Finite Group Databasebeta

← #14809901

Subgroups — #14809901

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×#10623110C211yesmaximal, characteristic
2C2×#10622315C211yesmaximal, characteristic, complemented
3C2×#10622459C211yesmaximal, characteristic
4#13073821C211yesmaximal, characteristic, complemented
5#13069955C212yesmaximal, complemented
6#13069945C212yesmaximal, complemented
7#13069571C211yesmaximal, characteristic, complemented
8#13068880C212yesmaximal
9#13068866C212yesmaximal
10#13068442C211yesmaximal, characteristic
11C11×#1985C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999—21no—
14#10623110—24no—
15#10623110—24no—
16C2×#66949—21no—
17C2×#66949—21no—
18C2×C4⋊C4×D11—21no—
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C2×#66923C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#97C2211yescharacteristic
28#10622843—21no—
29C2×#66885C2212yes—
30C2×#66885C2212yes—
31C2×#66882C2212yes—
32C2×#66882C2212yes—
33C2×#66881C2212yes—
34#10622592—21no—
35#10622592—21no—
36#10622589—21no—
37C4×C4⋊Dic11C2211yescharacteristic
38#10622541C2212yes—
39#10622541C2212yes—
40#10622459—24no—
41#10622315—24no—
42C11×#336C2212yes—
43C11×#336C2212yes—
44#10622189C2212yes—
45#10622189C2212yes—
46#10622189C2212yes—
47C22×Q8×C11D411yescharacteristic
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×C4×D11—21no—
51C22×C4×D11—21no—
52C22×Dic22—21no—
53C22×Dic22—21no—
54C22×C8×C11C2312yes—
55C22×C8×C11C2312yes—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C42×C11C2311yescharacteristic
64#66999—28no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—21no—
82#66949—28no—
83#66949—28no—
84C4⋊C4×D11—28no—
85C4×D44—22no—
86C4×D44—22no—
87C4×D44—22no—
88C4×D44—22no—
89C4×D44—22no—
90C4×D44D414yes—
91#66923—22no—
92#66923—22no—
93#66923—22no—
94#66923D414yes—
95#66922—22no—
96#66922—22no—
97#66922—22no—
98#66922—22no—
99C11×C4⋊C8—22no—
100C11×#97—22no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—21no—
104#66885—24no—
105#66885Q818yescomplemented
106#66882—24no—
107#66882—24no—
108#66881—24no—
109#25850—111nomaximal, Sylow
110C23×D11—21no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—41no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C2×D44—21no—
127C2×D44—22no—
128C2×D44C2×D412yes—
129C2×D44C2×Q814yes—
130C2×C4×D11—24no—
131C2×C4×D11—24no—
132C2×C4×D11—24no—
133C2×C4×D11—42no—
134C2×C4×D11—42no—
135C2×C4×D11—82no—
136C2×C4×D11—82no—
137C2×Dic22—24no—
138C2×Dic22—42no—
139C2×Dic22—82no—
140C2×Dic22—82no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11—24no—
145C2×C8×C11C2×Q814yes—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11C2×D412yes—
154C42×C11C2×D412yes—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—24no—
158C4⋊Dic11—24no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—42no—
166C4⋊Dic11C2×D412yes—
167C4⋊Dic11C2×D412yes—
168C4⋊Dic11C2×D412yes—
169C4⋊Dic11C2×Q814yes—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4—24no—
173Dic11⋊C4—24no—
174Dic11⋊C4—82no—
175Dic11⋊C4—82no—
176C4×Dic11—42no—
177C2×#554—111no—
178C2×#501—111no—
179C2×#474—111no—
180#2567—111no—
181#2059—112no—
182#2057—112no—
183#1989—111no—
184#1985D1111yescharacteristic, complemented
185#1864—112no—
186#1862—112no—
187#1762—111no—
188C23×C11C22×D411yescharacteristic
189C22×D11—22no—
190C22×D11—24no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—42no—
194Q8×C11—44no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11#12012yes—
208C2×C4×C11#12012yes—
209C2×C4×C11#13712yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×Q812yes—
213C2×C4×C112−1+412yes—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—24no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227D44—22no—
228D44—24no—
229D44C4⋊Q814yes—
230C4×D11—48no—
231C4×D11—84no—
232C4×D11—84no—
233Dic22—84no—
234Dic22—84no—
235C8×C11—24no—
236C8×C11—42no—
237#554—224no—
238#554—224no—
239C2×C4⋊Q8—111no—
240C2×C4⋊Q8—111no—
241C2×#125—111no—
242C2×#125—111no—
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8—221no—
245C2×C22⋊Q8—221no—
246C2×C4×Q8C2×D1111yescharacteristic
247C2×C4×D4—111no—
248C2×C4×D4—111no—
249C2×C4×D4—111no—
250C22×C4⋊C4—221no—
251#501—224no—
252#474—224no—
253C2×#107—112no—
254C2×#107—112no—
255C2×#106—112no—
256C2×C4⋊C8C2×D1111yescharacteristic
257C2×#102—112no—
258C2×#102—112no—
259C2×#97C2×D1111yescharacteristic
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#336C2×D1112yes—
271#336C2×D1112yes—
272C22×C11C2×#12011yescharacteristic
273C22×C11D4×Q812yes—
274C22×C11C2×#13711yescharacteristic
