Finite Group Databasebeta

← #14795237

Subgroups — #14795237

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078425C211yesmaximal, characteristic, complemented
2C4×#66985C211yesmaximal, characteristic
3#13077281C211yesmaximal, characteristic, complemented
4#13070062C212yesmaximal, complemented
5#13069909C212yesmaximal
6#13069606C211yesmaximal, characteristic, complemented
7#13069394C212yesmaximal, complemented
8#13069392C211yesmaximal, characteristic, complemented
9#13069275C212yesmaximal, complemented
10#13068608C211yesmaximal, characteristic, complemented
11C2×C11×#476C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66985C2211yescharacteristic
15C4×#4339C2211yescharacteristic
16C11×#476—21no—
17C11×#476—21no—
18C11×#476—22no—
19C2×C11×#106C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#102C2212yes—
22C2×#66897C2212yes—
23#10622828C2211yescharacteristic
24#10622723C2212yes—
25C2×#66883C2212yes—
26#10622714C2212yes—
27#10622707—21no—
28#10622704—21no—
29#10622700—21no—
30#10622697—21no—
31#10622631—21no—
32C4×#4324—21no—
33#10622627—21no—
34C4×#4323—21no—
35#10622579C2212yes—
36#10622579C2211yescharacteristic
37#10622577C2211yescharacteristic
38#10622577C2212yes—
39#10622537C2211yescharacteristic
40#10622537C2211yescharacteristic
41C4×#4318C2211yescharacteristic
42#10622453—22no—
43#10622448—21no—
44#10622446—21no—
45#10622190C2212yes—
46#10622168C2212yes—
47#10622168C2212yes—
48#10622168C2212yes—
49C22×Q8×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C2×#4339C2311yescharacteristic
53C22×C8×C11C2312yes—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C4×D4×C11—21no—
59C4×D4×C11—21no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67C2×#4324—21no—
68#66985—22no—
69#66985—22no—
70C2×#4323—21no—
71C4×C22⋊D11—21no—
72C4×C22⋊D11—21no—
73#66979C2311yescharacteristic
74C2×#4318C2312yes—
75C2×#4318C2312yes—
76C2×#4318C2311yescharacteristic
77C2×#4318C2311yescharacteristic
78C4×D44D411yescharacteristic
79C4×D44D411yescharacteristic
80#66925—21no—
81C42×D11—21no—
82C4×Dic22D411yescharacteristic
83C4×Dic22D411yescharacteristic
84C11×#106—22no—
85C11×#106—22no—
86C11×C4⋊C8D411yescharacteristic
87C11×C4⋊C8D411yescharacteristic
88C11×C4⋊C8D412yes—
89C11×#102—22no—
90C11×#102—22no—
91#66897—24no—
92#66896—21no—
93#66896—21no—
94(C2×D11)⋊C8—22no—
95(C2×D11)⋊C8—22no—
96#66883—24no—
97#66879—22no—
98C8×Dic11—22no—
99#66874—21no—
100#66874—22no—
101#66873—21no—
102#66873—22no—
103#66872—21no—
104#66872—22no—
105#66871—21no—
106#66871—22no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)—21no—
109C4⋊(C11⋊C8)—21no—
110C4⋊(C11⋊C8)—21no—
111#66867—21no—
112C4×C11⋊C8—21no—
113#24721—111nomaximal, Sylow
114C24×C11—21no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—82no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11#4112yes—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—41no—
127C22×C4×C11—41no—
128C22×C4×C11—82no—
129C22×C4×C11#4111yescharacteristic
130C22×C4×C11#4111yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—21no—
133#4339—21no—
134#4339—21no—
135#4339—21no—
136#4339—21no—
137C2×D44C2×D411yescharacteristic
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×Dic22C2×D411yescharacteristic
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11C2×D412yes—
145C2×C8×C11C2×D412yes—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C22⋊Dic11—21no—
159#4324—24no—
160#4323—24no—
161(C2×D11)⋊C4—21no—
162(C2×D11)⋊C4—21no—
163C4⋊Dic11C2×D411yescharacteristic
164C4⋊Dic11C2×D411yescharacteristic
165Dic11⋊C4—21no—
166Dic11⋊C4—21no—
