Finite Group Databasebeta

← #14769898

Subgroups — #14769898

Order 2816.

1168 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2C2×#10622319C212yesmaximal, complemented
3#13069556C212yesmaximal, complemented
4#13068910C212yesmaximal, complemented
5#13068905C212yesmaximal, complemented
6#13068686C212yesmaximal, complemented
7#13068596C211yesmaximal, characteristic, complemented
8#13068311C212yesmaximal, complemented
9C11×#1749C211yesmaximal, characteristic, complemented
10C22×C42×C11C2211yescharacteristic
11C2×#66983C411yescharacteristic
12C2×#66982C412yes—
13C2×C4×C22⋊D11C2212yes—
14C2×#66977C411yescharacteristic
15C22×#4313C2212yes—
16C22×C8×D11C2212yes—
17#10623010—28no—
18C2×#66929C412yes—
19C2×#66928C411yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66925C2212yes—
22C2×#66923C411yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C22⋊C8C2212yes—
25C2×C11×#97C2212yes—
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×(C2×D11)⋊C8C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×C4⋊(C11⋊C8)C2212yes—
31#10622319—28no—
32C11×#336C2211yescharacteristic
33C11×#336C2211yescharacteristic
34#10622188C2212yes—
35#10622188C2212yes—
36#10622188C2212yes—
37#10622188C2212yes—
38#10622162C2212yes—
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11C2×C412yes—
43C22×D44C2×C411yescharacteristic
44C22×C4×D11C2312yes—
45C22×Dic22C2×C411yescharacteristic
46C22×C8×C11C2312yes—
47C22×C8×C11C2312yes—
48C2×C42×C11—24no—
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11C2×C412yes—
54#66983—24no—
55#66982—28no—
56C4×C22⋊D11—24no—
57C4×C22⋊D11—24no—
58C2×(C2×D11)⋊C4C2×C412yes—
59C2×(C2×D11)⋊C4C2×C412yes—
60C2×(C2×D11)⋊C4C2×C412yes—
61C2×(C2×D11)⋊C4C2×C412yes—
62C2×C4⋊Dic11C2×C411yescharacteristic
63C2×C4⋊Dic11C2×C411yescharacteristic
64#66977—24no—
65C2×Dic11⋊C4C2×C412yes—
66C2×Dic11⋊C4C2×C412yes—
67C2×Dic11⋊C4C2×C412yes—
68C2×Dic11⋊C4C2×C412yes—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8C2312yes—
71C22×C11⋊C8C2312yes—
72C2×#4313—24no—
73C2×#4313—24no—
74C2×#4313—42no—
75C2×C8×D11—24no—
76C2×C8×D11—24no—
77C2×C8×D11—42no—
78#66929—28no—
79#66928—24no—
80C4×D44D418yes—
81#66925—24no—
82#66925—24no—
83#66923—24no—
84C4×Dic22—24no—
85C11×C22⋊C8—24no—
86C11×#97—24no—
87C22⋊(C11⋊C8)—41no—
88C22⋊(C11⋊C8)—41no—
89(C2×D11)⋊C8—24no—
90(C2×D11)⋊C8—24no—
91C4⋊(C11⋊C8)—24no—
92#22475—111nomaximal, Sylow
93C24×C11C22×C411yescharacteristic
94C23×D11C22×C412yes—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C2×C22⋊D11—24no—
112C2×C22⋊D11—24no—
113C2×C22⋊D11—42no—
114C22×Dic11C22×C412yes—
115C22×Dic11C22×C412yes—
116C22×Dic11C22×C412yes—
117C2×D44—41no—
118C2×D44—41no—
119C2×D44C22⋊C414yes—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11C2×D414yes—
125C2×C4×D11C2×D414yes—
126C2×Dic22—22no—
127C2×Dic22—41no—
128C2×Dic22—41no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11#4114yes—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11C2×D414yes—
139C22⋊Dic11—24no—
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4C22⋊C418yes—
144C4⋊Dic11—22no—
145C4⋊Dic11C22⋊C414yes—
146Dic11⋊C4—24no—
147Dic11⋊C4—24no—
148Dic11⋊C4—24no—
149Dic11⋊C4—24no—
150C4×Dic11—22no—
