Finite Group Databasebeta

← #14796425

Subgroups — #14796425

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622407C211yesmaximal, characteristic, complemented
2C2×SD16×Dic11C211yesmaximal, characteristic
3#13073787C211yesmaximal, characteristic
4Q8×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13070102C211yesmaximal, characteristic, complemented
6#13070099C211yesmaximal, characteristic, complemented
7#13070004C211yesmaximal, characteristic
8#13070002C211yesmaximal, characteristic
9#13069575C211yesmaximal, characteristic, complemented
10#13069333C211yesmaximal, characteristic, complemented
11#13068973C211yesmaximal, characteristic
12#13068631C211yesmaximal, characteristic, complemented
13#13068629C211yesmaximal, characteristic, complemented
14#13068614C211yesmaximal, characteristic
15C11×#1880C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27#10622834C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30SD16×Dic11—24no—
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622590C2211yescharacteristic
37#10622589—21no—
38#10622589C2211yescharacteristic
39#10622586—21no—
40#10622586C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622560—21no—
43#10622560—21no—
44#10622555—21no—
45#10622555—21no—
46#10622549C2211yescharacteristic
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52#10622407—24no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×Dic22—21no—
65C2×C11×SD16—22no—
66C2×C11×SD16—22no—
67C2×C11×SD16Q814yescomplemented
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×Q8×C11—22no—
71C4×Q8×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85Q8×Dic11D414yes—
86D4×Dic11—22no—
87D4×Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66941—22no—
108#66941—22no—
109C11×#103—22no—
110C11×#102—41no—
111#66899—22no—
112#66899—22no—
113#66896—22no—
114#66896—41no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66882—22no—
124#66881—22no—
125Dic11⋊C8—22no—
126Dic11⋊C8—41no—
127C8×Dic11—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—41no—
130#24814—111nomaximal, Sylow
131C24×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×Q812yes—
137C2×Q8×C11#4112yes—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×Dic22—42no—
162C2×Dic22—81no—
163C2×Dic22—81no—
164C11×SD16—28no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×Q812yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—42no—
176C11×C22⋊C4—81no—
177C11×C22⋊C4—81no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—42no—
181C22⋊Dic11—42no—
182C22⋊Dic11—81no—
183C22⋊Dic11—81no—
184C4⋊Dic11—24no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11C2×D412yes—
194Dic11⋊C4—22no—
195Dic11⋊C4—22no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201C4×Dic11—24no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11C2×D412yes—
206C4×Dic11#4112yes—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×#477—111no—
214C2×C4×SD16—111no—
215#2563—111no—
216Q8×C4⋊C4—111no—
217#2085—111no—
218#2085—111no—
219#2067—111no—
220#2067—111no—
221#1990—111no—
222#1939—111no—
223#1880—111no—
224#1880D1111yescharacteristic
225#1805—111no—
226#1805—111no—
227#1802—111no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11C22⋊Q814yes—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—41no—
243D4×C11—41no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
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×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×Q811yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—84no—
286C2×Dic11#12112yes—
287C2×Dic11#12112yes—
288C2×Dic11#13512yes—
289C2×Dic11#13712yes—
290Dic22—84no—
291C8×C11—22no—
292C8×C11—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C22×SD16C2×D1111yescharacteristic
296C2×C4⋊Q8—111no—
297C2×C4×Q8—111no—
298C2×C4×Q8—111no—
299C2×C4×Q8C2×D1111yescharacteristic
300C2×C4×D4—111no—
301#477—224no—
302C4×SD16—224no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#106—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103C2×D1111yescharacteristic
312C2×#102—111no—
313C2×#102—111no—
314C2×#102C2×D1111yescharacteristic
315C2×C4×C8—111no—
316#393—221no—
317#393—221no—
318#390—111no—
319#390C2×D1111yescharacteristic
320#389—111no—
321#389—111no—
322#389—221no—
323#389—221no—
324#384—111no—
325#384—221no—
326#382—111no—
327#382—111no—
328#380—221no—
329#380—221no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—221no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#336—111no—
339#336C2×D1111yescharacteristic
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11C2×#12111yescharacteristic
348C22×C11#54611yescharacteristic
349C22×C11D4×Q811yescharacteristic
