Finite Group Databasebeta

← #14770605

Subgroups — #14770605

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic
2C2×#10622637C211yesmaximal, characteristic, complemented
3#13069543C211yesmaximal, characteristic, complemented
4#13069543C212yesmaximal, complemented
5#13069439C212yesmaximal, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13068623C212yesmaximal, complemented
8#13068613C211yesmaximal, characteristic, complemented
9#13068444C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#2355C211yesmaximal, characteristic, complemented
12C22×#4343—21no—
13C2×C4×Q8×C11C2211yescharacteristic
14#10623108—24no—
15#10623108C418yescomplemented
16C2×#66948—21no—
17C2×#66948—22no—
18C2×#66927C2211yescharacteristic
19C2×#66927C2212yes—
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2212yes—
22C11×#391—21no—
23C11×#387—22no—
24C11×#384C2211yescharacteristic
25C11×#382C2212yes—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2212yes—
29#10622637—24no—
30C2×#66873C2212yes—
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×#66867C2212yes—
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11D411yescharacteristic
45C2×#4343—28no—
46C2×#4343—44no—
47C2×#4343—44no—
48C22×D44—22no—
49C22×D44—21no—
50C22×D44—22no—
51C22×D44—21no—
52C22×D44C2311yescharacteristic
53C22×D44C2312yes—
54C22×C4×D11—22no—
55C22×C4×D11—21no—
56C4×Q8×C11C2×C414yes—
57C4×Q8×C11D414yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11—22no—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2312yes—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75#66948—216no—
76#66948—28no—
77#66927—22no—
78#66927—24no—
79#66927C2×C414yes—
80#66927C2×C418yes—
81C4×D44—22no—
82C4×D44—24no—
83C4×D44C2×C414yes—
84C4×D44C2×C418yes—
85C11×#95—22no—
86C11×#95—21no—
87C11×#95—22no—
88C11×#95—22no—
89#66873—22no—
90#66873—24no—
91#66873—24no—
92#66873—22no—
93#66873—42no—
94#66873—42no—
95#66873—42no—
96C4⋊(C11⋊C8)—24no—
97C4⋊(C11⋊C8)—22no—
98#66867—24no—
99C4×C11⋊C8—22no—
100#22545—111nomaximal, Sylow
101C23×D11—22no—
102C23×D11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11C22⋊C414yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—21no—
115#4343—432no—
116C2×D44—28no—
117C2×D44—24no—
118C2×D44—24no—
119C2×D44—28no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44—21no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—22no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—44no—
131C2×D44—44no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—82no—
135C2×D44—81no—
136C2×D44—82no—
137C2×D44—81no—
138C2×D44C22×C412yes—
139C2×D44C22×C414yes—
140C2×C4×D11—28no—
141C2×C4×D11—24no—
142C2×C4×D11—44no—
143C2×C4×D11—44no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—81no—
153C11×C4⋊C4C22⋊C418yes—
154C11×C4⋊C4C22⋊C414yes—
155C11×C4⋊C4#4112yescomplemented
156C42×C11—42no—
157C42×C11—82no—
158C42×C11C22×C414yes—
159C42×C11C22×C412yes—
160C42×C11C2×D412yes—
161C42×C11C2×D414yes—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—28no—
164C4⋊Dic11—21no—
165C4⋊Dic11C22×C412yes—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8#4112yescomplemented
175C2×#550—111no—
176C2×#446—111no—
177#2355D1111yescharacteristic, complemented
178#1982—111no—
179#1982—112no—
180#1961—112no—
181#1957—111no—
182#1804—112no—
183#1802—111no—
184#1762—112no—
185C4×#102—111no—
186C23×C11C22×D411yescharacteristic
187C22×D11—24no—
188C22×D11—22no—
189C22×D11—42no—
190C22×D11—41no—
191C22×D11—42no—
192C22×D11—41no—
193C22×D11—42no—
194C22×D11—41no—
195C22×D11—42no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—41no—
201Q8×C11—28no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11C2×C22⋊C414yes—
