Finite Group Databasebeta

← #14764948

Subgroups — #14764948

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×#10622663C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic
3#13069476C212yesmaximal, complemented
4#13069291C212yesmaximal, complemented
5#13069257C212yesmaximal, complemented
6#13068957C212yesmaximal, complemented
7#13068924C211yesmaximal, characteristic
8#13068803C211yesmaximal, characteristic
9#13068550C211yesmaximal, characteristic
10C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
11C4×C11×C22⋊Q8C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×#4326C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C11×#391C2211yescharacteristic
19C11×#389C2211yescharacteristic
20C11×#387—21no—
21C11×#385—21no—
22C11×#380C2211yescharacteristic
23C4×C11×C4⋊C4—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C22⋊C4—21no—
26C2×#66899C2212yes—
27C2×C11⋊#95—21no—
28C2×C11⋊#95—21no—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622663C418yescomplemented
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35C2×#66871C2212yes—
36#10622542—21no—
37#10622542—21no—
38#10622542C2212yes—
39#10622542C2212yes—
40C2×C4×C11⋊C8C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11—21no—
50C22×Dic22—21no—
51C22×Dic22—22no—
52C22×Dic22—42no—
53C22×Dic22—42no—
54C22×Dic22C2×C414yes—
55C22×Dic22C2312yes—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8C2×C414yes—
58C4×Q8×C11—42no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11—42no—
70C2×C42×C11D411yescharacteristic
71C2×C42×C11D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×#4326—42no—
75C2×#4326—42no—
76C2×#4326C2×C418yescomplemented
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—42no—
79C2×C4⋊Dic11C2312yes—
80C22×C11⋊C8C2312yes—
81C22×C11⋊C8C2312yes—
82C11×#95—21no—
83C11×#95—21no—
84C11×#95—21no—
85C11×#95—21no—
86C11×#95—21no—
87#66899—42no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C22⋊(C11⋊C8)—22no—
93C22⋊(C11⋊C8)C2×C414yes—
94#66874—42no—
95#66874—42no—
96#66874C2×C418yescomplemented
97#66871—42no—
98C4×C11⋊C8—42no—
99#22044—111nomaximal, Sylow
100C24×C11C2×D411yescharacteristic
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11C22×C412yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—41no—
114C22×C4×C11—41no—
115C22×C4×C11—41no—
116C22×C4×C11Q1614yescomplemented
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11#4112yes—
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—24no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—42no—
129C22×Dic11—42no—
130C22×Dic11—42no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C2×Dic22—24no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—48no—
140C2×Dic22—42no—
141C2×Dic22—42no—
142C2×Dic22—48no—
143C2×Dic22C22×C414yes—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4C22×C412yes—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—42no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—41no—
156C42×C11—41no—
157C42×C11—42no—
158C42×C11—42no—
159#4326—48no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
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⋊Q8D1111yescharacteristic
171C2×#391—111no—
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—42no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11C4×D412yes—
218C2×C4×C11C2×Q1612yes—
219C2×C4×C11C2×Q1612yes—
220C2×C4×C11#13712yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)12yes—
224C2×C4×C11H(5,𝔽2)12yes—
225C2×Dic11—24no—
226C2×Dic11—48no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—84no—
233Dic22—24no—
234Dic22—24no—
235Dic22—48no—
236Dic22—42no—
237Dic22—42no—
238C11⋊C8—24no—
239C11⋊C8—42no—
240C23×Q8—111no—
241C22×Q16—112no—
242C2×C22⋊Q8C2×D1111yescharacteristic
243C2×C4×Q8C2×D1111yescharacteristic
244C22×C4⋊C4—111no—
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—112no—
256#391—112no—
257#391—221no—
258#391—221no—
259#391C2×D1111yescharacteristic
260#389C2×D1111yescharacteristic
261#387—21no—
262#385—21no—
263#380C2×D1111yescharacteristic
264C4×C4⋊C4—21no—
265C4×C4⋊C4C2×D1111yescharacteristic
266C4×C22⋊C4—21no—
267C2×#95—221no—
268C2×#95—221no—
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—42no—
291C4×C11—41no—
292C4×C11—42no—
293C4×C11—81no—
294C4×C11—81no—
295C4×C11#51812yes—
296C4×C11#53812yes—
297Dic11—44no—
298Dic11—82no—
299C22×Q8—114no—
300C22×Q8—112no—
301C22×Q8—222no—
302C22×Q8—221no—
303C22×Q8—442no—
304C22×Q8—442no—
305C22×Q8C22×D1111yescharacteristic
306C23×C4—221no—
307C23×C4—221no—
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—22no—
317C22⋊Q8C4×D1114yes—
318C4×Q8—42no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—442no—
325C2×C4⋊C4C22×D1111yescharacteristic
326C2×C4⋊C4C22×D1111yescharacteristic
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—42no—
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—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—222no—
351#95—222no—
352#95—222no—
353#95—222no—
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—21no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—114no—
367C2×Q8—224no—
368C2×Q8—222no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×Q8—448no—
374C2×Q8—442no—
375C2×Q8—442no—
376C2×Q8—448no—
377C2×Q8C2×C4×D1112yes—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—224no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—442no—
393C22×C4—442no—
394C22×C4—442no—
395C22×C4—442no—
396C22×C4—442no—
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—24no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C4⋊C4—222no—
420C4⋊C4—222no—
421C4⋊C4—442no—
422C4⋊C4C2×C4×D1112yes—
423C22⋊C4—24no—
424C22⋊C4—42no—
425C42—22no—
426C42—22no—
427C42—41no—
428C42—41no—
429C42—42no—
430C42—42no—
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—42no—
442Q8—224no—
443Q8—224no—
444Q8—448no—
445Q8—442no—
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—22no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—224no—
475C2×C4—448no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—884no—
482C2×C4C4×C22⋊D1112yes—
483C2×C4C2×#432612yes—
484C2×C4C2×#432612yes—
485C2×C4#6700412yes—
486C2×C4C22×C4×D1111yescharacteristic
487C2×C4C2×#433911yescharacteristic
488C2×C4#6703712yes—
489C2×C4#6704212yes—
490C8—224no—
491C8—442no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22C4×#432614yes—
499C22C2×C4×C22⋊D1111yescharacteristic
500C22#1062333511yescharacteristic
501C22C22×#432611yescharacteristic
502C22C2×#6700311yescharacteristic
503C22#1062335311yescharacteristic
504C22C2×#6700411yescharacteristic
505C22#1062336111yescharacteristic
506C4—22no—
507C4—22no—
508C4—22no—
509C4—22no—
510C4—41no—
511C4—42no—
512C4—42no—
513C4—81no—
514C4—81no—
515C4—444no—
516C4—882no—
517C4#1062307612yes—
518C4#1062309112yes—
519C2—24no—
520C2#1307127011yescharacteristic
521C2C2×C4×#432611yescharacteristic
522C2C4×#6700411yescharacteristic
523C2#1307938811yescharacteristic
524C2#1307939311yescharacteristic
525C2#1307956111yescharacteristic
526C2#1307957711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊Q8D11
hypocenterC11#22044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13069476C2semidirect
4. #13069291C2semidirect
5. #13069257C2semidirect
6. #13068957C2semidirect
31. #10622663C4semidirect
76. C2×#4326C2×C4semidirect
96. #66874C2×C4semidirect
116. 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×#106226632
C2×#106225422
#130694762
#130692912
#130692572
#130689572
#130689242
#130688032
#130685502
C4×C22⋊(C11⋊C8)2
C4×C11×C22⋊Q82
#2204411