Finite Group Databasebeta

← #14822282

Subgroups — #14822282

Order 2816.

832 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073132C211yesmaximal, characteristic, complemented
2#13071680C211yesmaximal, characteristic
3#13070021C211yesmaximal, characteristic, complemented
4#13070003C211yesmaximal, characteristic, complemented
5#13069851C211yesmaximal, characteristic
6#13069851C211yesmaximal, characteristic
7#13069299C211yesmaximal, characteristic, complemented
8#13069237C211yesmaximal, characteristic, complemented
9#13069188C211yesmaximal, characteristic, complemented
10#13069188C211yesmaximal, characteristic, complemented
11#13068866C211yesmaximal, characteristic, complemented
12#13068866C211yesmaximal, characteristic, complemented
13#13068617C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C2×#66946—21no—
17C2×#66942—21no—
18C2×#66927C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34#10622601—21no—
35#10622596—21no—
36#10622552C2211yescharacteristic
37#10622552C2211yescharacteristic
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622278—21no—
46#10622278—21no—
47#10622272—21no—
48#10622266—21no—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94#66946—44no—
95#66942—44no—
96#66927—22no—
97#66927—22no—
98C4×D44—22no—
99C4×D44—22no—
100C4×D44—41no—
101C4×D44—41no—
102C11×C4⋊C8—41no—
103C4×C8×C11—41no—
104C11×#95D411yescharacteristic
105C11×#95D411yescharacteristic
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—22no—
116#66885—22no—
117#66885—22no—
118#66885—41no—
119#66885—41no—
120#66882—22no—
121#66882—22no—
122#26752—111nomaximal, Sylow
123C23×D11—21no—
124C23×D11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C2×D44—24no—
139C2×D44—24no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—42no—
151C2×D44—42no—
152C2×D44—81no—
153C2×D44—81no—
154C2×D44#4112yes—
155C2×D44#4112yes—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
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—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4D814yes—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—81no—
187(C2×D11)⋊C4—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11#4112yes—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208#2506—111no—
209#2366—111no—
210#2071—111no—
211#2067—111no—
212#2041—111no—
213#2041—111no—
214#1934—111no—
215#1925—111no—
216#1918—111no—
217#1918—111no—
218#1916D1111yescharacteristic, complemented
219#1862—111no—
220#1862—111no—
221#1802—111no—
222C4×#102—111no—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
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—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11C2×D812yes—
254C2×C4×C11C2×D812yes—
255C2×C4×C11C2×D812yes—
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×Dic11—22no—
263C2×Dic11—22no—
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—
280D44—22no—
281D44—22no—
282D44—22no—
283D44—22no—
284D44—48no—
285D44—41no—
286D44—41no—
287D44—41no—
288D44—41no—
289D44—84no—
290C4×D11—84no—
291C4×D11—84no—
292C8×C11—41no—
293C8×C11—41no—
294C8×C11—41no—
295C8×C11—41no—
296C2×#127—111no—
297C2×#125—221no—
298C2×C4×D4—111no—
299C2×C4×D4—111no—
300C2×C4×D4—221no—
301C2×#107—111no—
302C2×#107—111no—
303C2×C4⋊C8C2×D1111yescharacteristic
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×C4×C8C2×D1111yescharacteristic
313#400—221no—
314#398—221no—
315#390—111no—
316#390—111no—
317#390—221no—
318#389—111no—
319#389—111no—
320#389—111no—
321#389—111no—
322#387—221no—
323#386—221no—
324#386—221no—
325#384—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4C2×D1111yescharacteristic
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#336C2×D1111yescharacteristic
336#336C2×D1111yescharacteristic
337#336C2×D1111yescharacteristic
338#336C2×D1111yescharacteristic
339C22×C11#52511yescharacteristic
340C22×C11#54611yescharacteristic
341C22×C11#54811yescharacteristic
342C22×C11C22×D811yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57711yescharacteristic
345C22×C11#57711yescharacteristic
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—22no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11#52911yescharacteristic
367C4×C11#53911yescharacteristic
368C4×C11#55211yescharacteristic
369C4×C11#55311yescharacteristic
