Finite Group Databasebeta

← #14736609

Subgroups — #14736609

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079012C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic
3D4×#4318C211yesmaximal, characteristic, complemented
4#13068193C212yesmaximal, complemented
5#13068151C212yesmaximal, complemented
6#13068069C212yesmaximal, complemented
7#13068027C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067297C211yesmaximal, characteristic, complemented
10#13067291C211yesmaximal, characteristic, complemented
11C2×C11×#476C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4318—21no—
15#10623008C2211yescharacteristic
16C11×#476—21no—
17C11×#476—21no—
18C11×#476C2212yes—
19C11×#476C2212yes—
20C2×C11×#106—21no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102—21no—
23#10622830—21no—
24#10622820—21no—
25#10622706C2212yescomplemented
26#10622702—22no—
27#10622701C2212yescomplemented
28#10622628C2211yescharacteristic
29#10622628C2211yescharacteristic
30C4×#4323—21no—
31C4×#4323—21no—
32#10622625C2212yes—
33#10622624—22no—
34D4×C11⋊C8C2212yes—
35#10622620C2211yescharacteristic
36#10622620C2211yescharacteristic
37#10622580—21no—
38#10622579—21no—
39#10622579—21no—
40#10622538C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622184C2212yescomplemented
44#10622184C2212yescomplemented
45#10622124C2212yescomplemented
46#10622123C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×Q8×C11—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C2×#4339—21no—
53C22×C8×C11—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8C2312yes—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11D411yescharacteristic
61C4×D4×C11D411yescharacteristic
62C4×D4×C11C2311yescharacteristic
63C4×D4×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4323—21no—
70C2×#4323—21no—
71#66983—21no—
72#66983—21no—
73C2×#4318—21no—
74C2×#4318—22no—
75C2×#4318—44no—
76C2×#4318D411yescharacteristic
77C2×#4318D411yescharacteristic
78C22×C11⋊C8—22no—
79#66928—21no—
80#66927C2311yescharacteristic
81C4×D44—21no—
82C4×D44—21no—
83#66922C2311yescharacteristic
84C11×#106—22no—
85C11×#106—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2312yes—
88C11×#102—22no—
89C11×#102—22no—
90#66896—21no—
91#66896—21no—
92C22⋊(C11⋊C8)—21no—
93C22⋊(C11⋊C8)—22no—
94C22⋊(C11⋊C8)—22no—
95#66874—22no—
96#66874—22no—
97#66873—21no—
98#66873—21no—
99#66873—22no—
100#66873—22no—
101#66871—21no—
102#66871—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)C2312yes—
105C4⋊(C11⋊C8)C2311yescharacteristic
106C4⋊(C11⋊C8)C2311yescharacteristic
107#66867D412yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8C2312yes—
110#19168—111nomaximal, Sylow
111C24×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—41no—
114C2×Q8×C11—82no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C2×D4×C11C2×D411yescharacteristic
119C2×D4×C11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—41no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C2×C22⋊D11—41no—
132#4339—42no—
133#4339—42no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×C4×D11—41no—
138C2×Dic22—21no—
139C2×C8×C11—22no—
140C2×C8×C11—42no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4C2×D411yescharacteristic
147C11×C4⋊C4C2×D411yescharacteristic
148C11×C22⋊C4—21no—
149C11×C22⋊C4—21no—
150C11×C22⋊C4—21no—
151C11×C22⋊C4—21no—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11#4111yescharacteristic
155C42×C11C2411yescharacteristic
156#4323—42no—
157#4323—42no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162#4318—22no—
163#4318—22no—
164#4318—44no—
165#4318—42no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—44no—
170C2×C11⋊C8C2×D412yes—
171C2×C11⋊C8C2×D412yes—
172#3141—111no—
173#3100—111no—
174C2×#476D1111yescharacteristic, complemented
175D4×M16—111no—
176#1703—112no—
177#1697—112no—
178#1683—112no—
179#1677—112no—
180#1565—111no—
181#1548—111no—
182#1547—111no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—81no—
188C23×C11#12111yescharacteristic
189C22×D11—41no—
190Q8×C11—82no—
191Q8×C11—82no—
192D4×C11—21no—
193D4×C11—21no—
194D4×C11—21no—
195D4×C11—42no—
196D4×C11#13712yes—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—82no—
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#13512yes—
215C2×C4×C11AGL(1,ℤ/8)12yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C22⋊D11—82no—
220C2×Dic11—41no—
221D44—41no—
222D44—41no—
223D44—41no—
224D44—41no—
225D44—81no—
226C4×D11—82no—
227Dic22—41no—
228Dic22—41no—
229C8×C11—42no—
230C11⋊C8—22no—
231C11⋊C8—22no—
232C11⋊C8—42no—
233C11⋊C8—41no—
234C11⋊C8—41no—
235C22×M16—221no—
236#532—111no—
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×C4×D4C2×D1111yescharacteristic
239#489—222no—
240#487—112no—
241#486—112no—
242#480—221no—
243#476—21no—
244#476—21no—
245#476C2×D1112yes—
246#476C2×D1112yes—
247#474—111no—
248#474—111no—
249#459—111no—
250#459—111no—
251#447—221no—
252C4×D8—221no—
253C4×D8—221no—
254#436—112no—
255#435—222no—
256C8×D4—112no—
257#431—111no—
258C2×#106—21no—
259#423—111no—
260C2×C4⋊C8C2×D1111yescharacteristic
261#417—221no—
262#417—221no—
263C2×#102—21no—
