Finite Group Databasebeta

← #14736816

Subgroups — #14736816

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078681C211yesmaximal, characteristic
2#13078398C211yesmaximal, characteristic
3#13077634C211yesmaximal, characteristic
4#13068188C211yesmaximal, characteristic, complemented
5#13068160C211yesmaximal, characteristic, complemented
6#13068112C211yesmaximal, characteristic, complemented
7#13068102C211yesmaximal, characteristic, complemented
8#13068071C211yesmaximal, characteristic, complemented
9#13068043C211yesmaximal, characteristic, complemented
10#13067995C211yesmaximal, characteristic, complemented
11#13067983C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067316C211yesmaximal, characteristic, complemented
15C11×#3185C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#498C2211yescharacteristic
20C11×#494C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#470—21no—
24C11×#470—21no—
25C11×#441—21no—
26C11×#441—21no—
27C4×C11×M16C2211yescharacteristic
28#10622741—21no—
29#10622741—21no—
30#10622707C2211yescharacteristic
31#10622707C2211yescharacteristic
32#10622704C2211yescharacteristic
33#10622703C2211yescharacteristic
34#10622700C2211yescharacteristic
35#10622700C2211yescharacteristic
36#10622697C2211yescharacteristic
37#10622696C2211yescharacteristic
38#10622679—21no—
39#10622676—21no—
40#10622660—21no—
41#10622658—21no—
42C4×#4326—21no—
43C4×#4325—21no—
44#10622615—21no—
45#10622611—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622320—21no—
50#10622318—21no—
51#10622301C2211yescharacteristic
52#10622301C2211yescharacteristic
53C8×Dic22C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622185C2211yescharacteristic
60#10622185C2211yescharacteristic
61#10622184C2211yescharacteristic
62#10622184C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×#4339D411yescharacteristic
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#125—21no—
77C11×#125—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11—21no—
86C11×#117—21no—
87C11×#117—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4326—21no—
90C2×#4325—21no—
91C4×C22⋊D11—21no—
92C4×C22⋊D11—21no—
93#66979D411yescharacteristic
94C22×C11⋊C8—21no—
95C2×#4313—21no—
96C2×#4313—21no—
97C4×D44D411yescharacteristic
98C4×D44C2311yescharacteristic
99#66925—21no—
100C42×D11—21no—
101C4×Dic22D411yescharacteristic
102C4×Dic22C2311yescharacteristic
103C11×#106—21no—
104C11×#106—21no—
105C11×#103—21no—
106C11×#103—21no—
107C11×#103—21no—
108C11×#103—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899—21no—
114#66899—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121C8×Dic11—21no—
122C8×Dic11—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66872—21no—
130#66872—21no—
131#66872—21no—
132#66871—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#19185—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×C22⋊D11—21no—
153#4339—22no—
154#4339—41no—
155C2×D44C2×D411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×Dic22C2×D411yescharacteristic
160C11×Q16—42no—
161C11×Q16—42no—
162C11×M16—22no—
163C11×M16—41no—
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—41no—
182C42×C11—41no—
183C42×C11—41no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—21no—
189#4326—42no—
190#4325—42no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11C2×D411yescharacteristic
194C4⋊Dic11C2×D411yescharacteristic
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207#4313—42no—
208#4313—42no—
209#3185D1111yescharacteristic, complemented
210#3107—111no—
211#3076—111no—
212#2971—111no—
213#1703—111no—
214#1699—111no—
215#1691—111no—
216#1689—111no—
217#1684—111no—
218#1680—111no—
219#1672—111no—
220#1670—111no—
221#1565—111no—
222#1554—111no—
223#1552—111no—
224C23×C11#12111yescharacteristic
225C22×D11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—81no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C22⋊D11—42no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252D44—21no—
253D44—21no—
254C4×D11—42no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11—81no—
258Dic22—21no—
259Dic22#13712yes—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11#13512yes—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270#533C2×D1111yescharacteristic
271#533C2×D1111yescharacteristic
272C4×#41—111no—
273#498C2×D1111yescharacteristic
274#494C2×D1111yescharacteristic
275#487C2×D1111yescharacteristic
276#487C2×D1111yescharacteristic
277#485—221no—
278#479—221no—
279#478—221no—
280#477—111no—
281#476—111no—
282#475—111no—
283#475—111no—
284#474—111no—
285#474—111no—
286#470—21no—
287#470—21no—
288#462—111no—
289#461—111no—
