Finite Group Databasebeta

← #14760320

Subgroups — #14760320

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622801C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622302C211yesmaximal, characteristic
4#13071301C212yesmaximal
5#13069349C211yesmaximal, characteristic, complemented
6#13069309C212yesmaximal, complemented
7#13069046C212yesmaximal
8#13068642C211yesmaximal, characteristic
9#107×Dic11C211yesmaximal, characteristic, complemented
10#13068448C212yesmaximal, complemented
11C11×#1969C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×#66999C2212yes—
14C2×Q8×Dic11C2212yes—
15C22×#4313C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#103C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#391C2212yes—
22C2×#66899C2212yes—
23C2×#66899C2212yes—
24#10622801C418yescomplemented
25Q16×Dic11—24no—
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622600C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622541C2212yes—
33C2×#66867C2211yescharacteristic
34#10622302—24no—
35#10622283—22no—
36#10622282—22no—
37#10622265—22no—
38#10622260—22no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2312yes—
43C22×C4×D11C2311yescharacteristic
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11C2311yescharacteristic
51#66999—24no—
52#66999C2×C418yes—
53Q8×Dic11—24no—
54Q8×Dic11—24no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4D411yescharacteristic
58C2×(C2×D11)⋊C4D411yescharacteristic
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4D411yescharacteristic
65C2×Dic11⋊C4D411yescharacteristic
66C2×C4×Dic11—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C2×#4313—22no—
72C2×#4313—22no—
73C2×#4313—22no—
74C2×C8×D11—22no—
75C2×C8×D11—22no—
76C2×C8×D11C2×C414yes—
77#66925—22no—
78#66925—22no—
79C11×#107—22no—
80C11×#103—24no—
81C4×C8×C11—22no—
82C11×#95—22no—
83C11×#95—22no—
84#66899—24no—
85#66899C2×C418yes—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66882—22no—
90#66882C2×C414yes—
91#66879—22no—
92C8×Dic11D414yes—
93#66867—22no—
94#21525—111nomaximal, Sylow
95C23×D11C2×D411yescharacteristic
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C22×C414yes—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11C22×C412yes—
117C2×C4×D11#4112yes—
118C11×Q16—28no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11C22×C412yes—
122C2×C8×C11C2×D412yes—
123C2×C8×C11#4112yes—
124C2×C8×C11#4112yes—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C42×C11—21no—
128C42×C11—21no—
129(C2×D11)⋊C4—22no—
130(C2×D11)⋊C4—22no—
131(C2×D11)⋊C4—28no—
132(C2×D11)⋊C4—82no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—44no—
137C4⋊Dic11C22×C414yes—
138Dic11⋊C4—28no—
139Dic11⋊C4—22no—
140Dic11⋊C4—22no—
141Dic11⋊C4—82no—
142C4×Dic11—44no—
143C4×Dic11—82no—
144C4×Dic11C2×D412yes—
145C4×Dic11#4112yes—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C22×C412yes—
151C2×C11⋊C8C2×D412yes—
152#4313—28no—
153C8×D11—28no—
154C2×#467—111no—
155C2×C4×Q16—111no—
156C2×#405—111no—
157#2323—112no—
158#1969D1111yescharacteristic, complemented
159#1942—111no—
160#1935—112no—
161#1894—112no—
162#1808—111no—
163C4×#107—111no—
164#1763—112no—
165C23×C11C22×D411yescharacteristic
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—21no—
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—21no—
172C22×D11C4×D412yes—
173Q8×C11—24no—
174Q8×C11—24no—
175Q8×C11—42no—
176Q8×C11—42no—
177C2×C4×C11—24no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—24no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11C4×D412yes—
208C2×Dic11#12112yes—
209C2×Dic11#12112yes—
210C4×D11—22no—
211C4×D11—22no—
212C4×D11—22no—
213C4×D11—22no—
214C8×C11—22no—
215C8×C11C4×D414yes—
216C11⋊C8—22no—
217C11⋊C8—22no—
218C22×Q16C2×D1111yescharacteristic
219C22×M16—111no—
220C23×C8—111no—
221C2×C22⋊Q8—112no—
222C2×C4×Q8—112no—
223C2×#117—111no—
224#467—118no—
225C4×Q16—224no—
226C2×#107—111no—
227C2×#107—111no—
228C2×#107C2×D1111yescharacteristic
229C2×#103—112no—
230C2×#103—112no—
231C2×#103C2×D1112yes—
232#405—224no—
233C2×#97—111no—
234C2×#97—111no—
235C2×C4×C8—111no—
236C2×C4×C8C2×D1111yescharacteristic
237#391C2×D1112yes—
238#389—112no—
239#389—222no—
240#388—222no—
241#388—222no—
242#387—222no—
243#380—112no—
244C4×C4⋊C4—112no—
245#340—112no—
246#340—112no—
247#340—112no—
248C22×C11C2×C4×D411yescharacteristic
249C22×C11C2×#12111yescharacteristic
250C22×C11#53211yescharacteristic
251C22×C11#57611yescharacteristic
252C22×C11#57811yescharacteristic
253C22×C11#57811yescharacteristic
254C22×C11#57811yescharacteristic
255C2×D11—22no—
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—41no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C4×C11—41no—