350C22×C11C2×#13511yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C22×C11#57611yescharacteristic
353C22×C11#57711yescharacteristic
354C4×C11—24no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11C2×C22⋊Q811yescharacteristic
360C4×C11#53711yescharacteristic
361C4×C11#55211yescharacteristic
362C4×C11#55411yescharacteristic
363Dic11—22no—
364Dic11—41no—
365Dic11—42no—
366Dic11—41no—
367Dic11—81no—
368Dic11—81no—
369Dic11—81no—
370Dic11#46414yes—
371C22×Q8—221no—
372C22×Q8C22×D1111yescharacteristic
373C22×D4C22×D1111yescharacteristic
374C23×C4—221no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16Dic2214yescomplemented
378C22×C8—111no—
379C22×C8—111no—
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C4⋊Q8—222no—
383C4⋊Q8—222no—
384C4×Q8—22no—
385C4×Q8—41no—
386C4×Q8—114no—
387C4×Q8—222no—
388C4×Q8—222no—
389C4×Q8—441no—
390C4×D4—222no—
391C4×D4—222no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—221no—
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⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—21no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#107—222no—
420#107—222no—
421#106—222no—
422C4⋊C8—222no—
423C4⋊C8—441no—
424C4⋊C8—441no—
425#103—22no—
426#103—222no—
427#103—222no—
428#102—41no—
429#102—222no—
430#102—441no—
431C4×C8—222no—
432#95—111no—
433#95—111no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440C2×C11—82no—
441C2×C11#241711yescharacteristic
442C2×C11C2×#46411yescharacteristic
443C2×C11#304511yescharacteristic
444C2×C11#330511yescharacteristic
445C2×C11#332911yescharacteristic
446C2×C11#338111yescharacteristic
447C2×C11#338511yescharacteristic
448C24—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—442no—
453C2×Q8—881no—
454C2×Q8—881no—
455C2×Q8C2×Dic2212yes—
456C2×Q8D4×D1112yes—
457C2×Q8#434112yes—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4C2×Dic2212yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481SD16—28no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8C2×Dic2212yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—112no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—224no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—881no—
514C4⋊C4—881no—
515C4⋊C4—881no—
516C22⋊C4—81no—
517C22⋊C4—81no—
518C22⋊C4—442no—
519C22⋊C4—881no—
520C22⋊C4—881no—
521C42—21no—
522C42—21no—
523C42—42no—
524C42—112no—
525C42—112no—
526C42—224no—
527C42—221no—
528C42—221no—
529C42—442no—
530C11#2481411yescharacteristic, complemented, Sylow
531C23—22no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23C2×D4×D1111yescharacteristic
539Q8—22no—
540Q8—22no—
541Q8—22no—
542Q8—884no—
543Q8#6693114yes—
544D4—22no—
545D4—22no—
546D4—41no—
547D4—41no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
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—884no—
588C2×C4C22×Dic2211yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×#434111yescharacteristic
591C2×C4#6703711yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#6704311yescharacteristic
594C8—22no—
595C8—41no—
596C8—441no—
597C8—441no—
598C22—42no—
599C22—42no—
600C22—42no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22D4×Dic2211yescharacteristic
606C22#1062312211yescharacteristic
607C22D11×#12111yescharacteristic
608C22#1062329311yescharacteristic
609C22D11×#13511yescharacteristic
610C22#1062330511yescharacteristic
611C22D11×#13711yescharacteristic
612C4—24no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4—114no—
618C4—222no—
619C4—441no—
620C4—442no—
621C4—441no—
622C4—881no—
623C4—881no—
624C4—881no—
625C4C2×#6693111yescharacteristic
626C4#1062307011yescharacteristic
627C4#1062312811yescharacteristic
628C4#1062318111yescharacteristic
629C2—82no—
630C2#1307206411yescharacteristic
631C2D11×#46411yescharacteristic
632C2#1307815211yescharacteristic
633C2#1308055911yescharacteristic
634C2#1308090311yescharacteristic
635C2#1308149211yescharacteristic
636C2#1308152711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1880C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1880D11
hypocenterC11#24814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×#10622407C2semidirect
4. Q8×Dic11⋊C4C2semidirect
5. #13070102C2semidirect
6. #13070099C2semidirect
9. #13069575C2semidirect
10. #13069333C2semidirect
12. #13068631C2semidirect
13. #13068629C2semidirect
67. C2×C11×SD16Q8semidirect
377. C2×SD16Dic22semidirect
530. C11#24814semidirect

Maximal subgroups

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

subgroupindex
C2×#106224072
C2×SD16×Dic112
#130737872
Q8×Dic11⋊C42
#130701022
#130700992
#130700042
#130700022
#130695752
#130693332
#130689732
#130686312
#130686292
#130686142
C11×#18802
#2481411