Finite Group Databasebeta

← #14723345

Subgroups — #14723345

Order 2816.

688 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077577C211yesmaximal, characteristic, complemented
2#13077572C211yesmaximal, characteristic, complemented
3C4×#66957C211yesmaximal, characteristic
4#13067493C212yesmaximal, complemented
5#13067486C212yesmaximal, complemented
6#13067479C212yesmaximal, complemented
7#13067472C212yesmaximal, complemented
8#13066996C211yesmaximal, characteristic, complemented
9#13066996C211yesmaximal, characteristic, complemented
10C2×#10622092C211yesmaximal, characteristic, complemented
11C11×#1564C211yesmaximal, characteristic, complemented
12C2×#66957C411yescharacteristic
13C4×#4339C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#431C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622726C411yescharacteristic
19#10622726C411yescharacteristic
20#10622719C411yescharacteristic
21C2×C4×C11⋊C8C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622451C2212yes—
24#10622447C2212yes—
25#10622444C2212yes—
26#10622443C2212yes—
27#10622343—22no—
28(C22⋊D11)⋊C8—22no—
29C4×Dic44C411yescharacteristic
30C4×Dic44C2211yescharacteristic
31C4×D88C411yescharacteristic
32C4×D88C2211yescharacteristic
33C4×#4314C411yescharacteristic
34C4×#4314C411yescharacteristic
35C4×#4314C2211yescharacteristic
36C4×#4314C2211yescharacteristic
37C4×#4313—21no—
38#10622298—21no—
39#10622298—21no—
40C4×C8×D11—21no—
41C11×#335C2212yes—
42C11×#334C2212yes—
43#10622122C2212yes—
44#10622122C2212yes—
45#10622121C2212yes—
46#10622121C2212yes—
47#10622092C2212yes—
48#10622092C2212yes—
49C2×#4339C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C22×C8×C11C2×C411yescharacteristic
52C22×C8×C11C2×C411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C4×C22⋊D11—21no—
55C4×C22⋊D11—21no—
56C4×C22⋊D11—21no—
57C4×C22⋊D11—21no—
58#66979C2×C411yescharacteristic
59#66979C2×C411yescharacteristic
60C22×C11⋊C8—21no—
61C22×C11⋊C8D412yes—
62C2×Dic44C2×C411yescharacteristic
63#66957—24no—
64C2×D88C2×C411yescharacteristic
65C2×#4314C2×C411yescharacteristic
66C2×#4314C2×C411yescharacteristic
67C2×#4313—22no—
68C2×C8×D11—22no—
69C4×D44C2×C411yescharacteristic
70C4×D44C2×C411yescharacteristic
71C4×D44C2311yescharacteristic
72C4×D44C2311yescharacteristic
73#66925—21no—
74#66925—21no—
75C42×D11—21no—
76C42×D11—21no—
77C4×Dic22C2×C411yescharacteristic
78C4×Dic22C2×C411yescharacteristic
79C4×Dic22C2311yescharacteristic
80C4×Dic22C2311yescharacteristic
81C11×C4⋊C8C2312yes—
82C11×C4⋊C8C2312yes—
83C11×C22⋊C8—21no—
84C11×C22⋊C8—21no—
85C4×C8×C11—21no—
86C4×C8×C11—21no—
87C4×C8×C11C2×C411yescharacteristic
88C4×C8×C11C2×C411yescharacteristic
89C4×C8×C11C2311yescharacteristic
90C4×C8×C11C2311yescharacteristic
91#66885C2×C411yescharacteristic
92#66885C2×C411yescharacteristic
93#66885C2×C411yescharacteristic
94#66885C2×C411yescharacteristic
95(C2×D11)⋊C8—22no—
96(C2×D11)⋊C8—22no—
97#66882C2×C411yescharacteristic
98#66882C2×C411yescharacteristic
99#66881C2×C411yescharacteristic
100#66881C2×C411yescharacteristic
101#66880C2×C411yescharacteristic
102#66880C2×C411yescharacteristic
103#66880C2×C411yescharacteristic
104#66880C2×C411yescharacteristic
105#66879—22no—
106Dic11⋊C8—22no—
107Dic11⋊C8—22no—
108C8×Dic11—22no—
109C4×C11⋊C8—21no—
110C4×C11⋊C8D411yescharacteristic
111C4×C11⋊C8D411yescharacteristic
112C4×C11⋊C8C2312yes—
113C4×C11⋊C8C2312yes—
114#17868—111nomaximal, Sylow
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×C22⋊D11—21no—
119C2×C22⋊D11—21no—
120#4339—22no—
121#4339—22no—
122#4339—22no—
123#4339M1614yescomplemented
124C2×D44C22×C411yescharacteristic
125C2×D44C22×C411yescharacteristic
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×Dic22C22×C411yescharacteristic
133C2×Dic22C22×C411yescharacteristic
