Finite Group Databasebeta

← #14724685

Subgroups — #14724685

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077630C211yesmaximal, characteristic, complemented
2#13077621C211yesmaximal, characteristic, complemented
3#13067513C211yesmaximal, characteristic, complemented
4#13067507C211yesmaximal, characteristic, complemented
5#13067467C211yesmaximal, characteristic, complemented
6#13067453C211yesmaximal, characteristic, complemented
7#13067453C211yesmaximal, characteristic, complemented
8#13067446C211yesmaximal, characteristic, complemented
9SD16×C11⋊C8C211yesmaximal, characteristic, complemented
10D8×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067396C211yesmaximal, characteristic, complemented
12#13067076C211yesmaximal, characteristic, complemented
13#13066998C211yesmaximal, characteristic, complemented
14#13066897C211yesmaximal, characteristic, complemented
15C11×#3102C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C11×#485C411yescharacteristic
19C11×#482C411yescharacteristic
20C11×#479C411yescharacteristic
21C11×#478C411yescharacteristic
22C11×#464C411yescharacteristic
23C11×#463C411yescharacteristic
24C11×#452C411yescharacteristic
25C11×#449C411yescharacteristic
26C4×C11×Q16C2211yescharacteristic
27C4×C11×SD16C2211yescharacteristic
28C4×C11×SD16C2211yescharacteristic
29C4×C11×D8C2211yescharacteristic
30C11×#431C2211yescharacteristic
31#10622637C2211yescharacteristic
32#10622637C2211yescharacteristic
33#10622637C2211yescharacteristic
34Q8×C11⋊C8C2211yescharacteristic
35#10622625—21no—
36#10622625C2211yescharacteristic
37#10622624—21no—
38#10622624—21no—
39#10622624—21no—
40D4×C11⋊C8C2211yescharacteristic
41D4×C11⋊C8C2211yescharacteristic
42D4×C11⋊C8C2211yescharacteristic
43#10622613—21no—
44#10622610—21no—
45#10622539—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49C2×#66867—21no—
50C2×C4×C11⋊C8C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57D4⋊(C11⋊C8)C2211yescharacteristic
58D4⋊(C11⋊C8)C2211yescharacteristic
59#10622096C2211yescharacteristic
60#10622096C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622092C2211yescharacteristic
64#10622092C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×D8C2×C411yescharacteristic
72C11×#126—21no—
73C11×#125C2×C411yescharacteristic
74C11×#124C2×C411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8C2×C411yescharacteristic
77C11×#121C2×C411yescharacteristic
78C4×Q8×C11C2×C411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11C2×C411yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C4×D4×C11C2311yescharacteristic
87C11×#117—21no—
88C11×#117—21no—
89C11×#117C2×C411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×#4318—21no—
93C2×#4318D411yescharacteristic
94C2×#4318D411yescharacteristic
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C11×#107C2×C411yescharacteristic
100C11×#107C2×C411yescharacteristic
101C11×#106C2×C411yescharacteristic
102C11×#106C2×C411yescharacteristic
103C11×C4⋊C8C2×C411yescharacteristic
104C11×C4⋊C8C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#103C2×C411yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×#102C2×C411yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×C22⋊C8C2×C411yescharacteristic
114C11×C22⋊C8C2×C411yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123C4⋊(C11⋊C8)—21no—
124C4⋊(C11⋊C8)—21no—
125C4⋊(C11⋊C8)—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)C2311yescharacteristic
128C4⋊(C11⋊C8)C2311yescharacteristic
129C4⋊(C11⋊C8)C2311yescharacteristic
130C4⋊(C11⋊C8)C2311yescharacteristic
131#66867—21no—
132#66867—21no—
133#66867—21no—
134#66867—21no—
135#66867D411yescharacteristic
136#66867D411yescharacteristic
