Finite Group Databasebeta

← #14723876

Subgroups — #14723876

Order 2816.

598 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#13078688C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic
3#13077713C211yesmaximal, characteristic, complemented
4#13067486C211yesmaximal, characteristic, complemented
5#13067472C211yesmaximal, characteristic, complemented
6#13067465C211yesmaximal, characteristic, complemented
7#13067451C211yesmaximal, characteristic, complemented
8#13067434C211yesmaximal, characteristic, complemented
9#13067427C211yesmaximal, characteristic, complemented
10#13067422C211yesmaximal, characteristic, complemented
11#13067415C211yesmaximal, characteristic, complemented
12#13067048C211yesmaximal, characteristic
13#13067018C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1573C211yesmaximal, characteristic, complemented
16C4×#4339C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C8×C22⋊D11—21no—
22C8×C22⋊D11—21no—
23#10622538C2211yescharacteristic
24#10622538C2211yescharacteristic
25#10622464C411yescharacteristic
26#10622462C411yescharacteristic
27#10622459C411yescharacteristic
28#10622454C411yescharacteristic
29#10622447C2211yescharacteristic
30#10622447C2211yescharacteristic
31#10622446—21no—
32D11×C4⋊C8—21no—
33#10622444C2211yescharacteristic
34#10622444C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622443C2211yescharacteristic
38#10622443C2211yescharacteristic
39#10622346C411yescharacteristic
40#10622346C411yescharacteristic
41#10622336C411yescharacteristic
42#10622336C411yescharacteristic
43#10622333—21no—
44#10622333—21no—
45#10622314—21no—
46#10622314—21no—
47C4×Dic44C2211yescharacteristic
48C4×Dic44C2211yescharacteristic
49C4×#4314C2211yescharacteristic
50C4×#4314C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622122C2211yescharacteristic
60#10622122C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C22×C8×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C4×C22⋊D11—21no—
71C4×C22⋊D11—21no—
72#66979—21no—
73#66979C2×C411yescharacteristic
74#66977—21no—
75#66977C2×C411yescharacteristic
76#66977C2×C411yescharacteristic
77C2×Dic44C2×C411yescharacteristic
78C2×Dic44C2×C411yescharacteristic
79C2×#4314C2×C411yescharacteristic
80C2×#4314C2×C411yescharacteristic
81C2×C8×D11—21no—
82C2×C8×D11—21no—
83C4×D44C2×C411yescharacteristic
84C4×D44C2311yescharacteristic
85#66925—21no—
86C42×D11—21no—
87#66923—21no—
88#66922C2×C411yescharacteristic
89#66922C2×C411yescharacteristic
90C4×Dic22—21no—
91C4×Dic22C2×C411yescharacteristic
92C4×Dic22C2311yescharacteristic
93C4×Dic22C2311yescharacteristic
94C4×Dic22C2311yescharacteristic
95C11×C4⋊C8—21no—
96C11×C4⋊C8C2×C411yescharacteristic
97C11×C4⋊C8C2×C411yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C11×C22⋊C8C2×C411yescharacteristic
104C11×C22⋊C8C2×C411yescharacteristic
105C11×#97—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)D411yescharacteristic
110C22⋊(C11⋊C8)D411yescharacteristic
111#66885C2×C411yescharacteristic
112#66885C2×C411yescharacteristic
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115#66882C2×C411yescharacteristic
116#66882C2×C411yescharacteristic
117#66881C2×C411yescharacteristic
118#66881C2×C411yescharacteristic
119#66880C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66879—21no—
126#66879—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#17921—111nomaximal, Sylow
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C2×C22⋊D11—21no—
149#4339—22no—
150#4339—22no—
151C2×D44C22×C411yescharacteristic
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C411yescharacteristic
157C2×Dic22C22×C411yescharacteristic
158C2×Dic22C22×C411yescharacteristic
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—81no—
164C2×C8×C11C22×C411yescharacteristic
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C22×C411yescharacteristic
168C42×C11C22×C411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11#4111yescharacteristic
171C42×C11C2411yescharacteristic
172C22⋊Dic11—21no—
173C22⋊Dic11—21no—
174C22⋊Dic11—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11C22×C411yescharacteristic
181C4⋊Dic11C22×C411yescharacteristic
182C4⋊Dic11C22×C411yescharacteristic
183C4⋊Dic11C22×C411yescharacteristic
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×Dic11—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201Dic44—22no—
202Dic44—22no—
203#4314—22no—
204#4314—22no—
205C8×D11—81no—
206C8×D11—81no—
207#3107—111no—
208#2988—111no—
209#2985—111no—
210#1587—111no—
211#1585—111no—
212#1584—111no—
213#1582—111no—
214#1579—111no—
215SD16⋊C8—111no—
216C8×Q16—111no—
217C8×SD16—111no—
218#1573D1111yescharacteristic, complemented
219#1488—111no—
220#1481—111no—
221#1454—111no—
222C23×C11C4×D411yescharacteristic
223C22×D11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C22⋊D11—24no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243D44—21no—
244D44#13112yes—
245C4×D11—24no—
246C4×D11—41no—
247C4×D11—41no—
248C4×D11—81no—
249Dic22—21no—
250Dic22—21no—
251Dic22—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—81no—
255Dic22#13112yes—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11—41no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270#533—111no—
271C4×#41—111no—
272#485—111no—
273#485—111no—
274#475—111no—
275#474—111no—
276#462—111no—
277#461—111no—
278#452—111no—
279#452—111no—
280#446—111no—
281#446—111no—
