Finite Group Databasebeta

← #14756322

Subgroups — #14756322

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#13077206C211yesmaximal, characteristic, complemented
2#13077136C211yesmaximal, characteristic
3C2×#10622726C211yesmaximal, characteristic
4C2×#10622745C211yesmaximal, characteristic
5C2×#10622714C211yesmaximal, characteristic, complemented
6#13069279C214yesmaximal, complemented
7#13069272C214yesmaximal, complemented
8#13068354C211yesmaximal, characteristic, complemented
9C2×C11×#341C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×#66888C2212yes—
18#10622746—22no—
19#10622745C418yescomplemented
20#10622744C2212yes—
21C2×#66887C2212yes—
22#10622734—22no—
23#10622734C2214yes—
24#10622733C2212yes—
25#10622726—21no—
26#10622726—21no—
27#10622726—22no—
28#10622726—22no—
29C2×#66885C2212yes—
30#10622719—22no—
31C2×#66880C2212yes—
32#10622714—22no—
33#10622714C2214yes—
34C2×#66879—21no—
35C2×C8×Dic11—21no—
36C11×#341C2214yes—
37#10622192C2214yes—
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×M16—21no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C2×C11×M16C2×C414yes—
57C2×C11×M16C2312yes—
58C2×C11×M16C2312yes—
59C22×C8×C11—21no—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11—21no—
63C22×C8×C11D411yescharacteristic
64C22×C8×C11D411yescharacteristic
65C22×C8×C11D412yes—
66C22×C8×C11C2312yes—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69#66979—21no—
70#66979—21no—
71#66979—21no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979D412yes—
76#66979C2312yes—
77C2×C4⋊Dic11D412yes—
78C2×C4⋊Dic11C2312yes—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×#4318—21no—
82C2×#4318—22no—
83C2×#4318C2×C414yes—
84C2×#4318C2312yes—
85C22×C11⋊C8—21no—
86#66888C2×C418yescomplemented
87#66887C2×C418yescomplemented
88#66885—22no—
89#66885—22no—
90#66885—24no—
91#66882—24no—
92#66881—24no—
93#66880—22no—
94#66880—22no—
95#66880—24no—
96#66879—24no—
97C8×Dic11—24no—
98#21075—111nomaximal, Sylow
99C24×C11#4111yescharacteristic
100C23×D11—21no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C2×C22⋊D11—24no—
112C2×C22⋊D11—41no—
113C2×C22⋊D11—41no—
114C2×C22⋊D11—42no—
115C22×Dic11—22no—
116C22×Dic11—21no—
117C22×Dic11—22no—
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×M16—22no—
145C11×M16—22no—
146C11×M16—42no—
147C11×M16C22×C414yes—
148C2×C8×C11—24no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—24no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—42no—
157C2×C8×C11C2×D412yes—
158C2×C8×C11C2×D412yes—
159C22⋊Dic11—22no—
160C22⋊Dic11—22no—
161C22⋊Dic11—41no—
162C22⋊Dic11—41no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11C2×D414yes—
167C4×Dic11—22no—
168C4×Dic11—22no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171#4318—24no—
172#4318—22no—
173#4318C22×C414yes—
174C2×C11⋊C8—24no—
175C2×C11⋊C8—22no—
176#2911—111no—
177#2896—111no—
178C2×#416—111no—
179C2×#413—111no—
180C2×#405—111no—
181#1931—114no—
182#1930—114no—
183#1742—111no—
184C2×#341D1111yescharacteristic, complemented
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#11712yes—
196C2×C4×C11C4×D412yes—
197C2×C4×C11C4×D412yes—
198C2×C4×C11C4×D412yes—
199C2×C4×C11C4×D412yes—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12312yes—
203C2×C4×C11#12312yes—
204C2×C4×C11#12412yes—
205C2×C4×C11#12412yes—
206C2×C4×C11#12612yes—
207C2×C4×C11C23×C411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C22⋊D11—44no—
214C22⋊D11—44no—
215C2×Dic11—22no—
216C2×Dic11—24no—
217C2×Dic11—44no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—42no—
221C2×Dic11—82no—
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—
233C8×C11—22no—
234C8×C11—22no—
235C8×C11—42no—
236C11⋊C8—24no—
237C22×#41—111no—
238C22×M16—111no—
239C22×M16C2×D1111yescharacteristic
240C22×M16C2×D1111yescharacteristic
241C23×C8C2×D1111yescharacteristic
242C2×#117—111no—
243C2×#117—111no—
244#428—114no—
245#428—222no—
246#427—222no—
247#419—112no—
248#418—112no—
249#417—222no—
250#416—222no—
251#416—221no—
252#416—221no—
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#341C2×D1114yes—
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#38812yes—
280C4×C11#38812yes—
281C4×C11C2×C4×D411yescharacteristic
282C4×C11C2×C4×D411yescharacteristic
283C4×C11C2×#12311yescharacteristic
284C4×C11C2×#12411yescharacteristic
285Dic11—42no—
286Dic11—44no—
287Dic11—82no—
288C2×#41—114no—
289C2×#41—222no—
290C2×#41—221no—
291C2×#41—221no—
292C2×#41—222no—
293C2×#41—221no—
294C2×#41—221no—
295C2×#41—222no—