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11C22×C411yescharacteristic
139C2×C8×C11C22×C411yescharacteristic
140C2×C8×C11C22×C411yescharacteristic
141C2×C8×C11C22×C411yescharacteristic
142C42×C11C22×C411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11#4111yescharacteristic
145C42×C11C2411yescharacteristic
146C22⋊Dic11—21no—
147C22⋊Dic11—21no—
148(C2×D11)⋊C4—21no—
149(C2×D11)⋊C4—21no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152C4⋊Dic11C22×C411yescharacteristic
153C4⋊Dic11C22×C411yescharacteristic
154C4⋊Dic11C22×C411yescharacteristic
155C4⋊Dic11C22×C411yescharacteristic
156Dic11⋊C4—21no—
157Dic11⋊C4—21no—
158Dic11⋊C4—21no—
159Dic11⋊C4—21no—
160C4×Dic11—21no—
161C4×Dic11—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C2×C11⋊C8—24no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—42no—
169C2×C11⋊C8C2×D412yes—
170C2×C11⋊C8C2×D412yes—
171Dic44—22no—
172D88—22no—
173#4314—22no—
174#4314—22no—
175#4313—44no—
176C8×D11—44no—
177#2965—111no—
178C8×#41—111no—
179C4×#135—111no—
180#1588—112no—
181#1587—112no—
182#1586—112no—
183#1585—112no—
184#1564D1111yescharacteristic, complemented
185#1476—111no—
186#1476—111no—
187C2×#322—111no—
188C23×C11C4×D411yescharacteristic
189C22×D11—21no—
190C22×D11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11C4×D411yescharacteristic
194C2×C4×C11C4×D411yescharacteristic
195C2×C4×C11C4×D411yescharacteristic
196C2×C4×C11C2×M1612yes—
197C2×C4×C11#13112yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C22⋊D11—24no—
202C22⋊D11—42no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209D44—21no—
210D44—21no—
211D44—21no—
212D44C2×M1612yes—
213C4×D11—24no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—42no—
217C4×D11—42no—
218C4×D11—42no—
219Dic22—21no—
220Dic22—21no—
221Dic22—21no—
222Dic22C2×M1612yes—
223C8×C11—21no—
224C8×C11—21no—
225C8×C11—21no—
226C8×C11—21no—
227C8×C11—42no—
228C8×C11—42no—
229C11⋊C8—24no—
230C11⋊C8—22no—
231C11⋊C8—22no—
232C2×#135—111no—
233C4×#41—111no—
234C4×#41—111no—
235#446—112no—
236C8×Q8—112no—
237C4×Q16—111no—
238C4×Q16—111no—
239C4×SD16—111no—
240C4×SD16—111no—
241C4×SD16—111no—
242C4×SD16—111no—
243C4×D8—111no—
244C4×D8—111no—
245#436—112no—
246#435—222no—
247C8×D4—112no—
248C8×D4—222no—
249#431—221no—
250#431—221no—
251#431C2×D1111yescharacteristic
252#431C2×D1111yescharacteristic
253#427—111no—
254#416—111no—
255#416—111no—
256C4×M16—221no—
257C2×C4×C8—111no—
258C2×C4×C8—111no—
259C2×C4×C8—221no—
260C2×C4×C8C2×D1111yescharacteristic
261#335C2×D1112yes—
262#334C2×D1112yes—
263Q8⋊C8—112no—
264Q8⋊C8—112no—
265D4⋊C8—112no—
266D4⋊C8—112no—
267#322—112no—
268#322—112no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11#43512yes—
272C22×C11C2×C4×D411yescharacteristic
273C2×D11—22no—
274C2×D11—41no—
275C2×D11—41no—
276C2×D11—41no—
277C2×D11—41no—
278C2×D11—41no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11#43512yes—
282C4×C11#44312yes—
283C4×C11C22×M1611yescharacteristic
284C4×C11C2×#13111yescharacteristic
285C4×C11#57512yes—
286Dic11—22no—
287Dic11—41no—
288Dic11—41no—
289Dic11—41no—
290Dic11—41no—
291Dic11—41no—
292C2×#41—111no—
293C2×#41—111no—
294#135—224no—
295C2×Q16—111no—
296C2×SD16—111no—
297C2×SD16—111no—
298C2×D8—111no—
299C2×M16—222no—
300C22×C8—112no—
301C22×C8—222no—
302C22×C8—221no—
303C22×C8C4×D1111yescharacteristic
304C22×C8C4×D1111yescharacteristic
305C4×Q8—111no—
306C4×Q8—111no—
307C4×Q8—111no—
308C4×Q8—111no—
309C4×D4—111no—
310C4×D4—111no—
311C4×D4—111no—
312C4×D4—111no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4—221no—
316C4×D4—221no—
317#117—111no—
318#117—111no—
319#117—221no—
320#117—221no—
321C2×C42—221no—
322C2×C42—221no—
323C2×C42C22×D1111yescharacteristic
324#107—111no—
325#107—111no—
326#106—111no—
327#106—111no—
328C4⋊C8—222no—
329C4⋊C8—222no—
330C4⋊C8C22×D1112yes—
331C4⋊C8C22×D1112yes—
