Finite Group Databasebeta

← #14725491

Subgroups — #14725491

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077748C211yesmaximal, characteristic, complemented
2#13077741C211yesmaximal, characteristic, complemented
3#13067519C212yesmaximal, complemented
4#13067467C212yesmaximal, complemented
5#13067446C212yesmaximal, complemented
6SD16⋊(C11⋊C8)C212yesmaximal, complemented
7#13067375C211yesmaximal, characteristic, complemented
8#13067055C211yesmaximal, characteristic, complemented
9#13067055C211yesmaximal, characteristic, complemented
10#13066905C211yesmaximal, characteristic, complemented
11C4×C11×#135C211yesmaximal, characteristic
12C2×C11×#135C411yescharacteristic
13C4×C11×#41C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15C4×C11×Q16C411yescharacteristic
16C4×C11×Q16C2211yescharacteristic
17C4×C11×SD16C411yescharacteristic
18C4×C11×SD16C411yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C4×C11×D8C411yescharacteristic
22C4×C11×D8C2211yescharacteristic
23C11×#427C411yescharacteristic
24C11×#416C411yescharacteristic
25C11×#416C411yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27#10622637C2212yes—
28Q8×C11⋊C8C2212yes—
29#10622625—22no—
30#10622625C2212yes—
31#10622624—22no—
32D4×C11⋊C8C2212yes—
33#10622539—21no—
34#10622538—21no—
35#10622538C2211yescharacteristic
36#10622537—21no—
37#10622537C2211yescharacteristic
38#10622537C2211yescharacteristic
39C2×C4⋊(C11⋊C8)—21no—
40C4×#4318C2211yescharacteristic
41Q8⋊(C11⋊C8)C2212yes—
42Q8⋊(C11⋊C8)C2212yes—
43D4⋊(C11⋊C8)C2212yes—
44D4⋊(C11⋊C8)C2212yes—
45#10622096C2212yes—
46#10622096C2212yes—
47#10622093C2212yes—
48#10622092C2212yes—
49C2×C11×#41C2×C411yescharacteristic
50C2×C11×#41C2×C411yescharacteristic
51C11×#135—24no—
52C2×C11×Q16C2×C411yescharacteristic
53C2×C11×SD16C2×C411yescharacteristic
54C2×C11×SD16C2×C411yescharacteristic
55C2×C11×D8C2×C411yescharacteristic
56C22×C8×C11C2×C411yescharacteristic
57C22×C8×C11C2×C411yescharacteristic
58C4×Q8×C11C2×C411yescharacteristic
59C4×Q8×C11C2×C411yescharacteristic
60C4×Q8×C11C2311yescharacteristic
61C4×Q8×C11C2311yescharacteristic
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11C2×C411yescharacteristic
67C4×D4×C11C2×C411yescharacteristic
68C4×D4×C11C2311yescharacteristic
69C4×D4×C11C2311yescharacteristic
70C11×#117—21no—
71C11×#117—21no—
72C11×#117C2×C411yescharacteristic
73C11×#117C2×C411yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×#4318—21no—
78C2×#4318—21no—
79C2×#4318—21no—
80C2×#4318—22no—
81C22×C11⋊C8—22no—
82C11×#107C2×C411yescharacteristic
83C11×#107C2×C411yescharacteristic
84C11×#106C2×C411yescharacteristic
85C11×#106C2×C411yescharacteristic
86C11×#103C2×C411yescharacteristic
87C11×#103C2×C411yescharacteristic
88C11×#103C2×C411yescharacteristic
89C11×#103C2×C411yescharacteristic
90C11×#102C2×C411yescharacteristic
91C11×#102C2×C411yescharacteristic
92C11×#102C2×C411yescharacteristic
93C11×#102C2×C411yescharacteristic
94C4×C8×C11C2×C411yescharacteristic
95C4×C8×C11C2×C411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97C4×C8×C11C2311yescharacteristic
98C22⋊(C11⋊C8)—22no—
99C22⋊(C11⋊C8)—22no—
100C22⋊(C11⋊C8)D412yes—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)—22no—
105C4⋊(C11⋊C8)D411yescharacteristic
106C4⋊(C11⋊C8)D411yescharacteristic
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109#66867—21no—
110#66867—22no—
111C4×C11⋊C8—22no—
112C4×C11⋊C8C2312yes—
113C4×C11⋊C8C2312yes—
114#18061—111nomaximal, Sylow
115C11×#41—22no—
116C11×#41—22no—
117C11×#41—41no—
118C11×#41—41no—
119C2×Q8×C11C22×C411yescharacteristic
120C2×Q8×C11C22×C411yescharacteristic
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11C22×C411yescharacteristic
124C2×D4×C11C22×C411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C11×Q16—22no—
135C11×SD16—22no—
136C11×SD16M1614yescomplemented
137C11×D8—22no—
138C2×C8×C11—22no—
139C2×C8×C11—41no—
140C2×C8×C11C22×C411yescharacteristic
