Finite Group Databasebeta

← #14752491

Subgroups — #14752491

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622340C211yesmaximal, characteristic
2C2×#10622340C211yesmaximal, characteristic
3#13071104C211yesmaximal, characteristic
4#13068401C211yesmaximal, characteristic, complemented
5#13068399C211yesmaximal, characteristic, complemented
6#13068398C211yesmaximal, characteristic, complemented
7#13068396C211yesmaximal, characteristic, complemented
8#13068393C211yesmaximal, characteristic, complemented
9#13068391C211yesmaximal, characteristic, complemented
10C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11#13068386C211yesmaximal, characteristic, complemented
12#13068382C211yesmaximal, characteristic, complemented
13#13068380C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1750C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622601C412yes—
38#10622587C412yes—
39#10622571C412yes—
40#10622571C412yes—
41C4×(C2×D11)⋊C4C2211yescharacteristic
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×(C2×D11)⋊C4C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622340C418yescomplemented
48#10622340C418yescomplemented
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11C2×C411yescharacteristic
59C22×C22⋊D11C2×C411yescharacteristic
60C23×Dic11C2×C412yes—
61C2×#4339—41no—
62C2×#4339—41no—
63C2×#4339—41no—
64C2×#4339—41no—
65C2×#4339C2×C414yes—
66C2×#4339C2×C414yes—
67C22×D44C2×C411yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×C4×D11C2311yescharacteristic
70C22×Dic22C2×C411yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#117—41no—
76C11×#117—41no—
77C2×C11×C4⋊C4C2×C412yes—
78C2×C11×C22⋊C4C2×C412yes—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×(C2×D11)⋊C4C2×C412yes—
82C2×(C2×D11)⋊C4C2×C412yes—
83C2×(C2×D11)⋊C4C2×C412yes—
84C2×(C2×D11)⋊C4C2×C412yes—
85C2×C4×Dic11—41no—
86C2×C4×Dic11—41no—
87C2×C4×Dic11C2×C412yes—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×#4313—41no—
95C2×#4313—41no—
96C2×#4313—41no—
97C2×#4313—41no—
98C2×#4313C2×C414yescomplemented
99C2×#4313C2×C414yescomplemented
100C2×C8×D11—41no—
101C2×C8×D11—41no—
102C2×C8×D11—41no—
103C2×C8×D11—41no—
104C2×C8×D11C2×C414yescomplemented
105C2×C8×D11C2×C414yescomplemented
106C11×C22⋊C8C2×C414yes—
107C11×C22⋊C8C2×C414yes—
108C11×#97—41no—
109C4×C8×C11—41no—
110C11⋊#95C2×C412yes—
111C11⋊#95C2×C412yes—
112C11⋊#95C2×C412yes—
113C11⋊#95C2×C412yes—
114C22⋊(C11⋊C8)C2×C414yes—
115C22⋊(C11⋊C8)C2×C414yes—
116(C2×D11)⋊C8C2×C414yescomplemented
117(C2×D11)⋊C8C2×C414yescomplemented
118(C2×D11)⋊C8C2×C414yescomplemented
119(C2×D11)⋊C8C2×C414yescomplemented
120#66879—41no—
121#66879—41no—
122C8×Dic11—41no—
123C8×Dic11—41no—
124#66867—41no—
125C4×C11⋊C8—41no—
126#20531—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C23×D11C22×C411yescharacteristic
129C23×D11C22×C411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C2×C22⋊D11C4214yes—
145C2×C22⋊D11C4214yes—
146C22×Dic11—24no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11C22×C412yes—
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C412yes—
153#4339—44no—
154#4339—44no—
155#4339—44no—
156#4339—44no—
157C2×D44—41no—
158C2×D44—41no—
159C2×D44C4214yes—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11C22×C412yes—
169C2×C4×D11C22×C412yes—
170C2×C4×D11C22×C412yes—
171C2×C4×D11C22×C412yes—
172C2×Dic22—41no—
173C2×Dic22—41no—
174C2×Dic22C4214yes—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11C22×C412yes—
184C2×C8×C11C22×C412yes—
185C2×C8×C11C22×C412yes—
186C2×C8×C11C22×C412yes—
187C11×C4⋊C4—42no—
188C11×C22⋊C4—42no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—24no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
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⋊C8C22×C412yes—
211C2×C11⋊C8C22×C412yes—
212C2×C11⋊C8C22×C412yes—
213C2×C11⋊C8C22×C412yes—
