Finite Group Databasebeta

← #14725165

Subgroups — #14725165

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078656C211yesmaximal, characteristic
2#13077717C211yesmaximal, characteristic
3#13077706C211yesmaximal, characteristic
4#13067524C211yesmaximal, characteristic, complemented
5#13067512C211yesmaximal, characteristic, complemented
6#13067486C211yesmaximal, characteristic, complemented
7#13067486C211yesmaximal, characteristic, complemented
8#13067465C211yesmaximal, characteristic, complemented
9#13067465C211yesmaximal, characteristic, complemented
10#13067434C211yesmaximal, characteristic, complemented
11#13067422C211yesmaximal, characteristic, complemented
12#13067088C211yesmaximal, characteristic
13#13067010C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic
15C11×#1572C211yesmaximal, characteristic
16#10623001C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622463C411yescharacteristic
24#10622463C411yescharacteristic
25#10622462C411yescharacteristic
26#10622462C411yescharacteristic
27#10622444C2211yescharacteristic
28#10622444C2211yescharacteristic
29#10622444C2211yescharacteristic
30#10622444C2211yescharacteristic
31#10622443C2211yescharacteristic
32#10622443C2211yescharacteristic
33#10622443C2211yescharacteristic
34#10622443C2211yescharacteristic
35#10622352C411yescharacteristic
36#10622352C411yescharacteristic
37#10622335C411yescharacteristic
38#10622335C411yescharacteristic
39#10622333—21no—
40#10622333—21no—
41#10622332—21no—
42#10622331—21no—
43#10622314—21no—
44#10622314—21no—
45C4×Dic44C2211yescharacteristic
46C4×Dic44C2211yescharacteristic
47C4×Dic44C2211yescharacteristic
48C4×Dic44C2211yescharacteristic
49#10622292—21no—
50C8×Dic22—21no—
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622122C2211yescharacteristic
60#10622122C2211yescharacteristic
61#10622122C2211yescharacteristic
62#10622122C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C22×Dic22C2×C411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69#66979—21no—
70C2×C4⋊Dic11C2×C411yescharacteristic
71#66977—21no—
72#66977C2×C411yescharacteristic
73#66977C2×C411yescharacteristic
74C2×Dic11⋊C4—21no—
75C2×C4×Dic11—21no—
76C2×Dic44C2×C411yescharacteristic
77C2×Dic44C2×C411yescharacteristic
78C2×Dic44C2×C411yescharacteristic
79C2×Dic44C2×C411yescharacteristic
80#66923—21no—
81#66922C2×C411yescharacteristic
82#66922C2×C411yescharacteristic
83C4×Dic22—21no—
84C4×Dic22—21no—
85C4×Dic22—21no—
86C4×Dic22C2×C411yescharacteristic
87C4×Dic22C2×C411yescharacteristic
88C4×Dic22C2311yescharacteristic
89C4×Dic22C2311yescharacteristic
90C4×Dic22C2311yescharacteristic
91C4×Dic22C2311yescharacteristic
92C11×C4⋊C8C2×C411yescharacteristic
93C11×C4⋊C8C2×C411yescharacteristic
94C11×C4⋊C8C2311yescharacteristic
95C11×C4⋊C8C2311yescharacteristic
96C11×C4⋊C8C2311yescharacteristic
97C11×C4⋊C8C2311yescharacteristic
98C11×C22⋊C8—21no—
99C11×C22⋊C8—21no—
100C11×C22⋊C8C2×C411yescharacteristic
101C11×C22⋊C8C2×C411yescharacteristic
102C11×#97—21no—
103C4×C8×C11—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)D411yescharacteristic
108C22⋊(C11⋊C8)D411yescharacteristic
109#66882C2×C411yescharacteristic
110#66882C2×C411yescharacteristic
111#66882C2×C411yescharacteristic
112#66882C2×C411yescharacteristic
113#66880C2×C411yescharacteristic
114#66880C2×C411yescharacteristic
115#66880C2×C411yescharacteristic
116#66880C2×C411yescharacteristic
117#66880C2×C411yescharacteristic
118#66880C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66879—21no—
122#66879—21no—
123#66879—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133C8×Dic11—21no—
134C8×Dic11—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)D411yescharacteristic
