Finite Group Databasebeta

← #14719662

Subgroups — #14719662

Order 2816.

1214 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2#13077245C212yesmaximal
3#13066958C214yesmaximal, complemented
4#13066946C211yesmaximal, characteristic
5#13066945C212yesmaximal
6#13066938C214yesmaximal, complemented
7C11×#1463C211yesmaximal, characteristic
8C23×Dic22C411yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×Dic11⋊C4C411yescharacteristic
11C22×Dic11⋊C4C2211yescharacteristic
12C22×C4×Dic11C411yescharacteristic
13C22×C4×Dic11C411yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C2×#66940—22no—
16C2×#66940—22no—
17C2×#66940—22no—
18C2×#66940—22no—
19C2×#66940C412yes—
20C2×#66940C412yes—
21C2×#66940C2212yes—
22C2×#66940C2212yes—
23C11×#407C2212yes—
24#10622820C2212yes—
25#10622731—22no—
26M16×Dic11—22no—
27#10622332—22no—
28#10622332C2214yes—
29#10622331—22no—
30#10622331C2214yes—
31C11×#324C2214yes—
32#10622166C2214yes—
33#10622107C2218yes—
34C23×C4×C11C2×C411yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2×C411yescharacteristic
38C23×Dic11C2×C411yescharacteristic
39C23×Dic11C2×C411yescharacteristic
40C23×Dic11C2×C411yescharacteristic
41C22×Dic22—22no—
42C22×Dic22—22no—
43C22×Dic22—28no—
44C22×Dic22C2×C412yes—
45C22×Dic22C2×C412yes—
46C2×C11×M16—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2×C412yes—
50C2×C11×C4⋊C4C2312yes—
51C2×Dic11⋊C4—22no—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C2×Dic11⋊C4—22no—
55C2×Dic11⋊C4C2×C412yes—
56C2×Dic11⋊C4C2×C412yes—
57C2×Dic11⋊C4C2×C412yes—
58C2×Dic11⋊C4C2312yes—
59C2×C4×Dic11—21no—
60C2×C4×Dic11—21no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11—21no—
63C2×C4×Dic11—21no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11C2×C412yes—
68C2×C4×Dic11C2×C412yes—
69C2×C4×Dic11C2×C412yes—
70C2×C4×Dic11C2×C412yes—
71C2×C4×Dic11C2×C411yescharacteristic
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11D412yes—
74C2×C4×Dic11D412yes—
75C2×C4×Dic11D412yes—
76C2×C4×Dic11D412yes—
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C2×#4318—22no—
80#66940—24no—
81#66940—24no—
82#66940—24no—
83#66940—24no—
84#66940—24no—
85#66940—24no—
86#66940—24no—
87#66940—24no—
88C11×C22⋊C8—22no—
89C11×C22⋊C8C2314yes—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)C2314yes—
92#66879—24no—
93Dic11⋊C8—24no—
94Dic11⋊C8—24no—
95C8×Dic11—24no—
96#17365—111nomaximal, Sylow
97C24×C11C22×C411yescharacteristic
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—24no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—24no—
112C22×Dic11—24no—
113C22×Dic11—24no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—42no—
119C22×Dic11C22⋊C411yescharacteristic
120C22×Dic11C22⋊C411yescharacteristic
121C22×Dic11C22⋊C411yescharacteristic
122C22×Dic11C22⋊C412yes—
123C22×Dic11C22⋊C412yes—
124C22×Dic11C22⋊C411yescharacteristic
125C22×Dic11C22×C411yescharacteristic
126C22×Dic11C22×C411yescharacteristic
127C22×Dic11C22×C411yescharacteristic
128C22×Dic11C22×C412yes—
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C411yescharacteristic
131C2×Dic22—216no—
132C2×Dic22—216no—
133C2×Dic22—24no—
