Finite Group Databasebeta

← #14770493

Subgroups — #14770493

Order 2816.

1136 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3C2×C8×Dic22C211yesmaximal, characteristic, complemented
4#13069412C212yesmaximal, complemented
5#13069410C211yesmaximal, characteristic, complemented
6#13069410C211yesmaximal, characteristic, complemented
7#13069408C212yesmaximal, complemented
8#13068599C212yesmaximal, complemented
9#13068596C211yesmaximal, characteristic, complemented
10#13068381C212yesmaximal, complemented
11C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×C42×C11C2211yescharacteristic
13C2×#66983C411yescharacteristic
14C2×#66982C412yes—
15C2×C4×C22⋊D11C2212yes—
16C2×#66977C411yescharacteristic
17#10623010—24no—
18#10623010—24no—
19C2×#66929C412yes—
20C2×#66928C411yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66925C2212yes—
23C2×#66923C411yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×#66879C2212yes—
35C2×Dic11⋊C8C2212yes—
36C2×Dic11⋊C8C2212yes—
37C2×C8×Dic11C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622292—24no—
41C8×Dic22—24no—
42C11×#336C2211yescharacteristic
43C11×#336C2211yescharacteristic
44#10622162C2212yes—
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11C2×C412yes—
49C22×D44C2×C411yescharacteristic
50C22×C4×D11C2312yes—
51C22×Dic22C2×C411yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11C2×C411yescharacteristic
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11C2×C412yes—
63#66983—24no—
64#66982—28no—
65C4×C22⋊D11—24no—
66C4×C22⋊D11—24no—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C411yescharacteristic
73#66977—24no—
74C2×Dic11⋊C4C2×C412yes—
75C2×Dic11⋊C4C2×C412yes—
76C2×Dic11⋊C4C2×C412yes—
77C2×Dic11⋊C4C2×C412yes—
78C2×C4×Dic11C2312yes—
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2312yes—
81#66929—28no—
82#66928—24no—
83C4×D44—22no—
84C4×D44—22no—
85#66925—24no—
86#66925—24no—
87#66923—24no—
88C4×Dic22D414yes—
89C4×Dic22D414yes—
90C11×C22⋊C8—22no—
91C11×C22⋊C8—22no—
92C4×C8×C11—22no—
93C4×C8×C11—22no—
94C22⋊(C11⋊C8)—42no—
95(C2×D11)⋊C8—24no—
96(C2×D11)⋊C8—24no—
97(C2×D11)⋊C8—42no—
98(C2×D11)⋊C8—42no—
99#66879—24no—
100Dic11⋊C8—24no—
101Dic11⋊C8—24no—
102C8×Dic11—24no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)—22no—
105#22531—111nomaximal, Sylow
106C24×C11C22×C411yescharacteristic
107C23×D11C22×C412yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—41no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—24no—
127C2×C22⋊D11—24no—
128C2×C22⋊D11—42no—
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C412yes—
131C22×Dic11C22×C412yes—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22C22⋊C414yes—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11#4112yes—
155C2×C8×C11#4112yes—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—24no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—24no—
167C4⋊Dic11—22no—
168C4⋊Dic11C22⋊C414yes—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4C22⋊C418yes—
173C4×Dic11C2×D414yes—
174C4×Dic11C2×D414yes—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×#529—111no—
182C2×#446—111no—
183C2×C8×Q8—111no—
184#1955—112no—
185#1954—112no—
186#1954—111no—
187#1954—111no—
188#1798—112no—
189#1797—111no—
190#1750—112no—
191C4×C22⋊C8D1111yescharacteristic, complemented
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11#13112yes—
199C23×C11C23×C411yescharacteristic
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—44no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—44no—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11#13112yes—
227C2×C4×C11#13112yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C22⋊D11—48no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11C2×C22⋊C414yes—
243C2×Dic11C2×C22⋊C414yes—
244D44—44no—
245C4×D11—42no—
246C4×D11—42no—
247C4×D11—42no—
248C4×D11—42no—
249Dic22—28no—
250C8×C11—22no—
251C8×C11—22no—
252C8×C11—41no—
253C8×C11—41no—
254C11⋊C8—42no—
255C11⋊C8—42no—
256#529—224no—
257#529—224no—
258C2×#126—112no—
259C2×#125—111no—
260C2×#124—111no—
261C2×#123—112no—
262C2×C22⋊Q8—111no—
263C2×#121—111no—
264C2×C4×Q8—111no—
265C2×C4×D4—112no—
266C2×C4×D4—111no—
267C2×#117—112no—
268C22×C42C2×D1111yescharacteristic
269#446—224no—
270C8×Q8—224no—
271C2×C4⋊C8—112no—
272C2×C4⋊C8—112no—
273C2×C4⋊C8—111no—
274C2×C4⋊C8—111no—
275C2×C22⋊C8—112no—
276C2×C22⋊C8—112no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8—112no—
280C2×C22⋊C8C2×D1111yescharacteristic
281C2×C22⋊C8C2×D1111yescharacteristic
282C2×#97—112no—
283C2×C4×C8—112no—
284C2×C4×C8C2×D1111yescharacteristic
285C2×C4×C8C2×D1111yescharacteristic
286#336—112no—
287#336C2×D1111yescharacteristic
288#336C2×D1111yescharacteristic
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11C22×C22⋊C411yescharacteristic
297C22×C11C4×#4111yescharacteristic
298C22×C11#52011yescharacteristic
299C22×C11C2×#13111yescharacteristic
300C22×C11C2×#13111yescharacteristic
301C22×C11C2×#13111yescharacteristic
302C22×C11#56811yescharacteristic
