Finite Group Databasebeta

← #14764952

Subgroups — #14764952

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622841C211yesmaximal, characteristic
2C4×#66977C211yesmaximal, characteristic
3#13069476C212yesmaximal, complemented
4#13069295C212yesmaximal, complemented
5#13069254C212yesmaximal, complemented
6#13068960C212yesmaximal, complemented
7#13068923C211yesmaximal, characteristic
8#13068804C211yesmaximal, characteristic
9#13068551C211yesmaximal, characteristic
10C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
11C2×C11×#391C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×#4326C2212yes—
16C2×#66977C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C11×#391—21no—
19C11×#391—21no—
20C11×#391C2212yes—
21C11×#391C2212yes—
22C2×C11×#95—21no—
23C2×C11×#95—21no—
24#10622841C418yescomplemented
25C2×#66899C2212yes—
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28#10622825C2211yescharacteristic
29#10622823—21no—
30C4×C22⋊Dic11—21no—
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66874C2212yes—
34C2×#66871C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36#10622546—21no—
37C4×Dic11⋊C4—21no—
38#10622542C2211yescharacteristic
39#10622541C2211yescharacteristic
40C2×C4×C11⋊C8C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—42no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2×C414yes—
49C22×Q8×C11C2312yes—
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×Dic22C2311yescharacteristic
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4C2312yes—
59C2×C42×C11—42no—
60C2×C42×C11D411yescharacteristic
61C2×C42×C11D411yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×#4326—42no—
67C2×#4326—42no—
68C2×#4326C2×C418yescomplemented
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72#66977—22no—
73#66977C2×C414yes—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2312yes—
81C4×Dic22—42no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—22no—
85C11×#95—22no—
86#66899—42no—
87#66899—42no—
88#66899C2×C418yescomplemented
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—21no—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)C2×C414yes—
96#66874—42no—
97#66871—42no—
98C4×C11⋊C8—42no—
99#22044—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—24no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—48no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×Q8×C11—48no—
111C2×Q8×C11C22×C414yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11Q1614yescomplemented
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C2×Dic22—21no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22C22×C412yes—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—42no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—41no—
150C42×C11—41no—
151C22⋊Dic11—24no—
152C22⋊Dic11—42no—
153#4326—48no—
154C4⋊Dic11—21no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11C22×C412yes—
158Dic11⋊C4—24no—
159Dic11⋊C4—42no—
160Dic11⋊C4—42no—
161C4×Dic11—42no—
162C4×Dic11—42no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8C22×C414yes—
169C2×#451—111no—
170C4×C22⋊Q8—111no—
171C2×#391D1111yescharacteristic
172#1969—112no—
173#1933—112no—
174#1928—112no—
175#1878—112no—
176#1872—111no—
177#1852—111no—
178#1787—111no—
179C4×C22⋊C8—111no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11C4×D412yes—
185C23×C11C2×Q1612yes—
186C23×C11#13512yes—
187C23×C11C22×D411yescharacteristic
188Q8×C11—24no—
189Q8×C11—24no—
190Q8×C11—48no—
191Q8×C11—42no—
192Q8×C11—42no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—44no—
208C2×C4×C11—44no—
209C2×C4×C11—48no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—84no—
216C2×C4×C11C4×D412yes—
217C2×C4×C11C2×Q1612yes—
218C2×C4×C11C2×Q1612yes—
219C2×C4×C11#13712yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)12yes—
223C2×C4×C11H(5,𝔽2)12yes—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236Dic22—24no—
237Dic22—42no—
238C11⋊C8—24no—
239C11⋊C8—42no—
240C23×Q8C2×D1111yescharacteristic
241C22×Q16—112no—
242C2×C22⋊Q8—111no—
243C2×C4×Q8—111no—
244C22×C4⋊C4C2×D1111yescharacteristic
245C22×C42C2×D1111yescharacteristic
246#451—118no—
247C2×#107—112no—
248C2×#103—112no—
249C2×#103—112no—
250C2×#103—112no—
251C2×#103—112no—
252C2×C22⋊C8—111no—
253C2×C22⋊C8—111no—
254C2×C4×C8—112no—
255#391—21no—
256#391—21no—
257#391—111no—
258#391C2×D1112yes—
259#391C2×D1112yes—
260#389—111no—
261#387—221no—
262#385—221no—
263#380—111no—
264C4×C4⋊C4—111no—
265C4×C4⋊C4—221no—
266C4×C22⋊C4—221no—
267C2×#95—21no—
268C2×#95—21no—
269#340—112no—
270#340—112no—
271#336—112no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—22no—
278C22×C11C4×Q1614yes—
