Finite Group Databasebeta

← #14764957

Subgroups — #14764957

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
2C22⋊Q8×Dic11C211yesmaximal, characteristic
3C2×#10622587C211yesmaximal, characteristic
4#13069474C212yesmaximal, complemented
5#13069293C212yesmaximal, complemented
6#13069255C212yesmaximal, complemented
7#13068955C212yesmaximal, complemented
8#13068804C211yesmaximal, characteristic
9#13068552C211yesmaximal, characteristic
10C22⋊C8×Dic11C211yesmaximal, characteristic
11C11×#1872C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×Q8×Dic11C2211yescharacteristic
16C22×#4326C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C2×C11×#103C2212yes—
19C2×C11×C22⋊C8C2211yescharacteristic
20#10622843C2211yescharacteristic
21#10622825C2211yescharacteristic
22C2×C11⋊#95—21no—
23C2×C11⋊#95—21no—
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×#66880C2212yes—
26C2×#66880C2212yes—
27C2×C8×Dic11C2212yes—
28#10622663C418yescomplemented
29#10622598C2211yescharacteristic
30#10622594—21no—
31C4⋊C4×Dic11—21no—
32C4⋊C4×Dic11C2211yescharacteristic
33#10622587—21no—
34#10622587—21no—
35#10622587C2212yes—
36#10622587C2212yes—
37C2×#66874C2212yes—
38C2×#66871C2212yes—
39#10622563—21no—
40C22⋊C4×Dic11—21no—
41C11×#340C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×Dic22—21no—
51C22×Dic22—22no—
52C22×Dic22—42no—
53C22×Dic22—42no—
54C22×Dic22C2×C414yes—
55C22×Dic22C2312yes—
56C22×C8×C11C2312yes—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8C2×C414yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—42no—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C22⋊Dic11—21no—
66Q8×Dic11—42no—
67C2×#4326—42no—
68C2×#4326—42no—
69C2×#4326C2×C418yescomplemented
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4×Dic11—21no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—42no—
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C22×C11⋊C8C2312yes—
82C11×#103—42no—
83C11×C22⋊C8—22no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88C11⋊#95—21no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C22⋊(C11⋊C8)C2×C414yes—
94#66880—42no—
95#66880—42no—
96C8×Dic11—42no—
97#66874C2×C418yescomplemented
98#66871—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—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4112yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—22no—
118C22×Dic11—24no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11Q1614yescomplemented
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
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—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4C22×C412yes—
153C11×C22⋊C4—24no—
154C22⋊Dic11—42no—
155#4326—48no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—42no—
159C4⋊Dic11—42no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11—42no—
165C4×Dic11—42no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8C22×C414yes—
169C2×#451—111no—
170C4×C22⋊Q8—111no—
171C2×#391—111no—
172#1969—112no—
173#1933—112no—
174#1928—112no—
175#1878—112no—
176#1872D1111yescharacteristic
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—24no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—84no—
204C2×C4×C11C4×D412yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11H(5,𝔽2)12yes—
208C2×C4×C11H(5,𝔽2)12yes—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—24no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—44no—
220C2×Dic11—44no—
221C2×Dic11—48no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11C2×Q1612yes—
231C2×Dic11C2×Q1612yes—
232C2×Dic11#13712yes—
233Dic22—24no—
234Dic22—24no—
235Dic22—48no—
236Dic22—42no—
237Dic22—42no—
238C8×C11—42no—
239C11⋊C8—24no—
240C23×Q8—111no—
241C22×Q16—112no—
242C2×C22⋊Q8C2×D1111yescharacteristic
243C2×C4×Q8—111no—
244C22×C4⋊C4C2×D1111yescharacteristic
245C22×C42—111no—
246#451—118no—
247C2×#107—112no—
248C2×#103—112no—
249C2×#103—112no—
250C2×#103—112no—
251C2×#103C2×D1112yes—
252C2×C22⋊C8—111no—
253C2×C22⋊C8C2×D1111yescharacteristic
254C2×C4×C8—112no—
255#391—111no—
256#391—112no—
257#391—112no—
258#391—221no—
259#391—221no—
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—221no—