214#4313—44no—
215#4313—44no—
216C8×D11—44no—
217C8×D11—44no—
218C2×#408—111no—
219C2×#408—111no—
220#2297—111no—
221#1753—111no—
222#1753—111no—
223#1753—111no—
224#1753—111no—
225#1752—111no—
226#1752—111no—
227C8×C22⋊C4—111no—
228C8×C22⋊C4—111no—
229#1750—111no—
230#1750D1111yescharacteristic, complemented
231#1749—111no—
232C4×C22⋊C8—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11C2×C4212yes—
238C23×C11C23×C411yescharacteristic
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11C2×C4212yes—
248C22×D11C2×C4212yes—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11C2×C4212yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C22⋊D11—44no—
269C22⋊D11—44no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—48no—
280C2×Dic11C2×C4212yes—
281C2×Dic11C2×C4212yes—
282C2×Dic11#13114yes—
283D44—44no—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—22no—
292Dic22—44no—
293C8×C11—22no—
294C8×C11—22no—
295C8×C11—22no—
296C8×C11—22no—
297C11⋊C8—22no—
298C11⋊C8—22no—
299C11⋊C8—22no—
300C11⋊C8—22no—
301C22×#41—111no—
302C22×M16—111no—
303C22×M16—111no—
304C23×C8—111no—
305C23×C8—111no—
306C2×#117C2×D1111yescharacteristic
307C22×C42—111no—
308#408—118no—
309#408—118no—
310C2×C22⋊C8—111no—
311C2×C22⋊C8—111no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8C2×D1111yescharacteristic
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×#97—111no—
319C2×#97—111no—
320C2×#97—111no—
321C2×#97C2×D1111yescharacteristic
322C2×C4×C8—111no—
323C2×C4×C8—111no—
324C2×C4×C8—111no—
325C2×C4×C8C2×D1111yescharacteristic
326#391—112no—
327#390—112no—
328#386—112no—
329#386—112no—
330C4×C22⋊C4—111no—
331C4×C22⋊C4—111no—
332C4×C22⋊C4—111no—
333C4×C22⋊C4—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336C2×D1111yescharacteristic
341#336C2×D1111yescharacteristic
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11C22×C4211yescharacteristic
348C22×C11#51811yescharacteristic
349C22×C11#51811yescharacteristic
350C22×C11C2×#13112yes—
351C22×C11#56812yes—
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C4×C11—22no—
363C4×C11—42no—
364C4×C11—42no—
365C4×C11#51811yescharacteristic
366C4×C11#51811yescharacteristic
367C4×C11#51811yescharacteristic
368C4×C11#51811yescharacteristic
369Dic11—24no—
370Dic11—22no—
371Dic11—22no—
372Dic11—42no—
373C2×#41—114no—
374C2×#41—114no—
375C2×#41—441no—
376C2×#41—441no—
377C2×#41—441no—
378C2×#41—441no—
379C22×Q8—111no—
380C22×D4—111no—
381C22×D4—111no—
382C22×D4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—112no—
386C23×C4C22×D1111yescharacteristic
387C2×M16—114no—
388C2×M16—114no—
389C2×M16—441no—
390C2×M16—441no—
391C2×M16—441no—
392C2×M16—441no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—114no—
398C22×C8—114no—
399C22×C8—441no—
400C22×C8—441no—
401C22×C8—441no—
402C22×C8—441no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406C22×C8C22×D1111yescharacteristic
407#117—41no—
408#117—41no—
409C2×C4⋊C4C4×D1112yes—
410C2×C22⋊C4—112no—
411C2×C22⋊C4—112no—
412C2×C22⋊C4—112no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4C4×D1112yes—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—112no—
418C2×C42—441no—
419C2×C42—441no—
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C22⋊C8—114no—
423C22⋊C8—114no—
424C22⋊C8—114no—
425C22⋊C8—114no—
426C22⋊C8—114no—
427C22⋊C8—114no—
428C22⋊C8C4×D1114yes—
429C22⋊C8C4×D1114yes—
430#97—41no—
431#97—441no—
432#97—441no—
433#97—441no—
434C4×C8—41no—
435C4×C8—441no—
436C4×C8—441no—
437C4×C8—441no—
438#95—112no—
439#95—112no—
440#95—112no—
441#95—112no—
442C2×C11—42no—
443C2×C11#227311yescharacteristic
444C2×C11C4×#13111yescharacteristic
445C2×C11#287511yescharacteristic
446C2×C11#297612yes—
447C2×C11#298112yes—
448D11—42no—
449D11—42no—
450C24—111no—
451C24—111no—
452C24C2×C4×D1111yescharacteristic
453#41—444no—
454#41—444no—
