Finite Group Databasebeta

← #14721540

Subgroups — #14721540

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082419C211yesmaximal, characteristic
2#13077645C211yesmaximal, characteristic
3#13067187C212yesmaximal, complemented
4#13067166C212yesmaximal, complemented
5#13067148C212yesmaximal, complemented
6#13067135C212yesmaximal, complemented
7#13067127C212yesmaximal, complemented
8C2×#10622090C212yesmaximal, complemented
9C11×#2353C211yesmaximal, characteristic
10C2×C4×D4×C11C2211yescharacteristic
11#10623329—21no—
12C2×#66977C2212yes—
13C2×#66977C2212yes—
14#10623074C414yescomplemented
15#10623070—24no—
16D4×Dic22C414yescomplemented
17#10623031—21no—
18#10623014—21no—
19#10623014—21no—
20#10623001C2212yes—
21C11×#388—21no—
22C11×#387—21no—
23C11×#386—21no—
24C11×#383C2211yescharacteristic
25C11×#381C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4C2211yescharacteristic
29C11×#376C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31#10622820C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622624—24no—
34#10622539C2212yes—
35#10622090C2214yes—
36#10622090C2214yes—
37#10622090C2214yes—
38#10622090C2214yes—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C22×Dic22C2×C412yes—
44C22×Dic22C2×C412yescomplemented
45C4×D4×C11C2×C414yes—
46C4×D4×C11D414yes—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4D411yescharacteristic
53C2×C11×C22⋊C4D411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59D4×Dic11—24no—
60D4×Dic11—24no—
61#66979—22no—
62C2×C4⋊Dic11C2×C412yes—
63C2×C4⋊Dic11C2×C412yescomplemented
64#66977—22no—
65#66977—22no—
66#66977—22no—
67#66977—22no—
68#66977—22no—
69#66977C2×C414yes—
70#66977C2×C414yescomplemented
71#66977C2314yes—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×#4318—22no—
75C22×C11⋊C8—22no—
76#66943—24no—
77#66941—24no—
78#66931—24no—
79#66931—24no—
80#66931—24no—
81#66931—24no—
82#66923—22no—
83#66922C2×C412yescomplemented
84#66922C2×C412yescomplemented
85C4×Dic22—22no—
86C4×Dic22C2×C414yescomplemented
87C11×#95—21no—
88C11×#95—21no—
89C11×#95—21no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95C2311yescharacteristic
93C11×#95C2311yescharacteristic
94C11×#95C2311yescharacteristic
95C11×#95C2311yescharacteristic
96C22⋊(C11⋊C8)—22no—
97C22⋊(C11⋊C8)—22no—
98C22⋊(C11⋊C8)C2314yes—
99C4⋊(C11⋊C8)—22no—
100#66867—22no—
101#17621—111nomaximal, Sylow
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11C22⋊C414yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11—81no—
114C22×C4×C11—81no—
115C22×C4×C11—81no—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—82no—
133C2×Dic22—82no—
134C2×Dic22C22×C414yes—
135C11×C4⋊C4—81no—
136C11×C4⋊C4C22⋊C414yes—
137C11×C22⋊C4—42no—
138C11×C22⋊C4—42no—
139C11×C22⋊C4—81no—
140C11×C22⋊C4C22⋊C414yes—
141C11×C22⋊C4C22⋊C414yes—
142C42×C11—42no—
143C42×C11—81no—
144C42×C11C22×C412yes—
145C42×C11C2×D412yes—
146C22⋊Dic11—24no—
147C22⋊Dic11—24no—
148C22⋊Dic11—24no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11C22×C414yes—
155Dic11⋊C4—24no—
156Dic11⋊C4—24no—
157Dic11⋊C4—24no—
