Finite Group Databasebeta

← #14809900

Subgroups — #14809900

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623070C211yesmaximal, characteristic
2C2×#10622693C211yesmaximal, characteristic, complemented
3#13073825C211yesmaximal, characteristic, complemented
4#13069952C212yesmaximal, complemented
5#13069942C212yesmaximal, complemented
6#13069571C211yesmaximal, characteristic, complemented
7#13069555C211yesmaximal, characteristic, complemented
8#13068875C212yesmaximal
9#13068861C212yesmaximal
10#13068441C211yesmaximal, characteristic
11C2×C11×#474C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×D4×Dic11C2211yescharacteristic
15C2×D4×Dic11C2211yescharacteristic
16C2×#66977—21no—
17C22×Dic11⋊C4—21no—
18#10623070—24no—
19#10623070—24no—
20C2×#66943C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×#66931—21no—
23C2×#66931—21no—
24C2×#66923C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C11×#474—24no—
27C2×C11×#107C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#102C2212yes—
30#10622842—21no—
31#10622842—21no—
32C2×#66896C2212yes—
33#10622693—24no—
34#10622589—21no—
35#10622587—21no—
36#10622586C2212yes—
37#10622586C2212yes—
38C2×#66872C2212yes—
39C2×#66871C2212yes—
40C4×C4⋊Dic11C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2212yes—
44#10622188C2212yes—
45#10622188C2212yes—
46#10622167C2212yes—
47C22×Q8×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×Dic11—21no—
51C23×Dic11—21no—
52C22×Dic22—21no—
53C22×Dic22D411yescharacteristic
54C22×C8×C11C2312yes—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—22no—
57C4×D4×C11—22no—
58C4×D4×C11D414yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66D4×Dic11—22no—
67D4×Dic11—22no—
68D4×Dic11—22no—
69D4×Dic11—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2312yes—
75#66977—28no—
76C2×Dic11⋊C4—28no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4D411yescharacteristic
84C2×Dic11⋊C4D411yescharacteristic
85C2×C4×Dic11—21no—
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89#66943—22no—
90#66943—22no—
91#66941—22no—
92#66941—22no—
93#66931—28no—
94#66931—28no—
95#66923—22no—
96#66923D414yes—
97C4×Dic22—22no—
98C4×Dic22—22no—
99C11×#107—24no—
100C11×C4⋊C8—22no—
101C11×#102—24no—
102#66896Q818yescomplemented
103C11⋊#95—21no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106#66872—24no—
107#66871—24no—
108#66867—22no—
109#25850—111nomaximal, Sylow
110C24×C11—21no—
111C2×Q8×C11—42no—
112C2×Q8×C11—82no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11C2×D412yes—
116C2×D4×C11C2×Q814yes—
117C22×C4×C11—21no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—82no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—24no—
125C22×Dic11—24no—
126C22×Dic11—22no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—42no—
130C22×Dic11—42no—
131C22×Dic11—82no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×Dic22—22no—
137C2×Dic22—24no—
138C2×Dic22—22no—
139C2×Dic22—41no—
140C2×Dic22—82no—
141C2×C8×C11—22no—
142C2×C8×C11—24no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—24no—
149C42×C11C2×D412yes—
150C42×C11C2×D412yes—
151C22⋊Dic11—24no—
152C22⋊Dic11—24no—
153C4⋊Dic11—24no—
154C4⋊Dic11—22no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—22no—
158C4⋊Dic11C2×D412yes—
159C4⋊Dic11C2×D412yes—
160C4⋊Dic11C2×Q814yes—
161Dic11⋊C4—24no—
162Dic11⋊C4—24no—
163Dic11⋊C4—22no—
164Dic11⋊C4—22no—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167Dic11⋊C4—82no—
168Dic11⋊C4—82no—
169C4×Dic11—21no—
170C4×Dic11—21no—
171C4×Dic11—21no—
172C4×Dic11—21no—
173C4×Dic11—42no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8C2×Q814yes—
177C2×#554—111no—
178C2×#501—111no—
179C2×#474D1111yescharacteristic
180#2567—111no—
181#2059—112no—
182#2057—112no—
183#1989—111no—
184#1985—111no—
185#1864—112no—
186#1862—112no—
187#1762—111no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—42no—
193C23×C11C22×D411yescharacteristic
194Q8×C11—84no—
195D4×C11—22no—
196D4×C11—24no—
197D4×C11C4⋊Q814yes—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—84no—
207C2×C4×C11#12012yes—
208C2×C4×C11#12012yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×Q812yes—
212C2×C4×C112−1+412yes—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—24no—
221C2×Dic11—21no—
222C2×Dic11—21no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—48no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—84no—
232C2×Dic11#13712yes—
233Dic22—44no—
234Dic22—84no—
235C8×C11—42no—
236C11⋊C8—24no—
237#554—224no—
238#554—224no—
239C2×C4⋊Q8—111no—
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×#125—111no—
242C2×#125—111no—
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8—221no—
245C2×C22⋊Q8—221no—
246C2×C4×Q8—111no—
247C2×C4×D4—111no—
248C2×C4×D4—111no—
249C2×C4×D4C2×D1111yescharacteristic
250C22×C4⋊C4—221no—
251#501—224no—
252#474—24no—
253C2×#107—112no—
254C2×#107C2×D1112yes—
255C2×#106—112no—
