Finite Group Databasebeta

← #14752637

Subgroups — #14752637

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622453C211yesmaximal, characteristic
2C2×#10622452C211yesmaximal, characteristic
3#13071113C211yesmaximal, characteristic
4#13068490C211yesmaximal, characteristic, complemented
5#13068489C211yesmaximal, characteristic, complemented
6#13068482C211yesmaximal, characteristic, complemented
7C8×Dic11⋊C4C211yesmaximal, characteristic, complemented
8#13068475C211yesmaximal, characteristic, complemented
9#13068475C211yesmaximal, characteristic, complemented
10#13068469C211yesmaximal, characteristic, complemented
11#13068399C211yesmaximal, characteristic
12#13068398C211yesmaximal, characteristic
13#13068391C211yesmaximal, characteristic
14C8×(C2×D11)⋊C4C211yesmaximal, characteristic
15C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66925C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C43×C11C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622553C412yes—
35#10622553C412yes—
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38#10622546C412yes—
39#10622546C412yes—
40#10622545C2211yescharacteristic
41C4×Dic11⋊C4C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622453C418yescomplemented
48#10622452C418yescomplemented
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57C22×C4×D11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C2×C42×C11C2×C412yes—
63C2×C42×C11C2×C412yes—
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C411yescharacteristic
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×Dic11⋊C4C2×C412yes—
72C2×Dic11⋊C4C2×C412yes—
73C2×Dic11⋊C4C2×C411yescharacteristic
74C2×Dic11⋊C4C2×C411yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C2×#4313—41no—
83C2×#4313—41no—
84C2×#4313C2×C414yes—
85C2×C8×D11—41no—
86C2×C8×D11—41no—
87C2×C8×D11C2×C414yes—
88#66925C2×C414yes—
89#66925C2×C414yes—
90C11×C4⋊C8C2×C414yes—
91C11×C4⋊C8C2×C414yes—
92C4×C8×C11—41no—
93C4×C8×C11—41no—
94C11⋊#95C2×C412yes—
95C11⋊#95C2×C412yes—
96C11⋊#95C2×C412yes—
97C11⋊#95C2×C412yes—
98C11⋊#95C2×C412yes—
99C11⋊#95C2×C412yes—
100(C2×D11)⋊C8C2×C414yes—
101(C2×D11)⋊C8C2×C414yes—
102#66879—41no—
103#66879—41no—
104#66879C2×C414yes—
105Dic11⋊C8C2×C414yes—
106Dic11⋊C8C2×C414yes—
107C8×Dic11—41no—
108C8×Dic11—41no—
109C8×Dic11C2×C414yes—
110C4⋊(C11⋊C8)C2×C414yes—
111C4⋊(C11⋊C8)C2×C414yes—
112#66867—41no—
113#66867—41no—
114#20553—111nomaximal, Sylow
115C23×D11C22×C411yescharacteristic
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11C22×C412yes—
122C22×Dic11C22×C412yes—
123C22×Dic11C22×C411yescharacteristic
124C22×Dic11C22×C411yescharacteristic
125C22×Dic11C22×C411yescharacteristic
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11C22×C412yes—
131C2×C4×D11C22×C412yes—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11C22×C412yes—
141C2×C8×C11C22×C412yes—
142C2×C8×C11C22×C412yes—
143C2×C8×C11C22×C412yes—
144C42×C11—24no—
145C42×C11—21no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—42no—
150C42×C11C22×C412yes—
151C42×C11C22×C412yes—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—42no—
154(C2×D11)⋊C4C4214yes—
155(C2×D11)⋊C4C4214yes—
156Dic11⋊C4—24no—
157Dic11⋊C4—42no—
158Dic11⋊C4C4214yes—
159Dic11⋊C4C4214yes—
160C4×Dic11—21no—
161C4×Dic11—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11C22×C412yes—
