Finite Group Databasebeta

← #14771446

Subgroups — #14771446

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#106C211yesmaximal, characteristic
2#13071492C211yesmaximal, characteristic
3#13071481C211yesmaximal, characteristic
4#13069358C211yesmaximal, characteristic, complemented
5#13069356C211yesmaximal, characteristic, complemented
6#13069202C211yesmaximal, characteristic, complemented
7#13069200C211yesmaximal, characteristic, complemented
8#13069196C211yesmaximal, characteristic, complemented
9#13068705C211yesmaximal, characteristic
10#13068701C211yesmaximal, characteristic
11#13068644C211yesmaximal, characteristic
12#13068514C211yesmaximal, characteristic, complemented
13#13068512C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic
15C11×#1919C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66925—21no—
20C2×C11×#106C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26#10622600—21no—
27#10622600C2211yescharacteristic
28#10622600C2211yescharacteristic
29#10622598C2211yescharacteristic
30#10622591—21no—
31C4⋊C4×Dic11C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622546—21no—
41#10622541C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43D11×#106C418yescomplemented
44#10622279—21no—
45#10622277—21no—
46#10622268—21no—
47#10622265—21no—
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C2×C8×D11—22no—
92C2×C8×D11—22no—
93C2×C8×D11C2×C414yes—
94C4⋊C4×D11—22no—
95C4⋊C4×D11—22no—
96C4⋊C4×D11C2×C414yes—
97C4⋊C4×D11C2×C414yes—
98#66925—44no—
99C11×#106C2×C414yes—
100C11×#95—21no—
101C11×#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112(C2×D11)⋊C8—22no—
113#66881C2×C414yes—
114#66879—22no—
115#66872C2×C414yes—
116#66872C2×C414yes—
117#66871—22no—
118#66871—22no—
119#66867—22no—
120#22615—111nomaximal, Sylow
121C23×D11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×C4×D11—24no—
137C2×C4×D11—24no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—81no—
145C2×C4×D11—81no—
146C2×C4×D11C22×C412yes—
147C2×C4×D11#4112yes—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11C22×C412yes—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—81no—
161C11×C4⋊C4C22×C412yes—
162C11×C4⋊C4C22×C412yes—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—42no—
166(C2×D11)⋊C4—22no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4—42no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—81no—
177C4⋊Dic11C22×C412yes—
178C4⋊Dic11C22×C412yes—
179Dic11⋊C4—24no—
180Dic11⋊C4—24no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—42no—
186C4×Dic11—81no—
187C4×Dic11—81no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8C22×C412yes—
192C2×C11⋊C8#4112yes—
193C2×C11⋊C8#4112yes—
194C8×D11—28no—
195C22×#106—111no—
196#2345—111no—
197#2344—111no—
198#1944—111no—
199#1944—111no—
200#1920—111no—
201#1920—111no—
202#1919—111no—
203#1919D1111yescharacteristic, complemented
204#1824—111no—
205#1823—111no—
206#1808—111no—
207#1776—111no—
208#1776—111no—
209#1752—111no—
210C23×C11C22×D411yescharacteristic
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11C4×D412yes—
216C22×D11AGL(1,ℤ/8)12yes—
217C22×D11#13712yes—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
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—41no—
227C2×C4×C11—41no—
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×C11C23×C411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—22no—
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×Dic11C4×D412yes—
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—48no—
268C4×D11—84no—
269C8×C11—22no—
270C8×C11—41no—
271C11⋊C8—41no—
272C11⋊C8#11714yescomplemented
273C23×C8—111no—
274C2×#117—221no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—111no—
277C2×#107—111no—
278C2×#107—111no—
279C2×#106—111no—
280C2×#106—111no—
281C2×#106—111no—
282C2×#106—118no—
283C2×#106C2×D1111yescharacteristic
284C2×C22⋊C8—111no—
285C2×#97—111no—
286C2×#97—111no—
287#389—111no—
288#389—111no—
289#389—111no—
290#389C2×D1111yescharacteristic
291#387—221no—
292#387—221no—
293#387—221no—
294#387—221no—
295#381—221no—
296#380—111no—
297#380—111no—
298#380—221no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4C2×D1111yescharacteristic
303C4×C22⋊C4—111no—
304C4×C22⋊C4—221no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340C2×D1111yescharacteristic
313#340C2×D1111yescharacteristic
314#340C2×D1111yescharacteristic
315#336—111no—
316#336C2×D1111yescharacteristic
317C22×C11C2×C4×D411yescharacteristic
318C22×C11#54711yescharacteristic
