Finite Group Databasebeta

← #14769819

Subgroups — #14769819

Order 2816.

1316 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
1C2×#10623302C211yesmaximal, characteristic
2C2×#10622809C211yesmaximal, characteristic, complemented
3#13077146C212yesmaximal, complemented
4#13069531C211yesmaximal, characteristic, complemented
5#13069475C211yesmaximal, characteristic, complemented
6#13069129C212yesmaximal, complemented
7#13068985C212yesmaximal, complemented
8#13068681C211yesmaximal, characteristic, complemented
9#13068573C212yesmaximal, complemented
10#13068455C211yesmaximal, characteristic, complemented
11C11×#2951C211yesmaximal, characteristic, complemented
12C2×#67043C2212yes—
13C2×C11×#135C2211yescharacteristic
14C11×#520C2212yes—
15C2×#67004C2212yes—
16C2×#67001C2212yes—
17#10623302—24no—
18#10623302C418yescomplemented
19C2×Q16×D11—21no—
20C2×#66968—22no—
21C2×#66965—21no—
22C22×Dic44C2211yescharacteristic
23C2×#66954C2211yescharacteristic
24C11×#440—22no—
25C4×C11×Q16—21no—
26C4×C11×D8—21no—
27C2×C11×#107C2211yescharacteristic
28C11×#417C2212yes—
29C11×#405C2211yescharacteristic
30C2×#66901C2212yes—
31#10622809—24no—
32C2×#66889C2211yescharacteristic
33C2×#66888C2212yes—
34C2×#66883C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622617—22no—
37#10622617C2212yes—
38#10622615—22no—
39#10622615C2211yescharacteristic
40#10622587C2212yes—
41C2×#66874—22no—
42C2×#66874C2212yes—
43#10622579—22no—
44#10622579C2212yes—
45#10622196C2211yescharacteristic
46#10622170C2211yescharacteristic
47#10622168C2212yes—
48C2×C11×#41C2312yes—
49#67043—24no—
50#67043—24no—
51#67043—42no—
52#67043C2×C418yescomplemented
53C2×Q8×D11—22no—
54C2×#4341—22no—
55C2×#4341—42no—
56C2×#4339—22no—
57C2×#4339C2311yescharacteristic
58C22×Dic22—22no—
59C22×Dic22C2312yes—
60C11×#135C2×C414yes—
61C11×#135D414yes—
62C2×C11×Q16D411yescharacteristic
63C2×C11×SD16D412yes—
64C2×C11×D8D411yescharacteristic
65C2×C11×M16C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—42no—
70C11×#117—22no—
71C11×#117C2311yescharacteristic
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4C2312yes—
74#67004—24no—
75#67004C2×C418yescomplemented
76#67001—24no—
77#67001—42no—
78C2×#4326—22no—
79C2×#4324—22no—
80C2×C4×Dic11C2311yescharacteristic
81C2×#4318—22no—
82C2×#4318C2312yes—
83C2×#4318C2311yescharacteristic
84C22×C11⋊C8—22no—
85C22×C11⋊C8C2311yescharacteristic
86Q16×D11—28no—
87#66968—216no—
88#66965—28no—
89C2×Dic44—21no—
90C2×Dic44—21no—
91C2×Dic44—22no—
92C2×Dic44C2×C414yescomplemented
93#66954—22no—
94#66954C2×C414yescomplemented
95C2×#4313—21no—
96C2×C8×D11—21no—
97C11×#107—21no—
98C11×#107—21no—
99C11×#103—22no—
100C11×#102—22no—
101C11×#97—21no—
102C4×C8×C11—21no—
103#66901—24no—
104C11⋊#95—42no—
105#66889—22no—
106#66888—42no—
107#66883—22no—
108C8×Dic11—22no—
109#66874—22no—
110#66874—22no—
111#66874—22no—
112#66874—22no—
113#66874—22no—
114#66874D411yescharacteristic
115#66874D411yescharacteristic
116#66873—22no—
117#66873D411yescharacteristic
