Finite Group Databasebeta

← #14739279

Subgroups — #14739279

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078772C211yesmaximal, characteristic
2#13078681C211yesmaximal, characteristic
3#13077724C211yesmaximal, characteristic
4#13068071C211yesmaximal, characteristic, complemented
5#13068064C211yesmaximal, characteristic, complemented
6#13068043C211yesmaximal, characteristic, complemented
7#13068036C211yesmaximal, characteristic, complemented
8#13068007C211yesmaximal, characteristic, complemented
9#13068002C211yesmaximal, characteristic, complemented
10#13067995C211yesmaximal, characteristic, complemented
11#13067988C211yesmaximal, characteristic, complemented
12#13067396C211yesmaximal, characteristic, complemented
13#13067316C211yesmaximal, characteristic, complemented
14#13067273C211yesmaximal, characteristic, complemented
15C11×#3231C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#485—21no—
24C11×#485—21no—
25C11×#479—21no—
26C11×#479—21no—
27C11×#431C2211yescharacteristic
28#10622707C2211yescharacteristic
29#10622704C2211yescharacteristic
30#10622703C2211yescharacteristic
31#10622703C2211yescharacteristic
32#10622700C2211yescharacteristic
33#10622697C2211yescharacteristic
34#10622696C2211yescharacteristic
35#10622696C2211yescharacteristic
36#10622660—21no—
37#10622660—21no—
38#10622658—21no—
39#10622658—21no—
40#10622643—21no—
41C4×#4326—21no—
42#10622639—21no—
43C4×#4325—21no—
44#10622539C2211yescharacteristic
45#10622538C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622446—21no—
48D11×C4⋊C8—21no—
49(C22⋊D11)⋊C8—21no—
50(C22⋊D11)⋊C8—21no—
51C8×D44C2211yescharacteristic
52C8×D44C2211yescharacteristic
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
68C11×C4⋊Q8C2311yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#125—21no—
73C11×#125—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C11×#117—21no—
83C11×#117—21no—
84C2×C42×C11C2311yescharacteristic
85C2×#4326—21no—
86C2×#4326—21no—
87C2×#4325—21no—
88C2×#4325—21no—
89C4×C22⋊D11—21no—
90C4×C22⋊D11—21no—
91#66979D411yescharacteristic
92C22×C11⋊C8—21no—
93C2×C8×D11—21no—
94C2×C8×D11—21no—
95C4×D44D411yescharacteristic
96C4×D44C2311yescharacteristic
97#66925—21no—
98C42×D11—21no—
99C4×Dic22D411yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×#107—21no—
102C11×#107—21no—
103C11×#106—21no—
104C11×#106—21no—
105C11×C4⋊C8D411yescharacteristic
106C11×C4⋊C8D411yescharacteristic
107C11×#103—21no—
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×C22⋊C8D411yescharacteristic
112C11×C22⋊C8D411yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66899—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125C8×Dic11—21no—
126C8×Dic11—21no—
127#66874—21no—
128#66874—21no—
129#66873—21no—
130#66873—21no—
131#66872—21no—
132#66872—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#19418—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—22no—
155C2×D44C2×D411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×Dic22C2×D411yescharacteristic
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C42×C11—41no—
179C42×C11—41no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185#4326—42no—
186#4326—42no—
187#4325—42no—
188#4325—42no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11C2×D411yescharacteristic
192C4⋊Dic11C2×D411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—81no—
205C8×D11—81no—
206C8×D11—81no—
207#3231D1111yescharacteristic, complemented
208#3116—111no—
209#3107—111no—
210#2988—111no—
211#1684—111no—
212#1683—111no—
213#1680—111no—
214#1679—111no—
215#1674—111no—
216#1673—111no—
217#1672—111no—
218#1671—111no—
219#1572—111no—
220#1552—111no—
221#1542—111no—
222C23×C11#12111yescharacteristic
223C22×D11—21no—
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—81no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—24no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250D44—21no—
251D44#13512yes—
252C4×D11—24no—
253C4×D11—41no—
254C4×D11—41no—
255C4×D11—81no—
256Dic22—21no—
257Dic22#13512yes—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C11⋊C8—41no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533C2×D1111yescharacteristic
269#533C2×D1111yescharacteristic
270C4×#41—111no—
271#500C2×D1111yescharacteristic
272#498C2×D1111yescharacteristic
273#487C2×D1111yescharacteristic
274#487C2×D1111yescharacteristic
275#485—21no—
276#485—21no—
277#485—221no—
278#485—221no—
279#479—21no—
280#479—21no—
281#477—111no—
282#476—111no—
283#475—111no—
284#474—111no—
285#462—111no—
286#462—111no—
287#461—111no—
288#461—111no—
289#452—221no—
290#452—221no—
291C8×Q8—111no—
292C8×Q8—111no—
293#441—221no—
294#440—221no—
