Finite Group Databasebeta

← #14764173

Subgroups — #14764173

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622450C211yesmaximal, characteristic
2#13071021C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13069380C211yesmaximal, characteristic, complemented
5#13069379C211yesmaximal, characteristic, complemented
6#13069378C212yesmaximal, complemented
7#13069372C211yesmaximal, characteristic, complemented
8#13069371C212yesmaximal, complemented
9#13068650C212yesmaximal
10#13068648C212yesmaximal
11C11×#1947C211yesmaximal, characteristic, complemented
12C22×#4313C2212yes—
13C2×#66945—21no—
14C2×#66925—21no—
15C2×C42×D11C2211yescharacteristic
16C2×C11×#107C2212yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C11×#384C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20C2×#66881C2212yes—
21C2×Dic11⋊C8C2212yes—
22#10622600—21no—
23#10622600C2211yescharacteristic
24#10622600C2212yes—
25#10622600C2211yescharacteristic
26#10622590—21no—
27#10622589C2211yescharacteristic
28#10622589C2211yescharacteristic
29C4⋊C4×Dic11—21no—
30C4⋊C4×Dic11C2212yes—
31C2×#66872C2212yes—
32C2×#66871C2212yes—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C4×Dic11⋊C4—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622450C418yescomplemented
38#10622280—21no—
39#10622263—21no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×Dic11⋊C4—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73C2×#4313—42no—
74C2×#4313—42no—
75C2×#4313C2×C418yes—
76#66945—44no—
77#66925—44no—
78C42×D11C2×C414yes—
79C42×D11Q814yes—
80C11×#107—42no—
81C11×C4⋊C8C2×C414yes—
82C11×#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66881—42no—
89Dic11⋊C8C2×C418yes—
90#66872—42no—
91#66871—42no—
92C4⋊(C11⋊C8)C2×C414yes—
93#21964—111nomaximal, Sylow
94C23×D11C2×D411yescharacteristic
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11C4⋊C414yes—
116C2×C4×D11C4⋊C414yes—
117C2×C4×D11C22×C412yes—
118C2×C4×D11C2×Q812yes—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11C22×C414yes—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—42no—
130C42×C11—42no—
131C42×C11C22×C412yes—
132C42×C11C2×Q812yes—
133(C2×D11)⋊C4—42no—
134(C2×D11)⋊C4—42no—
135(C2×D11)⋊C4—44no—
136C4⋊Dic11—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—42no—
143C4⋊Dic11—42no—
144Dic11⋊C4—42no—
145Dic11⋊C4—42no—
146Dic11⋊C4—42no—
147Dic11⋊C4—42no—
148C4×Dic11—44no—
149C4×Dic11—42no—
150C4×Dic11C4⋊C414yes—
151C4×Dic11C4⋊C414yes—
152C4×Dic11C22×C412yes—
153C4×Dic11C2×Q812yes—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8C22×C414yes—
157#4313—48no—
158C2×#423—111no—
159#2285—111no—
160#2285—111no—
161#1948—111no—
162#1948—111no—
163#1948—112no—
164#1947—112no—
165#1947—111no—
166#1947D1111yescharacteristic, complemented
167#1809—112no—
168#1809—112no—
169C23×C11C22×D411yescharacteristic
170C22×D11—21no—
171C22×D11—21no—
172C22×D11—21no—
173C22×D11—21no—
174C22×D11—21no—
175C22×D11—21no—
176C22×D11C2×C4⋊C412yes—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11C2×C4⋊C412yes—
189C2×C4×C11C2×C4⋊C412yes—
190C2×C4×C11AGL(1,ℤ/8)12yes—
191C2×C4×C11#13712yes—
192C2×C4×C11C23×C411yescharacteristic
193C2×C4×C11C22×Q811yescharacteristic
194C2×C4×C11H(5,𝔽2)11yescharacteristic
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×C4×C112−1+411yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11C2×C4⋊C412yes—
212C2×Dic11C2×C4⋊C412yes—
213C2×Dic11C2×C4⋊C412yes—
214C2×Dic11AGL(1,ℤ/8)12yes—
215C2×Dic11#13712yes—
216C4×D11—22no—
217C4×D11—22no—
218C4×D11—22no—
219C4×D11—22no—
220C4×D11—28no—
221C4×D11—28no—
222C8×C11—24no—
223C11⋊C8—24no—
224C22×M16—112no—
225C2×#117—221no—
226C2×#117—221no—
227C22×C42—111no—
228C2×#107—112no—
229C2×#107C2×D1112yes—
230C2×#106—112no—
231C2×#106—112no—
232#423—118no—
233C2×C4⋊C8—112no—
234C2×C4⋊C8—111no—
235C2×C4⋊C8C2×D1111yescharacteristic
236#384—111no—
237#384—111no—
238#384—111no—
239#384C2×D1111yescharacteristic
240#382—221no—
241#382—221no—
242#380—111no—
243#380—112no—
244#380—111no—
245#380—221no—
246#380—221no—
247C4×C4⋊C4—112no—
248C4×C4⋊C4—111no—
249C4×C4⋊C4—221no—
250C4×C4⋊C4—221no—
251C4×C4⋊C4C2×D1111yescharacteristic
252#340—112no—
253#340—112no—
254#340—112no—
255#340C2×D1112yes—
256C22×C11C22×C4⋊C411yescharacteristic
257C22×C11#53711yescharacteristic
258C22×C11#53711yescharacteristic
259C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C11C2×#13711yescharacteristic
262C22×C11C2×#13711yescharacteristic
263C2×D11—22no—
264C2×D11—22no—
265C2×D11—22no—
