Finite Group Databasebeta

← #14724516

Subgroups — #14724516

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079199C211yesmaximal, characteristic
2#13077547C211yesmaximal, characteristic
3#13077545C211yesmaximal, characteristic
4#13067490C211yesmaximal, characteristic, complemented
5#13067489C211yesmaximal, characteristic, complemented
6#13067488C211yesmaximal, characteristic, complemented
7#13067487C211yesmaximal, characteristic, complemented
8#13067486C211yesmaximal, characteristic, complemented
9#13067485C211yesmaximal, characteristic, complemented
10#13067484C211yesmaximal, characteristic, complemented
11#13067370C211yesmaximal, characteristic
12#13067069C211yesmaximal, characteristic
13#13067069C211yesmaximal, characteristic
14D11×#322C211yesmaximal, characteristic
15C11×#1587C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17#10623109C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21#10622801C411yescharacteristic
22#10622794C411yescharacteristic
23C4×#4326C2211yescharacteristic
24C4×#4326C2211yescharacteristic
25#10622637C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27#10622500C411yescharacteristic
28#10622487C411yescharacteristic
29#10622452—21no—
30#10622452—21no—
31#10622450C2211yescharacteristic
32#10622450C2211yescharacteristic
33#10622444C2211yescharacteristic
34#10622443—21no—
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622426C411yescharacteristic
38#10622426C411yescharacteristic
39#10622405C411yescharacteristic
40#10622405C411yescharacteristic
41#10622321—21no—
42#10622314—21no—
43C4×Dic44C2211yescharacteristic
44#10622302—21no—
45C4×C8×D11C2211yescharacteristic
46C4×C8×D11C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22—21no—
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×Q8⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56Q8⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66#10622092C2211yescharacteristic
67C2×C11×Q16C2×C411yescharacteristic
68C4×Q8×C11C2311yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70#66999C2×C411yescharacteristic
71#66999C2×C411yescharacteristic
72#66997C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75C2×#4326C2×C411yescharacteristic
76C2×Dic44C2×C411yescharacteristic
77C2×#4313—21no—
78C2×#4313—21no—
79C2×C8×D11—21no—
80C2×C8×D11C2×C411yescharacteristic
81C2×C8×D11C2×C411yescharacteristic
82C2×C8×D11D411yescharacteristic
83C2×C8×D11D411yescharacteristic
84#66950C2×C411yescharacteristic
85#66950C2×C411yescharacteristic
86#66949—21no—
87#66949—21no—
88#66942—21no—
89#66942—21no—
90#66941C2×C411yescharacteristic
91#66941C2×C411yescharacteristic
92#66925—21no—
93#66925—21no—
94C42×D11C2311yescharacteristic
95C4×Dic22—21no—
96C4×Dic22—21no—
97C4×Dic22C2311yescharacteristic
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#66882C2×C411yescharacteristic
114#66880C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66879—21no—
117#66879—21no—
118Dic11⋊C8—21no—
119Dic11⋊C8—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—21no—
125C8×Dic11—21no—
126C8×Dic11—21no—
127C8×Dic11C2×C411yescharacteristic
128C8×Dic11C2×C411yescharacteristic
129C8×Dic11D411yescharacteristic
130C8×Dic11D411yescharacteristic
131#66874C2×C411yescharacteristic
132#66874C2×C411yescharacteristic
133#66871C2×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#17980—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147C2×C4×D11C22×C411yescharacteristic
148C2×C4×D11C2×D411yescharacteristic
149C2×C4×D11#4111yescharacteristic
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22C22×C411yescharacteristic
153C2×Dic22C22×C411yescharacteristic
