Finite Group Databasebeta

← #14816707

Subgroups — #14816707

Order 2816.

804 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622442C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic
3#13072340C211yesmaximal, characteristic
4#13071641C211yesmaximal, characteristic
5#13070163C211yesmaximal, characteristic, complemented
6#13070109C211yesmaximal, characteristic, complemented
7#13070010C211yesmaximal, characteristic, complemented
8#13069955C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069195C211yesmaximal, characteristic, complemented
11#13069049C211yesmaximal, characteristic
12#13068921C211yesmaximal, characteristic
13#13068887C211yesmaximal, characteristic, complemented
14#13068817C211yesmaximal, characteristic
15C11×#1851C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622734—24no—
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38#10622559—21no—
39#10622558—21no—
40#10622557—21no—
41#10622555—21no—
42#10622549C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622442—24no—
49#10622273—21no—
50#10622270—21no—
51#10622265—21no—
52#10622262—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22C2311yescharacteristic
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78#66979—22no—
79#66979—41no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—41no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90#66977—22no—
91#66977Q814yes—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102#66923—22no—
103#66923—41no—
104C4×Dic22—22no—
105C4×Dic22—41no—
106C11×C4⋊C8—22no—
107C11×C4⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66882—22no—
121#66882—22no—
122#66882—22no—
123#66881—22no—
124#66881—41no—
125#66881D414yes—
126#66880—22no—
127#66880—22no—
128#66880—22no—
129#66880—41no—
130#26367—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×Q812yes—
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—81no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C2×Q812yes—
161C11×M16—28no—
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×C11C2×D412yes—
173C2×C8×C11#4112yes—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C22⋊Dic11—24no—
181C22⋊Dic11—42no—
182C22⋊Dic11—42no—
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—42no—
195C4⋊Dic11C2×D412yes—
196C4⋊Dic11C2×D412yes—
197C4⋊Dic11C2×Q812yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—81no—
204Dic11⋊C4—81no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C2×#479—111no—
209C2×#428—111no—
210#2442—111no—
211#2362—111no—
212#2097—111no—
213#2087—111no—
214#2068—111no—
215#2059—111no—
216#1949—111no—
217#1919—111no—
218#1894—111no—
219#1872—111no—
220#1865—111no—
221#1854—111no—
222#1851D1111yescharacteristic
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C22⋊Q812yes—
230C23×C11C22×D411yescharacteristic
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
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—21no—
249C2×C4×C11C22⋊Q812yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×Q811yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
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—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—84no—
281Dic22—22no—
282Dic22—22no—
283Dic22—41no—
284Dic22—41no—
285C8×C11—22no—
286C8×C11—22no—
287C8×C11—41no—
288C8×C11—41no—
289C22×M16C2×D1111yescharacteristic
290C2×#125—111no—
291C2×C22⋊Q8—111no—
292C2×C4×Q8—111no—
293C2×#117—111no—
294C22×C4⋊C4—111no—
295#479—224no—
296#428—224no—
297C2×#107—111no—
298C2×#107—111no—
299C2×#107—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×C4⋊C8C2×D1111yescharacteristic
304C2×C4⋊C8C2×D1111yescharacteristic
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×C22⋊C8C2×D1111yescharacteristic
310#400—221no—
311#398—221no—
312#391—111no—
313#389—111no—
314#389—111no—
315#389—111no—
316#388—221no—
317#388—221no—
318#387—221no—
319#385—221no—
320#382—111no—
321#380—111no—
322#380—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—221no—
325C4×C22⋊C4C2×D1111yescharacteristic
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#336C2×D1111yescharacteristic
333#336C2×D1111yescharacteristic
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×C22⋊Q811yescharacteristic
342C22×C11D4211yescharacteristic
343C22×C11#54711yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57711yescharacteristic
