Finite Group Databasebeta

← #14805663

Subgroups — #14805663

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×C8×Dic22C211yesmaximal, characteristic, complemented
3#13074005C211yesmaximal, characteristic, complemented
4#13073975C211yesmaximal, characteristic
5#13070119C211yesmaximal, characteristic, complemented
6#13070113C211yesmaximal, characteristic, complemented
7#13070005C211yesmaximal, characteristic
8#13069991C211yesmaximal, characteristic
9#13069382C211yesmaximal, characteristic, complemented
10#13069348C211yesmaximal, characteristic, complemented
11#13069343C211yesmaximal, characteristic, complemented
12#13069297C211yesmaximal, characteristic
13#13069297C211yesmaximal, characteristic
14C4×#66885C211yesmaximal, characteristic
15C11×#1991C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20C11×#382C2211yescharacteristic
21C2×#66885C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×Dic11⋊C8C2211yescharacteristic
24C2×Dic11⋊C8C2211yescharacteristic
25C2×C8×Dic11C2211yescharacteristic
26C2×C8×Dic11C2211yescharacteristic
27#10622679—24no—
28#10622601C2211yescharacteristic
29#10622601C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622596—21no—
33#10622592—21no—
34#10622586C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622585—21no—
39#10622585—21no—
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C8×Dic22—24no—
49#10622290—21no—
50#10622286—21no—
51#10622281—21no—
52#10622281—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22D411yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#125—22no—
67C11×#125—22no—
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⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4D411yescharacteristic
91C2×Dic11⋊C4D411yescharacteristic
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C4×D44—22no—
98C4×D44—22no—
99C4×Dic22—22no—
100C4×Dic22—22no—
101C4×C8×C11—22no—
102C11×#95—21no—
103C11×#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111#66885—22no—
112#66885Q814yescomplemented
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115C8×Dic11—22no—
116C8×Dic11—22no—
117#66873—22no—
118#66873—22no—
119#66872—22no—
120#66872—22no—
121#66871—22no—
122#66871—22no—
123C4⋊(C11⋊C8)D414yes—
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×C11—21no—
157C2×C8×C11C2×Q812yes—
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⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—42no—
168C42×C11C2×D412yes—
169C42×C11#4112yes—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—42no—
173(C2×D11)⋊C4—81no—
174(C2×D11)⋊C4—81no—
175C4⋊Dic11—22no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—81no—
181C4⋊Dic11—81no—
182C4⋊Dic11C2×Q812yes—
183C4⋊Dic11#4112yes—
184Dic11⋊C4—22no—
185Dic11⋊C4—22no—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—81no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C2×D412yes—
200C2×C11⋊C8C2×D412yes—
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#1991D1111yescharacteristic, complemented
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—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
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—22no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
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—41no—
277C11⋊C8—22no—
278C11⋊C8—22no—
279C2×#125C2×D1111yescharacteristic
280C2×C4×Q8—111no—
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×C8C2×D1111yescharacteristic
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⋊C4—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340C2×D1111yescharacteristic
321#340C2×D1111yescharacteristic
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—81no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11#53311yescharacteristic
345C4×C11#54111yescharacteristic
346C4×C11#54711yescharacteristic
347C4×C11D4×Q811yescharacteristic
348Dic11—22no—
349Dic11—22no—
350Dic11—42no—
351Dic11—42no—
352Dic11—41no—
353Dic11—41no—
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—22no—
363#125—22no—
364C4×Q8—222no—
365C4×Q8—222no—
366C4×D4—222no—
367C4×D4—222no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
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—111no—
392C2×C42—111no—
393C2×C42—221no—
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—22no—
407C4×C8—222no—
408C4×C8—222no—
409#95—21no—
410#95—21no—
411#95—221no—
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—21no—
458C2×C8—112no—
459C2×C8—112no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8Q8×D1112yes—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—112no—
476C4⋊C4—112no—
477C4⋊C4—222no—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—881no—
487C4⋊C4—881no—
488C4⋊C4—881no—
489C4⋊C4—881no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C22⋊C4—442no—
493C22⋊C4—881no—
494C22⋊C4—881no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—881no—
500C42#433912yes—
501C42D4×D1112yes—
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—41no—
521C2×C4—41no—
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—222no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—222no—
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#6693712yes—
555C2×C4#6693712yes—
556C2×C4C2×#433911yescharacteristic
557C2×C4C2×D4×D1111yescharacteristic
558C2×C4C2×Q8×D1111yescharacteristic
559C2×C4#6704011yescharacteristic
560C2×C4#41×D1111yescharacteristic
561C2×C4#6704311yescharacteristic
562C8—22no—
563C8—41no—
564C8—222no—
565C8—222no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—881no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22C2×#6693711yescharacteristic
574C22#1062320811yescharacteristic
575C22#1062325811yescharacteristic
576C22D11×#13511yescharacteristic
577C22D11×#13511yescharacteristic
578C22#1062330011yescharacteristic
579C22#1062330111yescharacteristic
580C4—22no—
581C4—22no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—222no—
587C4—222no—
588C4—441no—
589C4—441no—
590C4—442no—
591C4—442no—
592C4—881no—
593C4#1062310911yescharacteristic
594C4#1062311411yescharacteristic
595C4#1062316211yescharacteristic
596C4#1062316311yescharacteristic
597C2—882no—
598C2#1307221611yescharacteristic
599C2#1307819611yescharacteristic
600C2#1307829911yescharacteristic
601C2#1308127311yescharacteristic
602C2#1308130911yescharacteristic
603C2#1308148011yescharacteristic
604C2#1308148811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1991C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1991D11
hypocenterC11#25473
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1991

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13074005C2semidirect
5. #13070119C2semidirect
6. #13070113C2semidirect
9. #13069382C2semidirect
10. #13069348C2semidirect
11. #13069343C2semidirect
15. C11×#1991C2semidirect
112. #66885Q8semidirect
209. #1991D11semidirect
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×C8×Dic222
#130740052
#130739752
#130701192
#130701132
#130700052
#130699912
#130693822
#130693482
#130693432
#130692972
C4×#668852
C11×#19912
#2547311