Finite Group Databasebeta

← #14765809

Subgroups — #14765809

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622372C211yesmaximal, characteristic
2C4×#66941C211yesmaximal, characteristic, complemented
3#13071078C211yesmaximal, characteristic
4#13069566C211yesmaximal, characteristic, complemented
5#13069371C211yesmaximal, characteristic, complemented
6#13069348C211yesmaximal, characteristic, complemented
7#13069347C211yesmaximal, characteristic, complemented
8#13069301C211yesmaximal, characteristic
9#13069296C211yesmaximal, characteristic
10#13069233C211yesmaximal, characteristic
11#13069188C211yesmaximal, characteristic, complemented
12#13069187C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic
14#13068464C211yesmaximal, characteristic, complemented
15C11×#1925C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C2×#66941C2211yescharacteristic
18C2×#66930—21no—
19C2×C4×Dic22—21no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622589C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622558—21no—
41#10622557—21no—
42C22⋊C4×Dic11—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44C4×Dic11⋊C4—21no—
45C42×Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622372C418yescomplemented
48#10622260—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×Dic22—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75D4×Dic11—22no—
76D4×Dic11C2×C414yes—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66941—22no—
99#66941C2×C414yes—
100#66930—44no—
101C4×Dic22—44no—
102C11×#107—41no—
103C11×#102—41no—
104C11×#102C2×C414yes—
105C11×#95—21no—
106#66896—41no—
107#66896C2×C414yes—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114#66882C2×C414yes—
115Dic11⋊C8—22no—
116Dic11⋊C8C2×C414yes—
117C8×Dic11—41no—
118C8×Dic11—41no—
119#66871—41no—
120#66871C2×C414yes—
121#22110—111nomaximal, Sylow
122C24×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11C22×C412yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—24no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C2×Dic22—24no—
147C2×Dic22—42no—
148C2×Dic22—42no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C22×C412yes—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4C22×C412yes—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—42no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—42no—
166C22⋊Dic11—24no—
167C22⋊Dic11—42no—
168C22⋊Dic11—42no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—42no—
176C4⋊Dic11C22×C412yes—
177C4⋊Dic11C22×C412yes—
178Dic11⋊C4—24no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—41no—
189C4×Dic11—42no—
190C4×Dic11—42no—
191C4×Dic11D814yes—
192C4×Dic11C22×C412yes—
193C4×Dic11#4112yes—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C412yes—
200C2×#474—111no—
201C4×C4⋊Q8—111no—
202#2293—111no—
203#1988—111no—
204#1947—111no—
205#1942—111no—
206#1942—111no—
207#1934—111no—
208#1934—111no—
209#1925—111no—
210#1925D1111yescharacteristic
211#1918—111no—
212#1918—111no—
213#1802—111no—
214C4×C4⋊C8—111no—
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11C22×D411yescharacteristic
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
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—41no—
241C2×C4×C11C2×D812yes—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C112−1+411yescharacteristic
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—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—48no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11C4×D412yes—
268C2×Dic11C4×D412yes—
269C2×Dic11C2×D812yes—
270C2×Dic11C2×D812yes—
271C2×Dic11#13512yes—
272C2×Dic11#13712yes—
273Dic22—48no—
274C8×C11—22no—
275C8×C11—41no—
276C11⋊C8—22no—
277C11⋊C8—41no—
278C2×C4⋊Q8—111no—
279C2×C4×Q8—221no—
280C2×C4×D4—111no—
281C2×#117—221no—
282#474—118no—
283C2×#107—111no—
284C2×#107—111no—
285C2×#107—111no—
286C2×#107C2×D1111yescharacteristic
287C2×C4⋊C8—111no—
288C2×C4⋊C8—111no—
289C2×#102—111no—
290C2×#102—111no—
291C2×#102C2×D1111yescharacteristic
292C2×#102C2×D1111yescharacteristic
293C2×C4×C8—111no—
294C2×C4×C8—111no—
295#391—221no—
296#390—111no—
297#390C2×D1111yescharacteristic
298#389—111no—
299#389—111no—
300#389—111no—
301#389—111no—
302#389—221no—
303#388—221no—
304#388—221no—
305#384—111no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4—221no—
309C4×C4⋊C4C2×D1111yescharacteristic
310C4×C22⋊C4—221no—
311C43—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340C2×D1111yescharacteristic
320#336—111no—
321#336C2×D1111yescharacteristic
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11C2×C4×D411yescharacteristic
330C22×C11#53611yescharacteristic
