Finite Group Databasebeta

← #14816889

Subgroups — #14816889

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622635C211yesmaximal, characteristic, complemented
2C2×C4×#4325C211yesmaximal, characteristic
3#13072488C211yesmaximal, characteristic
4#13070145C211yesmaximal, characteristic
5#13070093C211yesmaximal, characteristic, complemented
6#13070001C211yesmaximal, characteristic
7#13069954C211yesmaximal, characteristic, complemented
8#13069346C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic
11#13068971C211yesmaximal, characteristic
12#13068876C211yesmaximal, characteristic
13#13068870C211yesmaximal, characteristic, complemented
14#13068870C211yesmaximal, characteristic, complemented
15Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#389—21no—
23C11×#389—21no—
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#384—21no—
27C11×#384C2211yescharacteristic
28C4×C11×C4⋊C4—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C4×#4325—24no—
34#10622635—24no—
35#10622605—21no—
36#10622602—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622289—21no—
52#10622280—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—41no—
69C4×Q8×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×#4325—22no—
89C2×#4325—22no—
90C2×#4325Q814yes—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C4×D44—22no—
108C4×D44—41no—
109#66923—22no—
110#66923—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115#66899—22no—
116#66899—22no—
117#66899D414yes—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66873—22no—
121#66873—22no—
122#66873—41no—
123#66872—22no—
124#66872—22no—
125#66871—22no—
126#66871—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129C4×C11⋊C8—22no—
130#26379—111nomaximal, Sylow
131C23×D11—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—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44C2×Q812yes—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4—81no—
175C11×C4⋊C4#4112yes—
176C42×C11—24no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C42×C11—42no—
185#4325—28no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190(C2×D11)⋊C4—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C2×D412yes—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8C2×D412yes—
212C2×C11⋊C8C2×Q812yes—
213C2×#479—111no—
214C2×C4×SD16—111no—
215#2454—111no—
216Q8×C4⋊C4D1111yescharacteristic, complemented
217#2093—111no—
218#2084—111no—
219#2067—111no—
220#2059—111no—
221#1942—111no—
222#1916—111no—
223#1880—111no—
224#1880—111no—
225#1864—111no—
226#1863—111no—
227#1863—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11C22⋊Q814yes—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
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×C11#13712yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×Q811yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285D44—22no—
286D44—22no—
287D44—41no—
288D44—41no—
289C4×D11—84no—
290C11⋊C8—22no—
291C11⋊C8—22no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C22×SD16—111no—
295C2×#125—111no—
296C2×C4×Q8C2×D1111yescharacteristic
297C2×C4×Q8C2×D1111yescharacteristic
298C2×C4×Q8C2×D1111yescharacteristic
299C2×C4×D4—111no—
300#479—224no—
301C4×SD16—224no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#106—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×C4×C8—111no—
315#399—221no—
316#396—221no—
317#390—111no—
318#390—111no—
319#389—21no—
320#389—21no—
321#389—111no—
322#389—111no—
323#389C2×D1111yescharacteristic
324#389C2×D1111yescharacteristic
325#385—221no—
326#384—21no—
327#384C2×D1111yescharacteristic
328#380—221no—
329C4×C4⋊C4—21no—
330C4×C4⋊C4C2×D1111yescharacteristic
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339C22×C11#52511yescharacteristic
340C22×C11D4211yescharacteristic
341C22×C11D4×Q811yescharacteristic
342C22×C11C2×#13511yescharacteristic
343C22×C11C2×#13711yescharacteristic
344C22×C11#57611yescharacteristic
345C22×C11#57711yescharacteristic
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C4×C11—22no—
354C4×C11—24no—
355C4×C11—22no—
356C4×C11—41no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11C2×C22⋊Q811yescharacteristic
364C4×C11#53911yescharacteristic
