Finite Group Databasebeta

← #14757239

Subgroups — #14757239

Order 2816.

1082 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622494C212yesmaximal
2C2×#10622450C211yesmaximal, characteristic
3#13071021C211yesmaximal, characteristic
4C4×C4⋊C4×D11C211yesmaximal, characteristic
5#13069383C212yesmaximal, complemented
6#13069381C212yesmaximal, complemented
7#13069380C211yesmaximal, characteristic, complemented
8#13069379C211yesmaximal, characteristic, complemented
9#13069372C211yesmaximal, characteristic, complemented
10#13068334C212yesmaximal
11C11×#1947C211yesmaximal, characteristic, complemented
12C22×#4313C2212yes—
13C2×#66945C2212yes—
14C2×C4⋊C4×D11C2211yescharacteristic
15C2×C4⋊C4×D11C2211yescharacteristic
16C2×C42×D11—21no—
17C2×C42×D11C2211yescharacteristic
18C2×C11×#107C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C11×#384C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66881C2212yes—
23C2×Dic11⋊C8C2212yes—
24#10622600—21no—
25#10622600—21no—
26#10622590C2212yes—
27C4⋊C4×Dic11—21no—
28C4⋊C4×Dic11—21no—
29C4⋊C4×Dic11C2211yescharacteristic
30C4⋊C4×Dic11C2211yescharacteristic
31C2×#66872C2212yes—
32C2×#66871C2212yes—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C4×Dic11⋊C4—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622494—28no—
38#10622450C418yescomplemented
39D11×#95—21no—
40#10622262—21no—
41C11×#340C2212yes—
42#10622189C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×C4×D11—21no—
46C22×C4×D11—21no—
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74C2×#4313—24no—
75C2×#4313—24no—
76C2×#4313C2×C418yes—
77#66945—24no—
78#66945—24no—
79C4⋊C4×D11—22no—
80C4⋊C4×D11—22no—
81C4⋊C4×D11D414yes—
82C4⋊C4×D11Q814yes—
83C42×D11—44no—
84C42×D11C2×C414yes—
85C42×D11Q814yes—
86C11×#107—24no—
87C11×C4⋊C8C2×C414yescomplemented
88C11×#95—21no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94#66881—24no—
95Dic11⋊C8C2×C418yescomplemented
96#66872—24no—
97#66871—24no—
98C4⋊(C11⋊C8)C2×C414yescomplemented
99#21170—111nomaximal, Sylow
100C23×D11C2×D411yescharacteristic
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C22×Dic11C2×D411yescharacteristic
113C2×C4×D11—24no—
114C2×C4×D11—24no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—41no—
118C2×C4×D11—41no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C2×C4×D11C4⋊C414yes—
124C2×C4×D11C4⋊C414yes—
125C2×C4×D11C22×C412yes—
126C2×C4×D11C2×D412yes—
127C2×C4×D11C2×Q812yes—
128C2×C4×D11C2×Q812yes—
129C2×C4×D11#4112yes—
130C2×C4×D11#4112yes—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11C22×C414yes—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4C2×D412yes—
141C11×C4⋊C4C2×Q812yes—
142C42×C11—42no—
143C42×C11C22×C412yes—
144C42×C11C2×Q812yes—
145(C2×D11)⋊C4—44no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—42no—
151C4⋊Dic11—42no—
152C4⋊Dic11C2×D412yes—
153C4⋊Dic11C2×Q812yes—
154Dic11⋊C4—24no—
155Dic11⋊C4—24no—
156C4×Dic11—42no—
157C4×Dic11—42no—
158C4×Dic11—44no—
159C4×Dic11—42no—
160C4×Dic11C4⋊C414yes—
161C4×Dic11C4⋊C414yes—
162C4×Dic11C22×C412yes—
163C4×Dic11C2×Q812yes—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8C22×C414yes—
167#4313—216no—
168C2×#428—112no—
169C2×#423—111no—
170#2285—111no—
171C2×C4×C4⋊C4—111no—
172#1949—112no—
173#1949—112no—
174#1948—111no—
175#1948—111no—
176#1947—111no—
177#1947D1111yescharacteristic, complemented
178#1736—112no—
