Finite Group Databasebeta

← #14723804

Subgroups — #14723804

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#13078683C211yesmaximal, characteristic
2C8×#4341C211yesmaximal, characteristic
3#13077545C211yesmaximal, characteristic, complemented
4#13067469C211yesmaximal, characteristic, complemented
5#13067465C211yesmaximal, characteristic, complemented
6#13067453C211yesmaximal, characteristic, complemented
7#13067449C211yesmaximal, characteristic, complemented
8#13067436C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10#13067428C211yesmaximal, characteristic, complemented
11#13067406C211yesmaximal, characteristic, complemented
12#13067052C211yesmaximal, characteristic
13#13067035C211yesmaximal, characteristic, complemented
14#13066904C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17C4×#4341C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622786C411yescharacteristic
22#10622775C411yescharacteristic
23C8×C22⋊D11—21no—
24C2×C8×Dic11—21no—
25C4×#4326C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622480C411yescharacteristic
30#10622467C411yescharacteristic
31#10622452—21no—
32#10622450C2211yescharacteristic
33#10622446C2211yescharacteristic
34#10622444C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622427C411yescharacteristic
38#10622406C411yescharacteristic
39#10622396C411yescharacteristic
40#10622372C411yescharacteristic
41(C22⋊D11)⋊C8—21no—
42#10622331—21no—
43C4×Dic44C2211yescharacteristic
44#10622302—21no—
45C4×#4313C2211yescharacteristic
46#10622298C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48C8×Dic22—21no—
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×#4341C2×C411yescharacteristic
68C2×C11×SD16C2×C411yescharacteristic
69C22×C8×C11—21no—
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11C2311yescharacteristic
72#66999C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8—21no—
80C2×Dic44C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313—21no—
83C2×C8×D11D411yescharacteristic
84C2×C8×D11D411yescharacteristic
85#66950C2×C411yescharacteristic
86#66949—21no—
87#66945C2×C411yescharacteristic
88#66942—21no—
89#66941C2×C411yescharacteristic
90#66940C2×C411yescharacteristic
91(C22⋊D11)⋊C4—21no—
92#66930—21no—
93#66925—21no—
94C42×D11C2311yescharacteristic
95C4×Dic22—21no—
96C4×Dic22C2311yescharacteristic
97C4×Dic22C2311yescharacteristic
98C11×#106C2×C411yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×#103C2×C411yescharacteristic
103C11×#102C2×C411yescharacteristic
104C11×C22⋊C8—21no—
105C4×C8×C11—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66899C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111C22⋊(C11⋊C8)—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8C2×C411yescharacteristic
114(C2×D11)⋊C8C2×C411yescharacteristic
115#66882C2×C411yescharacteristic
116#66880C2×C411yescharacteristic
117#66880C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8C2×C411yescharacteristic
126Dic11⋊C8C2×C411yescharacteristic
127C8×Dic11—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11D411yescharacteristic
132C8×Dic11D411yescharacteristic
133#66874C2×C411yescharacteristic
134#66874C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136#66871C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17916—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151#4341—22no—
152#4341—22no—
153C2×C4×D11C22×C411yescharacteristic
154C2×C4×D11C2×D411yescharacteristic
155C2×C4×D11#4111yescharacteristic
156C2×Dic22—21no—
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C11×SD16—22no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—42no—
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C22⋊C4—21no—
172C42×C11—21no—
173C42×C11C2411yescharacteristic
174C22⋊Dic11—21no—
175#4326—22no—
176#4324—22no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11C22×C411yescharacteristic
182C4⋊Dic11C22×C411yescharacteristic
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
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×Dic11—21no—
194C4×Dic11C22×C411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C4×Dic11#4111yescharacteristic
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—42no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205Dic44—22no—
206#4313—42no—
207#4313—42no—
208C8×D11—22no—
209C8×D11—41no—
210#3107—111no—
211C8×#41—111no—
212#2960—111no—
213#1584—111no—
214#1584—111no—
215#1582—111no—
216#1582—111no—
217#1579—111no—
218#1579—111no—
219SD16⋊C8—111no—
220SD16⋊C8D1111yescharacteristic, complemented
221#1574—111no—
222#1489—111no—
223#1485—111no—
224#1451—111no—
225C23×C11—21no—
226C22×D11C4×D411yescharacteristic
227Q8×C11—21no—
228Q8×C11—21no—
229D4×C11—21no—
230D4×C11#13112yes—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C22⋊D11—24no—
240C2×Dic11—24no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—42no—
246C2×Dic11C4×D411yescharacteristic
247C2×Dic11C4×D411yescharacteristic
248C2×Dic11C4×D411yescharacteristic
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—22no—
254Dic22—21no—
255Dic22—21no—
256Dic22—21no—
257Dic22—42no—
258Dic22#13112yes—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—41no—
264C8×C11—41no—
265C8×C11—41no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8#13712yes—
273#533—111no—
274C4×#41—111no—
275#485—111no—
