Finite Group Databasebeta

← #14724550

Subgroups — #14724550

Order 2816.

578 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#13079220C211yesmaximal, characteristic
2#13077593C211yesmaximal, characteristic
3#13077547C211yesmaximal, characteristic, complemented
4#13067487C211yesmaximal, characteristic, complemented
5#13067475C211yesmaximal, characteristic, complemented
6#13067471C211yesmaximal, characteristic, complemented
7#13067469C211yesmaximal, characteristic, complemented
8#13067467C211yesmaximal, characteristic, complemented
9#13067458C211yesmaximal, characteristic, complemented
10#13067456C211yesmaximal, characteristic, complemented
11#13067380C211yesmaximal, characteristic, complemented
12#13067087C211yesmaximal, characteristic, complemented
13#13067080C211yesmaximal, characteristic
14#13066904C211yesmaximal, characteristic, complemented
15C11×#1587C211yesmaximal, characteristic, complemented
16#10623111C2211yescharacteristic
17#10623109C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622803C411yescharacteristic
22#10622802C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622499C411yescharacteristic
28#10622489C411yescharacteristic
29#10622453—21no—
30#10622452—21no—
31#10622451C2211yescharacteristic
32#10622450C2211yescharacteristic
33#10622449—21no—
34#10622448C2211yescharacteristic
35#10622443—21no—
36#10622443C2211yescharacteristic
37#10622429C411yescharacteristic
38#10622425C411yescharacteristic
39#10622410C411yescharacteristic
40#10622408C411yescharacteristic
41#10622321—21no—
42#10622314—21no—
43C4×#4314C2211yescharacteristic
44#10622302—21no—
45C4×#4313C2211yescharacteristic
46C8×D44—21no—
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
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#10622096C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×C11×Q16C2×C411yescharacteristic
68C4×Q8×C11C2311yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70#67000C2×C411yescharacteristic
71#66999C2×C411yescharacteristic
72#66999C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76C2×#4314C2×C411yescharacteristic
77C2×#4313—21no—
78C2×#4313—21no—
79C2×#4313C2×C411yescharacteristic
80C2×#4313C2×C411yescharacteristic
81C2×C8×D11—21no—
82C2×C8×D11D411yescharacteristic
83C2×C8×D11D411yescharacteristic
84#66951—21no—
85#66950C2×C411yescharacteristic
86#66949—21no—
87#66948C2×C411yescharacteristic
88#66947—21no—
89#66943C2×C411yescharacteristic
90#66942—21no—
91#66941C2×C411yescharacteristic
92C4×D44—21no—
93C4×D44C2311yescharacteristic
94#66925—21no—
95#66925—21no—
96C42×D11C2311yescharacteristic
97C4×Dic22—21no—
98C4×Dic22C2311yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#97—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66899C2×C411yescharacteristic
113#66885C2×C411yescharacteristic
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118#66881C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66879—21no—
121#66879—21no—
122#66879C2×C411yescharacteristic
123#66879C2×C411yescharacteristic
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—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
139#66867—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17984—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147C2×D44—21no—
148C2×D44C22×C411yescharacteristic
149C2×C4×D11—21no—
150C2×C4×D11C22×C411yescharacteristic
151C2×C4×D11C2×D411yescharacteristic
152C2×C4×D11#4111yescharacteristic
153C2×Dic22—21no—
154C2×Dic22C22×C411yescharacteristic
155C11×Q16—41no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C22×C411yescharacteristic
160C2×C8×C11C22×C411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C411yescharacteristic
166C11×C4⋊C4C22×C411yescharacteristic
167C42×C11—21no—
168C42×C11—21no—
169C42×C11C2411yescharacteristic
170#4326—41no—
171#4325—41no—
172(C2×D11)⋊C4—21no—
173(C2×D11)⋊C4—21no—
174(C2×D11)⋊C4—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177(C2×D11)⋊C4—21no—
178(C2×D11)⋊C4—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×Dic11C22×C411yescharacteristic
192C4×Dic11C2×D411yescharacteristic
193C4×Dic11#4111yescharacteristic
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C22×C411yescharacteristic
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201#4314—41no—
202#4313—41no—
203#4313—41no—
204#4313—42no—
205#4313—42no—
206C8×D11—22no—
207C8×D11—41no—
208C8×D11—42no—
209#3172—111no—
210#2966—111no—
211#2960—111no—
212#1587—111no—
213#1587D1111yescharacteristic, complemented
214#1585—111no—
215#1585—111no—
216#1584—111no—
217#1584—111no—
218#1583—111no—
219#1583—111no—
220#1569—111no—
221#1497—111no—
222#1495—111no—
223#1451—111no—
224C22×D11—21no—
225C22×D11C4×D411yescharacteristic
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229Q8×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11C4×D411yescharacteristic
241C2×Dic11C4×D411yescharacteristic
242C2×Dic11C4×D411yescharacteristic
243D44—21no—
244D44—21no—
245D44—42no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—21no—
250C4×D11—41no—
251C4×D11—41no—
252C4×D11—41no—
253Dic22—21no—
254Dic22—21no—
255Dic22—42no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11—41no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8#13712yes—
270#533—111no—
271#529—111no—
272#501—111no—
273#497—111no—
274#491—111no—
275#489—111no—
276#470—111no—
