Finite Group Databasebeta

← #14788085

Subgroups — #14788085

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C2×#10622696C211yesmaximal, characteristic, complemented
3C4×#66983C211yesmaximal, characteristic
4#13069809C212yesmaximal, complemented
5#13069617C212yesmaximal
6#13069565C211yesmaximal, characteristic, complemented
7#13069540C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal, complemented
9#13068884C212yesmaximal, complemented
10#13068596C211yesmaximal, characteristic, complemented
11C2×C11×#533C211yesmaximal, characteristic, complemented
12C11×#533—24no—
13C11×#533—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C11×#117—21no—
22C22×C42×C11C2211yescharacteristic
23C22×#4325C2212yes—
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C2×C4×D44C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30#10622826—21no—
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622697—24no—
34#10622696—24no—
35C2×#66873C2212yes—
36C2×#66872C2212yes—
37#10622553—21no—
38#10622552C2211yescharacteristic
39C4×(C2×D11)⋊C4—21no—
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2312yes—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—21no—
53C22×D44C2311yescharacteristic
54C22×C4×D11—21no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8D414yescomplemented
58C11×C4⋊Q8D414yescomplemented
59C11×#125—28no—
60C11×C22⋊Q8—28no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—24no—
63C4×Q8×C11—28no—
64C4×Q8×C11—24no—
65C4×Q8×C11—24no—
66C11×#117—28no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11—22no—
75C2×C42×C11—22no—
76C2×C42×C11—22no—
77C2×C42×C11D411yescharacteristic
78C2×C42×C11D411yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×#4325—24no—
83C2×#4325—24no—
84C2×#4325—42no—
85#66983—22no—
86#66983—22no—
87C4×C22⋊D11—44no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2312yes—
98C22×C11⋊C8C2312yes—
99C4×D44—22no—
100C4×D44—22no—
101#66899—24no—
102#66899—24no—
103#66899—42no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C22⋊(C11⋊C8)—42no—
108#66873—24no—
109#66872—24no—
110C4⋊(C11⋊C8)—22no—
111C4⋊(C11⋊C8)—22no—
112#24151—111nomaximal, Sylow
113C24×C11C2×D411yescharacteristic
114C23×D11—21no—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C2×Q8×C11C2×D414yes—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—41no—
136C22×C4×C11—41no—
137C22×C4×C11SD1614yescomplemented
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—42no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
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—42no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4C2×D414yes—
166C11×C22⋊C4—28no—
167C42×C11—28no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11C2×D412yes—
173C42×C11C2×D412yes—
174C22⋊Dic11—42no—
175#4325—48no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—42no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11#4112yes—
186Dic11⋊C4—42no—
187C4×Dic11—42no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×#533D1111yescharacteristic, complemented
195C2×#476—111no—
196C2×#461—111no—
197C4×#121—111no—
198#2035—112no—
199#2000—112no—
200#1987—111no—
201#1981—111no—
202#1880—112no—
203#1865—112no—
204#1797—111no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11C2×SD1612yes—
212C23×C11C22×D411yescharacteristic
213C22×D11—22no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220Q8×C11—24no—
221Q8×C11—24no—
222Q8×C11—48no—
223Q8×C11—42no—
224Q8×C11—42no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—28no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11#12012yes—
248C2×C4×C11#12012yes—
249C2×C4×C11C2×SD1612yes—
250C2×C4×C11C2×SD1612yes—
251C2×C4×C11#13712yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C22⋊D11—48no—
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—
268D44—22no—
269D44—22no—
270D44—41no—
271D44—41no—
272C4×D11—84no—
273C11⋊C8—42no—
274C11⋊C8—42no—
275C22×SD16—112no—
276#533—24no—
277#533—24no—
278C2×C4⋊Q8C2×D1111yescharacteristic
279C2×C4⋊Q8C2×D1111yescharacteristic
280C2×#125—21no—
281C2×C22⋊Q8—21no—
282C2×C22⋊Q8C2×D1112yes—
283C2×#121—111no—
284C2×C4×Q8—21no—
285C2×C4×Q8C2×D1112yes—
286C2×C4×D4—111no—
287C2×C4×D4—221no—
288C2×#117—21no—
289C22×C42C2×D1111yescharacteristic
290#476—224no—
291#461—224no—
292C2×#106—112no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#103—112no—
298C2×#102—112no—
299C2×C22⋊C8—112no—
300#390—111no—
301#389—111no—
302#388—221no—
303#386—221no—
304#380—111no—
305C4×C4⋊C4—111no—
306C4×C22⋊C4—221no—
307#340—112no—
308#340—112no—
309#336—112no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11C2×#12011yescharacteristic
318C22×C11#52511yescharacteristic
319C22×C11#53711yescharacteristic
320C22×C11C22×SD1611yescharacteristic
321C22×C11C2×#13711yescharacteristic
322C22×C11#57511yescharacteristic
323C22×C11#57511yescharacteristic
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—41no—
334C4×C11—44no—
335C4×C11—41no—