332#103—111no—
333#103—111no—
334#103—111no—
335#103—111no—
336#102—111no—
337#102—111no—
338#102—111no—
339#102—111no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—222no—
343C22⋊C8—222no—
344#97—222no—
345C4×C8—21no—
346C4×C8—21no—
347C4×C8—111no—
348C4×C8—111no—
349C4×C8—112no—
350C4×C8—112no—
351C4×C8—222no—
352C4×C8—221no—
353C4×C8C4×D1111yescharacteristic
354C4×C8C4×D1111yescharacteristic
355C4×C8C22×D1111yescharacteristic
356C4×C8C22×D1111yescharacteristic
357C2×C11—22no—
358C2×C11C2×#43511yescharacteristic
359C2×C11#294311yescharacteristic
360C2×C11C2×#44311yescharacteristic
361D11—42no—
362D11—81no—
363#41—114no—
364#41—222no—
365#41—222no—
366#41—222no—
367C2×Q8—111no—
368C2×Q8—111no—
369C2×D4—111no—
370C2×D4—111no—
371C2×D4—221no—
372C2×D4—221no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4C2×C4×D1111yescharacteristic
380C22×C4D4×D1111yescharacteristic
381C22×C4#434311yescharacteristic
382Q16—222no—
383SD16—222no—
384SD16—222no—
385D8—222no—
386M16—444no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—112no—
392C2×C8—112no—
393C2×C8—224no—
394C2×C8—222no—
395C2×C8—444no—
396C2×C8—442no—
397C2×C8C2×C4×D1111yescharacteristic
398C2×C8C2×C4×D1111yescharacteristic
399C2×C8C2×C4×D1111yescharacteristic
400C2×C8C2×C4×D1111yescharacteristic
401C4⋊C4—111no—
402C4⋊C4—111no—
403C4⋊C4—111no—
404C4⋊C4—111no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C22⋊C4—221no—
410C22⋊C4—221no—
411C22⋊C4—221no—
412C22⋊C4—221no—
413C22⋊C4—221no—
414C22⋊C4—221no—
415C42—221no—
416C42—221no—
417C42—221no—
418C42—221no—
419C42—221no—
420C42—221no—
421C42C2×C4×D1111yescharacteristic
422C42D4×D1111yescharacteristic
423C42#434311yescharacteristic
424C42C23×D1111yescharacteristic
425C11#1786811yescharacteristic, complemented, Sylow
426C23—221no—
427C23—221no—
428C23#6694611yescharacteristic
429Q8—112no—
430Q8—221no—
431Q8—221no—
432Q8—221no—
433D4—112no—
434D4—224no—
435D4—221no—
436D4—221no—
437D4—221no—
438D4—442no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—221no—
442C2×C4—224no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4#6694611yescharacteristic
454C2×C4#6694611yescharacteristic
455C2×C4#6694611yescharacteristic
456C2×C4#6695412yes—
457C2×C4M16×D1112yes—
458C2×C4C22×C4×D1111yescharacteristic
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×#434311yescharacteristic
461C8—21no—
462C8—21no—
463C8—21no—
464C8—21no—
465C8—42no—
466C8—42no—
467C8—224no—
468C8—222no—
469C8—222no—
470C22—21no—
471C22—21no—
472C22—222no—
473C22—441no—
474C22—441no—
475C22—441no—
476C22—441no—
477C22—441no—
478C22#1062244912yes—
479C22C2×#6694611yescharacteristic
480C4—21no—
481C4—21no—
482C4—222no—
483C4—441no—
484C4—441no—
485C4—441no—
486C4—441no—
487C4—441no—
488C4#1062244912yes—
489C4#1062250812yes—
490C4C2×#6695411yescharacteristic
491C4C2×M16×D1111yescharacteristic
492C4#1062329912yes—
493C2—22no—
494C2—442no—
495C2—881no—
496C2C2×#1062244911yescharacteristic
497C2#1307741611yescharacteristic
498C2C2×#1062250811yescharacteristic
subgroupG/H
centerC42D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1564C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C4
cosocleC42×C11C24
hypercenter#1564D11
hypocenterC11#17868
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
1. #13077577C2semidirect
2. #13077572C2semidirect
4. #13067493C2semidirect
5. #13067486C2semidirect
6. #13067479C2semidirect
7. #13067472C2semidirect
8. #13066996C2semidirect
9. #13066996C2semidirect
10. C2×#10622092C2semidirect
11. C11×#1564C2semidirect
123. #4339M16semidirect
184. #1564D11semidirect
425. C11#17868semidirect

Maximal subgroups

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

subgroupindex
#130775772
#130775722
C4×#669572
#130674932
#130674862
#130674792
#130674722
#130669962
C2×#106220922
C11×#15642
#1786811