Finite Group Databasebeta

← #14719655

Subgroups — #14719655

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2D11×#432C212yesmaximal, complemented
3#13066960C211yesmaximal, characteristic, complemented
4#13066956C212yesmaximal, complemented
5#13066949C214yesmaximal, complemented
6#13066933C214yesmaximal, complemented
7C11×#1467C211yesmaximal, characteristic, complemented
8C22×#4343C411yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×Q8×Dic11C411yescharacteristic
11C4×#4343—22no—
12C4×#4343—22no—
13C4×#4343—22no—
14C4×#4343—22no—
15C2×#66946C411yescharacteristic
16C2×#66946C2212yes—
17C2×#66945C411yescharacteristic
18C2×#66945C2212yes—
19C2×C4×D44C412yes—
20C2×C4×D44C2211yescharacteristic
21C2×C42×D11C412yes—
22C2×C42×D11C2211yescharacteristic
23C11×#432C2212yes—
24#10622539C2212yes—
25#10622448—22no—
26D11×C4⋊C8—22no—
27D11×C22⋊C8C2214yes—
28#10622332C2214yes—
29#10622318—22no—
30D11×#97—22no—
31C11×#324C2214yes—
32#10622166C2214yes—
33#10622106C2218yes—
34C22×Q8×C11C2×C411yescharacteristic
35C2×#4343—28no—
36C2×#4343—22no—
37C2×#4343—22no—
38C22×D44C2×C411yescharacteristic
39C22×D44C2×C412yes—
40C22×C4×D11C2×C412yes—
41C22×C4×D11C2×C411yescharacteristic
42C22×C4×D11C2×C412yes—
43C22×C4×D11C2×C412yes—
44C22×C4×D11C2×C411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C4×Q8×C11—22no—
47C4×Q8×C11—22no—
48C2×C11×C4⋊C4C2×C411yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11C2×C412yes—
51C2×C42×C11C2311yescharacteristic
52Q8×Dic11—22no—
53Q8×Dic11—22no—
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×(C2×D11)⋊C4C2×C412yes—
56C2×(C2×D11)⋊C4C2312yes—
57C2×C4⋊Dic11C2×C412yes—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×C4×Dic11C2×C412yes—
60C2×C4×Dic11C2×C412yes—
61C2×C4×Dic11C2×C411yescharacteristic
62C2×C4×Dic11C2×C411yescharacteristic
63C2×C4×Dic11C2311yescharacteristic
64C2×C8×D11—24no—
65#66946—24no—
66#66946—24no—
67#66946—22no—
68#66946—22no—
69#66945—22no—
70#66945—22no—
71#66945—24no—
72#66945—24no—
73C4×D44—24no—
74C4×D44—24no—
75C4×D44—22no—
76C4×D44—22no—
77C42×D11—22no—
78C42×D11—22no—
79C42×D11—22no—
80C42×D11—22no—
81C42×D11D412yes—
82C42×D11D412yes—
83C42×D11D412yes—
84C42×D11D412yes—
85C11×C4⋊C8—22no—
86C11×C22⋊C8C2314yes—
87C11×#97—22no—
88C22⋊(C11⋊C8)C2314yes—
89(C2×D11)⋊C8—24no—
90#66879—24no—
91Dic11⋊C8—24no—
92C4⋊(C11⋊C8)—22no—
93#66867—22no—
94#17363—111nomaximal, Sylow
95C23×D11C22×C412yes—
96C23×D11C22×C411yescharacteristic
97C2×Q8×C11—22no—
98C2×Q8×C11—24no—
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C22×C412yes—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11C22×C411yescharacteristic
105C22×Dic11C22×C411yescharacteristic
106C22×Dic11C22×C412yes—
107C22×Dic11C22×C411yescharacteristic
108#4343—216no—
109#4343—216no—
110C2×D44—24no—
111C2×D44—24no—
112C2×D44—24no—
113C2×D44—22no—
114C2×D44M1618yes—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—24no—
120C2×C4×D11—24no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—24no—
124C2×C4×D11—42no—
125C2×C4×D11—44no—
126C2×C4×D11—42no—
127C2×C4×D11—44no—
128C2×C4×D11C22⋊C412yes—
129C2×C4×D11C22⋊C412yes—
130C2×C4×D11C22⋊C412yes—
131C2×C4×D11C22⋊C412yes—
132C2×C4×D11C2×D412yes—
133C2×C4×D11C2×D412yes—
134C2×C8×C11—24no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—24no—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11C2×D412yes—
