Finite Group Databasebeta

← #14765962

Subgroups — #14765962

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622460C211yesmaximal, characteristic
2#13071357C211yesmaximal, characteristic, complemented
3#13071260C211yesmaximal, characteristic
4#13069571C211yesmaximal, characteristic, complemented
5#13069380C211yesmaximal, characteristic, complemented
6#13069354C211yesmaximal, characteristic, complemented
7#13069344C211yesmaximal, characteristic, complemented
8#13069313C211yesmaximal, characteristic
9#13069299C211yesmaximal, characteristic
10#13069244C211yesmaximal, characteristic
11#13069244C211yesmaximal, characteristic
12#13069202C211yesmaximal, characteristic, complemented
13#13069188C211yesmaximal, characteristic, complemented
14#13068617C211yesmaximal, characteristic
15C11×#1768C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×#66923C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C11×#376C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31#10622552C2211yescharacteristic
32#10622552C2211yescharacteristic
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37#10622541C2211yescharacteristic
38#10622541C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622460C418yescomplemented
42#10622282—21no—
43#10622282—21no—
44#10622280—21no—
45#10622277—21no—
46#10622268—21no—
47#10622268—21no—
48#10622260—21no—
49#10622260—21no—
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C4×D44—22no—
93C4×D44C2×C414yes—
94#66923—22no—
95#66923C2×C414yes—
96C11×C4⋊C8—22no—
97C11×C4⋊C8C2×C414yes—
98C11×#97—41no—
99C4×C8×C11—41no—
100C11×#95D411yescharacteristic
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111#66885—41no—
112#66885—41no—
113#66885C2×C414yes—
114#66885C2×C414yes—
115#66882C2×C414yes—
116#66881—41no—
117#66881—41no—
118#66881C2×C414yes—
119#22122—111nomaximal, Sylow
120C23×D11—21no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C22×C412yes—
141C2×C4×D11—24no—
142C2×C4×D11—81no—
143C2×C4×D11—81no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C22×C412yes—
155C2×C8×C11C22×C412yes—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11C22×C412yes—
161C42×C11#4112yes—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—81no—
164(C2×D11)⋊C4—81no—
165(C2×D11)⋊C4—81no—
166(C2×D11)⋊C4—81no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—81no—
179C4⋊Dic11—81no—
180C4⋊Dic11C22×C412yes—
181C4⋊Dic11C22×C412yes—
182C4⋊Dic11C22×C412yes—
183Dic11⋊C4—24no—
184Dic11⋊C4—24no—
185Dic11⋊C4—81no—
186Dic11⋊C4—81no—
187Dic11⋊C4—81no—
188Dic11⋊C4—81no—
189C4×Dic11—81no—
190C4×Dic11—81no—
191C4×Dic11—81no—
192C2×#478—111no—
193#2330—111no—
194#2319—111no—
195#1989—111no—
196#1948—111no—
197#1943—111no—
198#1941—111no—
199#1936—111no—
200#1934—111no—
201#1926—111no—
202#1926—111no—
203#1920—111no—
204#1918—111no—
205#1802—111no—
206#1768D1111yescharacteristic, complemented
207C23×C11C22×D411yescharacteristic
208C22×D11—22no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11C4×D412yes—
232C2×C4×C11C4×D412yes—
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260D44—22no—
261D44—22no—
262D44—41no—
263D44—41no—
264C4×D11—84no—
265C8×C11—22no—
266C8×C11—22no—
267C8×C11—41no—
268C8×C11—41no—
269C2×#125—111no—
270C2×C4×D4—111no—
271#478—118no—
272C2×#107—111no—
273C2×#106—111no—
274C2×#106—111no—
275C2×#106—111no—
276C2×C4⋊C8C2×D1111yescharacteristic
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×#102—111no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#97C2×D1111yescharacteristic
283C2×C4×C8C2×D1111yescharacteristic
284#390—111no—
285#390—111no—
286#389—111no—
287#389—111no—
288#389—111no—
289#389—111no—
290#389—221no—
291#389—221no—
292#388—221no—
293#388—221no—
294#387—221no—
295#387—221no—
296#384—111no—
297#381—221no—
298#380—221no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302#376C2×D1111yescharacteristic
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#336C2×D1111yescharacteristic
312#336C2×D1111yescharacteristic
313C22×C11C2×C4×D411yescharacteristic
314C22×C11#53611yescharacteristic
315C22×C11#53711yescharacteristic
316C22×C11#57611yescharacteristic
317C22×C11#57711yescharacteristic
318C22×C11#57711yescharacteristic
319C22×C11#57711yescharacteristic
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11#51911yescharacteristic
334C4×C11#52011yescharacteristic
