Finite Group Databasebeta

← #14770393

Subgroups — #14770393

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623070C211yesmaximal, characteristic
2C2×#10622441C211yesmaximal, characteristic, complemented
3#13071528C211yesmaximal, characteristic, complemented
4#13069584C211yesmaximal, characteristic, complemented
5#13069583C211yesmaximal, characteristic, complemented
6#13069575C211yesmaximal, characteristic, complemented
7#13069572C211yesmaximal, characteristic, complemented
8#13069571C211yesmaximal, characteristic, complemented
9#13069562C211yesmaximal, characteristic, complemented
10#13068614C211yesmaximal, characteristic
11#13068614C211yesmaximal, characteristic
12#13068443C211yesmaximal, characteristic
13#13068441C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C11×#1802C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66977—21no—
20C22×Dic11⋊C4—21no—
21#10623070—24no—
22#10623070C418yescomplemented
23C2×#66943C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66940—21no—
26C2×#66931—21no—
27C2×#66931—21no—
28C2×#66923C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C11×#384C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40#10622589C2211yescharacteristic
41#10622589C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622586—21no—
45#10622585—21no—
46#10622585—21no—
47C4×C4⋊Dic11C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622441—24no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22—21no—
67C22×Dic22D411yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×D4×C11—22no—
71C4×D4×C11C2×C414yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83D4×Dic11C2×C414yes—
84D4×Dic11C2×C414yes—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91#66977—28no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—28no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4D411yescharacteristic
102C2×Dic11⋊C4D411yescharacteristic
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110#66943—22no—
111#66943C2×C414yes—
112#66941—22no—
113#66941C2×C414yes—
114#66940—44no—
115#66931—28no—
116#66931—28no—
117#66923—22no—
118#66923C2×C414yes—
119C4×Dic22C2×C414yes—
120C4×Dic22D414yes—
121C11×C4⋊C8—22no—
122C11×#102—22no—
123C11×#102—22no—
124#66896—22no—
125#66896Q814yescomplemented
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129#66879—22no—
130Dic11⋊C8—22no—
131Dic11⋊C8—22no—
132C8×Dic11—22no—
133#66867—22no—
134#22522—111nomaximal, Sylow
135C24×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C22×C412yes—
140C2×D4×C11C2×Q812yes—
141C2×D4×C11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—81no—
147C22×C4×C11—81no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—81no—
160C22×Dic11—81no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×Dic22—22no—
166C2×Dic22—22no—
167C2×Dic22—24no—
168C2×Dic22—81no—
169C2×Dic22—81no—
170C2×Dic22C22⋊C414yes—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—24no—
186C42×C11C22×C412yes—
187C42×C11C2×D412yes—
188C22⋊Dic11—24no—
189C22⋊Dic11—24no—
190C4⋊Dic11—24no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C22⋊C414yes—
197C4⋊Dic11C22×C412yes—
198C4⋊Dic11C22×C412yes—
199C4⋊Dic11C2×Q812yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—24no—
202Dic11⋊C4—24no—
203Dic11⋊C4—24no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—81no—
207Dic11⋊C4—81no—
208Dic11⋊C4C22⋊C414yes—
209Dic11⋊C4C22⋊C414yes—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11C22×C412yes—
214C4×Dic11C22×C412yes—
215C4×Dic11C2×D412yes—
216C4×Dic11C2×D412yes—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C2×Q812yes—
223C2×#554—111no—
224C2×#446—111no—
225Q8×C4⋊C4—111no—
226#1992—111no—
227#1992—111no—
228#1990—111no—
229#1989—111no—
230#1989—111no—
231#1987—111no—
232#1802—111no—
233#1802—111no—
234#1802D1111yescharacteristic
235#1762—111no—
236#1762—111no—
237C4×#102—111no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11C22×D411yescharacteristic
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11C4×Q814yescomplemented
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—84no—
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×Q811yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—48no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—84no—
292C2×Dic11C2×C22⋊C412yes—
293C2×Dic11C2×C22⋊C412yes—
294C2×Dic11C2×C22⋊C412yes—
295C2×Dic11C2×C22⋊C412yes—
296C2×Dic11AGL(1,ℤ/8)12yes—
297C2×Dic11#13712yes—
298Dic22—28no—
299Dic22—84no—
300C8×C11—41no—
301C8×C11—41no—
302C11⋊C8—22no—
303C11⋊C8—41no—
304#554—118no—
305#554—224no—
306C2×C4⋊Q8—111no—
307C2×#125—111no—
308C2×#125—111no—
309C2×C22⋊Q8—221no—
310C2×C22⋊Q8—221no—
311C2×C22⋊Q8—221no—
312C2×C4×Q8—111no—
313C2×C4×Q8—221no—
314C2×C4×D4—111no—
315C2×C4×D4—111no—
316C2×C4×D4C2×D1111yescharacteristic
317C22×C4⋊C4—221no—
318#446—224no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8C2×D1111yescharacteristic
322C2×#102—111no—
323C2×#102—111no—
324C2×#102C2×D1111yescharacteristic
325C2×#102C2×D1111yescharacteristic
326C2×#97—111no—
327C2×#97—111no—
328C2×C4×C8—111no—
329#389—221no—
330#389—221no—
331#389—221no—
332#384—111no—
333#384—111no—
