Finite Group Databasebeta

← #14783700

Subgroups — #14783700

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071097C211yesmaximal, characteristic
2D11×#382C211yesmaximal, characteristic
3#13070189C211yesmaximal, characteristic, complemented
4#13070188C211yesmaximal, characteristic, complemented
5#13070187C211yesmaximal, characteristic, complemented
6#13070186C211yesmaximal, characteristic, complemented
7#13070185C211yesmaximal, characteristic, complemented
8#13070184C211yesmaximal, characteristic, complemented
9#13070183C211yesmaximal, characteristic, complemented
10#13068334C211yesmaximal, characteristic
11#13068334C211yesmaximal, characteristic
12#13068334C211yesmaximal, characteristic
13#13068334C211yesmaximal, characteristic
14#13068308C211yesmaximal, characteristic
15C11×#2101C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#382C2211yescharacteristic
25#10622602—21no—
26#10622598C2211yescharacteristic
27#10622590C2211yescharacteristic
28#10622590C2211yescharacteristic
29C4⋊C4×Dic11—21no—
30#10622586C2211yescharacteristic
31#10622549C2211yescharacteristic
32#10622541C2211yescharacteristic
33#10622281—21no—
34D11×#95—21no—
35D11×#95—21no—
36#10622263—21no—
37#10622263—21no—
38#10622262—21no—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43C11×#336C2211yescharacteristic
44#10622189C2211yescharacteristic
45#10622189C2211yescharacteristic
46#10622189C2211yescharacteristic
47#10622189C2211yescharacteristic
48#10622188C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11—21no—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C2×#4313—22no—
91C2×#4313—22no—
92C2×#4313—22no—
93C2×#4313—22no—
94C2×#4313—22no—
95C2×#4313—22no—
96#66945—22no—
97#66945—22no—
98#66945—22no—
99#66945Q814yes—
100C4⋊C4×D11—22no—
101C4⋊C4×D11—22no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—22no—
104C42×D11—22no—
105C42×D11—22no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#23746—111nomaximal, Sylow
119C23×D11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×C4×D11C2×Q812yes—
147C2×C4×D11#4112yes—
148C2×C4×D11#4112yes—
149C2×C4×D11#4112yes—
150C2×C4×D11#4112yes—
151C2×C4×D11#4112yes—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4C2×Q812yes—
167C42×C11—21no—
168C42×C11—21no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—42no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—42no—
179C4⋊Dic11C2×Q812yes—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184C4×Dic11—24no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—42no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196#4313—44no—
197#4313—44no—
198#2296—111no—
199C2×#382—111no—
200#2101—111no—
201#2101—111no—
202#2101—111no—
203#2101—111no—
204#2101—111no—
205#2101—111no—
206#2101—111no—
207#2101D1111yescharacteristic, complemented
208#1736—111no—
209#1736—111no—
210#1736—111no—
211#1736—111no—
212#1728—111no—
213C23×C11C22×D411yescharacteristic
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11C22⋊Q812yes—
219C22×D11#12312yes—
220C22×D11#12412yes—
221C2×C4×C11—22no—
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—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×Dic11—22no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11C22⋊Q812yes—
264C2×Dic11#12312yes—
265C2×Dic11#12412yes—
266C4×D11—44no—
267C4×D11—44no—
268C4×D11—84no—
269C4×D11—84no—
270C4×D11#12514yes—
271C4×D11#12514yes—
272C4×D11#12614yes—
273C4×D11#12614yes—
274C8×C11—41no—
275C8×C11—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C22×M16—111no—
279C22×M16—111no—
280C2×#117—111no—
281C2×#117—111no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—111no—
284C22×C42—111no—
285#389—111no—
286#389—111no—
287#389—111no—
288#389C2×D1111yescharacteristic
289#385—221no—
290#385—221no—
291#382—111no—
292#382—111no—
293#382—111no—
294#382—221no—
295#382—221no—
296#382C2×D1111yescharacteristic
297C4×C4⋊C4—221no—
298C4×C4⋊C4—221no—
299C2×#95—221no—
300C2×#95—221no—
301#340—111no—
302#340—111no—
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#340—111no—
312#340—111no—
313#340C2×D1111yescharacteristic
314#340C2×D1111yescharacteristic
315#340C2×D1111yescharacteristic
316#340C2×D1111yescharacteristic
317#336—111no—
318#336—111no—
319#336—111no—
320#336C2×D1111yescharacteristic
321C22×C11C2×C22⋊Q811yescharacteristic
322C22×C11C2×#12311yescharacteristic