167C4×Dic11—21no—
168C4×Dic11—21no—
169C4×Dic11—21no—
170#4318—21no—
171#4318—22no—
172#4318—22no—
173#4318—22no—
174#4318—21no—
175#4318—22no—
176#4318—21no—
177#4318#4112yes—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182#3079—111no—
183C2×#476D1111yescharacteristic, complemented
184C4×AGL(1,ℤ/8)—111no—
185#2925—111no—
186#2079—112no—
187#2051—112no—
188#1997—111no—
189#1951—112no—
190#1950—111no—
191#1931—112no—
192#1800—111no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—81no—
197C23×C11—81no—
198C23×C11C2×#4111yescharacteristic
199C22×D11—21no—
200Q8×C11—82no—
201Q8×C11—82no—
202D4×C11—22no—
203D4×C11—22no—
204D4×C11—41no—
205D4×C11—41no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—82no—
211C2×C4×C11—82no—
212C2×C4×C11—81no—
213C2×C4×C11—82no—
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11#12111yescharacteristic
217C2×C4×C11#12111yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C112−1+411yescharacteristic
223C2×C4×C112−1+411yescharacteristic
224C22⋊D11—41no—
225C22⋊D11—41no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229D44—21no—
230D44—21no—
231C4×D11—41no—
232C4×D11—41no—
233C4×D11—42no—
234C4×D11—81no—
235Dic22—21no—
236Dic22—21no—
237C8×C11—22no—
238C8×C11—22no—
239C11⋊C8—22no—
240C11⋊C8—42no—
241C11⋊C8—41no—
242C11⋊C8—42no—
243C2×AGL(1,ℤ/8)—111no—
244C2×C4⋊Q8C2×D1111yescharacteristic
245C4×#41—111no—
246C2×C4×D4C2×D1111yescharacteristic
247#477—221no—
248#476—21no—
249#476—21no—
250#476—22no—
251#476—221no—
252#475—221no—
253#474—221no—
254#442—221no—
255#440—221no—
256C4×SD16—221no—
257C4×D8—221no—
258#433—222no—
259#432—221no—
260#431—221no—
261C2×#108—112no—
262#428—112no—
263#428—111no—
264C2×#106C2×D1112yes—
265#423—111no—
266#423—111no—
267C2×C4⋊C8C2×D1111yescharacteristic
268#418—111no—
269#417—112no—
270#417—111no—
271C2×#102C2×D1112yes—
272C2×#100—112no—
273#408—112no—
274#405—112no—
275C4×M16—111no—
276#343—112no—
277#343—112no—
278#343—112no—
279#341—112no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—42no—
283C22×C11—82no—
284C22×C11—82no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11C2×#12111yescharacteristic
288C22×C11#55211yescharacteristic
289C22×C11#55611yescharacteristic
290C2×D11—41no—
291C2×D11—41no—
292C2×D11—41no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—81no—
297C4×C11—82no—
298C4×C11#47112yes—
299C4×C11#52511yescharacteristic
300C4×C11#53611yescharacteristic
301C4×C11#54711yescharacteristic
302C4×C11#54811yescharacteristic
303Dic11—41no—
304Dic11—41no—
305Dic11—41no—
306C2×#41—111no—
307C22×Q8—21no—
308C22×D4C22×D1111yescharacteristic
309C23×C4—21no—
310AGL(1,ℤ/8)—222no—
311AGL(1,ℤ/8)—222no—
312C2×SD16—221no—
313C2×D8—221no—
314C2×M16—111no—
315C2×M16—111no—
316C2×M16—112no—
317C2×M16—112no—
318C22×C8C22×D1112yes—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4×Q8—111no—
324C4×Q8—111no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—111no—
330C4×D4—111no—
331C4×D4—221no—
332C4×D4—221no—
333#117—111no—
334#117—221no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C4⋊C4C22×D1112yes—
338C2×C22⋊C4—21no—
339C2×C42—221no—
340C2×C42C22×D1111yescharacteristic
341#108—224no—
342#107—221no—
343#107—222no—
344#106—22no—
345#106—22no—
346#106—221no—
347#106—222no—
348C4⋊C8—221no—
349C4⋊C8—221no—
350C4⋊C8—221no—
351C4⋊C8—221no—
352C4⋊C8C22⋊D1111yescharacteristic
353C4⋊C8C22⋊D1111yescharacteristic
354C4⋊C8C22⋊D1112yes—
355#103—221no—
356#103—222no—
357#102—22no—
358#102—22no—
359#102—221no—
360#102—222no—
361#102—221no—
362#102—221no—
363#100—224no—
364C22⋊C8—222no—
