Finite Group Databasebeta

← #14764420

Subgroups — #14764420

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C42×D44C211yesmaximal, characteristic
2#13069223C212yesmaximal, complemented
3#13069172C212yesmaximal, complemented
4#13068907C212yesmaximal
5#13068795C212yesmaximal, complemented
6#13068733C211yesmaximal, characteristic, complemented
7#13068683C211yesmaximal, characteristic, complemented
8#13068595C211yesmaximal, characteristic, complemented
9#13068373C211yesmaximal, characteristic, complemented
10D11×#336C211yesmaximal, characteristic, complemented
11C11×#1839C211yesmaximal, characteristic, complemented
12C22×C8×D11C2212yes—
13C2×C4×D44C411yescharacteristic
14C2×C4×D44C411yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C2×C42×D11C2211yescharacteristic
17C2×C42×D11C2211yescharacteristic
18C43×C11C2211yescharacteristic
19C2×(C2×D11)⋊C8C2212yes—
20C2×(C2×D11)⋊C8C2212yes—
21C2×(C2×D11)⋊C8C2212yes—
22C2×Dic11⋊C8C2212yes—
23C2×C8×Dic11C2212yes—
24C4×(C2×D11)⋊C4C411yescharacteristic
25C4×(C2×D11)⋊C4C411yescharacteristic
26C4×(C2×D11)⋊C4C411yescharacteristic
27C4×(C2×D11)⋊C4C411yescharacteristic
28C4×(C2×D11)⋊C4C2211yescharacteristic
29C4×(C2×D11)⋊C4C2211yescharacteristic
30C4×C4⋊Dic11C411yescharacteristic
31C4×C4⋊Dic11C411yescharacteristic
32C4×C4⋊Dic11C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34C11×#336C2211yescharacteristic
35C11×#336C2211yescharacteristic
36C11×#336C2212yes—
37C11×#336C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40#10622162C2211yescharacteristic
41#10622162C2211yescharacteristic
42#10622162C2212yes—
43C22×D44C2×C411yescharacteristic
44C22×C4×D11C2×C411yescharacteristic
45C22×C4×D11C2×C411yescharacteristic
46C22×C4×D11C2×C411yescharacteristic
47C22×C4×D11C2×C411yescharacteristic
48C22×C4×D11C2311yescharacteristic
49C22×C4×D11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C2×C42×C11C2×C411yescharacteristic
53C2×C42×C11C2×C411yescharacteristic
54C2×C42×C11C2×C411yescharacteristic
55C2×C42×C11C2×C411yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2311yescharacteristic
59C2×(C2×D11)⋊C4C2×C411yescharacteristic
60C2×(C2×D11)⋊C4C2×C411yescharacteristic
61C2×(C2×D11)⋊C4C2×C411yescharacteristic
62C2×(C2×D11)⋊C4C2×C411yescharacteristic
63C2×(C2×D11)⋊C4C2×C411yescharacteristic
64C2×(C2×D11)⋊C4C2×C411yescharacteristic
65C2×C4⋊Dic11C2×C411yescharacteristic
66C2×C4⋊Dic11C2×C411yescharacteristic
67C2×C4⋊Dic11C2×C411yescharacteristic
68C2×C4×Dic11C2×C411yescharacteristic
69C2×C4×Dic11C2×C411yescharacteristic
70C2×C4×Dic11C2×C411yescharacteristic
71C2×C4×Dic11C2×C411yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75C22×C11⋊C8C2312yes—
76C2×C8×D11—24no—
77C2×C8×D11—42no—
78C2×C8×D11—42no—
79C4×D44—24no—
80C4×D44—24no—
81C4×D44C818yescomplemented
82C42×D11—42no—
83C42×D11—42no—
84C11⋊#95C2×C411yescharacteristic
85C11⋊#95C2×C411yescharacteristic
86C11⋊#95C2×C411yescharacteristic
87C11⋊#95C2×C411yescharacteristic
88C11⋊#95C2×C411yescharacteristic
89C11⋊#95C2×C411yescharacteristic