256C2×C4⋊C8C2×D1111yescharacteristic
257C2×#102—112no—
258C2×#102C2×D1112yes—
259C2×#97—111no—
260#395—221no—
261#395—221no—
262#391—221no—
263#389—112no—
264#389—112no—
265#384—221no—
266C4×C4⋊C4—111no—
267#340—112no—
268#340—112no—
269#340—112no—
270#336—112no—
271#336—112no—
272C22×C11—24no—
273C22×C11—44no—
274C22×C11—44no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11C2×#12011yescharacteristic
278C22×C11D4×Q812yes—
279C22×C11C2×#13711yescharacteristic
280C22×C11#57511yescharacteristic
281C22×C11#57612yes—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—82no—
286C4×C11C2×C4⋊Q811yescharacteristic
287C4×C11#53611yescharacteristic
288C4×C11D4×Q812yes—
289Dic11—22no—
290Dic11—44no—
291Dic11—41no—
292Dic11—42no—
293Dic11—41no—
294Dic11—42no—
295Dic11—41no—
296C22×Q8—21no—
297C22×Q8—111no—
298C22×Q8—221no—
299C22×D4C22×D1111yescharacteristic
300C23×C4—21no—
301C23×C4—221no—
302C23×C4—221no—
303C22×C8—112no—
304C22×C8C22×D1112yes—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—222no—
308C4⋊Q8—222no—
309#125—114no—
310#125—222no—
311#125—222no—
312#125—222no—
313C22⋊Q8—228no—
314C22⋊Q8—228no—
315C22⋊Q8—228no—
316C4×Q8—222no—
317C4×Q8—222no—
318C4×D4—22no—
319C4×D4—222no—
320C4×D4—222no—
321C4×D4—222no—
322C4×D4—222no—
323C4×D4C22⋊D1114yes—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—228no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4C22×D1112yes—
340C2×C4⋊C4C22×D1111yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4—221no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—221no—
347C2×C42C22×D1111yescharacteristic
348#107—24no—
349#107—224no—
350#106—224no—
351C4⋊C8—22no—
352#102—24no—
353#102—118no—
354#97—222no—
355#95—222no—
356#95—222no—
357#95—221no—
358C2×C11—44no—
359C2×C11#243411yescharacteristic
360C2×C11#300711yescharacteristic
361C2×C11#300811yescharacteristic
362C2×C11#338512yes—
363C2×C11#338912yes—
364C24—21no—
365C2×Q8—42no—
366C2×Q8—82no—
367C2×Q8—222no—
368C2×Q8—224no—
369C2×Q8—222no—
370C2×Q8—441no—
371C2×Q8—882no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4Q8×D1114yes—
375C2×D4C2×C22⋊D1112yes—
376C22×C4—21no—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—82no—
380C22×C4—111no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—111no—
384C22×C4—224no—
385C22×C4—222no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—224no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4—882no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395C2×C8—24no—
396C2×C8—22no—
397C2×C8—114no—
398C2×C8—222no—
399C2×C8—222no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4—112no—
405C4⋊C4—112no—
406C4⋊C4—114no—
407C4⋊C4—224no—
408C4⋊C4—224no—
409C4⋊C4—224no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—224no—
414C4⋊C4—224no—
415C4⋊C4—222no—
416C4⋊C4—221no—
417C4⋊C4—221no—
418C4⋊C4—882no—
419C4⋊C4—882no—
420C4⋊C4C2×C22⋊D1112yes—
421C22⋊C4—24no—
422C22⋊C4—224no—
423C22⋊C4—224no—
424C42—221no—
425C42—221no—
426C42—221no—
427C42—221no—
428C42—442no—
429C42D4×D1112yes—
430C42C2×C22⋊D1112yes—
431C11#2585011yescharacteristic, complemented, Sylow
432C23—22no—
433C23—24no—
434C23—42no—
435C23—41no—
436C23—41no—
437C23C2×D4×D1111yescharacteristic
438Q8—84no—
439Q8—444no—
440Q8—884no—
441D4—22no—
442D4—24no—
443D4#6699714yes—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—84no—
453C2×C4—112no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—224no—
466C2×C4—448no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—441no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—884no—
473C2×C4#6699012yes—
474C2×C4#6699012yes—
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4C2×Q8×D1112yes—
477C2×C4#6704312yes—
478C2×C4C22×C22⋊D1111yescharacteristic
479C8—42no—
480C8—224no—
481C22—24no—
482C22—42no—
483C22—42no—
484C22—44no—
485C22—44no—
486C22#1062316312yes—
487C22#1062328812yes—
488C22D11×#13711yescharacteristic
489C22#1062330811yescharacteristic
490C22C2×#6699011yescharacteristic
491C4—22no—
492C4—22no—
493C4—42no—
494C4—82no—
495C4—222no—
496C4—441no—
497C4—442no—
498C4—441no—
499C4—441no—
500C4—442no—
501C4—444no—
502C4#1062316312yes—
503C4C2×#6699711yescharacteristic
504C4#1062335611yescharacteristic
505C2—44no—
506C2#1307226111yescharacteristic
507C2#1307787211yescharacteristic
508C2#1307788011yescharacteristic
509C2#1308152112yes—
510C2#1308156912yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#474D11
hypocenterC11#25850
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
2. C2×#10622693C2semidirect
3. #13073825C2semidirect
4. #13069952C2semidirect
5. #13069942C2semidirect
6. #13069571C2semidirect
7. #13069555C2semidirect
102. #66896Q8semidirect
431. C11#25850semidirect

Maximal subgroups

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

subgroupindex
C2×#106230702
C2×#106226932
#130738252
#130699522
#130699422
#130695712
#130695552
#130688752
#130688612
#130684412
C2×C11×#4742
#2585011