295C4×Q16—221no—
296C4×SD16—221no—
297C8×D4—111no—
298C8×D4—111no—
299C8×D4—221no—
300C8×D4—221no—
301#432—111no—
302#431—111no—
303#431—221no—
304#431C2×D1111yescharacteristic
305C2×C4⋊C8—111no—
306C2×C4⋊C8—221no—
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311#333—111no—
312#333—111no—
313#332—111no—
314#332—111no—
315#332—111no—
316#332—111no—
317#332—111no—
318#332—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11C2×#12111yescharacteristic
323C2×D11—22no—
324C2×D11—41no—
325C2×D11—41no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11C2×#13511yescharacteristic
335C4×C11C2×#13511yescharacteristic
336C4×C11#57711yescharacteristic
337C4×C11#57811yescharacteristic
338Dic11—22no—
339Dic11—41no—
340Dic11—41no—
341C2×#41—111no—
342C2×Q16—221no—
343C2×Q16—221no—
344C2×SD16—221no—
345C2×SD16—221no—
346C22×C8—221no—
347C22×C8—221no—
348C22×C8—221no—
349C4⋊Q8C22×D1111yescharacteristic
350C4⋊Q8C22×D1111yescharacteristic
351C4⋊Q8C22×D1111yescharacteristic
352C4⋊Q8C22×D1111yescharacteristic
353#125—21no—
354#125—21no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×D4—111no—
366C4×D4—111no—
367C4×D4—221no—
368C4×D4—221no—
369#117—21no—
370#117—21no—
371#117—111no—
372#117—221no—
373C2×C42—221no—
374C2×C42C22×D1111yescharacteristic
375#107—21no—
376#107—21no—
377#107—221no—
378#107—221no—
379#106—21no—
380#106—21no—
381#106—221no—
382#106—221no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—111no—
388C4⋊C8—111no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8C22⋊D1111yescharacteristic
393C4⋊C8C22⋊D1111yescharacteristic
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#102—221no—
405#102—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408C22⋊C8—221no—
409C22⋊C8—221no—
410C22⋊C8C22⋊D1111yescharacteristic
411C22⋊C8C22⋊D1111yescharacteristic
412#97—221no—
413C4×C8—221no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11—41no—
419C2×C11#304611yescharacteristic
420C2×C11#305011yescharacteristic
421C2×C11#306911yescharacteristic
422D11—42no—
423#41—222no—
424#41—222no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—111no—
430C2×D4—111no—
431C2×D4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4D4×D1111yescharacteristic
436C22×C4#434111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438Q16—442no—
439Q16—442no—
440SD16—442no—
441SD16—442no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—881no—
449C2×C8—881no—
450C2×C8—881no—
451C2×C8C2×C22⋊D1111yescharacteristic
452C2×C8C2×C22⋊D1111yescharacteristic
453C2×C8C2×C22⋊D1111yescharacteristic
454C2×C8C2×C22⋊D1111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—111no—
468C4⋊C4—111no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C42—41no—
477C42—41no—
478C42—221no—
479C42—221no—
480C42—221no—
481C42D4×D1111yescharacteristic
482C42#434111yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1941811yescharacteristic, complemented, Sylow
486C23—221no—
487C23#6699111yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—112no—
496Q8—221no—
497D4—112no—
498D4—224no—
499D4—221no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—224no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—881no—
516C2×C4#6699111yescharacteristic
517C2×C4#6699111yescharacteristic
518C2×C4#6699111yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—441no—
527C8—441no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8—441no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—222no—
536C22—441no—
537C22—441no—
538C22C2×#6699111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—222no—
548C4—441no—
549C4—441no—
550C4D11×#13511yescharacteristic
551C4D11×#13511yescharacteristic
552C4#1062336811yescharacteristic
553C4#1062336911yescharacteristic
554C2—41no—
555C2—442no—
556C2#1307816211yescharacteristic
557C2#1307819311yescharacteristic
558C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3231C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#3231D11
hypocenterC11#19418
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
4. #13068071C2semidirect
5. #13068064C2semidirect
6. #13068043C2semidirect
7. #13068036C2semidirect
8. #13068007C2semidirect
9. #13068002C2semidirect
10. #13067995C2semidirect
11. #13067988C2semidirect
12. #13067396C2semidirect
13. #13067316C2semidirect
14. #13067273C2semidirect
15. C11×#3231C2semidirect
207. #3231D11semidirect
485. C11#19418semidirect

Maximal subgroups

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

subgroupindex
#130787722
#130786812
#130777242
#130680712
#130680642
#130680432
#130680362
#130680072
#130680022
#130679952
#130679882
#130673962
#130673162
#130672732
C11×#32312
#1941811