Finite Group Databasebeta

← #14736855

Subgroups — #14736855

Order 2816.

746 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079923C211yesmaximal, characteristic, complemented
2#13079042C211yesmaximal, characteristic, complemented
3#13077328C211yesmaximal, characteristic, complemented
4#13068103C212yesmaximal, complemented
5#13068093C212yesmaximal, complemented
6#13067959C212yesmaximal, complemented
7#13067955C212yesmaximal, complemented
8C2×#10622118C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10#13067291C211yesmaximal, characteristic, complemented
11C11×#3245C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C11×#532C2211yescharacteristic
14C2×#67003—21no—
15C2×#67003—21no—
16C2×#67001—21no—
17#10623008C2211yescharacteristic
18C11×#474—21no—
19C11×#474C2212yes—
20C11×#466—22no—
21C11×#459—21no—
22C11×#459C2212yes—
23C2×C11×C4⋊C8C2211yescharacteristic
24#10622847—21no—
25#10622705C2211yescharacteristic
26#10622700—21no—
27#10622698C2211yescharacteristic
28#10622689C2211yescharacteristic
29#10622686C2211yescharacteristic
30#10622685—21no—
31#10622672—21no—
32#10622672—21no—
33#10622651—22no—
34#10622628C2212yes—
35#10622625—21no—
36#10622625C2212yes—
37D4×C11⋊C8—21no—
38D4×C11⋊C8C2212yes—
39#10622620C2212yes—
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622185C2212yes—
44#10622182C2212yes—
45#10622124C2212yes—
46#10622123C2212yes—
47#10622118C2212yes—
48#10622118C2212yes—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×#4339—21no—
52C2×C11×D8—22no—
53C22×C8×C11—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127D411yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#124—21no—
60C11×#121—21no—
61C11×#121—21no—
62C11×#121—21no—
63C11×#121D412yes—
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C4×D4×C11C2312yes—
68C2×C42×C11C2311yescharacteristic
69#67003—44no—
70#67003—44no—
71#67001—44no—
72C2×#4326—21no—
73C2×#4326—21no—
74C2×#4325—21no—
75C2×#4325—21no—
76C2×#4324—21no—
77C2×#4324—21no—
78C2×#4323—22no—
79C2×#4323—21no—
80C2×#4323—21no—
81#66983—21no—
82#66983—21no—
83C2×#4318—21no—
84C2×#4318—22no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—22no—
87C22×C11⋊C8D411yescharacteristic
88C22×C11⋊C8D411yescharacteristic
89#66928—21no—
90#66927C2311yescharacteristic
91C4×D44—21no—
92C4×D44—21no—
93#66922C2311yescharacteristic
94C11×#107—22no—
95C11×C4⋊C8—21no—
96C11×C4⋊C8C2312yes—
97C11×#102—22no—
98C11×#102—22no—
99#66896—22no—
100C22⋊(C11⋊C8)—22no—
101C22⋊(C11⋊C8)—22no—
102#66873—22no—
103#66871—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8D411yescharacteristic
109C4×C11⋊C8D411yescharacteristic
110C4×C11⋊C8C2311yescharacteristic
111C4×C11⋊C8C2311yescharacteristic
112#19189—111nomaximal, Sylow
113C11×#41—42no—
114C11×#41—42no—
115C11×#41—42no—
116C11×#41—42no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—41no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—22no—
128C22×C4×C11—41no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C2×C22⋊D11—41no—
133#4339—42no—
134#4339—42no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×C4×D11—41no—
139C2×Dic22—21no—
140C11×D8—82no—
141C2×C8×C11—22no—
142C2×C8×C11—81no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4C2×D412yes—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155#4326—42no—
156#4326—42no—
157#4325—42no—
158#4325—42no—
159#4324—42no—
160#4324—42no—
