Finite Group Databasebeta

← #14723835

Subgroups — #14723835

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077765C211yesmaximal, characteristic, complemented
2#13077640C211yesmaximal, characteristic, complemented
3#13067481C211yesmaximal, characteristic, complemented
4#13067474C211yesmaximal, characteristic, complemented
5#13067453C211yesmaximal, characteristic, complemented
6#13067446C211yesmaximal, characteristic, complemented
7#13067440C211yesmaximal, characteristic, complemented
8SD16⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
9SD16×C11⋊C8C211yesmaximal, characteristic, complemented
10D8×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067405C211yesmaximal, characteristic, complemented
12#13067041C211yesmaximal, characteristic, complemented
13#13067024C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#3105C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#484C411yescharacteristic
19C11×#481C411yescharacteristic
20C11×#478C411yescharacteristic
21C11×#478C411yescharacteristic
22C11×#463C411yescharacteristic
23C11×#463C411yescharacteristic
24C11×#450C411yescharacteristic
25C11×#447C411yescharacteristic
26C4×C11×SD16C2211yescharacteristic
27C4×C11×SD16C2211yescharacteristic
28C4×C11×D8C2211yescharacteristic
29C4×C11×D8C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C2×C22⋊(C11⋊C8)—21no—
32C2×C22⋊(C11⋊C8)—21no—
33#10622637C2211yescharacteristic, complemented
34Q8×C11⋊C8C2211yescharacteristic, complemented
35#10622625—21no—
36#10622625C2211yescharacteristic, complemented
37#10622624—21no—
38D4×C11⋊C8—21no—
39D4×C11⋊C8—21no—
40D4×C11⋊C8C2211yescharacteristic
41D4×C11⋊C8C2211yescharacteristic
42D4×C11⋊C8C2211yescharacteristic
43D4×C11⋊C8C2211yescharacteristic
44D4×C11⋊C8C2211yescharacteristic, complemented
45#10622613—21no—
46#10622612—21no—
47#10622538C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622538C2211yescharacteristic
50#10622537C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57D4⋊(C11⋊C8)C2211yescharacteristic, complemented
58D4⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622096C2211yescharacteristic, complemented
60#10622096C2211yescharacteristic, complemented
61#10622095C2211yescharacteristic, complemented
62#10622095C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×D8C2×C411yescharacteristic
72C2×C11×D8C2×C411yescharacteristic
73C11×#126—21no—
74C11×#125C2×C411yescharacteristic
75C11×#124C2×C411yescharacteristic
76C11×#123—21no—
77C11×C22⋊Q8C2×C411yescharacteristic
78C11×#121C2×C411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11C2×C411yescharacteristic
84C4×D4×C11C2×C411yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C4×D4×C11C2311yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C2×C11×C4⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C42×C11C2311yescharacteristic
92C2×#4318—21no—
93C2×#4318—21no—
94C22×C11⋊C8—21no—
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×#102C2×C411yescharacteristic
108C11×#102C2×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—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)D411yescharacteristic
126C22⋊(C11⋊C8)D411yescharacteristic
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)D411yescharacteristic
132C4⋊(C11⋊C8)D411yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17918—111nomaximal, Sylow
145C24×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C22×C411yescharacteristic
152C2×D4×C11C22×C411yescharacteristic
153C2×D4×C11C22×C411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—81no—
161C22×C4×C11—81no—
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C11×SD16—22no—
166C11×SD16—22no—
167C11×D8—22no—
168C11×D8—22no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C42×C11—21no—
192C42×C11C22×C411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11#4111yescharacteristic
195C42×C11C2411yescharacteristic
196#4318—81no—
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8—81no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8—81no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#3105D1111yescharacteristic
214#2993—111no—
215#2972—111no—
216#1586—111no—
217#1585—111no—
218#1582—111no—
219#1581—111no—
220#1580—111no—
221SD16⋊C8—111no—
222C8×SD16—111no—
223C8×D8—111no—
224#1574—111no—
225#1486—111no—
226#1482—111no—
227#1454—111no—
228C23×C11—24no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—81no—
233C23×C11—81no—
234C23×C11C4×D411yescharacteristic
235Q8×C11—21no—
236Q8×C11—21no—
237D4×C11—24no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—81no—
243D4×C11#13112yes—
244D4×C11#13112yes—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
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—81no—
262C2×C4×C11—81no—
263C2×C4×C11—81no—
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C4×D411yescharacteristic
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#529C2×D1111yescharacteristic
285C2×C4×D4C2×D1111yescharacteristic
286#484Dic1111yescharacteristic
287#481Dic1111yescharacteristic
288#478Dic1111yescharacteristic
289#478Dic1111yescharacteristic
290#463Dic1111yescharacteristic
291#463Dic1111yescharacteristic
292#450Dic1111yescharacteristic
293#447Dic1111yescharacteristic
294#446—111no—
295C8×Q8—111no—
296C4×SD16C2×D1111yescharacteristic
297C4×SD16C2×D1111yescharacteristic
298C4×D8C2×D1111yescharacteristic
299C4×D8C2×D1111yescharacteristic
300#436—111no—
301#436—221no—
302#435—221no—
303C8×D4—111no—
304C8×D4—111no—
305C8×D4—111no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—221no—
309C8×D4—221no—
310#433—221no—
311#431—111no—
312#431—111no—
313#431—111no—
314#431C2×D1111yescharacteristic
315#424—221no—
316#423—111no—
317C2×C22⋊C8—221no—
318C2×C22⋊C8—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331#322—111no—
332#322—111no—
333#322—111no—
334C82—111no—
335C22×C11—21no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—84no—
348C22×C11C2×C4×D411yescharacteristic
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11C2×#13111yescharacteristic
359C4×C11C2×#13111yescharacteristic
360C4×C11#57611yescharacteristic
361C4×C11#57711yescharacteristic
362C22×D4C2×Dic1111yescharacteristic
363C23×C4—21no—
364C2×SD16C2×Dic1111yescharacteristic
365C2×SD16C2×Dic1111yescharacteristic
366C2×D8C2×Dic1111yescharacteristic
367C2×D8C2×Dic1111yescharacteristic
368C2×M16—221no—
369C2×M16—221no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375#126—21no—
376#125C2×Dic1111yescharacteristic
377#124C2×Dic1111yescharacteristic
378#123—21no—
379C22⋊Q8C2×Dic1111yescharacteristic
380#121C2×Dic1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C2×Dic1111yescharacteristic
386C4×D4C2×Dic1111yescharacteristic
387C4×D4C22×D1111yescharacteristic
388C4×D4C22×D1111yescharacteristic
389C4×D4C22×D1111yescharacteristic
390#117—21no—
391C2×C4⋊C4C2×Dic1111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C42C22×D1111yescharacteristic
394#107C2×Dic1111yescharacteristic
395#107C2×Dic1111yescharacteristic
396#106C2×Dic1111yescharacteristic
397#106C2×Dic1111yescharacteristic
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C2×Dic1111yescharacteristic
409C4⋊C8C2×Dic1111yescharacteristic
410#103C2×Dic1111yescharacteristic
411#103C2×Dic1111yescharacteristic
412#102C2×Dic1111yescharacteristic
413#102C2×Dic1111yescharacteristic
414#102C2×Dic1111yescharacteristic
415#102C2×Dic1111yescharacteristic
416#102C2×Dic1111yescharacteristic
417#102C2×Dic1111yescharacteristic
418C22⋊C8—111no—
419C22⋊C8—111no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8C2×Dic1111yescharacteristic
429C22⋊C8C2×Dic1111yescharacteristic
430#97—221no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—221no—
436C4×C8—221no—
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C2×C11—41no—
440C2×C11—42no—
441C2×C11—42no—
442C2×C11—81no—
443C2×C11#292911yescharacteristic
444C2×C11#294611yescharacteristic
445C2×C11#295711yescharacteristic
446C24—21no—
447C2×Q8C22×Dic1111yescharacteristic
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4C22×Dic1111yescharacteristic
453C2×D4C22×Dic1111yescharacteristic
454C2×D4C22×Dic1111yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4D4×D1111yescharacteristic
464C22×C4#434111yescharacteristic
465C22×C4C22×Dic1111yescharacteristic
466SD16—22no—
467SD16—22no—
468D8—22no—
469D8—22no—
470M16—881no—
471M16—881no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—881no—
483C2×C8—881no—
484C2×C8—881no—
485C2×C8—881no—
486C2×C8—881no—
487C2×C8C22×Dic1111yescharacteristic
488C2×C8C22×Dic1111yescharacteristic
489C2×C8C22×Dic1111yescharacteristic
490C2×C8C22×Dic1111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C22×Dic1111yescharacteristic
497C4⋊C4C22×Dic1111yescharacteristic
498C4⋊C4C22×Dic1111yescharacteristic
499C4⋊C4C22×Dic1111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C42—21no—
510C42D4×D1111yescharacteristic
511C42#434111yescharacteristic
512C42C22×Dic1111yescharacteristic
513C42C23×D1111yescharacteristic
514C11#1791811yescharacteristic, complemented, Sylow
515C23—24no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—81no—
520C23—81no—
521C23D4×Dic1111yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—81no—
530D4#6700112yes—
531D4#6700112yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4D4×Dic1111yescharacteristic
552C2×C4D4×Dic1111yescharacteristic
553C2×C4D4×Dic1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4C2×#434111yescharacteristic
556C2×C4C23×Dic1111yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—221no—
565C8—441no—
566C8—441no—
567C8—441no—
568C8—441no—
569C8—441no—
570C8—441no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—22no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—84no—
584C22C2×D4×Dic1111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4#1062330511yescharacteristic
595C4#1062330611yescharacteristic
596C4C2×#6700111yescharacteristic
597C4C2×#6700111yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—81no—
602C2#1307731111yescharacteristic
603C2#1307744911yescharacteristic
604C2#1307753311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3105C2
socleC22×C11C2×C4×D4
prime radicalC11×#447C4
cosocleC42×C11C24
hypercenter#3105D11
hypocenterC11#17918
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