263C4×C11—41no—
264C4×C11—44no—
265C4×C11—82no—
266C4×C11C2×C4×D411yescharacteristic
267C4×C11C4×#4111yescharacteristic
268C4×C11#52511yescharacteristic
269C4×C11#52911yescharacteristic
270Dic11—22no—
271Dic11—22no—
272Dic11—22no—
273Dic11—44no—
274Dic11—82no—
275C22×Q8C22×D1112yes—
276C23×C4—111no—
277C2×Q16—22no—
278C2×Q16—22no—
279C2×Q16C4×D1114yes—
280C2×M16—222no—
281C2×M16—222no—
282C2×M16—222no—
283C22×C8—111no—
284C22×C8—111no—
285C22×C8—114no—
286C22×C8—222no—
287C22×C8—222no—
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1111yescharacteristic
290C22⋊Q8—118no—
291C22⋊Q8—224no—
292C4×Q8—224no—
293C4×Q8—224no—
294#117—222no—
295#117—222no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—222no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4C22×D1112yes—
304C2×C22⋊C4—111no—
305C2×C22⋊C4—111no—
306C2×C22⋊C4—222no—
307C2×C22⋊C4—222no—
308C2×C42—111no—
309C2×C42—222no—
310C2×C42—222no—
311C2×C42C22×D1111yescharacteristic
312#107—22no—
313#107—114no—
314#107—222no—
315#103—24no—
316#103—118no—
317#103—224no—
318#97—222no—
319#97—222no—
320C4×C8—22no—
321C4×C8—114no—
322#95—22no—
323#95—22no—
324#95—222no—
325#95—222no—
326#95—222no—
327C2×C11C4×#12111yescharacteristic
328C2×C11#295011yescharacteristic
329C2×C11#295111yescharacteristic
330C2×C11#305911yescharacteristic
331C2×C11#306111yescharacteristic
332C2×C11#317511yescharacteristic
333C2×C11#317711yescharacteristic
334D11—42no—
335C24—111no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8C2×C4×D1114yes—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—111no—
347C22×C4—112no—
348C22×C4—112no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4D4×D1111yescharacteristic
356C22×C4D4×D1111yescharacteristic
357C22×C4C23×D1111yescharacteristic
358Q16—28no—
359M16—228no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—112no—
363C2×C8—112no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8—228no—
369C2×C8C2×C4×D1112yes—
370C2×C8D4×D1112yes—
371C2×C8#434112yes—
372C2×C8#434112yes—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—114no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—228no—
379C4⋊C4—222no—
380C4⋊C4—222no—
381C4⋊C4—222no—
382C4⋊C4—444no—
383C4⋊C4—882no—
384C22⋊C4—222no—
385C22⋊C4—222no—
386C22⋊C4—228no—
387C22⋊C4—882no—
388C42—21no—
389C42—21no—
390C42—112no—
391C42—112no—
392C42—444no—
393C42—882no—
394C11#2152511yescharacteristic, complemented, Sylow
395C23—112no—
396C23—221no—
397C23—221no—
398C23—221no—
399C23—221no—
400C23—221no—
401C23—221no—
402C23C2×D4×D1111yescharacteristic
403Q8—24no—
404Q8—24no—
405Q8—42no—
406Q8—42no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—24no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—112no—
420C2×C4—112no—
421C2×C4—112no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—224no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4C22×C4×D1111yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C2×C4C2×#434111yescharacteristic
441C2×C4C2×#434111yescharacteristic
442C2×C4#41×D1111yescharacteristic
443C2×C4#41×D1111yescharacteristic
444C8—22no—
445C8—222no—
446C8—222no—
447C8(C22⋊D11)⋊C414yes—
448C22—222no—
449C22—222no—
450C22—222no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22—441no—
455C22C4×D4×D1111yescharacteristic
456C22D11×#12111yescharacteristic
457C22#1062324711yescharacteristic
458C22#1062329711yescharacteristic
459C22#1062329711yescharacteristic
460C22#1062330011yescharacteristic
461C22#1062330211yescharacteristic
462C4—41no—
463C4—44no—
464C4—41no—
465C4—82no—
466C4—222no—
467C4—222no—
468C4—222no—
469C4—444no—
470C4—882no—
471C4C2×(C22⋊D11)⋊C411yescharacteristic
472C4C4×#434111yescharacteristic
473C4#1062313711yescharacteristic
474C4#1062321111yescharacteristic
475C2—442no—
476C2#1307113211yescharacteristic
477C2#1307747911yescharacteristic
478C2#1307749111yescharacteristic
479C2#1307826611yescharacteristic
480C2#1307828711yescharacteristic
481C2#1307925211yescharacteristic
482C2#1307927211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1969C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1969D11
hypocenterC11#21525
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1969

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic11C2semidirect
5. #13069349C2semidirect
6. #13069309C2semidirect
9. #107×Dic11C2semidirect
10. #13068448C2semidirect
11. C11×#1969C2semidirect
24. #10622801C4semidirect
158. #1969D11semidirect
394. C11#21525semidirect

Maximal subgroups

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

subgroupindex
C2×#106228012
C2×Q16×Dic112
C2×#106223022
#130713012
#130693492
#130693092
#130690462
#130686422
#107×Dic112
#130684482
C11×#19692
#2152511