290#452—221no—
291C8×Q8—111no—
292C8×Q8—111no—
293#441—21no—
294#441—21no—
295C4×Q16—221no—
296C4×SD16—221no—
297#436—111no—
298#436—111no—
299#436—221no—
300#436—221no—
301#432—111no—
302#432—221no—
303#431—111no—
304#427—221no—
305C2×C4⋊C8—111no—
306#416—221no—
307C4×M16—221no—
308C4×M16C2×D1111yescharacteristic
309#335—111no—
310#335—111no—
311#334—111no—
312#334—111no—
313#333—111no—
314#333—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11C2×#12111yescharacteristic
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11C2×#13511yescharacteristic
337C4×C11C2×#13711yescharacteristic
338C4×C11#57511yescharacteristic
339C4×C11#57511yescharacteristic
340Dic11—22no—
341Dic11—41no—
342Dic11—41no—
343C2×#41—111no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—221no—
347C2×SD16—221no—
348C2×M16—221no—
349C2×M16—221no—
350C2×M16C22⋊D1111yescharacteristic
351C2×M16C22⋊D1111yescharacteristic
352C22×C8—221no—
353C4⋊Q8C22×D1111yescharacteristic
354C4⋊Q8C22×D1111yescharacteristic
355C4⋊Q8C22×D1111yescharacteristic
356C4⋊Q8C22×D1111yescharacteristic
357#125—21no—
358#125—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—111no—
368C4×Q8—111no—
369C4×D4—111no—
370C4×D4—111no—
371C4×D4—221no—
372C4×D4—221no—
373#117—21no—
374#117—21no—
375#117—111no—
376#117—221no—
377C2×C42—221no—
378C2×C42C22×D1111yescharacteristic
379#107—221no—
380#107—221no—
381#107—221no—
382#106—21no—
383#106—21no—
384#106—221no—
385#106—221no—
386#106—221no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#103—221no—
405#102—221no—
406#102—221no—
407#102—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412#97—221no—
413#97C22⋊D1111yescharacteristic
414#97C22⋊D1111yescharacteristic
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11—41no—
421C2×C11#303511yescharacteristic
422C2×C11#305611yescharacteristic
423C2×C11#306911yescharacteristic
424D11—81no—
425#41—222no—
426#41—441no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—111no—
432C2×D4—111no—
433C2×D4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4D4×D1111yescharacteristic
438C22×C4#434111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440Q16—42no—
441Q16—42no—
442Q16—442no—
443SD16—442no—
444M16—22no—
445M16—41no—
446M16—442no—
447M16—442no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—442no—
455C2×C8C2×C22⋊D1111yescharacteristic
456C2×C8C2×C22⋊D1111yescharacteristic
457C2×C8C2×C22⋊D1111yescharacteristic
458C2×C8C2×C22⋊D1111yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—111no—
472C4⋊C4—111no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C42—41no—
481C42—41no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42D4×D1111yescharacteristic
486C42#434111yescharacteristic
487C42C2×C22⋊D1111yescharacteristic
488C42C23×D1111yescharacteristic
489C11#1918511yescharacteristic, complemented, Sylow
490C23—221no—
491C23#6699111yescharacteristic
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—112no—
500Q8—221no—
501D4—221no—
502D4—221no—
503D4—442no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—442no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—881no—
520C2×C4#6699111yescharacteristic
521C2×C4#6699111yescharacteristic
522C2×C4#6699111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—441no—
530C8—441no—
531C8—441no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8#6700312yes—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—441no—
540C22—441no—
541C22—441no—
542C22C2×#6699111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—222no—
552C4—441no—
553C4—441no—
554C4D11×#13711yescharacteristic
555C4#1062330811yescharacteristic
556C4C2×#6700311yescharacteristic
557C4#1062335311yescharacteristic
558C2—41no—
559C2—881no—
560C2#1307806511yescharacteristic
561C2#1307824011yescharacteristic
562C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3185C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#3185D11
hypocenterC11#19185
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3185

Complements

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

NH ≅ G/Ntype
4. #13068188C2semidirect
5. #13068160C2semidirect
6. #13068112C2semidirect
7. #13068102C2semidirect
8. #13068071C2semidirect
9. #13068043C2semidirect
10. #13067995C2semidirect
11. #13067983C2semidirect
12. #13067368C2semidirect
13. #13067326C2semidirect
14. #13067316C2semidirect
15. C11×#3185C2semidirect
209. #3185D11semidirect
489. C11#19185semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130783982
#130776342
#130681882
#130681602
#130681122
#130681022
#130680712
#130680432
#130679952
#130679832
#130673682
#130673262
#130673162
C11×#31852
#1918511