Finite Group Databasebeta

← #14822445

Subgroups — #14822445

Order 2816.

712 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
1#13071685C211yesmaximal, characteristic
2#13070020C211yesmaximal, characteristic
3#13070001C211yesmaximal, characteristic
4#13069857C211yesmaximal, characteristic
5#13069857C211yesmaximal, characteristic
6#13069291C211yesmaximal, characteristic, complemented
7#13069257C211yesmaximal, characteristic, complemented
8#13069191C211yesmaximal, characteristic, complemented
9#13069184C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068883C211yesmaximal, characteristic, complemented
12#13068876C211yesmaximal, characteristic
13#13068618C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic
15C11×#2507C211yesmaximal, characteristic, complemented
16C2×#66928C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#398—21no—
20C11×#398—21no—
21C11×#389—21no—
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#387—21no—
27C11×#384C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30#10622603—21no—
31#10622602—21no—
32C2×#66874C2211yescharacteristic
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622552C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622542C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622282—21no—
48#10622279—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2311yescharacteristic
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92#66928—22no—
93#66928—22no—
94C4×D44—22no—
95C4×D44—41no—
96C4×Dic22—22no—
97C4×Dic22—41no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108#66874—22no—
109#66874—22no—
110#66874—22no—
111#66874—41no—
112#66873—22no—
113#66873—22no—
114#66873—22no—
115#66873—41no—
116#66872—22no—
117#66871—22no—
118C4⋊(C11⋊C8)—41no—
119C4×C11⋊C8—41no—
120#26763—111nomaximal, Sylow
121C23×D11—21no—
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×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44#4112yes—
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—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—81no—
162C11×C4⋊C4—81no—
163C11×C4⋊C4—81no—
164C11×C4⋊C4—81no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4#4112yes—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—81no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—81no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11#4112yes—
183Dic11⋊C4—42no—
184C4×Dic11—42no—
185C4×Dic11—81no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
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—
198#2507D1111yescharacteristic, complemented
199#2367—111no—
200#2071—111no—
201#2067—111no—
202#2042—111no—
203#2042—111no—
204#1933—111no—
205#1928—111no—
206#1919—111no—
207#1918—111no—
208#1916—111no—
209#1865—111no—
210#1864—111no—
211#1803—111no—
212C4×#102—111no—
213C23×C11C22×D411yescharacteristic
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
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—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
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#13512yes—
250C2×C4×C11#13712yes—
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266D44—22no—
267D44—22no—
268D44—41no—
269D44—41no—
270C4×D11—84no—
271Dic22—22no—
272Dic22—22no—
273Dic22—41no—
274Dic22—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C2×#124—111no—
280C2×C4×Q8—111no—
281C2×C4×D4—111no—
282C2×#107—111no—
283C2×#106—111no—
284C2×C4⋊C8—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103—111no—
288C2×#103—111no—
289C2×#102—111no—
290C2×#102—111no—
291C2×#102—111no—
292C2×#102—111no—
293C2×C4×C8—111no—
294#398—21no—
295#398—21no—
296#391—111no—
297#390—111no—
298#389—21no—
299#389C2×D1111yescharacteristic
300#389C2×D1111yescharacteristic
301#389C2×D1111yescharacteristic
302#389C2×D1111yescharacteristic
303#388—221no—
304#388—221no—
305#387—21no—
306#385—221no—
307#384C2×D1111yescharacteristic
308C4×C4⋊C4—111no—
309C4×C4⋊C4C2×D1111yescharacteristic
310C4×C4⋊C4C2×D1111yescharacteristic
311C4×C22⋊C4—221no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#336—111no—
319#336—111no—
320#336—111no—
321#336—111no—
322C22×C11#52511yescharacteristic
323C22×C11#54611yescharacteristic
324C22×C11#54811yescharacteristic
325C22×C11C2×#13511yescharacteristic
326C22×C11C2×#13711yescharacteristic
327C22×C11#57611yescharacteristic
328C22×C11#57711yescharacteristic
