Finite Group Databasebeta

← #14826428

Subgroups — #14826428

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073038C211yesmaximal, characteristic, complemented
2#13071630C211yesmaximal, characteristic
3#13070021C211yesmaximal, characteristic, complemented
4#13070003C211yesmaximal, characteristic, complemented
5#13069799C211yesmaximal, characteristic
6#13069799C211yesmaximal, characteristic
7#13069375C211yesmaximal, characteristic, complemented
8#13069349C211yesmaximal, characteristic, complemented
9#13069188C211yesmaximal, characteristic, complemented
10#13069188C211yesmaximal, characteristic, complemented
11#13068866C211yesmaximal, characteristic, complemented
12#13068806C211yesmaximal, characteristic, complemented
13#13068703C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1923C211yesmaximal, characteristic, complemented
16C2×#66983C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C2×(C22⋊D11)⋊C4—21no—
19C2×#66932—21no—
20C2×C4×D44C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36#10622571—21no—
37#10622566—21no—
38#10622552C2211yescharacteristic
39#10622548C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622283—21no—
46#10622281—21no—
47#10622272—21no—
48#10622266—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—
61C23×Dic11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
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—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—41no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97(C22⋊D11)⋊C4—44no—
98#66932—44no—
99C4×D44—22no—
100C4×D44—41no—
101C11×C4⋊C8—22no—
102C11×C22⋊C8—22no—
103C11×C22⋊C8—41no—
104C4×C8×C11—41no—
105C11×#95D411yescharacteristic
106C11×#95D411yescharacteristic
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114#66885—22no—
115#66885—22no—
116#66885—22no—
117#66885—41no—
118#66882—22no—
119#66882—22no—
120#66882—22no—
121#66882—41no—
122#27030—111nomaximal, Sylow
123C24×C11C2×D411yescharacteristic
124C23×D11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—24no—
138C2×C22⋊D11—42no—
139C2×C22⋊D11—42no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—81no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44#4112yes—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—81no—
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—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11#4112yes—
171C11×C22⋊C4—41no—
172C11×C22⋊C4D814yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C22⋊Dic11—42no—
178C22⋊Dic11—42no—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—81no—
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—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11#4112yes—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205#2496—111no—
206#2361—111no—
207#2071—111no—
208#2067—111no—
209#2033—111no—
210#2033—111no—
211#1947—111no—
212#1942—111no—
213#1923D1111yescharacteristic, complemented
214#1918—111no—
215#1918—111no—
216#1862—111no—
217#1852—111no—
218#1823—111no—
219C4×#102—111no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11C2×D812yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—22no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
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—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11C2×D812yes—
253C2×C4×C11C2×D812yes—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C22⋊D11—48no—
261C2×Dic11—22no—
262C2×Dic11—22no—
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—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—84no—
283D44—22no—
284D44—22no—
285D44—41no—
286D44—41no—
287C4×D11—84no—
288C8×C11—22no—
289C8×C11—41no—
290C8×C11—41no—
291C8×C11—41no—
292C2×#126—221no—
293C2×#121—111no—
294C2×C4×D4—111no—
295C2×C4×D4—221no—
296C22×C4⋊C4—111no—
297C2×#107—111no—
298C2×#107—111no—
299C2×#107—111no—
300C2×#107—111no—
301C2×C4⋊C8C2×D1111yescharacteristic
302C2×#102—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×C22⋊C8C2×D1111yescharacteristic
307C2×C22⋊C8C2×D1111yescharacteristic
308C2×C4×C8C2×D1111yescharacteristic
309#400—221no—
310#397—221no—
311#390—111no—
312#389—111no—
313#389—111no—
314#389—111no—
315#388—221no—
316#387—221no—
317#386—221no—
318#385—221no—
319#384—111no—
320#380—111no—
321#380—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C22⋊C4C2×D1111yescharacteristic
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#336C2×D1111yescharacteristic
334#336C2×D1111yescharacteristic
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11#52511yescharacteristic
343C22×C11#54611yescharacteristic
344C22×C11#54711yescharacteristic
345C22×C11C22×D811yescharacteristic