Complements

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

NH ≅ G/Ntype
1. #13077765C2semidirect
2. #13077640C2semidirect
3. #13067481C2semidirect
4. #13067474C2semidirect
5. #13067453C2semidirect
6. #13067446C2semidirect
7. #13067440C2semidirect
8. SD16⋊(C11⋊C8)C2semidirect
9. SD16×C11⋊C8C2semidirect
10. D8×C11⋊C8C2semidirect
11. #13067405C2semidirect
12. #13067041C2semidirect
13. #13067024C2semidirect
14. #13066916C2semidirect
33. #10622637C22semidirect
34. Q8×C11⋊C8C22semidirect
36. #10622625C22semidirect
44. D4×C11⋊C8C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
57. D4⋊(C11⋊C8)C22semidirect
58. D4⋊(C11⋊C8)C22semidirect
59. #10622096C22semidirect
60. #10622096C22semidirect
61. #10622095C22semidirect
62. #10622095C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
514. C11#17918semidirect

Maximal subgroups

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

subgroupindex
#130777652
#130776402
#130674812
#130674742
#130674532
#130674462
#130674402
SD16⋊(C11⋊C8)2
SD16×C11⋊C82
D8×C11⋊C82
#130674052
#130670412
#130670242
#130669162
C11×#31052
#1791811