Finite Group Databasebeta

← #14816897

Subgroups — #14816897

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C2×#10622485C211yesmaximal, characteristic
3#13072462C211yesmaximal, characteristic, complemented
4#13071525C211yesmaximal, characteristic, complemented
5#13070134C211yesmaximal, characteristic, complemented
6#13070100C211yesmaximal, characteristic, complemented
7#13069987C211yesmaximal, characteristic, complemented
8#13069343C211yesmaximal, characteristic, complemented
9#13069176C211yesmaximal, characteristic, complemented
10#13068965C211yesmaximal, characteristic
11#13068963C211yesmaximal, characteristic
12#13068878C211yesmaximal, characteristic, complemented
13#13068878C211yesmaximal, characteristic, complemented
14#13068860C211yesmaximal, characteristic, complemented
15C11×#2057C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999—21no—
18C22×D88C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C11×#389C2211yescharacteristic
26#10622844—21no—
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622697—24no—
31#10622607—21no—
32#10622602—21no—
33#10622602—21no—
34#10622601C2211yescharacteristic
35#10622600—21no—
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622590C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47#10622552C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622485—24no—
51#10622281—21no—
52D11×#95—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D44C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79#66999—44no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4D411yescharacteristic
94C2×Dic11⋊C4D411yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×D88—22no—
100C2×D88—22no—
101C2×D88Q814yescomplemented
102#66946—22no—
103#66946—22no—
104#66946—22no—
105#66946—22no—
106#66946—41no—
107#66946—41no—
108C4×D44—22no—
109C4×D44—41no—
110C11×#107—22no—
111C11×#107—41no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120#66885—22no—
121#66885—41no—
122C8×Dic11—22no—
123#66873—22no—
124#66873—22no—
125#66873—22no—
126#66873D414yes—
127#66872—22no—
128#66872—22no—
129#66872—22no—
130C4⋊(C11⋊C8)—22no—
131#26380—111nomaximal, Sylow
132C23×D11—21no—
133C23×D11—21no—
134C2×Q8×C11—42no—
135C2×Q8×C11—42no—
136C2×Q8×C11—81no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C2×D412yes—
159C2×D44C2×Q812yes—
160C2×D44C2×Q812yes—
161C2×D44#4112yes—
162C2×C4×D11—24no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×C4×D11—81no—
172C2×C4×D11—81no—
173C2×C4×D11—81no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11C2×Q812yes—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—81no—
188C11×C4⋊C4C2×D412yes—
189C11×C4⋊C4#4112yes—
190C42×C11—21no—
191C42×C11—21no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—81no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205C4⋊Dic11—81no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—42no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8C2×D412yes—
219D88—28no—
220C2×#476—111no—
221C2×C4×D8—111no—
222#2452—111no—
223#2349—111no—
224#2092—111no—
225#2085—111no—
226#2065—111no—
227#2057D1111yescharacteristic, complemented
228#1941—111no—
229#1916—111no—
230#1879—111no—
231#1879—111no—
232#1864—111no—
233#1864—111no—
234#1862—111no—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250Q8×C11—84no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11#13512yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×Q811yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11AGL(1,ℤ/8)12yes—
293D44—22no—
294D44—22no—
295D44—22no—
296D44—22no—
297D44—22no—
298D44—41no—
299D44—41no—
300D44C22⋊Q814yescomplemented
301C4×D11—84no—
302C4×D11—84no—
303C4×D11—84no—
304C4×D11—84no—
305C8×C11—22no—
306C8×C11—41no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C22×D8—111no—
310C2×C4⋊Q8C2×D1111yescharacteristic
311C2×C22⋊Q8—221no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—111no—
315C2×C4×D4—111no—
316#476—224no—
317C4×D8—224no—
318C2×#107C2×D1111yescharacteristic
319C2×#107C2×D1111yescharacteristic
320C2×#106—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×C4⋊C8—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×C4×C8—111no—
331#396—221no—
332#393—221no—
333#390—111no—
334#390—111no—
335#389—111no—
336#389—111no—
337#389—111no—
338#389C2×D1111yescharacteristic
339#385—221no—
340#385—221no—
341#385—221no—
342#382—111no—
343#380—221no—
344C4×C4⋊C4—111no—
345C2×#95—221no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350#336—111no—
351#336—111no—
352#336—111no—
353#336C2×D1111yescharacteristic
354C22×C11#52511yescharacteristic
355C22×C11D4211yescharacteristic
356C22×C11D4×Q811yescharacteristic
357C22×C11C2×#13511yescharacteristic
358C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57711yescharacteristic
361C2×D11—24no—
