Finite Group Databasebeta

← #14759331

Subgroups — #14759331

Order 2816.

1456 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622741C212yesmaximal, complemented
2C2×#10622724C211yesmaximal, characteristic, complemented
3#13071829C211yesmaximal, characteristic
4#13068913C211yesmaximal, characteristic, complemented
5#13068908C212yesmaximal, complemented
6#13068799C211yesmaximal, characteristic, complemented
7#13068794C212yesmaximal, complemented
8#13068528C211yesmaximal, characteristic, complemented
9#13068397C212yesmaximal, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C22×C11×#131C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×C11×#131—28no—
14C2×C11×#131—24no—
15C22×C11×M16C2211yescharacteristic
16C22×C11×M16C2212yes—
17C23×C8×C11C2212yes—
18C23×C8×C11C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×C4×C22⋊D11C2212yes—
21C22×#4313C2211yescharacteristic
22#10622844C411yescharacteristic
23#10622842C411yescharacteristic
24#10622836C411yescharacteristic
25#10622836C412yes—
26#10622835C412yes—
27#10622835C411yescharacteristic
28C4×C22⋊Dic11C2211yescharacteristic
29C4×C22⋊Dic11C2212yes—
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622741—28no—
35#10622724—24no—
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2212yes—
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622188C2212yes—
45C2×C11×#41—24no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—24no—
49C22×Q8×C11C2×C411yescharacteristic
50C22×D4×C11C2×C412yes—
51C22×D4×C11C2×C411yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11C2×C412yes—
55C22×C22⋊D11C2×C411yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C11×#131—232no—
58C2×C11×M16—22no—
59C2×C11×M16—24no—
60C2×C11×M16—24no—
61C2×C11×M16—24no—
62C2×C11×M16D418yescomplemented
63C22×C8×C11—24no—
64C22×C8×C11—24no—
65C22×C8×C11—24no—
66C22×C8×C11—24no—
67C22×C8×C11D414yescomplemented
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2312yes—
70C22×C8×C11C2311yescharacteristic
71C2×C22⋊Dic11C2×C411yescharacteristic
72C2×C22⋊Dic11C2×C412yes—
73C2×C22⋊Dic11C2×C412yes—
74C2×C22⋊Dic11C2×C412yes—
75C2×C22⋊Dic11C2×C412yes—
76C4×C22⋊D11—22no—
77C4×C22⋊D11—24no—
78C4×C22⋊D11—22no—
79C4×C22⋊D11—24no—
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C412yes—
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C412yes—
84C2×C4×Dic11C2312yes—
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8C2312yes—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C2×#4313—22no—
90C2×#4313—24no—
91C11⋊#95C2×C411yescharacteristic
92C11⋊#95C2×C412yes—
93C11⋊#95C2×C412yes—
94C11⋊#95C2×C411yescharacteristic
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)—24no—
97C22⋊(C11⋊C8)—22no—
98C22⋊(C11⋊C8)—24no—
99(C2×D11)⋊C8—22no—
100(C2×D11)⋊C8—24no—
101#66879—22no—
102Dic11⋊C8—22no—
103Dic11⋊C8—24no—
104C8×Dic11—24no—
105#21445—111nomaximal, Sylow
106C24×C11C22×C411yescharacteristic
107C24×C11C22×C412yes—
108C23×D11C22×C411yescharacteristic
109C11×#41—28no—
110C11×#41—216no—
111C11×#41—28no—
112C2×Q8×C11—22no—
113C2×Q8×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—24no—
117C2×D4×C11—22no—
118C2×D4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4114yes—
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—24no—
133C2×C22⋊D11—24no—
134C2×C22⋊D11—22no—
135C2×C22⋊D11—42no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C412yes—
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C412yes—
143C2×C4×D11—21no—
144C2×C4×D11—22no—
145C2×C4×D11—21no—
146C2×C4×D11—22no—
147C11×M16—28no—
148C11×M16—216no—
149C2×C8×C11—216no—
150C2×C8×C11—28no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11C2×D412yes—
155C2×C8×C11C2×D414yes—
156C2×C8×C11C2×D414yes—
157C2×C8×C11C2×D412yes—
158C22⋊Dic11—24no—
159C22⋊Dic11—24no—
160C22⋊Dic11—22no—
