Finite Group Databasebeta

← #14782464

Subgroups — #14782464

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622577C211yesmaximal, characteristic, complemented
2C2×#10622537C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic
4C2×#10622579C211yesmaximal, characteristic
5#13071106C211yesmaximal, characteristic
6#13070008C212yesmaximal, complemented
7#13070001C212yesmaximal, complemented
8#13069994C212yesmaximal, complemented
9#13069987C212yesmaximal, complemented
10#13068335C211yesmaximal, characteristic, complemented
11C2×C11×#389C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×C4⋊C4—21no—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C11×#389—21no—
21C11×#389—21no—
22C11×#389C2212yes—
23C11×#389C2212yes—
24C2×C11×#95—21no—
25#10622826—21no—
26#10622826—21no—
27C2×#66874C2212yes—
28C2×#66874C2212yes—
29#10622579—24no—
30#10622579—24no—
31C2×#66873C2212yes—
32C2×#66873C2212yes—
33#10622577—24no—
34C2×#66872C2212yes—
35C2×#66871C2212yes—
36#10622552C2211yescharacteristic
37#10622552C2211yescharacteristic
38C4×(C2×D11)⋊C4—21no—
39C4×(C2×D11)⋊C4—21no—
40#10622542C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622537—24no—
43C2×C4⋊(C11⋊C8)C2212yes—
44C2×C4⋊(C11⋊C8)C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—21no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C2×#4339Q814yes—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2311yescharacteristic
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—44no—
70C2×C11×C4⋊C4D414yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C42×C11—22no—
74C2×C42×C11—22no—
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84#66979—22no—
85#66979—22no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4×Dic11—21no—
89C2×#4318—22no—
90C2×#4318—22no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318D414yes—
95C22×C11⋊C8C2312yes—
96C22×C11⋊C8C2312yes—
97C11×#95—22no—
98C11×#95—22no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103#66874—24no—
104#66874—24no—
105#66873—24no—
106#66873—24no—
107#66872—24no—
108#66871—24no—
109C4⋊(C11⋊C8)—24no—
110C4⋊(C11⋊C8)—24no—
111#23617—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×Q812yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—24no—
141C2×C22⋊D11—42no—
142C2×C22⋊D11—42no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146#4339—28no—
147#4339—28no—
148#4339—44no—
149#4339—44no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C2×Q812yes—
156C2×C4×D11—24no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22C2×Q812yes—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—44no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—44no—
172C11×C4⋊C4C2×D414yes—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C22⋊Dic11—42no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—42no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4×Dic11—42no—
189#4318—28no—
190#4318—44no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8C2×D414yes—
197C2×#428—111no—
198C2×#423—111no—
199C2×#417—111no—
200C2×#417—111no—
201#2297—111no—
202C2×#389D1111yescharacteristic, complemented
203#2068—112no—
204#2067—112no—
205#2066—112no—
206#2065—112no—
207#1736—111no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11#12112yes—
213C23×C11#12112yes—
214C23×C11C22⋊Q812yes—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—24no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—48no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—84no—
243C2×C4×C11#12114yes—
244C2×C4×C11#12112yes—
245C2×C4×C11#12112yes—
246C2×C4×C11C22⋊Q814yes—
247C2×C4×C11C22⋊Q814yes—
248C2×C4×C11C22⋊Q812yes—
249C2×C4×C11#12614yes—
250C2×C4×C11AGL(1,ℤ/8)12yes—
251C2×C4×C11#13712yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×Q811yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
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—48no—
273Dic22—22no—
274Dic22—22no—
275Dic22—41no—
276Dic22—41no—
277C11⋊C8—24no—
278C11⋊C8—42no—
279C22×#41—111no—
280C22×M16—111no—
281C22×M16—111no—
282C2×#117—111no—
283C22×C4⋊C4—21no—
284C22×C4⋊C4C2×D1111yescharacteristic
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C42C2×D1111yescharacteristic
287#428—224no—
288C2×#107—112no—
289C2×#106—112no—
290#423—224no—
291C2×C4⋊C8—112no—
292C2×C4⋊C8—112no—
293#417—224no—
294#417—224no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#102—112no—
298C2×#102—112no—
299#391—111no—
300#391—111no—
301#390—111no—
302#390—111no—
303#389—21no—
304#389—21no—
305#389C2×D1112yes—
306#389C2×D1112yes—
307#386—221no—
308#386—221no—
309C4×C22⋊C4—221no—
310C4×C22⋊C4—221no—
311C2×#95—21no—
312#340—112no—
313#340—112no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11#39614yes—
321C22×C11C2×#12111yescharacteristic
322C22×C11C2×#12111yescharacteristic
323C22×C11C2×C22⋊Q811yescharacteristic
324C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C11C2×#13711yescharacteristic
326C22×C11#57511yescharacteristic
327C22×C11#57511yescharacteristic
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—44no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—82no—