268C2×#95—221no—
269#340—112no—
270#340C2×D1112yes—
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—42no—
288C4×C11—42no—
289C4×C11—82no—
290C4×C11#51812yes—
291C4×C11#53812yes—
292Dic11—22no—
293Dic11—22no—
294Dic11—22no—
295Dic11—44no—
296Dic11—41no—
297Dic11—81no—
298Dic11—81no—
299C22×Q8—114no—
300C22×Q8—112no—
301C22×Q8—221no—
302C22×Q8—222no—
303C22×Q8—442no—
304C22×Q8—442no—
305C22×Q8C22×D1111yescharacteristic
306C23×C4—21no—
307C23×C4—111no—
308C23×C4—111no—
309C23×C4—221no—
310C23×C4C22×D1111yescharacteristic
311C2×Q16—118no—
312C2×Q16—442no—
313C2×Q16—442no—
314C22×C8—112no—
315C22×C8C22×D1112yes—
316C22⋊Q8—22no—
317C22⋊Q8C4×D1114yes—
318C4×Q8—442no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4C22×D1112yes—
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—221no—
330C2×C42—111no—
331C2×C42—111no—
332C2×C42—111no—
333C2×C42—111no—
334C2×C42—221no—
335C2×C42—221no—
336C2×C42—442no—
337#107—442no—
338#103—42no—
339#103—118no—
340#103—442no—
341#103—442no—
342C22⋊C8—22no—
343C22⋊C8—114no—
344C4×C8—442no—
345#95—222no—
346#95—222no—
347#95—222no—
348#95—222no—
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
362C24D4×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—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—111no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—114no—
390C22×C4—111no—
391C22×C4—222no—
392C22×C4—224no—
393C22×C4—222no—
394C22×C4—222no—
395C22×C4—221no—
396C22×C4—221no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—442no—
401C22×C4—442no—
402C22×C4C2×C4×D1112yes—
403C22×C4D4×D1111yescharacteristic
404C22×C4#434112yes—
405C22×C4C23×D1111yescharacteristic
406Q16—448no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—114no—
411C2×C8—222no—
412C2×C8—222no—
413C4⋊C4—24no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—42no—
418C4⋊C4—222no—
419C4⋊C4—222no—
420C4⋊C4—442no—
421C4⋊C4—442no—
422C4⋊C4C2×C4×D1112yes—
423C22⋊C4—24no—
424C22⋊C4—442no—
425C42—222no—
426C42—222no—
427C42—441no—
428C42—441no—
429C42—442no—
430C42—442no—
431C11#2204411yescharacteristic, complemented, Sylow
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23(C22⋊D11)⋊C412yes—
437C23#6696912yes—
438C23Q16×D1112yes—
439C23C2×D4×D1111yescharacteristic
440Q8—24no—
441Q8—42no—
442Q8—224no—
443Q8—224no—
444Q8—448no—
445Q8—442no—
446Q8—442no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—84no—
461C2×C4—112no—
462C2×C4—112no—
463C2×C4—112no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—224no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—444no—
475C2×C4—444no—
476C2×C4—448no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4(C22⋊D11)⋊C412yes—
486C2×C4C22×C4×D1111yescharacteristic
487C2×C4C2×#434111yescharacteristic
488C2×C4#6703712yes—
489C2×C4#6704212yes—
490C8—42no—
491C8—224no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22#1062240314yes—
499C22C2×(C22⋊D11)⋊C411yescharacteristic
500C22#1062312311yescharacteristic
501C22#1062318411yescharacteristic
502C22C2×#6696911yescharacteristic
503C22C2×Q16×D1111yescharacteristic
504C22#1062330411yescharacteristic
505C22D11×#13711yescharacteristic
506C4—22no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4—222no—
511C4—222no—
512C4—222no—
513C4—441no—
514C4—444no—
515C4—881no—
516C4—881no—
517C4#1062307612yes—
518C4#1062314812yes—
519C2—24no—
520C2#1307127911yescharacteristic
521C2C2×#1062240311yescharacteristic
522C2#1307744011yescharacteristic
523C2#1307939011yescharacteristic
524C2#1307940211yescharacteristic
525C2#1307956211yescharacteristic
526C2#1307958411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1872D11
hypocenterC11#22044
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
4. #13069474C2semidirect
5. #13069293C2semidirect
6. #13069255C2semidirect
7. #13068955C2semidirect
28. #10622663C4semidirect
69. C2×#4326C2×C4semidirect
97. #66874C2×C4semidirect
128. C22×Dic11Q16semidirect
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
C22⋊Q8×Dic112
C2×#106225872
#130694742
#130692932
#130692552
#130689552
#130688042
#130685522
C22⋊C8×Dic112
C11×#18722
#2204411