154C11×Q16—41no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11C22×C411yescharacteristic
159C2×C8×C11C22×C411yescharacteristic
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C22×C411yescharacteristic
165C11×C4⋊C4C22×C411yescharacteristic
166C42×C11—21no—
167C42×C11—21no—
168C42×C11C2411yescharacteristic
169#4326—41no—
170#4326—41no—
171(C2×D11)⋊C4—21no—
172(C2×D11)⋊C4—21no—
173(C2×D11)⋊C4—21no—
174(C2×D11)⋊C4—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11C22×C411yescharacteristic
178C4⋊Dic11C22×C411yescharacteristic
179Dic11⋊C4—21no—
180Dic11⋊C4—21no—
181Dic11⋊C4—21no—
182Dic11⋊C4—21no—
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189C4×Dic11—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
201Dic44—41no—
202#4313—42no—
203#4313—42no—
204C8×D11—24no—
205C8×D11—22no—
206C8×D11—22no—
207C8×D11—41no—
208C8×D11—41no—
209#3170—111no—
210#2960—111no—
211#2960—111no—
212#1587—111no—
213#1587—111no—
214#1587—111no—
215#1587—111no—
216#1587—111no—
217#1587—111no—
218#1587—111no—
219#1587D1111yescharacteristic, complemented
220#1566—111no—
221#1493—111no—
222#1493—111no—
223C2×#322—111no—
224C22×D11C4×D411yescharacteristic
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11C4×D411yescharacteristic
241C2×Dic11C4×D411yescharacteristic
242C2×Dic11C4×D411yescharacteristic
243C4×D11—21no—
244C4×D11—21no—
245C4×D11—22no—
246C4×D11#13712yes—
247C4×D11#13712yes—
248Dic22—21no—
249Dic22—21no—
250Dic22—21no—
251Dic22—21no—
252Dic22—42no—
253Dic22—42no—
254C8×C11—22no—
255C8×C11—21no—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—41no—
260C8×C11—41no—
261C11⋊C8—22no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533—111no—
269#533—111no—
270#500—111no—
271#494—111no—
272#487—111no—
273#487—111no—
274#467—111no—
275#467—111no—
276#467—111no—
277#467—111no—
278#446—111no—
279#446—111no—
280#446—111no—
281#446—221no—
282#446—221no—
283#446C2×D1111yescharacteristic
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C8×Q8—221no—
288C8×Q8—221no—
289C8×Q8C2×D1111yescharacteristic
290C4×Q16—111no—
291C4×Q16—111no—
292C4×Q16—111no—
293C4×Q16C2×D1111yescharacteristic
294#424—221no—
295#424—221no—
296#423—111no—
297#423—111no—
298#405—221no—
299#405—221no—
300C2×C4×C8—111no—
301C2×C4×C8—111no—
302C2×C4×C8—111no—
303#334—111no—
304#334—111no—
305#334—111no—
306#334C2×D1111yescharacteristic
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8C2×D1111yescharacteristic
314Q8⋊C8C2×D1111yescharacteristic
315#322—111no—
316#322—111no—
317#322—111no—
318#322C2×D1111yescharacteristic
319C22×C11C2×C4×D411yescharacteristic
320C2×D11—21no—
321C2×D11—21no—
322C2×D11#44112yes—
323C4×C11—21no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11#56811yescharacteristic
329C4×C11#56811yescharacteristic
330C4×C11C2×#13711yescharacteristic
331C4×C11C2×#13711yescharacteristic
332Dic11—21no—
333Dic11—41no—
334Dic11—41no—
335Dic11—41no—
336Dic11—41no—
337Dic11#44112yes—
338Dic11#44312yes—
339C2×Q16—111no—
340C2×Q16—111no—
341C2×Q16—111no—
342C2×Q16C4×D1111yescharacteristic
343C2×M16—221no—
344C2×M16—221no—
345C22×C8—111no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—111no—
349C22×C8—221no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8—111no—
353C4⋊Q8—111no—
354#125—221no—
355#125—221no—
356C22⋊Q8—111no—
357C22⋊Q8—111no—
358C22⋊Q8—111no—
359C22⋊Q8—111no—
360C22⋊Q8—221no—
361C22⋊Q8—221no—
362C4×Q8—111no—
363C4×Q8—111no—
364C4×Q8—221no—
365C4×Q8—221no—
366C4×Q8C22×D1111yescharacteristic
367C4×Q8C22×D1111yescharacteristic
368#117—221no—
369#117—221no—
370C2×C42—111no—
371#107—111no—
372#107—111no—
373#107—111no—
