Finite Group Databasebeta

← #14826593

Subgroups — #14826593

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073049C211yesmaximal, characteristic, complemented
2#13071652C211yesmaximal, characteristic
3#13070021C211yesmaximal, characteristic, complemented
4#13070003C211yesmaximal, characteristic, complemented
5#13069799C211yesmaximal, characteristic
6#13069799C211yesmaximal, characteristic
7#13069375C211yesmaximal, characteristic, complemented
8#13069349C211yesmaximal, characteristic, complemented
9#13069209C211yesmaximal, characteristic, complemented
10#13069195C211yesmaximal, characteristic, complemented
11#13068880C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic, complemented
13#13068712C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1923C211yesmaximal, characteristic, complemented
16C2×#66983C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24#10622825C2211yescharacteristic
25#10622825C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34#10622570—21no—
35#10622569—21no—
36#10622564—21no—
37#10622561—21no—
38#10622552C2211yescharacteristic
39#10622548C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622282—21no—
46#10622279—21no—
47#10622273—21no—
48#10622268—21no—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C22⋊C4D411yescharacteristic
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74#66983—22no—
75#66983—22no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80#66979—22no—
81#66979—41no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C4×D44—22no—
98C4×D44—41no—
99C11×C4⋊C8—22no—
100C11×C22⋊C8—22no—
101C11×C22⋊C8—41no—
102C4×C8×C11—41no—
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112#66885—22no—
113#66885—22no—
114#66885—22no—
115#66885—41no—
116#66882—22no—
117#66882—22no—
118#66882—41no—
119#66881—22no—
120#27041—111nomaximal, Sylow
121C24×C11C2×D411yescharacteristic
122C23×D11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—24no—
136C2×C22⋊D11—81no—
137C2×C22⋊D11—81no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44#4112yes—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—81no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11#4112yes—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C22⋊Dic11—42no—
173C22⋊Dic11—81no—
174C22⋊Dic11—81no—
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—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—81no—
192C4⋊Dic11—81no—
193C4⋊Dic11#4112yes—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—42no—
196Dic11⋊C4—81no—
197Dic11⋊C4—81no—
198C4×Dic11—42no—
199C4×Dic11—81no—
200C4×Dic11—81no—
201#2497—111no—
202#2363—111no—
203#2071—111no—
204#2067—111no—
205#2033—111no—
206#2033—111no—
207#1947—111no—
208#1942—111no—
209#1923D1111yescharacteristic, complemented
210#1921—111no—
211#1919—111no—
212#1864—111no—
213#1854—111no—
214#1825—111no—
215C4×#102—111no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
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—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11#13512yes—
249C2×C4×C11#13712yes—
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C22⋊D11—84no—
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—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278D44—22no—
279D44—22no—
280D44—41no—
281D44—41no—
282C4×D11—84no—
283C8×C11—22no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11—41no—
287C2×#121—111no—
288C2×C4×D4—111no—
289C2×#117—111no—
290C2×#107—111no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#106—111no—
294C2×C4⋊C8C2×D1111yescharacteristic
295C2×#102—111no—
296C2×#102—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×C22⋊C8C2×D1111yescharacteristic
300C2×C22⋊C8C2×D1111yescharacteristic
301C2×C4×C8C2×D1111yescharacteristic
302#400—221no—
303#396—221no—
304#390—111no—
305#390—221no—
306#389—111no—
307#389—111no—
308#389—111no—
309#388—221no—
310#388—221no—
311#387—221no—
312#386—221no—
313#384—111no—
314#380—111no—
315#380—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C22⋊C4—221no—
319C4×C22⋊C4C2×D1111yescharacteristic
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#336C2×D1111yescharacteristic
329#336C2×D1111yescharacteristic
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11#52511yescharacteristic
338C22×C11#54611yescharacteristic
339C22×C11#54711yescharacteristic
340C22×C11C2×#13511yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11#57611yescharacteristic
343C22×C11#57611yescharacteristic
