1062302111yescharacteristic
674C4#1062303811yescharacteristic
675C4#1062304611yescharacteristic
676C2—42no—
677C2—882no—
678C2#1307216711yescharacteristic
679C2#1307807911yescharacteristic
680C2#1307816511yescharacteristic
681C2#1308063811yescharacteristic
682C2#1308088011yescharacteristic
683C2#1308116211yescharacteristic
684C2#1308119611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1736D11
hypocenterC11#25216
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. #13073065C2semidirect
5. #13070091C2semidirect
6. #13070033C2semidirect
7. #13069998C2semidirect
8. #13069935C2semidirect
9. #13069387C2semidirect
10. #13069255C2semidirect
11. #13068951C2semidirect
12. #13068923C2semidirect
13. #13068799C2semidirect
14. #13068615C2semidirect
15. C11×#1736C2semidirect
235. #1736D11semidirect
562. C11#25216semidirect

Maximal subgroups

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

subgroupindex
C2×#106226162
C2×#106227472
#130730652
#130716322
#130700912
#130700332
#130699982
#130699352
#130693872
#130692552
#130689512
#130689232
#130687992
#130686152
C11×#17362
#2521611