Finite Group Databasebeta

← #14784662

Subgroups — #14784662

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077557C211yesmaximal, characteristic, complemented
2#13077515C211yesmaximal, characteristic
3#13070199C211yesmaximal, characteristic, complemented
4#13070194C211yesmaximal, characteristic, complemented
5#13070068C211yesmaximal, characteristic, complemented
6#13070066C211yesmaximal, characteristic, complemented
7#13069921C211yesmaximal, characteristic
8#13069902C211yesmaximal, characteristic
9#13069785C211yesmaximal, characteristic, complemented
10#13068461C211yesmaximal, characteristic, complemented
11#13068457C211yesmaximal, characteristic, complemented
12#13068418C211yesmaximal, characteristic, complemented
13#13068415C211yesmaximal, characteristic, complemented
14#13068370C211yesmaximal, characteristic, complemented
15C11×#2031C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17#10623353C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19C2×#66960C2211yescharacteristic
20C11×#421C2211yescharacteristic
21C2×C11×#104C2211yescharacteristic
22C11×#410C2211yescharacteristic
23#10622850C2211yescharacteristic
24#10622846C2211yescharacteristic
25#10622745C2211yescharacteristic
26#10622737C2211yescharacteristic
27#10622735C2211yescharacteristic
28#10622637—22no—
29#10622637—22no—
30#10622619C2211yescharacteristic
31#10622618C2211yescharacteristic
32#10622615C2211yescharacteristic
33#10622612C2211yescharacteristic
34#10622612C2211yescharacteristic
35#10622610C2211yescharacteristic
36#10622610C2211yescharacteristic
37#10622610C2211yescharacteristic
38C2×#66869C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×#66867C2211yescharacteristic
41#10622437—22no—
42#10622436—22no—
43C11×#344C2211yescharacteristic
44C11×#339C2211yescharacteristic
45C11×H(3,ℤ/4)C2211yescharacteristic
46C11⋊#338C2211yescharacteristic
47#10622196C2211yescharacteristic
48#10622196C2211yescharacteristic
49#10622194C2211yescharacteristic
50#10622171C2211yescharacteristic
51#10622171C2211yescharacteristic
52#10622169C2211yescharacteristic
53#10622169C2211yescharacteristic
54#10622161C2211yescharacteristic
55C2×C11×#41C2311yescharacteristic
56C2×#4339C2311yescharacteristic
57C2×C11×M16C2311yescharacteristic
58C2×C11×M16C2311yescharacteristic
59C11×C4⋊Q8—21no—
60C11×#125—21no—
61C11×C22⋊Q8—22no—
62C4×Q8×C11—22no—
63C11×#117C2311yescharacteristic
64C11×#117C2311yescharacteristic
65C11×#117C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67#67004—21no—
68#67003—22no—
69#67002—21no—
70#67001—21no—
71#67001—21no—
72#67001—21no—
73#67001—21no—
74#66995—21no—
75#66985—21no—
76#66979C2311yescharacteristic
77C2×#4318—21no—
78C2×#4318C2311yescharacteristic
79C2×#4318C2311yescharacteristic
80C2×#4318C2311yescharacteristic
81C2×#4318C2311yescharacteristic
82C22×C11⋊C8—21no—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85#66960—21no—
86#66960—21no—
87#66960—21no—
88#66960—21no—
89C2×#4313—21no—
90C2×C8×D11—21no—
91C11×#104—22no—
92C11×#104—21no—
93C11×#104—21no—
94C11×#99—22no—
95#66900—21no—
96#66899—21no—
97#66897—21no—
98#66896—21no—
99#66888—21no—
100#66887—21no—
101#66886—22no—
102#66879—21no—
103C8×Dic11—21no—
104#66874—21no—
105#66873—21no—
106#66870—22no—
107#66869—22no—
108#66869—21no—
109#66869—21no—
110C4⋊(C11⋊C8)—22no—
111C4⋊(C11⋊C8)—22no—
112C4⋊(C11⋊C8)—22no—
113#66867—21no—
114#66867—21no—
115#66867—21no—
116#66867—21no—
117#66867D412yes—
118C4×C11⋊C8—21no—
119C4×C11⋊C8—21no—
120C4×C11⋊C8D412yes—
121#23834—111nomaximal, Sylow
122C11×#41—21no—
123C11×#41—21no—
124C11×#41—21no—
125C11×#41—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11#4111yescharacteristic
128C2×D4×C11—21no—
129C2×D4×C11#4111yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—21no—
134#4339—21no—
135#4339—21no—
136#4339—21no—
137#4339—21no—
138C2×D44#4111yescharacteristic
139C2×C4×D11—21no—
140C2×Dic22#4111yescharacteristic