158Dic11⋊C4—24no—
159C4×Dic11—24no—
160#4318—82no—
161C2×C11⋊C8—24no—
162C2×C11⋊C8—82no—
163#3501—111no—
164#2973—111no—
165#2353D1111yescharacteristic
166#1520—112no—
167#1515—112no—
168#1511—112no—
169#1508—112no—
170#1506—112no—
171C2×#328—112no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11C2×C22⋊C412yes—
179C23×C11C2×C22⋊C412yes—
180C23×C11#13712yes—
181C23×C11#13712yes—
182C23×C11C22×D411yescharacteristic
183D4×C11—28no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—84no—
207C2×C4×C11C2×C22⋊C412yes—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C2×C22⋊C412yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—82no—
216C2×Dic11—82no—
217C2×Dic11—82no—
218C2×Dic11—82no—
219Dic22—44no—
220Dic22—82no—
221Dic22—82no—
222Dic22—82no—
223C11⋊C8—44no—
224#554—114no—
225#554—224no—
226D4×Q8—114no—
227#544—221no—
228#543—221no—
229#543—221no—
230#533—112no—
231C2×C22⋊Q8—112no—
232C2×C22⋊Q8—112no—
233#518—221no—
234C2×C4×D4C2×D1111yescharacteristic
235#435—224no—
236#432—112no—
237#407—112no—
238C2×C22⋊C8—112no—
239#388—21no—
240#387—21no—
241#386—21no—
242#383C2×D1111yescharacteristic
243#381C2×D1111yescharacteristic
244#380C2×D1111yescharacteristic
245C4×C22⋊C4—21no—
246C4×C22⋊C4C2×D1111yescharacteristic
247#376C2×D1111yescharacteristic
248C2×#95C2×D1111yescharacteristic
249#328—114no—
250#328—114no—
251#328—114no—
252#328—114no—
253C22×C11—21no—
254C22×C11—22no—
255C22×C11—21no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11#41914yes—
265C22×C11C22×C22⋊C411yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278Dic11—44no—
279Dic11—44no—
280C22×Q8—112no—
281C22×Q8—112no—
282C22×D4C22⋊D1111yescharacteristic
283C23×C4—21no—
284C23×C4C22×D1111yescharacteristic
285C23×C4C22×D1111yescharacteristic
286C2×M16—222no—
287C22×C8—222no—
288C4⋊Q8—112no—
289C4⋊Q8—112no—
290C4⋊Q8—224no—
291#125—224no—
292#125—222no—
293C22⋊Q8—114no—
294C22⋊Q8—114no—
295C22⋊Q8—114no—
296C22⋊Q8—222no—
297C22⋊Q8—222no—
298C22⋊Q8—222no—
299C22⋊Q8—222no—
300C22⋊Q8—222no—
301C22⋊Q8—224no—
302C22⋊Q8—224no—
303C22⋊Q8—224no—
304C22⋊Q8—224no—
305C4×Q8—114no—
306C4×Q8—222no—
307C4×D4—224no—
308C4×D4—224no—
309C4×D4C4×D1114yes—
310C4×D4D4414yes—
311#117—222no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4C22⋊D1111yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4C22⋊D1111yescharacteristic
324C2×C22⋊C4C22⋊D1111yescharacteristic
325C2×C42—21no—
326C2×C42—21no—
327C2×C42C22×D1111yescharacteristic
328C4⋊C8—222no—
329C22⋊C8—114no—
330C22⋊C8—222no—
331C22⋊C8—222no—
332#97—222no—
333#95—21no—
334#95—21no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95C22×D1111yescharacteristic
339#95C22×D1111yescharacteristic
340#95C22×D1111yescharacteristic
341#95C22×D1111yescharacteristic
342C2×C11—21no—
343C2×C11—21no—
344C2×C11—24no—
345C2×C11—42no—
346C2×C11#288311yescharacteristic
347C2×C11C2×#41911yescharacteristic
348C2×C11#290111yescharacteristic
349C24C2×C22⋊D1111yescharacteristic
350C24C2×C22⋊D1111yescharacteristic
351C2×Q8—114no—
352C2×Q8—222no—
353C2×Q8—222no—
354C2×Q8—222no—