264#407—221no—
265C4×M16—111no—
266#335—112no—
267#334—112no—
268#333—112no—
269#333—112no—
270#332—112no—
271#331—112no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—22no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—84no—
281C22×C11#46312yes—
282C22×C11C2×#12111yescharacteristic
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—41no—
290C4×C11—41no—
291C4×C11—82no—
292C4×C11#46312yes—
293C4×C11C2×#13511yescharacteristic
294C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C11C2×#13711yescharacteristic
296C4×C11#57511yescharacteristic
297Dic11—81no—
298C2×#41—221no—
299C22×Q8—21no—
300C22×D4C22⋊D1111yescharacteristic
301C23×C4—21no—
302C2×D8—221no—
303C2×D8—221no—
304C2×M16—111no—
305C2×M16—111no—
306C2×M16—222no—
307C2×M16—221no—
308C2×M16—444no—
309C22×C8—21no—
310C22×C8—222no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—111no—
315C4⋊Q8C22×D1112yes—
316#127—111no—
317#124—221no—
318#121—221no—
319#121—221no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—221no—
323C4×D4—221no—
324C4×D4C22⋊D1111yescharacteristic
325C4×D4C22⋊D1111yescharacteristic
326C4×D4C22×D1111yescharacteristic
327C4×D4C22×D1111yescharacteristic
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4C22⋊D1111yescharacteristic
331C2×C22⋊C4—21no—
332C2×C42C22×D1111yescharacteristic
333#107—221no—
334#107—221no—
335#106—22no—
336#106—22no—
337C4⋊C8—21no—
338C4⋊C8—112no—
339C4⋊C8—111no—
340C4⋊C8—111no—
341C4⋊C8—221no—
342C4⋊C8C22×D1112yes—
343#103—222no—
344#103—222no—
345#102—22no—
346#102—22no—
347#102—222no—
348#102—222no—
349#102—221no—
350#102—221no—
351#102—221no—
352#102—221no—
353C22⋊C8—222no—
354C22⋊C8—222no—
355C22⋊C8—221no—
356#97—112no—
357C4×C8—112no—
358C4×C8—221no—
359C2×C11—22no—
360C2×C11—42no—
361C2×C11—81no—
362C2×C11C2×#46311yescharacteristic
363C2×C11#305611yescharacteristic
364C2×C11#306811yescharacteristic
365D11—161no—
366C24—21no—
367#41—442no—
368#41—442no—
369C2×Q8—22no—
370C2×Q8—41no—
371C2×Q8—82no—
372C2×Q8—221no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—41no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—441no—
380C2×D4C2×C22⋊D1111yescharacteristic
381C2×D4C2×C22⋊D1111yescharacteristic
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—41no—
390C22×C4—441no—
391C22×C4D4×D1111yescharacteristic
392C22×C4#434111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394D8—442no—
395D8—442no—
396M16—222no—
397M16—222no—
398M16—444no—
399M16—442no—
400C2×C8—22no—
401C2×C8—42no—
402C2×C8—112no—
403C2×C8—112no—
404C2×C8—222no—
405C2×C8—221no—
406C2×C8—221no—
407C2×C8—444no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4C2×C22⋊D1111yescharacteristic
416C4⋊C4C2×C22⋊D1111yescharacteristic
417C22⋊C4—21no—
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C42D4×D1111yescharacteristic
424C42#434111yescharacteristic
425C42C2×C22⋊D1111yescharacteristic
426C42C23×D1111yescharacteristic
427C11#1916811yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430C23—42no—
431C23—42no—
432C23—81no—
433C23—441no—
434C23#6699211yescharacteristic
435Q8—82no—
436Q8—82no—
437Q8—441no—
438Q8—441no—
439D4—21no—
440D4—21no—
441D4—21no—
442D4—42no—
443D4—441no—
444D4—441no—
445D4—441no—
446D4—441no—
447D4—881no—
448D4—882no—
449D4#6699512yes—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—82no—
464C2×C4—441no—
465C2×C4—882no—
466C2×C4#6696712yes—
467C2×C4#6696912yes—
468C2×C4#6699211yescharacteristic
469C2×C4#6699211yescharacteristic
470C2×C4#6699211yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4C2×#434111yescharacteristic
473C2×C4C22×C22⋊D1111yescharacteristic
474C8—42no—
475C8—222no—
476C8—222no—
477C8—442no—
478C8—441no—
479C8—441no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—84no—
489C22—881no—
490C22—881no—
491C22—881no—
492C22#1062277812yes—
493C22C2×#6699211yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—82no—
500C4—881no—
501C4#1062277812yes—
502C4C2×#6696711yescharacteristic
503C4C2×#6696911yescharacteristic
504C4C2×#6699511yescharacteristic
505C4#1062335311yescharacteristic
506C2—22no—
507C2—42no—
508C2—81no—
509C2—1761no—
510C2C2×#1062277811yescharacteristic
511C2#1307824211yescharacteristic
512C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#476C2
socleC22×C11C2×#121
prime radical#13078616C2
hypercenterC2×#476D11
hypocenterC11#19168
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13079012C2semidirect
3. D4×#4318C2semidirect
4. #13068193C2semidirect
5. #13068151C2semidirect
6. #13068069C2semidirect
7. #13068027C2semidirect
8. #13067366C2semidirect
9. #13067297C2semidirect
10. #13067291C2semidirect
11. C2×C11×#476C2semidirect
25. #10622706C22semidirect
27. #10622701C22semidirect
43. #10622184C22semidirect
44. #10622184C22semidirect
45. #10622124C22semidirect
46. #10622123C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
174. C2×#476D11semidirect
427. C11#19168semidirect

Maximal subgroups

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

subgroupindex
#130790122
#130786162
D4×#43182
#130681932
#130681512
#130680692
#130680272
#130673662
#130672972
#130672912
C2×C11×#4762
#1916811