139C4⋊(C11⋊C8)D411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18032—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C2×Dic22—22no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—41no—
154C2×Dic22C22×C411yescharacteristic
155C2×Dic22C22×C411yescharacteristic
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C411yescharacteristic
163C2×C8×C11C22×C411yescharacteristic
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C42×C11C22×C411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11#4111yescharacteristic
169C42×C11C2411yescharacteristic
170C22⋊Dic11—21no—
171C22⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11C22×C411yescharacteristic
177C4⋊Dic11C22×C411yescharacteristic
178C4⋊Dic11C22×C411yescharacteristic
179C4⋊Dic11C22×C411yescharacteristic
180Dic11⋊C4—21no—
181Dic11⋊C4—21no—
182Dic11⋊C4—21no—
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8C2×D411yescharacteristic
197C2×C11⋊C8C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200Dic44—22no—
201Dic44—22no—
202Dic44—41no—
203Dic44—41no—
204#3104—111no—
205#2986—111no—
206#2984—111no—
207#1593—111no—
208#1591—111no—
209#1587—111no—
210#1587—111no—
211#1584—111no—
212#1584—111no—
213#1579—111no—
214C8×Q16—111no—
215#1572D1111yescharacteristic
216#1497—111no—
217#1479—111no—
218#1454—111no—
219C23×C11C4×D411yescharacteristic
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—41no—
225C2×C4×C11C4×D411yescharacteristic
226C2×C4×C11C4×D411yescharacteristic
227C2×C4×C11C4×D411yescharacteristic
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241Dic22—21no—
242Dic22—21no—
243Dic22—21no—
244Dic22—21no—
245Dic22—21no—
246Dic22—21no—
247Dic22—21no—
248Dic22—42no—
249Dic22—42no—
250Dic22#13112yes—
251C8×C11—21no—
252C8×C11—21no—
253C8×C11—21no—
254C8×C11—21no—
255C8×C11—41no—
256C8×C11—41no—
257C8×C11—41no—
258C8×C11—41no—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—41no—
264C11⋊C8—41no—
265#533—111no—
266C2×C4×Q8—111no—
267#484—111no—
268#484—111no—
269#477—111no—
270#477—111no—
271#462—111no—
272#462—111no—
273#451—111no—
274#451—111no—
275#446—111no—
276#446—111no—
277#446—111no—
278#446—111no—
279#446—221no—
280#446—221no—
281#446—221no—
282C8×Q8—111no—
283C8×Q8—111no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—221no—
287C4×Q16—111no—
288C4×Q16—111no—
289C4×Q16—111no—
290C4×Q16—111no—
291#433—221no—
292#433—221no—
293#432—221no—
294#432C2×D1111yescharacteristic
295#431—111no—
296#431—111no—
297#431—221no—
298#431C2×D1111yescharacteristic
299#431C2×D1111yescharacteristic
300#335C2×D1111yescharacteristic
301#335C2×D1111yescharacteristic
302#334C2×D1111yescharacteristic
303#334C2×D1111yescharacteristic
304Q8⋊C8—111no—
305Q8⋊C8—111no—
306Q8⋊C8—111no—
307Q8⋊C8—111no—
308Q8⋊C8—111no—
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312#322—111no—
313#322—111no—
314#322—111no—
315C82—111no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11C2×C4×D411yescharacteristic
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11C2×#13111yescharacteristic
325C4×C11#56811yescharacteristic
326C4×C11#57811yescharacteristic
327C4×C11#57811yescharacteristic
328Dic11—22no—
329Dic11—41no—
330Dic11—41no—
331Dic11—41no—
332Dic11—41no—
333Dic11—41no—
334Dic11—41no—
335Dic11—41no—
336C22×Q8—111no—
337C2×Q16—111no—
338C2×Q16—111no—
339C2×Q16—111no—
340C2×Q16—111no—
341C4⋊Q8—111no—
342C4⋊Q8—111no—
343#125—221no—
344C22⋊Q8—111no—
345C22⋊Q8—111no—
346C22⋊Q8—221no—
347C4×Q8—111no—
348C4×Q8—111no—
349C4×Q8—111no—
350C4×Q8—111no—
351C4×Q8—111no—
352C4×Q8—111no—
353C4×Q8—221no—
354C4×Q8—221no—
355C4×Q8—221no—
356#117—221no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—221no—
359C2×C42—221no—
360C2×C42C22×D1111yescharacteristic
361#107—111no—
362#107—111no—
363#107—111no—
364#107—111no—
365C4⋊C8—111no—
366C4⋊C8—111no—
367C4⋊C8—221no—
