Finite Group Databasebeta

← #14719664

Subgroups — #14719664

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2#13077246C212yesmaximal
3#13066960C211yesmaximal, characteristic, complemented
4#13066959C212yesmaximal, complemented
5#13066944C214yesmaximal
6#13066938C214yesmaximal, complemented
7C11×#1467C211yesmaximal, characteristic, complemented
8C22×Q8×D11C411yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×Q8×Dic11C411yescharacteristic
11C4×Q8×D11—22no—
12C4×Q8×D11—22no—
13C4×Q8×D11—22no—
14C4×Q8×D11—22no—
15C2×C4⋊C4×D11C411yescharacteristic
16C2×C4⋊C4×D11C2212yes—
17C2×#66940C411yescharacteristic
18C2×#66940C2212yes—
19C2×C42×D11C412yes—
20C2×C42×D11C2211yescharacteristic
21C2×C4×Dic22C412yes—
22C2×C4×Dic22C2211yescharacteristic
23C11×#432C2212yes—
24#10622539C2212yes—
25#10622450—22no—
26#10622446—22no—
27#10622339C2214yes—
28#10622331C2214yes—
29#10622320—22no—
30#10622318—22no—
31C11×#324C2214yes—
32#10622166C2214yes—
33#10622107C2218yes—
34C22×Q8×C11C2×C411yescharacteristic
35C2×Q8×D11—22no—
36C2×Q8×D11—22no—
37C2×Q8×D11—28no—
38C22×C4×D11C2×C412yes—
39C22×C4×D11C2×C411yescharacteristic
40C22×C4×D11C2×C411yescharacteristic
41C22×C4×D11C2×C412yes—
42C22×C4×D11C2311yescharacteristic
43C22×Dic22C2×C411yescharacteristic
44C22×Dic22C2×C412yes—
45C4×Q8×C11—22no—
46C4×Q8×C11—22no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11C2×C412yes—
50C2×C42×C11C2311yescharacteristic
51Q8×Dic11—22no—
52Q8×Dic11—22no—
53C2×C4⋊Dic11C2×C412yes—
54C2×C4⋊Dic11C2×C411yescharacteristic
55C2×Dic11⋊C4C2×C412yes—
56C2×Dic11⋊C4C2×C412yes—
57C2×Dic11⋊C4C2312yes—
58C2×C4×Dic11C2×C412yes—
59C2×C4×Dic11C2×C412yes—
60C2×C4×Dic11C2×C412yes—
61C2×C4×Dic11C2×C411yescharacteristic
62C2×C4×Dic11C2×C411yescharacteristic
63C2×C4×Dic11C2311yescharacteristic
64C2×#4313—24no—
65C4⋊C4×D11—22no—
66C4⋊C4×D11—22no—
67C4⋊C4×D11—24no—
68C4⋊C4×D11—24no—
69#66940—22no—
70#66940—22no—
71#66940—24no—
72#66940—24no—
73C42×D11—22no—
74C42×D11—22no—
75C42×D11—22no—
76C42×D11—22no—
77C42×D11D412yes—
78C42×D11D412yes—
79C42×D11D412yes—
80C42×D11D412yes—
81C4×Dic22—22no—
82C4×Dic22—22no—
83C4×Dic22—24no—
84C4×Dic22—24no—
85C11×C4⋊C8—22no—
86C11×C22⋊C8C2314yes—
87C11×#97—22no—
88C22⋊(C11⋊C8)C2314yes—
89(C2×D11)⋊C8—24no—
90Dic11⋊C8—24no—
91C8×Dic11—24no—
92C4⋊(C11⋊C8)—22no—
93#66867—22no—
94#17365—111nomaximal, Sylow
95C23×D11C22×C411yescharacteristic
96C2×Q8×C11—22no—
97C2×Q8×C11—24no—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C22×C412yes—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11C22×C411yescharacteristic
104C22×Dic11C22×C412yes—
105C22×Dic11C22×C412yes—
106C22×Dic11C22×C411yescharacteristic
107C22×Dic11C22×C411yescharacteristic
108Q8×D11—216no—
109Q8×D11—216no—
110C2×C4×D11—24no—
111C2×C4×D11—24no—
112C2×C4×D11—24no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—24no—
118C2×C4×D11—42no—
119C2×C4×D11—44no—
120C2×C4×D11C22⋊C411yescharacteristic
121C2×C4×D11C22⋊C411yescharacteristic
122C2×C4×D11C22⋊C411yescharacteristic
123C2×C4×D11C22⋊C412yes—
124C2×C4×D11C22⋊C412yes—
125C2×C4×D11C22⋊C411yescharacteristic
126C2×C4×D11C2×D412yes—
127C2×C4×D11C2×D412yes—
128C2×Dic22—24no—
129C2×Dic22—24no—
130C2×Dic22—24no—
131C2×Dic22—22no—
