Finite Group Databasebeta

← #14720108

Subgroups — #14720108

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic
2#13077703C212yesmaximal
3#13066971C212yesmaximal
4#13066970C214yesmaximal
5#13066960C211yesmaximal, characteristic
6#13066958C212yesmaximal
7#13066938C212yesmaximal
8C11×#1461C211yesmaximal, characteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66997C412yes—
11#10623098—22no—
12#10623098—22no—
13#10623098—24no—
14C2×#66942C412yes—
15C2×#66942C2212yes—
16C2×#66940C2212yes—
17C2×#66923C411yescharacteristic
18C2×#66923C2211yescharacteristic
19C2×#66922C411yescharacteristic
20C2×C4×Dic22C411yescharacteristic
21C2×C4×Dic22C411yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#431C2212yes—
24#10622539C2212yes—
25#10622441—24no—
26#10622332C2214yes—
27#10622331C2214yes—
28#10622292—22no—
29C8×Dic22—22no—
30C11×#324C2211yescharacteristic
31C11×#324C2211yescharacteristic
32C11×#324C2212yes—
33#10622166C2212yes—
34#10622166C2212yes—
35#10622107C2214yes—
36#10622107C2214yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×Dic22C2×C412yes—
39C22×Dic22C2×C411yescharacteristic
40C4×Q8×C11—22no—
41C4×Q8×C11—22no—
42C2×C11×C4⋊C4C2×C411yescharacteristic
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C11×C4⋊C4C2311yescharacteristic
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48#66997—24no—
49#66997—24no—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×C4⋊Dic11C2×C411yescharacteristic
52C2×C4⋊Dic11C2×C412yes—
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×Dic11⋊C4C2×C412yes—
55C2×Dic11⋊C4C2×C412yes—
56C2×Dic11⋊C4C2×C412yes—
57C2×Dic11⋊C4C2×C412yes—
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2×C412yes—
60C2×Dic11⋊C4C2312yes—
61C2×C4×Dic11C2×C412yes—
62C2×C4×Dic11C2×C412yes—
63C2×C4×Dic11C2312yes—
64#66942—24no—
65#66942—24no—
66#66942—24no—
67#66942—24no—
68#66940—24no—
69#66940—24no—
70#66923—22no—
71#66923—22no—
72#66923—22no—
73#66923—22no—
74#66922—22no—
75#66922—22no—
76C4×Dic22—21no—
77C4×Dic22—22no—
78C4×Dic22—21no—
79C4×Dic22—21no—
80C4×Dic22—22no—
81C4×Dic22—21no—
82C4×Dic22D412yes—
83C4×Dic22D412yes—
84C4×Dic22D414yes—
85C11×C4⋊C8—22no—
86C11×C22⋊C8C2312yes—
87C11×C22⋊C8C2312yes—
88C4×C8×C11—22no—
89C22⋊(C11⋊C8)C2314yes—
90#66879—24no—
91Dic11⋊C8—24no—
92Dic11⋊C8—24no—
93C8×Dic11—24no—
94C4⋊(C11⋊C8)—22no—
95#66867—22no—
96#17430—111nomaximal, Sylow
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—41no—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11C22×C412yes—
108C22×Dic11C22×C412yes—
109C22×Dic11C22×C412yes—
110C22×Dic11C22×C412yes—
111C2×Dic22—24no—
112C2×Dic22—24no—
113C2×Dic22—24no—
114C2×Dic22—42no—
115C2×Dic22C22⋊C412yes—
116C2×Dic22C22⋊C411yescharacteristic
117C2×Dic22C22⋊C411yescharacteristic
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C42×C11—21no—
124C42×C11—21no—
125C42×C11—21no—
126C42×C11—21no—
127C42×C11C2×D412yes—
128C42×C11C2×D412yes—
129C4⋊Dic11—24no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—21no—
133C4⋊Dic11—21no—
134C4⋊Dic11C22⋊C412yes—
135C4⋊Dic11C22⋊C412yes—
136Dic11⋊C4—22no—
137Dic11⋊C4—22no—
138Dic11⋊C4—22no—
139Dic11⋊C4—22no—
140Dic11⋊C4—24no—
141Dic11⋊C4—24no—
142Dic11⋊C4—24no—
143Dic11⋊C4—24no—
144Dic11⋊C4C22⋊C414yes—
145Dic11⋊C4C22⋊C414yes—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11C2×D414yes—
151C4×Dic11C2×D414yes—
152C2×C11⋊C8—24no—
153C2×#557—111no—
154#2984—112no—
155#1470—112no—
156#1470—114no—
157#1467—112no—
158#1467—111no—
159#1461—112no—
160#1461D1111yescharacteristic
161C23×C11C23×C411yescharacteristic
162Q8×C11—44no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11C2×C22⋊C412yes—
177C2×C4×C11C2×C22⋊C411yescharacteristic
178C2×C4×C11C2×C22⋊C411yescharacteristic
179C2×C4×C11#13112yes—
180C2×C4×C11C22×D412yes—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—24no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—42no—
189C2×Dic11C2×C22⋊C412yes—
190C2×Dic11C2×C22⋊C414yes—
191C2×Dic11C2×C22⋊C412yes—
192Dic22—22no—
193Dic22—24no—
194Dic22—48no—
195Dic22#10114yes—
196C8×C11—42no—
197C8×C11—42no—
198C11⋊C8—44no—
199#557—222no—
200#557—222no—
201#557—224no—
202C2×C4⋊Q8—112no—
203C2×C4⋊Q8—111no—
204C2×#125—112no—
205C2×#125—112no—
206C2×#125—111no—
207C2×#125—111no—
208C2×C4×Q8—112no—
209C2×C4×Q8—111no—
210C2×C4×Q8—111no—
211C2×C4×Q8—111no—
212C2×C4×Q8C2×D1111yescharacteristic
