Finite Group Databasebeta

← #14805667

Subgroups — #14805667

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622679C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073974C211yesmaximal, characteristic
4#13070117C211yesmaximal, characteristic, complemented
5#13070112C211yesmaximal, characteristic, complemented
6#13070001C211yesmaximal, characteristic
7#13069987C211yesmaximal, characteristic
8#13069582C211yesmaximal, characteristic, complemented
9#13069384C211yesmaximal, characteristic, complemented
10#13069346C211yesmaximal, characteristic, complemented
11#13069341C211yesmaximal, characteristic, complemented
12#13069298C211yesmaximal, characteristic
13#13069298C211yesmaximal, characteristic
14C4×#66873C211yesmaximal, characteristic
15C11×#2584C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C11×#398—21no—
20C11×#395—21no—
21C11×#389—21no—
22C11×#389—21no—
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28#10622844—21no—
29#10622679—24no—
30Q8×C11⋊C8—24no—
31#10622605—21no—
32#10622602—21no—
33#10622602—21no—
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622552C2211yescharacteristic
44#10622549C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11D411yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C11×#125—22no—
65C11×#125—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C4×D44—22no—
100C4×D44—22no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110#66873—22no—
111#66873—22no—
112#66873—22no—
113#66873Q814yescomplemented
114#66872—22no—
115#66872—22no—
116#66871—22no—
117#66871—22no—
118C4⋊(C11⋊C8)—22no—
119C4⋊(C11⋊C8)—22no—
120C4⋊(C11⋊C8)D414yes—
121C4×C11⋊C8—22no—
122C4×C11⋊C8—22no—
123C4×C11⋊C8—22no—
124#25473—111nomaximal, Sylow
125C23×D11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
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×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
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—81no—
151C2×C4×D11—81no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4C2×Q812yes—
168C11×C4⋊C4#4112yes—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—81no—
174C42×C11C2×D412yes—
175C42×C11#4112yes—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—81no—
180(C2×D11)⋊C4—81no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187Dic11⋊C4—81no—
188Dic11⋊C4—81no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8C2×D412yes—
199C2×C11⋊C8C2×D412yes—
200C2×C11⋊C8C2×Q812yes—
201C2×#478—111no—
202C2×C8×Q8—111no—
203#2584D1111yescharacteristic, complemented
204#2580—111no—
205#2088—111no—
206#2087—111no—
207#2067—111no—
208#2065—111no—
209#1991—111no—
210#1949—111no—
211#1942—111no—
212#1941—111no—
213#1934—111no—
214#1934—111no—
215C4×#102—111no—
216C23×C11C22×D411yescharacteristic
217C22×D11—22no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224Q8×C11—28no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
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×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11#12112yes—
252C2×C4×C11#12112yes—
253C2×C4×C11#13512yes—
254C2×C4×C11#13512yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270D44—22no—
271D44—22no—
272D44—41no—
273D44—41no—
274C4×D11—84no—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C11⋊C8—22no—
278C11⋊C8—41no—
279C2×#125C2×D1111yescharacteristic
280C2×C4×Q8C2×D1111yescharacteristic
281C2×C4×D4—111no—
282#478—224no—
283C8×Q8—224no—
284C2×#107—111no—
285C2×#107—111no—
286C2×#106—111no—
287C2×#106—111no—
288C2×C4⋊C8—111no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8—111no—
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×C4×C8—111no—
296C2×C4×C8—111no—
297C2×C4×C8—111no—
298#399—221no—
299#398—21no—
300#395—21no—
301#393—221no—
302#390—111no—
303#390—111no—
304#389—21no—
305#389—21no—
306#389—111no—
307#389—111no—
308#389C2×D1111yescharacteristic
309#389C2×D1111yescharacteristic
310#389C2×D1111yescharacteristic
311#389C2×D1111yescharacteristic
312#385—221no—
313#385—221no—
314#382—111no—
315C4×C4⋊C4C2×D1111yescharacteristic
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324C22×C11C2×#12111yescharacteristic
325C22×C11#54811yescharacteristic
326C22×C11D4×Q811yescharacteristic
327C22×C11C2×#13511yescharacteristic
328C22×C11C2×#13511yescharacteristic
329C22×C11#57611yescharacteristic