118#66873D411yescharacteristic
119#22468—111nomaximal, Sylow
120C11×#41—22no—
121C11×#41—22no—
122C11×#41C22×C414yes—
123C11×#41C2×D414yes—
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—22no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—21no—
132C2×C22⋊D11—42no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—42no—
136Q8×D11—28no—
137Q8×D11—44no—
138#4341—28no—
139#4341—44no—
140#4341—48no—
141#4341—48no—
142#4339—28no—
143#4339—21no—
144#4339—21no—
145#4339—44no—
146#4339C22×C412yes—
147#4339#4112yes—
148C2×D44C2×D411yescharacteristic
149C2×C4×D11—21no—
150C2×C4×D11—42no—
151C2×Dic22—28no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—44no—
158C2×Dic22—42no—
159C2×Dic22C22×C414yes—
160C2×Dic22C2×D411yescharacteristic
161C11×Q16C22⋊C414yes—
162C11×SD16C22⋊C418yes—
163C11×D8C22⋊C414yes—
164C11×M16—21no—
165C11×M16—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C412yes—
168C2×C8×C11C2×D412yes—
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—42no—
178C42×C11—21no—
179C42×C11—42no—
180#4326—28no—
181#4324—28no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184#4318—21no—
185#4318—22no—
186#4318—22no—
187#4318—44no—
188#4318C22×C412yes—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—44no—
194C2×C11⋊C8C2×D411yescharacteristic
195C2×C11⋊C8C2×D411yescharacteristic
196Dic44—24no—
197Dic44—24no—
198#4313—24no—
199C8×D11—24no—
200C2×#578—111no—
201C2×#443—111no—
202#2951D1111yescharacteristic, complemented
203#2898—112no—
204#1979—111no—
205#1969—111no—
206#1908—112no—
207#1882—112no—
208#1816—111no—
209#1793—112no—
210#1764—111no—
211C23×C11—22no—
212C23×C11H(5,𝔽2)11yescharacteristic
213C22×D11—21no—
214Q8×C11—22no—
215Q8×C11C2×C22⋊C414yes—
216D4×C11—24no—
217D4×C11—24no—
218D4×C11—22no—
219D4×C11C2×C22⋊C414yes—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—42no—
226C2×C4×C11—82no—
227C2×C4×C11—162no—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C22⋊D11—22no—
235C22⋊D11—22no—
236C22⋊D11—48no—
237C2×Dic11—21no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—48no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245D44—21no—
246D44C4×D412yes—
247C4×D11—22no—
248C4×D11—22no—
249C4×D11—48no—
250Dic22—21no—
251Dic22—24no—
252Dic22—24no—
253Dic22—48no—
254Dic22—42no—
255Dic22—42no—
256Dic22C4×D412yes—
257C8×C11—41no—
258C8×C11C2×C22⋊C412yes—
259C8×C11C2×C22⋊C412yes—
260C11⋊C8—22no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—42no—
264C2×2−1+4—112no—
265#578—118no—
266#578—224no—
267C2×#137—112no—
268C2×#137—222no—
269C2×#135—221no—
270C2×#135C2×D1111yescharacteristic
271C22×Q16—111no—
272C22×Q16—221no—
273C2×#131—112no—
274C2×#131—111no—
275#520C2×D1112yes—
276#443—224no—
277#440—22no—
278C4×Q16—21no—
279C4×D8—21no—
280C2×#108—111no—
281C2×#107C2×D1111yescharacteristic
282C2×#104—112no—
283C2×#104—111no—
284#419—112no—
285#419—222no—
286#417—112no—
287#417—222no—
288#417C2×D1112yes—
289#416—111no—
290#416—222no—
291C2×#103—112no—
292C2×#103—222no—
293C2×#101—112no—