161#4323—42no—
162#4323—42no—
163#4323—82no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168#4318—44no—
169#4318—42no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—44no—
174C2×C11⋊C8—81no—
175C2×C11⋊C8D814yescomplemented
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178C2×C11⋊C8C2×D411yescharacteristic
179C2×C11⋊C8C2×D411yescharacteristic
180#3245—111no—
181#3245D1111yescharacteristic, complemented
182#3147—111no—
183#2931—111no—
184#1689—112no—
185#1687—112no—
186#1665—112no—
187#1665—112no—
188C2×#334—111no—
189#1547—111no—
190#1547—111no—
191C23×C11—22no—
192C23×C11—41no—
193C23×C11#12111yescharacteristic
194C22×D11—41no—
195Q8×C11—42no—
196Q8×C11—41no—
197Q8×C11—41no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—42no—
201D4×C11—44no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—42no—
207D4×C11—81no—
208D4×C11—82no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—82no—
217C2×C4×C11#12111yescharacteristic
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11C2×D812yes—
221C2×C4×C11AGL(1,ℤ/8)12yes—
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C22⋊D11—82no—
226C2×Dic11—41no—
227D44—41no—
228D44—41no—
229D44—41no—
230D44—41no—
231D44—81no—
232C4×D11—82no—
233Dic22—41no—
234Dic22—41no—
235C8×C11—42no—
236C11⋊C8—21no—
237C11⋊C8—21no—
238C11⋊C8—42no—
239C11⋊C8—42no—
240C11⋊C8C2×D812yes—
241C11⋊C8C2×D812yes—
242C2×#135—221no—
243C2×#135—221no—
244C2×#131—221no—
245#532—111no—
246#532C2×D1111yescharacteristic
247#532C2×D1111yescharacteristic
248#495—221no—
249#495—221no—
250#494—111no—
251#493—111no—
252#492—111no—
253#492—111no—
254#474—21no—
255#474—112no—
256#474—221no—
257#474C2×D1112yes—
258#466—22no—
259#466—222no—
260#459—21no—
261#459—112no—
262#459—221no—
263#459C2×D1112yes—
264#436—112no—
265#436—221no—
266C8×D4—112no—
267C8×D4—221no—
268#423—111no—
269C2×C4⋊C8—111no—
270C2×C4⋊C8C2×D1111yescharacteristic
271#408—221no—
272C2×C4×C8—111no—
273#334—112no—
274#334—112no—
275#332—112no—
276#332—112no—
277#331—112no—
278#331—112no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11#45912yes—
288C22×C11C2×#12111yescharacteristic
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—81no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—42no—
296C4×C11—81no—
297C4×C11#45912yes—
298C4×C11C22×D811yescharacteristic
299C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C11#57711yescharacteristic
301C4×C11#57711yescharacteristic
302Dic11—81no—
303C2×#41—21no—
304C2×#41—21no—
305C2×#41—221no—
306#135—444no—
307#135—444no—
308C2×Q16—221no—
309C2×Q16—221no—
310C2×SD16—221no—
311C2×SD16—221no—
312C2×SD16—221no—
313C2×SD16—221no—
314C2×D8—22no—
315C2×D8—221no—
316C2×D8—221no—
317C2×D8—222no—
318#131—444no—
319C2×M16—222no—
320C2×M16—221no—
321C22×C8—21no—
322C22×C8—111no—
323C22×C8—111no—
324C22×C8—222no—
325C22×C8—221no—
326C4⋊Q8—111no—
327C4⋊Q8C22⋊D1111yescharacteristic
328C4⋊Q8C22×D1111yescharacteristic
329#127—111no—
330#127C22⋊D1111yescharacteristic
331#127C22×D1111yescharacteristic
332#124—21no—
333#124—21no—
334#124—221no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—221no—
339#121—221no—
340#121C22⋊D1112yes—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—221no—
345C4×D4—221no—
346C4×D4C22×D1112yes—
347C2×C42C22×D1111yescharacteristic
348#107—22no—
349#107—222no—
350C4⋊C8—21no—
351C4⋊C8—112no—
352C4⋊C8—112no—
