Finite Group Databasebeta

← #14770423

Subgroups — #14770423

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623216C211yesmaximal, characteristic
2C2×#10622441C211yesmaximal, characteristic
3C4⋊C4×Dic22C211yesmaximal, characteristic
4#13069586C211yesmaximal, characteristic
5#13069583C211yesmaximal, characteristic
6#13069575C211yesmaximal, characteristic
7#13069572C211yesmaximal, characteristic
8#13069566C211yesmaximal, characteristic
9#13068622C211yesmaximal, characteristic
10#13068620C211yesmaximal, characteristic
11#13068620C211yesmaximal, characteristic
12#13068449C211yesmaximal, characteristic
13#13068445C211yesmaximal, characteristic
14#13068435C211yesmaximal, characteristic
15C11×#1989C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17#10623216—24no—
18#10623216C418yescomplemented
19C2×#66943C2211yescharacteristic
20C2×#66942—21no—
21C2×#66942—21no—
22C2×#66941—21no—
23C2×#66941C2211yescharacteristic
24C2×#66940—21no—
25C2×#66940C2211yescharacteristic
26C2×#66940C2211yescharacteristic
27C2×C4×Dic22—21no—
28C2×C4×Dic22C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622589C2211yescharacteristic
39#10622589C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44#10622548C2211yescharacteristic
45#10622541—21no—
46C2×#66867C2211yescharacteristic
47#10622441—24no—
48#10622260—21no—
49#10622260—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Dic22—21no—
63C22×Dic22D411yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#125—22no—
68C11×#125C2×C414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4D411yescharacteristic
94C2×Dic11⋊C4D411yescharacteristic
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66943—22no—
105#66943C2×C414yes—
106#66942—28no—
107#66942—28no—
108#66941—28no—
109#66941—22no—
110#66941C2×C414yes—
111#66940—28no—
112#66940—22no—
113#66940—22no—
114#66940C2×C414yes—
115#66940C2×C414yes—
116C4×Dic22—22no—
117C4×Dic22—44no—
118C4×Dic22C2×C414yes—
119C4×Dic22C2×C414yes—
120C4×Dic22D414yes—
121C11×C4⋊C8—22no—
122C11×#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66880—22no—
126#66880—22no—
127#66879—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—22no—
130C8×Dic11—22no—
131#66874—22no—
132#66874Q814yescomplemented
133#66867—22no—
134#22524—111nomaximal, Sylow
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—24no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—42no—
157C2×Dic22—42no—
158C2×Dic22C22⋊C414yes—
159C2×Dic22C22×C412yes—
160C2×Dic22C2×Q812yes—
161C2×Dic22#4112yes—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C412yes—
176C11×C4⋊C4C22×C412yes—
177C11×C4⋊C4C2×Q812yes—
178C42×C11—42no—
179C42×C11C22×C412yes—
180C42×C11C2×D412yes—
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—42no—
188C4⋊Dic11—81no—
189C4⋊Dic11C22⋊C414yes—
190C4⋊Dic11C22×C412yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—24no—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195Dic11⋊C4—24no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—81no—
199Dic11⋊C4—81no—
200Dic11⋊C4C22⋊C414yes—
201Dic11⋊C4C22⋊C414yes—
202C4×Dic11—24no—
203C4×Dic11—24no—
204C4×Dic11—24no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11C22×C412yes—
208C4×Dic11C22×C412yes—
209C4×Dic11C2×D412yes—
210C4×Dic11C2×D412yes—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×Q812yes—
217C2×#557—111no—
218C2×#446—111no—
219Q8×C4⋊C4—111no—
220#1992—111no—
221#1992—111no—
222#1990—111no—
223#1989—111no—
224#1989D1111yescharacteristic
225#1988—111no—
226#1803—111no—
227#1803—111no—
228#1803—111no—
229#1763—111no—
230#1763—111no—
231C4×#103—111no—
232C23×C11C22×D411yescharacteristic
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C2×C22⋊C412yes—
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×Q811yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11C2×C22⋊C412yes—
276C2×Dic11C2×C22⋊C412yes—
277C2×Dic11C2×C22⋊C412yes—
278C2×Dic11C2×C22⋊C412yes—
279C2×Dic11AGL(1,ℤ/8)12yes—
280C2×Dic11#13712yes—
281Dic22—22no—
282Dic22—22no—
283Dic22—22no—
284Dic22—28no—
285Dic22—48no—
286Dic22C4×Q814yescomplemented
287C8×C11—41no—
288C8×C11—41no—
289C11⋊C8—22no—
290C11⋊C8—41no—
291#557—118no—
292#557—224no—
293C2×C4⋊Q8—111no—
294C2×C4⋊Q8—221no—
295C2×#125—111no—
296C2×#125—221no—
297C2×#125—221no—
298C2×#125C2×D1111yescharacteristic
299C2×C4×Q8—111no—
300C2×C4×Q8—111no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—221no—
304C2×C4×Q8—221no—
305#446—224no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8C2×D1111yescharacteristic
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#97—111no—
314C2×#97—111no—
315C2×C4×C8—111no—
316#389—221no—
317#389—221no—
318#389—221no—
319#384—111no—
320#384—111no—
