Finite Group Databasebeta

← #14723874

Subgroups — #14723874

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#13078681C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic
3#13067485C211yesmaximal, characteristic, complemented
4#13067471C211yesmaximal, characteristic, complemented
5#13067464C211yesmaximal, characteristic, complemented
6#13067450C211yesmaximal, characteristic, complemented
7#13067433C211yesmaximal, characteristic, complemented
8#13067426C211yesmaximal, characteristic, complemented
9C8×#4326C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11#13067402C211yesmaximal, characteristic, complemented
12#13067048C211yesmaximal, characteristic
13#13067019C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#2985C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#446—21no—
19C11×#446—21no—
20C11×#446C2211yescharacteristic
21C11×#446C2211yescharacteristic
22C8×Q8×C11C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C11×#433—21no—
25C11×#433—21no—
26C11×#432C2211yescharacteristic
27C11×#431C2211yescharacteristic
28#10622707C411yescharacteristic
29#10622703C411yescharacteristic
30#10622700C411yescharacteristic
31#10622696C411yescharacteristic
32#10622660C411yescharacteristic
33#10622660C411yescharacteristic
34#10622658C411yescharacteristic
35#10622658C411yescharacteristic
36C4×#4326C2211yescharacteristic
37C4×#4326C2211yescharacteristic
38C4×#4325C2211yescharacteristic
39C4×#4325C2211yescharacteristic
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622446—21no—
44D11×C4⋊C8—21no—
45(C22⋊D11)⋊C8—21no—
46(C22⋊D11)⋊C8—21no—
47C8×D44C2211yescharacteristic
48C8×D44C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53Q8⋊(C11⋊C8)C2211yescharacteristic
54Q8⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C11×C4⋊Q8C2×C411yescharacteristic
69C11×C4⋊Q8C2×C411yescharacteristic
70C11×#125—21no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8C2×C411yescharacteristic
73C11×C22⋊Q8C2×C411yescharacteristic
74C4×Q8×C11—21no—
75C4×Q8×C11C2311yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C11×#117—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4326C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83C4×C22⋊D11—21no—
84C4×C22⋊D11—21no—
85#66979C2×C411yescharacteristic
86C22×C11⋊C8—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89C4×D44C2×C411yescharacteristic
90C4×D44C2311yescharacteristic
91#66925—21no—
92C42×D11—21no—
93C4×Dic22C2×C411yescharacteristic
94C4×Dic22C2311yescharacteristic
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8D411yescharacteristic
100C11×C4⋊C8D411yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C4⋊C8C2311yescharacteristic
103C11×C22⋊C8—21no—
104C11×C22⋊C8D411yescharacteristic
105C11×C22⋊C8D411yescharacteristic
106C11×#97—21no—
107C11×#97—21no—
108C11×#97—21no—
109C4×C8×C11—21no—
110C4×C8×C11—21no—
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899C2×C411yescharacteristic
114#66899C2×C411yescharacteristic
115#66899C2×C411yescharacteristic
116#66899C2×C411yescharacteristic
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)C2×C411yescharacteristic
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2×C411yescharacteristic
137C4⋊(C11⋊C8)C2×C411yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17921—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×Q8×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C2×C22⋊D11—21no—
152#4339—22no—
153#4339—22no—
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22C22×C411yescharacteristic
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11#4111yescharacteristic
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183#4326—22no—
184#4326—22no—
185#4325—22no—
186#4325—22no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—81no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C8×D11—81no—
206C8×D11—81no—
207#3107—111no—
208#2988—111no—
209#2985D1111yescharacteristic, complemented
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#1573—111no—
219#1488—111no—
220#1481—111no—
221#1454—111no—
222C23×C11C4×D411yescharacteristic
223C22×D11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—81no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—24no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248D44—21no—
249D44#13112yes—
250C4×D11—24no—
251C4×D11—41no—
252C4×D11—41no—
253C4×D11—81no—
254Dic22—21no—
255Dic22#13112yes—
256C8×C11—21no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270#533C2×D1111yescharacteristic
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—21no—
281#446—21no—
282#446C2×D1111yescharacteristic