277#470—111no—
278#468—111no—
279#468—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446C2×D1111yescharacteristic
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—221no—
287C8×Q8C2×D1111yescharacteristic
288C4×Q16—111no—
289C4×Q16C2×D1111yescharacteristic
290C4×SD16—111no—
291C4×SD16—111no—
292#436—111no—
293#435—221no—
294C8×D4—111no—
295C8×D4—221no—
296#433—221no—
297#432—111no—
298#431—111no—
299#424—221no—
300#423—111no—
301#405—221no—
302#405—221no—
303C4×M16—111no—
304C2×C4×C8—111no—
305#335—111no—
306#335—111no—
307#334—111no—
308#334C2×D1111yescharacteristic
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8C2×D1111yescharacteristic
314Q8⋊C8C2×D1111yescharacteristic
315D4⋊C8—111no—
316D4⋊C8—111no—
317#322—111no—
318#322—111no—
319#322—111no—
320#322C2×D1111yescharacteristic
321C22×C11C2×C4×D411yescharacteristic
322C2×D11—21no—
323C2×D11—21no—
324C2×D11—21no—
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C4×C11—21no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11#56811yescharacteristic
334C4×C11#56811yescharacteristic
335C4×C11C2×#13711yescharacteristic
336C4×C11#57511yescharacteristic
337Dic11—21no—
338Dic11—21no—
339Dic11—21no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343C2×Q16—111no—
344C2×Q16C4×D1111yescharacteristic
345C2×SD16—111no—
346C2×SD16—111no—
347C2×M16—111no—
348C2×M16—111no—
349C2×M16—221no—
350C2×M16—221no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—221no—
354C4⋊Q8—111no—
355C4⋊Q8—111no—
356#126—221no—
357#125—111no—
358#125—221no—
359#124—111no—
360#123—221no—
361C22⋊Q8—111no—
362C22⋊Q8—111no—
363C22⋊Q8—111no—
364C22⋊Q8—221no—
365#121—111no—
366C4×Q8—111no—
367C4×Q8—221no—
368C4×Q8C22×D1111yescharacteristic
369C4×Q8C22×D1111yescharacteristic
370C4×D4—111no—
371C4×D4—221no—
372#117—221no—
373#117—221no—
374C2×C42—111no—
375#107—111no—
376#107C4×D1111yescharacteristic
377#106—111no—
378#106—111no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103C4×D1111yescharacteristic
396#103C4×D1111yescharacteristic
397#102—111no—
398#102—111no—
399C22⋊C8—221no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—21no—
404#97—111no—
405#97—111no—
406#97—221no—
407#97—221no—
408#97—221no—
409C4×C8—21no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8C22×D1111yescharacteristic
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11#293211yescharacteristic
421C2×C11C4×#13711yescharacteristic
422C2×C11#295511yescharacteristic
423D11—41no—
424D11—81no—
425C2×Q8—111no—
426C2×Q8—221no—
427C2×Q8C2×C4×D1111yescharacteristic
428C2×Q8C2×C4×D1111yescharacteristic
429C2×D4—111no—
430C2×D4—221no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—221no—
435Q16—41no—
436Q16—441no—
437SD16—441no—
438SD16—441no—
439M16—441no—
440M16—441no—
441M16—442no—
442M16—442no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—222no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—441no—
455C2×C8—442no—
456C2×C8C2×C4×D1111yescharacteristic
457C2×C8C2×C4×D1111yescharacteristic
458C2×C8D4×D1111yescharacteristic
459C2×C8D4×D1111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—111no—
463C4⋊C4—111no—
464C4⋊C4—221no—
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⋊C4C2×C4×D1111yescharacteristic
474C4⋊C4C2×C4×D1111yescharacteristic
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C22⋊C4—221no—
479C22⋊C4—221no—
480C22⋊C4—221no—
481C22⋊C4—221no—
482C42—21no—
483C42—21no—
484C42—111no—
485C42—111no—
486C42—111no—
487C42—221no—
488C42C23×D1111yescharacteristic
489C11#1798411yescharacteristic, complemented, Sylow
490C23—111no—
491C23—221no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—221no—
497Q8—221no—
498Q8—442no—
499D4—221no—
500D4—221no—
501D4—442no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—111no—
507C2×C4—111no—
508C2×C4—111no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4#41×D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—112no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—441no—
534C8—441no—
535C8—441no—
536C22—221no—
537C22—221no—
538C22—221no—
539C22—441no—
540C22—441no—
541C22—441no—
542C22C4×D4×D1111yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—221no—
549C4—221no—
550C4—221no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4#1062327611yescharacteristic
555C4#1062328111yescharacteristic
556C4D11×#13711yescharacteristic
557C4#1062330811yescharacteristic
558C2—441no—
559C2—881no—
560C2#1307733011yescharacteristic
561C2#1307743211yescharacteristic
562C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1587C2
socleC22×C11C2×C4×D4
prime radical#66948C2×C4
cosocleC42×C11C24
hypercenter#1587D11
hypocenterC11#17984
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
3. #13077547C2semidirect
4. #13067487C2semidirect
5. #13067475C2semidirect
6. #13067471C2semidirect
7. #13067469C2semidirect
8. #13067467C2semidirect
9. #13067458C2semidirect
10. #13067456C2semidirect
11. #13067380C2semidirect
12. #13067087C2semidirect
14. #13066904C2semidirect
15. C11×#1587C2semidirect
213. #1587D11semidirect
489. C11#17984semidirect

Maximal subgroups

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

subgroupindex
#130792202
#130775932
#130775472
#130674872
#130674752
#130674712
#130674692
#130674672
#130674582
#130674562
#130673802
#130670872
#130670802
#130669042
C11×#15872
#1798411