Finite Group Databasebeta

← #14645716

Subgroups — #14645716

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082435C211yesmaximal, characteristic
2#13069538C211yesmaximal, characteristic, complemented
3#13068636C211yesmaximal, characteristic
4#13067304C211yesmaximal, characteristic, complemented
5#13067296C211yesmaximal, characteristic, complemented
6#13067116C211yesmaximal, characteristic, complemented
7C11×#1477C211yesmaximal, characteristic
8C4×C11×#41C2211yescharacteristic
9#10623358—21no—
10#10623101—21no—
11Q8×Dic22C412yescomplemented
12#10623074—22no—
13#10623074C412yescomplemented
14D4×Dic22—22no—
15D4×Dic22—21no—
16#10623050—21no—
17#10623050—22no—
18#10623001—21no—
19#10623001C2211yescharacteristic
20C2×#66922—21no—
21C2×#66922C2211yescharacteristic
22C11×#431C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×#66901—21no—
25C2×#66880—22no—
26C4×C4⋊Dic11C2211yescharacteristic
27#10622537C2211yescharacteristic
28C11×Q8⋊C8—21no—
29C11×D4⋊C8—21no—
30#10622170—21no—
31#10622120—21no—
32#10622119—22no—
33#10622119—21no—
34#10622105—22no—
35C2×C11×#41D411yescharacteristic
36C22×Dic22—22no—
37C22×Dic22D412yes—
38C22×C8×C11—21no—
39C4×Q8×C11C2×C411yescharacteristic
40C4×Q8×C11D411yescharacteristic
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11C2×C411yescharacteristic
44C4×D4×C11D411yescharacteristic
45C11×#117—21no—
46C11×#117D411yescharacteristic
47C2×C42×C11—21no—
48C2×C42×C11C2311yescharacteristic
49Q8×Dic11—22no—
50D4×Dic11—24no—
51D4×Dic11—22no—
52#66979—22no—
53#66979—21no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—21no—
59#66977—22no—
60#66977—21no—
61#66977—22no—
62#66977D412yes—
63C2×C4×Dic11—21no—
64C2×#4318—21no—
65#66943—24no—
66#66943—22no—
67#66941—24no—
68#66941—22no—
69#66931—24no—
70#66931—24no—
71#66931—24no—
72#66923—22no—
73#66923—21no—
74#66922—22no—
75#66922—22no—
76#66922—21no—
77#66922—21no—
78#66922—22no—
79#66922C2×C412yes—
80#66922D412yes—
81#66922D411yescharacteristic
82#66922D411yescharacteristic
83C4×Dic22—22no—
84C4×Dic22—22no—
85C4×Dic22—21no—
86C4×Dic22C2×C412yes—
87C11×C4⋊C8—21no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8—21no—
90C11×C22⋊C8—21no—
91C4×C8×C11—21no—
92#66901—42no—
93C11⋊#95—21no—
94#66880—44no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97#8425—111nomaximal, Sylow
98C11×#41—21no—
99C11×#41—21no—
100C11×#41SD1612yes—
101C11×#41Q1612yes—
102C2×Q8×C11C22⋊C411yescharacteristic
103C2×D4×C11—21no—
104C2×D4×C11C22⋊C411yescharacteristic
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×Dic11—24no—
112C22×Dic11—22no—
113C22×Dic11—41no—
114C2×Dic22—24no—
115C2×Dic22—22no—
116C2×Dic22—21no—
117C2×Dic22—42no—
118C2×Dic22—42no—
119C2×Dic22—82no—
120C2×Dic22—82no—
121C2×Dic22C22⋊C412yes—
122C2×Dic22C22⋊C414yes—
123C2×C8×C11—42no—
124C2×C8×C11—41no—
125C2×C8×C11—41no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4C22⋊C411yescharacteristic
129C11×C4⋊C4C22⋊C411yescharacteristic
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11C22×C411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C22⋊Dic11—24no—
141C22⋊Dic11—22no—
142C4⋊Dic11—24no—
143C4⋊Dic11—24no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—41no—
153C4⋊Dic11C22⋊C412yes—
154Dic11⋊C4—24no—
155Dic11⋊C4—24no—
156Dic11⋊C4—22no—
157Dic11⋊C4—22no—
158C4×Dic11—24no—
159C4×Dic11—22no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162#4318—41no—