331C22×C11#53711yescharacteristic
332C22×C11C22×D811yescharacteristic
333C22×C11C2×#13511yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C22×C11#57511yescharacteristic
336C4×C11—22no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#51911yescharacteristic
342C4×C11#52011yescharacteristic
343C4×C11#54111yescharacteristic
344C4×C11#54211yescharacteristic
345Dic11—22no—
346Dic11—22no—
347Dic11—22no—
348Dic11—42no—
349Dic11—42no—
350Dic11—81no—
351Dic11—81no—
352Dic11C4×D814yes—
353C22×Q8—221no—
354C22×D4C22×D1111yescharacteristic
355C23×C4—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360C4⋊Q8—114no—
361C4⋊Q8—222no—
362C4×Q8—444no—
363C4×D4—114no—
364C4×D4—222no—
365#117—444no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C42—21no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—221no—
393C2×C42—221no—
394C2×C42C22×D1111yescharacteristic
395#107—41no—
396#107—114no—
397#107—114no—
398#107—441no—
399C4⋊C8—114no—
400C4⋊C8—222no—
401#102—41no—
402#102—114no—
403#102—441no—
404#102C4×D1114yes—
405C4×C8—441no—
406C4×C8—441no—
407#95—21no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414C2×C11—82no—
415C2×C11#232311yescharacteristic
416C2×C11C2×C4×D811yescharacteristic
417C2×C11C4×#13711yescharacteristic
418C2×C11#322611yescharacteristic
419C2×C11#323311yescharacteristic
420C2×C11#324511yescharacteristic
421C2×C11#324811yescharacteristic
422C24—21no—
423C2×Q8—224no—
424C2×Q8—442no—
425C2×Q8—442no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4C2×C4×D1112yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—224no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4D4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—112no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8C2×C4×D1112yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—112no—
467C4⋊C4—112no—
468C4⋊C4—224no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4—442no—
480C4⋊C4—442no—
481C4⋊C4C2×C4×D1112yes—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—224no—
485C22⋊C4—442no—
486C22⋊C4—442no—
487C42—21no—
488C42—21no—
489C42—42no—
490C42—114no—
491C42—112no—
492C42—112no—
493C42—222no—
494C42—222no—
495C42—221no—
496C42—221no—
497C42—441no—
498C42—442no—
499C42—442no—
500C11#2211011yescharacteristic, complemented, Sylow
501C23—22no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C2×D4×D1111yescharacteristic
509Q8—448no—
510D4—22no—
511D4—22no—
512D4—41no—
513D4—41no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
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—112no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—112no—
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—222no—
541C2×C4—222no—
542C2×C4—448no—
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—441no—
552C2×C4—441no—
553C2×C4D8×D1112yes—
554C2×C4C22×C4×D1111yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#6704311yescharacteristic
558C2×C4#6704311yescharacteristic
559C2×C4#6704311yescharacteristic
560C8—22no—
561C8—41no—
562C8—222no—
563C8—441no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22C4×D4×D1111yescharacteristic
572C22#1062313911yescharacteristic
573C22#1062317911yescharacteristic
574C22C2×D8×D1111yescharacteristic
575C22D11×#13511yescharacteristic
576C22#1062330411yescharacteristic
577C22D11×#13711yescharacteristic
578C4—22no—
579C4—42no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—114no—
584C4—222no—
585C4—222no—
586C4—222no—
587C4—442no—
588C4—442no—
589C4—881no—
590C4—881no—
591C4#1062304711yescharacteristic
592C4#1062307711yescharacteristic
593C4#1062320011yescharacteristic
594C4#1062323211yescharacteristic
595C2—82no—
596C2#1307129511yescharacteristic
597C2C4×D8×D1111yescharacteristic
598C2#1307743811yescharacteristic
599C2#1307973511yescharacteristic
600C2#1307979211yescharacteristic
601C2#1307992411yescharacteristic
602C2#1307995011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1925C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1925D11
hypocenterC11#22110
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. C4×#66941C2semidirect
4. #13069566C2semidirect
5. #13069371C2semidirect
6. #13069348C2semidirect
7. #13069347C2semidirect
11. #13069188C2semidirect
12. #13069187C2semidirect
14. #13068464C2semidirect
47. #10622372C4semidirect
500. C11#22110semidirect

Maximal subgroups

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

subgroupindex
C2×#106223722
C4×#669412
#130710782
#130695662
#130693712
#130693482
#130693472
#130693012
#130692962
#130692332
#130691882
#130691872
#130686142
#130684642
C11×#19252
#2211011