283#446C2×D1111yescharacteristic
284C8×Q8—111no—
285C8×Q8—111no—
286C8×Q8C2×D1111yescharacteristic
287C8×Q8C2×D1111yescharacteristic
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—21no—
297#433—21no—
298#432C2×D1111yescharacteristic
299#431—111no—
300#431—111no—
301#431—221no—
302#431C2×D1111yescharacteristic
303C2×C4⋊C8—111no—
304C2×C4⋊C8—221no—
305#335—111no—
306#335—111no—
307#334—111no—
308#334—111no—
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×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11C2×#13111yescharacteristic
337C4×C11C2×#13111yescharacteristic
338C4×C11#57711yescharacteristic
339C4×C11#57811yescharacteristic
340Dic11—22no—
341Dic11—41no—
342Dic11—41no—
343C2×#41—111no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C22×C8—221no—
349C22×C8—221no—
350C22×C8—221no—
351C4⋊Q8C4×D1111yescharacteristic
352C4⋊Q8C4×D1111yescharacteristic
353#125—21no—
354C22⋊Q8—21no—
355C22⋊Q8C4×D1111yescharacteristic
356C22⋊Q8C4×D1111yescharacteristic
357C4×Q8—21no—
358C4×Q8—111no—
359C4×Q8—111no—
360C4×Q8C22×D1111yescharacteristic
361C4×Q8C22×D1111yescharacteristic
362C4×D4—111no—
363C4×D4—111no—
364C4×D4—221no—
365C4×D4—221no—
366#117—21no—
367#117—111no—
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—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
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⋊C8C22⋊D1111yescharacteristic
406C22⋊C8C22⋊D1111yescharacteristic
407#97—21no—
408#97—21no—
409#97—21no—
410C4×C8—21no—
411C4×C8—21no—
412C4×C8—111no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
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—21no—
428C2×Q8—111no—
429C2×Q8C2×C4×D1111yescharacteristic
430C2×Q8C2×C4×D1111yescharacteristic
431C2×D4—111no—
432C2×D4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4#433911yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439Q16—222no—
440Q16—222no—
441SD16—222no—
442SD16—222no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—111no—
446C2×C8—111no—
447C2×C8—111no—
448C2×C8—111no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—881no—
454C2×C8—881no—
455C2×C8—881no—
456C2×C8C2×C22⋊D1111yescharacteristic
457C2×C8C2×C22⋊D1111yescharacteristic
458C2×C8C2×C22⋊D1111yescharacteristic
459C2×C8C2×C22⋊D1111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—111no—
468C4⋊C4—111no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4C2×C4×D1111yescharacteristic
472C4⋊C4C2×C4×D1111yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—221no—
476C22⋊C4—221no—
477C22⋊C4—221no—
478C42—21no—
479C42—21no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42C2×C4×D1111yescharacteristic
484C42#433911yescharacteristic
485C42C2×C22⋊D1111yescharacteristic
486C42C23×D1111yescharacteristic
487C11#1792111yescharacteristic, complemented, Sylow
488C23—221no—
489C23C4×C22⋊D1111yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—112no—
496Q8—221no—
497D4—112no—
498D4—224no—
499D4—221no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—224no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—881no—
516C2×C4C4×C22⋊D1111yescharacteristic
517C2×C4C4×C22⋊D1111yescharacteristic
518C2×C4C4×C22⋊D1111yescharacteristic
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—221no—
529C8—221no—
530C8—221no—
531C8—221no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8—441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—222no—
540C22—441no—
541C22—441no—
542C22C2×C4×C22⋊D1111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—222no—
552C4—441no—
553C4—441no—
554C4D11×#13111yescharacteristic
555C4D11×#13111yescharacteristic
556C4#1062336811yescharacteristic
557C4#1062336911yescharacteristic
558C2—41no—
559C2—442no—
560C2#1307730811yescharacteristic
561C2#1307745911yescharacteristic
562C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2985C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#2985D11
hypocenterC11#17921
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2985

Complements

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

NH ≅ G/Ntype
3. #13067485C2semidirect
4. #13067471C2semidirect
5. #13067464C2semidirect
6. #13067450C2semidirect
7. #13067433C2semidirect
8. #13067426C2semidirect
9. C8×#4326C2semidirect
10. C8×#4325C2semidirect
11. #13067402C2semidirect
13. #13067019C2semidirect
14. #13066916C2semidirect
15. C11×#2985C2semidirect
209. #2985D11semidirect
487. C11#17921semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130777242
#130674852
#130674712
#130674642
#130674502
#130674332
#130674262
C8×#43262
C8×#43252
#130674022
#130670482
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