Finite Group Databasebeta

← #14826264

Subgroups — #14826264

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072464C211yesmaximal, characteristic
2#13071705C211yesmaximal, characteristic, complemented
3#13069991C211yesmaximal, characteristic
4#13069949C211yesmaximal, characteristic, complemented
5#13069942C211yesmaximal, characteristic, complemented
6#13069753C211yesmaximal, characteristic
7#13069562C211yesmaximal, characteristic, complemented
8#13069358C211yesmaximal, characteristic, complemented
9#13069241C211yesmaximal, characteristic
10#13069236C211yesmaximal, characteristic
11#13069204C211yesmaximal, characteristic, complemented
12#13069181C211yesmaximal, characteristic, complemented
13#13068860C211yesmaximal, characteristic
14#13068440C211yesmaximal, characteristic
15C11×#1918C211yesmaximal, characteristic, complemented
16C2×#66950—21no—
17C2×#66946C2211yescharacteristic
18C2×#66941C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27#10622607—21no—
28#10622601C2211yescharacteristic
29#10622598C2211yescharacteristic
30C4⋊C4×Dic11C2211yescharacteristic
31C4⋊C4×Dic11C2211yescharacteristic
32#10622586C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622552C2211yescharacteristic
40C4×C4⋊Dic11—21no—
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541—21no—
43#10622286—21no—
44#10622281—21no—
45#10622259—21no—
46#10622259—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22—21no—
62C22×Dic22—21no—
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)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66950—44no—
94#66946—22no—
95#66946—41no—
96#66941—22no—
97#66941—41no—
98#66922—22no—
99#66922—22no—
100C11×#107—22no—
101C11×#95—21no—
102C11×#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66885—22no—
111#66885—22no—
112#66879—41no—
113Dic11⋊C8—41no—
114#66873—41no—
115#66873Q814yescomplemented
116#66872—22no—
117#66872—22no—
118#66871—41no—
119#27019—111nomaximal, Sylow
120C23×D11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C2×Q812yes—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—81no—
144C2×Dic22—24no—
145C2×Dic22—42no—
146C2×Dic22—42no—
147C2×Dic22—81no—
148C2×Dic22—81no—
149C2×Dic22—81no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4C2×Q812yes—
164C11×C4⋊C4#4112yes—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—42no—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—81no—
173C4⋊Dic11—24no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—42no—
181C4⋊Dic11#4112yes—
182C4⋊Dic11#4112yes—
183Dic11⋊C4—42no—
184Dic11⋊C4—81no—
185Dic11⋊C4—81no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—81no—
191C4×Dic11—81no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8C2×Q812yes—
198#2452—111no—
199#2369—111no—
200#2065—111no—
201#2058—111no—
202#2057—111no—
203#2023—111no—
204#1987—111no—
205#1944—111no—
206#1926—111no—
207#1925—111no—
208#1920—111no—
209#1918D1111yescharacteristic, complemented
210#1917—111no—
211#1862—111no—
212#1762—111no—
213C23×C11C22×D411yescharacteristic
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
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×C11AGL(1,ℤ/8)12yes—
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11#13712yes—
266D44—22no—
267D44—22no—
268D44—41no—
269D44—41no—
270C4×D11—84no—
271Dic22—84no—
272Dic22—84no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—22no—
276C11⋊C8—41no—
277C2×C4⋊Q8—111no—
278C2×C4⋊Q8—111no—
279C2×C22⋊Q8—221no—
280C2×C4×D4—111no—
281C2×#107—111no—
282C2×#107C2×D1111yescharacteristic
283C2×#106—111no—
284C2×#106—111no—
285C2×C4⋊C8—111no—
286C2×#102—111no—
287C2×#102—111no—
288C2×#102—111no—
289C2×#102—111no—
290C2×#97—111no—
291#396—221no—
292#393—221no—
293#391—221no—
294#391—221no—
295#390—111no—
296#390—111no—
297#389—111no—
298#389—111no—
299#389—111no—
300#389—221no—
301#389C2×D1111yescharacteristic
302#385—221no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—221no—
307C4×C4⋊C4C2×D1111yescharacteristic
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#336—111no—
317#336—111no—
318#336—111no—
319#336C2×D1111yescharacteristic
320C22×C11#52511yescharacteristic
321C22×C11#54611yescharacteristic
322C22×C11D4×Q811yescharacteristic
