Finite Group Databasebeta

← #14736605

Subgroups — #14736605

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#13079010C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic
3C2×#10622621C211yesmaximal, characteristic, complemented
4#13068191C212yesmaximal, complemented
5#13068149C212yesmaximal, complemented
6#13068067C212yesmaximal, complemented
7#13068025C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067298C211yesmaximal, characteristic, complemented
10#13067294C211yesmaximal, characteristic, complemented
11D4×C11×M16C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C2×C4×D4×C11C2211yescharacteristic
14#10623008C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#436C2212yes—
17C11×#435—22no—
18C8×D4×C11C2212yes—
19C11×#423C2211yescharacteristic
20C11×#407—21no—
21C4×C11×M16C2211yescharacteristic
22#10622830—21no—
23C2×#66896—21no—
24#10622746—21no—
25#10622746—21no—
26#10622628C2211yescharacteristic
27#10622628C2211yescharacteristic
28C4×#4323—21no—
29C4×#4323—21no—
30#10622621—21no—
31#10622621—21no—
32#10622621C2212yes—
33#10622621C2212yes—
34#10622620C2211yescharacteristic
35#10622620C2211yescharacteristic
36#10622580—21no—
37C2×#66872—21no—
38#10622538C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622327—22no—
41#10622307C2212yescomplemented
42#10622294C2212yescomplemented
43#10622123C2212yescomplemented
44#10622120C2212yescomplemented
45#10622119C2212yescomplemented
46#10622119C2212yescomplemented
47#10622096C2212yescomplemented
48#10622095C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C2×#4339—21no—
52C22×Dic22—21no—
53C2×C11×M16—21no—
54C2×C11×M16—22no—
55C2×C11×M16—44no—
56C2×C11×M16D411yescharacteristic
57C2×C11×M16D411yescharacteristic
58C22×C8×C11—22no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11D411yescharacteristic
62C4×D4×C11D411yescharacteristic
63C4×D4×C11C2311yescharacteristic
64C4×D4×C11C2311yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×#4323—21no—
69C2×#4323—21no—
70#66983—21no—
71#66983—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C22×C11⋊C8—21no—
75#66928—21no—
76#66927C2311yescharacteristic
77C4×D44—21no—
78C4×D44—21no—
79#66922—21no—
80#66922—21no—
81#66922—21no—
82#66922C2312yes—
83#66922C2311yescharacteristic
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×C22⋊C8—22no—
87C11×C22⋊C8—22no—
88C11×#97D412yes—
89C4×C8×C11C2312yes—
90#66896—22no—
91#66896—22no—
92#66896—21no—
93#66896—21no—
94C22⋊(C11⋊C8)—21no—
95#66885—22no—
96#66885—22no—
97#66880—22no—
98#66880—22no—
99#66873—21no—
100#66873—21no—
101#66872—22no—
102#66872—22no—
103#66871—21no—
104#66871—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4×C11⋊C8—21no—
110#19168—111nomaximal, Sylow
111C24×C11—21no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—41no—
115C2×D4×C11C2×D411yescharacteristic
116C2×D4×C11C2×D411yescharacteristic
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4111yescharacteristic
127C2×C22⋊D11—41no—
128C22×Dic11—41no—
129#4339—42no—
130#4339—42no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×C4×D11—41no—
135C2×Dic22—21no—
136C2×Dic22—22no—
137C2×Dic22—41no—
138C2×Dic22—82no—
139C11×M16—22no—
140C11×M16—22no—
141C11×M16—44no—
142C11×M16—42no—
143C2×C8×C11—22no—
144C2×C8×C11—44no—
145C2×C8×C11C2×D412yes—
146C2×C8×C11C2×D412yes—
147C11×C4⋊C4—21no—
148C11×C4⋊C4C2×D411yescharacteristic
149C11×C4⋊C4C2×D411yescharacteristic
150C11×C22⋊C4—21no—
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11#4111yescharacteristic
157C42×C11C2411yescharacteristic
158#4323—42no—
159#4323—42no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162C4⋊Dic11—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—42no—
172#3141—111no—
173#3100—111no—
174C2×#476—111no—
175D4×M16D1111yescharacteristic, complemented
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—
190D4×C11—21no—
191D4×C11—21no—
192D4×C11—21no—
193D4×C11—42no—
194D4×C11#13712yes—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#13512yes—
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C22⋊D11—82no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C2×Dic11—82no—
219D44—41no—
220D44—41no—
221D44—41no—
222D44—41no—
223D44—81no—
224C4×D11—82no—
225Dic22—41no—
226Dic22—41no—
227Dic22—82no—
228Dic22—82no—
229C8×C11—22no—
230C8×C11—22no—
231C8×C11—42no—
232C11⋊C8—41no—
233C11⋊C8—42no—
234C11⋊C8—41no—
235C22×M16—21no—
236#532—111no—
237C2×C4⋊Q8—111no—
238C2×C4×D4C2×D1111yescharacteristic
239#489—222no—
240#487—112no—
241#486—112no—
242#480—221no—
243#476—112no—
244#476—112no—
245#476—221no—
246#476—221no—
247#474—111no—
248#474—111no—
249#459—111no—
250#459—111no—
251#447—221no—
252C4×D8—221no—
253C4×D8—221no—