90(C2×D11)⋊C8—24no—
91(C2×D11)⋊C8—42no—
92(C2×D11)⋊C8—42no—
93Dic11⋊C8—42no—
94C8×Dic11—42no—
95C4⋊(C11⋊C8)—42no—
96#21996—111nomaximal, Sylow
97C23×D11C22×C411yescharacteristic
98C23×D11C22×C411yescharacteristic
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11C22×C411yescharacteristic
107C22×Dic11C22×C411yescharacteristic
108C22×Dic11C22×C411yescharacteristic
109C22×Dic11C22×C411yescharacteristic
110C22×Dic11C22×C411yescharacteristic
111C22×Dic11C22×C411yescharacteristic
112C2×D44—22no—
113C2×D44—22no—
114C2×D44C2×C814yes—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—22no—
121C2×C4×D11—21no—
122C2×C4×D11—21no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11—41no—
130C2×C4×D11—41no—
131C2×C4×D11C2×C814yes—
132C2×C4×D11C2×C814yescomplemented
133C2×C4×D11M1614yes—
134C2×C4×D11#4114yes—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—21no—
144C42×C11—22no—
145C42×C11—21no—
146C42×C11—41no—
147C42×C11—41no—
148C42×C11C2×C814yescomplemented
149(C2×D11)⋊C4—22no—
150(C2×D11)⋊C4—22no—
151(C2×D11)⋊C4—22no—
152(C2×D11)⋊C4—22no—
153(C2×D11)⋊C4C2×C814yes—
154(C2×D11)⋊C4C2×C814yescomplemented
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C2×C814yescomplemented
158C4×Dic11—22no—
159C4×Dic11—22no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C8×D11—48no—
171C42×D4—111no—
172#1923—112no—
173#1916—112no—
174#1869—112no—
175#1850—112no—
176#1839D1111yescharacteristic, complemented
177#1831—111no—
178#1817—111no—
179#1797—111no—
180C4×C22⋊C8—111no—
181C2×#336—111no—
182C23×C11C23×C411yescharacteristic
183C22×D11—21no—
184C22×D11—21no—
185C22×D11—21no—
186C22×D11—21no—
187C22×D11—21no—
188C22×D11—21no—
189C22×D11—21no—
190C22×D11—21no—
191C22×D11—21no—
192C22×D11—21no—
193C22×D11#11712yes—
194C22×D11C22×C812yes—
195C22×D11C22×C812yes—
196C22×D11C2×M1612yes—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11C22×C812yes—
212C2×C4×C11C22×C812yes—
213C2×C4×C11C22×C812yes—
214C2×C4×C11C2×M1612yes—
215C2×C4×C11C2×#4112yes—
216C2×C4×C11H(5,𝔽2)11yescharacteristic
217C2×C4×C11H(5,𝔽2)12yes—
218C2×C4×C112−1+411yescharacteristic
219C2×Dic11—21no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11#11712yes—
234C2×Dic11C22×C812yes—
235C2×Dic11C22×C812yes—
236C2×Dic11C2×M1612yes—
237D44—28no—
238C4×D11—24no—
239C4×D11—24no—
240C4×D11—44no—
241C4×D11—44no—
242C4×D11—44no—
243C4×D11—44no—
244C4×D11—42no—
245C4×D11—42no—
246C8×C11—42no—
247C8×C11—42no—
248C11⋊C8—42no—
249C11⋊C8—42no—
250C23×C8—112no—
251C2×C4×D4—111no—
252C2×C4×D4—111no—
253C2×C4×D4—111no—
254C22×C42—111no—
255C22×C42—111no—
256C2×C4⋊C8—112no—
257C2×C4⋊C8—112no—
258C2×C22⋊C8—112no—
259C2×C22⋊C8—112no—
260C2×C22⋊C8—112no—
261C2×C4×C8—112no—
262C4×C4⋊C4—111no—
263C4×C4⋊C4—111no—
264C4×C4⋊C4—111no—
265C4×C22⋊C4—111no—
266C4×C22⋊C4—111no—
267C4×C22⋊C4—111no—
268C4×C22⋊C4—111no—
269C4×C22⋊C4—111no—
270C4×C22⋊C4—111no—
271C43C2×D1111yescharacteristic
272#336—112no—
273#336—112no—
274#336—111no—
275#336—111no—
276#336—112no—
277#336C2×D1111yescharacteristic
