Finite Group Databasebeta

← #14725635

Subgroups — #14725635

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079218C211yesmaximal, characteristic
2#13077617C211yesmaximal, characteristic
3#13077558C211yesmaximal, characteristic, complemented
4#13067519C211yesmaximal, characteristic, complemented
5#13067514C211yesmaximal, characteristic, complemented
6#13067497C211yesmaximal, characteristic, complemented
7#13067490C211yesmaximal, characteristic, complemented
8#13067466C211yesmaximal, characteristic, complemented
9#13067452C211yesmaximal, characteristic, complemented
10#13067434C211yesmaximal, characteristic, complemented
11#13067365C211yesmaximal, characteristic, complemented
12#13067035C211yesmaximal, characteristic, complemented
13#13067026C211yesmaximal, characteristic
14#13066918C211yesmaximal, characteristic, complemented
15C8×C11×SD16C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17#10623088C2211yescharacteristic
18C8×Q8×C11C2211yescharacteristic
19C4×C11×SD16C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622787C411yescharacteristic
22#10622780C411yescharacteristic
23#10622724—21no—
24#10622714—21no—
25C4×#4326C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622481C411yescharacteristic
30#10622469C411yescharacteristic
31#10622452—21no—
32#10622446C2211yescharacteristic
33D11×C4⋊C8C2211yescharacteristic
34#10622443C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622429C411yescharacteristic
38#10622410C411yescharacteristic
39#10622393C411yescharacteristic
40#10622378C411yescharacteristic
41#10622342—21no—
42#10622333—21no—
43C4×Dic44C2211yescharacteristic
44#10622302—21no—
45C4×#4313C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48#10622292—21no—
49#10622292C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622093C2211yescharacteristic
66#10622093C2211yescharacteristic
67C2×C11×SD16C2×C411yescharacteristic
68C22×C8×C11—21no—
69C4×Q8×C11C2311yescharacteristic
70C4×D4×C11C2311yescharacteristic
71#66999C2×C411yescharacteristic
72#66997C2×C411yescharacteristic
73C2×#4326C2×C411yescharacteristic
74#66991C2×C411yescharacteristic
75#66989C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78#66979—21no—
79C2×#4318—21no—
80C2×Dic44C2×C411yescharacteristic
81C2×#4313—21no—
82C2×#4313C2×C411yescharacteristic
83C2×#4313C2×C411yescharacteristic
84C2×#4313D411yescharacteristic
85C2×#4313D411yescharacteristic
86C2×C8×D11—21no—
87#66950C2×C411yescharacteristic
88#66950C2×C411yescharacteristic
89#66949—21no—
90#66943C2×C411yescharacteristic
91#66942—21no—
92#66941C2×C411yescharacteristic
93#66936—21no—
94#66932—21no—
95#66925—21no—
96C42×D11C2311yescharacteristic
97C4×Dic22—21no—
98C4×Dic22C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×C22⋊C8—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113C22⋊(C11⋊C8)—21no—
114(C2×D11)⋊C8—21no—
115#66882C2×C411yescharacteristic
116#66880C2×C411yescharacteristic
117#66880C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120#66879—21no—
121#66879C2×C411yescharacteristic
122#66879C2×C411yescharacteristic
123#66879D411yescharacteristic
124#66879D411yescharacteristic
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130C8×Dic11—21no—
131C8×Dic11—21no—
132C8×Dic11—21no—
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#18077—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C2×C22⋊D11—21no—
149C2×C4×D11C22×C411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×C4×D11#4111yescharacteristic
152C2×Dic22—21no—
153C2×Dic22C22×C411yescharacteristic
154C2×Dic22C22×C411yescharacteristic
155C11×SD16—22no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—42no—
160C2×C8×C11C22×C411yescharacteristic
161C2×C8×C11C22×C411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C411yescharacteristic
166C11×C4⋊C4C22×C411yescharacteristic
167C11×C22⋊C4—21no—
168C42×C11—21no—
169C42×C11C2411yescharacteristic
170C22⋊Dic11—21no—
171C22⋊Dic11—21no—
172C22⋊Dic11—21no—
173#4326—41no—
174#4324—41no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—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×Dic11C22×C411yescharacteristic
193C4×Dic11C2×D411yescharacteristic
194C4×Dic11#4111yescharacteristic
195#4318—42no—
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
203Dic44—22no—
204#4313—22no—
205#4313—22no—
206#4313—41no—
207#4313—41no—
208#4313—42no—
209C8×D11—42no—
210#3172—111no—
211#2969—111no—
212#2962—111no—
213#1592—111no—
214#1591—111no—
215#1588—111no—
216#1587—111no—
217#1584—111no—
218#1582—111no—
219#1579—111no—
220C8×SD16D1111yescharacteristic, complemented
221#1565—111no—
222#1485—111no—
223#1483—111no—
224#1455—111no—
225C23×C11—21no—
226C22×D11C4×D411yescharacteristic
227Q8×C11—21no—
228Q8×C11—21no—
229D4×C11—21no—
230D4×C11—21no—
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—81no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11C4×D411yescharacteristic
245C2×Dic11C4×D411yescharacteristic
246C2×Dic11C4×D411yescharacteristic
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—21no—
250C4×D11—21no—
251C4×D11—41no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—81no—
257C8×C11—22no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11#13112yes—
263C8×C11#13712yes—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271#533—111no—
272#529—111no—
273#501—111no—
274#497—111no—
275#491—111no—
276#489—111no—
277#470—111no—
278#470—111no—
279#468—111no—