335C4×C11#54111yescharacteristic
336C4×C11#54211yescharacteristic
337Dic11—42no—
338Dic11—42no—
339Dic11—42no—
340Dic11—81no—
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344C22×D4—111no—
345C23×C4—221no—
346C22×C8C22×D1111yescharacteristic
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349C22×C8C22×D1111yescharacteristic
350#125—114no—
351#125—222no—
352C4×D4—114no—
353C4×D4—222no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C42—221no—
375C2×C42—221no—
376C2×C42—221no—
377C2×C42C22×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379C2×C42C22×D1111yescharacteristic
380#107—114no—
381#106—114no—
382#106—441no—
383#106—441no—
384C4⋊C8—22no—
385C4⋊C8C4×D1114yes—
386#102—114no—
387#102—114no—
388#102—441no—
389#102—441no—
390#97—41no—
391C4×C8—41no—
392#95—221no—
393#95—221no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95D4411yescharacteristic
400#95D4411yescharacteristic
401#95D4411yescharacteristic
402#95D4411yescharacteristic
403C2×C11#232311yescharacteristic
404C2×C11#294611yescharacteristic
405C2×C11#295211yescharacteristic
406C2×C11#324111yescharacteristic
407C2×C11#324411yescharacteristic
408C2×C11#325711yescharacteristic
409C2×C11#326011yescharacteristic
410D11—82no—
411C24—221no—
412C2×D4—112no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—221no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—224no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—881no—
427C22×C4—881no—
428C22×C4C2×D4411yescharacteristic
429C22×C4C2×D4411yescharacteristic
430C22×C4C2×D4411yescharacteristic
431C22×C4C2×D4411yescharacteristic
432C22×C4C2×D4411yescharacteristic
433C22×C4C2×D4411yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C2×C4×D1112yes—
446C2×C8C2×C4×D1112yes—
447C4⋊C4—112no—
448C4⋊C4—112no—
449C4⋊C4—112no—
450C4⋊C4—224no—
451C4⋊C4—224no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—881no—
464C4⋊C4—881no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4—881no—
469C22⋊C4—224no—
470C22⋊C4—881no—
471C22⋊C4—881no—
472C22⋊C4—881no—
473C22⋊C4—881no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—881no—
479C42—881no—
480C42—881no—
481C42C2×C4×D1112yes—
482C42#433912yes—
483C11#2212211yescharacteristic, complemented, Sylow
484C23—222no—
485C23—441no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23C22×D4411yescharacteristic
492D4—222no—
493D4—222no—
494D4—441no—
495D4—441no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
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—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—884no—
534C2×C4C4×D4412yes—
535C2×C4C4×D4412yes—
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4#6703711yescharacteristic
539C2×C4#6704011yescharacteristic
540C2×C4#6704311yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—22no—
543C8—22no—
544C8—41no—
545C8—41no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22—881no—
553C22C2×C4×D4411yescharacteristic
554C22#1062304111yescharacteristic
555C22#1062305711yescharacteristic
556C22#1062328211yescharacteristic
557C22#1062328211yescharacteristic
558C22#1062328211yescharacteristic
559C22#1062328311yescharacteristic
560C4—22no—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—442no—
567C4—442no—
568C4—442no—
569C4—881no—
570C4—881no—
571C4—881no—
572C4—881no—
573C4#1062307711yescharacteristic
574C4#1062309211yescharacteristic
575C4#1062310311yescharacteristic
576C4#1062311411yescharacteristic
577C2—882no—
578C2#1307129911yescharacteristic
579C2#1307745011yescharacteristic
580C2#1307750111yescharacteristic
581C2#1307987111yescharacteristic
582C2#1307991611yescharacteristic
583C2#1308002911yescharacteristic
584C2#1308006311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1768C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1768D11
hypocenterC11#22122
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
2. #13071357C2semidirect
4. #13069571C2semidirect
5. #13069380C2semidirect
6. #13069354C2semidirect
7. #13069344C2semidirect
12. #13069202C2semidirect
13. #13069188C2semidirect
15. C11×#1768C2semidirect
41. #10622460C4semidirect
206. #1768D11semidirect
483. C11#22122semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
#130713572
#130712602
#130695712
#130693802
#130693542
#130693442
#130693132
#130692992
#130692442
#130692022
#130691882
#130686172
C11×#17682
#2212211