179C23×C11C22×D411yescharacteristic
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—21no—
184C22×D11C2×C4⋊C412yes—
185C22×D11#12112yes—
186C22×D11C22⋊Q812yes—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11C2×C4⋊C412yes—
199C2×C4×C11C2×C4⋊C412yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×Q811yescharacteristic
205C2×C4×C11C22×Q811yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11C2×C4⋊C412yes—
222C2×Dic11C2×C4⋊C412yes—
223C2×Dic11C2×C4⋊C412yes—
224C2×Dic11#12112yes—
225C2×Dic11C22⋊Q812yes—
226C4×D11—28no—
227C4×D11—44no—
228C4×D11—48no—
229C4×D11—48no—
230C4×D11C4×D414yes—
231C4×D11C4×Q814yes—
232C4×D11#12514yes—
233C4×D11C4⋊Q814yes—
234C8×C11—24no—
235C11⋊C8—24no—
236C22×M16—112no—
237C2×#117—112no—
238C22×C4⋊C4—111no—
239C22×C4⋊C4—111no—
240C22×C42—111no—
241C22×C42—221no—
242#428—228no—
243C2×#107—112no—
244C2×#107C2×D1112yes—
245C2×#106—112no—
246C2×#106—112no—
247#423—118no—
248C2×C4⋊C8—112no—
249C2×C4⋊C8—111no—
250C2×C4⋊C8C2×D1111yescharacteristic
251#384—111no—
252#384C2×D1111yescharacteristic
253#382—112no—
254#380—221no—
255#380—221no—
256C4×C4⋊C4—111no—
257C4×C4⋊C4—111no—
258C4×C4⋊C4—111no—
259C4×C4⋊C4—221no—
260C4×C4⋊C4—221no—
261C4×C4⋊C4—221no—
262C4×C4⋊C4—221no—
263C4×C4⋊C4C2×D1111yescharacteristic
264C2×#95—221no—
265#340—112no—
266#340—112no—
267#340—112no—
268#340C2×D1112yes—
269C22×C11C22×C4⋊C411yescharacteristic
270C22×C11C2×#12111yescharacteristic
271C22×C11C2×C22⋊Q811yescharacteristic
272C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C11C2×#13711yescharacteristic
274C22×C11#57511yescharacteristic
275C22×C11#57511yescharacteristic
276C2×D11—22no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—22no—
282C2×D11#38914yes—
283C4×C11—22no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—82no—
287C4×C11#42814yescomplemented
288C4×C11C2×C4×D411yescharacteristic
289C4×C11C2×C4×Q811yescharacteristic
290C4×C11C2×#12511yescharacteristic
291C4×C11C2×C4⋊Q811yescharacteristic
292Dic11—22no—
293Dic11—22no—
294Dic11—42no—
295Dic11—42no—
296Dic11—82no—
297Dic11#38914yes—
298C23×C4—111no—
299C23×C4—111no—
300C23×C4—111no—
301C23×C4—221no—
302C23×C4—221no—
303C2×M16—118no—
304C2×M16—224no—
305C2×M16—224no—
306C22×C8—112no—
307C22×C8C22×D1112yes—
308#117—224no—
309#117—224no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—114no—
315C2×C4⋊C4—114no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4C22×D1112yes—
324C2×C4⋊C4C22×D1111yescharacteristic
325C2×C4⋊C4C22×D1111yescharacteristic
326C2×C22⋊C4—222no—
327C2×C42—21no—
328C2×C42—111no—
329C2×C42—111no—
330C2×C42—111no—
331C2×C42—114no—
332C2×C42—114no—
333C2×C42—222no—
334C2×C42—221no—
335C2×C42—221no—
336C2×C42—221no—
337C2×C42—444no—
338C2×C42C22×D1111yescharacteristic
339#107—24no—
340#107—224no—
341#106—224no—
342#106—224no—
343C4⋊C8—118no—
344C4⋊C8—114no—
345C4⋊C8C4×D1114yescomplemented
346#95—21no—
347#95—221no—
348#95—221no—
349#95—222no—
350#95—222no—
351#95—221no—
352C2×C11C2×#38911yescharacteristic
353C2×C11C2×#42811yescharacteristic
354C2×C11#291111yescharacteristic
355C2×C11#303611yescharacteristic
356C2×C11#303711yescharacteristic
357C2×C11#307711yescharacteristic
358C2×C11#307811yescharacteristic
359D11—24no—
360C24—111no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—111no—
365C22×C4—112no—
366C22×C4—112no—
367C22×C4—112no—
368C22×C4—112no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—114no—