134C2×Dic22—24no—
135C2×Dic22—24no—
136C2×Dic22—24no—
137C2×Dic22—24no—
138C2×Dic22M1618yescomplemented
139C11×M16—44no—
140C2×C8×C11—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143Dic11⋊C4—24no—
144Dic11⋊C4—24no—
145Dic11⋊C4—24no—
146Dic11⋊C4—24no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C4×Dic11—22no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C4×Dic11C22⋊C412yes—
156C4×Dic11C22⋊C412yes—
157C4×Dic11C22⋊C412yes—
158C4×Dic11C22⋊C412yes—
159C4×Dic11C2×D412yes—
160C4×Dic11C2×D412yes—
161C4×Dic11C2×D412yes—
162C4×Dic11C2×D412yes—
163#4318—44no—
164C2×C11⋊C8—24no—
165C22×C4×Q8—111no—
166#2920—112no—
167#1467—114no—
168#1463—112no—
169#1463—111no—
170#1463D1111yescharacteristic
171#1461—114no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11C2×C22⋊C411yescharacteristic
176C23×C11C2×C22⋊C411yescharacteristic
177C23×C11C23×C411yescharacteristic
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—22no—
184C2×C4×C11—41no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11C2×C22⋊C412yes—
191C2×C4×C11C2×M1614yes—
192C2×C4×C11C22×D412yes—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11#10114yes—
210C2×Dic11C2×C22⋊C411yescharacteristic
211C2×Dic11C2×C22⋊C411yescharacteristic
212C2×Dic11C2×C22⋊C412yes—
213C2×Dic11C2×C22⋊C412yes—
214C2×Dic11C2×C22⋊C411yescharacteristic
215C2×Dic11C2×C22⋊C411yescharacteristic
216C2×Dic11C2×M1614yes—
217C2×Dic11C2×M1614yes—
218Dic22—216no—
219Dic22—216no—
220C8×C11—44no—
221C11⋊C8—44no—
222C23×Q8—111no—
223C2×C4×Q8—112no—
224C2×C4×Q8—112no—
225C2×C4×Q8—112no—
226C2×C4×Q8—112no—
227C2×C4×Q8—222no—
228C2×C4×Q8—222no—
229C2×C4×Q8—222no—
230C2×C4×Q8—222no—
231C22×C4⋊C4—111no—
232C22×C4⋊C4—111no—
233C22×C4⋊C4C2×D1111yescharacteristic
234C22×C42—111no—
235C22×C42—111no—
236C22×C42—111no—
237#432—114no—
238#432—222no—
239#431—114no—
240#431—222no—
241#423—222no—
242#407—112no—
243#407C2×D1112yes—
244C4×M16—222no—
245#324—114no—
246#324—118no—
247#324C2×D1114yes—
248C22×C11—28no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11#41012yes—
256C22×C11C2×#10112yes—
257C22×C11C22×C22⋊C411yescharacteristic
258C22×C11C22×M1612yes—
259C4×C11—24no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—42no—
263Dic11—22no—
264Dic11—24no—
265Dic11—21no—
266Dic11—21no—
267Dic11—42no—
268Dic11#40714yes—
269Dic11C2×#10112yes—
270Dic11C2×#10112yes—
271C22×Q8—112no—
272C22×Q8—112no—
273C22×Q8—222no—
274C22×Q8—222no—
275C22×Q8—228no—
276C23×C4—111no—
277C23×C4—111no—
278C23×C4—111no—
279C23×C4—111no—
280C23×C4C4×D1111yescharacteristic
281C23×C4C4×D1111yescharacteristic
282C23×C4C22×D1111yescharacteristic
283C2×M16—22no—
284C2×M16—222no—
285C4×Q8—224no—
286C4×Q8—224no—
287C4×Q8—224no—
288C4×Q8—224no—
289C4×Q8—224no—
290C4×Q8—224no—
291C4×Q8—224no—
292C4×Q8—224no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—112no—
296C2×C4⋊C4—112no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4—222no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4C4×D1112yes—
304C2×C4⋊C4C22×D1112yes—
305C2×C42—111no—
306C2×C42—111no—
307C2×C42—112no—
308C2×C42—112no—
309C2×C42—112no—
310C2×C42—112no—
311C2×C42—111no—
