Finite Group Databasebeta

← #14826527

Subgroups — #14826527

Order 2816.

708 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
1#13073047C211yesmaximal, characteristic
2#13071623C211yesmaximal, characteristic
3#13070026C211yesmaximal, characteristic, complemented
4#13070008C211yesmaximal, characteristic, complemented
5#13069822C211yesmaximal, characteristic
6#13069822C211yesmaximal, characteristic
7#13069374C211yesmaximal, characteristic, complemented
8#13069348C211yesmaximal, characteristic, complemented
9#13069223C211yesmaximal, characteristic
10#13069211C211yesmaximal, characteristic, complemented
11#13068867C211yesmaximal, characteristic, complemented
12#13068802C211yesmaximal, characteristic
13#13068705C211yesmaximal, characteristic
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1921C211yesmaximal, characteristic, complemented
16C2×#66950C2211yescharacteristic
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×#66880C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×C8×Dic11C2211yescharacteristic
27#10622607—21no—
28#10622600C2211yescharacteristic
29#10622600C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622594—21no—
32C4⋊C4×Dic11C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C4×(C2×D11)⋊C4—21no—
40C4×(C2×D11)⋊C4C2211yescharacteristic
41#10622548C2211yescharacteristic
42#10622542C2211yescharacteristic
43#10622541—21no—
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622283—21no—
46#10622281—21no—
47#10622273—21no—
48#10622266—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66950—22no—
92#66950—22no—
93C4⋊C4×D11—22no—
94C4⋊C4×D11—41no—
95#66940—22no—
96#66940—41no—
97C11×#107—22no—
98C11×#95—21no—
99C11×#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109(C2×D11)⋊C8—22no—
110(C2×D11)⋊C8—41no—
111#66880—22no—
112#66880—22no—
113C8×Dic11—41no—
114#66874—22no—
115#66874—41no—
116#66871—22no—
117#66871—22no—
118#66871—41no—
119C4⋊(C11⋊C8)—22no—
120#27036—111nomaximal, Sylow
121C23×D11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—81no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22#4112yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4#4112yes—
165C11×C4⋊C4#4112yes—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—81no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—81no—
172(C2×D11)⋊C4—81no—
173(C2×D11)⋊C4Q1614yes—
174C4⋊Dic11—24no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—81no—
182C4⋊Dic11—81no—
183C4⋊Dic11—81no—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186Dic11⋊C4—81no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—42no—
190C4×Dic11—81no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8#4112yes—
197#2497—111no—
198#2360—111no—
199#2072—111no—
200#2068—111no—
201#2036—111no—
202#2036—111no—
203#1947—111no—
204#1942—111no—
205#1923—111no—
206#1921—111no—
207#1921D1111yescharacteristic, complemented
208#1863—111no—
209#1852—111no—
210#1824—111no—
211C4×#103—111no—
212C23×C11C22×D411yescharacteristic
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—21no—
219C22×D11C2×Q1612yes—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—41no—
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×C11C2×Q1612yes—
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11C2×Q1612yes—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—84no—
270Dic22—22no—
271Dic22—22no—
272Dic22—41no—
273Dic22—41no—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—22no—
277C11⋊C8—41no—
278C2×C22⋊Q8—111no—
279C2×C4×Q8—111no—
280C22×C4⋊C4—111no—
281C2×#107—111no—
282C2×#107—111no—
283C2×#107—111no—
284C2×#107C2×D1111yescharacteristic
285C2×C4⋊C8—111no—
286C2×#103—111no—
287C2×#103—111no—
288C2×#103—111no—
289C2×#103—111no—
290C2×C22⋊C8—111no—
291C2×C22⋊C8—111no—
292C2×C4×C8—111no—
293#400—221no—
294#396—221no—
295#391—111no—
296#389—111no—
297#389—111no—
298#389—221no—
299#389C2×D1111yescharacteristic
300#388—221no—
301#387—221no—
302#387—221no—
303#385—221no—
304#384—111no—
305#380—111no—
306#380—111no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4C2×D1111yescharacteristic
309C4×C22⋊C4—111no—
310C4×C22⋊C4—221no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340C2×D1111yescharacteristic
317#340C2×D1111yescharacteristic
318#340C2×D1111yescharacteristic
319#336—111no—
320#336C2×D1111yescharacteristic
321C22×C11#52511yescharacteristic
322C22×C11#54611yescharacteristic
323C22×C11#54711yescharacteristic
324C22×C11C22×Q1611yescharacteristic
