Finite Group Databasebeta

← #14771578

Subgroups — #14771578

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊C4×D11C211yesmaximal, characteristic
2#13069339C211yesmaximal, characteristic, complemented
3#13069337C211yesmaximal, characteristic, complemented
4#13069180C211yesmaximal, characteristic, complemented
5#13069178C211yesmaximal, characteristic, complemented
6#13069173C211yesmaximal, characteristic, complemented
7#13069171C211yesmaximal, characteristic, complemented
8#13068595C211yesmaximal, characteristic
9#13068595C211yesmaximal, characteristic
10#13068593C211yesmaximal, characteristic
11#13068491C211yesmaximal, characteristic, complemented
12#13068379C211yesmaximal, characteristic
13#13068379C211yesmaximal, characteristic
14C4×(C2×D11)⋊C8C211yesmaximal, characteristic
15C11×#1771C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D11C411yescharacteristic
17C2×C4⋊C4×D11C411yescharacteristic
18C2×C42×D11C2211yescharacteristic
19C2×C42×D11C2211yescharacteristic
20C2×C42×D11C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C4⋊C4×Dic11C411yescharacteristic
35C4⋊C4×Dic11C411yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C4×Dic11⋊C4C2211yescharacteristic
38C4×Dic11⋊C4C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×#66867C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43D11×#95C411yescharacteristic
44D11×#95C411yescharacteristic
45#10622262C411yescharacteristic
46#10622262C411yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11C2×C411yescharacteristic
60C22×C4×D11C2×C411yescharacteristic
61C22×C4×D11C2×C411yescharacteristic
62C22×C4×D11C2×C411yescharacteristic
63C22×C4×D11C2×C411yescharacteristic
64C22×C4×D11C2×C411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×C4×Dic11C2×C411yescharacteristic
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C4⋊C4×D11—24no—
95C4⋊C4×D11—24no—
96C42×D11—22no—
97C42×D11—22no—
98C42×D11—41no—
99C42×D11—41no—
100C42×D11—41no—
101C42×D11—41no—
102C11×C4⋊C8—22no—
103C11×#97—22no—
104C11×#97—41no—
105C4×C8×C11—41no—
106C11×#95C2×C411yescharacteristic
107C11×#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C11⋊#95C2×C411yescharacteristic
113C11⋊#95C2×C411yescharacteristic
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117(C2×D11)⋊C8Q814yes—
118Dic11⋊C8—41no—
119Dic11⋊C8—41no—
120Dic11⋊C8—41no—
121Dic11⋊C8—41no—
122C4⋊(C11⋊C8)—22no—
123#66867—22no—
124#66867—41no—
125C4×C11⋊C8—41no—
126#22627—111nomaximal, Sylow
127C23×D11C22×C411yescharacteristic
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×C4×D11—41no—
159C2×C4×D11—41no—
160C2×C4×D11—41no—
161C2×C4×D11—41no—
162C2×C4×D11—41no—
163C2×C4×D11M1614yes—
164C2×C4×D11C2×Q812yes—
165C2×C4×D11#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×Q812yes—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11#4112yes—
185C42×C11#4112yes—
186C4⋊Dic11—22no—
187C4⋊Dic11—22no—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—22no—
191Dic11⋊C4M1614yes—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—41no—
201C4×Dic11—41no—
202C4×Dic11—41no—
203C4×Dic11—41no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×Q812yes—
216C2×C4×C4⋊C4—111no—
217#1940—111no—
218#1940—111no—
219#1917—111no—
220#1917—111no—
221#1916—111no—
222#1916—111no—
223#1797—111no—
224#1797—111no—
225#1797—111no—
226#1771—111no—
227#1771D1111yescharacteristic, complemented
228#1749—111no—
229#1749—111no—
230C4×C22⋊C8—111no—
231C23×C11C23×C411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11C4×Q812yes—
237C22×D11C2×M1612yes—
238C22×D11#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—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11#11712yes—
254C2×C4×C11#11712yes—
255C2×C4×C11C2×M1612yes—
256C2×C4×C11C2×M1612yes—
257C2×C4×C11C22×Q811yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11C4×Q812yes—
281C2×Dic11C2×M1612yes—
282C2×Dic11C2×M1612yes—
283C2×Dic11C2×M1612yes—
284C4×D11—28no—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—44no—
290C4×D11—44no—
291C4×D11—44no—
292C4×D11—44no—
293C4×D11—44no—
294C8×C11—22no—
295C8×C11—41no—
296C8×C11—41no—
297C8×C11—41no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—111no—
304C22×C42—111no—
305C22×C42—111no—
306C22×C42—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8C2×D1111yescharacteristic
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×#97—111no—
318C2×#97—111no—
319C2×#97C2×D1111yescharacteristic
320C2×#97C2×D1111yescharacteristic
321C2×C4×C8—111no—
322C2×C4×C8C2×D1111yescharacteristic
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4C2×D1111yescharacteristic
331C2×#95—111no—
332C2×#95—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342#336—111no—
343#336C2×D1111yescharacteristic
344#336C2×D1111yescharacteristic
345C22×C11C2×#11711yescharacteristic
346C22×C11C2×C4×Q811yescharacteristic
347C22×C11#51811yescharacteristic
348C22×C11C22×M1611yescharacteristic
349C22×C11C22×M1611yescharacteristic