370Dic11—42no—
371Dic11—42no—
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375Dic11—81no—
376C22×D4—111no—
377C22×D4—111no—
378C22×D4—221no—
379C22×D4—221no—
380C23×C4—221no—
381C23×C4—221no—
382C22×C8C22×D1111yescharacteristic
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386#127—222no—
387#127—222no—
388#125—444no—
389C4×D4—222no—
390C4×D4—222no—
391C4×D4—441no—
392C4×D4—441no—
393C4×D4—444no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4D4411yescharacteristic
407C2×C4⋊C4D4411yescharacteristic
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419#107—222no—
420#107—222no—
421C4⋊C8—41no—
422#102—222no—
423#102—222no—
424#102—222no—
425#102—222no—
426#102—222no—
427#102—222no—
428#102—441no—
429#102—441no—
430C4×C8—41no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95D4411yescharacteristic
438#95D4411yescharacteristic
439C2×C11#246011yescharacteristic
440C2×C11#310011yescharacteristic
441C2×C11#312311yescharacteristic
442C2×C11#329411yescharacteristic
443C2×C11#331711yescharacteristic
444C2×C11#335811yescharacteristic
445C2×C11#337111yescharacteristic
446D11—82no—
447D11—82no—
448C24—221no—
449C24—221no—
450C2×D4—112no—
451C2×D4—112no—
452C2×D4—224no—
453C2×D4—224no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—442no—
465C2×D4—442no—
466C2×D4—881no—
467C2×D4—881no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—881no—
479C22×C4—881no—
480C22×C4C2×D4411yescharacteristic
481C22×C4C2×D4411yescharacteristic
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×D4411yescharacteristic
485C22×C4C2×D4411yescharacteristic
486C22×C4C23×D1111yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C4⋊C4—41no—
500C4⋊C4—112no—
501C4⋊C4—112no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4D8814yes—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—442no—
532C42—442no—
533C11#2675211yescharacteristic, complemented, Sylow
534C23—222no—
535C23—222no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23C22×D4411yescharacteristic
549D4—222no—
550D4—222no—
551D4—222no—
552D4—222no—
553D4—448no—
554D4—441no—
555D4—441no—
556D4—441no—
557D4—441no—
558D4—884no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—222no—
575C2×C4—222no—
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—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—884no—
593C2×C4—884no—
594C2×C4C2×D8812yes—
595C2×C4C2×D8812yes—
596C2×C4C2×D8812yes—
597C2×C4#6703711yescharacteristic
598C2×C4#6704011yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#41×D1111yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C8—41no—
604C8—41no—
605C8—41no—
606C8—41no—
607C22—442no—
608C22—442no—
609C22—442no—
610C22—442no—
611C22—442no—
612C22—442no—
613C22—881no—
614C22—881no—
615C22—881no—
616C22—881no—
617C22—881no—
618C22—881no—
619C22—881no—
620C22—881no—
621C22#1062305511yescharacteristic
622C22#1062308511yescharacteristic
623C22#1062310711yescharacteristic
624C22C22×D8811yescharacteristic
625C22#1062327911yescharacteristic
626C22#1062328211yescharacteristic
627C22#1062328211yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—442no—
635C4—442no—
636C4—881no—
637C4—881no—
638C4—881no—
639C4—881no—
640C4#1062316911yescharacteristic
641C4#1062319211yescharacteristic
642C4#1062322411yescharacteristic
643C4#1062323711yescharacteristic
644C2—882no—
645C2—882no—
646C2#1307256611yescharacteristic
647C2#1307861711yescharacteristic
648C2#1307886911yescharacteristic
649C2#1308043011yescharacteristic
650C2#1308074411yescharacteristic
651C2#1308125211yescharacteristic
652C2#1308138611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1916D11
hypocenterC11#26752
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. #13073132C2semidirect
3. #13070021C2semidirect
4. #13070003C2semidirect
7. #13069299C2semidirect
8. #13069237C2semidirect
9. #13069188C2semidirect
10. #13069188C2semidirect
11. #13068866C2semidirect
12. #13068866C2semidirect
13. #13068617C2semidirect
14. C4×#66885C2semidirect
15. C11×#1916C2semidirect
218. #1916D11semidirect
533. C11#26752semidirect

Maximal subgroups

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

subgroupindex
#130731322
#130716802
#130700212
#130700032
#130698512
#130692992
#130692372
#130691882
#130688662
#130686172
C4×#668852
C11×#19162
#2675211