Finite Group Databasebeta

← #14756320

Subgroups — #14756320

Order 2816.

1014 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
1#13077133C211yesmaximal, characteristic
2C2×#10622615C211yesmaximal, characteristic
3C2×#10622745C211yesmaximal, characteristic
4C2×#10622610C211yesmaximal, characteristic, complemented
5#13069277C214yesmaximal, complemented
6#13069270C214yesmaximal, complemented
7#13068355C211yesmaximal, characteristic, complemented
8C2×#10622196C211yesmaximal, characteristic, complemented
9C11×#2911C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17C11×#428—22no—
18C11×#428C2214yes—
19C11×#427—22no—
20C2×#66888C2212yes—
21#10622745C418yescomplemented
22C2×#66887C2212yes—
23#10622617C2212yes—
24#10622615—22no—
25#10622615—21no—
26#10622615—21no—
27#10622615—22no—
28#10622614C2212yes—
29#10622610—22no—
30#10622610C2214yes—
31C2×#66874C2212yes—
32#10622579—22no—
33C2×#66873C2212yes—
34C2×#66867—21no—
35C2×C4×C11⋊C8—21no—
36#10622196C2214yes—
37#10622168C2214yes—
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—21no—
40C2×#4339—22no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339C2×C414yes—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×Dic22C2311yescharacteristic
51C2×C11×M16—21no—
52C2×C11×M16—22no—
53C2×C11×M16C2×C414yes—
54C2×C11×M16C2312yes—
55C22×C8×C11—21no—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117—21no—
62C11×#117D412yes—
63C11×#117C2312yes—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C42×C11—21no—
69C2×C42×C11—21no—
70C2×#4318—21no—
71C2×#4318—22no—
72C2×#4318—21no—
73C2×#4318—22no—
74C2×#4318—22no—
75C2×#4318C2×C414yes—
76C2×#4318C2312yes—
77C2×#4318C2312yes—
78C22×C11⋊C8—21no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8—21no—
82C22×C11⋊C8D411yescharacteristic
83C22×C11⋊C8D411yescharacteristic
84C22×C11⋊C8D412yes—
85C22×C11⋊C8C2312yes—
86C11×#107—24no—
87C11×#106—24no—
88#66888C2×C418yescomplemented
89#66887C2×C418yescomplemented
90#66874—24no—
91#66874—22no—
92#66874—22no—
93#66873—24no—
94#66873—22no—
95#66873—22no—
96#66867—24no—
97C4×C11⋊C8—24no—
98#21075—111nomaximal, Sylow
99C24×C11#4111yescharacteristic
100C23×D11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—24no—
114C2×C22⋊D11—41no—
115C2×C22⋊D11—41no—
116C2×C22⋊D11—42no—
117C22×Dic11—21no—
118#4339—24no—
119#4339—24no—
120#4339—24no—
121#4339—24no—
122#4339—42no—
123#4339—42no—
124#4339—42no—
125#4339—42no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44C22×C412yes—
132C2×C4×D11—24no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11—42no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22—21no—
141C2×Dic22C22×C412yes—
142C11×M16—24no—
143C11×M16—22no—
144C11×M16C22×C414yes—
145C2×C8×C11—24no—
146C2×C8×C11—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4C2×D414yes—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—41no—
158C42×C11—41no—
159#4318—24no—
160#4318—22no—
161#4318—22no—
162#4318—22no—
163#4318—42no—
164#4318C22×C414yes—
165C2×C11⋊C8—24no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—24no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—42no—
174C2×C11⋊C8C2×D412yes—
175C2×C11⋊C8C2×D412yes—
176#2911D1111yescharacteristic, complemented
177#2896—111no—
178C2×#416—111no—
179C2×#413—111no—
180C2×#405—111no—
181#1931—114no—
182#1930—114no—
183#1742—111no—
184C2×#341—111no—
185C23×C11—42no—
186C23×C11#11712yes—
187C23×C11#12111yescharacteristic
188C23×C11#12111yescharacteristic
