Finite Group Databasebeta

← #14805344

Subgroups — #14805344

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622487C211yesmaximal, characteristic, complemented
2C2×#10622503C211yesmaximal, characteristic
3#13073568C211yesmaximal, characteristic
4#13071669C211yesmaximal, characteristic, complemented
5#13070091C211yesmaximal, characteristic, complemented
6#13070005C211yesmaximal, characteristic
7#13070001C211yesmaximal, characteristic
8#13069566C211yesmaximal, characteristic, complemented
9#13069372C211yesmaximal, characteristic, complemented
10#13069371C211yesmaximal, characteristic, complemented
11#13069333C211yesmaximal, characteristic, complemented
12#13069237C211yesmaximal, characteristic
13#13069235C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#2083C211yesmaximal, characteristic, complemented
16C2×#66949—21no—
17C2×#66949—21no—
18C2×#66946C2211yescharacteristic
19C2×#66941C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×#66940—21no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#384C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622605—21no—
33#10622605—21no—
34#10622601C2211yescharacteristic
35#10622591—21no—
36#10622589C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622503—24no—
50#10622487—24no—
51#10622265—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22—21no—
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4D411yescharacteristic
89C2×Dic11⋊C4D411yescharacteristic
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66949—44no—
98#66949—44no—
99#66946—22no—
100#66946—22no—
101#66941—22no—
102#66941—22no—
103#66941—22no—
104#66941D414yes—
105#66940—44no—
106C11×#107—22no—
107C11×#107—22no—
108C11×#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115#66885—22no—
116#66885Q814yescomplemented
117#66882—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120C8×Dic11—22no—
121#66873—22no—
122#66873—22no—
123#66871—22no—
124#66871—22no—
125#66871—22no—
126C4⋊(C11⋊C8)—22no—
127#25449—111nomaximal, Sylow
128C23×D11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44C2×Q812yes—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—42no—
152C2×Dic22—24no—
153C2×Dic22—42no—
154C2×Dic22—42no—
155C2×Dic22—42no—
156C2×Dic22—42no—
157C2×Dic22—42no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C2×Q812yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C2×D412yes—
175C42×C11—21no—
176C42×C11—21no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C2×D412yes—
187C4⋊Dic11C2×Q812yes—
188Dic11⋊C4—24no—
189Dic11⋊C4—22no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4D814yes—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11C2×D412yes—
201C4×Dic11#4112yes—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8#4112yes—
208C2×#500—111no—
209C2×#474—111no—
210#2542—111no—
211#2365—111no—
212#2083—111no—
213#2083D1111yescharacteristic, complemented
214#2067—111no—
215#2067—111no—
216#1988—111no—
217#1947—111no—
218#1947—111no—
219#1939—111no—
220#1925—111no—
221#1925—111no—
222C4×#102—111no—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C2×D812yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×Q811yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11#12112yes—
272C2×Dic11#12112yes—
273C2×Dic11C2×D812yes—
274C2×Dic11C2×D812yes—
275C2×Dic11AGL(1,ℤ/8)12yes—
276D44—22no—
277D44—22no—
278D44—41no—
279D44—41no—
280C4×D11—84no—
281Dic22—48no—
282Dic22—84no—
283C8×C11—22no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C2×C4⋊Q8—111no—
288C2×C4⋊Q8—111no—
289C2×C22⋊Q8—221no—
290C2×C22⋊Q8—221no—
291C2×C4×Q8—221no—
292C2×C4×D4—111no—
293#500—224no—
294#474—224no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#107—111no—
299C2×#107C2×D1111yescharacteristic
300C2×#107C2×D1111yescharacteristic
301C2×C4⋊C8—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×C4×C8—111no—
309#399—221no—
310#399—221no—
311#391—221no—
312#390—111no—
313#390—111no—
314#389—111no—
315#389C2×D1111yescharacteristic
316#387—221no—
317#387—221no—
318#384—111no—
319#384C2×D1111yescharacteristic
320C4×C4⋊C4—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#336—111no—
331#336C2×D1111yescharacteristic
332C22×C11C2×#12111yescharacteristic
333C22×C11#54711yescharacteristic
334C22×C11D4×Q811yescharacteristic
335C22×C11C22×D811yescharacteristic
336C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C11#57811yescharacteristic
338C22×C11#57811yescharacteristic