141C2×C8×C11C22×C411yescharacteristic
142C2×C8×C11C22×C411yescharacteristic
143C2×C8×C11C22×C411yescharacteristic
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4C22×C411yescharacteristic
149C11×C4⋊C4C22×C411yescharacteristic
150C11×C4⋊C4C22×C411yescharacteristic
151C11×C4⋊C4C22×C411yescharacteristic
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C11×C22⋊C4—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11C22×C411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11#4111yescharacteristic
167C42×C11C2411yescharacteristic
168#4318—42no—
169#4318—81no—
170#4318—81no—
171#4318—82no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—82no—
176C2×C11⋊C8C2×D412yes—
177C2×C11⋊C8C2×D412yes—
178#2991—111no—
179#2990—111no—
180C4×#135D1111yescharacteristic
181#1592—112no—
182#1584—112no—
183#1581—112no—
184SD16⋊C8—112no—
185#1567—111no—
186#1489—111no—
187#1489—111no—
188#1451—111no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11C4×D411yescharacteristic
192Q8×C11—21no—
193Q8×C11—21no—
194Q8×C11—21no—
195Q8×C11C2×M1612yes—
196D4×C11—21no—
197D4×C11—21no—
198D4×C11—21no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11C2×M1612yes—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11C4×D411yescharacteristic
222C2×C4×C11C4×D411yescharacteristic
223C2×C4×C11C4×D411yescharacteristic
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C8×C11—21no—
228C8×C11—21no—
229C8×C11—21no—
230C8×C11C2×M1612yes—
231C11⋊C8—22no—
232C11⋊C8—22no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C11⋊C8—42no—
236C2×#135Dic1111yescharacteristic
237C4×#41C2×D1111yescharacteristic
238C4×#41C2×D1111yescharacteristic
239#446—112no—
240C8×Q8—112no—
241C4×Q16Dic1111yescharacteristic
242C4×Q16C2×D1111yescharacteristic
243C4×SD16Dic1111yescharacteristic
244C4×SD16Dic1111yescharacteristic
245C4×SD16C2×D1111yescharacteristic
246C4×SD16C2×D1111yescharacteristic
247C4×D8Dic1111yescharacteristic
248C4×D8C2×D1111yescharacteristic
249#436—112no—
250#436—222no—
251#435—222no—
252C8×D4—112no—
253#432—221no—
254#431—111no—
255#431—221no—
256#427Dic1111yescharacteristic
257#423—111no—
258#423—111no—
259#423—221no—
260C2×C4⋊C8—221no—
261#416Dic1111yescharacteristic
262#416Dic1111yescharacteristic
263C4×M16—111no—
264C2×C4×C8C2×D1111yescharacteristic
265#335—112no—
266#335—112no—
267Q8⋊C8—112no—
268Q8⋊C8—112no—
269D4⋊C8—112no—
270D4⋊C8—112no—
271#322—112no—
272#322—112no—
273C22×C11—21no—
274C22×C11—22no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—41no—
281C22×C11—41no—
282C22×C11C2×C4×D411yescharacteristic
283C4×C11—21no—
284C4×C11—22no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—41no—
288C4×C11—41no—
289C4×C11—41no—
290C4×C11—41no—
291C4×C11—41no—
292C4×C11#44412yes—
293C4×C11C22×M1611yescharacteristic
294C4×C11#56811yescharacteristic
295C4×C11#57611yescharacteristic
296C4×C11#57811yescharacteristic
297C2×#41C2×Dic1111yescharacteristic
298C2×#41C2×Dic1111yescharacteristic
299#135—24no—
300C2×Q16C2×Dic1111yescharacteristic
301C2×SD16C2×Dic1111yescharacteristic
302C2×SD16C2×Dic1111yescharacteristic
303C2×D8C2×Dic1111yescharacteristic
304C2×M16—222no—
305C2×M16—221no—
306C2×M16—221no—
307C2×M16—221no—
308C22×C8—222no—
309C22×C8C2×Dic1111yescharacteristic
310C22×C8C2×Dic1111yescharacteristic
311C4×Q8C2×Dic1111yescharacteristic
312C4×Q8C2×Dic1111yescharacteristic
313C4×Q8C22×D1111yescharacteristic
314C4×Q8C22×D1111yescharacteristic
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4C2×Dic1111yescharacteristic
320C4×D4C2×Dic1111yescharacteristic
321C4×D4C22×D1111yescharacteristic
322C4×D4C22×D1111yescharacteristic
323#117—21no—
324#117—21no—
325#117C2×Dic1111yescharacteristic
326#117C2×Dic1111yescharacteristic
327C2×C42—21no—
328C2×C42—21no—
329C2×C42C22×D1111yescharacteristic
330#107C2×Dic1111yescharacteristic
331#107C2×Dic1111yescharacteristic
332#106C2×Dic1111yescharacteristic