355C2×Q8—882no—
356C2×Q8—882no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4(C2×D11)⋊C414yes—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—81no—
367C22×C4—81no—
368C22×C4—81no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4C2×C4×D1112yes—
374C22×C4C2×C4×D1112yes—
375C22×C4C2×D4412yes—
376C22×C4C2×D4412yes—
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C2×C22⋊D1111yescharacteristic
380C22×C4C2×C22⋊D1111yescharacteristic
381C22×C4C23×D1111yescharacteristic
382M16—882no—
383C2×C8—224no—
384C2×C8—882no—
385C4⋊C4—81no—
386C4⋊C4—114no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—224no—
390C4⋊C4—224no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—224no—
394C4⋊C4—222no—
395C4⋊C4—224no—
396C4⋊C4(C2×D11)⋊C414yes—
397C22⋊C4—42no—
398C22⋊C4—42no—
399C22⋊C4—81no—
400C22⋊C4—224no—
401C22⋊C4—224no—
402C22⋊C4—224no—
403C22⋊C4(C2×D11)⋊C414yes—
404C22⋊C4(C2×D11)⋊C414yes—
405C42—42no—
406C42—81no—
407C42—224no—
408C42C2×C4×D1112yes—
409C42C2×D4412yes—
410C11#1762111yescharacteristic, complemented, Sylow
411C23—21no—
412C23—21no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23C2×(C2×D11)⋊C412yes—
418C23C2×(C2×D11)⋊C412yes—
419C23#6700412yes—
420C23#6700412yes—
421C23C22×C22⋊D1111yescharacteristic
422Q8—444no—
423Q8—882no—
424Q8—882no—
425Q8—882no—
426D4—28no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—84no—
450C2×C4—224no—
451C2×C4—224no—
452C2×C4—882no—
453C2×C4—882no—
454C2×C4—882no—
455C2×C4—882no—
456C2×C4C2×(C2×D11)⋊C412yes—
457C2×C4C2×(C2×D11)⋊C412yes—
458C2×C4C2×(C2×D11)⋊C412yes—
459C2×C4C2×(C2×D11)⋊C412yes—
460C2×C4C22×C4×D1111yescharacteristic
461C2×C4C22×D4411yescharacteristic
462C8—444no—
463C22—21no—
464C22—22no—
465C22—21no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—42no—
471C22—42no—
472C22—81no—
473C22—81no—
474C22#1062261714yes—
475C22C22×(C2×D11)⋊C411yescharacteristic
476C22C2×#6700411yescharacteristic
477C22C2×#6700411yescharacteristic
478C4—21no—
479C4—21no—
480C4—22no—
481C4—22no—
482C4—22no—
483C4—22no—
484C4—42no—
485C4—81no—
486C4—81no—
487C4—81no—
488C4—444no—
489C4—444no—
490C2—21no—
491C2—21no—
492C2—24no—
493C2—42no—
494C2#1307707611yescharacteristic
495C2C2×#1062261711yescharacteristic
496C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2353C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenter#2353D11
hypocenterC11#17621
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2353

Complements

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

NH ≅ G/Ntype
3. #13067187C2semidirect
4. #13067166C2semidirect
5. #13067148C2semidirect
6. #13067135C2semidirect
7. #13067127C2semidirect
8. C2×#10622090C2semidirect
14. #10623074C4semidirect
16. D4×Dic22C4semidirect
44. C22×Dic22C2×C4semidirect
63. C2×C4⋊Dic11C2×C4semidirect
70. #66977C2×C4semidirect
83. #66922C2×C4semidirect
84. #66922C2×C4semidirect
86. C4×Dic22C2×C4semidirect
410. C11#17621semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130776452
#130671872
#130671662
#130671482
#130671352
#130671272
C2×#106220902
C11×#23532
#1762111