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—81no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11#52911yescharacteristic
347C4×C11#53911yescharacteristic
348C4×C11#55211yescharacteristic
349C4×C11#55311yescharacteristic
350Dic11—42no—
351Dic11—42no—
352Dic11—81no—
353C22×Q8—111no—
354C22×D4—111no—
355C23×C4—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—111no—
360#124—222no—
361#124—222no—
362C4×Q8—222no—
363C4×Q8—441no—
364C4×D4—222no—
365C4×D4—441no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22⋊D1111yescharacteristic
376C2×C4⋊C4C22⋊D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—21no—
387C2×C42—221no—
388C2×C42—221no—
389C2×C42C22×D1111yescharacteristic
390C2×C42C22×D1111yescharacteristic
391C2×C42C22×D1111yescharacteristic
392#107—222no—
393#106—222no—
394C4⋊C8—441no—
395#103—222no—
396#103—222no—
397#103—222no—
398#103—441no—
399#102—222no—
400#102—222no—
401#102—222no—
402#102—441no—
403C4×C8—441no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95C22⋊D1111yescharacteristic
413#95C22⋊D1111yescharacteristic
414C2×C11#246011yescharacteristic
415C2×C11#310711yescharacteristic
416C2×C11#311911yescharacteristic
417C2×C11#330111yescharacteristic
418C2×C11#331411yescharacteristic
419C2×C11#336111yescharacteristic
420C2×C11#336911yescharacteristic
421D11—82no—
422C24—221no—
423C2×Q8—112no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×D4—112no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—442no—
443C22×C4—442no—
444C22×C4—881no—
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C23×D1111yescharacteristic
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C4⋊C4—22no—
465C4⋊C4—22no—
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—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—112no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—442no—
484C4⋊C4#434312yes—
485C22⋊C4—224no—
486C22⋊C4—224no—
487C22⋊C4—442no—
488C22⋊C4—442no—
489C22⋊C4—881no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—81no—
497C42—442no—
498C42—881no—
499C11#2676311yescharacteristic, complemented, Sylow
500C23—222no—
501C23—441no—
502C23—441no—
503C23—441no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23C22×C22⋊D1111yescharacteristic
508Q8—222no—
509Q8—222no—
510Q8—441no—
511Q8—441no—
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—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
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—41no—
543C2×C4—41no—
544C2×C4—222no—
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#6699512yes—
555C2×C4#6700312yes—
556C2×C4C2×#434311yescharacteristic
557C2×C4#6704011yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C2×C4#41×D1111yescharacteristic
561C2×C4#6704211yescharacteristic
562C8—441no—
563C8—441no—
564C8—441no—
565C8—441no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—881no—
570C22—881no—
571C22—881no—
572C22—881no—
573C22C2×#6699511yescharacteristic
574C22#1062334811yescharacteristic
575C22C2×#6700311yescharacteristic
576C22#1062335911yescharacteristic
577C22#1062336011yescharacteristic
578C22#1062336611yescharacteristic
579C22#1062336711yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—442no—
591C4—442no—
592C4—881no—
593C4#1062322211yescharacteristic
594C4#1062322311yescharacteristic
595C4#1062322411yescharacteristic
596C4#1062322611yescharacteristic
597C2—882no—
598C2#1307256411yescharacteristic
599C2#1307868111yescharacteristic
600C2#1307880911yescharacteristic
601C2#1308051211yescharacteristic
602C2#1308069111yescharacteristic
603C2#1308127611yescharacteristic
604C2#1308135611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2507C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2507D11
hypocenterC11#26763
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2507

Complements

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

NH ≅ G/Ntype
6. #13069291C2semidirect
7. #13069257C2semidirect
8. #13069191C2semidirect
9. #13069184C2semidirect
10. #13069175C2semidirect
11. #13068883C2semidirect
13. #13068618C2semidirect
15. C11×#2507C2semidirect
198. #2507D11semidirect
499. C11#26763semidirect

Maximal subgroups

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

subgroupindex
#130716852
#130700202
#130700012
#130698572
#130692912
#130692572
#130691912
#130691842
#130691752
#130688832
#130688762
#130686182
C4×#668732
C11×#25072
#2676311