333#106C2×Dic1111yescharacteristic
334C4⋊C8—111no—
335C4⋊C8—111no—
336C4⋊C8—112no—
337C4⋊C8—112no—
338C4⋊C8—222no—
339C4⋊C8—222no—
340C4⋊C8—221no—
341C4⋊C8—221no—
342#103C2×Dic1111yescharacteristic
343#103C2×Dic1111yescharacteristic
344#103C2×Dic1111yescharacteristic
345#103C2×Dic1111yescharacteristic
346#102C2×Dic1111yescharacteristic
347#102C2×Dic1111yescharacteristic
348#102C2×Dic1111yescharacteristic
349#102C2×Dic1111yescharacteristic
350C22⋊C8—112no—
351C22⋊C8—222no—
352C22⋊C8—222no—
353#97—222no—
354#97—221no—
355C4×C8—112no—
356C4×C8—112no—
357C4×C8—222no—
358C4×C8C2×Dic1111yescharacteristic
359C4×C8C2×Dic1111yescharacteristic
360C4×C8C22×D1111yescharacteristic
361C4×C8C22×D1111yescharacteristic
362C2×C11—41no—
363C2×C11—42no—
364C2×C11—81no—
365C2×C11D4×M1611yescharacteristic
366C2×C11#295111yescharacteristic
367C2×C11C2×#44411yescharacteristic
368#41—22no—
369#41—22no—
370#41—41no—
371#41—41no—
372C2×Q8C22×Dic1111yescharacteristic
373C2×Q8C22×Dic1111yescharacteristic
374C2×D4—21no—
375C2×D4—21no—
376C2×D4C22×Dic1111yescharacteristic
377C2×D4C22×Dic1111yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4D4×D1111yescharacteristic
385C22×C4#434111yescharacteristic
386C22×C4C22×Dic1111yescharacteristic
387Q16—22no—
388SD16—22no—
389SD16#431814yescomplemented
390D8—22no—
391M16—442no—
392M16—882no—
393M16—881no—
394M16—881no—
395C2×C8—22no—
396C2×C8—41no—
397C2×C8—112no—
398C2×C8—112no—
399C2×C8—222no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8—882no—
403C2×C8C22×Dic1111yescharacteristic
404C2×C8C22×Dic1111yescharacteristic
405C2×C8C22×Dic1111yescharacteristic
406C2×C8C22×Dic1111yescharacteristic
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4C22×Dic1111yescharacteristic
412C4⋊C4C22×Dic1111yescharacteristic
413C4⋊C4C22×Dic1111yescharacteristic
414C4⋊C4C22×Dic1111yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42D4×D1111yescharacteristic
428C42#434111yescharacteristic
429C42C22×Dic1111yescharacteristic
430C42C23×D1111yescharacteristic
431C11#1806111yescharacteristic, complemented, Sylow
432C23—21no—
433C23—21no—
434C23D4×Dic1111yescharacteristic
435Q8—21no—
436Q8—21no—
437Q8—21no—
438Q8C2×#431812yes—
439D4—21no—
440D4—21no—
441D4—21no—
442D4—42no—
443D4—42no—
444D4C2×#431812yes—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4D4×Dic1111yescharacteristic
465C2×C4D4×Dic1111yescharacteristic
466C2×C4D4×Dic1111yescharacteristic
467C2×C4C2×D4×D1111yescharacteristic
468C2×C4C2×#434111yescharacteristic
469C2×C4C23×Dic1111yescharacteristic
470C8—21no—
471C8—21no—
472C8—21no—
473C8—222no—
474C8—222no—
475C8—442no—
476C8—442no—
477C8—442no—
478C8C2×#431812yes—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22C2×D4×Dic1111yescharacteristic
489C4—21no—
490C4—21no—
491C4—22no—
492C4—21no—
493C4—41no—
494C4—41no—
495C4—41no—
496C4—41no—
497C4—41no—
498C4#1062281012yes—
499C4#1062330011yescharacteristic
500C4#1062330211yescharacteristic
501C4C22×#431811yescharacteristic
502C4#1062335011yescharacteristic
503C2—41no—
504C2—42no—
505C2—81no—
506C2D4×#431811yescharacteristic
507C2#1307749211yescharacteristic
508C2C2×#1062281011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC4×C11×#135C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#135C4
cosocleC42×C11C24
hypercenterC4×#135D11
hypocenterC11#18061
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13077748C2semidirect
2. #13077741C2semidirect
3. #13067519C2semidirect
4. #13067467C2semidirect
5. #13067446C2semidirect
6. SD16⋊(C11⋊C8)C2semidirect
7. #13067375C2semidirect
8. #13067055C2semidirect
9. #13067055C2semidirect
10. #13066905C2semidirect
136. C11×SD16M16semidirect
389. SD16#4318semidirect
431. C11#18061semidirect

Maximal subgroups

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

subgroupindex
#130777482
#130777412
#130675192
#130674672
#130674462
SD16⋊(C11⋊C8)2
#130673752
#130670552
#130669052
C4×C11×#1352
#1806111