Finite Group Databasebeta

← #14775868

Subgroups — #14775868

Order 2816.

692 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
1#13077565C211yesmaximal, characteristic, complemented
2#13077184C211yesmaximal, characteristic
3#13069598C211yesmaximal, characteristic, complemented
4#13069392C211yesmaximal, characteristic, complemented
5#13069370C211yesmaximal, characteristic, complemented
6#13069365C211yesmaximal, characteristic, complemented
7#13069217C211yesmaximal, characteristic, complemented
8#13069217C211yesmaximal, characteristic, complemented
9#13068893C211yesmaximal, characteristic
10#13068893C211yesmaximal, characteristic
11#13068475C211yesmaximal, characteristic, complemented
12#13068463C211yesmaximal, characteristic
13#13068456C211yesmaximal, characteristic
14#13068426C211yesmaximal, characteristic
15C11×#3076C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19C2×#67001C2211yescharacteristic
20C11×#479C411yescharacteristic, complemented
21C11×#479C411yescharacteristic, complemented
22C11×#478C411yescharacteristic, complemented
23C11×#478C411yescharacteristic, complemented
24C11×#477C411yescharacteristic, complemented
25C11×#476C411yescharacteristic, complemented
26C11×#475C411yescharacteristic, complemented
27C11×#474C411yescharacteristic, complemented
28C11×#427C2211yescharacteristic
29C11×#427C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C11×#416C2211yescharacteristic
32C11×#416C2211yescharacteristic
33C2×#66901C2211yescharacteristic
34C2×#66901C2211yescharacteristic
35C2×#66883C2211yescharacteristic
36C2×#66883C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622637—21no—
40#10622637—21no—
41#10622637—21no—
42Q8×C11⋊C8—21no—
43#10622612—21no—
44#10622612—21no—
45#10622612C2211yescharacteristic
46#10622612C2211yescharacteristic
47#10622612C2211yescharacteristic
48#10622612C2211yescharacteristic
49#10622610C2211yescharacteristic
50#10622610C2211yescharacteristic
51#10622545C2211yescharacteristic
52#10622537—21no—
53#10622537C2211yescharacteristic
54C2×C4⋊(C11⋊C8)—21no—
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C4×#4318C2211yescharacteristic
57#10622190C2211yescharacteristic
58#10622190C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622170C2211yescharacteristic
62#10622170C2211yescharacteristic
63#10622170C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622170C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8C2×C411yescharacteristic
71C11×C4⋊Q8C2×C411yescharacteristic
72C11×#125C2×C411yescharacteristic
73C11×#125C2×C411yescharacteristic
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11C2×C411yescharacteristic
79C4×Q8×C11C2×C411yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11C2×C411yescharacteristic
83C4×D4×C11C2×C411yescharacteristic
84C11×#117—21no—
85C11×#117C2311yescharacteristic
86C11×#117C2311yescharacteristic
87C11×#117C2311yescharacteristic
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90#67001—22no—
91#67001—22no—
92#67001—41no—
93#67001—41no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318C2311yescharacteristic
99C2×#4318C2311yescharacteristic
100C2×#4318C2311yescharacteristic
101C2×#4318C2311yescharacteristic
102C22×C11⋊C8—21no—
103C22×C11⋊C8—21no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C11×#107C2×C411yescharacteristic
107C11×#107C2×C411yescharacteristic
108C11×#107C2×C411yescharacteristic
109C11×#107C2×C411yescharacteristic
110C11×#106C2×C411yescharacteristic
111C11×#106C2×C411yescharacteristic
112C11×#106C2×C411yescharacteristic