325C22×C11#57511yescharacteristic
326C22×C11#57611yescharacteristic
327C22×C11#57711yescharacteristic
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11—41no—
335C4×C11—22no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#52911yescharacteristic
342C4×C11#53911yescharacteristic
343C4×C11#55311yescharacteristic
344C4×C11#55611yescharacteristic
345Dic11—22no—
346Dic11—42no—
347Dic11—41no—
348Dic11—41no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352C22×Q8—111no—
353C23×C4—111no—
354C23×C4—221no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8C22×D1111yescharacteristic
358C22×C8C22×D1111yescharacteristic
359C22⋊Q8—222no—
360C22⋊Q8—222no—
361C4×Q8—222no—
362C4×Q8—441no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—441no—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—111no—
381C2×C22⋊C4—111no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C42—21no—
386C2×C42—111no—
387C2×C42—221no—
388C2×C42—221no—
389C2×C42C22×D1111yescharacteristic
390#107—22no—
391#107—222no—
392#107—222no—
393#107—441no—
394C4⋊C8—222no—
395#103—222no—
396#103—222no—
397#103—222no—
398#103—441no—
399C22⋊C8—222no—
400C22⋊C8—441no—
401C4×C8—441no—
402#95—21no—
403#95—21no—
404#95—111no—
405#95—111no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413C2×C11#246611yescharacteristic
414C2×C11#310411yescharacteristic
415C2×C11#311911yescharacteristic
416C2×C11#329911yescharacteristic
417C2×C11#331911yescharacteristic
418C2×C11#333811yescharacteristic
419C2×C11#335111yescharacteristic
420D11—42no—
421C24—111no—
422C2×Q8—112no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—881no—
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
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—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—42no—
470C4⋊C4—224no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4—881no—
480C4⋊C4—881no—
481C4⋊C4—881no—
482C4⋊C4—881no—
483C4⋊C4#433912yes—
484C4⋊C4#434312yes—
485C22⋊C4—114no—
486C22⋊C4—224no—
487C22⋊C4—441no—
488C22⋊C4—881no—
489C22⋊C4—881no—
490C42—21no—
491C42—21no—
492C42—81no—
493C42—221no—
494C42—221no—
495C42—442no—
496C42—881no—
497C11#2703611yescharacteristic, complemented, Sylow
498C23—112no—
499C23—221no—
500C23—221no—
501C23—221no—
502C23—221no—
503C23—221no—
504C23—221no—
505C23C2×D4×D1111yescharacteristic
506Q8—222no—
507Q8—222no—
508Q8—441no—
509Q8—441no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—112no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—222no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
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—441no—
552C2×C4—884no—
553C2×C4Q16×D1112yes—
554C2×C4C2×#433911yescharacteristic
555C2×C4C2×#434311yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C2×C4#6704211yescharacteristic
559C2×C4#6704311yescharacteristic
560C8—41no—
561C8—41no—
562C8—222no—
563C8—441no—
564C22—222no—
565C22—222no—
566C22—222no—
567C22—441no—
568C22—441no—
569C22—441no—
570C22—441no—
571C22#1062308111yescharacteristic
572C22#1062315811yescharacteristic
573C22#1062318611yescharacteristic
574C22C2×Q16×D1111yescharacteristic
575C22#1062330111yescharacteristic
576C22#1062330411yescharacteristic
577C22#1062330511yescharacteristic
578C4—22no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—222no—
585C4—441no—
586C4—442no—
587C4—441no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4#1062305911yescharacteristic
592C4#1062311511yescharacteristic
593C4#1062322611yescharacteristic
594C4#1062323811yescharacteristic
595C2—442no—
596C2#1307265911yescharacteristic
597C2#1307865711yescharacteristic
598C2#1307882011yescharacteristic
599C2#1308049411yescharacteristic
600C2#1308077711yescharacteristic
601C2#1308100311yescharacteristic
602C2#1308116911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1921C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1921D11
hypocenterC11#27036
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
3. #13070026C2semidirect
4. #13070008C2semidirect
7. #13069374C2semidirect
8. #13069348C2semidirect
10. #13069211C2semidirect
11. #13068867C2semidirect
14. #13068435C2semidirect
15. C11×#1921C2semidirect
207. #1921D11semidirect
497. C11#27036semidirect

Maximal subgroups

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

subgroupindex
#130730472
#130716232
#130700262
#130700082
#130698222
#130693742
#130693482
#130692232
#130692112
#130688672
#130688022
#130687052
#130684352
C11×#19212
#2703611