278#336C2×D1111yescharacteristic
279#336C2×D1112yes—
280#336C2×D1112yes—
281C22×C11C2×#11711yescharacteristic
282C22×C11#51811yescharacteristic
283C22×C11#52011yescharacteristic
284C22×C11C23×C811yescharacteristic
285C22×C11C22×M1611yescharacteristic
286C22×C11#56811yescharacteristic
287C22×C11#56811yescharacteristic
288C2×D11—22no—
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—22no—
292C2×D11—22no—
293C2×D11—22no—
294C2×D11—22no—
295C2×D11—22no—
296C2×D11—22no—
297C2×D11—41no—
298C2×D11—41no—
299C2×D11—41no—
300C2×D11—41no—
301C2×D11#43114yes—
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—41no—
307C4×C11—41no—
308C4×C11#53812yes—
309C4×C11#53912yes—
310Dic11—22no—
311Dic11—22no—
312Dic11—22no—
313Dic11—22no—
314Dic11—41no—
315Dic11—41no—
316C22×D4—111no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—111no—
323C22×C8—112no—
324C22×C8—112no—
325C22×C8—224no—
326C22×C8—442no—
327C22×C8—442no—
328C22×C8C22×D1112yes—
329C22×C8C22×D1112yes—
330C4×D4—118no—
331C4×D4—224no—
332C4×D4—224no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C22⋊C4—111no—
337C2×C22⋊C4—111no—
338C2×C22⋊C4—111no—
339C2×C22⋊C4—111no—
340C2×C22⋊C4—111no—
341C2×C22⋊C4—111no—
342C2×C42—111no—
343C2×C42—111no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—111no—
347C2×C42—111no—
348C2×C42—442no—
349C2×C42—442no—
350C2×C42C4×D1111yescharacteristic
351C2×C42C4×D1111yescharacteristic
352C2×C42C4×D1111yescharacteristic
353C2×C42C4×D1111yescharacteristic
354C2×C42C22×D1111yescharacteristic
355C2×C42C22×D1111yescharacteristic
356C2×C42C22×D1111yescharacteristic
357C4⋊C8—442no—
358C4⋊C8—442no—
359C22⋊C8—224no—
360C22⋊C8—442no—
361C22⋊C8—442no—
362C4×C8—442no—
363#95—111no—
364#95—111no—
365#95—111no—
366#95—111no—
367#95—111no—
368#95—111no—
369C2×C11#231811yescharacteristic
370C2×C11C2×#43111yescharacteristic
371C2×C11#292311yescharacteristic
372C2×C11#297211yescharacteristic
373C2×C11#297311yescharacteristic
374C2×C11#298811yescharacteristic
375C2×C11#298911yescharacteristic
376D11—24no—
377D11—42no—
378C24—111no—
379C24—111no—
380C2×D4—114no—
381C2×D4—222no—
382C2×D4—222no—
383C22×C4—111no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—114no—
388C22×C4—114no—
389C22×C4—114no—
390C22×C4—114no—
391C22×C4—111no—
392C22×C4—111no—
393C22×C4—222no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—221no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4—441no—
405C22×C4—441no—
406C22×C4—441no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4C2×C4×D1111yescharacteristic
410C22×C4C2×C4×D1111yescharacteristic
411C22×C4C2×C4×D1111yescharacteristic
412C22×C4C2×C4×D1111yescharacteristic
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4C2×C4×D1111yescharacteristic
415C22×C4C23×D1111yescharacteristic
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—222no—
428C2×C8—448no—
429C4⋊C4—114no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C22⋊C4—114no—
433C22⋊C4—114no—
434C22⋊C4—222no—
435C22⋊C4—222no—
436C22⋊C4—222no—