132C2×Dic22M1618yescomplemented
133C2×C8×C11—24no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—24no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11C2×D412yes—
139C42×C11C2×D412yes—
140C4⋊Dic11—24no—
141C4⋊Dic11—22no—
142Dic11⋊C4—24no—
143Dic11⋊C4—24no—
144Dic11⋊C4—24no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C4×Dic11C22⋊C412yes—
152C4×Dic11C22⋊C412yes—
153C4×Dic11C22⋊C412yes—
154C4×Dic11C22⋊C412yes—
155C4×Dic11C2×D412yes—
156C4×Dic11C2×D412yes—
157C2×C11⋊C8—24no—
158#4313—48no—
159C22×C4×Q8—111no—
160#2920—112no—
161#1467—112no—
162#1467—111no—
163#1467D1111yescharacteristic, complemented
164#1463—114no—
165#1461—114no—
166C23×C11C23×C411yescharacteristic
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—22no—
170C22×D11C2×C22⋊C411yescharacteristic
171C22×D11C2×C22⋊C411yescharacteristic
172Q8×C11—28no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11C2×C22⋊C411yescharacteristic
181C2×C4×C11C2×C22⋊C412yes—
182C2×C4×C11C2×C22⋊C411yescharacteristic
183C2×C4×C11C2×M1614yes—
184C2×C4×C11C22×D412yes—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11C2×C22⋊C411yescharacteristic
192C2×Dic11C2×C22⋊C412yes—
193C2×Dic11C2×C22⋊C412yes—
194C2×Dic11C2×C22⋊C411yescharacteristic
195C2×Dic11C2×M1614yes—
196C2×Dic11C2×M1614yes—
197C4×D11—28no—
198C4×D11—28no—
199C4×D11—24no—
200C4×D11—22no—
201C4×D11—22no—
202C4×D11—24no—
203C4×D11—24no—
204C4×D11—22no—
205C4×D11—42no—
206C4×D11—44no—
207C4×D11—44no—
208C4×D11#10114yes—
209Dic22—28no—
210Dic22—216no—
211C8×C11—44no—
212C11⋊C8—44no—
213C23×Q8—111no—
214C2×C4×Q8—111no—
215C2×C4×Q8—112no—
216C2×C4×Q8—111no—
217C2×C4×Q8—111no—
218C2×C4×Q8—112no—
219C2×C4×Q8—222no—
220C2×C4×Q8—222no—
221C2×C4×Q8—222no—
222C2×C4×Q8—222no—
223C2×C4×Q8C2×D1111yescharacteristic
224C22×C4⋊C4—112no—
225C22×C4⋊C4—111no—
226C22×C42—111no—
227C22×C42—112no—
228#432—112no—
229#432—222no—
230#432C2×D1112yes—
231#431—114no—
232#431—222no—
233#423—222no—
234#407—114no—
235C4×M16—222no—
236#324—114no—
237#324—118no—
238#324C2×D1114yes—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11C22×C22⋊C411yescharacteristic
242C22×C11C22×M1612yes—
243C2×D11—28no—
244C2×D11—21no—
245C2×D11—21no—
246C2×D11—21no—
247C2×D11—21no—
248C2×D11#41012yes—
249C2×D11C2×#10112yes—
250C4×C11—22no—
251C4×C11—24no—
252C4×C11—22no—
253C4×C11—21no—
254C4×C11—42no—
255C4×C11C2×#10112yes—
256Dic11—24no—
257Dic11—22no—
258Dic11—21no—
259Dic11—42no—
260Dic11#40714yes—
261Dic11C2×#10112yes—
262C22×Q8—112no—
263C22×Q8—111no—
264C22×Q8—222no—
265C22×Q8—222no—
266C22×Q8—228no—
267C22×Q8C4×D1111yescharacteristic
268C23×C4—111no—
269C23×C4—111no—
270C23×C4—111no—
271C23×C4—112no—
272C23×C4—112no—
273C2×M16—224no—
274C4×Q8—22no—
275C4×Q8—22no—
276C4×Q8—224no—
277C4×Q8—224no—
278C4×Q8—222no—
279C4×Q8—222no—
280C4×Q8—224no—
281C4×Q8—224no—
282C4×Q8—222no—
283C4×Q8—222no—
284C4×Q8—222no—
285C4×Q8—222no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—224no—
294C2×C4⋊C4—224no—
295C2×C4⋊C4C4×D1111yescharacteristic
296C2×C4⋊C4C22×D1112yes—
297C2×C42—111no—
298C2×C42—111no—
299C2×C42—111no—
300C2×C42—112no—
301C2×C42—112no—
302C2×C42—112no—
303C2×C42—112no—
304C2×C42—112no—
305C2×C42—112no—
306C2×C42—112no—