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11#52911yescharacteristic
357C4×C11#53911yescharacteristic
358C4×C11#55311yescharacteristic
359C4×C11#55611yescharacteristic
360Dic11—42no—
361Dic11—42no—
362Dic11—81no—
363Dic11—81no—
364Dic11—81no—
365Dic11—81no—
366Dic11—81no—
367C22×D4—111no—
368C22×D4—221no—
369C23×C4—221no—
370C23×C4C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375#121—222no—
376#121—222no—
377C4×D4—222no—
378C4×D4—441no—
379#117—222no—
380#117—441no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4D4411yescharacteristic
401C2×C22⋊C4D4411yescharacteristic
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406C2×C42C22×D1111yescharacteristic
407#107—222no—
408#107—222no—
409#107—441no—
410#106—222no—
411C4⋊C8—22no—
412#102—222no—
413#102—222no—
414#102—222no—
415#102—441no—
416C22⋊C8—22no—
417C22⋊C8—41no—
418C4×C8—41no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95D4411yescharacteristic
427#95D4411yescharacteristic
428C2×C11—81no—
429C2×C11#246611yescharacteristic
430C2×C11#310711yescharacteristic
431C2×C11#312211yescharacteristic
432C2×C11#330511yescharacteristic
433C2×C11#331411yescharacteristic
434C2×C11#333911yescharacteristic
435C2×C11#335711yescharacteristic
436D11—82no—
437C24—221no—
438C24C2×D4411yescharacteristic
439C2×D4—112no—
440C2×D4—224no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—881no—
447C2×D4—881no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4—881no—
464C22×C4C2×D4411yescharacteristic
465C22×C4C2×D4411yescharacteristic
466C22×C4C2×D4411yescharacteristic
467C22×C4C2×D4411yescharacteristic
468C22×C4C2×D4411yescharacteristic
469C22×C4C23×D1111yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8#434112yes—
482C4⋊C4—112no—
483C4⋊C4—112no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—442no—
497C4⋊C4—881no—
498C4⋊C4—881no—
499C4⋊C4—881no—
500C4⋊C4—881no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—224no—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C22⋊C4—442no—
507C22⋊C4—881no—
508C22⋊C4—881no—
509C22⋊C4—881no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—442no—
515C42—881no—
516C42—881no—
517C11#2704111yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—222no—
526C23—441no—
527C23—441no—
528C23—441no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23C22×D4411yescharacteristic
533D4—222no—
534D4—222no—
535D4—441no—
536D4—441no—
537D4—884no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—884no—
577C2×C4#6695712yes—
578C2×C4#6696212yes—
579C2×C4C2×#434111yescharacteristic
580C2×C4#6703711yescharacteristic
581C2×C4#41×D1111yescharacteristic
582C2×C4#41×D1111yescharacteristic
583C2×C4#41×D1111yescharacteristic
584C2×C4#6704311yescharacteristic
585C8—22no—
586C8—41no—
587C8—41no—
588C8—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—442no—
597C22—442no—
598C22—442no—
599C22—881no—
600C22—881no—
601C22—881no—
602C22—881no—
603C22#1062305511yescharacteristic
604C22#1062308511yescharacteristic
605C22#1062308611yescharacteristic
606C22C2×#6695711yescharacteristic
607C22C2×#6696211yescharacteristic
608C22#1062328311yescharacteristic
609C22#1062328311yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—442no—
616C4—442no—
617C4—881no—
618C4—881no—
619C4—881no—
620C4—881no—
621C4—881no—
622C4#1062313211yescharacteristic
623C4#1062319111yescharacteristic
624C4#1062321111yescharacteristic
625C4#1062323311yescharacteristic
626C2—81no—
627C2—882no—
628C2#1307265011yescharacteristic
629C2#1307868811yescharacteristic
630C2#1307886011yescharacteristic
631C2#1308056711yescharacteristic
632C2#1308069911yescharacteristic
633C2#1308101911yescharacteristic
634C2#1308124311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1923C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1923D11
hypocenterC11#27041
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. #13073049C2semidirect
3. #13070021C2semidirect
4. #13070003C2semidirect
7. #13069375C2semidirect
8. #13069349C2semidirect
9. #13069209C2semidirect
10. #13069195C2semidirect
11. #13068880C2semidirect
12. #13068817C2semidirect
13. #13068712C2semidirect
14. C4×#66885C2semidirect
15. C11×#1923C2semidirect
209. #1923D11semidirect
517. C11#27041semidirect

Maximal subgroups

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

subgroupindex
#130730492
#130716522
#130700212
#130700032
#130697992
#130693752
#130693492
#130692092
#130691952
#130688802
#130688172
#130687122
C4×#668852
C11×#19232
#2704111