296C22×Q8—111no—
297C22×D4—111no—
298C22×D4—221no—
299C23×C4—221no—
300C23×C4C22×D1111yescharacteristic
301C2×M16—21no—
302C2×M16—22no—
303C2×M16—21no—
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—114no—
307C2×M16—112no—
308C2×M16—221no—
309C2×M16—222no—
310C2×M16C4×D1114yes—
311C2×M16C22×D1112yes—
312C2×M16C22×D1112yes—
313C22×C8—21no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—21no—
317C22×C8—221no—
318C22×C8D4411yescharacteristic
319C22×C8D4411yescharacteristic
320C22×C8D4412yes—
321C22×C8C22×D1112yes—
322#117—112no—
323#117—112no—
324#117—221no—
325#117—221no—
326#117—221no—
327#117—221no—
328#117—221no—
329#117—221no—
330C2×C4⋊C4—112no—
331C2×C4⋊C4—112no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—221no—
334C2×C42—221no—
335C2×C42—221no—
336#107—224no—
337#106—224no—
338#103—224no—
339#103—222no—
340#103—222no—
341#102—224no—
342#102—222no—
343#102—222no—
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#434311yescharacteristic
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—441no—
379C2×D4—441no—
380C2×D4—442no—
381C22×C4—222no—
382C22×C4—221no—
383C22×C4—224no—
384C22×C4—222no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—442no—
388C22×C4C2×C4×D1112yes—
389C22×C4C2×D4411yescharacteristic
390C22×C4C2×D4411yescharacteristic
391C22×C4#433912yes—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4#434112yes—
395C22×C4#434112yes—
396C22×C4#434311yescharacteristic
397C22×C4C23×D1111yescharacteristic
398M16—24no—
399M16—22no—
400M16—22no—
401M16—22no—
402M16—42no—
403M16—114no—
404M16—224no—
405M16—222no—
406M16C2×C4×D1114yes—
407C2×C8—24no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—24no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—42no—
416C2×C8—224no—
417C2×C8—222no—
418C2×C8C2×D4412yes—
419C2×C8C2×D4412yes—
420C4⋊C4—114no—
421C4⋊C4—222no—
422C4⋊C4—222no—
423C4⋊C4—222no—
424C22⋊C4—222no—
425C22⋊C4—222no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C42—222no—
429C42—222no—
430C42—441no—
431C42—441no—
432C11#2107511yescharacteristic, complemented, Sylow
433C23—42no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—882no—
438C23#6694512yes—
439C23#6694811yescharacteristic
440C23#6694811yescharacteristic
441C23#6695112yes—
442C23C2×#434311yescharacteristic
443Q8—222no—
444Q8—222no—
445Q8—441no—
446Q8—441no—
447D4—222no—
448D4—222no—
449D4—444no—
450D4—444no—
451D4—441no—
452D4—441no—
453C2×C4—222no—
454C2×C4—224no—
455C2×C4—444no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—444no—
459C2×C4—444no—
460C2×C4—442no—
461C2×C4—882no—
462C2×C4C4×D4412yes—
463C2×C4C4×D4412yes—
464C2×C4(C22⋊D11)⋊C412yes—
465C2×C4(C22⋊D11)⋊C412yes—
466C2×C4#6693812yes—
467C2×C4#6693812yes—
468C2×C4#6693912yes—
469C2×C4#6693912yes—
470C2×C4#6694512yes—
471C2×C4#6694811yescharacteristic
472C2×C4#6694811yescharacteristic
473C2×C4#6695112yes—
474C2×C4C22×C4×D1111yescharacteristic
475C2×C4C22×D4411yescharacteristic
476C2×C4C2×#433911yescharacteristic
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4C2×#434111yescharacteristic
479C2×C4C2×#434111yescharacteristic
480C8—24no—
481C8—22no—
482C8—22no—
483C8—42no—
484C8—224no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—42no—
489C22—42no—
490C22—442no—
491C22—882no—
492C22—882no—
493C22—882no—
494C22#1062228312yes—
495C22#1062228312yes—
496C22C2×#6694511yescharacteristic
497C22C2×#6694811yescharacteristic
498C22C2×#6695111yescharacteristic
499C4—444no—
500C4—442no—
501C4—882no—
502C4#1062228312yes—
503C4#1062228312yes—
504C4C2×C4×D4411yescharacteristic
505C4C2×(C22⋊D11)⋊C411yescharacteristic
506C4C2×#6693811yescharacteristic
507C4C2×#6693911yescharacteristic
508C2—21no—
509C2—21no—
510C2—22no—
511C2—22no—
512C2—882no—
513C2C2×#1062228311yescharacteristic
514C2#1307833712yes—
subgroupG/H
centerC2×C4#66948
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#341C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#341D11
hypocenterC11#21075
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
1. #13077206C2semidirect
5. C2×#10622714C2semidirect
6. #13069279C2semidirect
7. #13069272C2semidirect
8. #13068354C2semidirect
9. C2×C11×#341C2semidirect
19. #10622745C4semidirect
86. #66888C2×C4semidirect
87. #66887C2×C4semidirect
184. C2×#341D11semidirect
432. C11#21075semidirect

Maximal subgroups

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

subgroupindex
#130772062
#130771362
C2×#106227262
C2×#106227452
C2×#106227142
#130692792
#130692722
#130683542
C2×C11×#3412
#2107511