Finite Group Databasebeta

← #14764985

Subgroups — #14764985

Order 2816.

1080 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622653C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic, complemented
3#13069496C212yesmaximal, complemented
4#13069305C212yesmaximal, complemented
5#13069257C212yesmaximal, complemented
6#13068950C212yesmaximal, complemented
7#13068934C211yesmaximal, characteristic
8#13068803C211yesmaximal, characteristic, complemented
9#13068550C211yesmaximal, characteristic, complemented
10#13068378C211yesmaximal, characteristic, complemented
11C4×C11×#121C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×#4324C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C11×#390C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C11×#388—21no—
22C11×#386—21no—
23C11×#380C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C22⋊C4—21no—
26C2×#66896C2212yes—
27C2×C11⋊#95—21no—
28C2×C11⋊#95—21no—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622653C418yescomplemented
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35C2×#66871C2212yes—
36#10622542—21no—
37#10622542—21no—
38#10622542C2212yes—
39#10622542C2212yes—
40C2×#66867C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622162C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C23×Dic11—21no—
52C22×Dic22—21no—
53C22×Dic22—22no—
54C22×Dic22—42no—
55C22×Dic22—42no—
56C22×Dic22C2×C414yescomplemented
57C22×Dic22C2312yes—
58C11×#121—22no—
59C11×#121C2×C414yes—
60C4×D4×C11—42no—
61C4×D4×C11—44no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11—42no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×#4324—42no—
78C2×#4324—42no—
79C2×#4324C2×C418yescomplemented
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—42no—
82C2×C4⋊Dic11C2312yes—
83C22×C11⋊C8C2312yes—
84C22×C11⋊C8C2312yes—
85C11×#95—21no—
86C11×#95—21no—
87C11×#95—21no—
88#66896—42no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C22⋊(C11⋊C8)—22no—
94C22⋊(C11⋊C8)C2×C414yescomplemented
95#66874—42no—
96#66874—42no—
97#66874C2×C418yescomplemented
98#66871—42no—
99#66867—42no—
100#22047—111nomaximal, Sylow
101C24×C11—21no—
102C24×C11C2×D411yescharacteristic
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11C22×C412yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—24no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—42no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C2×Dic22—24no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—48no—
147C2×Dic22—42no—
148C2×Dic22—42no—
149C2×Dic22—48no—
150C2×Dic22C22×C414yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4C22×C412yes—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—42no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—42no—
160C11×C22⋊C4—42no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11—41no—
164C42×C11—41no—
165C42×C11—42no—
166#4324—48no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—42no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8C22×C414yes—
176C2×#448—111no—
177C4×#121D1111yescharacteristic
178C2×#391—111no—
179#1973—112no—
180#1935—112no—
181#1928—112no—
182#1877—112no—
183#1874—111no—
184#1852—111no—
185#1787—111no—
186#1749—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11—22no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11C4×D412yes—
199C23×C11AGL(1,ℤ/8)12yes—
200C23×C11#13712yes—
201C23×C11C22×D411yescharacteristic
202D4×C11—24no—
203D4×C11—48no—
204D4×C11—42no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
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—44no—
222C2×C4×C11—44no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—84no—
232C2×C4×C11C4×D412yes—
233C2×C4×C11#13712yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11H(5,𝔽2)12yes—
237C2×C4×C11H(5,𝔽2)12yes—
238C2×Dic11—24no—
239C2×Dic11—48no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—84no—
246Dic22—24no—
247Dic22—24no—
248Dic22—48no—
249Dic22—42no—
250Dic22—42no—
251C11⋊C8—24no—
252C11⋊C8—42no—
253C23×Q8—111no—
254C22×SD16—112no—
255C2×#121C2×D1111yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4C2×D1111yescharacteristic
258C22×C4⋊C4—111no—
259C22×C42C2×D1111yescharacteristic
260#448—118no—
261C2×#107—112no—
262C2×#103—112no—
263C2×#103—112no—
264C2×#103—112no—
265C2×#102—112no—
266C2×C22⋊C8—111no—
267C2×C22⋊C8—111no—
268C2×#97—112no—
269#391—112no—
270#391—112no—
271#391—221no—
272#391—221no—
273#390C2×D1111yescharacteristic
274#389C2×D1111yescharacteristic
275#388—21no—
276#386—21no—
277#380C2×D1111yescharacteristic
278C4×C4⋊C4C2×D1111yescharacteristic
279C4×C22⋊C4—21no—
280C2×#95—221no—
281C2×#95—221no—
282#340—112no—
283#340—112no—
284#336—112no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11#44014yes—
