Finite Group Databasebeta

← #14721598

Subgroups — #14721598

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082417C211yesmaximal, characteristic
2#13077656C211yesmaximal, characteristic
3#13071587C211yesmaximal, characteristic
4#13067181C211yesmaximal, characteristic, complemented
5#13067180C211yesmaximal, characteristic, complemented
6#13067147C214yesmaximal, complemented
7#13067134C214yesmaximal, complemented
8#13067114C211yesmaximal, characteristic, complemented
9C11×#1503C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11#10623261C412yescomplemented
12#10623258C412yescomplemented
13#10623221—22no—
14#10623165—22no—
15D11×C22⋊Q8C2214yes—
16#10623110—22no—
17#10623110C412yescomplemented
18Q8×D44C412yescomplemented
19#10623052—21no—
20#10623050—21no—
21C2×C4×D44C2211yescharacteristic
22#10623001C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622603—22no—
26#10622552—21no—
27#10622549C2211yescharacteristic
28C4×C4⋊Dic11—21no—
29#10622538C2211yescharacteristic
30#10622451—22no—
31#10622339C2214yes—
32#10622301—22no—
33#10622279C2212yes—
34#10622277C2212yes—
35C11×#328C2212yes—
36C11×#328C2212yes—
37#10622176C2214yes—
38#10622105C2214yes—
39#10622090C2212yes—
40#10622090C2212yes—
41C2×Q8×D11C2×C414yes—
42C22×D44D411yescharacteristic
43C22×C4×D11C2312yes—
44C11×C4⋊Q8C2×C411yescharacteristic
45C11×C4⋊Q8C2×C411yescharacteristic
46C11×#125—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8C2312yes—
49C4×Q8×C11—21no—
50C4×Q8×C11C2×C412yes—
51C11×#117—21no—
52C2×C11×C4⋊C4—21no—
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55#66999—24no—
56#66999C2×C414yes—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4D412yes—
60#66979—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D411yescharacteristic
63#66977—21no—
64#66977C2312yes—
65C2×C4×Dic11—22no—
66C2×#4313—24no—
67#66950—24no—
68#66950C2×C414yes—
69#66949—24no—
70#66949—24no—
71#66949—24no—
72#66946—22no—
73#66946—22no—
74C4⋊C4×D11—24no—
75C4⋊C4×D11C2×C414yes—
76#66943—22no—
77#66941—22no—
78C22⋊C4×D11—24no—
79#66931—24no—
80C4×D44—22no—
81C4×D44—22no—
82C4×D44C2×C412yes—
83C4×D44C2×C412yes—
84C4×D44D412yes—
85C4×D44D412yes—
86#66923—21no—
87#66923—22no—
88#66922—22no—
89#66922C2×C411yescharacteristic
90#66922C2×C411yescharacteristic
91C4×Dic22—21no—
92C4×Dic22C2×C412yes—
93C11×C4⋊C8—21no—
94C11×C22⋊C8C2312yes—
95C4×C8×C11—21no—
96C11×#95C2311yescharacteristic
97C11×#95C2311yescharacteristic
98C11⋊#95—21no—
99C11⋊#95—22no—
100C11⋊#95C2312yes—
101C22⋊(C11⋊C8)C2312yes—
102(C2×D11)⋊C8—24no—
103C4⋊(C11⋊C8)—21no—
104C4×C11⋊C8—21no—
105#17627—111nomaximal, Sylow
106C23×D11C2×D412yes—
107C2×Q8×C11—21no—
108C2×Q8×C11C22×C412yes—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11C2×D412yes—
116Q8×D11—84no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44C22⋊C412yes—
120C2×D44C22⋊C412yes—
121C2×C4×D11—24no—
122C2×C4×D11—24no—
123C2×C4×D11—82no—
124C2×C4×D11C22×C414yes—
125C2×C4×D11C2×D414yes—
126C2×Dic22—24no—
127C2×Dic22—21no—
128C2×Dic22C22×C412yes—
129C2×C8×C11—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4C22×C412yes—
137C11×C22⋊C4—22no—
138C42×C11—22no—
139C42×C11—42no—
140C42×C11C22×C411yescharacteristic
141C42×C11C22×C411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C22⋊Dic11—22no—