213#446—222no—
214#446—224no—
215C8×Q8—222no—
216#432—112no—
217#432—114no—
218#431—114no—
219#431C2×D1112yes—
220#324—112no—
221#324—112no—
222#324—114no—
223#324—114no—
224#324C2×D1111yescharacteristic
225#324C2×D1111yescharacteristic
226#324C2×D1112yes—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11C22×C22⋊C411yescharacteristic
230C22×C11C2×#13111yescharacteristic
231C22×C11#56811yescharacteristic
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—21no—
236C4×C11—41no—
237C4×C11—41no—
238C4×C11—41no—
239C4×C11C2×#10112yes—
240Dic11—24no—
241Dic11—22no—
242Dic11—42no—
243Dic11—42no—
244Dic11C2×#10114yes—
245C22×Q8—111no—
246C22×Q8—112no—
247C22×Q8C4×D1111yescharacteristic
248C4⋊Q8—222no—
249C4⋊Q8—222no—
250C4⋊Q8—224no—
251C4⋊Q8—224no—
252#125—222no—
253#125—222no—
254#125—224no—
255#125—224no—
256#125—224no—
257#125—224no—
258#125—222no—
259#125—222no—
260C4×Q8—22no—
261C4×Q8—22no—
262C4×Q8—112no—
263C4×Q8—114no—
264C4×Q8—112no—
265C4×Q8—221no—
266C4×Q8—222no—
267C4×Q8—221no—
268C4×Q8—221no—
269C4×Q8—222no—
270C4×Q8—221no—
271C4×Q8—224no—
272C4×Q8—224no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—112no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—112no—
279C2×C4⋊C4—111no—
280C2×C4⋊C4—112no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4C4×D1111yescharacteristic
285C2×C4⋊C4C22×D1111yescharacteristic
286C2×C4⋊C4C22×D1111yescharacteristic
287C2×C42—112no—
288C2×C42—112no—
289C2×C42—112no—
290C2×C42C4×D1111yescharacteristic
291C2×C42C4×D1111yescharacteristic
292C2×C42C22×D1111yescharacteristic
293C4⋊C8—22no—
294C4⋊C8—224no—
295C4⋊C8—224no—
296C4⋊C8—222no—
297C22⋊C8—114no—
298C22⋊C8C22×D1112yes—
299C22⋊C8C22×D1112yes—
300#97—224no—
301#97—222no—
302C4×C8—22no—
303C4×C8—224no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11#288011yescharacteristic
307C2×C11#288411yescharacteristic
308C2×C11C22×#10111yescharacteristic
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—41no—
312C2×Q8—111no—
313C2×Q8—112no—
314C2×Q8—111no—
315C2×Q8—224no—
316C2×Q8—224no—
317C2×Q8—224no—
318C2×Q8—442no—
319C22×C4—112no—
320C22×C4—112no—
321C22×C4—112no—
322C22×C4—112no—
323C22×C4C2×C4×D1111yescharacteristic
324C22×C4C2×C4×D1111yescharacteristic
325C22×C4C2×C4×D1111yescharacteristic
326C22×C4C2×C4×D1111yescharacteristic
327C22×C4C2×C4×D1111yescharacteristic
328C22×C4C2×C4×D1111yescharacteristic
329C22×C4C23×D1111yescharacteristic
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—224no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—114no—
337C4⋊C4—114no—
338C4⋊C4—112no—
339C4⋊C4—112no—
340C4⋊C4—224no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—224no—
346C4⋊C4—224no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—224no—
352C4⋊C4—224no—
353C42—21no—
354C42—21no—
355C42—21no—
356C42—21no—
357C42—114no—
358C42—114no—
359C42—222no—
360C42—222no—
361C42—222no—
362C42—222no—
363C42D4×D1112yes—
364C42D4×D1112yes—
365C11#1743011yescharacteristic, complemented, Sylow
366C23C22×C4×D1111yescharacteristic
367Q8—44no—
368Q8—114no—
369Q8—224no—
370Q8—222no—
371Q8—448no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—112no—
386C2×C4—112no—
387C2×C4—114no—
388C2×C4—224no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—442no—
396C2×C4C22⋊C4×D1111yescharacteristic
397C2×C4C22⋊C4×D1112yes—
398C2×C4C22⋊C4×D1111yescharacteristic
399C2×C4#6695412yes—
400C2×C4C2×D4×D1112yes—
401C8—42no—
402C8—42no—
403C8—444no—
404C22—21no—
405C22—21no—
406C22C2×C22⋊C4×D1111yescharacteristic
407C22C2×#6695411yescharacteristic
408C22#1062327611yescharacteristic
409C4—22no—
410C4—22no—
411C4—22no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—114no—
417C4—224no—
418C4—222no—
419C4—442no—
420C4—442no—
421C4D11×#10112yes—
422C2—21no—
423C2—21no—
424C2#1307706211yescharacteristic
425C2#1307707811yescharacteristic
426C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutator, prime radicalC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1461C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#1461D11
hypocenterC11#17430
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
365. C11#17430semidirect

Maximal subgroups

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

subgroupindex
C2×#106230982
#130777032
#130669712
#130669702
#130669602
#130669582
#130669382
C11×#14612
#1743011