113C11×#106C2×C411yescharacteristic
114C11×C4⋊C8C2×C411yescharacteristic
115C11×C4⋊C8C2×C411yescharacteristic
116C11×C4⋊C8C2×C411yescharacteristic
117C11×C4⋊C8C2×C411yescharacteristic
118C11×#103C2×C411yescharacteristic
119C11×#103C2×C411yescharacteristic
120C11×#103C2×C411yescharacteristic
121C11×#103C2×C411yescharacteristic
122C11×#102C2×C411yescharacteristic
123C11×#102C2×C411yescharacteristic
124C11×#102C2×C411yescharacteristic
125C11×#102C2×C411yescharacteristic
126#66901—22no—
127#66901Q814yescomplemented
128C11⋊#95—21no—
129C11⋊#95—21no—
130#66883—41no—
131#66883—41no—
132#66879—41no—
133C8×Dic11—41no—
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)—21no—
144C4⋊(C11⋊C8)D411yescharacteristic
145C4⋊(C11⋊C8)D411yescharacteristic
146C4⋊(C11⋊C8)D411yescharacteristic
147C4⋊(C11⋊C8)D411yescharacteristic
148#66867—21no—
149#66867—21no—
150#66867—21no—
151C4×C11⋊C8—21no—
152C4×C11⋊C8—21no—
153C4×C11⋊C8—21no—
154#22984—111nomaximal, Sylow
155C11×#41—21no—
156C11×#41—21no—
157C11×#41C2×Q812yes—
158C11×#41#4112yes—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11C22×C411yescharacteristic
162C2×D4×C11—21no—
163C2×D4×C11C22×C411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11#4111yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—21no—
171C22×Dic11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C22×C411yescharacteristic
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C4⋊C4C22×C411yescharacteristic
191C11×C4⋊C4C22×C411yescharacteristic
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11C22×C411yescharacteristic
205C42×C11C22×C411yescharacteristic
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11C2×Q812yes—
212#4318—21no—
213#4318—21no—
214#4318—21no—
215#4318—21no—
216#4318—21no—
217#4318—21no—
218#4318—21no—
219#4318—42no—
220#4318—42no—
221#4318C2×Q812yes—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—42no—
231C2×C11⋊C8—42no—
232C2×C11⋊C8C2×D411yescharacteristic
233C2×C11⋊C8C2×D411yescharacteristic
234C2×C11⋊C8C2×D411yescharacteristic
235C2×C11⋊C8C2×D411yescharacteristic
236#3076D1111yescharacteristic
237#2962—111no—
238#2906—111no—
239#1995—111no—
240#1950—111no—
241#1946—111no—
242#1945—111no—
243#1922—111no—
244#1922—111no—
245#1866—111no—
246#1866—111no—
247#1768—111no—
248#1765—111no—
249#1764—111no—
250#1759—111no—
251C23×C11—21no—
252C23×C11C2×#4111yescharacteristic
253Q8×C11—21no—
254Q8×C11—42no—
255Q8×C11—81no—
256Q8×C11C4×Q812yes—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—21no—
260D4×C11C4×Q812yes—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—81no—
274C2×C4×C11C4×D411yescharacteristic
275C2×C4×C11C4×D411yescharacteristic
276C2×C4×C11C4×D411yescharacteristic
277C2×C4×C11C4×D411yescharacteristic
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×Q811yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C2×Dic11—22no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C8×C11—21no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—21no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—21no—
297C11⋊C8—21no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C2×#131—111no—
303C2×#131—111no—
304#533C2×D1111yescharacteristic
305C4×#41C2×D1111yescharacteristic
306#479Dic1111yescharacteristic, complemented
307#479Dic1111yescharacteristic, complemented
308#478Dic1111yescharacteristic, complemented
309#478Dic1111yescharacteristic, complemented
310#477Dic1111yescharacteristic, complemented
311#476Dic1111yescharacteristic, complemented
312#475Dic1111yescharacteristic, complemented