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C4×C11—22no—
311C4×C11—41no—
312C4×C11—41no—
313C4×C11—41no—
314C4×C11#40814yes—
315C4×C11#54811yescharacteristic
316C4×C11#54811yescharacteristic
317C4×C11#55011yescharacteristic
318C4×C11#55011yescharacteristic
319Dic11—24no—
320Dic11—24no—
321Dic11—42no—
322C22×Q8—111no—
323C22×D4—112no—
324C22×D4—111no—
325C23×C4—112no—
326C23×C4C4×D1111yescharacteristic
327C23×C4C4×D1111yescharacteristic
328C23×C4C22×D1111yescharacteristic
329C22×C8—112no—
330C22×C8—112no—
331C22×C8C22×D1111yescharacteristic
332C22×C8C22×D1111yescharacteristic
333C22×C8C22×D1111yescharacteristic
334C22×C8C22×D1111yescharacteristic
335#126—228no—
336#125—224no—
337#124—224no—
338#123—228no—
339C22⋊Q8—224no—
340#121—224no—
341C4×Q8—114no—
342C4×Q8—114no—
343C4×D4—224no—
344C4×D4—224no—
345C4×D4—222no—
346C4×D4—222no—
347#117—224no—
348#117—224no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—112no—
355C2×C22⋊C4—112no—
356C2×C22⋊C4—112no—
357C2×C22⋊C4—112no—
358C2×C22⋊C4—112no—
359C2×C22⋊C4—112no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—112no—
363C2×C42C4×D1111yescharacteristic
364C2×C42C4×D1111yescharacteristic
365C2×C42C22×D1111yescharacteristic
366C2×C42C22×D1111yescharacteristic
367C4⋊C8—224no—
368C4⋊C8—224no—
369C4⋊C8—222no—
370C4⋊C8—222no—
371C22⋊C8—22no—
372C22⋊C8—22no—
373C22⋊C8—224no—
374C22⋊C8—224no—
375C22⋊C8—442no—
376C22⋊C8—442no—
377C22⋊C8—442no—
378#97—224no—
379C4×C8—22no—
380C4×C8—22no—
381C4×C8—224no—
382C2×C11—42no—
383C2×C11#234111yescharacteristic
384C2×C11C2×#40811yescharacteristic
385C2×C11#288011yescharacteristic
386C2×C11#296611yescharacteristic
387C2×C11#296911yescharacteristic
388C2×C11#299311yescharacteristic
389C2×C11#299411yescharacteristic
390D11—82no—
391C24—112no—
392C24C2×C4×D1111yescharacteristic
393C2×Q8—114no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×D4—224no—
397C2×D4—224no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—442no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—41no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4C2×C4×D1111yescharacteristic
424C22×C4C2×C4×D1111yescharacteristic
425C22×C4C2×C4×D1111yescharacteristic
426C22×C4C2×C4×D1111yescharacteristic
427C22×C4C2×C4×D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C2×C8#433912yes—
446C2×C8#433912yes—
447C4⋊C4—114no—
448C4⋊C4—118no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—224no—
452C4⋊C4—222no—
453C22⋊C4—224no—
454C22⋊C4—224no—
455C22⋊C4—224no—
456C22⋊C4—224no—
457C22⋊C4—224no—
458C42—22no—
459C42—22no—
460C42—21no—
461C42—21no—
462C42—114no—
463C42—114no—
464C42D4×D1112yes—
465C42D4×D1112yes—
466C11#2253111yescharacteristic, complemented, Sylow
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—222no—
474C23—222no—
475C23—222no—
476C23—222no—
477C23—222no—
478C23—222no—
479C23—222no—
480C23#6695412yes—
481C23C22×C4×D1111yescharacteristic
482Q8—228no—
483D4—448no—
484D4—444no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—44no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—44no—
502C2×C4—114no—
503C2×C4—114no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4C22⋊C4×D1112yes—
516C2×C4C22⋊C4×D1112yes—
517C2×C4#6695412yes—
518C2×C4#6696012yes—
519C2×C4C2×#433911yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4#6704211yescharacteristic
524C2×C4#6704311yescharacteristic
525C8—22no—
526C8—22no—
527C8—41no—
528C8—41no—
529C8—442no—
530C8—442no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—442no—
539C22—442no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—442no—
544C22—442no—
545C22C4×#433911yescharacteristic
546C22C2×C22⋊C4×D1111yescharacteristic
547C22#1062305411yescharacteristic
548C22C2×#6695411yescharacteristic
549C22C2×#6695411yescharacteristic
550C22C2×#6696011yescharacteristic
551C22#1062327611yescharacteristic
552C4—22no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—224no—
557C4—224no—
558C4—442no—
559C4#1062234014yes—
560C4#1062308311yescharacteristic
561C4#1062308311yescharacteristic
562C4#1062308411yescharacteristic
563C4#1062308411yescharacteristic
564C2—42no—
565C2—882no—
566C2#1307145611yescharacteristic
567C2C2×#1062234011yescharacteristic
568C2#1307706211yescharacteristic
569C2#1307759111yescharacteristic
570C2#1307762011yescharacteristic
571C2#1307776711yescharacteristic
572C2#1307777811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×C22⋊C8C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11#22531
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. C2×C8×Dic22C2semidirect
4. #13069412C2semidirect
5. #13069410C2semidirect
6. #13069410C2semidirect
7. #13069408C2semidirect
8. #13068599C2semidirect
9. #13068596C2semidirect
10. #13068381C2semidirect
11. C4×C11×C22⋊C8C2semidirect
191. C4×C22⋊C8D11semidirect
466. C11#22531semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C2×#106222922
C2×C8×Dic222
#130694122
#130694102
#130694082
#130685992
#130685962
#130683812
C4×C11×C22⋊C82
#2253111