254#436C2×D1112yes—
255#435—22no—
256C8×D4C2×D1112yes—
257#431—111no—
258C2×#106—221no—
259#423C2×D1111yescharacteristic
260C2×C4⋊C8—111no—
261#417—221no—
262#417—221no—
263C2×#102—221no—
264#407—21no—
265C4×M16C2×D1111yescharacteristic
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#46312yes—
292C4×C11C2×#13511yescharacteristic
293C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C11C2×#13711yescharacteristic
295C4×C11#57511yescharacteristic
296Dic11—81no—
297Dic11—82no—
298C2×#41—221no—
299C22×Q8—221no—
300C22×D4D4411yescharacteristic
301C23×C4—21no—
302C2×D8—221no—
303C2×D8—221no—
304C2×M16—21no—
305C2×M16—22no—
306C2×M16—44no—
307C2×M16C22⋊D1111yescharacteristic
308C2×M16C22⋊D1111yescharacteristic
309C22×C8—22no—
310C22×C8—221no—
311C4⋊Q8—112no—
312C4⋊Q8—111no—
313C4⋊Q8—221no—
314C4⋊Q8—221no—
315C4⋊Q8—221no—
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×D4D4411yescharacteristic
325C4×D4D4411yescharacteristic
326C4×D4C22×D1111yescharacteristic
327C4×D4C22×D1111yescharacteristic
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4D4411yescharacteristic
331C2×C22⋊C4—21no—
332C2×C42C22×D1111yescharacteristic
333#107—221no—
334#107—221no—
335#106—222no—
336#106—222no—
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—222no—
346#102—222no—
347#102—221no—
348#102—221no—
349#102—222no—
350#102—222no—
351#102—221no—
352#102—221no—
353C22⋊C8—22no—
354C22⋊C8—22no—
355C22⋊C8—221no—
356#97C22⋊D1112yes—
357C4×C8—221no—
358C4×C8C22×D1112yes—
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—222no—
370C2×Q8—221no—
371C2×Q8—441no—
372C2×Q8—882no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—41no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—441no—
380C2×D4C2×D4411yescharacteristic
381C2×D4C2×D4411yescharacteristic
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4C2×D4411yescharacteristic
392C22×C4#433911yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394D8—442no—
395D8—442no—
396M16—22no—
397M16—22no—
398M16—44no—
399M16—42no—
400C2×C8—22no—
401C2×C8—44no—
402C2×C8—221no—
403C2×C8—221no—
404C2×C8—222no—
405C2×C8—442no—
406C2×C8C2×C22⋊D1112yes—
407C2×C8C2×C22⋊D1112yes—
408C4⋊C4—21no—
409C4⋊C4—222no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4C2×D4411yescharacteristic
416C4⋊C4C2×D4411yescharacteristic
417C22⋊C4—21no—
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C42C2×D4411yescharacteristic
424C42#433911yescharacteristic
425C42C2×C22⋊D1111yescharacteristic
426C42C23×D1111yescharacteristic
427C11#1916811yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430C23—42no—
431C23—42no—
432C23—81no—
433C23—441no—
434C23#6698311yescharacteristic
435Q8—441no—
436Q8—441no—
437Q8—882no—
438Q8—882no—
439D4—21no—
440D4—21no—
441D4—21no—
442D4—42no—
443D4—441no—
444D4—441no—
445D4—441no—
446D4—441no—
447D4—881no—
448D4—882no—
449D4#6696212yes—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—441no—
463C2×C4—442no—
464C2×C4—882no—
465C2×C4—882no—
466C2×C4#6698311yescharacteristic
467C2×C4#6698311yescharacteristic
468C2×C4#6698311yescharacteristic
469C2×C4#6698512yes—
470C2×C4#6700312yes—
471C2×C4C22×D4411yescharacteristic
472C2×C4C2×#433911yescharacteristic
473C2×C4C22×C22⋊D1111yescharacteristic
474C8—22no—
475C8—22no—
476C8—42no—
477C8—441no—
478C8—442no—
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#1062262912yes—
493C22C2×#6698311yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—881no—
500C4—882no—
501C4#1062262912yes—
502C4C2×#6696211yescharacteristic
503C4#1062327911yescharacteristic
504C4C2×#6698511yescharacteristic
505C4C2×#6700311yescharacteristic
506C2—22no—
507C2—42no—
508C2—81no—
509C2—1761no—
510C2C2×#1062262911yescharacteristic
511C2#1307824611yescharacteristic
512C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×M16C2
socleC22×C11C2×#121
prime radical#13078616C2
hypercenterD4×M16D11
hypocenterC11#19168
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
1. #13079010C2semidirect
3. C2×#10622621C2semidirect
4. #13068191C2semidirect
5. #13068149C2semidirect
6. #13068067C2semidirect
7. #13068025C2semidirect
8. #13067368C2semidirect
9. #13067298C2semidirect
10. #13067294C2semidirect
11. D4×C11×M16C2semidirect
41. #10622307C22semidirect
42. #10622294C22semidirect
43. #10622123C22semidirect
44. #10622120C22semidirect
45. #10622119C22semidirect
46. #10622119C22semidirect
47. #10622096C22semidirect
48. #10622095C22semidirect
175. D4×M16D11semidirect
427. C11#19168semidirect

Maximal subgroups

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

subgroupindex
#130790102
#130786162
C2×#106226212
#130681912
#130681492
#130680672
#130680252
#130673682
#130672982
#130672942
D4×C11×M162
#1916811