321#384—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4C2×D1111yescharacteristic
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340C2×D1111yescharacteristic
334#340C2×D1111yescharacteristic
335#340C2×D1111yescharacteristic
336#340C2×D1111yescharacteristic
337C22×C11C22×C22⋊C411yescharacteristic
338C22×C11#54811yescharacteristic
339C22×C11D4×Q811yescharacteristic
340C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11#57711yescharacteristic
343C22×C11#57811yescharacteristic
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11C2×C4×Q811yescharacteristic
351C4×C11#51911yescharacteristic
352C4×C11#54811yescharacteristic
353C4×C11D4×Q811yescharacteristic
354Dic11—24no—
355Dic11—22no—
356Dic11—22no—
357Dic11—22no—
358Dic11—42no—
359Dic11—81no—
360Dic11—81no—
361Dic11#41714yes—
362C22×Q8—111no—
363C22×Q8—111no—
364C22×Q8—221no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C4⋊Q8—114no—
370C4⋊Q8—222no—
371C4⋊Q8—228no—
372#125—22no—
373#125—114no—
374#125—222no—
375#125—228no—
376#125—228no—
377#125C4×D1114yes—
378C4×Q8—114no—
379C4×Q8—114no—
380C4×Q8—114no—
381C4×Q8—114no—
382C4×Q8—114no—
383C4×Q8—222no—
384C4×Q8—222no—
385C4×Q8—228no—
386C4×Q8—222no—
387C4×Q8—444no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
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⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C42—21no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421C4⋊C8—22no—
422C4⋊C8—222no—
423C4⋊C8—222no—
424#103—114no—
425#103—222no—
426#103—222no—
427#103—222no—
428#97—222no—
429#97—222no—
430C4×C8—222no—
431#95—21no—
432#95—221no—
433#95—221no—
434C2×C11Q8×C22⋊C411yescharacteristic
435C2×C11C2×#41711yescharacteristic
436C2×C11#289811yescharacteristic
437C2×C11#336811yescharacteristic
438C2×C11#337411yescharacteristic
439C2×C11#338611yescharacteristic
440C2×C11#338711yescharacteristic
441C2×Q8—114no—
442C2×Q8—112no—
443C2×Q8—112no—
444C2×Q8—112no—
445C2×Q8—222no—
446C2×Q8—222no—
447C2×Q8—224no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—442no—
452C2×Q8—442no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4D4×D1111yescharacteristic
466C22×C4D4×D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—114no—
488C4⋊C4—114no—
489C4⋊C4—114no—
490C4⋊C4—112no—
491C4⋊C4—224no—
492C4⋊C4—224no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—224no—
496C4⋊C4—224no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—881no—
506C4⋊C4—881no—
507C4⋊C4—881no—
508C4⋊C4C2×C4×D1112yes—
509C4⋊C4C2×C4×D1112yes—
510C4⋊C4Q8×D1112yes—
511C42—42no—
512C42—112no—
513C42—112no—
514C42—112no—
515C42—112no—
516C42—224no—
517C42—224no—
518C42—224no—
519C42—442no—
520C42—442no—
521C42C2×C4×D1112yes—
522C42D4×D1112yes—
523C11#2252411yescharacteristic, complemented, Sylow
524C23C2×D4×D1111yescharacteristic
525Q8—114no—
526Q8—228no—
527Q8—222no—
528Q8—222no—
529Q8—222no—
530Q8—448no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—112no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—222no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4C22⋊C4×D1112yes—
572C2×C4C22⋊C4×D1112yes—
573C2×C4C22×C4×D1111yescharacteristic
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4C2×Q8×D1111yescharacteristic
576C2×C4#6704011yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#6704311yescharacteristic
579C8—41no—
580C8—41no—
581C8—222no—
582C8—441no—
583C22C2×C22⋊C4×D1111yescharacteristic
584C22#1062316311yescharacteristic
585C22#1062316411yescharacteristic
586C22#1062330111yescharacteristic
587C22#1062330211yescharacteristic
588C22D11×AGL(1,ℤ/8)11yescharacteristic
589C22D11×#13711yescharacteristic
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—42no—
595C4—81no—
596C4—114no—
597C4—224no—
598C4—222no—
599C4—222no—
600C4—222no—
601C4—442no—
602C4—881no—
603C4—881no—
604C4C4×Q8×D1111yescharacteristic
605C4#1062310311yescharacteristic
606C4#1062320811yescharacteristic
607C4#1062325811yescharacteristic
608C2#1307145011yescharacteristic
609C2D11×#41711yescharacteristic
610C2#1307714511yescharacteristic
611C2#1308134811yescharacteristic
612C2#1308142211yescharacteristic
613C2#1308153211yescharacteristic
614C2#1308155111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1989D11
hypocenterC11#22524
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
18. #10623216C4semidirect
132. #66874Q8semidirect
286. Dic22C4×Q8semidirect
523. C11#22524semidirect

Maximal subgroups

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

subgroupindex
C2×#106232162
C2×#106224412
C4⋊C4×Dic222
#130695862
#130695832
#130695752
#130695722
#130695662
#130686222
#130686202
#130684492
#130684452
#130684352
C11×#19892
#2252411