334#384C2×D1111yescharacteristic
335C4×C4⋊C4—111no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350C22×C11—24no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11C22×C22⋊C411yescharacteristic
358C22×C11#54811yescharacteristic
359C22×C11D4×Q811yescharacteristic
360C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C11C2×#13711yescharacteristic
362C22×C11#57611yescharacteristic
363C22×C11#57711yescharacteristic
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11C2×C4×Q811yescharacteristic
370C4×C11#51911yescharacteristic
371C4×C11#54811yescharacteristic
372C4×C11D4×Q811yescharacteristic
373Dic11—22no—
374Dic11—22no—
375Dic11—22no—
376Dic11—42no—
377Dic11—42no—
378Dic11—42no—
379Dic11—81no—
380Dic11#41714yes—
381C22×Q8—111no—
382C22×Q8—221no—
383C22×D4C22×D1111yescharacteristic
384C23×C4—21no—
385C23×C4—221no—
386C23×C4—221no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C4⋊Q8—114no—
392C4⋊Q8—222no—
393#125—114no—
394#125—114no—
395#125—222no—
396#125—222no—
397C22⋊Q8—228no—
398C22⋊Q8—228no—
399C22⋊Q8—228no—
400C4×Q8—114no—
401C4×Q8—114no—
402C4×Q8—444no—
403C4×D4—22no—
404C4×D4—114no—
405C4×D4—114no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4C4×D1114yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—228no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440C4⋊C8—22no—
441C4⋊C8—222no—
442C4⋊C8—222no—
443#102—22no—
444#102—22no—
445#102—114no—
446#102—222no—
447#97—222no—
448#97—222no—
449C4×C8—222no—
450#95—221no—
451#95—221no—
452#95—221no—
453C2×C11—44no—
454C2×C11Q8×C22⋊C411yescharacteristic
455C2×C11C2×#41711yescharacteristic
456C2×C11#289711yescharacteristic
457C2×C11#336611yescharacteristic
458C2×C11#337211yescharacteristic
459C2×C11#338411yescharacteristic
460C2×C11#338511yescharacteristic
461C24—21no—
462C2×Q8—114no—
463C2×Q8—222no—
464C2×Q8—222no—
465C2×Q8—224no—
466C2×Q8—881no—
467C2×Q8—881no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4C2×C4×D1112yes—
472C2×D4#434112yes—
473C2×D4Q8×D1112yes—
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—881no—
493C22×C4—881no—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—112no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—81no—
516C4⋊C4—114no—
517C4⋊C4—114no—
518C4⋊C4—114no—
519C4⋊C4—112no—
520C4⋊C4—112no—
521C4⋊C4—112no—
522C4⋊C4—224no—
523C4⋊C4—224no—
524C4⋊C4—224no—
525C4⋊C4—224no—
526C4⋊C4—224no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—881no—
535C4⋊C4—881no—
536C4⋊C4C2×C4×D1112yes—
537C22⋊C4—24no—
538C22⋊C4—224no—
539C22⋊C4—224no—
540C42—112no—
541C42—112no—
542C42—112no—
543C42—112no—
544C42—442no—
545C42—442no—
546C42—442no—
547C42C2×C4×D1112yes—
548C42D4×D1112yes—
549C11#2252211yescharacteristic, complemented, Sylow
550C23—22no—
551C23—22no—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C2×D4×D1111yescharacteristic
558Q8—228no—
559Q8—884no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4#6694014yescomplemented
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—84no—
578C2×C4—112no—
579C2×C4—112no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—112no—
583C2×C4—112no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—448no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—884no—
604C2×C4C22⋊C4×D1112yes—
605C2×C4C22⋊C4×D1112yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×D4×D1111yescharacteristic
608C2×C4C2×#434111yescharacteristic
609C2×C4C2×Q8×D1111yescharacteristic
610C2×C4#6704311yescharacteristic
611C2×C4#6704311yescharacteristic
612C8—41no—
613C8—41no—
614C8—222no—
615C8—441no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C2×C22⋊C4×D1111yescharacteristic
624C22#1062312911yescharacteristic
625C22#1062316311yescharacteristic
626C22#1062328811yescharacteristic
627C22#1062329311yescharacteristic
628C22D11×AGL(1,ℤ/8)11yescharacteristic
629C22D11×#13711yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—114no—
636C4—222no—
637C4—222no—
638C4—222no—
639C4—442no—
640C4—442no—
641C4—442no—
642C4—881no—
643C4C2×#6694011yescharacteristic
644C4#1062304711yescharacteristic
645C4#1062312911yescharacteristic
646C4#1062316311yescharacteristic
647C2—44no—
648C2#1307144811yescharacteristic
649C2D11×#41711yescharacteristic
650C2#1307713711yescharacteristic
651C2#1308131811yescharacteristic
652C2#1308139211yescharacteristic
653C2#1308151011yescharacteristic
654C2#1308152111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1802C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1802D11
hypocenterC11#22522
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#10622441C2semidirect
3. #13071528C2semidirect
4. #13069584C2semidirect
5. #13069583C2semidirect
6. #13069575C2semidirect
7. #13069572C2semidirect
8. #13069571C2semidirect
9. #13069562C2semidirect
22. #10623070C4semidirect
125. #66896Q8semidirect
249. D4×C11C4×Q8semidirect
549. C11#22522semidirect
563. D4#66940semidirect

Maximal subgroups

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

subgroupindex
C2×#106230702
C2×#106224412
#130715282
#130695842
#130695832
#130695752
#130695722
#130695712
#130695622
#130686142
#130684432
#130684412
#102×Dic112
C11×#18022
#2252211