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17996—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—41no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C22×C411yescharacteristic
152C2×D4×C11C22×C411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C11×Q16—41no—
161C11×SD16—22no—
162C11×SD16—41no—
163C11×D8—22no—
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11C22×C411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11#4111yescharacteristic
193C42×C11C2411yescharacteristic
194#4318—22no—
195#4318—22no—
196#4318—42no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—42no—
204C2×C11⋊C8—42no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211#3102D1111yescharacteristic
212#2970—111no—
213#2969—111no—
214#1591—111no—
215#1590—111no—
216#1584—111no—
217#1582—111no—
218#1582—111no—
219#1581—111no—
220C8×SD16—111no—
221C8×D8—111no—
222#1572—111no—
223#1494—111no—
224#1476—111no—
225C8×M16—111no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11C4×D411yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—42no—
237D4×C11—81no—
238D4×C11#13112yes—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—81no—
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C11⋊C8—22no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8#13512yes—
275C11⋊C8#13512yes—
276#529C2×D1111yescharacteristic
277C4×#41C2×D1111yescharacteristic
278#485Dic1111yescharacteristic
279#482Dic1111yescharacteristic
280#479Dic1111yescharacteristic
281#478Dic1111yescharacteristic
282#464Dic1111yescharacteristic
283#463Dic1111yescharacteristic
284#452Dic1111yescharacteristic
285#449Dic1111yescharacteristic
286#446—111no—
287#446—111no—
288#446—111no—
289C8×Q8—111no—
290C4×Q16C2×D1111yescharacteristic
291C4×SD16C2×D1111yescharacteristic
292C4×SD16C2×D1111yescharacteristic
293C4×D8C2×D1111yescharacteristic
294#436—111no—
295#436—221no—
296#435—221no—
297#435—221no—
298#435—221no—
299C8×D4—111no—
300C8×D4—111no—
301C8×D4—111no—
302#433—221no—
303#432—111no—
304#432—221no—
305#431—111no—
306#431C2×D1111yescharacteristic
307#405—221no—
308C4×M16—111no—
309C2×#97—221no—
310C2×C4×C8—111no—
311#335—111no—
312#335—111no—
313#334—111no—
314#334—111no—
315Q8⋊C8—111no—
316Q8⋊C8—111no—
317Q8⋊C8—111no—
318Q8⋊C8—111no—
319D4⋊C8—111no—
320D4⋊C8—111no—
321D4⋊C8—111no—
322D4⋊C8—111no—
323#322—111no—
324#322—111no—
325C82—111no—
326C82—111no—
327C22×C11—21no—
328C22×C11—22no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×C4×D411yescharacteristic
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11C2×#13111yescharacteristic
348C4×C11#56811yescharacteristic
349C4×C11C2×#13511yescharacteristic
350C4×C11C2×#13511yescharacteristic
351C2×#41C2×Dic1111yescharacteristic
352C2×Q16C2×Dic1111yescharacteristic
353C2×SD16C2×Dic1111yescharacteristic
354C2×SD16C2×Dic1111yescharacteristic
355C2×D8C2×Dic1111yescharacteristic
356C2×M16—111no—
357C2×M16—111no—
358C2×M16—221no—
359C22×C8—221no—
360C22×C8—221no—
361C22×C8—221no—
362C22×C8—221no—
363#126—21no—
364#125C2×Dic1111yescharacteristic
365#124C2×Dic1111yescharacteristic
366#123—21no—
367C22⋊Q8C2×Dic1111yescharacteristic
368#121C2×Dic1111yescharacteristic
369C4×Q8C2×Dic1111yescharacteristic
370C4×Q8C22×D1111yescharacteristic
371C4×Q8C22×D1111yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4C2×Dic1111yescharacteristic
376C4×D4C22×D1111yescharacteristic
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379#117—21no—
380#117C2×Dic1111yescharacteristic
381C2×C42—21no—
382C2×C42C22×D1111yescharacteristic
383#107C2×Dic1111yescharacteristic
384#107C2×Dic1111yescharacteristic
385#106C2×Dic1111yescharacteristic
386#106C2×Dic1111yescharacteristic
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8C2×Dic1111yescharacteristic
396C4⋊C8C2×Dic1111yescharacteristic
397#103C2×Dic1111yescharacteristic