323C22×C11C2×#12411yescharacteristic
324C22×C11#57511yescharacteristic
325C22×C11#57511yescharacteristic
326C22×C11#57511yescharacteristic
327C22×C11#57511yescharacteristic
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11#40014yes—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11C2×#12511yescharacteristic
342C4×C11C2×#12511yescharacteristic
343C4×C11C2×#12611yescharacteristic
344C4×C11C2×#12611yescharacteristic
345Dic11—42no—
346Dic11—41no—
347Dic11—41no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351Dic11#40014yes—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—221no—
356C23×C4—221no—
357C2×M16—222no—
358C2×M16—222no—
359C2×M16—222no—
360C2×M16—222no—
361C2×M16—222no—
362C2×M16—222no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367#117—114no—
368#117—222no—
369#117—222no—
370#117—222no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—222no—
395C2×C42—222no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42C22×D1111yescharacteristic
399#95—21no—
400#95—21no—
401#95—21no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411C2×C11C2×#40011yescharacteristic
412C2×C11#308011yescharacteristic
413C2×C11#308011yescharacteristic
414C2×C11#309311yescharacteristic
415C2×C11#309311yescharacteristic
416C2×C11#314011yescharacteristic
417C2×C11#314011yescharacteristic
418D11—24no—
419C24—111no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—111no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—112no—
430C22×C4—112no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—441no—
440C22×C4—441no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4—442no—
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1111yescharacteristic
451C22×C4C23×D1111yescharacteristic
452M16—444no—
453M16—444no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—42no—
474C4⋊C4—112no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C4⋊C4Q8×D1112yes—
488C22⋊C4—224no—
489C22⋊C4—442no—
490C42—21no—
491C42—21no—
492C42—222no—
493C42—222no—
494C42—224no—
495C42—221no—
496C42—221no—
497C42—442no—
498C11#2374611yescharacteristic, complemented, Sylow
499C23—112no—
500C23—112no—
501C23—112no—
502C23—221no—
503C23—221no—
504C23—221no—
505C23—221no—
506C23C2×D4×D1111yescharacteristic
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—112no—
526C2×C4—112no—
527C2×C4—112no—
528C2×C4—114no—
529C2×C4—114no—
530C2×C4—114no—
531C2×C4—114no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—222no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—444no—
540C2×C4—444no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—884no—
553C2×C4—884no—
554C2×C4C2×Q8×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C8—41no—
561C8—41no—
562C8—441no—
563C8—441no—
564C22—114no—
565C22—222no—
566C22—222no—
567C22—222no—
568C22—222no—
569C22—222no—
570C22—222no—
571C22D11×C22⋊Q811yescharacteristic
572C22D11×#12311yescharacteristic
573C22D11×#12411yescharacteristic
574C22#1062329911yescharacteristic
575C22#1062329911yescharacteristic
576C22#1062330411yescharacteristic
577C22#1062330811yescharacteristic
578C4—41no—
579C4—41no—
580C4—42no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—114no—
585C4—441no—
586C4—441no—
587C4—442no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4D11×#12511yescharacteristic
592C4D11×#12511yescharacteristic
593C4D11×#12611yescharacteristic
594C4D11×#12611yescharacteristic
595C2—224no—
596C2D11×#40011yescharacteristic
597C2#1307843311yescharacteristic
598C2#1307843511yescharacteristic
599C2#1307854411yescharacteristic
600C2#1307854811yescharacteristic
601C2#1307899911yescharacteristic
602C2#1307900111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2101C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2101D11
hypocenterC11#23746
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
3. #13070189C2semidirect
4. #13070188C2semidirect
5. #13070187C2semidirect
6. #13070186C2semidirect
7. #13070185C2semidirect
8. #13070184C2semidirect
9. #13070183C2semidirect
15. C11×#2101C2semidirect
207. #2101D11semidirect
498. C11#23746semidirect

Maximal subgroups

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

subgroupindex
#130710972
D11×#3822
#130701892
#130701882
#130701872
#130701862
#130701852
#130701842
#130701832
#130683342
#130683082
C11×#21012
#2374611