140C42×C11C2×D412yes—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4—24no—
144C4⋊Dic11—24no—
145C4⋊Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11C22⋊C411yescharacteristic
151C4×Dic11C22⋊C411yescharacteristic
152C4×Dic11C22⋊C411yescharacteristic
153C4×Dic11C22⋊C411yescharacteristic
154C4×Dic11C22⋊C412yes—
155C4×Dic11C22⋊C412yes—
156C4×Dic11C2×D412yes—
157C4×Dic11C2×D412yes—
158C2×C11⋊C8—24no—
159C8×D11—48no—
160C2×C4×#41—111no—
161C2×#432—112no—
162#1467—111no—
163#1467D1111yescharacteristic, complemented
164#1466—112no—
165#1464—114no—
166#1459—114no—
167C23×C11C23×C411yescharacteristic
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11C2×C22⋊C412yes—
175C22×D11C2×M1614yes—
176C22×D11C2×M1614yes—
177Q8×C11—28no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11C2×C22⋊C412yes—
186C2×C4×C11C2×C22⋊C411yescharacteristic
187C2×C4×C11C2×C22⋊C411yescharacteristic
188C2×C4×C11C2×M1614yes—
189C2×C4×C11C22×D412yes—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—41no—
194C2×Dic11—42no—
195C2×Dic11C2×C22⋊C411yescharacteristic
196C2×Dic11C2×C22⋊C411yescharacteristic
197C2×Dic11C2×C22⋊C411yescharacteristic
198C2×Dic11C2×C22⋊C412yes—
199C2×Dic11C2×C22⋊C411yescharacteristic
200D44—28no—
201D44—216no—
202C4×D11—28no—
203C4×D11—28no—
204C4×D11—24no—
205C4×D11—24no—
206C4×D11—24no—
207C4×D11—24no—
208C4×D11—42no—
209C4×D11—42no—
210C4×D11—44no—
211C4×D11—44no—
212C4×D11—44no—
213C4×D11—44no—
214C8×C11—44no—
215C11⋊C8—44no—
216C22×#41—111no—
217C4×#41—222no—
218C4×#41—222no—
219C4×#41—222no—
220C4×#41—222no—
221C2×C4×Q8—111no—
222C2×C4×Q8C2×D1111yescharacteristic
223C2×C4×D4—112no—
224C2×C4×D4—111no—
225C2×C4×D4—111no—
226C2×C4×D4—112no—
227C2×#117—112no—
228C2×#117—111no—
229C22×C42—111no—
230C22×C42—112no—
231#432—112no—
232#432—114no—
233#432—222no—
234#432—222no—
235#432C2×D1112yes—
236C2×C4⋊C8—222no—
237C2×C22⋊C8—114no—
238C2×#97—222no—
239#324—114no—
240#324C2×D1114yes—
241#323—118no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11C22×C22⋊C411yescharacteristic
245C22×C11C22×M1612yes—
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—24no—
249C2×D11—44no—
250C2×D11—44no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—44no—
254C2×D11#40714yes—
255C4×C11—22no—
256C4×C11—24no—
257C4×C11—22no—
258C4×C11—21no—
259C4×C11—42no—
260C4×C11#41312yes—
261Dic11—21no—
262Dic11—21no—
263Dic11—21no—
264Dic11—22no—
265Dic11—42no—
266Dic11#41012yes—
267C2×#41—222no—
268C2×#41—222no—
269C2×#41—228no—
270C22×Q8C4×D1111yescharacteristic
271C22×D4—112no—
272C22×D4—111no—
273C23×C4—111no—
274C23×C4—111no—
275C23×C4—111no—
276C23×C4—112no—
277C23×C4—112no—
278C23×C4—112no—
279C22×C8—224no—
280C4×Q8—22no—
281C4×Q8—22no—
282C4×Q8—222no—
283C4×Q8—222no—
284C4×D4—224no—
285C4×D4—224no—
286C4×D4—222no—
287C4×D4—222no—
288C4×D4—224no—
289C4×D4—224no—
290C4×D4—222no—
291C4×D4—222no—
292#117—224no—
293#117—224no—
294#117—222no—
295#117—222no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4C4×D1111yescharacteristic
299C2×C4⋊C4C22×D1112yes—
300C2×C22⋊C4—112no—
301C2×C22⋊C4—112no—
302C2×C22⋊C4—112no—
303C2×C42—111no—
304C2×C42—111no—
305C2×C42—111no—
306C2×C42—112no—
307C2×C42—112no—
308C2×C42—112no—
309C2×C42—112no—
310C2×C42—112no—
311C2×C42—112no—
312C2×C42—222no—
313C2×C42—222no—
314C2×C42—222no—
315C2×C42—222no—
316C2×C42C4×D1112yes—