151C4×Dic11—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158#4313—48no—
159C8×D11—48no—
160C2×#529—111no—
161C2×#435—112no—
162#1985—112no—
163#1870—112no—
164#1869—112no—
165#1818—112no—
166#1797—111no—
167#1749D1111yescharacteristic, complemented
168#1729—112no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11#13112yes—
176C23×C11C23×C411yescharacteristic
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—22no—
183C22×D11C2×C22⋊C414yes—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
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—44no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C2×C22⋊C412yes—
203C2×C4×C11C22×D412yes—
204C2×C4×C11C2×#4112yes—
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C22⋊D11—48no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11C2×C22⋊C414yes—
217D44—44no—
218C4×D11—24no—
219C4×D11—24no—
220C4×D11—24no—
221C4×D11—24no—
222Dic22—44no—
223C8×C11—24no—
224C8×C11—42no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C22×M16—112no—
228C23×C8—112no—
229#529—228no—
230C2×#126—112no—
231C2×#125—111no—
232C2×#124—111no—
233C2×#123—112no—
234C2×C22⋊Q8—111no—
235C2×#121—111no—
236C2×C4×Q8—111no—
237C2×C4×D4—112no—
238C2×C4×D4—111no—
239C2×#117—112no—
240C22×C42C2×D1111yescharacteristic
241#435—228no—
242C2×C4⋊C8—112no—
243C2×C22⋊C8—112no—
244C2×C22⋊C8—112no—
245C2×C22⋊C8—111no—
246C2×C22⋊C8—111no—
247C2×C22⋊C8C2×D1112yes—
248C2×#97C2×D1112yes—
249#336—112no—
250#336—112no—
251#336—112no—
252#336—112no—
253#336—112no—
254#336C2×D1111yescharacteristic
255#336C2×D1111yescharacteristic
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11C22×C22⋊C411yescharacteristic
264C22×C11C4×#4111yescharacteristic
265C22×C11#52011yescharacteristic
266C22×C11C2×#13111yescharacteristic
267C22×C11#56811yescharacteristic
268C22×C11#56811yescharacteristic
269C22×C11#56811yescharacteristic
270C2×D11—24no—
271C2×D11—24no—
272C2×D11—24no—
273C2×D11—42no—
274C2×D11—42no—
275C2×D11—42no—
276C2×D11—42no—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—41no—
280C4×C11—41no—
281C4×C11—41no—
282C4×C11#54612yes—
283C4×C11#54712yes—
284Dic11—24no—
285Dic11—42no—
286Dic11—42no—
287C22×Q8—111no—
288C22×D4—112no—
289C22×D4—111no—
290C23×C4—112no—
291C23×C4C4×D1111yescharacteristic
292C23×C4C4×D1111yescharacteristic
293C23×C4C22×D1111yescharacteristic
294C2×M16—224no—
295C2×M16—224no—
296C2×M16—442no—
297C22×C8—112no—
298C22×C8—112no—
299C22×C8—224no—
300C22×C8—224no—
301C22×C8—442no—
302C22×C8C22×D1112yes—
303C22×C8C22×D1112yes—
304#126—228no—
305#125—224no—
306#124—224no—
307#123—228no—
308C22⋊Q8—224no—
309#121—224no—
310C4×Q8—224no—
311C4×D4—118no—
312C4×D4—224no—
313C4×D4—224no—
314#117—224no—
315#117—224no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—112no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—112no—
322C2×C22⋊C4—112no—
323C2×C22⋊C4—112no—
324C2×C22⋊C4—112no—
325C2×C22⋊C4—112no—
326C2×C22⋊C4—112no—
327C2×C42—24no—
328C2×C42—112no—
329C2×C42C4×D1111yescharacteristic
330C2×C42C4×D1111yescharacteristic
331C2×C42C22×D1111yescharacteristic
332C2×C42C22×D1111yescharacteristic
333C4⋊C8—224no—
334C22⋊C8—24no—
335C22⋊C8—224no—
336C22⋊C8—224no—
337C22⋊C8—441no—
338C22⋊C8—441no—
