Finite Group Databasebeta

← #14723801

Subgroups — #14723801

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078700C211yesmaximal, characteristic
2#13077590C211yesmaximal, characteristic
3C8×Q8×D11C211yesmaximal, characteristic, complemented
4#13067464C211yesmaximal, characteristic, complemented
5#13067461C211yesmaximal, characteristic, complemented
6#13067459C211yesmaximal, characteristic, complemented
7#13067435C211yesmaximal, characteristic, complemented
8#13067432C211yesmaximal, characteristic, complemented
9#13067431C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067400C211yesmaximal, characteristic, complemented
12#13067061C211yesmaximal, characteristic, complemented
13#13067028C211yesmaximal, characteristic
14#13066902C211yesmaximal, characteristic, complemented
15C11×#1584C211yesmaximal, characteristic, complemented
16#10623111C2211yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622799C411yescharacteristic
22#10622798C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25Q8×C11⋊C8C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622495C411yescharacteristic
28#10622490C411yescharacteristic
29#10622453—21no—
30#10622448C2211yescharacteristic
31#10622447—21no—
32#10622447C2211yescharacteristic
33D11×C4⋊C8—21no—
34D11×C4⋊C8C2211yescharacteristic
35#10622443—21no—
36#10622443C2211yescharacteristic
37#10622419C411yescharacteristic
38#10622418C411yescharacteristic
39#10622412C411yescharacteristic
40#10622411C411yescharacteristic
41#10622321—21no—
42#10622319—21no—
43C4×#4314C2211yescharacteristic
44#10622301C2211yescharacteristic
45C4×#4313C2211yescharacteristic
46#10622298C2211yescharacteristic
47C4×C8×D11—21no—
48C4×C8×D11C2211yescharacteristic
49C8×Dic22—21no—
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622093C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×C11×Q16C2×C411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71#67000C2×C411yescharacteristic
72#66999C2×C411yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76C2×#4314C2×C411yescharacteristic
77C2×#4313—21no—
78C2×#4313—21no—
79C2×C8×D11—21no—
80C2×C8×D11—21no—
81C2×C8×D11D411yescharacteristic
82C2×C8×D11D411yescharacteristic
83#66951—21no—
84#66948C2×C411yescharacteristic
85#66947—21no—
86C4⋊C4×D11—21no—
87C4⋊C4×D11C2×C411yescharacteristic
88#66943C2×C411yescharacteristic
89#66940—21no—
90#66940C2×C411yescharacteristic
91C4×D44—21no—
92C4×D44C2311yescharacteristic
93#66925—21no—
94C42×D11—21no—
95C42×D11C2311yescharacteristic
96C4×Dic22—21no—
97C4×Dic22C2311yescharacteristic
98C11×#107C2×C411yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8—21no—
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×#103C2×C411yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#97—21no—
106C4×C8×C11—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#66899C2×C411yescharacteristic
111#66899C2×C411yescharacteristic
112#66885C2×C411yescharacteristic
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8C2×C411yescharacteristic
117(C2×D11)⋊C8C2×C411yescharacteristic
118#66881C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66879—21no—
121#66879—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8C2×C411yescharacteristic
126Dic11⋊C8C2×C411yescharacteristic
127C8×Dic11—21no—
128C8×Dic11—21no—
129C8×Dic11D411yescharacteristic
130C8×Dic11D411yescharacteristic
131#66874C2×C411yescharacteristic
132#66873C2×C411yescharacteristic
133#66872C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17915—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147Q8×D11—22no—
148Q8×D11—22no—
149C2×D44—21no—
150C2×D44C22×C411yescharacteristic
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11C22×C411yescharacteristic
155C2×C4×D11C2×D411yescharacteristic
156C2×C4×D11#4111yescharacteristic
157C2×Dic22—21no—
158C2×Dic22C22×C411yescharacteristic
159C11×Q16—22no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C42×C11—21no—
172C42×C11—21no—
173C42×C11C2411yescharacteristic
174#4326—22no—
175#4325—22no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C22×C411yescharacteristic
184C4⋊Dic11C22×C411yescharacteristic
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11#4111yescharacteristic
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203#4314—22no—
204#4313—42no—
205#4313—42no—
206C8×D11—22no—
207C8×D11—41no—
208C8×D11—42no—
209C8×D11—42no—
210#3108—111no—
211#2966—111no—
212C2×C8×Q8—111no—
213#1584—111no—
214#1584D1111yescharacteristic, complemented
215#1583—111no—
216#1583—111no—
217#1579—111no—
218#1579—111no—
219SD16⋊C8—111no—
220SD16⋊C8—111no—
221#1573—111no—
222#1491—111no—
223#1483—111no—
224#1451—111no—
225C22×D11—21no—
226C22×D11C4×D411yescharacteristic
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11#13112yes—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11C4×D411yescharacteristic
242C2×Dic11C4×D411yescharacteristic
243C2×Dic11C4×D411yescharacteristic
244D44—21no—
245D44—21no—
246D44—42no—
247C4×D11—24no—
248C4×D11—22no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—42no—
254C4×D11—41no—
255C4×D11—41no—
256Dic22—24no—
257Dic22—21no—
258Dic22#13112yes—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—41no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11#13712yes—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#529—111no—
274C2×C4×Q8—111no—
275#483—111no—
276#480—111no—
277#479—111no—
278#479—111no—
279#464—111no—
280#464—111no—
281#451—111no—
282#448—111no—
283#446C2×D1111yescharacteristic
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—221no—