163#4318—41no—
164C2×C11⋊C8—41no—
165#3503—111no—
166#1981—111no—
167#1806—111no—
168#1550—111no—
169#1548—111no—
170#1503—111no—
171#1477D1111yescharacteristic
172C23×C11—21no—
173C23×C11#12011yescharacteristic
174Q8×C11—21no—
175Q8×C11#10312yescomplemented
176D4×C11—22no—
177D4×C11—22no—
178D4×C11—21no—
179D4×C11#10312yescomplemented
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11C2×C22⋊C411yescharacteristic
192C2×C4×C11C2×C22⋊C411yescharacteristic
193C2×C4×C11C2×C22⋊C411yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11C2×SD1611yescharacteristic
198C2×C4×C11C2×Q1611yescharacteristic
199C2×C4×C11#13711yescharacteristic
200C2×C4×C11#13711yescharacteristic
201C2×Dic11—22no—
202C2×Dic11—24no—
203C2×Dic11—22no—
204C2×Dic11—42no—
205C2×Dic11—82no—
206C2×Dic11—84no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209Dic22—42no—
210Dic22—41no—
211Dic22—42no—
212Dic22—41no—
213Dic22—44no—
214Dic22—42no—
215Dic22—84no—
216C8×C11—81no—
217C8×C11—81no—
218C11⋊C8—81no—
219Q82—112no—
220#557—221no—
221#554—112no—
222#554—222no—
223D4×Q8—222no—
224D4×Q8—221no—
225#544—222no—
226#544—221no—
227#533—111no—
228#533—221no—
229C2×C4⋊Q8—111no—
230C2×C4⋊Q8—221no—
231#520—221no—
232C4×#41C2×D1111yescharacteristic
233#431C2×D1111yescharacteristic
234#423—111no—
235C2×C4⋊C8C2×D1111yescharacteristic
236C2×#104—221no—
237C2×#103—222no—
238C4×C4⋊C4—111no—
239#339—221no—
240#333—222no—
241#333—221no—
242#332—221no—
243#328—222no—
244Q8⋊C8—21no—
245D4⋊C8—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—22no—
249C22×C11—41no—
250C22×C11—41no—
251C22×C11#37911yescharacteristic
252C22×C11#44811yescharacteristic
253C22×C11#45111yescharacteristic
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—22no—
258C4×C11—41no—
259C4×C11—41no—
260C4×C11C2×#10311yescharacteristic
261C4×C11#41911yescharacteristic
262C4×C11#44811yescharacteristic
263C4×C11#45111yescharacteristic
264C4×C11#45311yescharacteristic
265C4×C11#45511yescharacteristic
266Dic11—44no—
267Dic11—42no—
268Dic11—42no—
269Dic11—82no—
270C2×#41D4411yescharacteristic
271C22×Q8—112no—
272C22×Q8—222no—
273C2×M16—221no—
274C22×C8—21no—
275C4⋊Q8—112no—
276C4⋊Q8—111no—
277C4⋊Q8—112no—
278C4⋊Q8—111no—
279C4⋊Q8—222no—
280C4⋊Q8—222no—
281C4⋊Q8—222no—
282C4⋊Q8—224no—
283C4⋊Q8—222no—
284C4⋊Q8—221no—
285C4⋊Q8—221no—
286#125—222no—
287#125—224no—
288#125—222no—
289#125—221no—
290C22⋊Q8—112no—
291C22⋊Q8—224no—
292C22⋊Q8—224no—
293C22⋊Q8—224no—
294C22⋊Q8—222no—
295C22⋊Q8—222no—
296C22⋊Q8—221no—
297C4×Q8—112no—
298C4×Q8—222no—
299C4×Q8—222no—
300C4×Q8—222no—
301C4×Q8—221no—
302C4×Q8C4×D1111yescharacteristic
303C4×Q8C22⋊D1111yescharacteristic
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—224no—
307C4×D4—222no—
308C4×D4C4×D1111yescharacteristic
309C4×D4C22⋊D1111yescharacteristic
310#117—21no—
311#117—222no—
312#117—221no—
313#117D4411yescharacteristic
314C2×C4⋊C4—222no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C42—21no—
320C2×C42—221no—
321C2×C42C22×D1111yescharacteristic
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8—21no—
325C4⋊C8—221no—
326C4⋊C8—221no—
327#104—442no—
328#103—444no—
329C22⋊C8—21no—
330C4×C8—21no—
331#95—221no—
332C2×C11—21no—
333C2×C11—21no—
334C2×C11—42no—
335C2×C11#178711yescharacteristic
336C2×C11#179211yescharacteristic
337C2×C11#179611yescharacteristic
338#41—21no—
339#41—21no—
340#41#431412yes—
