Finite Group Databasebeta

← #14719973

Subgroups — #14719973

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic
2#13077270C212yesmaximal, complemented
3#13066979C212yesmaximal, complemented
4#13066970C214yesmaximal, complemented
5#13066954C211yesmaximal, characteristic
6#13066947C212yesmaximal, complemented
7#13066927C212yesmaximal, complemented
8C11×#1459C211yesmaximal, characteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66988C412yes—
11C2×#66979C2211yescharacteristic
12C22×C4⋊Dic11C411yescharacteristic
13C2×#66977C411yescharacteristic
14C2×#66977C2211yescharacteristic
15#10623072—24no—
16#10623072—22no—
17#10623072—22no—
18C2×#66942C2212yes—
19C2×#66932C412yes—
20C2×#66930C2212yes—
21C2×#66923C411yescharacteristic
22C2×C4×Dic22C411yescharacteristic
23C2×C11×C22⋊C8C2212yes—
24#10622820C2212yes—
25#10622715—22no—
26#10622714—22no—
27#10622333—24no—
28#10622332C2214yes—
29#10622331C2214yes—
30C11×#324C2212yes—
31C11×#323C2211yescharacteristic
32C11×#323C2211yescharacteristic
33#10622166C2212yes—
34#10622163C2212yes—
35#10622107C2214yes—
36#10622107C2214yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2×C412yes—
41C22×Dic22C2×C411yescharacteristic
42C22×C8×C11—22no—
43C4×D4×C11—22no—
44C4×D4×C11—22no—
45C2×C11×C4⋊C4C2311yescharacteristic
46C2×C11×C22⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4C2311yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C22⋊Dic11C2×C412yes—
50C2×C22⋊Dic11C2×C412yes—
51C2×C22⋊Dic11C2×C412yes—
52#66988—24no—
53#66988—24no—
54#66979D414yes—
55#66979D412yes—
56#66979D412yes—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2×C411yescharacteristic
61C2×C4⋊Dic11C2×C412yes—
62C2×C4⋊Dic11C2×C411yescharacteristic
63C2×C4⋊Dic11C2×C411yescharacteristic
64#66977—22no—
65#66977—22no—
66#66977—22no—
67#66977—22no—
68C2×Dic11⋊C4C2×C412yes—
69C2×Dic11⋊C4C2×C412yes—
70C2×Dic11⋊C4C2×C412yes—
71C2×Dic11⋊C4C2×C412yes—
72C2×Dic11⋊C4C2312yes—
73C2×C4×Dic11C2×C412yes—
74C2×C4×Dic11C2312yes—
75C2×#4318—22no—
76#66942—24no—
77#66942—24no—
78#66932—24no—
79#66932—24no—
80#66930—24no—
81#66930—24no—
82#66923—22no—
83#66923—22no—
84C4×Dic22—22no—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C11×C22⋊C8—22no—
88C11×C22⋊C8C2312yes—
89C11×C22⋊C8C2312yes—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)C2314yes—
92#66879—24no—
93Dic11⋊C8—24no—
94Dic11⋊C8—24no—
95C8×Dic11—24no—
96#17413—111nomaximal, Sylow
97C24×C11C22×C411yescharacteristic
98C24×C11C22×C411yescharacteristic
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—41no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—24no—
116C22×Dic11—42no—
117C22×Dic11C22×C412yes—
118C22×Dic11C22×C412yes—
119C22×Dic11C22×C412yes—
120C22×Dic11C22×C412yes—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22—42no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—44no—
127C11×C4⋊C4—22no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—22no—
130C42×C11—21no—
131C42×C11—21no—
132C22⋊Dic11—24no—
133C22⋊Dic11—24no—
134C22⋊Dic11C22⋊C414yes—
135C22⋊Dic11C22⋊C414yes—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11C22⋊C412yes—
141C4⋊Dic11C22⋊C411yescharacteristic
142C4⋊Dic11C22⋊C411yescharacteristic
143C4⋊Dic11C22⋊C412yes—
144C4⋊Dic11C22⋊C412yes—
145Dic11⋊C4—22no—
146Dic11⋊C4—22no—
147Dic11⋊C4—24no—
148Dic11⋊C4—24no—
149Dic11⋊C4—24no—
150Dic11⋊C4—24no—
151C4×Dic11—22no—
152C4×Dic11—22no—
153C4×Dic11C2×D414yes—
154C4×Dic11C2×D414yes—
155#4318—44no—
156C2×C11⋊C8—24no—
157C2×#552—111no—
158#2924—112no—
159#1472—112no—
160#1470—114no—
161#1465—111no—
162#1464—112no—
163#1459D1111yescharacteristic
164#1458—112no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11C2×C22⋊C412yes—
174C23×C11#13112yes—
175C23×C11C23×C411yescharacteristic
176D4×C11—44no—
177C2×C4×C11—24no—
178C2×C4×C11—22no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11C2×C22⋊C411yescharacteristic
191C2×C4×C11C2×C22⋊C411yescharacteristic
192C2×C4×C11C22×D412yes—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—42no—
200C2×Dic11—44no—
201C2×Dic11—44no—
202C2×Dic11—42no—
203C2×Dic11C2×C22⋊C412yes—
204C2×Dic11C2×C22⋊C412yes—
205C2×Dic11C2×C22⋊C414yes—
206Dic22—42no—
207Dic22—42no—
208C8×C11—42no—
209C8×C11—42no—
210C11⋊C8—44no—
211#552—222no—
212#552—222no—
213#552—224no—
214C2×#126—112no—
215C2×#125—112no—
216C2×#125—111no—
217C2×#123—112no—
218C2×C22⋊Q8—111no—
219C2×C22⋊Q8—111no—
220C2×C4×Q8—111no—
221C2×C4×D4C2×D1111yescharacteristic
222C2×#117—111no—
223C2×#117—112no—
224C22×C4⋊C4—111no—
225#433—224no—
226#432—114no—
227#431—114no—