279C22×C11C2×C4×D411yescharacteristic
280C22×C11#53411yescharacteristic
281C22×C11#53511yescharacteristic
282C22×C11C22×Q1611yescharacteristic
283C22×C11C2×#13511yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C22×C11#57511yescharacteristic
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—44no—
291C4×C11—41no—
292C4×C11—82no—
293C4×C11#51812yes—
294C4×C11#53812yes—
295Dic11—42no—
296Dic11—42no—
297Dic11—81no—
298Dic11—81no—
299C22×Q8—22no—
300C22×Q8—21no—
301C22×Q8—42no—
302C22×Q8—42no—
303C22×Q8—111no—
304C22×Q8C4×D1114yes—
305C22×Q8C22×D1112yes—
306C23×C4—21no—
307C23×C4—21no—
308C23×C4C22⋊D1111yescharacteristic
309C23×C4C22⋊D1111yescharacteristic
310C23×C4C22×D1111yescharacteristic
311C2×Q16—118no—
312C2×Q16—442no—
313C2×Q16—442no—
314C22×C8—112no—
315C22×C8—112no—
316C22⋊Q8—114no—
317C22⋊Q8—222no—
318C4×Q8—442no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4C22×D1112yes—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C42—42no—
331C2×C42—221no—
332C2×C42—221no—
333C2×C42C22⋊D1111yescharacteristic
334C2×C42C22⋊D1111yescharacteristic
335C2×C42C22×D1111yescharacteristic
336C2×C42C22×D1111yescharacteristic
337#107—442no—
338#103—118no—
339#103—442no—
340#103—442no—
341#103—442no—
342C22⋊C8—114no—
343C22⋊C8—222no—
344C4×C8—442no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—22no—
349#95—221no—
350#95—221no—
351#95—221no—
352#95—221no—
353#95—221no—
354C2×C11—24no—
355C2×C11#232111yescharacteristic
356C2×C11C2×C4×Q1611yescharacteristic
357C2×C11C4×#13711yescharacteristic
358C2×C11#318911yescharacteristic
359C2×C11#319011yescharacteristic
360C2×C11#320911yescharacteristic
361C2×C11#321111yescharacteristic
362C24C2×C22⋊D1111yescharacteristic
363C2×Q8—24no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—48no—
370C2×Q8—42no—
371C2×Q8—42no—
372C2×Q8—48no—
373C2×Q8—112no—
374C2×Q8—221no—
375C2×Q8—222no—
376C2×Q8—222no—
377C2×Q8C2×C4×D1114yes—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—221no—
397C22×C4#432614yescomplemented
398C22×C4C2×C4×D1112yes—
399C22×C4#433912yes—
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C23×D1111yescharacteristic
406Q16—448no—
407C2×C8—114no—
408C2×C8—222no—
409C2×C8—222no—
410C2×C8—222no—
411C2×C8—222no—
412C2×C8—222no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—42no—
416C4⋊C4—112no—
417C4⋊C4—224no—
418C4⋊C4—221no—
419C4⋊C4—222no—
420C4⋊C4—222no—
421C4⋊C4—442no—
422C4⋊C4—442no—
423C22⋊C4—224no—
424C22⋊C4—442no—
425C42—22no—
426C42—22no—
427C42—41no—
428C42—41no—
429C42—442no—
430C42—442no—
431C11#2204411yescharacteristic, complemented, Sylow
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23C4×C22⋊D1112yes—
437C23C2×#432612yes—
438C23#6700312yes—
439C23C22×C22⋊D1111yescharacteristic
440Q8—24no—
441Q8—24no—
442Q8—48no—
443Q8—42no—
444Q8—42no—
445Q8—224no—
446Q8—442no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—48no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—84no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4C4×C22⋊D1112yes—
483C2×C4#6699512yes—
484C2×C4C2×#432612yes—
485C2×C4C2×#432612yes—
486C2×C4C22×C4×D1111yescharacteristic
487C2×C4C2×#433911yescharacteristic
488C2×C4#6703712yes—
489C2×C4#6703712yes—
490C8—224no—
491C8—442no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22C4×#432614yes—
499C22C2×C4×C22⋊D1111yescharacteristic
500C22#1062333511yescharacteristic
501C22#1062333611yescharacteristic
502C22C2×#6699511yescharacteristic
503C22C22×#432611yescharacteristic
504C22C2×#6700311yescharacteristic
505C22#1062335311yescharacteristic
506C4—22no—
507C4—22no—
508C4—22no—
509C4—22no—
510C4—41no—
511C4—44no—
512C4—82no—
513C4—442no—
514C4—442no—
515C4—881no—
516C4—881no—
517C4#1062301712yes—
518C4#1062302512yes—
519C2—24no—
520C2#1307127411yescharacteristic
521C2C2×C4×#432611yescharacteristic
522C2C4×#6699511yescharacteristic
523C2#1307938811yescharacteristic
524C2#1307939711yescharacteristic
525C2#1307956411yescharacteristic
526C2#1307958111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#391C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#391D11
hypocenterC11#22044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #13069476C2semidirect
4. #13069295C2semidirect
5. #13069254C2semidirect
6. #13068960C2semidirect
24. #10622841C4semidirect
68. C2×#4326C2×C4semidirect
88. #66899C2×C4semidirect
127. C22×C4×C11Q16semidirect
397. C22×C4#4326semidirect
431. C11#22044semidirect

Maximal subgroups

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

subgroupindex
C2×#106228412
C4×#669772
#130694762
#130692952
#130692542
#130689602
#130689232
#130688042
#130685512
C4×C22⋊(C11⋊C8)2
C2×C11×#3912
#2204411