141C11×M16—21no—
142C11×M16—21no—
143C11×M16—21no—
144C11×M16—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C11×C22⋊C4#4112yes—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11C2×D412yes—
159C42×C11#4111yescharacteristic
160C42×C11#4111yescharacteristic
161C22⋊Dic11—21no—
162#4326—22no—
163#4325—22no—
164#4324—22no—
165#4323—22no—
166C4⋊Dic11—21no—
167C4×Dic11—21no—
168#4318—21no—
169#4318—21no—
170#4318—21no—
171#4318—21no—
172#4318—21no—
173#4318—21no—
174#4318—21no—
175#4318—21no—
176#4318—41no—
177#4318—41no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—41no—
185C2×C11⋊C8—41no—
186C2×C11⋊C8C2×D412yes—
187C2×C11⋊C8C2×D411yescharacteristic
188C2×C11⋊C8C2×D411yescharacteristic
189C2×C11⋊C8#4111yescharacteristic
190C2×C11⋊C8#4111yescharacteristic
191C2×C11⋊C8#4111yescharacteristic
192C2×C11⋊C8#4111yescharacteristic
193#4313—41no—
194#4313—41no—
195C8×D11—41no—
196C8×D11—41no—
197#2961—111no—
198#2955—111no—
199#2103—111no—
200#2102—111no—
201#2080—111no—
202#2080—111no—
203#2053—111no—
204#2050—111no—
205#2031—111no—
206#2031D1111yescharacteristic, complemented
207#1765—111no—
208#1765—111no—
209#1757—111no—
210#1757—111no—
211#1747—111no—
212C23×C11—21no—
213C23×C11C2×#4111yescharacteristic
214C22×D11—21no—
215Q8×C11—21no—
216Q8×C11—21no—
217Q8×C11—82no—
218D4×C11—21no—
219D4×C11—21no—
220D4×C11—41no—
221D4×C11—41no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—81no—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C22⋊D11—41no—
238C22⋊D11—41no—
239C2×Dic11—21no—
240C2×Dic11—41no—
241D44—21no—
242D44—21no—
243C4×D11—41no—
244C4×D11—41no—
245Dic22—21no—
246Dic22—21no—
247C8×C11—41no—
248C8×C11—41no—
249C11⋊C8—22no—
250C11⋊C8—41no—
251C11⋊C8—41no—
252C11⋊C8—41no—
253C11⋊C8—41no—
254C11⋊C8#12411yescharacteristic
255C11⋊C8#12411yescharacteristic
256C11⋊C8#12411yescharacteristic
257C11⋊C8#12411yescharacteristic
258#575—111no—
259C2×#131—111no—
260C2×#131—111no—
261#533C2×D1111yescharacteristic
262#446—222no—
263#446—222no—
264#444—222no—
265#443—222no—
266#430—111no—
267#424—111no—
268#424—111no—
269#423—111no—
270#421—111no—
271#421C2×D1111yescharacteristic
272C2×#104—111no—
273C2×#104C2×D1111yescharacteristic
274#416—111no—
275#416—111no—
276#413—111no—
277#413—111no—
278#410—111no—
279#410C2×D1111yescharacteristic
280#405—111no—
281#405—111no—
282#405—111no—
283#405—111no—
284C2×#97—111no—
285#344—111no—
286#344—111no—
287#344—111no—
288#344C2×D1111yescharacteristic
289#341—111no—
290#341—111no—
291#339—111no—
292#339C2×D1111yescharacteristic
293#338—111no—
294H(3,ℤ/4)—111no—
295H(3,ℤ/4)—111no—
296H(3,ℤ/4)C2×D1111yescharacteristic
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—81no—
300C22×C11#52511yescharacteristic
301C22×C11#52911yescharacteristic
302C22×C11#52911yescharacteristic
303C2×D11—41no—
304C2×D11—81no—
305C4×C11—41no—
306C4×C11—41no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—41no—
310C4×C11—81no—
311C4×C11#52511yescharacteristic
312C4×C11C2×#12411yescharacteristic
313C4×C11#52911yescharacteristic
314C4×C11#52911yescharacteristic
315Dic11—41no—
316Dic11—81no—
317C2×#41—111no—
318C2×#41C22×D1111yescharacteristic
319#137—221no—
320#137—221no—
321AGL(1,ℤ/8)—221no—
322AGL(1,ℤ/8)—221no—
323#135—222no—
324#131—221no—
325#131—221no—
326#131—221no—
327#131—221no—
328#131—221no—
329#131—221no—
330#131—221no—
331#131—221no—
332C2×M16—111no—
333C2×M16—111no—
334C2×M16—111no—
335C2×M16—111no—
336C2×M16—221no—
337C2×M16—221no—
338C2×M16C22×D1111yescharacteristic
339C2×M16C22×D1111yescharacteristic
340C22×C8—111no—
341C22×C8—111no—
342C22×C8—221no—
343C22×C8—221no—
344C4⋊Q8—21no—
345#125—21no—
346C22⋊Q8—22no—
347C4×Q8—22no—
348#117—111no—
349#117C22×D1111yescharacteristic
350#117C22×D1111yescharacteristic
351#117C22×D1111yescharacteristic
352C2×C42C22×D1111yescharacteristic
353#108—222no—
354C4⋊C8—222no—
355C4⋊C8—222no—