228#424—222no—
229#407—112no—
230C2×C22⋊C8C2×D1112yes—
231#405—222no—
232#324—112no—
233#324—114no—
234#324—114no—
235#324C2×D1112yes—
236#323—112no—
237#323C2×D1111yescharacteristic
238#323C2×D1111yescharacteristic
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11C22×C22⋊C411yescharacteristic
252C22×C11C2×#13111yescharacteristic
253C22×C11#56811yescharacteristic
254C4×C11—21no—
255C4×C11—22no—
256C4×C11—41no—
257C4×C11—41no—
258C4×C11—41no—
259C4×C11#41012yes—
260Dic11—22no—
261Dic11—22no—
262Dic11—24no—
263Dic11—42no—
264Dic11—42no—
265C22×Q8—111no—
266C22×D4C4×D1111yescharacteristic
267C23×C4—112no—
268C23×C4C4×D1111yescharacteristic
269C23×C4C22×D1111yescharacteristic
270C2×M16—222no—
271C22×C8—22no—
272#126—224no—
273#126—224no—
274#125—222no—
275#125—222no—
276#125—224no—
277#125—224no—
278#123—224no—
279#123—224no—
280C22⋊Q8—222no—
281C22⋊Q8—222no—
282C22⋊Q8—222no—
283C22⋊Q8—222no—
284C4×Q8—222no—
285C4×Q8—221no—
286C4×Q8—221no—
287C4×D4—22no—
288C4×D4—22no—
289#117—112no—
290#117—112no—
291#117—114no—
292#117—224no—
293#117—224no—
294C2×C4⋊C4—111no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—112no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4C22×D1111yescharacteristic
307C2×C22⋊C4—112no—
308C2×C22⋊C4—112no—
309C2×C22⋊C4—112no—
310C2×C22⋊C4C4×D1111yescharacteristic
311C2×C22⋊C4C22×D1111yescharacteristic
312C2×C42—112no—
313C2×C42—112no—
314C2×C42C4×D1111yescharacteristic
315C4⋊C8—224no—
316C4⋊C8—224no—
317C22⋊C8—22no—
318C22⋊C8—114no—
319C22⋊C8—222no—
320C22⋊C8C22×D1112yes—
321C22⋊C8C22×D1112yes—
322#97—224no—
323C4×C8—224no—
324C2×C11—21no—
325C2×C11—21no—
326C2×C11—42no—
327C2×C11—42no—
328C2×C11#288011yescharacteristic
329C2×C11C2×#41011yescharacteristic
330C2×C11#288911yescharacteristic
331C24C2×C4×D1111yescharacteristic
332C24C2×C4×D1111yescharacteristic
333C2×Q8—221no—
334C2×Q8—221no—
335C2×Q8—442no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—41no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—112no—
344C22×C4—112no—
345C22×C4—112no—
346C22×C4—112no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—224no—
350C22×C4—442no—
351C22×C4C2×C4×D1111yescharacteristic
352C22×C4C2×C4×D1111yescharacteristic
353C22×C4C2×C4×D1111yescharacteristic
354C22×C4C2×C4×D1111yescharacteristic
355C22×C4D4×D1112yes—
356C22×C4D4×D1112yes—
357C22×C4C23×D1111yescharacteristic
358M16—444no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—44no—
362C2×C8—224no—
363C4⋊C4—22no—
364C4⋊C4—112no—
365C4⋊C4—111no—
366C4⋊C4—111no—
367C4⋊C4—112no—
368C4⋊C4—112no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—224no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—224no—
375C4⋊C4—224no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—224no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—114no—
382C22⋊C4—114no—
383C22⋊C4—224no—
384C22⋊C4—224no—
385C42—21no—
386C42—21no—
387C42—114no—
388C42—114no—
389C42—222no—
390C42—222no—
391C11#1741311yescharacteristic, complemented, Sylow
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23C22⋊C4×D1112yes—
401C23#6695412yes—
402C23C22×C4×D1111yescharacteristic
403Q8—442no—
404Q8—442no—
405D4—44no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—112no—
420C2×C4—112no—
421C2×C4—114no—
422C2×C4—222no—
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—442no—
432C2×C4C22⋊C4×D1111yescharacteristic
433C2×C4C22⋊C4×D1111yescharacteristic
434C2×C4C2×D4×D1112yes—
435C8—42no—
436C8—42no—
437C8—444no—
438C22—21no—
439C22—21no—
440C22—22no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—42no—
445C22—42no—
446C22—41no—
447C22—41no—
448C22—81no—
449C22—81no—
450C22C2×C22⋊C4×D1111yescharacteristic
451C22C2×#6695411yescharacteristic
452C22#1062327611yescharacteristic
453C4—22no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—222no—
459C4—222no—
460C4—224no—
461C4—442no—
462C4—442no—
463C4#1062235312yes—
464C2—21no—
465C2—21no—
466C2—42no—
467C2—42no—
468C2#1307706211yescharacteristic
469C2C2×#1062235311yescharacteristic
470C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1459C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1459D11
hypocenterC11#17413
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #13077270C2semidirect
3. #13066979C2semidirect
4. #13066970C2semidirect
6. #13066947C2semidirect
7. #13066927C2semidirect
391. C11#17413semidirect

Maximal subgroups

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

subgroupindex
C2×#106230722
#130772702
#130669792
#130669702
#130669542
#130669472
#130669272
C11×#14592
#1741311