294#405C2×D1111yescharacteristic
295C2×C4×C8—111no—
296#391—112no—
297#343—112no—
298#341—111no—
299#339—111no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—24no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11#51811yescharacteristic
306C22×C11D4211yescharacteristic
307C22×C11#54611yescharacteristic
308C2×D11—22no—
309C2×D11—41no—
310C2×D11—41no—
311C4×C11—24no—
312C4×C11—41no—
313C4×C11—41no—
314C4×C11—82no—
315C4×C11C22×C22⋊C411yescharacteristic
316C4×C11C2×C4×D411yescharacteristic
317C4×C11D4211yescharacteristic
318C4×C11#54611yescharacteristic
319Dic11—22no—
320Dic11—42no—
321Dic11—44no—
3222−1+4—118no—
3232−1+4—224no—
3242−1+4—224no—
3252−1+4—442no—
326C2×#41—111no—
327C2×#41—222no—
328C2×#41—222no—
329C2×#41—442no—
330C2×#41C22×D1112yes—
331C22×Q8—112no—
332C22×Q8—222no—
333C22×Q8—222no—
334#137—118no—
335#137—224no—
336#137—2216no—
337#135—228no—
338#135C4×D1114yes—
339#135D4414yes—
340C2×Q16—114no—
341C2×Q16—222no—
342C2×Q16—228no—
343C2×Q16—222no—
344C2×Q16—221no—
345C2×Q16—221no—
346C2×Q16C22⋊D1111yescharacteristic
347C2×SD16—222no—
348C2×SD16C22⋊D1112yes—
349C2×D8C22⋊D1111yescharacteristic
350#131—114no—
351#131—222no—
352#131—224no—
353#131—442no—
354C2×M16—111no—
355C2×M16—112no—
356C2×M16—222no—
357C2×M16—221no—
358C2×M16C22×D1111yescharacteristic
359C22×C8—111no—
360C22×C8—222no—
361C22×C8—221no—
362C22×C8C22×D1111yescharacteristic
363C4×Q8—22no—
364C4×D4—22no—
365C4×D4—42no—
366#117—22no—
367#117C22×D1111yescharacteristic
368C2×C4⋊C4—22no—
369C2×C4⋊C4C22×D1112yes—
370C2×C42—111no—
371#108—222no—
372#107—21no—
373#107—21no—
374#104—222no—
375#104—224no—
376#103—22no—
377#103—111no—
378#103—111no—
379#103—222no—
380#103—222no—
381#103—222no—
382#103—222no—
383#103—222no—
384#102—22no—
385#102—111no—
386#102—111no—
387#102—222no—
388#101—442no—
389#97—21no—
390C4×C8—21no—
391C4×C8—222no—
392#95—442no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—44no—
396C2×C11D4×C22⋊C411yescharacteristic
397C2×C11#329011yescharacteristic
398C2×C11#329311yescharacteristic
399D11—42no—
400#41—22no—
401#41—22no—
402#41—112no—
403#41—112no—
404#41—228no—
405#41—221no—
406#41—221no—
407#41—228no—
408#41—444no—
409#41—448no—
410#41—444no—
411#41—448no—
412#41C2×C4×D1114yes—
413#41C2×D4414yes—
414C2×Q8—114no—
415C2×Q8—111no—
416C2×Q8—228no—
417C2×Q8—222no—
418C2×Q8—228no—
419C2×Q8—222no—
420C2×Q8—222no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×Q8—442no—
424C2×Q8—444no—
425C2×Q8—444no—
426C2×Q8C2×C22⋊D1112yes—
427C2×D4—22no—
428C2×D4—111no—
429C2×D4—221no—
430C2×D4—442no—
431C2×D4C2×C22⋊D1112yes—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—42no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—222no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4C23×D1111yescharacteristic
441Q16—228no—
442Q16—224no—
443Q16—224no—
444Q16(C2×D11)⋊C414yes—
445SD16—228no—
446SD16(C2×D11)⋊C418yes—
447D8(C2×D11)⋊C414yes—
448M16—21no—
449M16—21no—
450M16—112no—
451M16—221no—
452M16—224no—