347C22×C11#57811yescharacteristic
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11#52511yescharacteristic
354C4×C11#53911yescharacteristic
355C4×C11D4×Q811yescharacteristic
356C4×C11#55411yescharacteristic
357Dic11—42no—
358Dic11—42no—
359Dic11—42no—
360Dic11—42no—
361Dic11—81no—
362Dic11—81no—
363Dic11—81no—
364Dic11—81no—
365C22×Q8—111no—
366C23×C4—221no—
367C23×C4C22×D1111yescharacteristic
368C2×M16—22no—
369C2×M16—22no—
370C2×M16—22no—
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375#125—222no—
376#125—441no—
377C22⋊Q8—114no—
378C22⋊Q8—222no—
379C4×Q8—222no—
380C4×Q8—441no—
381#117—222no—
382#117—441no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—441no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4D4411yescharacteristic
404C2×C22⋊C4D4411yescharacteristic
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410#107—222no—
411#107—222no—
412#107—222no—
413#106—114no—
414#106—222no—
415#106—441no—
416C4⋊C8—22no—
417C4⋊C8—22no—
418#103—222no—
419#103—222no—
420#103—222no—
421#103—441no—
422C22⋊C8—22no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95D4411yescharacteristic
433#95D4411yescharacteristic
434C2×C11—42no—
435C2×C11#244911yescharacteristic
436C2×C11#308011yescharacteristic
437C2×C11#308211yescharacteristic
438C2×C11#326911yescharacteristic
439C2×C11#327511yescharacteristic
440C2×C11#334911yescharacteristic
441C2×C11#335111yescharacteristic
442C24C2×D4411yescharacteristic
443C2×Q8—112no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—221no—
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×C4#434112yes—
470C22×C4Q8×D1112yes—
471C22×C4C23×D1111yescharacteristic
472M16—28no—
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—21no—
482C2×C8—21no—
483C2×C8D4×D1112yes—
484C2×C8#434112yes—
485C4⋊C4—112no—
486C4⋊C4—112no—
487C4⋊C4—112no—
488C4⋊C4—224no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—881no—
506C4⋊C4—881no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—224no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—442no—
517C42—442no—
518C42—442no—
519C11#2636711yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23#6695012yes—
527C23C22×D4411yescharacteristic
528Q8—222no—
529Q8—222no—
530Q8—441no—
531Q8—441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
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—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
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—884no—
575C2×C4#6695012yes—
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4C2×#434111yescharacteristic
578C2×C4C2×#434111yescharacteristic
579C2×C4C2×Q8×D1111yescharacteristic
580C2×C4#6704211yescharacteristic
581C2×C4#6704311yescharacteristic
582C8—22no—
583C8—22no—
584C8—41no—
585C8—41no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#6695011yescharacteristic
594C22D4×D4411yescharacteristic
595C22#1062308611yescharacteristic
596C22#1062327911yescharacteristic
597C22#1062327911yescharacteristic
598C22#1062328211yescharacteristic
599C22#1062328411yescharacteristic
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—442no—
606C4—442no—
607C4—442no—
608C4—442no—
609C4—881no—
610C4—881no—
611C4—881no—
612C4—881no—
613C4#1062311711yescharacteristic
614C4#1062316311yescharacteristic
615C4#1062316611yescharacteristic
616C4#1062319611yescharacteristic
617C2—42no—
618C2#1307242311yescharacteristic
619C2#1307843911yescharacteristic
620C2#1307845911yescharacteristic
621C2#1308017611yescharacteristic
622C2#1308025211yescharacteristic
623C2#1308114811yescharacteristic
624C2#1308117811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1851C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1851D11
hypocenterC11#26367
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#10622442C2semidirect
5. #13070163C2semidirect
6. #13070109C2semidirect
7. #13070010C2semidirect
8. #13069955C2semidirect
9. #13069386C2semidirect
10. #13069195C2semidirect
13. #13068887C2semidirect
519. C11#26367semidirect

Maximal subgroups

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

subgroupindex
C2×#106224422
C2×#106227342
#130723402
#130716412
#130701632
#130701092
#130700102
#130699552
#130693862
#130691952
#130690492
#130689212
#130688872
#130688172
C11×#18512
#2636711