Finite Group Databasebeta

← #14725226

Subgroups — #14725226

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077634C211yesmaximal, characteristic, complemented
2#13077631C211yesmaximal, characteristic, complemented
3C4×#66957C211yesmaximal, characteristic
4#13067508C212yesmaximal, complemented
5#13067468C212yesmaximal, complemented
6#13067447C212yesmaximal, complemented
7C8×#4314C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067051C211yesmaximal, characteristic, complemented
10#13067051C211yesmaximal, characteristic, complemented
11C8×C11×M16C211yesmaximal, characteristic, complemented
12C2×#66957C411yescharacteristic
13C4×#4339C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C4×C11×M16C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622741—22no—
19#10622740—22no—
20#10622726C411yescharacteristic
21#10622726C411yescharacteristic
22#10622719C411yescharacteristic
23#10622539C2211yescharacteristic
24#10622539C2211yescharacteristic
25#10622320—21no—
26#10622318—21no—
27#10622318—21no—
28D11×#97—21no—
29C4×Dic44C411yescharacteristic
30C4×Dic44C2211yescharacteristic
31C4×D88C411yescharacteristic
32C4×D88C2211yescharacteristic
33C4×#4314C411yescharacteristic
34C4×#4314C411yescharacteristic
35C4×#4314C2211yescharacteristic
36C4×#4314C2211yescharacteristic
37#10622301C2212yes—
38C8×D44C2212yes—
39#10622292C2212yes—
40C8×Dic22C2212yes—
41C11×#322C2212yes—
42C82×C11C2212yes—
43#10622097C2212yes—
44#10622097C2212yes—
45#10622096C2212yes—
46#10622095C2212yes—
47#10622094C2212yes—
48#10622094C2212yes—
49C2×#4339C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C2×C11×M16D412yes—
52C22×C8×C11C2×C411yescharacteristic
53C22×C8×C11C2×C411yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C4×C22⋊D11—21no—
56C4×C22⋊D11—21no—
57C4×C22⋊D11—21no—
58C4×C22⋊D11—21no—
59#66979C2×C411yescharacteristic
60#66979C2×C411yescharacteristic
61C2×Dic44C2×C411yescharacteristic
62#66957—24no—
63C2×D88C2×C411yescharacteristic
64C2×#4314C2×C411yescharacteristic
65C2×#4314C2×C411yescharacteristic
66C2×#4313—22no—
67C2×C8×D11—22no—
68C4×D44C2×C411yescharacteristic
69C4×D44C2×C411yescharacteristic
70C4×D44C2311yescharacteristic
71C4×D44C2311yescharacteristic
72#66925—21no—
73#66925—21no—
74C42×D11—21no—
75C42×D11—21no—
76C4×Dic22C2×C411yescharacteristic
77C4×Dic22C2×C411yescharacteristic
78C4×Dic22C2311yescharacteristic
79C4×Dic22C2311yescharacteristic
80C11×C4⋊C8—21no—
81C11×C22⋊C8—21no—
82C11×#97D411yescharacteristic
83C11×#97D411yescharacteristic
84C4×C8×C11C2×C411yescharacteristic
85C4×C8×C11C2×C411yescharacteristic
86C4×C8×C11C2312yes—
87C4×C8×C11C2311yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2312yes—
90C22⋊(C11⋊C8)—21no—
91C22⋊(C11⋊C8)—21no—
92#66885C2×C411yescharacteristic
93#66885C2×C411yescharacteristic
94#66885C2×C411yescharacteristic
95#66885C2×C411yescharacteristic
96(C2×D11)⋊C8—22no—
97(C2×D11)⋊C8—22no—
98#66882C2×C411yescharacteristic
99#66882C2×C411yescharacteristic
100#66881C2×C411yescharacteristic
101#66881C2×C411yescharacteristic
102#66880C2×C411yescharacteristic
103#66880C2×C411yescharacteristic
104#66880C2×C411yescharacteristic
105#66880C2×C411yescharacteristic
106#66879—22no—
107Dic11⋊C8—22no—
108Dic11⋊C8—22no—
109C8×Dic11—22no—
110C4⋊(C11⋊C8)C2312yes—
111C4⋊(C11⋊C8)C2312yes—
112#66867—21no—
113#66867—21no—
114#18037—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—41no—
123#4339—41no—
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
134C11×M16—24no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—41no—
138C2×C8×C11C22×C411yescharacteristic
139C2×C8×C11C22×C411yescharacteristic