189C23×C11#12612yes—
190C23×C11C2×#4111yescharacteristic
191C22×D11—22no—
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—82no—
195C2×C4×C11—24no—
196C2×C4×C11—44no—
197C2×C4×C11—42no—
198C2×C4×C11—82no—
199C2×C4×C11#11712yes—
200C2×C4×C11C4×D412yes—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C4×D412yes—
203C2×C4×C11C4×D412yes—
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12312yes—
207C2×C4×C11#12312yes—
208C2×C4×C11#12412yes—
209C2×C4×C11#12412yes—
210C2×C4×C11#12612yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C22⋊D11—44no—
218C22⋊D11—44no—
219C2×Dic11—22no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222D44—22no—
223D44—22no—
224D44—41no—
225D44—41no—
226C4×D11—44no—
227C4×D11—44no—
228Dic22—22no—
229Dic22—22no—
230Dic22—41no—
231Dic22—41no—
232C8×C11—24no—
233C11⋊C8—24no—
234C11⋊C8—22no—
235C11⋊C8—22no—
236C11⋊C8—42no—
237C22×#41—111no—
238C22×M16—111no—
239C22×M16—111no—
240C22×M16C2×D1111yescharacteristic
241C23×C8—111no—
242C2×#117C2×D1111yescharacteristic
243C2×#117C2×D1111yescharacteristic
244#428—22no—
245#428C2×D1114yes—
246#427—22no—
247#419—112no—
248#418—112no—
249#417—222no—
250#416—221no—
251#416—221no—
252#416—222no—
253#416—222no—
254C2×#103—112no—
255C2×#102—112no—
256#413—118no—
257C2×#101—112no—
258C2×#100—112no—
259#405—114no—
260#405—222no—
261C2×#97—221no—
262C2×C4×C8—221no—
263#343—114no—
264#341—114no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11#38812yes—
271C22×C11#38812yes—
272C22×C11C2×#11711yescharacteristic
273C22×C11C2×#12111yescharacteristic
274C22×C11C2×#12611yescharacteristic
275C2×D11—42no—
276C2×D11—82no—
277C2×D11—82no—
278C2×D11—82no—
279C4×C11—44no—
280C4×C11—82no—
281C4×C11#38812yes—
282C4×C11#38812yes—
283C4×C11C2×C4×D411yescharacteristic
284C4×C11C2×C4×D411yescharacteristic
285C4×C11C2×#12311yescharacteristic
286C4×C11C2×#12411yescharacteristic
287Dic11—42no—
288C2×#41—114no—
289C2×#41—222no—
290C2×#41—222no—
291C2×#41—221no—
292C2×#41—221no—
293C2×#41—222no—
294C2×#41—221no—
295C2×#41—221no—
296C22×Q8—111no—
297C22×D4—111no—
298C22×D4—221no—
299C23×C4—221no—
300C23×C4C22×D1111yescharacteristic
301C2×M16—22no—
302C2×M16—21no—
303C2×M16—114no—
304C2×M16—112no—
305C2×M16—112no—
306C2×M16—221no—
307C2×M16—222no—
308C2×M16—221no—
309C2×M16—222no—
310C2×M16—222no—
311C2×M16C4×D1114yes—
312C2×M16C22×D1112yes—
313C22×C8—21no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8—112no—
317C22×C8—112no—
318C22×C8—222no—
319C22×C8—221no—
320C22×C8—222no—
321C22×C8—221no—
322#117—21no—
323#117—21no—
324#117—21no—
325#117—21no—
326#117—21no—
327#117—21no—
328#117C22⋊D1112yes—
329#117C22×D1112yes—
330C2×C4⋊C4C22⋊D1112yes—
331C2×C4⋊C4C22×D1112yes—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C42—21no—
335C2×C42—21no—
336#107—24no—
337#106—24no—
338#103—222no—
339#103—222no—
340#103—224no—
341#102—222no—
342#102—222no—
343#102—224no—
344#101—118no—
345#100—118no—
346#97—224no—
347C4×C8—224no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11—22no—
352C2×C11C2×#38811yescharacteristic
353C2×C11#306712yes—
354D11—82no—
355C24—221no—
356C24#434111yescharacteristic
357#41—224no—
358#41—224no—
359#41—224no—
360#41—224no—
361#41—442no—
362#41—442no—
363#41—442no—
364#41—442no—
365C2×Q8—112no—
366C2×Q8—221no—
367C2×Q8—221no—
368C2×Q8—221no—
369C2×Q8—221no—
370C2×Q8—221no—
371C2×D4—112no—
372C2×D4—224no—
373C2×D4—221no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—442no—
379C2×D4—441no—