275C22×C11#57511yescharacteristic
276C22×C11#57612yes—
277C2×D11—24no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—42no—
281C2×D11—42no—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—22no—
285C4×C11—41no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11C2×C4⋊Q811yescharacteristic
289C4×C11#53611yescharacteristic
290C4×C11D4×Q812yes—
291Dic11—44no—
292Dic11—42no—
293Dic11—42no—
294Dic11—42no—
295Dic11—82no—
296C22×Q8—221no—
297C22×Q8—221no—
298C22×Q8D4411yescharacteristic
299C22×D4—111no—
300C23×C4—221no—
301C23×C4—221no—
302C23×C4—221no—
303C22×C8C22×D1112yes—
304C22×C8C22×D1112yes—
305C4⋊Q8—222no—
306C4⋊Q8—222no—
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—22no—
317C4×Q8—22no—
318C4×D4—114no—
319C4×D4—222no—
320C4×D4—222no—
321C4×D4—222no—
322C4×D4—222no—
323C4×D4—222no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—228no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4D4411yescharacteristic
339C2×C4⋊C4D4411yescharacteristic
340C2×C4⋊C4D4411yescharacteristic
341C2×C22⋊C4—221no—
342C2×C22⋊C4—221no—
343C2×C22⋊C4—221no—
344C2×C42—221no—
345C2×C42C22×D1111yescharacteristic
346C2×C42C22×D1111yescharacteristic
347C2×C42C22×D1111yescharacteristic
348#107—224no—
349#107—224no—
350#106—224no—
351C4⋊C8—22no—
352#102—118no—
353#102—224no—
354#97—22no—
355#95—221no—
356#95—222no—
357#95—222no—
358C2×C11#243411yescharacteristic
359C2×C11#300711yescharacteristic
360C2×C11#300811yescharacteristic
361C2×C11#338512yes—
362C2×C11#338912yes—
363D11—44no—
364C24—221no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—41no—
368C2×Q8—224no—
369C2×Q8—442no—
370C2×Q8—882no—
371C2×Q8—882no—
372C2×D4—112no—
373C2×D4—114no—
374C2×D4—221no—
375C2×D4—222no—
376C22×C4—224no—
377C22×C4—224no—
378C22×C4—222no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—224no—
383C22×C4—222no—
384C22×C4—442no—
385C22×C4—442no—
386C22×C4—882no—
387C22×C4—882no—
388C22×C4C2×D4411yescharacteristic
389C22×C4C2×D4411yescharacteristic
390C22×C4C2×D4411yescharacteristic
391C22×C4C2×D4411yescharacteristic
392C22×C4C2×D4411yescharacteristic
393C22×C4C2×D4411yescharacteristic
394C22×C4C23×D1111yescharacteristic
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—24no—
399C2×C8Q8×D1114yes—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—112no—
404C4⋊C4—112no—
405C4⋊C4—112no—
406C4⋊C4—114no—
407C4⋊C4—224no—
408C4⋊C4—224no—
409C4⋊C4—224no—
410C4⋊C4—224no—
411C4⋊C4—224no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—222no—
416C4⋊C4—222no—
417C4⋊C4—222no—
418C4⋊C4—442no—
419C4⋊C4—882no—
420C4⋊C4—882no—
421C22⋊C4—224no—
422C22⋊C4—224no—
423C22⋊C4—224no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—442no—
429C42D4×D1112yes—
430C42D4×D1112yes—
431C11#2585011yescharacteristic, complemented, Sylow
432C23—222no—
433C23—224no—
434C23—441no—
435C23—441no—
436C23—442no—
437C23C22×D4411yescharacteristic
438Q8—44no—
439Q8—884no—
440Q8—884no—
441D4—114no—
442D4—224no—
443D4—222no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—224no—
460C2×C4—448no—
461C2×C4—441no—
462C2×C4—442no—
463C2×C4—441no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—884no—
471C2×C4—884no—
472C2×C4#6693512yes—
473C2×C4#6693512yes—
474C2×C4#6696212yes—
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4C2×D4×D1111yescharacteristic
477C2×C4C2×Q8×D1112yes—
478C2×C4#6704312yes—
479C8—24no—
480C8—42no—
481C22—224no—
482C22—442no—
483C22—442no—
484C22—444no—
485C22—444no—
486C22C2×#6693511yescharacteristic
487C22Q8×D4412yes—
488C22C2×#6696211yescharacteristic
489C22#1062327911yescharacteristic
490C22#1062328312yes—
491C4—22no—
492C4—22no—
493C4—22no—
494C4—41no—
495C4—41no—
496C4—41no—
497C4—442no—
498C4—442no—
499C4—442no—
500C4—444no—
501C4—882no—
502C4#1062316312yes—
503C4#1062320611yescharacteristic
504C4D11×C4⋊Q811yescharacteristic
505C2—444no—
506C2#1307225911yescharacteristic
507C2#1307787811yescharacteristic
508C2#1307788611yescharacteristic
509C2#1308152812yes—
510C2#1308157612yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1985C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1985D11
hypocenterC11#25850
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#10622315C2semidirect
4. #13073821C2semidirect
5. #13069955C2semidirect
6. #13069945C2semidirect
7. #13069571C2semidirect
11. C11×#1985C2semidirect
105. #66885Q8semidirect
184. #1985D11semidirect
431. C11#25850semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106223152
C2×#106224592
#130738212
#130699552
#130699452
#130695712
#130688802
#130688662
#130684422
C11×#19852
#2585011