317C2×C42C22×D1111yescharacteristic
318C4⋊C8—22no—
319C4⋊C8—224no—
320C4⋊C8—222no—
321C22⋊C8—114no—
322C22⋊C8—224no—
323C22⋊C8C22×D1114yes—
324#97—22no—
325#97—224no—
326#97—222no—
327C2×C11—22no—
328C2×C11C2×#40711yescharacteristic
329C2×C11C2×#41011yescharacteristic
330C2×C11C2×#41311yescharacteristic
331D11—24no—
332D11—44no—
333C24—111no—
334C24—112no—
335#41—2216no—
336#41—2216no—
337C2×Q8—22no—
338C2×Q8—24no—
339C2×D4—118no—
340C2×D4—224no—
341C2×D4—224no—
342C2×D4—224no—
343C2×D4—222no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—111no—
347C22×C4—112no—
348C22×C4—112no—
349C22×C4—112no—
350C22×C4—112no—
351C22×C4—112no—
352C22×C4—112no—
353C22×C4—112no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—224no—
359C22×C4—224no—
360C22×C4—224no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—442no—
364C22×C4—444no—
365C22×C4—442no—
366C22×C4—444no—
367C22×C4C2×C4×D1111yescharacteristic
368C22×C4C2×C4×D1111yescharacteristic
369C22×C4C2×C4×D1112yes—
370C22×C4C2×C4×D1112yes—
371C22×C4C23×D1111yescharacteristic
372C2×C8—24no—
373C2×C8—224no—
374C2×C8—448no—
375C4⋊C4—22no—
376C4⋊C4—24no—
377C4⋊C4—224no—
378C4⋊C4—222no—
379C22⋊C4—224no—
380C22⋊C4—224no—
381C22⋊C4—224no—
382C42—22no—
383C42—22no—
384C42—111no—
385C42—111no—
386C42—111no—
387C42—111no—
388C42—112no—
389C42—112no—
390C42—112no—
391C42—112no—
392C42—222no—
393C42—222no—
394C42—222no—
395C42—222no—
396C42D4×D1112yes—
397C42D4×D1112yes—
398C11#1736311yescharacteristic, complemented, Sylow
399C23—112no—
400C23—114no—
401C23—114no—
402C23—222no—
403C23—222no—
404C23—441no—
405C23—441no—
406C23—442no—
407C23—442no—
408C23C22×C4×D1111yescharacteristic
409Q8—28no—
410D4—2216no—
411D4—228no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—111no—
420C2×C4—111no—
421C2×C4—111no—
422C2×C4—111no—
423C2×C4—112no—
424C2×C4—224no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—228no—
428C2×C4—228no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—224no—
432C2×C4—222no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—444no—
436C2×C4—444no—
437C2×C4—444no—
438C2×C4—441no—
439C2×C4—444no—
440C2×C4—442no—
441C2×C4C22⋊C4×D1111yescharacteristic
442C2×C4C22⋊C4×D1112yes—
443C2×C4C22⋊C4×D1111yescharacteristic
444C2×C4M16×D1114yes—
445C2×C4C2×D4×D1112yes—
446C8—44no—
447C8—444no—
448C22—21no—
449C22—21no—
450C22—114no—
451C22—222no—
452C22—222no—
453C22—224no—
454C22—444no—
455C22—444no—
456C22—444no—
457C22—442no—
458C22—442no—
459C22C2×C22⋊C4×D1111yescharacteristic
460C22C2×M16×D1112yes—
461C4—22no—
462C4—24no—
463C4—22no—
464C4—21no—
465C4—42no—
466C4—112no—
467C4—221no—
468C4—221no—
469C4—221no—
470C4—222no—
471C4—442no—
472C4#1062236412yes—
473C2—22no—
474C2—224no—
475C2—444no—
476C2D11×#40711yescharacteristic
477C2D11×#41011yescharacteristic
478C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1467C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4343C4
cosocleC22×C4×C11C24
hypercenter#1467D11
hypocenterC11#17363
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. D11×#432C2semidirect
3. #13066960C2semidirect
4. #13066956C2semidirect
5. #13066949C2semidirect
6. #13066933C2semidirect
7. C11×#1467C2semidirect
163. #1467D11semidirect
398. C11#17363semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
D11×#4322
#130669602
#130669562
#130669492
#130669332
C11×#14672
#1736311