145(C2×D11)⋊C4—24no—
146(C2×D11)⋊C4—24no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—82no—
149(C2×D11)⋊C4C22⋊C414yes—
150(C2×D11)⋊C4C22⋊C414yes—
151C4⋊Dic11—24no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—42no—
156C4⋊Dic11C22⋊C412yes—
157C4⋊Dic11C22⋊C412yes—
158C4⋊Dic11C22×C412yes—
159Dic11⋊C4—24no—
160Dic11⋊C4—24no—
161Dic11⋊C4—22no—
162Dic11⋊C4—22no—
163C4×Dic11—22no—
164C4×Dic11—82no—
165C2×C11⋊C8—22no—
166#4313—84no—
167#3501—111no—
168#2975—111no—
169#2357—111no—
170#1518—111no—
171#1518—111no—
172#1511—114no—
173#1508—114no—
174#1503—111no—
175#1503D1111yescharacteristic, complemented
176C23×C11C22×D411yescharacteristic
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11C2×C22⋊C414yes—
182Q8×C11—42no—
183Q8×C11—81no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11C2×C22⋊C411yescharacteristic
195C2×C4×C11C2×C22⋊C411yescharacteristic
196C2×C4×C11C2×C22⋊C411yescharacteristic
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11#13712yes—
199C2×C4×C11#13712yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11C2×C22⋊C414yes—
209D44—24no—
210D44—24no—
211C4×D11—44no—
212C4×D11—44no—
213C4×D11—84no—
214C4×D11—84no—
215Dic22—42no—
216Dic22—84no—
217Dic22—81no—
218C8×C11—42no—
219C11⋊C8—42no—
220#554—112no—
221#554—112no—
222#554—222no—
223#554—222no—
224D4×Q8—112no—
225D4×Q8—112no—
226#544—221no—
227#543—222no—
228#533—111no—
229#533C2×D1111yescharacteristic
230C2×C22⋊Q8—114no—
231#518—221no—
232C2×C4×D4—111no—
233#436—222no—
234#436—222no—
235#431—111no—
236#431C2×D1111yescharacteristic
237#407—114no—
238#390—221no—
239#388—222no—
240#382—111no—
241#381—112no—
242C4×C4⋊C4—221no—
243C4×C4⋊C4C2×D1111yescharacteristic
244C4×C22⋊C4—112no—
245#328—114no—
246#328—114no—
247#328—112no—
248#328—112no—
249#328C2×D1112yes—
250#328C2×D1112yes—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11C22×C22⋊C411yescharacteristic
254C22×C11C2×#13711yescharacteristic
255C22×C11C2×#13711yescharacteristic
256C2×D11—24no—
257C2×D11—24no—
258C2×D11—24no—
259C2×D11—82no—
260C2×D11—82no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—81no—
269C4×C11#41912yes—
270C4×C11#41912yes—
271Dic11—24no—
272Dic11—42no—
273Dic11—42no—
274Dic11—82no—
275C22×Q8—114no—
276C22×D4—111no—
277C23×C4—112no—
278C2×M16—224no—
279C4⋊Q8—111no—
280C4⋊Q8—111no—
281C4⋊Q8—222no—
282C4⋊Q8—222no—
283C4⋊Q8C4×D1111yescharacteristic
284C4⋊Q8C4×D1111yescharacteristic
285#125—21no—
286#125—222no—
287#125—222no—
288#125—221no—
289C22⋊Q8—21no—
290C22⋊Q8—114no—
291C22⋊Q8—112no—
292C22⋊Q8—114no—
293C22⋊Q8—224no—
294C22⋊Q8—224no—
295C22⋊Q8—224no—
296C22⋊Q8—224no—
297C22⋊Q8—224no—
298C22⋊Q8—224no—
299C22⋊Q8—221no—
300C22⋊Q8C22×D1112yes—
301C4×Q8—21no—
302C4×Q8—112no—
303C4×Q8—221no—
304C4×Q8C4×D1112yes—
305C4×D4—112no—
306C4×D4—112no—
307C4×D4—112no—
308C4×D4—112no—
309C4×D4—222no—
310C4×D4—222no—
311C4×D4—222no—
312C4×D4—222no—
313#117—21no—
314#117—221no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—114no—
318C2×C4⋊C4—224no—
319C2×C4⋊C4—221no—
320C2×C22⋊C4—112no—
321C2×C22⋊C4—224no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—222no—
324C2×C42—21no—
325C2×C42—222no—
326C2×C42C22×D1111yescharacteristic
327C4⋊C8—21no—
328C4⋊C8—221no—
329C22⋊C8—112no—
330C22⋊C8—224no—
331C22⋊C8C22×D1112yes—
332C4×C8—21no—