140C2×C8×C11C22×C411yescharacteristic
141C2×C8×C11C22×C411yescharacteristic
142C2×C8×C11C2×D412yes—
143C2×C8×C11C2×D412yes—
144C42×C11C22×C411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148C22⋊Dic11—21no—
149C22⋊Dic11—21no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152(C2×D11)⋊C4—21no—
153(C2×D11)⋊C4—21no—
154C4⋊Dic11C22×C411yescharacteristic
155C4⋊Dic11C22×C411yescharacteristic
156C4⋊Dic11C22×C411yescharacteristic
157C4⋊Dic11C22×C411yescharacteristic
158Dic11⋊C4—21no—
159Dic11⋊C4—21no—
160Dic11⋊C4—21no—
161Dic11⋊C4—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C4×Dic11—21no—
167C4×Dic11—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170Dic44—22no—
171D88—22no—
172#4314—22no—
173#4314M1614yescomplemented
174#4313—44no—
175C8×D11—44no—
176#2971—111no—
177#2970—111no—
178C4×#135—111no—
179#1590—112no—
180#1584—112no—
181#1581—112no—
182C8×SD16—112no—
183#1568—111no—
184#1488—111no—
185#1488—111no—
186C8×M16D1111yescharacteristic, complemented
187C23×C11C4×D411yescharacteristic
188C22×D11—21no—
189C22×D11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11C4×D411yescharacteristic
195C2×C4×C11C4×D411yescharacteristic
196C2×C4×C11C4×D411yescharacteristic
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C22⋊D11—42no—
201C22⋊D11—42no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208D44—21no—
209D44—21no—
210D44—21no—
211D44C2×M1612yes—
212C4×D11—42no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—81no—
217C4×D11—81no—
218Dic22—21no—
219Dic22—21no—
220Dic22—21no—
221Dic22C2×M1612yes—
222C8×C11—21no—
223C8×C11—21no—
224C8×C11—21no—
225C8×C11—22no—
226C8×C11—42no—
227C8×C11C2×M1612yes—
228C8×C11#13514yescomplemented
229C11⋊C8—42no—
230C11⋊C8—42no—
231C2×#135—111no—
232C4×#41—111no—
233C4×#41—111no—
234#446—112no—
235C8×Q8—112no—
236C4×Q16—111no—
237C4×Q16—111no—
238C4×SD16—111no—
239C4×SD16—111no—
240C4×SD16—111no—
241C4×SD16—111no—
242C4×D8—111no—
243C4×D8—111no—
244#436—112no—
245#436—222no—
246#435—222no—
247C8×D4—112no—
248#432—111no—
249#432—111no—
250#432—221no—
251#432—221no—
252#431C2×D1111yescharacteristic
253#427—111no—
254#416—111no—
255#416—111no—
256C4×M16—221no—
257C4×M16C2×D1111yescharacteristic
258C2×#97—221no—
259C2×C4×C8C2×D1111yescharacteristic
260#335—112no—
261#334—112no—
262Q8⋊C8—112no—
263Q8⋊C8—112no—
264D4⋊C8—112no—
265D4⋊C8—112no—
266#322C2×D1112yes—
267C82C2×D1112yes—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11C2×C4×D411yescharacteristic
272C2×D11—22no—
273C2×D11—41no—
274C2×D11—41no—
275C2×D11—41no—
276C2×D11—41no—
277C2×D11—41no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11C22×M1611yescharacteristic
283C4×C11#56811yescharacteristic
284C4×C11C2×#13512yes—
285Dic11—22no—
286Dic11—41no—
287Dic11—41no—
288Dic11—41no—
289Dic11—41no—
290Dic11—41no—
291C2×#41—111no—
292C2×#41—111no—
293#135—224no—
294C2×Q16—111no—
295C2×SD16—111no—
296C2×SD16—111no—
297C2×D8—111no—
298C2×M16—222no—
299C2×M16D4412yes—
300C22×C8—222no—
301C22×C8C4×D1111yescharacteristic
302C22×C8C4×D1111yescharacteristic
303C4×Q8—111no—
304C4×Q8—111no—
305C4×Q8—111no—
306C4×Q8—111no—
307C4×D4—111no—
308C4×D4—111no—
309C4×D4—111no—
310C4×D4—111no—
311C4×D4—221no—
312C4×D4—221no—
313C4×D4—221no—
314C4×D4—221no—
315#117—111no—
316#117—111no—
317#117—221no—
318#117—221no—
319C2×C42—221no—
320C2×C42—221no—
321C2×C42C22×D1111yescharacteristic
322#107—111no—
323#107—111no—
324#106—111no—
325#106—111no—
326C4⋊C8—21no—
327C4⋊C8—112no—
328C4⋊C8—112no—
329C4⋊C8—222no—
330C4⋊C8—222no—
331#103—111no—
332#103—111no—
333#103—111no—
334#103—111no—
335#102—111no—
336#102—111no—
337#102—111no—
338#102—111no—