368C4⋊C8—221no—
369C4⋊C8—221no—
370C4⋊C8—221no—
371C4⋊C8—221no—
372C4⋊C8—221no—
373C4⋊C8—221no—
374C4⋊C8—221no—
375C4⋊C8—221no—
376C4⋊C8C4×D1111yescharacteristic
377C4⋊C8C4×D1111yescharacteristic
378C4⋊C8C22×D1111yescharacteristic
379C4⋊C8C22×D1111yescharacteristic
380C4⋊C8C22×D1111yescharacteristic
381C4⋊C8C22×D1111yescharacteristic
382#103—111no—
383#103—111no—
384#103—111no—
385#103—111no—
386#103—111no—
387#103—111no—
388#103—111no—
389#103—111no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—111no—
393C22⋊C8—111no—
394C22⋊C8—221no—
395C22⋊C8C4×D1111yescharacteristic
396C22⋊C8C4×D1111yescharacteristic
397#97—21no—
398#97—221no—
399#97—221no—
400#97—221no—
401#97—221no—
402C4×C8—21no—
403C4×C8—111no—
404C4×C8—111no—
405C4×C8—111no—
406C4×C8—111no—
407C4×C8—221no—
408C4×C8—221no—
409C4×C8—221no—
410C4×C8—221no—
411C4×C8C22×D1111yescharacteristic
412C4×C8C22×D1111yescharacteristic
413C2×C11—41no—
414C2×C11#293311yescharacteristic
415C2×C11#295011yescharacteristic
416C2×C11#295511yescharacteristic
417C2×Q8—111no—
418C2×Q8—111no—
419C2×Q8—111no—
420C2×Q8—111no—
421C2×Q8—222no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—441no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4C2×C4×D1111yescharacteristic
428C22×C4D4×D1111yescharacteristic
429C22×C4#434311yescharacteristic
430Q16—222no—
431Q16—222no—
432Q16—441no—
433Q16—441no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—111no—
439C2×C8—111no—
440C2×C8—111no—
441C2×C8—111no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8C2×C4×D1111yescharacteristic
445C2×C8C2×C4×D1111yescharacteristic
446C2×C8C2×C4×D1111yescharacteristic
447C2×C8C2×C4×D1111yescharacteristic
448C4⋊C4—111no—
449C4⋊C4—111no—
450C4⋊C4—111no—
451C4⋊C4—111no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C22⋊C4—221no—
465C22⋊C4—221no—
466C42—221no—
467C42—221no—
468C42—221no—
469C42—221no—
470C42—221no—
471C42—221no—
472C42C2×C4×D1111yescharacteristic
473C42D4×D1111yescharacteristic
474C42#434311yescharacteristic
475C42C23×D1111yescharacteristic
476C11#1803211yescharacteristic, complemented, Sylow
477C23#6694611yescharacteristic
478Q8—112no—
479Q8—221no—
480Q8—221no—
481Q8—221no—
482Q8—221no—
483Q8—221no—
484Q8—221no—
485Q8—221no—
486Q8—442no—
487Q8—442no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4#6694611yescharacteristic
504C2×C4#6694611yescharacteristic
505C2×C4#6694611yescharacteristic
506C2×C4C22×C4×D1111yescharacteristic
507C2×C4C2×D4×D1111yescharacteristic
508C2×C4C2×#434311yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—221no—
518C8—221no—
519C8—221no—
520C8—221no—
521C8—441no—
522C8—441no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×#6694611yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—222no—
532C4—441no—
533C4—441no—
534C4—441no—
535C4—441no—
536C4—441no—
537C4—441no—
538C4—441no—
539C4D11×#13111yescharacteristic
540C4#1062328111yescharacteristic
541C4#1062330211yescharacteristic
542C4#1062330211yescharacteristic
543C2—41no—
544C2#1307734011yescharacteristic
545C2#1307748311yescharacteristic
546C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1572C2
socleC22×C11C2×C4×D4
prime radicalC23×C11C4×D4
cosocleC42×C11C24
hypercenter#1572D11
hypocenterC11#18032
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
4. #13067524C2semidirect
5. #13067512C2semidirect
6. #13067486C2semidirect
7. #13067486C2semidirect
8. #13067465C2semidirect
9. #13067465C2semidirect
10. #13067434C2semidirect
11. #13067422C2semidirect
476. C11#18032semidirect

Maximal subgroups

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

subgroupindex
#130786562
#130777172
#130777062
#130675242
#130675122
#130674862
#130674652
#130674342
#130674222
#130670882
#130670102
#130669162
C11×#15722
#1803211