398#103C2×Dic1111yescharacteristic
399#103C2×Dic1111yescharacteristic
400#103C2×Dic1111yescharacteristic
401#102C2×Dic1111yescharacteristic
402#102C2×Dic1111yescharacteristic
403#102C2×Dic1111yescharacteristic
404#102C2×Dic1111yescharacteristic
405C22⋊C8—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8C2×Dic1111yescharacteristic
412C22⋊C8C2×Dic1111yescharacteristic
413#97—111no—
414#97—111no—
415#97—221no—
416#97—221no—
417#97—221no—
418#97—221no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—221no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8C22×D1111yescharacteristic
427C4×C8C22×D1111yescharacteristic
428C2×C11—41no—
429C2×C11—42no—
430C2×C11—81no—
431C2×C11#293311yescharacteristic
432C2×C11C4×#13511yescharacteristic
433C2×C11#295611yescharacteristic
434#41—22no—
435#41—41no—
436C2×Q8C22×Dic1111yescharacteristic
437C2×Q8C22×Dic1111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C22×Dic1111yescharacteristic
441C2×D4C22×Dic1111yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4D4×D1111yescharacteristic
447C22×C4#434111yescharacteristic
448C22×C4C22×Dic1111yescharacteristic
449Q16—41no—
450SD16—22no—
451SD16—41no—
452D8—22no—
453M16—222no—
454M16—222no—
455M16—442no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—442no—
467C2×C8—442no—
468C2×C8—442no—
469C2×C8—442no—
470C2×C8C22×Dic1111yescharacteristic
471C2×C8C22×Dic1111yescharacteristic
472C2×C8C22×Dic1111yescharacteristic
473C2×C8C22×Dic1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4C22×Dic1111yescharacteristic
481C4⋊C4C22×Dic1111yescharacteristic
482C4⋊C4C22×Dic1111yescharacteristic
483C4⋊C4C22×Dic1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42D4×D1111yescharacteristic
497C42#434111yescharacteristic
498C42C22×Dic1111yescharacteristic
499C42C23×D1111yescharacteristic
500C11#1799611yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23D4×Dic1111yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—42no—
512D4—81no—
513D4#6700112yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4D4×Dic1111yescharacteristic
532C2×C4D4×Dic1111yescharacteristic
533C2×C4D4×Dic1111yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×#434111yescharacteristic
536C2×C4C23×Dic1111yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—112no—
542C8—112no—
543C8—222no—
544C8—221no—
545C8—221no—
546C8—441no—
547C8—441no—
548C8—441no—
549C8—441no—
550C8—441no—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×D4×Dic1111yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4D11×#13511yescharacteristic
572C4D11×#13511yescharacteristic
573C4C2×#6700111yescharacteristic
574C4#1062335011yescharacteristic
575C2—41no—
576C2—42no—
577C2—81no—
578C2#1307734311yescharacteristic
579C2#135×Dic1111yescharacteristic
580C2#1307752611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3102C2
socleC22×C11C2×C4×D4
prime radicalC11×#449C4
cosocleC42×C11C24
hypercenter#3102D11
hypocenterC11#17996
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3102

Complements

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

NH ≅ G/Ntype
1. #13077630C2semidirect
2. #13077621C2semidirect
3. #13067513C2semidirect
4. #13067507C2semidirect
5. #13067467C2semidirect
6. #13067453C2semidirect
7. #13067453C2semidirect
8. #13067446C2semidirect
9. SD16×C11⋊C8C2semidirect
10. D8×C11⋊C8C2semidirect
11. #13067396C2semidirect
12. #13067076C2semidirect
13. #13066998C2semidirect
14. #13066897C2semidirect
500. C11#17996semidirect

Maximal subgroups

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

subgroupindex
#130776302
#130776212
#130675132
#130675072
#130674672
#130674532
#130674462
SD16×C11⋊C82
D8×C11⋊C82
#130673962
#130670762
#130669982
#130668972
C11×#31022
#1799611