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C4×C11—22no—
376C4×C11—42no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11C2×C22⋊Q811yescharacteristic
382C4×C11#53911yescharacteristic
383C4×C11#54711yescharacteristic
384C4×C11#55411yescharacteristic
385Dic11—22no—
386Dic11—41no—
387Dic11—41no—
388Dic11—41no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—21no—
392C22×D4—111no—
393C22×D4—111no—
394C23×C4—221no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—221no—
398C2×D8—114no—
399C2×D8—222no—
400C2×D8—222no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C4⋊Q8—22no—
406C4⋊Q8—41no—
407C22⋊Q8—444no—
408C4×D4—222no—
409C4×D4—222no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4—441no—
414C4×D4—441no—
415C4×D4—441no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42C22×D1111yescharacteristic
440#107—22no—
441#107—41no—
442#106—222no—
443#106—222no—
444#106—222no—
445C4⋊C8—222no—
446#102—114no—
447#102—222no—
448#102—222no—
449#102—222no—
450#102—222no—
451#102—441no—
452C4×C8—222no—
453#95—21no—
454#95—111no—
455#95—111no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11#244911yescharacteristic
462C2×C11#310611yescharacteristic
463C2×C11#311811yescharacteristic
464C2×C11#326411yescharacteristic
465C2×C11#328211yescharacteristic
466C2×C11#338011yescharacteristic
467C2×C11#338411yescharacteristic
468D11—44no—
469D11—82no—
470C24—221no—
471C24—221no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—81no—
475C2×D4—112no—
476C2×D4—112no—
477C2×D4—112no—
478C2×D4—112no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—224no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—881no—
505C22×C4—881no—
506C22×C4—881no—
507C22×C4—881no—
508C22×C4—881no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512D8—228no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—112no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8Q8×D1112yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—42no—
532C4⋊C4—81no—
533C4⋊C4—222no—
534C4⋊C4—222no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4—881no—
542C4⋊C4D4×D1112yes—
543C4⋊C4#434312yes—
544C22⋊C4—224no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—442no—
551C22⋊C4—881no—
552C42—21no—
553C42—21no—
554C42—221no—
555C42—221no—
556C42—221no—
557C42—221no—
558C11#2638011yescharacteristic, complemented, Sylow
559C23—222no—
560C23—222no—
561C23—222no—
562C23—222no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23C2×D4×D1111yescharacteristic
574Q8—84no—
575D4—114no—
576D4—222no—
577D4—222no—
578D4—222no—
579D4—222no—
580D4—222no—
581D4—441no—
582D4—441no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—112no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—884no—
619C2×C4—884no—
620C2×C4—884no—
621C2×C4—884no—
622C2×C4#6697212yes—
623C2×C4C2×D4×D1111yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4C2×Q8×D1111yescharacteristic
626C2×C4C2×#434311yescharacteristic
627C2×C4#6704011yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C8—22no—
630C8—41no—
631C8—222no—
632C8—441no—
633C22—224no—
634C22—442no—
635C22—442no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—442no—
640C22—442no—
641C22—442no—
642C22—442no—
643C22—881no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22#1062312111yescharacteristic
648C22#1062315811yescharacteristic
649C22#1062325811yescharacteristic
650C22#1062328811yescharacteristic
651C22C2×#6697211yescharacteristic
652C22D11×AGL(1,ℤ/8)11yescharacteristic
653C22#1062330911yescharacteristic
654C4—22no—
655C4—42no—
656C4—41no—
657C4—42no—
658C4—81no—
659C4—81no—
660C4—222no—
661C4—441no—
662C4—441no—
663C4—441no—
664C4—881no—
665C4—881no—
666C4D11×C22⋊Q811yescharacteristic
667C4#1062316911yescharacteristic
668C4#1062325711yescharacteristic
669C4#1062326111yescharacteristic
670C2—444no—
671C2—882no—
672C2#1307241811yescharacteristic
673C2#1307867911yescharacteristic
674C2#1307880711yescharacteristic
675C2#1308009411yescharacteristic
676C2#1308031611yescharacteristic
677C2#1308148511yescharacteristic
678C2#1308151211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2057C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenter#2057D11
hypocenterC11#26380
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
3. #13072462C2semidirect
4. #13071525C2semidirect
5. #13070134C2semidirect
6. #13070100C2semidirect
7. #13069987C2semidirect
8. #13069343C2semidirect
9. #13069176C2semidirect
12. #13068878C2semidirect
13. #13068878C2semidirect
14. #13068860C2semidirect
15. C11×#2057C2semidirect
101. C2×D88Q8semidirect
227. #2057D11semidirect
300. D44C22⋊Q8semidirect
558. C11#26380semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×#106224852
#130724622
#130715252
#130701342
#130701002
#130699872
#130693432
#130691762
#130689652
#130689632
#130688782
#130688602
C11×#20572
#2638011