365C22⋊C8—222no—
366#97—222no—
367#97—221no—
368C4×C8—222no—
369C4×C8—221no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—82no—
373C2×C11#241511yescharacteristic
374C2×C11C2×#47111yescharacteristic
375C2×C11#306811yescharacteristic
376D11—81no—
377C24—21no—
378#41—221no—
379#41—221no—
380#41—221no—
381#41—221no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—82no—
385C2×Q8—111no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—111no—
392C2×D4—221no—
393C2×D4#434312yes—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—82no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—221no—
402C22×C4#434111yescharacteristic
403C22×C4#434111yescharacteristic
404C22×C4C23×D1111yescharacteristic
405SD16—224no—
406D8—224no—
407M16—112no—
408M16—221no—
409M16—222no—
410M16—222no—
411M16—222no—
412M16—221no—
413M16—222no—
414M16—221no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8C2×C22⋊D1112yes—
422C2×C8C2×C22⋊D1112yes—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—111no—
430C4⋊C4—111no—
431C4⋊C4—221no—
432C4⋊C4—221no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—221no—
436C22⋊C4—221no—
437C22⋊C4—221no—
438C42—221no—
439C42—221no—
440C42—221no—
441C42D4×D1111yescharacteristic
442C42D4×D1111yescharacteristic
443C42C2×C22⋊D1111yescharacteristic
444C42C2×C22⋊D1111yescharacteristic
445C11#2472111yescharacteristic, complemented, Sylow
446C23—22no—
447C23—41no—
448C23—41no—
449C23—81no—
450C23—81no—
451C23—221no—
452C23C2×#434111yescharacteristic
453Q8—82no—
454Q8—82no—
455Q8—221no—
456Q8—221no—
457D4—22no—
458D4—22no—
459D4—41no—
460D4—41no—
461D4—221no—
462D4—221no—
463D4—441no—
464D4—441no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—81no—
472C2×C4—82no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—442no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—881no—
480C2×C4#6699111yescharacteristic
481C2×C4#6699111yescharacteristic
482C2×C4#6699111yescharacteristic
483C2×C4#6699111yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×#434311yescharacteristic
486C2×C4#6704011yescharacteristic
487C2×C4#41×D1111yescharacteristic
488C2×C4#6704311yescharacteristic
489C2×C4C22×C22⋊D1111yescharacteristic
490C8—22no—
491C8—22no—
492C8—222no—
493C8—442no—
494C8—442no—
495C8—441no—
496C22—21no—
497C22—21no—
498C22—42no—
499C22—82no—
500C22—82no—
501C22—81no—
502C22—81no—
503C22—441no—
504C22—441no—
505C22—441no—
506C22#1062317211yescharacteristic
507C22#1062317311yescharacteristic
508C22C2×#6699111yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—81no—
513C4—82no—
514C4—441no—
515C4—441no—
516C4—441no—
517C4#1062279012yes—
518C4#1062315811yescharacteristic
519C4#1062315911yescharacteristic
520C4#1062334811yescharacteristic
521C4#1062335511yescharacteristic
522C2—21no—
523C2—21no—
524C2—82no—
525C2—881no—
526C2#1307204111yescharacteristic
527C2C2×#1062279011yescharacteristic
528C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC22×C11C2×#121
prime radicalC2×#66985C22
hypercenterC2×#476D11
hypocenterC11#24721
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #13078425C2semidirect
3. #13077281C2semidirect
4. #13070062C2semidirect
6. #13069606C2semidirect
7. #13069394C2semidirect
8. #13069392C2semidirect
9. #13069275C2semidirect
10. #13068608C2semidirect
11. C2×C11×#476C2semidirect
183. C2×#476D11semidirect
445. C11#24721semidirect

Maximal subgroups

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

subgroupindex
#130784252
C4×#669852
#130772812
#130700622
#130699092
#130696062
#130693942
#130693922
#130692752
#130686082
C2×C11×#4762
#2472111