319C22×C11#54711yescharacteristic
320C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C11C2×#13711yescharacteristic
322C22×C11#57711yescharacteristic
323C22×C11#57711yescharacteristic
324C2×D11—22no—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—22no—
330C2×D11#44014yes—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11C2×#11711yescharacteristic
338C4×C11#51911yescharacteristic
339C4×C11#55211yescharacteristic
340C4×C11#55211yescharacteristic
341Dic11—22no—
342Dic11—41no—
343Dic11—41no—
344Dic11—42no—
345Dic11—42no—
346Dic11—81no—
347Dic11—81no—
348C23×C4—111no—
349C23×C4—221no—
350C23×C4—221no—
351C22×C8—111no—
352C22×C8—114no—
353C22×C8—111no—
354C22×C8—222no—
355C22×C8—222no—
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358#117—444no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—111no—
378C2×C22⋊C4—111no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C42—21no—
382C2×C42—111no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42C22×D1111yescharacteristic
387#107—222no—
388#107—222no—
389#106—114no—
390#106—114no—
391#106—114no—
392#106C4×D1114yes—
393C22⋊C8—222no—
394#97—222no—
395#97—222no—
396#95—21no—
397#95—21no—
398#95—111no—
399#95—111no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408C2×C11#234411yescharacteristic
409C2×C11C2×#44011yescharacteristic
410C2×C11#294911yescharacteristic
411C2×C11#334411yescharacteristic
412C2×C11#334411yescharacteristic
413C2×C11#334511yescharacteristic
414C2×C11#334511yescharacteristic
415D11—24no—
416C24—111no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—111no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—442no—
437C22×C4—442no—
438C22×C4—881no—
439C22×C4—881no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—112no—
449C2×C8—112no—
450C2×C8—112no—
451C2×C8—228no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8C2×C4×D1112yes—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—81no—
463C4⋊C4—112no—
464C4⋊C4—112no—
465C4⋊C4—224no—
466C4⋊C4—224no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—442no—
474C4⋊C4—442no—
475C4⋊C4—881no—
476C4⋊C4C2×C4×D1112yes—
477C4⋊C4C2×C4×D1112yes—
478C22⋊C4—222no—
479C22⋊C4—222no—
480C22⋊C4—442no—
481C22⋊C4—442no—
482C42—21no—
483C42—21no—
484C42—42no—
485C42—221no—
486C42—221no—
487C42—442no—
488C42—881no—
489C42—881no—
490C11#2261511yescharacteristic, complemented, Sylow
491C23—112no—
492C23—112no—
493C23—112no—
494C23—221no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23C2×D4×D1111yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—112no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—448no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—884no—
544C2×C4C22×C4×D1111yescharacteristic
545C2×C4#6704011yescharacteristic
546C2×C4#41×D1111yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#6704311yescharacteristic
550C8—22no—
551C8—41no—
552C8—114no—
553C8—441no—
554C22—114no—
555C22—222no—
556C22—222no—
557C22—222no—
558C22—222no—
559C22—222no—
560C22—222no—
561C22C4×D4×D1111yescharacteristic
562C22#1062316211yescharacteristic
563C22#1062318611yescharacteristic
564C22#1062329311yescharacteristic
565C22#1062330111yescharacteristic
566C22D11×AGL(1,ℤ/8)11yescharacteristic
567C22D11×#13711yescharacteristic
568C4—42no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—222no—
575C4—442no—
576C4—442no—
577C4—441no—
578C4—441no—
579C4—881no—
580C4—881no—
581C4D11×#11711yescharacteristic
582C4#1062310311yescharacteristic
583C4#1062322411yescharacteristic
584C4#1062323911yescharacteristic
585C2—224no—
586C2#1307148211yescharacteristic
587C2D11×#44011yescharacteristic
588C2#1307747011yescharacteristic
589C2#1308106411yescharacteristic
590C2#1308106811yescharacteristic
591C2#1308107911yescharacteristic
592C2#1308108311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1919C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1919D11
hypocenterC11#22615
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
4. #13069358C2semidirect
5. #13069356C2semidirect
6. #13069202C2semidirect
7. #13069200C2semidirect
8. #13069196C2semidirect
12. #13068514C2semidirect
13. #13068512C2semidirect
15. C11×#1919C2semidirect
43. D11×#106C4semidirect
203. #1919D11semidirect
272. C11⋊C8#117semidirect
490. C11#22615semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1062
#130714922
#130714812
#130693582
#130693562
#130692022
#130692002
#130691962
#130687052
#130687012
#130686442
#130685142
#130685122
#130683912
C11×#19192
#2261511