Finite Group Databasebeta

← #14816805

Subgroups — #14816805

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622404C211yesmaximal, characteristic, complemented
2C2×SD16×Dic11C211yesmaximal, characteristic
3#13072469C211yesmaximal, characteristic
4Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13070149C211yesmaximal, characteristic
6#13070094C211yesmaximal, characteristic, complemented
7#13069986C211yesmaximal, characteristic
8#13069948C211yesmaximal, characteristic, complemented
9#13069343C211yesmaximal, characteristic, complemented
10#13069172C211yesmaximal, characteristic, complemented
11#13068973C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic, complemented
13#13068882C211yesmaximal, characteristic, complemented
14#13068879C211yesmaximal, characteristic
15C11×#1880C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×#66931—21no—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31SD16×Dic11—24no—
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622598—21no—
37#10622598—21no—
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44#10622561—21no—
45#10622560—21no—
46#10622559—21no—
47#10622548—21no—
48#10622548C2211yescharacteristic
49C4×C4⋊Dic11—21no—
50C4×C4⋊Dic11C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622404—24no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
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—22no—
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×Dic11—41no—
86D4×Dic11—22no—
87D4×Dic11—41no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66941—22no—
110#66941—41no—
111#66931—44no—
112C11×#103—22no—
113C11×#102—22no—
114#66899—22no—
115#66899D414yes—
116#66896—22no—
117#66896—41no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66881—22no—
125#66881—22no—
126Dic11⋊C8—22no—
127C8×Dic11—22no—
128#66872—22no—
129#66872—22no—
130#66872—41no—
131#26373—111nomaximal, Sylow
132C24×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11C2×Q812yes—
138C2×Q8×C11#4112yes—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11C2×Q812yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—81no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C2×Dic22—42no—
163C2×Dic22—42no—
164C2×Dic22—81no—
165C11×SD16—28no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×Q812yes—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4#4112yes—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—81no—
179C42×C11—24no—
180C42×C11—21no—
181C42×C11—21no—
182C22⋊Dic11—42no—
183C22⋊Dic11—42no—
184C22⋊Dic11—42no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—41no—
193C4⋊Dic11—42no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11—81no—
197C4⋊Dic11—81no—
198C4⋊Dic11—81no—
199C4⋊Dic11SD1614yescomplemented
200C4⋊Dic11C2×D412yes—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×D412yes—
216C2×#475—111no—
217C2×C4×SD16—111no—
218#2452—111no—
219Q8×C4⋊C4—111no—
220#2094—111no—
221#2084—111no—
222#2065—111no—
223#2058—111no—
224#1941—111no—
225#1916—111no—
226#1880—111no—
227#1880D1111yescharacteristic
228#1865—111no—
229#1865—111no—
230#1864—111no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C22×D411yescharacteristic
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11C22⋊Q814yescomplemented
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—41no—
246D4×C11—41no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C2×SD1612yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×Q811yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—84no—
291C2×Dic11C2×SD1612yes—
292C2×Dic11C2×SD1612yes—
293Dic22—84no—
294C8×C11—22no—
295C8×C11—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×SD16C2×D1111yescharacteristic
299C2×C4⋊Q8—111no—
300C2×C22⋊Q8—221no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8C2×D1111yescharacteristic
304C2×C4×D4—111no—
305#475—224no—
306C4×SD16—224no—
307C2×#106—111no—
308C2×#106—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×C4⋊C8—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103C2×D1111yescharacteristic
316C2×#102—111no—
317C2×#102—111no—
318C2×#102C2×D1111yescharacteristic
319C2×C4×C8—111no—
320#396—221no—
321#393—221no—
322#390—111no—
323#390C2×D1111yescharacteristic
324#389—111no—
325#389—111no—
326#389—111no—
327#389—111no—
328#389—221no—
329#389—221no—
330#385—221no—
331#384—111no—
332#384—221no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—221no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340C2×D1111yescharacteristic
339#336—111no—
340#336—111no—
341#336—111no—
342#336C2×D1111yescharacteristic
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11#52511yescharacteristic
351C22×C11D4211yescharacteristic
352C22×C11D4×Q811yescharacteristic
