Finite Group Databasebeta

← #14770618

Subgroups — #14770618

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2C2×#10622292C211yesmaximal, characteristic, complemented
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13069545C212yesmaximal, complemented
5#13069543C211yesmaximal, characteristic
6#13069429C212yesmaximal, complemented
7#13069422C211yesmaximal, characteristic
8#13068621C211yesmaximal, characteristic, complemented
9#13068615C212yesmaximal, complemented
10#13068440C212yesmaximal, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000C2212yes—
14#10623116—24no—
15#10623116C418yescomplemented
16C2×#66947—22no—
17C2×#66946C2212yes—
18C2×#66928—21no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44—21no—
21C2×C4×Dic22—21no—
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66885C2212yes—
29C2×#66885C2212yes—
30C2×#66879C2212yes—
31C2×Dic11⋊C8C2212yes—
32#10622589C2212yes—
33C4⋊C4×Dic11C2212yes—
34C2×#66873C2212yes—
35C2×#66873C2212yes—
36#10622548C2211yescharacteristic
37#10622541—21no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622292—24no—
40#10622260—22no—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43#10622167C2212yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D44—21no—
46C22×D44—21no—
47C22×D44C2312yes—
48C22×C4×D11—22no—
49C22×Dic22D411yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11—22no—
53C4×Q8×C11C2×C414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61#67000—24no—
62#67000C2×C418yes—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4D412yes—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2312yes—
75C22×C11⋊C8C2312yes—
76#66947—216no—
77#66946—24no—
78#66946C2×C418yes—
79#66928—28no—
80#66927—22no—
81#66927C2×C414yes—
82C4×D44—28no—
83C4×Dic22—44no—
84C4×Dic22C2×C414yes—
85C4×Dic22D414yes—
86C11×#103—22no—
87C11×#103—22no—
88C4×C8×C11—22no—
89C11×#95—21no—
90#66899—42no—
91C11⋊#95—22no—
92#66885—24no—
93#66885—42no—
94#66879—24no—
95Dic11⋊C8—24no—
96#66873—24no—
97#66873—42no—
98C4⋊(C11⋊C8)—22no—
99#22546—111nomaximal, Sylow
100C23×D11—22no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11C22×C412yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C2×D44—24no—
118C2×D44—24no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—42no—
125C2×D44—42no—
126C2×D44—81no—
127C2×D44—81no—
128C2×D44C22×C414yes—
129C2×C4×D11—28no—
130C2×C4×D11—82no—
131C2×C4×D11—82no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22C22⋊C414yes—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11#4112yes—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4C22×C412yes—
147C11×C4⋊C4#4112yes—
148C42×C11—24no—
149C42×C11—42no—
150C42×C11C22×C412yes—
151C42×C11C2×D412yes—
152(C2×D11)⋊C4—28no—
153(C2×D11)⋊C4—28no—
154(C2×D11)⋊C4—28no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11—42no—
158C4⋊Dic11—81no—
159C4⋊Dic11C22⋊C414yes—
160Dic11⋊C4—44no—
161Dic11⋊C4—82no—
162Dic11⋊C4C22⋊C418yes—
163C4×Dic11—44no—
164C4×Dic11C22×C414yes—
165C4×Dic11C2×D414yes—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×#559—111no—
170C2×#446—111no—
171Q8×C4⋊C4—111no—
172#1983—112no—
173#1982—111no—
174#1959—112no—
175#1957—111no—
176#1803—111no—
177#1802—112no—
178#1762—112no—
179C4×#103D1111yescharacteristic, complemented
180C23×C11C22×D411yescharacteristic
181C22×D11—24no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—41no—
191Q8×C11—41no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11C2×C22⋊C412yes—
207C2×C4×C11C2×C22⋊C412yes—
208C2×C4×C11AGL(1,ℤ/8)12yes—
209C2×C4×C11#13712yes—
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11C2×C22⋊C414yes—
224C2×Dic11C2×C22⋊C414yes—
225D44—24no—
226D44—24no—
227D44—42no—
228D44—42no—
229D44—48no—
230D44—84no—
231C4×D11—88no—
232Dic22—28no—
233C8×C11—22no—
234C8×C11—41no—
235C11⋊C8—42no—
236#559—118no—
237#559—224no—
238C2×#127—111no—
239C2×#124—112no—
240C2×#124—221no—
241C2×#123—222no—
242C2×C4×Q8—111no—
243C2×C4×Q8—221no—
244C2×C4×Q8C2×D1111yescharacteristic
245C2×C4×D4—112no—
246C2×C4×D4—221no—
247#446—224no—
248C2×C4⋊C8—112no—
249C2×C4⋊C8—111no—
250C2×#103—112no—
251C2×#103C2×D1111yescharacteristic
252C2×#103C2×D1111yescharacteristic
253C2×#102—112no—
254C2×#102—112no—
255C2×#102—112no—
256C2×#102—112no—
257C2×#97—112no—
258C2×C4×C8C2×D1111yescharacteristic
259#389—222no—
260#389—221no—
261#384—112no—
262#384—111no—
263C4×C4⋊C4—112no—
264C4×C4⋊C4C2×D1111yescharacteristic
265#340—112no—
266#340C2×D1111yescharacteristic
267#340C2×D1111yescharacteristic
268C22×C11C22×C22⋊C411yescharacteristic
269C22×C11#54811yescharacteristic
270C22×C11#55011yescharacteristic
271C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C22×C11#57611yescharacteristic