165C4×Dic11C22×C412yes—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8C22×C412yes—
175C2×C11⋊C8C22×C412yes—
176C2×C11⋊C8C22×C412yes—
177C2×C11⋊C8C22×C412yes—
178#4313—44no—
179C8×D11—44no—
180C2×#433—111no—
181C2×#424—111no—
182#2298—111no—
183#1771—111no—
184#1771—111no—
185#1770—111no—
186C8×C4⋊C4—111no—
187#1768—111no—
188#1768—111no—
189#1767—111no—
190C4×C4⋊C8D1111yescharacteristic, complemented
191#1753—111no—
192#1753—111no—
193#1752—111no—
194C8×C22⋊C4—111no—
195C23×C11C23×C411yescharacteristic
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11C2×C4212yes—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11C2×C4212yes—
209C2×C4×C11C2×C4212yes—
210C2×C4×C11#13114yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C2×C4×C112−1+411yescharacteristic
217C2×Dic11—21no—
218C2×Dic11—21no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11C2×C4212yes—
228C2×Dic11C2×C4212yes—
229C2×Dic11C2×C4212yes—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C8×C11—22no—
235C8×C11—22no—
236C8×C11—22no—
237C8×C11—22no—
238C11⋊C8—22no—
239C11⋊C8—22no—
240C11⋊C8—22no—
241C11⋊C8—22no—
242C22×M16—111no—
243C23×C8—111no—
244C2×#117—111no—
245#433—118no—
246#424—118no—
247C2×C4⋊C8—111no—
248C2×C4⋊C8—111no—
249C2×C4⋊C8—111no—
250C2×C4⋊C8—111no—
251C2×C4⋊C8C2×D1111yescharacteristic
252C2×C4⋊C8C2×D1111yescharacteristic
253C2×C22⋊C8—111no—
254C2×C22⋊C8—111no—
255C2×#97—111no—
256C2×#97—111no—
257C2×#97—111no—
258C2×#97—111no—
259C2×#97—111no—
260C2×C4×C8—111no—
261C2×C4×C8—111no—
262C2×C4×C8—111no—
263C2×C4×C8C2×D1111yescharacteristic
264C2×C4×C8C2×D1111yescharacteristic
265#388—112no—
266#388—112no—
267#387—112no—
268#387—112no—
269C4×C4⋊C4—111no—
270C4×C4⋊C4—111no—
271C4×C22⋊C4—111no—
272C4×C22⋊C4—111no—
273#376—111no—
274C43C2×D1111yescharacteristic
275#336—111no—
276#336—111no—
277#336—111no—
278#336—111no—
279#336—111no—
280#336—111no—
281#336C2×D1111yescharacteristic
282#336C2×D1111yescharacteristic
283C22×C11C22×C4211yescharacteristic
284C22×C11#52011yescharacteristic
285C22×C11#52011yescharacteristic
286C22×C11C2×#13112yes—
287C22×C11#56812yes—
288C2×D11—22no—
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—42no—
292C2×D11—42no—
293C4×C11—22no—
294C4×C11—22no—
295C4×C11—24no—
296C4×C11—42no—
297C4×C11#51811yescharacteristic
298C4×C11#51911yescharacteristic
299C4×C11#52011yescharacteristic
300C4×C11#52011yescharacteristic
301Dic11—22no—
302Dic11—22no—
303Dic11—22no—
304Dic11—42no—
305Dic11—42no—
306C23×C4—111no—
307C2×M16—114no—
308C2×M16—441no—
309C2×M16—441no—
310C22×C8—111no—
311C22×C8—111no—
312C22×C8—111no—
313C22×C8—111no—
314C22×C8—114no—
315C22×C8—441no—
316C22×C8—441no—
317C22×C8C22×D1111yescharacteristic
318C22×C8C22×D1111yescharacteristic
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321#117—114no—
322#117—114no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—112no—
327C2×C22⋊C4—111no—
328C2×C22⋊C4—111no—
329C2×C22⋊C4—112no—
330C2×C22⋊C4—112no—
331C2×C42—111no—
332C2×C42—111no—
333C2×C42—111no—
334C2×C42C4×D1112yes—
335C2×C42C4×D1112yes—
336C2×C42C22×D1111yescharacteristic
337C2×C42C22×D1111yescharacteristic
338C2×C42C22×D1111yescharacteristic
339C4⋊C8—114no—
340C4⋊C8—114no—
341C4⋊C8—114no—
342C4⋊C8—114no—
343C4⋊C8C4×D1114yes—
344C4⋊C8C4×D1114yes—
345C22⋊C8—114no—
346C22⋊C8—114no—
347#97—114no—
348#97—441no—
349#97—441no—
350#97—441no—