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C4×C11—22no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11#53311yescharacteristic
353C4×C11#54111yescharacteristic
354C4×C11#54811yescharacteristic
355C4×C11D4×Q811yescharacteristic
356Dic11—22no—
357Dic11—22no—
358Dic11—41no—
359Dic11—42no—
360Dic11—42no—
361Dic11—81no—
362Dic11#45914yes—
363C22×Q8—221no—
364C22×Q8—221no—
365C22×D4—111no—
366C23×C4—221no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C4⋊Q8—114no—
372C4⋊Q8—222no—
373C4⋊Q8—222no—
374C4⋊Q8—222no—
375C22⋊Q8—444no—
376C22⋊Q8—444no—
377C4×Q8—444no—
378C4×D4—222no—
379C4×D4—222no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408#107—22no—
409#107—22no—
410#107—222no—
411#107—222no—
412#107—222no—
413#107—222no—
414C4⋊C8—222no—
415C4⋊C8—222no—
416C4⋊C8—222no—
417#102—114no—
418#102—222no—
419#102—222no—
420#102—222no—
421C4×C8—222no—
422#95—21no—
423#95—111no—
424#95—111no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429C2×C11#242911yescharacteristic
430C2×C11C2×#45911yescharacteristic
431C2×C11#304411yescharacteristic
432C2×C11#333411yescharacteristic
433C2×C11#335311yescharacteristic
434C2×C11Q8×D811yescharacteristic
435C2×C11#338611yescharacteristic
436D11—82no—
437C24—221no—
438C2×Q8—224no—
439C2×Q8—442no—
440C2×Q8—442no—
441C2×Q8—442no—
442C2×Q8—442no—
443C2×Q8—442no—
444C2×D4—112no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4—442no—
464C22×C4D4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4C23×D1111yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—112no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8Q8×D1112yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—114no—
490C4⋊C4—112no—
491C4⋊C4—112no—
492C4⋊C4—222no—
493C4⋊C4—224no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4D4×D1112yes—
503C22⋊C4—442no—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C22⋊C4—442no—
507C22⋊C4—442no—
508C42—21no—
509C42—21no—
510C42—112no—
511C42—112no—
512C42—221no—
513C42—221no—
514C42—442no—
515C42—442no—
516C42—442no—
517C11#2544911yescharacteristic, complemented, Sylow
518C23—222no—
519C23—441no—
520C23—441no—
521C23—441no—
522C23—441no—
523C23—441no—
524C23—441no—
525C23C2×D4×D1111yescharacteristic
526Q8—448no—
527Q8—884no—
528D4—222no—
529D4—222no—
530D4—441no—
531D4—441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—112no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—222no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—222no—
562C2×C4—221no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—884no—
571C2×C4D8×D1112yes—
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×Q8×D1111yescharacteristic
574C2×C4#6704011yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#6704311yescharacteristic
578C8—22no—
579C8—41no—
580C8—222no—
581C8—441no—
582C22—442no—
583C22—442no—
584C22—442no—
585C22—881no—
586C22—881no—
587C22—881no—
588C22—881no—
589C22D11×#12111yescharacteristic
590C22#1062318611yescharacteristic
591C22#1062325811yescharacteristic
592C22C2×D8×D1111yescharacteristic
593C22#1062329711yescharacteristic
594C22D11×AGL(1,ℤ/8)11yescharacteristic
595C22#1062331011yescharacteristic
596C4—22no—
597C4—42no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—114no—
603C4—222no—
604C4—222no—
605C4—442no—
606C4—441no—
607C4—442no—
608C4—881no—
609C4#1062316311yescharacteristic
610C4#1062316411yescharacteristic
611C4#1062321911yescharacteristic
612C4#1062322711yescharacteristic
613C2—882no—
614C2#1307221011yescharacteristic
615C2D11×#45911yescharacteristic
616C2#1307814111yescharacteristic
617C2#1308095811yescharacteristic
618C2#1308119311yescharacteristic
619C2#1308146811yescharacteristic
620C2#1308153411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2083C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2083D11
hypocenterC11#25449
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
1. C2×#10622487C2semidirect
4. #13071669C2semidirect
5. #13070091C2semidirect
8. #13069566C2semidirect
9. #13069372C2semidirect
10. #13069371C2semidirect
11. #13069333C2semidirect
15. C11×#2083C2semidirect
116. #66885Q8semidirect
213. #2083D11semidirect
517. C11#25449semidirect

Maximal subgroups

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

subgroupindex
C2×#106224872
C2×#106225032
#130735682
#130716692
#130700912
#130700052
#130700012
#130695662
#130693722
#130693712
#130693332
#130692372
#130692352
#130684302
C11×#20832
#2544911