274C22×C11#57711yescharacteristic
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—82no—
279C2×D11—82no—
280C2×D11—82no—
281C2×D11—82no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—81no—
287C4×C11#41714yes—
288C4×C11C4×#4111yescharacteristic
289C4×C11#52011yescharacteristic
290C4×C11#54811yescharacteristic
291C4×C11#55011yescharacteristic
292Dic11—24no—
293Dic11—24no—
294Dic11—82no—
295C22×Q8—111no—
296C22×Q8C22×D1111yescharacteristic
297C22×D4—112no—
298C22×D4—221no—
299C22×D4—221no—
300C23×C4—222no—
301C22×C8—112no—
302C22×C8C22×D1111yescharacteristic
303C22×C8C22×D1111yescharacteristic
304#127—114no—
305#127—222no—
306#124—118no—
307#124—228no—
308#124—224no—
309#123—2216no—
310C4×Q8—22no—
311C4×Q8—114no—
312C4×Q8—114no—
313C4×Q8—444no—
314C4×Q8C4×D1114yes—
315C4×D4—118no—
316C4×D4—228no—
317C4×D4—224no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4C22×D1111yescharacteristic
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—112no—
335C2×C42—222no—
336C2×C42C22×D1111yescharacteristic
337C4⋊C8—224no—
338C4⋊C8—222no—
339#103—22no—
340#103—22no—
341#103—442no—
342#102—224no—
343#102—224no—
344#102—442no—
345#102—442no—
346#97—224no—
347C4×C8—22no—
348#95—21no—
349#95—222no—
350C2×C11#234111yescharacteristic
351C2×C11C2×#41711yescharacteristic
352C2×C11#289711yescharacteristic
353C2×C11#337311yescharacteristic
354C2×C11#337511yescharacteristic
355C2×C11#339911yescharacteristic
356C2×C11#340011yescharacteristic
357D11—84no—
358C24—222no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—114no—
365C2×Q8—222no—
366C2×Q8—222no—
367C2×Q8C2×C4×D1112yes—
368C2×D4—114no—
369C2×D4—224no—
370C2×D4—224no—
371C2×D4—222no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—222no—
376C2×D4—442no—
377C2×D4—442no—
378C2×D4—881no—
379C2×D4—881no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—112no—
385C22×C4—112no—
386C22×C4—228no—
387C22×C4—222no—
388C22×C4—882no—
389C22×C4—882no—
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8#433912yes—
402C4⋊C4—24no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—114no—
408C4⋊C4—118no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C4⋊C4—444no—
412C4⋊C4—442no—
413C4⋊C4—881no—
414C4⋊C4—882no—
415C4⋊C4C2×C4×D1112yes—
416C4⋊C4#433912yes—
417C22⋊C4—228no—
418C22⋊C4—228no—
419C22⋊C4—228no—
420C42—24no—
421C42—42no—
422C42—114no—
423C42—114no—
424C42—444no—
425C42C2×C4×D1112yes—
426C42D4×D1112yes—
427C11#2254611yescharacteristic, complemented, Sylow
428C23—224no—
429C23—442no—
430C23—442no—
431C23—442no—
432C23—442no—
433C23—442no—
434C23—442no—
435C23C2×D4×D1111yescharacteristic
436Q8—22no—
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—228no—
441D4—224no—
442D4—224no—
443D4—442no—
444D4—442no—
445D4—448no—
446D4—884no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—114no—
462C2×C4—114no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—888no—
471C2×C4C22⋊C4×D1112yes—
472C2×C4C22⋊C4×D1112yes—
473C2×C4#6696712yes—
474C2×C4#6697112yes—
475C2×C4C22×C4×D1111yescharacteristic
476C2×C4C2×#433911yescharacteristic
477C2×C4C2×#433911yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4#6704211yescharacteristic
480C2×C4#6704311yescharacteristic
481C8—22no—
482C8—41no—
483C8—442no—
484C22—444no—
485C22—444no—
486C22—444no—
487C22—882no—
488C22—882no—
489C22—882no—
490C22—882no—
491C22C2×C22⋊C4×D1111yescharacteristic
492C22#1062308311yescharacteristic
493C22#1062308411yescharacteristic
494C22C2×#6696711yescharacteristic
495C22C2×#6697111yescharacteristic
496C22#1062330011yescharacteristic
497C22#1062330111yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—81no—
503C4—224no—
504C4—224no—
505C4—882no—
506C4#1062241614yes—
507C4C4×#433911yescharacteristic
508C4#1062305411yescharacteristic
509C4#1062308311yescharacteristic
510C4#1062308411yescharacteristic
511C2—884no—
512C2#1307145611yescharacteristic
513C2C2×#1062241611yescharacteristic
514C2#1307713811yescharacteristic
515C2#1308140611yescharacteristic
516C2#1308142811yescharacteristic
517C2#1308165611yescharacteristic
518C2#1308166711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
cosocleC22×C4×C11C24
hypercenterC4×#103D11
hypocenterC11#22546
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
2. C2×#10622292C2semidirect
3. C4⋊C4×Dic22C2semidirect
4. #13069545C2semidirect
6. #13069429C2semidirect
8. #13068621C2semidirect
9. #13068615C2semidirect
10. #13068440C2semidirect
11. C4×C11×#103C2semidirect
15. #10623116C4semidirect
179. C4×#103D11semidirect
427. C11#22546semidirect

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106222922
C4⋊C4×Dic222
#130695452
#130695432
#130694292
#130694222
#130686212
#130686152
#130684402
C4×C11×#1032
#2254611