351#97—441no—
352C4×C8—41no—
353C4×C8—41no—
354C4×C8—114no—
355C4×C8—441no—
356C4×C8—441no—
357#95—112no—
358#95—112no—
359#95—112no—
360#95—112no—
361#95—112no—
362#95—112no—
363C2×C11#227411yescharacteristic
364C2×C11C4×#13111yescharacteristic
365C2×C11#287511yescharacteristic
366C2×C11#299212yes—
367C2×C11#299312yes—
368D11—42no—
369C24—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—112no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4C2×C4×D1112yes—
382C22×C4C2×C4×D1111yescharacteristic
383C22×C4C2×C4×D1111yescharacteristic
384C22×C4C2×C4×D1112yes—
385C22×C4C23×D1111yescharacteristic
386M16—444no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—112no—
396C2×C8—112no—
397C2×C8—112no—
398C2×C8—112no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8—221no—
407C2×C8—444no—
408C2×C8C2×C4×D1112yes—
409C2×C8C2×C4×D1112yes—
410C2×C8C2×C4×D1112yes—
411C2×C8C2×C4×D1112yes—
412C4⋊C4—114no—
413C4⋊C4—114no—
414C4⋊C4—224no—
415C4⋊C4—442no—
416C22⋊C4—114no—
417C22⋊C4—114no—
418C22⋊C4—224no—
419C22⋊C4—442no—
420C42—24no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—21no—
425C42—42no—
426C42—112no—
427C42—112no—
428C42—221no—
429C42—221no—
430C42—221no—
431C42—221no—
432C42C2×C4×D1112yes—
433C42C2×C4×D1112yes—
434C11#2055311yescharacteristic, complemented, Sylow
435C23—112no—
436C23—222no—
437C23—222no—
438C23—221no—
439C23—221no—
440C23C22×C4×D1111yescharacteristic
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—112no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4C42×D1112yes—
466C2×C4C42×D1112yes—
467C2×C4#6695414yes—
468C2×C4C22×C4×D1111yescharacteristic
469C2×C4C22×C4×D1111yescharacteristic
470C2×C4#6703711yescharacteristic
471C2×C4#6704011yescharacteristic
472C2×C4#6704211yescharacteristic
473C2×C4#6704311yescharacteristic
474C8—22no—
475C8—22no—
476C8—22no—
477C8—22no—
478C8—222no—
479C8—222no—
480C8—222no—
481C8—222no—
482C22—222no—
483C22—222no—
484C22—222no—
485C22—442no—
486C22—442no—
487C22C2×C42×D1111yescharacteristic
488C22#1062303511yescharacteristic
489C22#1062305411yescharacteristic
490C22C2×#6695412yes—
491C22#1062327612yes—
492C4—22no—
493C4—22no—
494C4—24no—
495C4—42no—
496C4—222no—
497C4—222no—
498C4—222no—
499C4—442no—
500C4—442no—
501C4#1062307611yescharacteristic
502C4#1062307711yescharacteristic
503C4#1062310311yescharacteristic
504C4#1062310511yescharacteristic
505C2—442no—
506C2#1307097011yescharacteristic
507C2C4×#6695411yescharacteristic
508C2#1307704511yescharacteristic
509C2#1307775212yes—
510C2#1307776712yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC4×C11×C4⋊C8C2
socleC23×C11C23×C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenterC4×C4⋊C8D11
hypocenterC11#20553
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #13068490C2semidirect
5. #13068489C2semidirect
6. #13068482C2semidirect
7. C8×Dic11⋊C4C2semidirect
8. #13068475C2semidirect
9. #13068475C2semidirect
10. #13068469C2semidirect
15. C4×C11×C4⋊C8C2semidirect
47. #10622453C4semidirect
48. #10622452C4semidirect
190. C4×C4⋊C8D11semidirect
434. C11#20553semidirect

Maximal subgroups

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

subgroupindex
C2×#106224532
C2×#106224522
#130711132
#130684902
#130684892
#130684822
C8×Dic11⋊C42
#130684752
#130684692
#130683992
#130683982
#130683912
C8×(C2×D11)⋊C42
C4×C11×C4⋊C82
#2055311