219C2×C4×C11C2×C22⋊C414yes—
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11AGL(1,ℤ/8)12yes—
222C2×C4×C11AGL(1,ℤ/8)12yes—
223C2×C4×C11C23×C411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C112−1+411yescharacteristic
229C2×Dic11—22no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232D44—22no—
233D44—24no—
234D44—22no—
235D44—24no—
236D44—416no—
237D44—41no—
238D44—42no—
239D44—41no—
240D44—42no—
241D44—48no—
242D44—88no—
243D44—84no—
244C4×D11—416no—
245C4×D11—48no—
246C11⋊C8—22no—
247C11⋊C8—41no—
248C11⋊C8—42no—
249C22×#41—221no—
250#550—118no—
251#550—224no—
252C2×#127—111no—
253C2×#127—112no—
254C2×#121—221no—
255C2×#121—222no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×D4—111no—
258C2×C4×D4—112no—
259#446—224no—
260C2×C4⋊C8—111no—
261C2×C4⋊C8—112no—
262C2×#102—112no—
263C2×#102—111no—
264C2×#102—111no—
265C2×#102—112no—
266C2×#102—112no—
267C2×#102—112no—
268C2×#102—112no—
269C2×#97—112no—
270C2×C4×C8—111no—
271#391—21no—
272#387—22no—
273#384C2×D1111yescharacteristic
274#382C2×D1112yes—
275C4×C4⋊C4—21no—
276C4×C4⋊C4C2×D1111yescharacteristic
277C4×C4⋊C4C2×D1112yes—
278#340—112no—
279#340—111no—
280#340—111no—
281C22×C11C22×C22⋊C411yescharacteristic
282C22×C11#54811yescharacteristic
283C22×C11#55011yescharacteristic
284C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C11#57611yescharacteristic
287C22×C11#57711yescharacteristic
288C2×D11—44no—
289C2×D11—42no—
290C2×D11—44no—
291C2×D11—42no—
292C2×D11—44no—
293C2×D11—42no—
294C2×D11—82no—
295C2×D11—81no—
296C2×D11—82no—
297C2×D11—81no—
298C2×D11—82no—
299C2×D11—81no—
300C2×D11—82no—
301C2×D11—81no—
302C4×C11—24no—
303C4×C11—24no—
304C4×C11—22no—
305C4×C11—42no—
306C4×C11—81no—
307C4×C11—82no—
308C4×C11#41814yes—
309C4×C11C4×#4111yescharacteristic
310C4×C11#52011yescharacteristic
311C4×C11#54811yescharacteristic
312C4×C11#55011yescharacteristic
313Dic11—42no—
314C2×#41—228no—
315C2×#41—444no—
316C2×#41—444no—
317C22×Q8C22⋊D1111yescharacteristic
318C22×D4—111no—
319C22×D4—112no—
320C22×D4—222no—
321C22×D4—221no—
322C22×D4—222no—
323C22×D4—221no—
324C23×C4—222no—
325C23×C4—221no—
326C22×C8—111no—
327C22×C8—111no—
328C22×C8—112no—
329#127—114no—
330#127—118no—
331#127—222no—
332#127—224no—
333#121—2216no—
334#121—228no—
335C4×Q8C4×D1114yes—
336C4×Q8D4414yes—
337C4×D4—114no—
338C4×D4—118no—
339C4×D4—222no—
340C4×D4—224no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4C22⋊D1111yescharacteristic
345C2×C4⋊C4C22⋊D1112yes—
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C4⋊C4C22×D1112yes—
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C22⋊C4—222no—
350C2×C22⋊C4—221no—
351C2×C42—21no—
352C2×C42—22no—
353C2×C42C22×D1112yes—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—222no—
356C4⋊C8—224no—
357#102—224no—
358#102—222no—
359#102—222no—
360#102—224no—
361#102—442no—
362#102—442no—
363#102—442no—
364#97—224no—
365C4×C8—222no—
366#95—22no—
367#95—21no—
368#95—22no—
369#95—22no—
370C2×C11#234111yescharacteristic
371C2×C11C2×#41811yescharacteristic
372C2×C11#289711yescharacteristic
373C2×C11#336611yescharacteristic
374C2×C11#336811yescharacteristic
375C2×C11#339711yescharacteristic
376C2×C11#339911yescharacteristic
377D11—84no—
378D11—82no—
379C24—222no—
380C24—221no—
381#41—4432no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8(C2×D11)⋊C414yes—
385C2×D4—112no—
386C2×D4—114no—
387C2×D4—228no—
388C2×D4—224no—
389C2×D4—224no—
390C2×D4—228no—
391C2×D4—221no—
392C2×D4—222no—
393C2×D4—221no—
394C2×D4—222no—
395C2×D4—221no—
396C2×D4—222no—
397C2×D4—222no—
398C2×D4—221no—
399C2×D4—221no—
400C2×D4—222no—
401C2×D4—444no—
402C2×D4—444no—
