Finite Group Databasebeta

← #14805659

Subgroups — #14805659

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×#10622460C211yesmaximal, characteristic
2C2×#10622443C211yesmaximal, characteristic, complemented
3#13073999C211yesmaximal, characteristic, complemented
4#13073975C211yesmaximal, characteristic
5#13070116C211yesmaximal, characteristic, complemented
6#13070111C211yesmaximal, characteristic, complemented
7#13069999C211yesmaximal, characteristic
8#13069985C211yesmaximal, characteristic
9#13069580C211yesmaximal, characteristic, complemented
10#13069350C211yesmaximal, characteristic, complemented
11#13069345C211yesmaximal, characteristic, complemented
12#13069300C211yesmaximal, characteristic
13#13069300C211yesmaximal, characteristic
14C4×#66873C211yesmaximal, characteristic
15C11×#1949C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×#66923C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#382C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622601C2211yescharacteristic
33#10622601C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42#10622541—21no—
43#10622541—21no—
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622460—24no—
46#10622443—24no—
47#10622290—21no—
48#10622286—21no—
49#10622281—21no—
50#10622281—21no—
51#10622274—21no—
52#10622269—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22D411yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4D411yescharacteristic
90C2×Dic11⋊C4D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C4×D44—22no—
96C4×D44—22no—
97#66923—22no—
98#66923—22no—
99C4×Dic22—22no—
100C4×Dic22—22no—
101C11×#107—22no—
102C11×#106—22no—
103C11×C4⋊C8D414yes—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113#66885—22no—
114#66885—22no—
115#66882—22no—
116#66881—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119C8×Dic11—22no—
120C8×Dic11—22no—
121#66873—22no—
122#66873Q814yescomplemented
123C4×C11⋊C8—22no—
124#25473—111nomaximal, Sylow
125C23×D11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44C2×Q812yes—
146C2×C4×D11—42no—
147C2×C4×D11—81no—
148C2×C4×D11—81no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C2×D412yes—
157C2×C8×C11C2×D412yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C2×Q812yes—
165C11×C4⋊C4#4112yes—
166C42×C11—81no—
167C42×C11C2×D412yes—
168C42×C11#4112yes—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—81no—
173(C2×D11)⋊C4—81no—
174C4⋊Dic11—22no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—42no—
182C4⋊Dic11—42no—
183C4⋊Dic11—81no—
184C4⋊Dic11—81no—
185C4⋊Dic11—81no—
186C4⋊Dic11—81no—
187Dic11⋊C4—22no—
188Dic11⋊C4—22no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8C2×Q812yes—
201C2×#478—111no—
202C2×C8×Q8—111no—
203#2584—111no—
204#2580—111no—
205#2088—111no—
206#2087—111no—
207#2067—111no—
208#2065—111no—
209#1991—111no—
210#1949D1111yescharacteristic, complemented
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—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11#12112yes—
241C2×C4×C11#12112yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×Q811yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11#13512yes—
268C2×Dic11#13512yes—
269D44—22no—
270D44—22no—
271D44—41no—
272D44—41no—
273C4×D11—84no—
274Dic22—28no—
275C8×C11—22no—
276C8×C11—22no—
277C11⋊C8—22no—
278C11⋊C8—41no—
279C2×#125—111no—
280C2×C4×Q8—111no—
281C2×C4×D4—111no—
282#478—224no—
283C8×Q8—224no—
284C2×#107—111no—
285C2×#107C2×D1111yescharacteristic
286C2×#106—111no—
287C2×#106C2×D1111yescharacteristic
288C2×C4⋊C8—111no—
289C2×C4⋊C8—111no—
290C2×C4⋊C8C2×D1111yescharacteristic
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—221no—
300#395—221no—
301#393—221no—
302#390—111no—
303#390—111no—
304#389—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389—111no—
310#389—221no—
311#389—221no—
312#385—221no—
313#385—221no—
314#382C2×D1111yescharacteristic
315C4×C4⋊C4C2×D1111yescharacteristic