289C8×Q8—221no—
290C8×Q8C2×D1111yescharacteristic
291C4×Q16—111no—
292C4×Q16C2×D1111yescharacteristic
293C4×SD16—111no—
294C4×SD16—111no—
295#436—111no—
296#435—221no—
297C8×D4—111no—
298C8×D4—221no—
299#433—221no—
300#432—111no—
301#431—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8—221no—
304#405—221no—
305C4×M16—111no—
306C2×C4×C8—111no—
307C2×C4×C8—221no—
308#335—111no—
309#335C2×D1111yescharacteristic
310#334—111no—
311#334—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316Q8⋊C8C2×D1111yescharacteristic
317Q8⋊C8C2×D1111yescharacteristic
318D4⋊C8—111no—
319D4⋊C8—111no—
320#322—111no—
321#322—111no—
322#322—111no—
323#322C2×D1111yescharacteristic
324C22×C11C2×C4×D411yescharacteristic
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11#44412yes—
331C4×C11—22no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11C2×#13111yescharacteristic
337C4×C11C2×#13111yescharacteristic
338C4×C11C2×#13711yescharacteristic
339C4×C11#57511yescharacteristic
340Dic11—21no—
341Dic11—22no—
342Dic11—21no—
343Dic11—21no—
344Dic11—41no—
345Dic11—41no—
346C22×Q8—111no—
347C2×Q16—111no—
348C2×Q16C4×D1111yescharacteristic
349C2×SD16—111no—
350C2×SD16—111no—
351C2×M16—221no—
352C2×M16—221no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—221no—
356C22×C8—221no—
357#126—221no—
358#125—111no—
359#124—111no—
360#123—221no—
361C22⋊Q8—111no—
362#121—111no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—221no—
367C4×Q8—221no—
368C4×Q8C22×D1111yescharacteristic
369C4×Q8C22×D1111yescharacteristic
370C4×D4—111no—
371C4×D4—221no—
372#117—221no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—221no—
375C2×C42—111no—
376C2×C42—221no—
377#107—111no—
378#107C4×D1111yescharacteristic
379#106—111no—
380#106—111no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—111no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8C22×D1111yescharacteristic
393C4⋊C8C22×D1111yescharacteristic
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#103C4×D1111yescharacteristic
399#103C4×D1111yescharacteristic
400#102—111no—
401#102—111no—
402C22⋊C8—111no—
403C22⋊C8—111no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—21no—
408#97—221no—
409#97—221no—
410C4×C8—21no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8—221no—
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C4×C8C22×D1111yescharacteristic
423C2×C11#292911yescharacteristic
424C2×C11C4×#13711yescharacteristic
425C2×C11C2×#44411yescharacteristic
426D11—22no—
427D11—81no—
428C2×Q8—111no—
429C2×Q8—221no—
430C2×Q8—222no—
431C2×Q8—222no—
432C2×Q8C2×C4×D1111yescharacteristic
433C2×Q8C2×C4×D1111yescharacteristic
434C2×D4—111no—
435C2×D4—221no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442Q16—22no—
443Q16—222no—
444SD16—222no—
445SD16—222no—
446M16—442no—
447M16—442no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—222no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—441no—
460C2×C8—442no—
461C2×C8—442no—
462C2×C8C2×C4×D1111yescharacteristic
463C2×C8C2×C4×D1111yescharacteristic
464C2×C8D4×D1111yescharacteristic
465C2×C8D4×D1111yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—111no—
469C4⋊C4—111no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4C2×C4×D1111yescharacteristic
478C4⋊C4C2×C4×D1111yescharacteristic
479C22⋊C4—221no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C42—21no—
485C42—21no—
486C42—111no—
487C42—111no—
488C42—111no—
489C42—221no—
490C42—221no—
491C42—221no—
492C42C23×D1111yescharacteristic
493C11#1791511yescharacteristic, complemented, Sylow
494C23—111no—
495C23—221no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—112no—
500Q8—224no—
501Q8—221no—
502Q8#6696012yes—
503D4—221no—
504D4—221no—
505D4—442no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—111no—
511C2×C4—111no—
512C2×C4—111no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—442no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4C22×C4×D1111yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4#41×D1111yescharacteristic
528C8—21no—
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—221no—
535C8—221no—
536C8—221no—
537C8—221no—
538C8—441no—
539C8—441no—
540C8—441no—
541C8#6697112yes—
542C22—112no—
543C22—221no—
544C22—221no—
545C22—441no—
546C22—441no—
547C22—441no—
548C22C4×D4×D1111yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—221no—
555C4—221no—
556C4—222no—
557C4—221no—
558C4—441no—
559C4—441no—
560C4C2×#6696011yescharacteristic
561C4D11×#13111yescharacteristic
562C4C2×#6697111yescharacteristic
563C4#1062329911yescharacteristic
564C2—222no—
565C2—881no—
566C2#1307730711yescharacteristic
567C2C4×#6697111yescharacteristic
568C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1584C2
socleC22×C11C2×C4×D4
prime radical#66948C2×C4
cosocleC42×C11C24
hypercenter#1584D11
hypocenterC11#17915
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
3. C8×Q8×D11C2semidirect
4. #13067464C2semidirect
5. #13067461C2semidirect
6. #13067459C2semidirect
7. #13067435C2semidirect
8. #13067432C2semidirect
9. #13067431C2semidirect
10. #13067427C2semidirect
11. #13067400C2semidirect
12. #13067061C2semidirect
14. #13066902C2semidirect
15. C11×#1584C2semidirect
214. #1584D11semidirect
493. C11#17915semidirect

Maximal subgroups

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

subgroupindex
#130787002
#130775902
C8×Q8×D112
#130674642
#130674612
#130674592
#130674352
#130674322
#130674312
#130674272
#130674002
#130670612
#130670282
#130669022
C11×#15842
#1791511