280#468—111no—
281#446—111no—
282#446—111no—
283#446—111no—
284#446—221no—
285#446—221no—
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8C2×D1111yescharacteristic
289C4×Q16—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16C2×D1111yescharacteristic
293#436—111no—
294#436—221no—
295#435—221no—
296C8×D4C2×D1111yescharacteristic
297#433—221no—
298#431—111no—
299#424—221no—
300C2×C4⋊C8—111no—
301#405—221no—
302#405—221no—
303C4×M16—111no—
304C4×M16—111no—
305C4×M16—111no—
306#335—111no—
307#335—111no—
308#334—111no—
309#334C2×D1111yescharacteristic
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8C2×D1111yescharacteristic
316D4⋊C8—111no—
317D4⋊C8C2×D1111yescharacteristic
318#322—111no—
319#322—111no—
320#322—111no—
321C82C2×D1111yescharacteristic
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11C2×C4×D411yescharacteristic
326C2×D11—21no—
327C2×D11—21no—
328C2×D11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11C2×#13111yescharacteristic
334C4×C11#56811yescharacteristic
335C4×C11C2×#13711yescharacteristic
336C4×C11#57511yescharacteristic
337Dic11—21no—
338Dic11—21no—
339Dic11—21no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16C4×D1111yescharacteristic
348C2×M16—111no—
349C2×M16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C2×M16—221no—
353C2×M16—221no—
354C22×C8—21no—
355C22×C8—221no—
356C4⋊Q8—111no—
357C4⋊Q8—111no—
358#126—221no—
359#125—111no—
360#125—221no—
361#124—111no—
362#123—221no—
363C22⋊Q8—111no—
364C22⋊Q8—111no—
365C22⋊Q8—111no—
366C22⋊Q8—221no—
367#121—111no—
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—221no—
371C4×Q8C22×D1111yescharacteristic
372C4×D4—221no—
373C4×D4C22×D1111yescharacteristic
374#117—221no—
375#117—221no—
376C2×C42—111no—
377#107—111no—
378#107—111no—
379#106—111no—
380#106C4×D1111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—111no—
383C4⋊C8—111no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C22×D1111yescharacteristic
391C4⋊C8C22×D1111yescharacteristic
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103C4×D1111yescharacteristic
398#102—111no—
399#102C4×D1111yescharacteristic
400C22⋊C8—21no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—111no—
404#97—111no—
405#97—111no—
406#97—111no—
407#97—221no—
408#97—221no—
409#97—221no—
410#97—221no—
411C4×C8—21no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—81no—
422C2×C11#293511yescharacteristic
423C2×C11C4×#13711yescharacteristic
424C2×C11#295611yescharacteristic
425D11—41no—
426C2×Q8—111no—
427C2×Q8—111no—
428C2×Q8—221no—
429C2×Q8C2×C4×D1111yescharacteristic
430C2×D4—221no—
431C2×D4C2×C4×D1111yescharacteristic
432C22×C4—21no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436Q16—222no—
437Q16—441no—
438SD16—22no—
439SD16—441no—
440M16—222no—
441M16—222no—
442M16—441no—
443M16—441no—
444M16—442no—
445M16—442no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—42no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—111no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—442no—
458C2×C8C2×C4×D1111yescharacteristic
459C2×C8C2×C4×D1111yescharacteristic
460C2×C8D4×D1111yescharacteristic
461C2×C8D4×D1111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—111no—
464C4⋊C4—111no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4C2×C4×D1111yescharacteristic
476C4⋊C4C2×C4×D1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C42—21no—
485C42—111no—
486C42—111no—
487C42—111no—
488C42—221no—
489C42—221no—
490C42C23×D1111yescharacteristic
491C11#1807711yescharacteristic, complemented, Sylow
492C23—21no—
493C23—111no—
494Q8—21no—
495Q8—21no—
496Q8—221no—
497Q8—221no—
498Q8—221no—
499Q8—221no—
500Q8—881no—
501D4—21no—
502D4—21no—
503D4—881no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—111no—
510C2×C4—111no—
511C2×C4—111no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—441no—
521C2×C4C22×C4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4#41×D1111yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—441no—
534C8—441no—
535C8—441no—
536C8#6695412yes—
537C8#6696812yes—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—221no—
542C22—221no—
543C22—221no—
544C22C4×D4×D1111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—221no—
550C4—221no—
551C4—221no—
552C4—441no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4C2×#6695411yescharacteristic
557C4#1062328111yescharacteristic
558C4C2×#6696811yescharacteristic
559C4#1062329911yescharacteristic
560C2—81no—
561C2—441no—
562C2#1307735511yescharacteristic
563C2C4×#6696811yescharacteristic
564C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC8×C11×SD16C2
socleC22×C11C2×C4×D4
prime radical#66991C2×C4
cosocleC42×C11C24
hypercenterC8×SD16D11
hypocenterC11#18077
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
3. #13077558C2semidirect
4. #13067519C2semidirect
5. #13067514C2semidirect
6. #13067497C2semidirect
7. #13067490C2semidirect
8. #13067466C2semidirect
9. #13067452C2semidirect
10. #13067434C2semidirect
11. #13067365C2semidirect
12. #13067035C2semidirect
14. #13066918C2semidirect
15. C8×C11×SD16C2semidirect
220. C8×SD16D11semidirect
491. C11#18077semidirect

Maximal subgroups

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

subgroupindex
#130792182
#130776172
#130775582
#130675192
#130675142
#130674972
#130674902
#130674662
#130674522
#130674342
#130673652
#130670352
#130670262
#130669182
C8×C11×SD162
#1807711