403C2×D4—442no—
404C2×D4—442no—
405C2×D4—882no—
406C2×D4—881no—
407C2×D4—882no—
408C2×D4—881no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—221no—
413C22×C4—228no—
414C22×C4—224no—
415C22×C4—444no—
416C22×C4—444no—
417C22×C4—442no—
418C22×C4—442no—
419C22×C4C2×C22⋊D1112yes—
420C22×C4C2×C22⋊D1112yes—
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C23×D1111yescharacteristic
424C2×C8—112no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—221no—
428C2×C8—222no—
429C2×C8—221no—
430C2×C8—222no—
431C2×C8—221no—
432C2×C8—222no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—42no—
439C4⋊C4—81no—
440C4⋊C4—112no—
441C4⋊C4—221no—
442C4⋊C4(C2×D11)⋊C418yes—
443C4⋊C4(C2×D11)⋊C414yes—
444C4⋊C4#434312yescomplemented
445C22⋊C4—224no—
446C22⋊C4—228no—
447C42—42no—
448C42—82no—
449C42C2×C4×D1114yes—
450C42C2×C4×D1112yes—
451C42C2×D4412yes—
452C42C2×D4414yes—
453C11#2254511yescharacteristic, complemented, Sylow
454C23—224no—
455C23—222no—
456C23—442no—
457C23—441no—
458C23—442no—
459C23—441no—
460C23—442no—
461C23—441no—
462C23—442no—
463C23—441no—
464C23—441no—
465C23—442no—
466C23—442no—
467C23—441no—
468C23C22×C22⋊D1111yescharacteristic
469Q8—28no—
470D4—222no—
471D4—224no—
472D4—222no—
473D4—224no—
474D4—4416no—
475D4—441no—
476D4—442no—
477D4—441no—
478D4—442no—
479D4—448no—
480D4—888no—
481D4—884no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—222no—
498C2×C4—4416no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—448no—
502C2×C4C2×(C2×D11)⋊C412yes—
503C2×C4C2×(C2×D11)⋊C414yes—
504C2×C4C2×(C2×D11)⋊C414yes—
505C2×C4C2×(C2×D11)⋊C412yes—
506C2×C4#6700212yes—
507C2×C4#6700212yes—
508C2×C4C22×C4×D1111yescharacteristic
509C2×C4C22×D4411yescharacteristic
510C2×C4C2×#434311yescharacteristic
511C2×C4#6704011yescharacteristic
512C2×C4#41×D1111yescharacteristic
513C2×C4#6704211yescharacteristic
514C8—222no—
515C8—441no—
516C8—442no—
517C22—444no—
518C22—442no—
519C22—444no—
520C22—442no—
521C22—444no—
522C22—442no—
523C22—882no—
524C22—881no—
525C22—882no—
526C22—881no—
527C22—882no—
528C22—881no—
529C22—882no—
530C22—881no—
531C22C22×(C2×D11)⋊C411yescharacteristic
532C22#1062334811yescharacteristic
533C22C2×#6700211yescharacteristic
534C22C2×#6700211yescharacteristic
535C22#1062336511yescharacteristic
536C22#1062336611yescharacteristic
537C22#1062336811yescharacteristic
538C4—24no—
539C4—24no—
540C4—22no—
541C4—42no—
542C4—81no—
543C4—82no—
544C4—442no—
545C4#1062261414yes—
546C4C4×#434311yescharacteristic
547C4#1062310511yescharacteristic
548C4#1062310711yescharacteristic
549C4#1062310811yescharacteristic
550C2—884no—
551C2—882no—
552C2#1307145411yescharacteristic
553C2C2×#1062261411yescharacteristic
554C2#1307713911yescharacteristic
555C2#1308132311yescharacteristic
556C2#1308134511yescharacteristic
557C2#1308163611yescharacteristic
558C2#1308165411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2355C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
cosocleC22×C4×C11C24
hypercenter#2355D11
hypocenterC11#22545
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. C2×#10622637C2semidirect
3. #13069543C2semidirect
4. #13069543C2semidirect
5. #13069439C2semidirect
6. #13069421C2semidirect
7. #13068623C2semidirect
8. #13068613C2semidirect
9. #13068444C2semidirect
10. C4×#66873C2semidirect
11. C11×#2355C2semidirect
15. #10623108C4semidirect
155. C11×C4⋊C4#41semidirect
174. C2×C11⋊C8#41semidirect
177. #2355D11semidirect
444. C4⋊C4#4343semidirect
453. C11#22545semidirect

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×#106226372
#130695432
#130694392
#130694212
#130686232
#130686132
#130684442
C4×#668732
C11×#23552
#2254511