336C4×C11—44no—
337C4×C11#44814yes—
338C4×C11#54611yescharacteristic
339C4×C11#54711yescharacteristic
340C4×C11#54811yescharacteristic
341C4×C11#55011yescharacteristic
342Dic11—42no—
343Dic11—81no—
344Dic11—81no—
345C22×Q8—21no—
346C22×Q8C22×D1112yes—
347C22×D4—111no—
348C22×D4—221no—
349C23×C4—221no—
350C23×C4C22⋊D1111yescharacteristic
351C23×C4C22⋊D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C2×SD16—224no—
354C2×SD16—224no—
355C2×SD16—442no—
356C22×C8—112no—
357C22×C8—112no—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360C4⋊Q8C22⋊D1114yescomplemented
361C4⋊Q8C22⋊D1114yescomplemented
362#125—28no—
363C22⋊Q8—28no—
364C22⋊Q8—24no—
365C22⋊Q8—24no—
366#121—222no—
367#121—222no—
368C4×Q8—28no—
369C4×Q8—24no—
370C4×Q8—24no—
371C4×D4—222no—
372C4×D4—222no—
373C4×D4—444no—
374#117—28no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4C22×D1112yes—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—221no—
395C2×C42C22⋊D1111yescharacteristic
396C2×C42C22⋊D1111yescharacteristic
397C2×C42C22×D1111yescharacteristic
398C2×C42C22×D1111yescharacteristic
399#106—224no—
400C4⋊C8—222no—
401C4⋊C8—222no—
402#103—224no—
403#103—224no—
404#103—442no—
405#102—224no—
406C22⋊C8—442no—
407#95—221no—
408#95—221no—
409#95—221no—
410C2×C11—42no—
411C2×C11#240711yescharacteristic
412C2×C11C2×#44811yescharacteristic
413C2×C11#300511yescharacteristic
414C2×C11#310111yescharacteristic
415C2×C11#311611yescharacteristic
416C2×C11#324611yescharacteristic
417C2×C11#325211yescharacteristic
418D11—82no—
419C24—221no—
420C24C2×C22⋊D1111yescharacteristic
421C2×Q8—24no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8C2×C22⋊D1114yes—
430C2×D4—112no—
431C2×D4—224no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—442no—
438C2×D4—442no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—442no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4#432514yescomplemented
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465SD16—448no—
466C2×C8—222no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—222no—
471C2×C8—222no—
472C4⋊C4—28no—
473C4⋊C4—28no—
474C4⋊C4—24no—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—22no—
478C4⋊C4—112no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—442no—
485C4⋊C4C2×C22⋊D1114yes—
486C22⋊C4—28no—
487C22⋊C4—224no—
488C22⋊C4—442no—
489C22⋊C4—442no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C42—28no—
493C42—22no—
494C42—22no—
495C42—21no—
496C42—21no—
497C42—442no—
498C42C2×C22⋊D1112yes—
499C42C2×C22⋊D1112yes—
500C11#2415111yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—222no—
508C23—441no—
509C23—441no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23—441no—
514C23C2×#432512yes—
515C23C22×C22⋊D1111yescharacteristic
516Q8—24no—
517Q8—24no—
518Q8—48no—
519Q8—42no—
520Q8—42no—
521D4—222no—
522D4—222no—
523D4—448no—
524D4—441no—
525D4—441no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—28no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—222no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—884no—
558C2×C4C2×#432512yes—
559C2×C4C2×#432512yes—
560C2×C4#6699512yes—
561C2×C4#6700612yes—
562C2×C4#6700612yes—
563C2×C4#41×D1111yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#6704211yescharacteristic
566C2×C4#6704311yescharacteristic
567C2×C4C22×C22⋊D1111yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C8—442no—
570C8—442no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22C22×#432511yescharacteristic
586C22C2×#6699511yescharacteristic
587C22#1062335311yescharacteristic
588C22#1062335311yescharacteristic
589C22#1062335911yescharacteristic
590C22#1062336411yescharacteristic
591C22C2×#6700611yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—44no—
596C4—41no—
597C4—44no—
598C4—442no—
599C4—881no—
600C4—881no—
601C4#1062284014yes—
602C4#1062335511yescharacteristic
603C4#1062336011yescharacteristic
604C4#1062336211yescharacteristic
605C4#1062336511yescharacteristic
606C2—42no—
607C2—882no—
608C2#1307195511yescharacteristic
609C2C2×#1062284011yescharacteristic
610C2#1307785811yescharacteristic
611C2#1307862011yescharacteristic
612C2#1307877211yescharacteristic
613C2#1307992811yescharacteristic
614C2#1307998311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#533D11
hypocenterC11#24151
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
2. C2×#10622696C2semidirect
4. #13069809C2semidirect
6. #13069565C2semidirect
7. #13069540C2semidirect
8. #13068971C2semidirect
9. #13068884C2semidirect
10. #13068596C2semidirect
11. C2×C11×#533C2semidirect
57. C11×C4⋊Q8D4semidirect
58. C11×C4⋊Q8D4semidirect
137. C22×C4×C11SD16semidirect
194. C2×#533D11semidirect
360. C4⋊Q8C22⋊D11semidirect
361. C4⋊Q8C22⋊D11semidirect
458. C22×C4#4325semidirect
500. C11#24151semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×#106226962
C4×#669832
#130698092
#130696172
#130695652
#130695402
#130689712
#130688842
#130685962
C2×C11×#5332
#2415111