339C22⋊C8—21no—
340C22⋊C8—221no—
341C22⋊C8—221no—
342C22⋊C8—222no—
343C22⋊C8—222no—
344#97—222no—
345#97—221no—
346#97—221no—
347#97D4411yescharacteristic
348#97D4411yescharacteristic
349C4×C8—222no—
350C4×C8C4×D1111yescharacteristic
351C4×C8C4×D1111yescharacteristic
352C4×C8C22×D1112yes—
353C4×C8C22×D1111yescharacteristic
354C4×C8C22×D1111yescharacteristic
355C4×C8C22×D1112yes—
356C2×C11—41no—
357C2×C11D4×M1611yescharacteristic
358C2×C11C4×#13511yescharacteristic
359C2×C11#295711yescharacteristic
360D11—42no—
361D11—81no—
362#41—222no—
363#41—222no—
364#41—441no—
365#41—441no—
366C2×Q8—111no—
367C2×Q8—111no—
368C2×D4—111no—
369C2×D4—111no—
370C2×D4—221no—
371C2×D4—221no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4C2×C4×D1111yescharacteristic
379C22×C4C2×D4411yescharacteristic
380C22×C4#433911yescharacteristic
381Q16—222no—
382SD16—114no—
383SD16—222no—
384D8—222no—
385M16—24no—
386M16—444no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—41no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—444no—
393C2×C8C2×C4×D1111yescharacteristic
394C2×C8C2×C4×D1111yescharacteristic
395C2×C8C2×C4×D1111yescharacteristic
396C2×C8C2×C4×D1111yescharacteristic
397C2×C8C2×D4412yes—
398C2×C8C2×D4412yes—
399C4⋊C4—111no—
400C4⋊C4—111no—
401C4⋊C4—111no—
402C4⋊C4—111no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C22⋊C4—221no—
408C22⋊C4—221no—
409C22⋊C4—221no—
410C22⋊C4—221no—
411C22⋊C4—221no—
412C22⋊C4—221no—
413C42—221no—
414C42—221no—
415C42—221no—
416C42—221no—
417C42—221no—
418C42—221no—
419C42C2×C4×D1111yescharacteristic
420C42C2×D4411yescharacteristic
421C42#433911yescharacteristic
422C42C23×D1111yescharacteristic
423C11#1803711yescharacteristic, complemented, Sylow
424C23—221no—
425C23—221no—
426C23C4×D4411yescharacteristic
427Q8—112no—
428Q8—221no—
429Q8—221no—
430Q8—221no—
431D4—112no—
432D4—221no—
433D4—221no—
434D4—221no—
435D4—442no—
436D4—442no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—881no—
452C2×C4—881no—
453C2×C4C4×D4411yescharacteristic
454C2×C4C4×D4411yescharacteristic
455C2×C4C4×D4411yescharacteristic
456C2×C4C22×C4×D1111yescharacteristic
457C2×C4C22×D4411yescharacteristic
458C2×C4C2×#433911yescharacteristic
459C8—22no—
460C8—21no—
461C8—21no—
462C8—21no—
463C8—42no—
464C8—442no—
465C8—442no—
466C8#6695714yescomplemented
467C8M16×D1112yes—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—222no—
472C22—441no—
473C22—441no—
474C22—441no—
475C22—441no—
476C22—441no—
477C22C2×C4×D4411yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—222no—
483C4—441no—
484C4—441no—
485C4—441no—
486C4—441no—
487C4—441no—
488C4C2×#6695712yes—
489C4C2×M16×D1111yescharacteristic
490C4#1062327611yescharacteristic
491C2—41no—
492C2—442no—
493C2—881no—
494C2M16×D4411yescharacteristic
495C2C4×#6695711yescharacteristic
496C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×M16C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C4
cosocleC42×C11C24
hypercenterC8×M16D11
hypocenterC11#18037
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
1. #13077634C2semidirect
2. #13077631C2semidirect
4. #13067508C2semidirect
5. #13067468C2semidirect
6. #13067447C2semidirect
7. C8×#4314C2semidirect
8. #13067379C2semidirect
9. #13067051C2semidirect
10. #13067051C2semidirect
11. C8×C11×M16C2semidirect
173. #4314M16semidirect
186. C8×M16D11semidirect
228. C8×C11#135semidirect
423. C11#18037semidirect
466. C8#66957semidirect

Maximal subgroups

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

subgroupindex
#130776342
#130776312
C4×#669572
#130675082
#130674682
#130674472
C8×#43142
#130673792
#130670512
C8×C11×M162
#1803711