161C22⋊Dic11—24no—
162C22⋊Dic11—42no—
163(C2×D11)⋊C4—22no—
164(C2×D11)⋊C4—24no—
165Dic11⋊C4—24no—
166Dic11⋊C4—22no—
167C4×Dic11—22no—
168C4×Dic11—21no—
169C4×Dic11—22no—
170C4×Dic11—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178#4313—44no—
179C22×#131D1111yescharacteristic, complemented
180C2×#436—112no—
181C2×#435—111no—
182#2388—111no—
183#1870—111no—
184#1869—112no—
185#1851—111no—
186#1850—112no—
187#1780—111no—
188#1753—112no—
189C8×C22⋊C4—111no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—22no—
200C23×C11C4×D412yes—
201C23×C11C4×D414yes—
202C23×C11C23×C411yescharacteristic
203C22×D11—21no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—21no—
207C22×D11—21no—
208Q8×C11—28no—
209D4×C11—216no—
210D4×C11—28no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11C4×D412yes—
222C2×C4×C11C4×D414yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D412yes—
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4112yes—
227C22⋊D11—48no—
228C22⋊D11—44no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—22no—
234C2×Dic11—21no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—21no—
239C2×Dic11—22no—
240C2×Dic11—21no—
241C2×Dic11#13114yescomplemented
242C4×D11—41no—
243C4×D11—41no—
244C4×D11—42no—
245C8×C11—22no—
246C8×C11—24no—
247C8×C11#12014yes—
248C11⋊C8—41no—
249C11⋊C8—42no—
250C11⋊C8—41no—
251C22×#41C2×D1111yescharacteristic
252C2×#131—28no—
253C2×#131—24no—
254C22×M16—111no—
255C22×M16C2×D1111yescharacteristic
256C22×M16C2×D1112yes—
257C23×C8C2×D1112yes—
258C23×C8C2×D1111yescharacteristic
259C2×C4×D4—112no—
260C2×C4×D4—111no—
261#436—228no—
262#435—224no—
263C2×C4⋊C8—111no—
264C2×C4⋊C8—112no—
265C2×C22⋊C8—112no—
266C2×C22⋊C8—111no—
267C2×C22⋊C8—112no—
268C2×C22⋊C8—111no—
269C2×C22⋊C8—111no—
270C2×C22⋊C8—112no—
271C2×#97—111no—
272C2×C4×C8—112no—
273#395—111no—
274#394—112no—
275#394—111no—
276#393—111no—
277#392—111no—
278#392—112no—
279C4×C22⋊C4—112no—
280C4×C22⋊C4—111no—
281#336—112no—
282#336—112no—
283#336—112no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—22no—
289C22×C11—24no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11C2×C4×D411yescharacteristic
297C22×C11C2×C4×D412yes—
298C22×C11C2×#13112yes—
299C22×C11#56811yescharacteristic
300C22×C11#56811yescharacteristic
301C2×D11—41no—
302C2×D11—41no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—41no—
306C4×C11—24no—
307C4×C11—22no—
308C4×C11C2×#12011yescharacteristic
309C4×C11#52512yes—
310C4×C11#52511yescharacteristic
311Dic11—24no—
312Dic11—41no—
313Dic11—41no—
314Dic11—42no—
315Dic11—41no—
316C2×#41—22no—
317C2×#41—24no—
318C2×#41—24no—
319C2×#41—22no—
320C22×Q8C4×D1111yescharacteristic
321C22×D4—112no—
322C22×D4—111no—
323C22×D4C4×D1112yes—
324C22×D4C4×D1111yescharacteristic
325C23×C4—111no—
326C23×C4C22×D1112yes—
327C23×C4C22×D1111yescharacteristic
328#131—232no—
329C2×M16—22no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—222no—
334C2×M16—224no—
335C2×M16C22⋊D1118yescomplemented
336C22×C8—24no—
337C22×C8—24no—
338C22×C8—24no—
339C22×C8—24no—
340C22×C8—111no—
341C22×C8—112no—
342C22×C8—111no—
343C22×C8C22⋊D1114yescomplemented
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1112yes—
346C22×C8C22×D1111yescharacteristic
347C4×D4—224no—
348C4×D4—222no—
349C4×D4—222no—
350C4×D4—224no—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—111no—
353C2×C22⋊C4—112no—
354C2×C22⋊C4—111no—
355C2×C22⋊C4—112no—
356C2×C22⋊C4—112no—
357C2×C22⋊C4—112no—
358C2×C22⋊C4—111no—
359C2×C22⋊C4—112no—
360C2×C42—112no—
361C2×C42—111no—
362C4⋊C8—222no—
363C4⋊C8—224no—
364C22⋊C8—224no—
365C22⋊C8—222no—
366C22⋊C8—222no—
367C22⋊C8—224no—
368C22⋊C8—222no—
369C22⋊C8—224no—
370#97—222no—
371C4×C8—224no—
372#95—111no—
373#95—112no—
374#95—112no—
375#95—111no—
376C2×C11—42no—
377C2×C11—44no—