455#41—444no—
456#41—444no—
457C2×Q8—114no—
458C2×Q8—441no—
459C2×Q8—441no—
460C2×D4—114no—
461C2×D4—114no—
462C2×D4—114no—
463C2×D4—441no—
464C2×D4—441no—
465C2×D4—441no—
466C2×D4—441no—
467C2×D4—441no—
468C2×D4—441no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—112no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—224no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4C2×C4×D1112yes—
493C22×C4C2×C4×D1112yes—
494C22×C4C2×C4×D1111yescharacteristic
495C22×C4C2×C4×D1112yes—
496C22×C4C2×C4×D1112yes—
497C22×C4C23×D1111yescharacteristic
498M16—444no—
499M16—444no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—112no—
509C2×C8—112no—
510C2×C8—112no—
511C2×C8—112no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—444no—
521C2×C8—444no—
522C2×C8C2×C4×D1112yes—
523C2×C8C2×C4×D1112yes—
524C2×C8C2×C4×D1112yes—
525C2×C8C2×C4×D1112yes—
526C4⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—224no—
529C22⋊C4—224no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—221no—
537C42—221no—
538C42—221no—
539C42—221no—
540C42—442no—
541C11#2053111yescharacteristic, complemented, Sylow
542C23—21no—
543C23—22no—
544C23—22no—
545C23—21no—
546C23—112no—
547C23—112no—
548C23—221no—
549C23—221no—
550C23—222no—
551C23—222no—
552C23—222no—
553C23—222no—
554C23—221no—
555C23—221no—
556C23C42×D1112yes—
557C23C22×C4×D1111yescharacteristic
558Q8—444no—
559D4—444no—
560D4—444no—
561D4—444no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—112no—
575C2×C4—112no—
576C2×C4—114no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—448no—
595C2×C4C42×D1112yes—
596C2×C4C22×C4×D1111yescharacteristic
597C2×C4C22×C4×D1111yescharacteristic
598C2×C4#6703711yescharacteristic
599C2×C4#6703711yescharacteristic
600C2×C4#6704211yescharacteristic
601C2×C4#6704211yescharacteristic
602C8—22no—
603C8—22no—
604C8—22no—
605C8—22no—
606C8—222no—
607C8—222no—
608C8—222no—
609C8—222no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—42no—
614C22—42no—
615C22—222no—
616C22—222no—
617C22—222no—
618C22—222no—
619C22—222no—
620C22—222no—
621C22—442no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22C2×C42×D1111yescharacteristic
626C22#1062301711yescharacteristic
627C22#1062305211yescharacteristic
628C22D11×#13112yes—
629C22#1062328112yes—
630C4—22no—
631C4—42no—
632C4—42no—
633C4—222no—
634C4—222no—
635C4—224no—
636C4—442no—
637C4#1062307611yescharacteristic
638C4#1062307611yescharacteristic
639C4#1062307611yescharacteristic
640C4#1062307611yescharacteristic
641C2—42no—
642C2—442no—
643C2—442no—
644C2#1307096811yescharacteristic
645C2#1307703811yescharacteristic
646C2#1307704311yescharacteristic
647C2#1307766212yes—
648C2#1307768912yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#1750C2
socleC23×C11C23×C4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1750D11
hypocenterC11#20531
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
4. #13068401C2semidirect
5. #13068399C2semidirect
6. #13068398C2semidirect
7. #13068396C2semidirect
8. #13068393C2semidirect
9. #13068391C2semidirect
10. C8×(C2×D11)⋊C4C2semidirect
11. #13068386C2semidirect
12. #13068382C2semidirect
13. #13068380C2semidirect
14. C22⋊C8×Dic11C2semidirect
15. C11×#1750C2semidirect
47. #10622340C4semidirect
48. #10622340C4semidirect
98. C2×#4313C2×C4semidirect
99. C2×#4313C2×C4semidirect
104. C2×C8×D11C2×C4semidirect
105. C2×C8×D11C2×C4semidirect
116. (C2×D11)⋊C8C2×C4semidirect
117. (C2×D11)⋊C8C2×C4semidirect
118. (C2×D11)⋊C8C2×C4semidirect
119. (C2×D11)⋊C8C2×C4semidirect
230. #1750D11semidirect
541. C11#20531semidirect

Maximal subgroups

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

subgroupindex
C2×#106223402
#130711042
#130684012
#130683992
#130683982
#130683962
#130683932
#130683912
C8×(C2×D11)⋊C42
#130683862
#130683822
#130683802
C22⋊C8×Dic112
C11×#17502
#2053111