353C4⋊C8—221no—
354C4⋊C8—221no—
355C4⋊C8C22×D1112yes—
356#102—22no—
357#102—22no—
358#102—222no—
359#102—222no—
360C22⋊C8—222no—
361C22⋊C8—222no—
362C4×C8—111no—
363C4×C8—111no—
364C4×C8—111no—
365C4×C8—111no—
366C2×C11—22no—
367C2×C11—82no—
368C2×C11—161no—
369C2×C11C2×#45911yescharacteristic
370C2×C11#306011yescharacteristic
371C2×C11#306711yescharacteristic
372D11—161no—
373#41—42no—
374#41—42no—
375#41—42no—
376#41—42no—
377#41—442no—
378#41—442no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—221no—
382C2×D4—22no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—441no—
393C2×D4C2×C22⋊D1112yes—
394C22×C4—22no—
395C22×C4—41no—
396C22×C4—441no—
397C22×C4D4×D1111yescharacteristic
398C22×C4#434111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400Q16—442no—
401Q16—442no—
402SD16—442no—
403SD16—442no—
404SD16—442no—
405SD16—442no—
406D8—82no—
407D8—442no—
408D8—442no—
409D8—882no—
410M16—444no—
411M16—442no—
412C2×C8—22no—
413C2×C8—81no—
414C2×C8—114no—
415C2×C8—111no—
416C2×C8—111no—
417C2×C8—111no—
418C2×C8—111no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—444no—
423C2×C8—881no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4C2×C22⋊D1112yes—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C42D4×D1111yescharacteristic
437C42#434111yescharacteristic
438C42C2×C22⋊D1111yescharacteristic
439C42C23×D1111yescharacteristic
440C11#1918911yescharacteristic, complemented, Sylow
441C23—22no—
442C23—41no—
443C23—441no—
444C23#6699211yescharacteristic
445Q8—42no—
446Q8—41no—
447Q8—41no—
448Q8—441no—
449Q8—441no—
450D4—22no—
451D4—22no—
452D4—42no—
453D4—44no—
454D4—42no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—41no—
459D4—81no—
460D4—82no—
461D4—441no—
462D4—441no—
463D4—441no—
464D4—441no—
465D4—881no—
466D4—882no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4—441no—
476C2×C4—882no—
477C2×C4D8×D1112yes—
478C2×C4#6696412yes—
479C2×C4#6699211yescharacteristic
480C2×C4#6699211yescharacteristic
481C2×C4#6699211yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×#434111yescharacteristic
484C2×C4C22×C22⋊D1111yescharacteristic
485C8—42no—
486C8—112no—
487C8—112no—
488C8—221no—
489C8—221no—
490C8—442no—
491C8—442no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22#1062276312yes—
504C22C2×#6699211yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—42no—
509C4—81no—
510C4—881no—
511C4#1062276312yes—
512C4C2×D8×D1111yescharacteristic
513C4C2×#6696411yescharacteristic
514C4#1062336711yescharacteristic
515C4#1062336811yescharacteristic
516C2—22no—
517C2—82no—
518C2—161no—
519C2—1761no—
520C2C2×#1062276311yescharacteristic
521C2#1307827511yescharacteristic
522C2#1307833311yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3245C2
socleC22×C11C2×#121
hypercenter#3245D11
hypocenterC11#19189
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13079923C2semidirect
2. #13079042C2semidirect
3. #13077328C2semidirect
4. #13068103C2semidirect
5. #13068093C2semidirect
6. #13067959C2semidirect
7. #13067955C2semidirect
8. C2×#10622118C2semidirect
9. #13067293C2semidirect
10. #13067291C2semidirect
11. C11×#3245C2semidirect
175. C2×C11⋊C8D8semidirect
181. #3245D11semidirect
440. C11#19189semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130790422
#130773282
#130681032
#130680932
#130679592
#130679552
C2×#106221182
#130672932
#130672912
C11×#32452
#1918911