312C2×C42—111no—
313C2×C42—112no—
314C2×C42—112no—
315C2×C42—112no—
316C2×C42—112no—
317C2×C42—221no—
318C2×C42—221no—
319C2×C42—221no—
320C2×C42—221no—
321C2×C42—221no—
322C2×C42—221no—
323C2×C42—221no—
324C2×C42—221no—
325C4⋊C8—224no—
326C4⋊C8—224no—
327C22⋊C8—22no—
328C22⋊C8—114no—
329C22⋊C8—222no—
330C22⋊C8C22×D1114yes—
331#97—224no—
332C4×C8—224no—
333C2×C11—22no—
334C2×C11—22no—
335C2×C11—22no—
336C2×C11C2×#40711yescharacteristic
337C2×C11C2×#41011yescharacteristic
338C2×C11C22×#10111yescharacteristic
339C24C2×C4×D1111yescharacteristic
340C2×Q8—118no—
341C2×Q8—224no—
342C2×Q8—224no—
343C2×Q8—224no—
344C2×Q8—224no—
345C2×Q8—2216no—
346C2×Q8—2216no—
347C2×Q8—224no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—24no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—111no—
358C22×C4—111no—
359C22×C4—111no—
360C22×C4—112no—
361C22×C4—112no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—112no—
366C22×C4—112no—
367C22×C4—224no—
368C22×C4—224no—
369C22×C4—224no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—442no—
375C22×C4C2×C4×D1112yes—
376C22×C4C2×C4×D1112yes—
377C22×C4C2×C4×D1111yescharacteristic
378C22×C4D4×D1112yes—
379C22×C4D4×D1112yes—
380C22×C4C23×D1111yescharacteristic
381M16—44no—
382M16—444no—
383C2×C8—24no—
384C2×C8—224no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—224no—
388C4⋊C4—224no—
389C4⋊C4—224no—
390C4⋊C4—224no—
391C42—112no—
392C42—112no—
393C42—112no—
394C42—112no—
395C42—112no—
396C42—112no—
397C42—112no—
398C42—112no—
399C42—222no—
400C42—222no—
401C42—222no—
402C42—222no—
403C42—222no—
404C42—222no—
405C42—222no—
406C42—222no—
407C11#1736511yescharacteristic, complemented, Sylow
408C23—22no—
409C23—22no—
410C23—22no—
411C23C22⋊C4×D1111yescharacteristic
412C23C22⋊C4×D1111yescharacteristic
413C23C22×C4×D1111yescharacteristic
414Q8—2216no—
415Q8—2216no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—111no—
429C2×C4—111no—
430C2×C4—112no—
431C2×C4—114no—
432C2×C4—114no—
433C2×C4—111no—
434C2×C4—111no—
435C2×C4—112no—
436C2×C4—114no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—224no—
444C2×C4—224no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4C22⋊C4×D1112yes—
454C2×C4M16×D1114yes—
455C2×C4C2×D4×D1112yes—
456C8—44no—
457C8—444no—
458C22—28no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22#1062235312yes—
466C22D11×#10112yes—
467C22C2×C22⋊C4×D1111yescharacteristic
468C22C2×M16×D1112yes—
469C4—24no—
470C4—22no—
471C4—22no—
472C4—42no—
473C4—114no—
474C4—112no—
475C4—112no—
476C4—222no—
477C4—224no—
478C4—221no—
479C4—221no—
480C4—442no—
481C2—22no—
482C2—22no—
483C2—22no—
484C2D11×#40711yescharacteristic
485C2C2×#1062235311yescharacteristic
486C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1463C2
socleC22×C11C22×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1463D11
hypocenterC11#17365
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #13066958C2semidirect
6. #13066938C2semidirect
138. C2×Dic22M16semidirect
407. C11#17365semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
#130772452
#130669582
#130669462
#130669452
#130669382
C11×#14632
#1736511