374C22×C4—114no—
375C22×C4—224no—
376C22×C4—224no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—222no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—442no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4C23×D1111yescharacteristic
391M16—2216no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—114no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8C2×C4×D1114yes—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—112no—
405C4⋊C4—112no—
406C4⋊C4—224no—
407C4⋊C4—224no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4—442no—
413C4⋊C4—442no—
414C4⋊C4D4×D1112yes—
415C4⋊C4Q8×D1112yes—
416C22⋊C4—444no—
417C42—42no—
418C42—114no—
419C42—114no—
420C42—112no—
421C42—112no—
422C42—444no—
423C42—442no—
424C42—442no—
425C42—442no—
426C42C2×C4×D1112yes—
427C42Q8×D1112yes—
428C11#2117011yescharacteristic, complemented, Sylow
429C23—112no—
430C23—112no—
431C23—112no—
432C23—221no—
433C23—221no—
434C23—221no—
435C23—221no—
436C23C2×D4×D1111yescharacteristic
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—112no—
449C2×C4—112no—
450C2×C4—112no—
451C2×C4—114no—
452C2×C4—114no—
453C2×C4—114no—
454C2×C4—114no—
455C2×C4—112no—
456C2×C4—112no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—221no—
461C2×C4—228no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—444no—
465C2×C4—448no—
466C2×C4—448no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4C4⋊C4×D1112yes—
475C2×C4C4⋊C4×D1112yes—
476C2×C4#6696412yes—
477C2×C4#6697112yes—
478C2×C4C22×C4×D1111yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4C2×Q8×D1111yescharacteristic
481C2×C4C2×Q8×D1111yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C2×C4#41×D1111yescharacteristic
484C8—24no—
485C8—224no—
486C22—114no—
487C22—222no—
488C22—222no—
489C22—222no—
490C22—222no—
491C22—222no—
492C22—222no—
493C22C2×C4⋊C4×D1111yescharacteristic
494C22D11×#12111yescharacteristic
495C22D11×C22⋊Q811yescharacteristic
496C22C2×#6696411yescharacteristic
497C22C2×#6697111yescharacteristic
498C22#1062330411yescharacteristic
499C22#1062330811yescharacteristic
500C4—22no—
501C4—42no—
502C4—42no—
503C4—82no—
504C4—114no—
505C4—222no—
506C4—222no—
507C4—442no—
508C4—442no—
509C4—882no—
510C4#1062249414yescomplemented
511C4C4×D4×D1111yescharacteristic
512C4C4×Q8×D1111yescharacteristic
513C4D11×#12511yescharacteristic
514C4D11×C4⋊Q811yescharacteristic
515C2—224no—
516C2D11×#38911yescharacteristic
517C2C2×#1062249411yescharacteristic
518C2#1307720311yescharacteristic
519C2#1307807511yescharacteristic
520C2#1307808911yescharacteristic
521C2#1307840811yescharacteristic
522C2#1307842211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1947D11
hypocenterC11#21170
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
5. #13069383C2semidirect
6. #13069381C2semidirect
7. #13069380C2semidirect
8. #13069379C2semidirect
9. #13069372C2semidirect
11. C11×#1947C2semidirect
38. #10622450C4semidirect
87. C11×C4⋊C8C2×C4semidirect
95. Dic11⋊C8C2×C4semidirect
98. C4⋊(C11⋊C8)C2×C4semidirect
177. #1947D11semidirect
287. C4×C11#428semidirect
345. C4⋊C8C4×D11semidirect
428. C11#21170semidirect
510. C4#10622494semidirect

Maximal subgroups

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

subgroupindex
C2×#106224942
C2×#106224502
#130710212
C4×C4⋊C4×D112
#130693832
#130693812
#130693802
#130693792
#130693722
#130683342
C11×#19472
#2117011