350C22×C11C2×#13111yescharacteristic
351C22×C11#56811yescharacteristic
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11#44614yes—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—22no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11#55311yescharacteristic
366C4×C11#55311yescharacteristic
367C4×C11#55411yescharacteristic
368C4×C11#55411yescharacteristic
369Dic11—22no—
370Dic11—22no—
371Dic11—22no—
372Dic11—22no—
373Dic11—41no—
374Dic11—41no—
375Dic11—41no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—111no—
382C23×C4—111no—
383C22×C8—111no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8C22×D1111yescharacteristic
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—224no—
398C2×C4⋊C4—224no—
399C2×C4⋊C4C4×D1111yescharacteristic
400C2×C4⋊C4C4×D1111yescharacteristic
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—222no—
411C2×C42—222no—
412C2×C42—441no—
413C2×C42—441no—
414C2×C42—441no—
415C2×C42—441no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419C4⋊C8—22no—
420C4⋊C8—222no—
421C4⋊C8—441no—
422C4⋊C8—441no—
423C4⋊C8—441no—
424C4⋊C8—441no—
425C22⋊C8—114no—
426C22⋊C8—222no—
427C22⋊C8—222no—
428C22⋊C8—222no—
429#97—22no—
430#97—41no—
431#97—222no—
432#97—441no—
433C4×C8—41no—
434C4×C8—441no—
435#95—111no—
436#95—111no—
437#95—111no—
438#95—111no—
439#95—111no—
440#95—111no—
441#95C4×D1111yescharacteristic
442#95C4×D1111yescharacteristic
443C2×C11#234511yescharacteristic
444C2×C11#292011yescharacteristic
445C2×C11#292411yescharacteristic
446C2×C11C2×#44611yescharacteristic
447C2×C11Q8×M1611yescharacteristic
448C2×C11#297311yescharacteristic
449C2×C11#297411yescharacteristic
450D11—24no—
451C24—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—112no—
457C22×C4—112no—
458C22×C4—114no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—441no—
477C22×C4—441no—
478C22×C4—441no—
479C22×C4—441no—
480C22×C4—441no—
481C22×C4—441no—
482C22×C4—441no—
483C22×C4C2×C4×D1111yescharacteristic
484C22×C4C2×C4×D1111yescharacteristic
485C22×C4C2×C4×D1111yescharacteristic
486C22×C4C2×C4×D1111yescharacteristic
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4C2×C4×D1111yescharacteristic
489C22×C4C23×D1111yescharacteristic
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—112no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8Q8×D1112yes—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—114no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—222no—
527C42—222no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—441no—
535C42—441no—
536C42—441no—
537C42—441no—
538C42#433912yes—
539C42#433912yes—
540C11#2262711yescharacteristic, complemented, Sylow
541C23—112no—
542C23—112no—
543C23—112no—
544C23—221no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23C22×C4×D1111yescharacteristic
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—112no—
564C2×C4—112no—
565C2×C4—112no—
566C2×C4—112no—
567C2×C4—228no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—444no—
590C2×C4—444no—
591C2×C4—444no—
592C2×C4—444no—
593C2×C4—444no—
594C2×C4#6692512yes—
595C2×C4#6692512yes—
596C2×C4M16×D1112yes—
597C2×C4M16×D1112yes—
598C2×C4C2×#433911yescharacteristic
599C2×C4C2×#433911yescharacteristic
600C2×C4#6703711yescharacteristic
601C2×C4C2×Q8×D1111yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#6704211yescharacteristic
604C8—22no—
605C8—41no—
606C8—41no—
607C8—41no—
608C8—222no—
609C8—441no—
610C8—441no—
611C8—441no—
612C22—114no—
613C22—222no—
614C22—222no—
615C22—222no—
616C22—222no—
617C22—222no—
618C22—222no—
619C22C2×#6692511yescharacteristic
620C22#1062307611yescharacteristic
621C22C4×Q8×D1111yescharacteristic
622C22C2×M16×D1111yescharacteristic
623C22C2×M16×D1111yescharacteristic
624C22D11×#13111yescharacteristic
625C22#1062328111yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—222no—
633C4—222no—
634C4—222no—
635C4—222no—
636C4—441no—
637C4—441no—
638C4—441no—
639C4#1062304211yescharacteristic
640C4#1062306111yescharacteristic
641C4#1062308911yescharacteristic
642C4#1062311011yescharacteristic
643C2—224no—
644C2#1307148911yescharacteristic
645C2#1307724711yescharacteristic
646C2#1307727111yescharacteristic
647C2D11×#44611yescharacteristic
648C2#1307756811yescharacteristic
649C2#1307764111yescharacteristic
650C2#1307764611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1771C2
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1771D11
hypocenterC11#22627
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #13069339C2semidirect
3. #13069337C2semidirect
4. #13069180C2semidirect
5. #13069178C2semidirect
6. #13069173C2semidirect
7. #13069171C2semidirect
11. #13068491C2semidirect
15. C11×#1771C2semidirect
227. #1771D11semidirect
540. C11#22627semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊C4×D112
#130693392
#130693372
#130691802
#130691782
#130691732
#130691712
#130685952
#130685932
#130684912
#130683792
C4×(C2×D11)⋊C82
C11×#17712
#2262711