341C4×C11#39614yes—
342C4×C11C2×#12111yescharacteristic
343C4×C11C2×C22⋊Q811yescharacteristic
344C4×C11C2×C22⋊Q811yescharacteristic
345C4×C11C2×#12611yescharacteristic
346Dic11—42no—
347Dic11—81no—
348Dic11—81no—
349C2×#41—114no—
350C2×#41—222no—
351C2×#41—222no—
352C2×#41—222no—
353C2×#41—222no—
354C2×#41—222no—
355C22×Q8—111no—
356C22×D4—111no—
357C22×D4—221no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—221no—
361C23×C4C22⋊D1111yescharacteristic
362C23×C4C22⋊D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×M16—114no—
365C2×M16—222no—
366C2×M16—222no—
367C2×M16—222no—
368C2×M16—222no—
369C2×M16—222no—
370C22×C8—112no—
371C22×C8—112no—
372#117—222no—
373#117—222no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4D4414yes—
385C2×C4⋊C4C22×D1112yes—
386C2×C4⋊C4C22×D1112yes—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—221no—
395C2×C42C22⋊D1111yescharacteristic
396C2×C42C22⋊D1111yescharacteristic
397C2×C42C22×D1111yescharacteristic
398C2×C42C22×D1111yescharacteristic
399#107—224no—
400#106—224no—
401C4⋊C8—224no—
402C4⋊C8—224no—
403#103—224no—
404#103—224no—
405#102—224no—
406#102—224no—
407#95—22no—
408#95—22no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413C2×C11—24no—
414C2×C11C2×#39611yescharacteristic
415C2×C11#303611yescharacteristic
416C2×C11#303711yescharacteristic
417C2×C11#305511yescharacteristic
418C2×C11#305611yescharacteristic
419C2×C11#307911yescharacteristic
420C2×C11#308011yescharacteristic
421D11—82no—
422C24—221no—
423C24C2×C22⋊D1111yescharacteristic
424#41—228no—
425#41—228no—
426#41—444no—
427#41—444no—
428C2×Q8—112no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×D4—112no—
435C2×D4—224no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—442no—
442C2×D4—442no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—221no—
458C22×C4—224no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4C2×D4412yes—
464C22×C4#433912yes—
465C22×C4D4×D1112yes—
466C22×C4#434112yes—
467C22×C4Q8×D1112yes—
468C22×C4#434312yes—
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475M16—228no—
476M16—444no—
477C2×C8—114no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C4⋊C4—24no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—44no—
488C4⋊C4—44no—
489C4⋊C4—42no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4C2×D4414yes—
495C22⋊C4—442no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C42—22no—
501C42—22no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—442no—
507C11#2361711yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—222no—
513C23—441no—
514C23—441no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23#6698312yes—
520C23#6699212yes—
521C23#6699912yes—
522C23C22×C22⋊D1111yescharacteristic
523Q8—222no—
524Q8—222no—
525Q8—441no—
526Q8—441no—
527D4—222no—
528D4—222no—
529D4—448no—
530D4—441no—
531D4—441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—24no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—48no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—84no—
552C2×C4—222no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—448no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4#6694814yes—
563C2×C4#6694914yes—
564C2×C4#6695014yes—
565C2×C4#6695114yes—
566C2×C4#6698312yes—
567C2×C4#6698512yes—
568C2×C4#6699212yes—
569C2×C4#6699512yes—
570C2×C4#6699912yes—
571C2×C4C22×D4411yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4C2×Q8×D1111yescharacteristic
576C2×C4C2×#434311yescharacteristic
577C8—224no—
578C8—442no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—442no—
586C22—442no—
587C22—442no—
588C22—881no—
589C22—881no—
590C22—881no—
591C22—881no—
592C22#1062260714yes—
593C22C2×#6698311yescharacteristic
594C22C2×#6698511yescharacteristic
595C22C2×#6699211yescharacteristic
596C22C2×#6699511yescharacteristic
597C22C2×#6699911yescharacteristic
598C22#1062335311yescharacteristic
599C22#1062335311yescharacteristic
600C4—22no—
601C4—22no—
602C4—44no—
603C4—41no—
604C4—41no—
605C4—82no—
606C4—442no—
607C4—881no—
608C4—881no—
609C4#1062260714yes—
610C4C2×#6694811yescharacteristic
611C4C2×#6694911yescharacteristic
612C4C2×#6695011yescharacteristic
613C4C2×#6695111yescharacteristic
614C2—24no—
615C2—882no—
616C2C2×#1062260711yescharacteristic
617C2#1307808011yescharacteristic
618C2#1307808811yescharacteristic
619C2#1307823111yescharacteristic
620C2#1307824211yescharacteristic
621C2#1307842511yescharacteristic
622C2#1307843411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#389C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#389D11
hypocenterC11#23617
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#10622577C2semidirect
2. C2×#10622537C2semidirect
6. #13070008C2semidirect
7. #13070001C2semidirect
8. #13069994C2semidirect
9. #13069987C2semidirect
10. #13068335C2semidirect
11. C2×C11×#389C2semidirect
202. C2×#389D11semidirect
507. C11#23617semidirect

Maximal subgroups

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

subgroupindex
C2×#106225772
C2×#106225372
C2×#106225792
#130711062
#130700082
#130700012
#130699942
#130699872
#130683352
C2×C11×#3892
#2361711