323C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C11C2×#13711yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—22no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11#53311yescharacteristic
341C4×C11#54211yescharacteristic
342C4×C11#55411yescharacteristic
343C4×C11#55611yescharacteristic
344Dic11—22no—
345Dic11—42no—
346Dic11—42no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350Dic11—81no—
351C22×Q8—221no—
352C22×Q8—221no—
353C22×D4—111no—
354C23×C4—221no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8C22×D1111yescharacteristic
358C22×C8C22×D1111yescharacteristic
359C4⋊Q8—222no—
360C4⋊Q8—222no—
361C4⋊Q8—222no—
362C4⋊Q8—441no—
363C22⋊Q8—444no—
364C4×D4—222no—
365C4×D4—441no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—21no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392#107—22no—
393#107—441no—
394#106—222no—
395#106—222no—
396C4⋊C8—441no—
397#102—114no—
398#102—222no—
399#102—222no—
400#102—441no—
401#97—441no—
402#95—21no—
403#95—21no—
404#95—111no—
405#95—111no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411C2×C11#246511yescharacteristic
412C2×C11#311211yescharacteristic
413C2×C11#311811yescharacteristic
414C2×C11#331611yescharacteristic
415C2×C11#332511yescharacteristic
416C2×C11#338411yescharacteristic
417C2×C11#338511yescharacteristic
418D11—82no—
419C24—221no—
420C2×Q8—224no—
421C2×Q8—442no—
422C2×Q8—442no—
423C2×Q8—881no—
424C2×Q8—881no—
425C2×Q8—881no—
426C2×D4—112no—
427C2×D4—221no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—881no—
446C22×C4D4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—112no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—42no—
468C4⋊C4—112no—
469C4⋊C4—112no—
470C4⋊C4—222no—
471C4⋊C4—224no—
472C4⋊C4—222no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4—881no—
480C4⋊C4—881no—
481C4⋊C4#433912yes—
482C4⋊C4Q8×D1112yes—
483C22⋊C4—442no—
484C22⋊C4—442no—
485C22⋊C4—442no—
486C22⋊C4—442no—
487C22⋊C4—881no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42—221no—
495C42—881no—
496C42—881no—
497C11#2701911yescharacteristic, complemented, Sylow
498C23—222no—
499C23—441no—
500C23—441no—
501C23—441no—
502C23—441no—
503C23—441no—
504C23—441no—
505C23C2×D4×D1111yescharacteristic
506Q8—884no—
507Q8—884no—
508D4—222no—
509D4—222no—
510D4—441no—
511D4—441no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—112no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—884no—
551C2×C4#6696412yes—
552C2×C4C2×#433911yescharacteristic
553C2×C4C2×Q8×D1111yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C2×C4#6704211yescharacteristic
557C2×C4#6704311yescharacteristic
558C8—41no—
559C8—41no—
560C8—222no—
561C8—441no—
562C22—442no—
563C22—442no—
564C22—442no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22#1062308111yescharacteristic
570C22#1062316311yescharacteristic
571C22#1062318711yescharacteristic
572C22C2×#6696411yescharacteristic
573C22#1062330011yescharacteristic
574C22D11×#13711yescharacteristic
575C22#1062330911yescharacteristic
576C4—22no—
577C4—41no—
578C4—42no—
579C4—42no—
580C4—81no—
581C4—81no—
582C4—222no—
583C4—442no—
584C4—442no—
585C4—441no—
586C4—441no—
587C4—441no—
588C4—881no—
589C4#1062306411yescharacteristic
590C4#1062310911yescharacteristic
591C4#1062322111yescharacteristic
592C4#1062324111yescharacteristic
593C2—882no—
594C2#1307263611yescharacteristic
595C2#1307873511yescharacteristic
596C2#1307880311yescharacteristic
597C2#1308073211yescharacteristic
598C2#1308086011yescharacteristic
599C2#1308151911yescharacteristic
600C2#1308152911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1918C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1918D11
hypocenterC11#27019
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
2. #13071705C2semidirect
4. #13069949C2semidirect
5. #13069942C2semidirect
7. #13069562C2semidirect
8. #13069358C2semidirect
11. #13069204C2semidirect
12. #13069181C2semidirect
15. C11×#1918C2semidirect
115. #66873Q8semidirect
209. #1918D11semidirect
497. C11#27019semidirect

Maximal subgroups

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

subgroupindex
#130724642
#130717052
#130699912
#130699492
#130699422
#130697532
#130695622
#130693582
#130692412
#130692362
#130692042
#130691812
#130688602
#130684402
C11×#19182
#2701911