346C22×C11#57511yescharacteristic
347C22×C11#57711yescharacteristic
348C22×C11#57811yescharacteristic
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11#52911yescharacteristic
362C4×C11#53911yescharacteristic
363C4×C11#55311yescharacteristic
364C4×C11#55611yescharacteristic
365Dic11—42no—
366Dic11—42no—
367Dic11—81no—
368Dic11—81no—
369Dic11—81no—
370Dic11—81no—
371Dic11—81no—
372C22×D4—111no—
373C22×D4—221no—
374C23×C4—221no—
375C23×C4—221no—
376C23×C4C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381#126—444no—
382#121—222no—
383#121—222no—
384C4×D4—222no—
385C4×D4—441no—
386C4×D4—444no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—441no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4D4411yescharacteristic
409C2×C22⋊C4D4411yescharacteristic
410C2×C42—221no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1111yescharacteristic
414#107—222no—
415#107—222no—
416#107—222no—
417#107—441no—
418C4⋊C8—22no—
419#102—222no—
420#102—222no—
421#102—222no—
422#102—441no—
423C22⋊C8—22no—
424C22⋊C8—41no—
425C4×C8—41no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95D4411yescharacteristic
434#95D4411yescharacteristic
435C2×C11—42no—
436C2×C11#246611yescharacteristic
437C2×C11#310011yescharacteristic
438C2×C11#312011yescharacteristic
439C2×C11#329411yescharacteristic
440C2×C11#331311yescharacteristic
441C2×C11#333411yescharacteristic
442C2×C11#335111yescharacteristic
443D11—82no—
444C24—221no—
445C24C2×D4411yescharacteristic
446C2×D4—112no—
447C2×D4—224no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—442no—
454C2×D4—442no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—881no—
473C22×C4—881no—
474C22×C4C2×D4411yescharacteristic
475C22×C4C2×D4411yescharacteristic
476C22×C4C2×D4411yescharacteristic
477C22×C4C2×D4411yescharacteristic
478C22×C4C2×D4411yescharacteristic
479C22×C4C23×D1111yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8#434112yes—
492C4⋊C4—112no—
493C4⋊C4—112no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C22⋊C4—41no—
513C22⋊C4—224no—
514C22⋊C4—442no—
515C22⋊C4—442no—
516C22⋊C4—442no—
517C22⋊C4—442no—
518C22⋊C4—881no—
519C22⋊C4D8814yes—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—442no—
525C42—442no—
526C11#2703011yescharacteristic, complemented, Sylow
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—222no—
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23C2×D8812yes—
541C23C22×D4411yescharacteristic
542D4—222no—
543D4—222no—
544D4—448no—
545D4—441no—
546D4—441no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—222no—
565C2×C4—222no—
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—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—884no—
586C2×C4—884no—
587C2×C4C2×D8812yes—
588C2×C4C2×D8812yes—
589C2×C4C2×#434111yescharacteristic
590C2×C4#6703711yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#6704311yescharacteristic
595C8—22no—
596C8—41no—
597C8—41no—
598C8—41no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—442no—
607C22—442no—
608C22—442no—
609C22—881no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22#1062305511yescharacteristic
614C22#1062308511yescharacteristic
615C22#1062308611yescharacteristic
616C22C22×D8811yescharacteristic
617C22#1062327911yescharacteristic
618C22#1062328211yescharacteristic
619C22#1062328411yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—442no—
626C4—442no—
627C4—881no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4—881no—
632C4#1062313211yescharacteristic
633C4#1062319111yescharacteristic
634C4#1062321111yescharacteristic
635C4#1062323311yescharacteristic
636C2—42no—
637C2—882no—
638C2#1307265011yescharacteristic
639C2#1307861711yescharacteristic
640C2#1307883211yescharacteristic
641C2#1308043011yescharacteristic
642C2#1308068411yescharacteristic
643C2#1308096411yescharacteristic
644C2#1308117811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1923C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1923D11
hypocenterC11#27030
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. #13073038C2semidirect
3. #13070021C2semidirect
4. #13070003C2semidirect
7. #13069375C2semidirect
8. #13069349C2semidirect
9. #13069188C2semidirect
10. #13069188C2semidirect
11. #13068866C2semidirect
12. #13068806C2semidirect
13. #13068703C2semidirect
14. C4×#66885C2semidirect
15. C11×#1923C2semidirect
213. #1923D11semidirect
526. C11#27030semidirect

Maximal subgroups

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

subgroupindex
#130730382
#130716302
#130700212
#130700032
#130697992
#130693752
#130693492
#130691882
#130688662
#130688062
#130687032
C4×#668852
C11×#19232
#2703011