299C22×C11C2×C4×D411yescharacteristic
300C22×C11#53411yescharacteristic
301C22×C11#53511yescharacteristic
302C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C11C2×#13711yescharacteristic
304C22×C11C2×#13711yescharacteristic
305C22×C11#57511yescharacteristic
306C4×C11—22no—
307C4×C11—22no—
308C4×C11—41no—
309C4×C11—42no—
310C4×C11—41no—
311C4×C11—41no—
312C4×C11—81no—
313C4×C11—81no—
314C4×C11#51812yes—
315C4×C11#53812yes—
316Dic11—44no—
317Dic11—82no—
318C22×Q8—114no—
319C22×Q8—112no—
320C22×Q8—222no—
321C22×Q8—221no—
322C22×Q8—442no—
323C22×Q8—442no—
324C22×D4—21no—
325C22×D4C22×D1111yescharacteristic
326C23×C4—21no—
327C23×C4—221no—
328C23×C4—221no—
329C23×C4C22⋊D1111yescharacteristic
330C23×C4C22⋊D1111yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C2×SD16—118no—
333C2×SD16—442no—
334C2×SD16—442no—
335C22×C8—112no—
336C22×C8—112no—
337#121—22no—
338#121C4×D1114yes—
339C4×D4—42no—
340C4×D4—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—442no—
345C2×C4⋊C4C22×D1111yescharacteristic
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C42—21no—
354C2×C42—42no—
355C2×C42C22⋊D1111yescharacteristic
356C2×C42C22⋊D1111yescharacteristic
357C2×C42C22×D1111yescharacteristic
358C2×C42C22×D1111yescharacteristic
359#107—442no—
360#103—118no—
361#103—442no—
362#103—442no—
363#102—442no—
364C22⋊C8—114no—
365C22⋊C8—222no—
366#97—442no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—222no—
371#95—222no—
372#95—222no—
373#95—222no—
374C2×C11—24no—
375C2×C11—82no—
376C2×C11#232111yescharacteristic
377C2×C11C2×#44011yescharacteristic
378C2×C11C4×#13711yescharacteristic
379C2×C11#319311yescharacteristic
380C2×C11#319611yescharacteristic
381C2×C11#321311yescharacteristic
382C2×C11#321811yescharacteristic
383C24—21no—
384C24C2×C22⋊D1111yescharacteristic
385C2×Q8—114no—
386C2×Q8—224no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—222no—
392C2×Q8—448no—
393C2×Q8—442no—
394C2×Q8—442no—
395C2×Q8—448no—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4C2×C4×D1112yes—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—224no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4C2×C4×D1112yes—
426C22×C4#433912yes—
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C23×D1111yescharacteristic
433SD16—448no—
434C2×C8—114no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—222no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4—222no—
445C4⋊C4—222no—
446C4⋊C4—442no—
447C4⋊C4C2×C4×D1112yes—
448C22⋊C4—24no—
449C22⋊C4—42no—
450C22⋊C4—42no—
451C22⋊C4—42no—
452C22⋊C4—42no—
453C42—22no—
454C42—22no—
455C42—41no—
456C42—41no—
457C42—42no—
458C11#2204711yescharacteristic, complemented, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—22no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23C4×C22⋊D1112yes—
471C23#6698512yes—
472C23#6700412yes—
473C23C22×C22⋊D1111yescharacteristic
474Q8—224no—
475Q8—224no—
476Q8—448no—
477Q8—442no—
478Q8—442no—
479D4—24no—
480D4—48no—
481D4—42no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—84no—
509C2×C4—224no—
510C2×C4—448no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—884no—
517C2×C4C4×C22⋊D1112yes—
518C2×C4#6700412yes—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4#6703712yes—
522C2×C4#6704212yes—
523C8—224no—
524C8—442no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22#1062263114yes—
539C22C2×C4×C22⋊D1111yescharacteristic
540C22C2×#6698511yescharacteristic
541C22#1062333511yescharacteristic
542C22#1062335311yescharacteristic
543C22C2×#6700411yescharacteristic
544C22C2×#6700411yescharacteristic
545C22#1062336111yescharacteristic
546C4—22no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—42no—
552C4—81no—
553C4—81no—
554C4—444no—
555C4—882no—
556C4#1062307612yes—
557C4#1062309112yes—
558C2—24no—
559C2—82no—
560C2#1307127011yescharacteristic
561C2C2×#1062263111yescharacteristic
562C2C4×#6700411yescharacteristic
563C2#1307942211yescharacteristic
564C2#1307944211yescharacteristic
565C2#1307959911yescharacteristic
566C2#1307964011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11#22047
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×#10622542C2semidirect
3. #13069496C2semidirect
4. #13069305C2semidirect
5. #13069257C2semidirect
6. #13068950C2semidirect
8. #13068803C2semidirect
9. #13068550C2semidirect
10. #13068378C2semidirect
31. #10622653C4semidirect
56. C22×Dic22C2×C4semidirect
79. C2×#4324C2×C4semidirect
94. C22⋊(C11⋊C8)C2×C4semidirect
97. #66874C2×C4semidirect
458. C11#22047semidirect

Maximal subgroups

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

subgroupindex
C2×#106226532
C2×#106225422
#130694962
#130693052
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C4×C11×#1212
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