365C4×C11#54711yescharacteristic
366C4×C11#55411yescharacteristic
367Dic11—42no—
368Dic11—81no—
369Dic11—81no—
370C22×Q8C22×D1111yescharacteristic
371C22×D4—111no—
372C23×C4—221no—
373C2×SD16—114no—
374C2×SD16—222no—
375C2×SD16—222no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8—111no—
380#125—222no—
381#125—441no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—41no—
387C4×Q8—41no—
388C4×D4—222no—
389C4×D4—441no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22⋊D1111yescharacteristic
405C2×C4⋊C4C22⋊D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420#107—222no—
421#107—222no—
422#107—441no—
423#106—222no—
424#106—222no—
425C4⋊C8—222no—
426#103—114no—
427#103—222no—
428#103—222no—
429#102—222no—
430#102—222no—
431#102—441no—
432C4×C8—222no—
433#95—21no—
434#95—21no—
435#95—221no—
436#95—221no—
437#95C22⋊D1111yescharacteristic
438#95C22⋊D1111yescharacteristic
439C2×C11#244911yescharacteristic
440C2×C11#310811yescharacteristic
441C2×C11#311911yescharacteristic
442C2×C11#326611yescharacteristic
443C2×C11#328711yescharacteristic
444C2×C11#338111yescharacteristic
445C2×C11#338511yescharacteristic
446D11—82no—
447C24—221no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8#433912yes—
452C2×Q8D4×D1112yes—
453C2×Q8Q8×D1112yes—
454C2×D4—112no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—442no—
468C22×C4—442no—
469C22×C4—881no—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477SD16—228no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C4⋊C4—24no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—81no—
502C4⋊C4—81no—
503C4⋊C4—81no—
504C4⋊C4—112no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4—881no—
513C4⋊C4—881no—
514C4⋊C4#433912yes—
515C22⋊C4—442no—
516C22⋊C4—442no—
517C22⋊C4—881no—
518C22⋊C4—881no—
519C22⋊C4—881no—
520C42—24no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—42no—
528C42—42no—
529C11#2637911yescharacteristic, complemented, Sylow
530C23—222no—
531C23—441no—
532C23—441no—
533C23—441no—
534C23—441no—
535C23—441no—
536C23—441no—
537C23C22×C22⋊D1111yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—22no—
541Q8#6694914yes—
542D4—222no—
543D4—222no—
544D4—441no—
545D4—441no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—222no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—884no—
584C2×C4#6699512yes—
585C2×C4#6700312yes—
586C2×C4C2×#433911yescharacteristic
587C2×C4C2×#433911yescharacteristic
588C2×C4C2×D4×D1111yescharacteristic
589C2×C4#6703711yescharacteristic
590C2×C4C2×Q8×D1111yescharacteristic
591C2×C4#6704011yescharacteristic
592C8—222no—
593C8—222no—
594C8—441no—
595C8—441no—
596C22—442no—
597C22—442no—
598C22—442no—
599C22—881no—
600C22—881no—
601C22—881no—
602C22—881no—
603C22#1062332211yescharacteristic
604C22D4×C22⋊D1111yescharacteristic
605C22C2×#6699511yescharacteristic
606C22Q8×C22⋊D1111yescharacteristic
607C22C2×#6700311yescharacteristic
608C22#1062336611yescharacteristic
609C22#1062336811yescharacteristic
610C4—24no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—42no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—81no—
619C4—81no—
620C4—442no—
621C4—881no—
622C4—881no—
623C4#1062303811yescharacteristic
624C4C2×#6694911yescharacteristic
625C4#1062304211yescharacteristic
626C4#1062304611yescharacteristic
627C2—882no—
628C2#1307242511yescharacteristic
629C2#1307869611yescharacteristic
630C2#1307881511yescharacteristic
631C2#1308012711yescharacteristic
632C2#1308037211yescharacteristic
633C2#1308148711yescharacteristic
634C2#1308152211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterQ8×C4⋊C4D11
hypocenterC11#26379
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622635C2semidirect
5. #13070093C2semidirect
7. #13069954C2semidirect
8. #13069346C2semidirect
9. #13069175C2semidirect
13. #13068870C2semidirect
14. #13068870C2semidirect
15. Q8×C11×C4⋊C4C2semidirect
216. Q8×C4⋊C4D11semidirect
529. C11#26379semidirect

Maximal subgroups

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

subgroupindex
C2×#106226352
C2×C4×#43252
#130724882
#130701452
#130700932
#130700012
#130699542
#130693462
#130691752
#130689712
#130688762
#130688702
Q8×C11×C4⋊C42
#2637911