341#41Dic4412yes—
342C2×Q8—112no—
343C2×Q8—114no—
344C2×Q8—224no—
345C2×Q8—221no—
346C2×Q8—222no—
347C2×Q8—442no—
348C2×Q8—442no—
349C2×Q8—882no—
350C2×Q8—882no—
351C2×Q8(C2×D11)⋊C411yescharacteristic
352C2×D4—21no—
353C2×D4(C2×D11)⋊C411yescharacteristic
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—224no—
358C22×C4—222no—
359C22×C4—441no—
360C22×C4C2×D4411yescharacteristic
361C22×C4D4×D1111yescharacteristic
362C22×C4D4×D1111yescharacteristic
363M16—441no—
364M16—441no—
365C2×C8—42no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—441no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—112no—
372C4⋊C4—224no—
373C4⋊C4—224no—
374C4⋊C4—224no—
375C4⋊C4—224no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—221no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—222no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C4⋊C4—441no—
387C4⋊C4(C2×D11)⋊C411yescharacteristic
388C4⋊C4(C2×D11)⋊C411yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—224no—
393C22⋊C4—222no—
394C42—21no—
395C42—21no—
396C42—21no—
397C42—224no—
398C42—222no—
399C42—441no—
400C42—441no—
401C42C2×C4×D1111yescharacteristic
402C42D4×D1111yescharacteristic
403C42D4×D1111yescharacteristic
404C42C2×C22⋊D1111yescharacteristic
405C11#842511yescharacteristic, complemented, Sylow
406C23—21no—
407C23#6693511yescharacteristic
408Q8—21no—
409Q8—444no—
410Q8—442no—
411Q8—442no—
412Q8—441no—
413Q8—442no—
414Q8—441no—
415Q8—884no—
416Q8#6688012yescomplemented
417D4—22no—
418D4—22no—
419D4—21no—
420D4#6688012yescomplemented
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—224no—
435C2×C4—442no—
436C2×C4—882no—
437C2×C4—884no—
438C2×C4—881no—
439C2×C4—881no—
440C2×C4C22⋊C4×D1111yescharacteristic
441C2×C4C22⋊C4×D1111yescharacteristic
442C2×C4#6693511yescharacteristic
443C2×C4C2×#431411yescharacteristic
444C2×C4C2×Dic4411yescharacteristic
445C2×C4#6696211yescharacteristic
446C2×C4#6696211yescharacteristic
447C2×C4C2×(C2×D11)⋊C411yescharacteristic
448C2×C4#6699011yescharacteristic
449C2×C4#6699011yescharacteristic
450C8—81no—
451C8—81no—
452C8—881no—
453C22—21no—
454C22—21no—
455C22—22no—
456C22—41no—
457C22—41no—
458C22#1062235111yescharacteristic
459C22#1062235211yescharacteristic
460C22#1062256811yescharacteristic
461C4—22no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—41no—
466C4—41no—
467C4—444no—
468C4—442no—
469C4—442no—
470C4—882no—
471C4#1062235111yescharacteristic
472C4#1062235211yescharacteristic
473C4C2×#6688011yescharacteristic
474C4#1062273311yescharacteristic
475C4#1062281111yescharacteristic
476C4#1062281511yescharacteristic
477C2—21no—
478C2—21no—
479C2—42no—
480C2#1306855211yescharacteristic
481C2#1306856811yescharacteristic
482C2#1306859011yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1477C2
socleC22×C11#379
prime radicalC2×C11×#41D4
cosocleC2×C42×C11C23
hypercenter#1477D11
hypocenterC11#8425
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #13069538C2semidirect
4. #13067304C2semidirect
5. #13067296C2semidirect
6. #13067116C2semidirect
11. Q8×Dic22C4semidirect
13. #10623074C4semidirect
175. Q8×C11#103semidirect
179. D4×C11#103semidirect
405. C11#8425semidirect
416. Q8#66880semidirect
420. D4#66880semidirect

Maximal subgroups

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

subgroupindex
#130824352
#130695382
#130686362
#130673042
#130672962
#130671162
C11×#14772
#842511