380C2×D4—441no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—221no—
384C22×C4—224no—
385C22×C4—442no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4C2×C4×D1112yes—
389C22×C4#433912yes—
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4#434111yescharacteristic
393C22×C4#434312yes—
394C22×C4#434312yes—
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C23×D1111yescharacteristic
398M16—24no—
399M16—22no—
400M16—114no—
401M16—224no—
402M16—222no—
403M16—222no—
404M16—222no—
405M16—442no—
406M16C2×C4×D1114yes—
407C2×C8—24no—
408C2×C8—22no—
409C2×C8—112no—
410C2×C8—112no—
411C2×C8—224no—
412C2×C8—222no—
413C2×C8—222no—
414C2×C8—224no—
415C2×C8—222no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—442no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4C2×C22⋊D1114yes—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C42—22no—
429C42—22no—
430C42—41no—
431C42—41no—
432C11#2107511yescharacteristic, complemented, Sylow
433C23—42no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—882no—
438C23#6694512yes—
439C23#6695112yes—
440C23#6699211yescharacteristic
441C23#6699211yescharacteristic
442C23C2×#434111yescharacteristic
443Q8—222no—
444Q8—222no—
445Q8—441no—
446Q8—441no—
447D4—222no—
448D4—222no—
449D4—444no—
450D4—444no—
451D4—441no—
452D4—441no—
453C2×C4—24no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4—222no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—444no—
461C2×C4—444no—
462C2×C4#6694512yes—
463C2×C4#6694612yes—
464C2×C4#6694612yes—
465C2×C4#6694712yes—
466C2×C4#6694712yes—
467C2×C4#6695112yes—
468C2×C4C4×C22⋊D1112yes—
469C2×C4C4×C22⋊D1112yes—
470C2×C4#6699211yescharacteristic
471C2×C4#6699211yescharacteristic
472C2×C4#6700012yes—
473C2×C4#6700012yes—
474C2×C4C22×C4×D1111yescharacteristic
475C2×C4C2×#433911yescharacteristic
476C2×C4C2×D4×D1111yescharacteristic
477C2×C4C2×#434311yescharacteristic
478C2×C4C2×#434311yescharacteristic
479C2×C4C22×C22⋊D1111yescharacteristic
480C8—24no—
481C8—224no—
482C8—222no—
483C8—222no—
484C8—442no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—42no—
489C22—42no—
490C22—442no—
491C22—882no—
492C22—882no—
493C22—882no—
494C22#1062260312yes—
495C22#1062260312yes—
496C22C2×#6694511yescharacteristic
497C22C2×#6695111yescharacteristic
498C22C2×#6699211yescharacteristic
499C4—44no—
500C4—82no—
501C4—442no—
502C4#1062260312yes—
503C4#1062260312yes—
504C4C2×#6694611yescharacteristic
505C4C2×#6694711yescharacteristic
506C4C2×C4×C22⋊D1111yescharacteristic
507C4C2×#6700011yescharacteristic
508C2—21no—
509C2—21no—
510C2—22no—
511C2—22no—
512C2—882no—
513C2C2×#1062260311yescharacteristic
514C2#1307833312yes—
subgroupG/H
centerC2×C4#66992
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2911C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#2911D11
hypocenterC11#21075
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2911

Complements

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

NH ≅ G/Ntype
4. C2×#10622610C2semidirect
5. #13069277C2semidirect
6. #13069270C2semidirect
7. #13068355C2semidirect
8. C2×#10622196C2semidirect
9. C11×#2911C2semidirect
21. #10622745C4semidirect
88. #66888C2×C4semidirect
89. #66887C2×C4semidirect
176. #2911D11semidirect
432. C11#21075semidirect

Maximal subgroups

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

subgroupindex
#130771332
C2×#106226152
C2×#106227452
C2×#106226102
#130692772
#130692702
#130683552
C2×#106221962
C11×#29112
#2107511