266C2×D11—41no—
267C2×D11—41no—
268C2×D11—41no—
269C2×D11—41no—
270C4×C11—22no—
271C4×C11—82no—
272C4×C11—81no—
273C4×C11—81no—
274C4×C11#42814yes—
275C4×C11#51811yescharacteristic
276C4×C11#51911yescharacteristic
277C4×C11#54411yescharacteristic
278C4×C11#54411yescharacteristic
279Dic11—22no—
280Dic11—22no—
281Dic11—81no—
282Dic11—82no—
283Dic11—81no—
284Dic11#42814yes—
285C23×C4—111no—
286C23×C4—111no—
287C23×C4—111no—
288C2×M16—118no—
289C2×M16—442no—
290C2×M16—442no—
291C22×C8—112no—
292C22×C8C22×D1112yes—
293#117—444no—
294#117—444no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4C22×D1111yescharacteristic
307C2×C4⋊C4C22×D1112yes—
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C22⋊C4—221no—
310C2×C22⋊C4—221no—
311C2×C22⋊C4—222no—
312C2×C42—21no—
313C2×C42—111no—
314C2×C42—111no—
315C2×C42—111no—
316C2×C42—114no—
317C2×C42—114no—
318C2×C42—222no—
319C2×C42—221no—
320C2×C42C22×D1111yescharacteristic
321#107—42no—
322#107—442no—
323#106—442no—
324#106—442no—
325C4⋊C8—118no—
326C4⋊C8—114no—
327C4⋊C8C4×D1114yes—
328#95—21no—
329#95—222no—
330#95—221no—
331#95—221no—
332#95—222no—
333#95—221no—
334C2×C11#231611yescharacteristic
335C2×C11C2×#42811yescharacteristic
336C2×C11C2×#42811yescharacteristic
337C2×C11#325311yescharacteristic
338C2×C11#325411yescharacteristic
339C2×C11#325411yescharacteristic
340C2×C11#325511yescharacteristic
341D11—42no—
342C24—111no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—111no—
347C22×C4—111no—
348C22×C4—111no—
349C22×C4—114no—
350C22×C4—114no—
351C22×C4—112no—
352C22×C4—112no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—222no—
364C22×C4D4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366C22×C4C23×D1111yescharacteristic
367M16—448no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—114no—
371C2×C8—222no—
372C2×C8—222no—
373C2×C8C2×C4×D1114yes—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—442no—
389C4⋊C4—442no—
390C4⋊C4—442no—
391C4⋊C4—442no—
392C4⋊C4—442no—
393C4⋊C4—442no—
394C22⋊C4—442no—
395C22⋊C4—442no—
396C22⋊C4—444no—
397C42—42no—
398C42—114no—
399C42—114no—
400C42—112no—
401C42—112no—
402C42—444no—
403C42—442no—
404C42C2×C4×D1112yes—
405C42Q8×D1112yes—
406C11#2196411yescharacteristic, complemented, Sylow
407C23—112no—
408C23—221no—
409C23—221no—
410C23—221no—
411C23—221no—
412C23—221no—
413C23—221no—
414C23C2×D4×D1111yescharacteristic
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—112no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—112no—
430C2×C4—112no—
431C2×C4—228no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—222no—
437C2×C4—228no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—442no—
449C2×C4—441no—
450C2×C4C4⋊C4×D1112yes—
451C2×C4C4⋊C4×D1112yes—
452C2×C4#6696412yes—
453C2×C4#6697112yes—
454C2×C4C22×C4×D1111yescharacteristic
455C2×C4#6703711yescharacteristic
456C2×C4C2×Q8×D1111yescharacteristic
457C2×C4#6704011yescharacteristic
458C2×C4#6704211yescharacteristic
459C2×C4#6704311yescharacteristic
460C8—24no—
461C8—224no—
462C22—222no—
463C22—222no—
464C22—222no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22C2×C4⋊C4×D1111yescharacteristic
470C22#1062313911yescharacteristic
471C22#1062316011yescharacteristic
472C22C2×#6696411yescharacteristic
473C22C2×#6697111yescharacteristic
474C22D11×AGL(1,ℤ/8)11yescharacteristic
475C22D11×#13711yescharacteristic
476C4—22no—
477C4—81no—
478C4—82no—
479C4—81no—
480C4—114no—
481C4—222no—
482C4—222no—
483C4—881no—
484C4—882no—
485C4—881no—
486C4#1062249414yes—
487C4#1062307611yescharacteristic
488C4#1062310311yescharacteristic
489C4#1062322011yescharacteristic
490C4#1062326011yescharacteristic
491C2—442no—
492C2#1307123111yescharacteristic
493C2D11×#42811yescharacteristic
494C2C2×#1062249411yescharacteristic
495C2#1307999511yescharacteristic
496C2#1308000211yescharacteristic
497C2#1308000511yescharacteristic
498C2#1308000811yescharacteristic
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#21964
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
4. #13069380C2semidirect
5. #13069379C2semidirect
6. #13069378C2semidirect
7. #13069372C2semidirect
8. #13069371C2semidirect
11. C11×#1947C2semidirect
37. #10622450C4semidirect
166. #1947D11semidirect
406. C11#21964semidirect

Maximal subgroups

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

subgroupindex
C2×#106224502
#130710212
#130710202
#130693802
#130693792
#130693782
#130693722
#130693712
#130686502
#130686482
C11×#19472
#2196411