333C4×C8—221no—
334#95—112no—
335#95—222no—
336#95—221no—
337#95C22×D1111yescharacteristic
338#95C22×D1111yescharacteristic
339C2×C11—21no—
340C2×C11—21no—
341C2×C11#288311yescharacteristic
342C2×C11C2×#41911yescharacteristic
343C2×C11#290111yescharacteristic
344D11—44no—
345C24—112no—
346C2×Q8—21no—
347C2×Q8—112no—
348C2×Q8—224no—
349C2×Q8—221no—
350C2×Q8—884no—
351C2×Q8C2×C4×D1112yes—
352C2×D4—112no—
353C2×D4—112no—
354C2×D4—222no—
355C2×D4—222no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—112no—
359C22×C4—114no—
360C22×C4—114no—
361C22×C4—224no—
362C22×C4—224no—
363C22×C4—222no—
364C22×C4—882no—
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4C23×D1111yescharacteristic
368M16—884no—
369C2×C8—22no—
370C2×C8—222no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—42no—
377C4⋊C4—112no—
378C4⋊C4—112no—
379C4⋊C4—112no—
380C4⋊C4—224no—
381C4⋊C4—224no—
382C4⋊C4—224no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C4⋊C4—221no—
387C4⋊C4—222no—
388C4⋊C4—442no—
389C4⋊C4C2×C4×D1112yes—
390C22⋊C4—22no—
391C22⋊C4—114no—
392C22⋊C4—114no—
393C22⋊C4—224no—
394C22⋊C4—224no—
395C22⋊C4—222no—
396C22⋊C4—444no—
397C22⋊C4—882no—
398C42—22no—
399C42—42no—
400C42—222no—
401C42—882no—
402C42C2×C4×D1111yescharacteristic
403C42C2×C4×D1111yescharacteristic
404C42D4×D1111yescharacteristic
405C42D4×D1111yescharacteristic
406C11#1762711yescharacteristic, complemented, Sylow
407C23—114no—
408C23—222no—
409C23—222no—
410C23—442no—
411C23—442no—
412C23C2×D4×D1111yescharacteristic
413Q8—42no—
414Q8—81no—
415Q8—442no—
416Q8—881no—
417Q8—884no—
418D4—224no—
419D4—224no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—114no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—444no—
434C2×C4—444no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—884no—
440C2×C4—884no—
441C2×C4C22⋊C4×D1111yescharacteristic
442C2×C4C22⋊C4×D1111yescharacteristic
443C2×C4C22⋊C4×D1111yescharacteristic
444C2×C4C22⋊C4×D1111yescharacteristic
445C2×C4#6696812yes—
446C2×C4#6697112yes—
447C2×C4C22×C4×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C8—42no—
450C8—442no—
451C22—21no—
452C22—21no—
453C22—224no—
454C22—224no—
455C22—224no—
456C22—882no—
457C22—882no—
458C22C2×C22⋊C4×D1111yescharacteristic
459C22C2×#6696811yescharacteristic
460C22C2×#6697111yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—81no—
469C4—224no—
470C4—442no—
471C4—442no—
472C4—882no—
473C4#1062241512yes—
474C4#1062241512yes—
475C2—21no—
476C2—21no—
477C2—444no—
478C2#1307707511yescharacteristic
479C2C2×#1062241511yescharacteristic
480C2#1307716011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1503C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenter#1503D11
hypocenterC11#17627
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
4. #13067181C2semidirect
5. #13067180C2semidirect
6. #13067147C2semidirect
7. #13067134C2semidirect
8. #13067114C2semidirect
9. C11×#1503C2semidirect
11. #10623261C4semidirect
12. #10623258C4semidirect
17. #10623110C4semidirect
18. Q8×D44C4semidirect
175. #1503D11semidirect
406. C11#17627semidirect

Maximal subgroups

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

subgroupindex
#130824172
#130776562
#130715872
#130671812
#130671802
#130671472
#130671342
#130671142
C11×#15032
#1762711