282#446—221no—
283#446—221no—
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8—111no—
287C8×Q8—111no—
288C4×Q16—111no—
289C4×Q16—111no—
290C4×SD16—111no—
291C4×SD16—111no—
292C8×D4—111no—
293C8×D4—111no—
294C8×D4—221no—
295C8×D4—221no—
296#433—221no—
297#433—221no—
298#432C2×D1111yescharacteristic
299#431—111no—
300#431—111no—
301#431—221no—
302#431C2×D1111yescharacteristic
303C2×C4⋊C8—221no—
304C2×C4⋊C8C2×D1111yescharacteristic
305#335C2×D1111yescharacteristic
306#335C2×D1111yescharacteristic
307#334C2×D1111yescharacteristic
308#334C2×D1111yescharacteristic
309Q8⋊C8—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315D4⋊C8—111no—
316D4⋊C8—111no—
317#322—111no—
318#322—111no—
319#322—111no—
320C82—111no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11C2×C4×D411yescharacteristic
325C2×D11—22no—
326C2×D11—41no—
327C2×D11—41no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11C2×#13111yescharacteristic
333C4×C11C2×#13111yescharacteristic
334C4×C11#57711yescharacteristic
335C4×C11#57811yescharacteristic
336Dic11—22no—
337Dic11—41no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343C2×#41—111no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C22×C8—21no—
349C22×C8—221no—
350C22×C8—221no—
351C4⋊Q8—111no—
352C4⋊Q8—111no—
353#125—221no—
354C22⋊Q8—111no—
355C22⋊Q8—111no—
356C22⋊Q8—221no—
357C4×Q8—111no—
358C4×Q8—111no—
359C4×Q8—111no—
360C4×Q8—111no—
361C4×Q8—221no—
362C4×D4—111no—
363C4×D4—111no—
364C4×D4—221no—
365C4×D4—221no—
366#117—111no—
367#117—221no—
368#117—221no—
369C2×C42—221no—
370C2×C42C22×D1111yescharacteristic
371#107—111no—
372#107—111no—
373#106—111no—
374#106—111no—
375C4⋊C8—21no—
376C4⋊C8—111no—
377C4⋊C8—111no—
378C4⋊C8—221no—
379C4⋊C8—221no—
380C4⋊C8—221no—
381C4⋊C8—221no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8C4×D1111yescharacteristic
386C4⋊C8C4×D1111yescharacteristic
387C4⋊C8C22×D1111yescharacteristic
388C4⋊C8C22×D1111yescharacteristic
389C4⋊C8C22×D1111yescharacteristic
390C4⋊C8C22×D1111yescharacteristic
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#102—111no—
398#102—111no—
399C22⋊C8—21no—
400C22⋊C8—111no—
401C22⋊C8—111no—
402C22⋊C8—221no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8C4×D1111yescharacteristic
406C22⋊C8C4×D1111yescharacteristic
407#97—21no—
408#97—221no—
409#97—221no—
410C4×C8—111no—
411C4×C8—111no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—221no—
415C4×C8—221no—
416C4×C8—221no—
417C4×C8—221no—
418C4×C8C22×D1111yescharacteristic
419C4×C8C22×D1111yescharacteristic
420C2×C11—41no—
421C2×C11#292911yescharacteristic
422C2×C11#294711yescharacteristic
423C2×C11#295711yescharacteristic
424D11—42no—
425#41—222no—
426#41—222no—
427C2×Q8—111no—
428C2×Q8—111no—
429C2×Q8—111no—
430C2×Q8—221no—
431C2×D4—111no—
432C2×D4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4#434311yescharacteristic
439Q16—222no—
440Q16—222no—
441SD16—222no—
442SD16—222no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8—111no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—881no—
455C2×C8—881no—
456C2×C8C2×C4×D1111yescharacteristic
457C2×C8C2×C4×D1111yescharacteristic
458C2×C8C2×C4×D1111yescharacteristic
459C2×C8C2×C4×D1111yescharacteristic
460C4⋊C4—111no—
461C4⋊C4—111no—
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—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—221no—
479C42—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42D4×D1111yescharacteristic
485C42#434311yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1792111yescharacteristic, complemented, Sylow
488C23—221no—
489C23#6694611yescharacteristic
490Q8—112no—
491Q8—221no—
492Q8—221no—
493Q8—221no—
494Q8—221no—
495Q8—221no—
496Q8—881no—
497D4—112no—
498D4—224no—
499D4—221no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—224no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—881no—
516C2×C4#6694611yescharacteristic
517C2×C4#6694611yescharacteristic
518C2×C4#6694611yescharacteristic
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4C2×#434311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—441no—
535C8—441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—222no—
540C22—441no—
541C22—441no—
542C22C2×#6694611yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—222no—
548C4—441no—
549C4—441no—
550C4—441no—
551C4—441no—
552C4—441no—
553C4—441no—
554C4D11×#13111yescharacteristic
555C4D11×#13111yescharacteristic
556C4#1062330611yescharacteristic
557C4#1062331011yescharacteristic
558C2—41no—
559C2—442no—
560C2#1307730911yescharacteristic
561C2#1307745711yescharacteristic
562C2#1307753211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1573C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1573D11
hypocenterC11#17921
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #13077713C2semidirect
4. #13067486C2semidirect
5. #13067472C2semidirect
6. #13067465C2semidirect
7. #13067451C2semidirect
8. #13067434C2semidirect
9. #13067427C2semidirect
10. #13067422C2semidirect
11. #13067415C2semidirect
13. #13067018C2semidirect
14. #13066916C2semidirect
15. C11×#1573C2semidirect
218. #1573D11semidirect
487. C11#17921semidirect

Maximal subgroups

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

subgroupindex
#130786882
#130777252
#130777132
#130674862
#130674722
#130674652
#130674512
#130674342
#130674272
#130674222
#130674152
#130670482
#130670182
#130669162
C11×#15732
#1792111