307C2×C42—222no—
308C2×C42—222no—
309C2×C42—222no—
310C2×C42—222no—
311C2×C42C4×D1112yes—
312C2×C42C22×D1111yescharacteristic
313C4⋊C8—22no—
314C4⋊C8—224no—
315C4⋊C8—222no—
316C22⋊C8—114no—
317C22⋊C8—224no—
318C22⋊C8C22×D1114yes—
319#97—22no—
320#97—222no—
321C4×C8—224no—
322C2×C11—22no—
323C2×C11C2×#40711yescharacteristic
324C2×C11C2×#41011yescharacteristic
325C2×C11C22×#10111yescharacteristic
326D11—22no—
327D11—22no—
328C24—111no—
329C2×Q8—22no—
330C2×Q8—24no—
331C2×Q8—118no—
332C2×Q8—224no—
333C2×Q8—224no—
334C2×Q8—224no—
335C2×Q8—2216no—
336C2×Q8—2216no—
337C2×Q8—222no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—112no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—111no—
346C22×C4—112no—
347C22×C4—112no—
348C22×C4—112no—
349C22×C4—112no—
350C22×C4—112no—
351C22×C4—224no—
352C22×C4—224no—
353C22×C4—224no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—224no—
359C22×C4—442no—
360C22×C4—444no—
361C22×C4C2×C4×D1111yescharacteristic
362C22×C4C2×C4×D1111yescharacteristic
363C22×C4C2×C4×D1112yes—
364C22×C4C2×C4×D1112yes—
365C22×C4C23×D1111yescharacteristic
366M16—448no—
367C2×C8—24no—
368C2×C8—224no—
369C4⋊C4—22no—
370C4⋊C4—24no—
371C4⋊C4—224no—
372C4⋊C4—224no—
373C4⋊C4—224no—
374C4⋊C4—222no—
375C4⋊C4—224no—
376C42—22no—
377C42—22no—
378C42—112no—
379C42—112no—
380C42—112no—
381C42—112no—
382C42—112no—
383C42—112no—
384C42—222no—
385C42—222no—
386C42—222no—
387C42—222no—
388C42—222no—
389C42—222no—
390C42D4×D1112yes—
391C42D4×D1112yes—
392C11#1736511yescharacteristic, complemented, Sylow
393C23—111no—
394C23—111no—
395C23—222no—
396C23—222no—
397C23—222no—
398C23C22×C4×D1111yescharacteristic
399Q8—28no—
400Q8—2216no—
401Q8—228no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—111no—
410C2×C4—112no—
411C2×C4—114no—
412C2×C4—114no—
413C2×C4—111no—
414C2×C4—112no—
415C2×C4—114no—
416C2×C4—224no—
417C2×C4—224no—
418C2×C4—222no—
419C2×C4—224no—
420C2×C4—222no—
421C2×C4—228no—
422C2×C4—228no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—442no—
429C2×C4—444no—
430C2×C4—444no—
431C2×C4—441no—
432C2×C4—442no—
433C2×C4C22⋊C4×D1111yescharacteristic
434C2×C4C22⋊C4×D1112yes—
435C2×C4C22⋊C4×D1111yescharacteristic
436C2×C4M16×D1114yes—
437C2×C4C2×D4×D1112yes—
438C8—44no—
439C8—444no—
440C22—21no—
441C22—21no—
442C22—112no—
443C22—112no—
444C22—228no—
445C22—221no—
446C22—221no—
447C22—221no—
448C22—221no—
449C22C2×C22⋊C4×D1111yescharacteristic
450C22C2×M16×D1112yes—
451C4—22no—
452C4—24no—
453C4—22no—
454C4—21no—
455C4—42no—
456C4—114no—
457C4—112no—
458C4—224no—
459C4—222no—
460C4—221no—
461C4—442no—
462C4D11×#10112yes—
463C2—22no—
464C2—222no—
465C2—222no—
466C2D11×#40711yescharacteristic
467C2D11×#41011yescharacteristic
468C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1467C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1467D11
hypocenterC11#17365
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
3. #13066960C2semidirect
4. #13066959C2semidirect
6. #13066938C2semidirect
7. C11×#1467C2semidirect
132. C2×Dic22M16semidirect
163. #1467D11semidirect
392. C11#17365semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130772462
#130669602
#130669592
#130669442
#130669382
C11×#14672
#1736511