374#107C4×D1111yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—221no—
380C4⋊C8—221no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8C22×D1111yescharacteristic
388C4⋊C8C22×D1111yescharacteristic
389#103—111no—
390#103—111no—
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103C4×D1111yescharacteristic
396#103C4×D1111yescharacteristic
397#97—21no—
398#97—221no—
399#97—221no—
400#97—221no—
401C4×C8—21no—
402C4×C8—111no—
403C4×C8—111no—
404C4×C8—111no—
405C4×C8—111no—
406C4×C8—111no—
407C4×C8—111no—
408C4×C8—111no—
409C4×C8—221no—
410C4×C8—221no—
411C4×C8—221no—
412C4×C8—221no—
413C4×C8C22×D1111yescharacteristic
414C4×C8C22×D1111yescharacteristic
415C4×C8C22×D1111yescharacteristic
416C2×C11#293211yescharacteristic
417C2×C11C2×#44111yescharacteristic
418C2×C11C2×#44311yescharacteristic
419D11—22no—
420C2×Q8—111no—
421C2×Q8—111no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8C2×C4×D1111yescharacteristic
425C2×Q8C2×C4×D1111yescharacteristic
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429Q16—41no—
430Q16—441no—
431Q16—441no—
432Q16—441no—
433M16—442no—
434M16—442no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—111no—
439C2×C8—111no—
440C2×C8—111no—
441C2×C8—111no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—224no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—441no—
449C2×C8—441no—
450C2×C8C2×C4×D1111yescharacteristic
451C2×C8C2×C4×D1111yescharacteristic
452C2×C8D4×D1111yescharacteristic
453C2×C8D4×D1111yescharacteristic
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—111no—
457C4⋊C4—111no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4C2×C4×D1111yescharacteristic
471C4⋊C4C2×C4×D1111yescharacteristic
472C22⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C42—21no—
477C42—21no—
478C42—111no—
479C42—111no—
480C42—111no—
481C42—221no—
482C42—221no—
483C42C23×D1111yescharacteristic
484C11#1798011yescharacteristic, complemented, Sylow
485C23—111no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—221no—
491Q8—221no—
492Q8—221no—
493Q8—221no—
494Q8—442no—
495Q8—442no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—111no—
501C2×C4—111no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—111no—
505C2×C4—222no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4C22×C4×D1111yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4#41×D1111yescharacteristic
515C8—22no—
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—222no—
523C8—221no—
524C8—221no—
525C8—221no—
526C8—221no—
527C8—441no—
528C8—441no—
529C22—112no—
530C22—221no—
531C22—221no—
532C22C4×D4×D1111yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—112no—
539C4—112no—
540C4—221no—
541C4—441no—
542C4—441no—
543C4—441no—
544C4—441no—
545C4#1062327611yescharacteristic
546C4#1062328111yescharacteristic
547C4D11×#13711yescharacteristic
548C4D11×#13711yescharacteristic
549C2—222no—
550C2#1307733011yescharacteristic
551C2D11×#44111yescharacteristic
552C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1587C2
socleC22×C11C2×C4×D4
prime radicalC22×D11C4×D4
cosocleC42×C11C24
hypercenter#1587D11
hypocenterC11#17980
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
4. #13067490C2semidirect
5. #13067489C2semidirect
6. #13067488C2semidirect
7. #13067487C2semidirect
8. #13067486C2semidirect
9. #13067485C2semidirect
10. #13067484C2semidirect
15. C11×#1587C2semidirect
219. #1587D11semidirect
484. C11#17980semidirect

Maximal subgroups

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

subgroupindex
#130791992
#130775472
#130775452
#130674902
#130674892
#130674882
#130674872
#130674862
#130674852
#130674842
#130673702
#130670692
D11×#3222
C11×#15872
#1798011