339#97—24no—
340C2×C11—42no—
341C2×C11#233911yescharacteristic
342C2×C11#287911yescharacteristic
343C2×C11#288011yescharacteristic
344C2×C11#296711yescharacteristic
345C2×C11#296811yescharacteristic
346C2×C11#299211yescharacteristic
347C2×C11#299511yescharacteristic
348D11—44no—
349C24—112no—
350C24C2×C4×D1111yescharacteristic
351C2×Q8—222no—
352C2×Q8—441no—
353C2×Q8—441no—
354C2×D4—114no—
355C2×D4—224no—
356C2×D4—224no—
357C2×D4—441no—
358C2×D4—441no—
359C2×D4—442no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—112no—
371C22×C4—114no—
372C22×C4—114no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4C2×C4×D1111yescharacteristic
380C22×C4C2×C4×D1111yescharacteristic
381C22×C4C2×C4×D1111yescharacteristic
382C22×C4C2×C4×D1111yescharacteristic
383C22×C4C2×C4×D1111yescharacteristic
384C22×C4C23×D1111yescharacteristic
385M16—448no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—448no—
398C2×C8#433914yes—
399C4⋊C4—114no—
400C4⋊C4—224no—
401C4⋊C4—224no—
402C4⋊C4—224no—
403C4⋊C4—222no—
404C4⋊C4—224no—
405C22⋊C4—118no—
406C22⋊C4—224no—
407C22⋊C4—224no—
408C22⋊C4—224no—
409C22⋊C4—224no—
410C42—22no—
411C42—22no—
412C42—22no—
413C42—222no—
414C42—222no—
415C42D4×D1114yes—
416C11#2247511yescharacteristic, complemented, Sylow
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—114no—
424C23—222no—
425C23—222no—
426C23—222no—
427C23—222no—
428C23—222no—
429C23—222no—
430C23#6696012yes—
431C23C22×C4×D1111yescharacteristic
432Q8—444no—
433D4—444no—
434D4—448no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—114no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4C22⋊C4×D1112yes—
466C2×C4C22⋊C4×D1112yes—
467C2×C4C2×#433912yes—
468C2×C4C2×D4×D1112yes—
469C2×C4#6704211yescharacteristic
470C2×C4#6704311yescharacteristic
471C8—24no—
472C8—42no—
473C8—442no—
474C8—442no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—224no—
483C22—224no—
484C22—224no—
485C22—442no—
486C22—442no—
487C22—442no—
488C22—442no—
489C22C4×#433911yescharacteristic
490C22C2×C22⋊C4×D1111yescharacteristic
491C22#1062305411yescharacteristic
492C22C2×#6696011yescharacteristic
493C22#1062327611yescharacteristic
494C22#1062327611yescharacteristic
495C22#1062327611yescharacteristic
496C4—22no—
497C4—22no—
498C4—41no—
499C4—41no—
500C4—41no—
501C4—224no—
502C4—442no—
503C4—442no—
504C4#1062308112yes—
505C4#1062308212yes—
506C2—42no—
507C2—444no—
508C2#1307144711yescharacteristic
509C2#1307705911yescharacteristic
510C2#1307706611yescharacteristic
511C2#1307760111yescharacteristic
512C2#1307761011yescharacteristic
513C2#1307775711yescharacteristic
514C2#1307778811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1749C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1749D11
hypocenterC11#22475
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#10622319C2semidirect
3. #13069556C2semidirect
4. #13068910C2semidirect
5. #13068905C2semidirect
6. #13068686C2semidirect
7. #13068596C2semidirect
8. #13068311C2semidirect
9. C11×#1749C2semidirect
167. #1749D11semidirect
416. C11#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C2×#106223192
#130695562
#130689102
#130689052
#130686862
#130685962
#130683112
C11×#17492
#2247511