313#474Dic1111yescharacteristic, complemented
314#446—221no—
315#446—221no—
316#446—221no—
317C8×Q8—221no—
318C2×#108—111no—
319C2×#108—111no—
320#427C2×D1111yescharacteristic
321#427C2×D1111yescharacteristic
322#424—111no—
323#424—111no—
324#424—111no—
325#424—111no—
326#424—221no—
327#424—221no—
328#423—111no—
329#423—221no—
330C2×C4⋊C8—111no—
331C2×C4⋊C8—221no—
332C2×C4⋊C8C2×D1111yescharacteristic
333C2×#104—111no—
334C2×#104—111no—
335#416C2×D1111yescharacteristic
336#416C2×D1111yescharacteristic
337#405—111no—
338#405—111no—
339C4×M16—111no—
340C2×#97—111no—
341C2×C4×C8—111no—
342#376—111no—
343#341—111no—
344#341—111no—
345#339—111no—
346#339—111no—
347#339—111no—
348#339—111no—
349#339—111no—
350#339—111no—
351#336—111no—
352#336—111no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11C2×C4×D411yescharacteristic
359C22×C11#55211yescharacteristic
360C22×C11#55411yescharacteristic
361C4×C11—22no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11C2×C4×Q811yescharacteristic
373C4×C11#52011yescharacteristic
374C4×C11#54611yescharacteristic
375C4×C11D4×Q811yescharacteristic
376Dic11—42no—
377Dic11—81no—
378C2×#41C22×D1111yescharacteristic
379#131—222no—
380#131—222no—
381#131—441no—
382#131—441no—
383C2×M16—111no—
384C2×M16—111no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16—221no—
388C2×M16—221no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—221no—
392C22×C8—221no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C4⋊Q8C2×Dic1111yescharacteristic
396C4⋊Q8C2×Dic1111yescharacteristic
397#125C2×Dic1111yescharacteristic
398#125C2×Dic1111yescharacteristic
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8C2×Dic1111yescharacteristic
404C4×Q8C2×Dic1111yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C2×Dic1111yescharacteristic
408C4×D4C2×Dic1111yescharacteristic
409#117—21no—
410#117C22×D1111yescharacteristic
411#117C22×D1111yescharacteristic
412#117C22×D1111yescharacteristic
413C2×C42—21no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42C22×D1111yescharacteristic
417#108—441no—
418#108—441no—
419#107C2×Dic1111yescharacteristic
420#107C2×Dic1111yescharacteristic
421#107C2×Dic1111yescharacteristic
422#107C2×Dic1111yescharacteristic
423#106C2×Dic1111yescharacteristic
424#106C2×Dic1111yescharacteristic
425#106C2×Dic1111yescharacteristic
426#106C2×Dic1111yescharacteristic
427C4⋊C8—111no—
428C4⋊C8—111no—
429C4⋊C8—111no—
430C4⋊C8—111no—
431C4⋊C8—221no—
432C4⋊C8—221no—
433C4⋊C8—221no—
434C4⋊C8—221no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439C4⋊C8—221no—
440C4⋊C8—221no—
441C4⋊C8C2×Dic1111yescharacteristic
442C4⋊C8C2×Dic1111yescharacteristic
443C4⋊C8C2×Dic1111yescharacteristic
444C4⋊C8C2×Dic1111yescharacteristic
445#104—114no—
446#104—222no—
447#103C2×Dic1111yescharacteristic
448#103C2×Dic1111yescharacteristic
449#103C2×Dic1111yescharacteristic
450#103C2×Dic1111yescharacteristic
451#102C2×Dic1111yescharacteristic
452#102C2×Dic1111yescharacteristic
453#102C2×Dic1111yescharacteristic
454#102C2×Dic1111yescharacteristic
455#97—221no—
456#97—221no—
457#97—221no—
458#97—441no—
459C4×C8—221no—
460C4×C8—221no—
461C4×C8—221no—
462C4×C8—441no—
463#95—221no—
464#95—221no—
465C2×C11—21no—
466C2×C11—21no—
467C2×C11—42no—
468C2×C11#236011yescharacteristic
469C2×C11#295511yescharacteristic
470C2×C11#295711yescharacteristic
471#41—21no—
472#41—21no—
473#41Q8×D1112yes—
474#41#434312yes—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C22×Dic1111yescharacteristic
478C2×D4—21no—