356C4⋊C8—222no—
357#104—22no—
358#104—21no—
359#104—21no—
360#104—222no—
361#104—221no—
362#104—221no—
363#103—221no—
364#103—221no—
365#102—221no—
366#102—221no—
367#101—221no—
368#101—221no—
369#100—221no—
370#100—221no—
371#99—22no—
372#99—222no—
373#97—112no—
374#97—221no—
375#97—221no—
376#97—221no—
377#97—221no—
378#97—221no—
379C4×C8—112no—
380C4×C8—221no—
381C4×C8—221no—
382C4×C8—221no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—21no—
386C2×C11—81no—
387C2×C11#239811yescharacteristic
388D11—81no—
389#41—21no—
390#41—21no—
391#41—21no—
392#41—21no—
393#41—221no—
394#41—221no—
395#41—221no—
396#41—221no—
397C2×Q8—22no—
398C2×Q8—111no—
399C2×Q8#434311yescharacteristic
400C2×D4—21no—
401C2×D4—111no—
402C2×D4—221no—
403C2×D4#434311yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—221no—
407C22×C4C23×D1111yescharacteristic
408Q16—222no—
409SD16—222no—
410SD16—222no—
411D8—222no—
412M16—21no—
413M16—21no—
414M16—21no—
415M16—21no—
416M16—221no—
417M16—221no—
418M16—221no—
419M16—221no—
420M16—221no—
421M16—221no—
422M16—221no—
423M16—221no—
424M16—441no—
425M16—441no—
426M16—441no—
427M16—441no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—111no—
431C2×C8—111no—
432C2×C8—111no—
433C2×C8—111no—
434C2×C8—111no—
435C2×C8—111no—
436C2×C8—112no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—441no—
444C2×C8—441no—
445C2×C8—441no—
446C2×C8—441no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—221no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—221no—
456C22⋊C4#434112yes—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—221no—
461C42D4×D1112yes—
462C42#434111yescharacteristic
463C42#434111yescharacteristic
464C11#2383411yescharacteristic, complemented, Sylow
465C23—21no—
466C23—221no—
467C23C2×#434111yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—82no—
471Q8—221no—
472Q8—221no—
473D4—21no—
474D4—21no—
475D4—41no—
476D4—41no—
477D4—221no—
478D4—221no—
479D4—441no—
480D4—441no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—81no—
490C2×C4—221no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4C2×D4×D1111yescharacteristic
495C2×C4C2×#434111yescharacteristic
496C2×C4C2×#434311yescharacteristic
497C2×C4#41×D1111yescharacteristic
498C2×C4#41×D1111yescharacteristic
499C2×C4#41×D1111yescharacteristic
500C8—41no—
501C8—41no—
502C8—111no—
503C8—111no—
504C8—111no—
505C8—111no—
506C8—222no—
507C8—441no—
508C8—441no—
509C8—441no—
510C8—441no—
511C22—41no—
512C22—41no—
513C22—81no—
514C22—441no—
515C22—881no—
516C22#1062311711yescharacteristic
517C22#1062315511yescharacteristic
518C22#1062321111yescharacteristic
519C4—41no—
520C4—41no—
521C4—42no—
522C4—42no—
523C4—41no—
524C4—81no—
525C4—441no—
526C4—881no—
527C4#1062315511yescharacteristic
528C4#1062315811yescharacteristic
529C4D11×#12411yescharacteristic
530C4#1062321111yescharacteristic
531C2—21no—
532C2—21no—
533C2—21no—
534C2—81no—
535C2—881no—
536C2#1307189811yescharacteristic
subgroupG/H
centerC4D11×#124
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2031C2
socleC2×C11#2398
prime radical#10623353C22
hypercenter#2031D11
hypocenterC11#23834
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #2031

Complements

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

NH ≅ G/Ntype
1. #13077557C2semidirect
3. #13070199C2semidirect
4. #13070194C2semidirect
5. #13070068C2semidirect
6. #13070066C2semidirect
9. #13069785C2semidirect
10. #13068461C2semidirect
11. #13068457C2semidirect
12. #13068418C2semidirect
13. #13068415C2semidirect
14. #13068370C2semidirect
15. C11×#2031C2semidirect
206. #2031D11semidirect
464. C11#23834semidirect

Maximal subgroups

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

subgroupindex
#130775572
#130775152
#130701992
#130701942
#130700682
#130700662
#130699212
#130699022
#130697852
#130684612
#130684572
#130684182
#130684152
#130683702
C11×#20312
#2383411