437C22⋊C4—222no—
438C42—22no—
439C42—22no—
440C42—21no—
441C42—22no—
442C42—21no—
443C42—41no—
444C42—41no—
445C42—222no—
446C42—222no—
447C42—441no—
448C42—441no—
449C42—441no—
450C42—441no—
451C42C8×D1114yescomplemented
452C11#2199611yescharacteristic, complemented, Sylow
453C23—112no—
454C23—112no—
455C23—112no—
456C23—112no—
457C23—221no—
458C23—221no—
459C23—221no—
460C23—221no—
461C23—221no—
462C23—221no—
463C23—221no—
464C23—221no—
465C23—221no—
466C23—221no—
467C23C22×C4×D1111yescharacteristic
468D4—228no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—112no—
484C2×C4—112no—
485C2×C4—112no—
486C2×C4—112no—
487C2×C4—221no—
488C2×C4—221no—
489C2×C4—221no—
490C2×C4—221no—
491C2×C4—221no—
492C2×C4—221no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—444no—
504C2×C4—444no—
505C2×C4—444no—
506C2×C4—444no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4C2×C8×D1112yes—
510C2×C4C2×C8×D1112yes—
511C2×C4C2×C8×D1112yes—
512C2×C4M16×D1112yes—
513C2×C4#41×D1112yes—
514C2×C4#6704211yescharacteristic
515C2×C4#6704212yes—
516C2×C4#6704311yescharacteristic
517C8—42no—
518C8—42no—
519C8—442no—
520C8—442no—
521C22—114no—
522C22—222no—
523C22—222no—
524C22—222no—
525C22—222no—
526C22—222no—
527C22—222no—
528C22—222no—
529C22—222no—
530C22—222no—
531C22—441no—
532C22—441no—
533C22—441no—
534C22—441no—
535C22D11×#11711yescharacteristic
536C22#1062305211yescharacteristic
537C22#1062305411yescharacteristic
538C22C22×C8×D1111yescharacteristic
539C22C2×M16×D1111yescharacteristic
540C22#1062327611yescharacteristic
541C22#1062327611yescharacteristic
542C4—22no—
543C4—22no—
544C4—22no—
545C4—22no—
546C4—41no—
547C4—41no—
548C4—222no—
549C4—222no—
550C4—222no—
551C4—222no—
552C4—441no—
553C4—441no—
554C4#1062323512yes—
555C4#1062323812yes—
556C2—224no—
557C2—442no—
558C2#1307124711yescharacteristic
559C2D11×#43111yescharacteristic
560C2#1307726211yescharacteristic
561C2#1307763911yescharacteristic
562C2#1307764411yescharacteristic
563C2#1307772411yescharacteristic
564C2#1307773511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC11×#1839C2
socleC23×C11C23×C4
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1839D11
hypocenterC11#21996
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1839

Complements

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

NH ≅ G/Ntype
2. #13069223C2semidirect
3. #13069172C2semidirect
5. #13068795C2semidirect
6. #13068733C2semidirect
7. #13068683C2semidirect
8. #13068595C2semidirect
9. #13068373C2semidirect
10. D11×#336C2semidirect
11. C11×#1839C2semidirect
81. C4×D44C8semidirect
132. C2×C4×D11C2×C8semidirect
148. C42×C11C2×C8semidirect
154. (C2×D11)⋊C4C2×C8semidirect
157. C4⋊Dic11C2×C8semidirect
176. #1839D11semidirect
451. C42C8×D11semidirect
452. C11#21996semidirect

Maximal subgroups

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

subgroupindex
C42×D442
#130692232
#130691722
#130689072
#130687952
#130687332
#130686832
#130685952
#130683732
D11×#3362
C11×#18392
#2199611