453M16—222no—
454M16—222no—
455M16—444no—
456C2×C8—21no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—224no—
463C2×C8—222no—
464C2×C8—444no—
465C2×C8C2×C4×D1112yes—
466C2×C8C2×D4412yes—
467C2×C8C2×C22⋊D1111yescharacteristic
468C2×C8C2×C22⋊D1111yescharacteristic
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—42no—
472C4⋊C4D4×D1111yescharacteristic
473C4⋊C4D4×D1111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—42no—
476C42—21no—
477C42—42no—
478C42—221no—
479C42—221no—
480C11#2246811yescharacteristic, complemented, Sylow
481C23—22no—
482C23—221no—
483C23#6703711yescharacteristic
484Q8—22no—
485Q8—112no—
486Q8—221no—
487Q8—224no—
488Q8—224no—
489Q8—448no—
490Q8—442no—
491Q8—442no—
492Q8C2×(C2×D11)⋊C414yes—
493D4—24no—
494D4—24no—
495D4—22no—
496D4—112no—
497D4—222no—
498D4—222no—
499D4—221no—
500D4—448no—
501D4C2×(C2×D11)⋊C414yes—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—42no—
508C2×C4—82no—
509C2×C4—162no—
510C2×C4—221no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—448no—
516C2×C4—448no—
517C2×C4—441no—
518C2×C4—442no—
519C2×C4—441no—
520C2×C4—442no—
521C2×C4C22×C4×D1111yescharacteristic
522C2×C4C22×D4411yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4#41×D1111yescharacteristic
525C2×C4#6704211yescharacteristic
526C2×C4C22×C22⋊D1111yescharacteristic
527C8—41no—
528C8—222no—
529C8—221no—
530C8—221no—
531C8—442no—
532C8C2×(C2×D11)⋊C412yes—
533C8C2×(C2×D11)⋊C412yes—
534C22—21no—
535C22—21no—
536C22—24no—
537C22—42no—
538C22—42no—
539C22—222no—
540C22—441no—
541C22—441no—
542C22#1062307611yescharacteristic
543C22#1062308511yescharacteristic
544C22D4×C22⋊D1111yescharacteristic
545C4—24no—
546C4—41no—
547C4—41no—
548C4—82no—
549C4—222no—
550C4—442no—
551C4—444no—
552C4C4×D4×D1111yescharacteristic
553C4D4×D4411yescharacteristic
554C4C22×(C2×D11)⋊C411yescharacteristic
555C4#1062336011yescharacteristic
556C2—21no—
557C2—21no—
558C2—44no—
559C2—442no—
560C2D4×(C2×D11)⋊C411yescharacteristic
561C2#1308039811yescharacteristic
562C2#1308041811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2951C2
socleC22×C11D42
prime radicalC2×#10623302C2
cosocleC22×C4×C11C24
hypercenter#2951D11
hypocenterC11#22468
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2951

Complements

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

NH ≅ G/Ntype
2. C2×#10622809C2semidirect
3. #13077146C2semidirect
4. #13069531C2semidirect
5. #13069475C2semidirect
6. #13069129C2semidirect
7. #13068985C2semidirect
8. #13068681C2semidirect
9. #13068573C2semidirect
10. #13068455C2semidirect
11. C11×#2951C2semidirect
18. #10623302C4semidirect
52. #67043C2×C4semidirect
75. #67004C2×C4semidirect
92. C2×Dic44C2×C4semidirect
94. #66954C2×C4semidirect
202. #2951D11semidirect
480. C11#22468semidirect

Maximal subgroups

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

subgroupindex
C2×#106233022
C2×#106228092
#130771462
#130695312
#130694752
#130691292
#130689852
#130686812
#130685732
#130684552
C11×#29512
#2246811