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340C2×D1111yescharacteristic
323#340C2×D1111yescharacteristic
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—42no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11#53311yescharacteristic
345C4×C11#54111yescharacteristic
346C4×C11#54711yescharacteristic
347C4×C11D4×Q811yescharacteristic
348Dic11—22no—
349Dic11—22no—
350Dic11—41no—
351Dic11—41no—
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355C22×Q8—111no—
356C22×D4—111no—
357C23×C4—221no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362#125—222no—
363#125—222no—
364C4×Q8—222no—
365C4×Q8—222no—
366C4×D4—222no—
367C4×D4—222no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
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×C42—111no—
393C2×C42—111no—
394C2×C42C22×D1111yescharacteristic
395#107—22no—
396#107—222no—
397#106—22no—
398#106—222no—
399C4⋊C8—222no—
400C4⋊C8—222no—
401C4⋊C8D4414yes—
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—221no—
413#95—221no—
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—222no—
428C2×Q8—222no—
429C2×Q8—222no—
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—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—442no—
448C22×C4—881no—
449C22×C4—881no—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—112no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8C2×D4412yes—
464C2×C8C2×D4412yes—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—222no—
472C4⋊C4—222no—
473C4⋊C4—222no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—442no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—881no—
485C4⋊C4—881no—
486C4⋊C4—881no—
487C4⋊C4—881no—
488C4⋊C4#434112yes—
489C4⋊C4Q8×D1112yes—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C22⋊C4—442no—
493C22⋊C4—881no—
494C22⋊C4—881no—
495C42—81no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42C2×D4412yes—
501C42#434312yes—
502C11#2547311yescharacteristic, complemented, Sylow
503C23—222no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23C2×D4×D1111yescharacteristic
511Q8—228no—
512D4—222no—
513D4—222no—
514D4—441no—
515D4—441no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—884no—
554C2×C4#6694812yes—
555C2×C4#6694812yes—
556C2×C4C22×D4411yescharacteristic
557C2×C4C2×#434111yescharacteristic
558C2×C4C2×Q8×D1111yescharacteristic
559C2×C4C2×#434311yescharacteristic
560C2×C4#6704311yescharacteristic
561C2×C4#6704311yescharacteristic
562C8—22no—
563C8—22no—
564C8—222no—
565C8—441no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—881no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22C2×#6694811yescharacteristic
574C22#1062312911yescharacteristic
575C22#1062316311yescharacteristic
576C22D11×#13511yescharacteristic
577C22D11×#13511yescharacteristic
578C22#1062330511yescharacteristic
579C22#1062330911yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—222no—
587C4—222no—
588C4—441no—
589C4—441no—
590C4—881no—
591C4—881no—
592C4—881no—
593C4#1062308611yescharacteristic
594C4Q8×D4411yescharacteristic
595C4#1062322811yescharacteristic
596C4#1062325911yescharacteristic
597C2—882no—
598C2#1307221311yescharacteristic
599C2#1307819811yescharacteristic
600C2#1307829711yescharacteristic
601C2#1308127111yescharacteristic
602C2#1308130711yescharacteristic
603C2#1308147811yescharacteristic
604C2#1308149411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1949D11
hypocenterC11#25473
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
2. C2×#10622443C2semidirect
3. #13073999C2semidirect
5. #13070116C2semidirect
6. #13070111C2semidirect
9. #13069580C2semidirect
10. #13069350C2semidirect
11. #13069345C2semidirect
15. C11×#1949C2semidirect
122. #66873Q8semidirect
210. #1949D11semidirect
502. C11#25473semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
C2×#106224432
#130739992
#130739752
#130701162
#130701112
#130699992
#130699852
#130695802
#130693502
#130693452
#130693002
C4×#668732
C11×#19492
#2547311