330C22×C11#57711yescharacteristic
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C4×C11—22no—
339C4×C11—22no—
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11#53311yescharacteristic
349C4×C11#54111yescharacteristic
350C4×C11#54711yescharacteristic
351C4×C11D4×Q811yescharacteristic
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355C22×Q8C22⋊D1111yescharacteristic
356C22×D4—111no—
357C23×C4—221no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8—111no—
361C22×C8—111no—
362#125—22no—
363#125—22no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×D4—222no—
367C4×D4—222no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22⋊D1111yescharacteristic
380C2×C4⋊C4C22⋊D1111yescharacteristic
381C2×C4⋊C4C22⋊D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—21no—
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394C2×C42C22×D1111yescharacteristic
395#107—222no—
396#107—222no—
397#106—222no—
398#106—222no—
399C4⋊C8—114no—
400C4⋊C8—222no—
401C4⋊C8—222no—
402#102—114no—
403#102—222no—
404#102—222no—
405#102—222no—
406C4×C8—222no—
407C4×C8—222no—
408C4×C8—222no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418C2×C11#242911yescharacteristic
419C2×C11#305011yescharacteristic
420C2×C11#306211yescharacteristic
421C2×C11#336111yescharacteristic
422C2×C11#336511yescharacteristic
423C2×C11#338011yescharacteristic
424C2×C11#338111yescharacteristic
425D11—82no—
426C24—221no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×D4—112no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—442no—
444C22×C4—881no—
445C22×C4—881no—
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453C2×C8—112no—
454C2×C8—112no—
455C2×C8—112no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—881no—
487C4⋊C4—881no—
488C4⋊C4Q8×D1112yes—
489C4⋊C4#434312yes—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C22⋊C4—442no—
493C22⋊C4—881no—
494C22⋊C4—881no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—81no—
500C42D4×D1112yes—
501C42#434112yes—
502C11#2547311yescharacteristic, complemented, Sylow
503C23—222no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23C22×C22⋊D1111yescharacteristic
511Q8—28no—
512D4—222no—
513D4—222no—
514D4—441no—
515D4—441no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—884no—
552C2×C4#6699212yes—
553C2×C4#6699212yes—
554C2×C4#6700312yes—
555C2×C4#6700312yes—
556C2×C4C2×D4×D1111yescharacteristic
557C2×C4C2×#434111yescharacteristic
558C2×C4C2×Q8×D1111yescharacteristic
559C2×C4C2×#434311yescharacteristic
560C2×C4#6704011yescharacteristic
561C2×C4#6704011yescharacteristic
562C8—222no—
563C8—222no—
564C8—222no—
565C8—441no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—881no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22C2×#6699211yescharacteristic
574C22Q8×C22⋊D1111yescharacteristic
575C22#1062334811yescharacteristic
576C22C2×#6700311yescharacteristic
577C22C2×#6700311yescharacteristic
578C22#1062336611yescharacteristic
579C22#1062336811yescharacteristic
580C4—22no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—41no—
585C4—41no—
586C4—42no—
587C4—42no—
588C4—81no—
589C4—81no—
590C4—881no—
591C4—881no—
592C4—881no—
593C4#1062325711yescharacteristic
594C4#1062325811yescharacteristic
595C4#1062325911yescharacteristic
596C4#1062326211yescharacteristic
597C2—882no—
598C2#1307221811yescharacteristic
599C2#1307819411yescharacteristic
600C2#1307829811yescharacteristic
601C2#1308127611yescharacteristic
602C2#1308131211yescharacteristic
603C2#1308147911yescharacteristic
604C2#1308148711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2584C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2584D11
hypocenterC11#25473
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2584

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
4. #13070117C2semidirect
5. #13070112C2semidirect
8. #13069582C2semidirect
9. #13069384C2semidirect
10. #13069346C2semidirect
11. #13069341C2semidirect
15. C11×#2584C2semidirect
113. #66873Q8semidirect
203. #2584D11semidirect
502. C11#25473semidirect

Maximal subgroups

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

subgroupindex
C2×#106226792
C2×Q8×C11⋊C82
#130739742
#130701172
#130701122
#130700012
#130699872
#130695822
#130693842
#130693462
#130693412
#130692982
C4×#668732
C11×#25842
#2547311