353C22×C11C22×SD1611yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57711yescharacteristic
356C22×C11#57711yescharacteristic
357C4×C11—22no—
358C4×C11—24no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—81no—
362C4×C11C2×C22⋊Q811yescharacteristic
363C4×C11#53911yescharacteristic
364C4×C11#54711yescharacteristic
365C4×C11#55411yescharacteristic
366Dic11—22no—
367Dic11—22no—
368Dic11—41no—
369Dic11—41no—
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—221no—
375C22×Q8C22×D1111yescharacteristic
376C22×D4C22×D1111yescharacteristic
377C23×C4—221no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16Dic2214yescomplemented
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C4⋊Q8—222no—
386C4⋊Q8—441no—
387C22⋊Q8—444no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×Q8—441no—
394C4×D4—222no—
395C4×D4—441no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—21no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425#106—222no—
426#106—222no—
427#106—222no—
428#106—222no—
429#106—441no—
430C4⋊C8—222no—
431#103—22no—
432#103—114no—
433#103—222no—
434#102—22no—
435#102—222no—
436#102—441no—
437C4×C8—222no—
438#95—111no—
439#95—111no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11—82no—
445C2×C11#244911yescharacteristic
446C2×C11#310311yescharacteristic
447C2×C11#312511yescharacteristic
448C2×C11#327111yescharacteristic
449C2×C11D4×SD1611yescharacteristic
450C2×C11Q8×SD1611yescharacteristic
451C2×C11#338811yescharacteristic
452C24—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—442no—
457C2×Q8—442no—
458C2×Q8—881no—
459C2×Q8C2×Dic2212yes—
460C2×Q8D4×D1112yes—
461C2×Q8#434112yes—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4C2×Dic2212yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—881no—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485SD16—28no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—112no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8C2×Dic2212yes—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—114no—
503C4⋊C4—112no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—441no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4—881no—
521C4⋊C4#434112yes—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C42—24no—
528C42—21no—
529C42—21no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—442no—
535C42—442no—
536C11#2637311yescharacteristic, complemented, Sylow
537C23—22no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23C2×D4×D1111yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—22no—
548Q8—884no—
549Q8#6693114yescomplemented
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—112no—
569C2×C4—112no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—222no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—884no—
593C2×C4SD16×D1112yes—
594C2×C4C22×Dic2211yescharacteristic
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4C2×#434111yescharacteristic
597C2×C4C2×#434111yescharacteristic
598C2×C4#6704211yescharacteristic
599C2×C4#6704311yescharacteristic
600C8—22no—
601C8—41no—
602C8—222no—
603C8—441no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22D4×Dic2211yescharacteristic
612C22#1062311711yescharacteristic
613C22#1062314011yescharacteristic
614C22C2×SD16×D1111yescharacteristic
615C22#1062330111yescharacteristic
616C22#1062330611yescharacteristic
617C22#1062330811yescharacteristic
618C4—24no—
619C4—22no—
620C4—41no—
621C4—42no—
622C4—81no—
623C4—222no—
624C4—222no—
625C4—441no—
626C4—441no—
627C4—442no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4C2×#6693111yescharacteristic
632C4#1062307411yescharacteristic
633C4#1062314211yescharacteristic
634C4#1062319611yescharacteristic
635C2—82no—
636C2#1307243111yescharacteristic
637C2#1307864211yescharacteristic
638C2#1307889411yescharacteristic
639C2#1308020711yescharacteristic
640C2#1308030711yescharacteristic
641C2SD16×Dic2211yescharacteristic
642C2#1308156211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1880C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1880D11
hypocenterC11#26373
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×#10622404C2semidirect
4. Q8×C4⋊Dic11C2semidirect
6. #13070094C2semidirect
8. #13069948C2semidirect
9. #13069343C2semidirect
10. #13069172C2semidirect
12. #13068884C2semidirect
13. #13068882C2semidirect
67. C2×C11×SD16Q8semidirect
199. C4⋊Dic11SD16semidirect
242. Q8×C11C22⋊Q8semidirect
380. C2×SD16Dic22semidirect
536. C11#26373semidirect
549. Q8#66931semidirect

Maximal subgroups

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

subgroupindex
C2×#106224042
C2×SD16×Dic112
#130724692
Q8×C4⋊Dic112
#130701492
#130700942
#130699862
#130699482
#130693432
#130691722
#130689732
#130688842
#130688822
#130688792
C11×#18802
#2637311