479C2×D4C22×Dic1111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4#434111yescharacteristic
486C22×C4#434111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488M16—112no—
489M16—221no—
490M16—221no—
491M16—221no—
492M16—221no—
493M16—221no—
494M16—221no—
495M16—221no—
496M16—442no—
497M16—442no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—111no—
503C2×C8—111no—
504C2×C8—111no—
505C2×C8—111no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—442no—
515C2×C8—442no—
516C2×C8C22×Dic1111yescharacteristic
517C2×C8C22×Dic1111yescharacteristic
518C2×C8C22×Dic1111yescharacteristic
519C2×C8C22×Dic1111yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4C22×Dic1111yescharacteristic
529C4⋊C4C22×Dic1111yescharacteristic
530C4⋊C4C22×Dic1111yescharacteristic
531C4⋊C4C22×Dic1111yescharacteristic
532C4⋊C4C22×Dic1111yescharacteristic
533C4⋊C4C22×Dic1111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—112no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42D4×D1111yescharacteristic
549C42D4×D1111yescharacteristic
550C42C22×Dic1111yescharacteristic
551C42C22×Dic1111yescharacteristic
552C11#2298411yescharacteristic, complemented, Sylow
553C23—21no—
554C23C2×#434111yescharacteristic
555Q8—21no—
556Q8—42no—
557Q8—81no—
558Q8Q8×Dic1112yes—
559D4—22no—
560D4—22no—
561D4—21no—
562D4Q8×Dic1112yes—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—81no—
576C2×C4—222no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4D4×Dic1111yescharacteristic
583C2×C4D4×Dic1111yescharacteristic
584C2×C4D4×Dic1111yescharacteristic
585C2×C4D4×Dic1111yescharacteristic
586C2×C4C2×D4×D1111yescharacteristic
587C2×C4C2×Q8×D1111yescharacteristic
588C2×C4C2×#434311yescharacteristic
589C2×C4#6704211yescharacteristic
590C2×C4#6704311yescharacteristic
591C2×C4C23×Dic1111yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—221no—
597C8—221no—
598C8—221no—
599C8—221no—
600C8—222no—
601C8—441no—
602C8—441no—
603C8—441no—
604C22—21no—
605C22—21no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22#1062316611yescharacteristic
610C22#1062317311yescharacteristic
611C22C2×D4×Dic1111yescharacteristic
612C4—22no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—442no—
624C4—881no—
625C4#1062316111yescharacteristic
626C4#1062316311yescharacteristic
627C4C2×Q8×Dic1111yescharacteristic
628C4#1062335811yescharacteristic
629C2—21no—
630C2—21no—
631C2—42no—
632C2#1307162511yescharacteristic
633C2#1307751911yescharacteristic
634C2#1307753311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#3076C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#3076D11
hypocenterC11#22984
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #13077565C2semidirect
3. #13069598C2semidirect
4. #13069392C2semidirect
5. #13069370C2semidirect
6. #13069365C2semidirect
7. #13069217C2semidirect
8. #13069217C2semidirect
11. #13068475C2semidirect
20. C11×#479C4semidirect
21. C11×#479C4semidirect
22. C11×#478C4semidirect
23. C11×#478C4semidirect
24. C11×#477C4semidirect
25. C11×#476C4semidirect
26. C11×#475C4semidirect
27. C11×#474C4semidirect
127. #66901Q8semidirect
306. #479Dic11semidirect
307. #479Dic11semidirect
308. #478Dic11semidirect
309. #478Dic11semidirect
310. #477Dic11semidirect
311. #476Dic11semidirect
312. #475Dic11semidirect
313. #474Dic11semidirect
552. C11#22984semidirect

Maximal subgroups

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

subgroupindex
#130775652
#130771842
#130695982
#130693922
#130693702
#130693652
#130692172
#130688932
#130684752
#130684632
#130684562
#130684262
C11×#30762
#2298411