378C2×C11C4×#12011yescharacteristic
379C2×C11#293011yescharacteristic
380C2×C11#293111yescharacteristic
381C2×C11#293312yes—
382C2×C11#293512yes—
383D11—81no—
384C24—111no—
385C24C2×C4×D1111yescharacteristic
386C24C2×C4×D1112yes—
387#41—28no—
388#41—216no—
389#41—28no—
390C2×Q8—22no—
391C2×Q8—24no—
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—24no—
397C2×D4—224no—
398C2×D4—224no—
399C2×D4—222no—
400C2×D4—442no—
401C2×D4—441no—
402C2×D4—441no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—112no—
410C22×C4—111no—
411C22×C4—112no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—221no—
417C22×C4—222no—
418C22×C4C2×C4×D1112yes—
419C22×C4C2×C4×D1111yescharacteristic
420C22×C4#433912yes—
421C22×C4#433914yes—
422C22×C4C2×C22⋊D1114yes—
423C22×C4C2×C22⋊D1112yes—
424C22×C4C23×D1111yescharacteristic
425M16—28no—
426M16—216no—
427M16—444no—
428C2×C8—216no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—28no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—222no—
440C2×C8C2×C22⋊D1112yes—
441C2×C8C2×C22⋊D1114yes—
442C2×C8C2×C22⋊D1114yes—
443C2×C8C2×C22⋊D1112yes—
444C4⋊C4—224no—
445C4⋊C4—222no—
446C22⋊C4—224no—
447C22⋊C4—224no—
448C22⋊C4—222no—
449C22⋊C4—224no—
450C22⋊C4—222no—
451C22⋊C4—224no—
452C22⋊C4—442no—
453C42—222no—
454C42—221no—
455C42—222no—
456C42—221no—
457C11#2144511yescharacteristic, complemented, Sylow
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—222no—
469C23—221no—
470C23—221no—
471C23—221no—
472C23—222no—
473C23C4×C22⋊D1112yes—
474C23C4×C22⋊D1114yes—
475C23C22×C4×D1111yescharacteristic
476Q8—28no—
477D4—216no—
478D4—28no—
479D4—448no—
480D4—444no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—114no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—221no—
497C2×C4—222no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—222no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—222no—
504C2×C4—441no—
505C2×C4—442no—
506C2×C4—441no—
507C2×C4C4×C22⋊D1112yes—
508C2×C4C4×C22⋊D1114yes—
509C2×C4C2×#433911yescharacteristic
510C2×C4C2×#433912yes—
511C2×C4C22×C22⋊D1111yescharacteristic
512C2×C4C22×C22⋊D1112yes—
513C8—22no—
514C8—24no—
515C8—442no—
516C8—441no—
517C8—441no—
518C8#6700614yes—
519C22—22no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—24no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—441no—
532C22—441no—
533C22—441no—
534C22—442no—
535C22—442no—
536C22D11×#13112yes—
537C22#1062328111yescharacteristic
538C22#1062328111yescharacteristic
539C22C2×C4×C22⋊D1111yescharacteristic
540C22C2×C4×C22⋊D1112yes—
541C4—24no—
542C4—22no—
543C4—224no—
544C4—441no—
545C4—441no—
546C4—441no—
547C4—442no—
548C4#1062332212yes—
549C4#1062332211yescharacteristic
550C4C2×#6700611yescharacteristic
551C2—42no—
552C2—44no—
553C2—881no—
554C2C4×#6700611yescharacteristic
555C2#1307731711yescharacteristic
556C2#1307732611yescharacteristic
557C2#1307733812yes—
558C2#1307735812yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC22×C11×#131C2
prime radical#13071829C2
cosocleC22×C4×C11C24
hypercenterC22×#131D11
hypocenterC11#21445
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
1. C2×#10622741C2semidirect
2. C2×#10622724C2semidirect
4. #13068913C2semidirect
5. #13068908C2semidirect
6. #13068799C2semidirect
7. #13068794C2semidirect
8. #13068528C2semidirect
9. #13068397C2semidirect
10. C8×C22⋊Dic11C2semidirect
11. C22×C11×#131C2semidirect
62. C2×C11×M16D4semidirect
67. C22×C8×C11D4semidirect
179. C22×#131D11semidirect
241. C2×Dic11#131semidirect
335. C2×M16C22⋊D11semidirect
343. C22×C8C22⋊D11semidirect
457. C11#21445semidirect

Maximal subgroups

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

subgroupindex
C2×#106227412
C2×#106227242
#130718292
#130689132
#130689082
#130687992
#130687942
#130685282
#130683972
C8×C22⋊Dic112
C22×C11×#1312
#2144511