276#485—111no—
277#475—111no—
278#474—111no—
279#462—111no—
280#461—111no—
281#452—111no—
282#452—111no—
283#446—111no—
284#446—111no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—221no—
290C8×Q8C2×D1111yescharacteristic
291C4×Q16—111no—
292C4×Q16—111no—
293C4×SD16—111no—
294C4×SD16C2×D1111yescharacteristic
295C8×D4—111no—
296C8×D4—221no—
297C8×D4—221no—
298C8×D4C2×D1111yescharacteristic
299#431—111no—
300#431—111no—
301#431—221no—
302#424—221no—
303#423—111no—
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⋊C8—111no—
317Q8⋊C8C2×D1111yescharacteristic
318D4⋊C8—111no—
319D4⋊C8C2×D1111yescharacteristic
320#322—111no—
321#322—111no—
322#322—111no—
323#322C2×D1111yescharacteristic
324C22×C11—22no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11C2×C4×D411yescharacteristic
328C2×D11—21no—
329C2×D11—21no—
330C2×D11—21no—
331C4×C11—21no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11C2×#13111yescharacteristic
336C4×C11C2×#13111yescharacteristic
337C4×C11C2×#13711yescharacteristic
338C4×C11#57511yescharacteristic
339Dic11—22no—
340Dic11—21no—
341Dic11—21no—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345Dic11#44412yes—
346C2×#41—111no—
347C2×Q16—111no—
348C2×Q16—111no—
349C2×SD16—111no—
350C2×SD16C4×D1111yescharacteristic
351C2×M16—221no—
352C2×M16—221no—
353C22×C8—21no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—221no—
357C4⋊Q8—111no—
358C4⋊Q8—111no—
359#125—221no—
360C22⋊Q8—111no—
361C22⋊Q8—111no—
362C22⋊Q8—221no—
363C4×Q8—111no—
364C4×Q8—111no—
365C4×Q8—111no—
366C4×Q8—221no—
367C4×Q8C22×D1111yescharacteristic
368C4×D4—111no—
369C4×D4—221no—
370C4×D4—221no—
371C4×D4C22×D1111yescharacteristic
372#117—111no—
373#117—221no—
374#117—221no—
375C2×C42—111no—
376C2×C42—221no—
377#107—111no—
378#107—111no—
379#106—111no—
380#106C4×D1111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—111no—
386C4⋊C8—221no—
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#103—111no—
399#103C4×D1111yescharacteristic
400#102—111no—
401#102C4×D1111yescharacteristic
402C22⋊C8—21no—
403C22⋊C8—111no—
404C22⋊C8—111no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407#97—221no—
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—42no—
424C2×C11#292911yescharacteristic
425C2×C11C4×#13711yescharacteristic
426C2×C11C2×#44411yescharacteristic
427D11—41no—
428#41—222no—
429#41—222no—
430C2×Q8—111no—
431C2×Q8—111no—
432C2×Q8—221no—
433C2×Q8C2×C4×D1111yescharacteristic
434C2×D4—221no—
435C2×D4C2×C4×D1111yescharacteristic
436C22×C4—21no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—221no—
441C22×C4—221no—
442Q16—222no—
443Q16—222no—
444SD16—22no—
445SD16—222no—
446M16—442no—
447M16—442no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—42no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—222no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—441no—
461C2×C8—442no—
462C2×C8C2×C4×D1111yescharacteristic
463C2×C8C2×C4×D1111yescharacteristic
464C2×C8D4×D1111yescharacteristic
465C2×C8D4×D1111yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—111no—
468C4⋊C4—111no—
469C4⋊C4—221no—
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—21no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C42—21no—
485C42—111no—
486C42—111no—
487C42—111no—
488C42—221no—
489C42—221no—
490C42—221no—
491C42—221no—
492C42C23×D1111yescharacteristic
493C11#1791611yescharacteristic, complemented, Sylow
494C23—21no—
495C23—111no—
496Q8—21no—
497Q8—21no—
498Q8—112no—
499Q8—221no—
500Q8—221no—
501Q8—221no—
502Q8—442no—
503D4—21no—
504D4—224no—
505D4#6695412yes—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—111no—
512C2×C4—111no—
513C2×C4—111no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—442no—
525C2×C4C22×C4×D1111yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4#41×D1111yescharacteristic
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—112no—
536C8—221no—
537C8—221no—
538C8—221no—
539C8—441no—
540C8—441no—
541C8—441no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—221no—
546C22—221no—
547C22—221no—
548C22C4×D4×D1111yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—112no—
554C4—221no—
555C4—222no—
556C4—221no—
557C4—441no—
558C4—441no—
559C4—441no—
560C4C2×#6695411yescharacteristic
561C4D11×#13111yescharacteristic
562C4#1062330411yescharacteristic
563C4D11×#13711yescharacteristic
564C2—42no—
565C2—441no—
566C2#1307730511yescharacteristic
567C2#1307743811yescharacteristic
568C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×SD16⋊C8C2
socleC22×C11C2×C4×D4
prime radicalC2×#4341C2×C4
cosocleC42×C11C24
hypercenterSD16⋊C8D11
hypocenterC11#17916
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
3. #13077545C2semidirect
4. #13067469C2semidirect
5. #13067465C2semidirect
6. #13067453C2semidirect
7. #13067449C2semidirect
8. #13067436C2semidirect
9. #13067433C2semidirect
10. #13067428C2semidirect
11. #13067406C2semidirect
13. #13067035C2semidirect
14. #13066904C2semidirect
15. C11×SD16⋊C8C2semidirect
220. SD16⋊C8D11semidirect
493. C11#17916semidirect

Maximal subgroups

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

subgroupindex
#130786832
C8×#43412
#130775452
#130674692
#130674652
#130674532
#130674492
#130674362
#130674332
#130674282
#130674062
#130670522
#130670352
#130669042
C11×SD16⋊C82
#1791611