Finite Group Databasebeta

← #14720093

Subgroups — #14720093

Order 2816.

916 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2#13077703C212yesmaximal, complemented
3#13066984C214yesmaximal, complemented
4#13066967C212yesmaximal
5#13066960C211yesmaximal, characteristic, complemented
6#13066949C212yesmaximal, complemented
7#13066929C212yesmaximal, complemented
8C11×#1461C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66999C412yes—
11#10623115—22no—
12#10623115—22no—
13#10623115—24no—
14C2×#66951C412yes—
15C2×#66951C2212yes—
16C2×#66945C2212yes—
17C2×#66928C411yescharacteristic
18C2×#66928C2211yescharacteristic
19C2×C4×D44C411yescharacteristic
20C2×#66922C411yescharacteristic
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#10622106C2214yes—
36#10622106C2214yes—
37C22×Q8×C11C2×C411yescharacteristic
38C22×D44C2×C411yescharacteristic
39C22×C4×D11C2×C412yes—
40C22×Dic22C2×C411yescharacteristic
41C22×Dic22C2×C411yescharacteristic
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C4⋊C4C2311yescharacteristic
46C2×C11×C4⋊C4C2311yescharacteristic
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11C2311yescharacteristic
50#66999—24no—
51#66999—24no—
52C2×(C2×D11)⋊C4C2×C412yes—
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×(C2×D11)⋊C4C2×C412yes—
56C2×(C2×D11)⋊C4C2312yes—
57C2×C4⋊Dic11C2×C412yes—
58C2×C4⋊Dic11C2×C412yes—
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×Dic11⋊C4C2×C412yes—
61C2×Dic11⋊C4C2×C412yes—
62C2×C4×Dic11C2×C412yes—
63C2×C4×Dic11C2312yes—
64#66951—24no—
65#66951—24no—
66#66951—24no—
67#66951—24no—
68#66945—24no—
69#66945—24no—
70#66928—22no—
71#66928—22no—
72#66928—22no—
73#66928—22no—
74C4×D44—22no—
75C4×D44—21no—
76C4×D44—21no—
77#66922—22no—
78#66922—22no—
79C4×Dic22—22no—
80C4×Dic22—21no—
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#17428—111nomaximal, Sylow
97C23×D11C22×C412yes—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—41no—
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11C22×C412yes—
109C22×Dic11C22×C412yes—
110C22×Dic11C22×C412yes—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—42no—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—24no—
117C2×C4×D11—42no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×Dic22C22⋊C412yes—
123C2×Dic22C22⋊C412yes—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C42×C11—21no—
130C42×C11—21no—
131C42×C11—21no—
132C42×C11—21no—
133C42×C11C2×D412yes—
134C42×C11C2×D412yes—
135(C2×D11)⋊C4—22no—
136(C2×D11)⋊C4—22no—
137(C2×D11)⋊C4—24no—
138(C2×D11)⋊C4—24no—
139(C2×D11)⋊C4—24no—
140(C2×D11)⋊C4—24no—
141C4⋊Dic11—24no—
142C4⋊Dic11—24no—
143C4⋊Dic11C22⋊C412yes—
144C4⋊Dic11C22⋊C411yescharacteristic
145C4⋊Dic11C22⋊C411yescharacteristic
146Dic11⋊C4—22no—
147Dic11⋊C4—22no—
148Dic11⋊C4C22⋊C414yes—
149Dic11⋊C4C22⋊C414yes—
150C4×Dic11—22no—
151C4×Dic11—22no—
152C4×Dic11C2×D414yes—
153C4×Dic11C2×D414yes—
154C2×C11⋊C8—24no—
155C2×#556—111no—
156#2984—112no—
157#1473—114no—
158#1469—112no—
159#1467—111no—
160#1464—112no—
161#1461D1111yescharacteristic, complemented
162#1458—112no—
163C23×C11C23×C411yescharacteristic
164C22×D11—22no—
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—42no—
168C22×D11—42no—
169Q8×C11—44no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11C2×C22⋊C412yes—
184C2×C4×C11C2×C22⋊C411yescharacteristic
185C2×C4×C11C2×C22⋊C411yescharacteristic
186C2×C4×C11#13112yes—
187C2×C4×C11C22×D412yes—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11C2×C22⋊C412yes—
194C2×Dic11C2×C22⋊C412yes—
195C2×Dic11C2×C22⋊C414yes—
196D44—42no—
197D44—42no—
198C4×D11—44no—
199C4×D11—44no—
200Dic22—24no—
201Dic22—42no—
202Dic22—42no—
203Dic22—42no—
204C8×C11—42no—
205C8×C11—42no—
206C11⋊C8—44no—
207#556—222no—
208#556—224no—
209#556—222no—
210C2×C4⋊Q8—111no—
211C2×#126—112no—
212C2×#126—112no—
213C2×#124—111no—
214C2×#124—111no—
215C2×C22⋊Q8—112no—
216C2×C4×Q8—111no—
217C2×C4×Q8—111no—
218C2×C4×Q8C2×D1111yescharacteristic
219C2×C4×D4—111no—
220C2×#117—112no—
221#446—222no—
222#446—224no—
223C8×Q8—222no—
224#432—112no—
225#432—114no—
226#431—114no—
227#431C2×D1112yes—
228#324—112no—
229#324—112no—
230#324C2×D1111yescharacteristic
231#324C2×D1111yescharacteristic
232#324C2×D1112yes—
233#323—114no—
234#323—114no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11C22×C22⋊C411yescharacteristic
238C22×C11C2×#13111yescharacteristic
239C22×C11#56811yescharacteristic
240C2×D11—42no—
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—82no—
244C2×D11—82no—
245C4×C11—22no—
246C4×C11—22no—
247C4×C11—22no—
248C4×C11—21no—
249C4×C11—41no—
250C4×C11—41no—
251C4×C11—41no—
252C4×C11#41312yes—
253Dic11—22no—
254Dic11—22no—
255Dic11—24no—
256Dic11—42no—
257C22×Q8—111no—
258C22×Q8—111no—
259C22×Q8C4×D1111yescharacteristic
260C22×D4—111no—
261C23×C4—112no—
262C4⋊Q8—222no—
263C4⋊Q8—222no—
264#126—224no—
265#126—224no—
266#126—224no—
267#126—224no—
268#124—222no—
269#124—222no—
270#124—222no—
271#124—222no—
272C22⋊Q8—224no—
273C22⋊Q8—224no—
274C4×Q8—22no—
275C4×Q8—22no—
276C4×Q8—112no—
277C4×Q8—114no—
278C4×Q8—112no—
279C4×Q8—222no—
280C4×Q8—221no—
281C4×Q8—221no—
282C4×D4—222no—
283C4×D4—221no—
284C4×D4—221no—
285#117—224no—
286#117—224no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4C4×D1111yescharacteristic
293C2×C4⋊C4C22×D1111yescharacteristic
294C2×C4⋊C4C22×D1111yescharacteristic
295C2×C22⋊C4—112no—
296C2×C22⋊C4—112no—
297C2×C22⋊C4—112no—
298C2×C22⋊C4—112no—
299C2×C22⋊C4—112no—
300C2×C42—112no—
301C2×C42—112no—
302C2×C42C4×D1111yescharacteristic
303C2×C42C4×D1111yescharacteristic
304C2×C42C22×D1111yescharacteristic
305C4⋊C8—22no—
306C4⋊C8—224no—
307C4⋊C8—224no—
308C4⋊C8—222no—
309C22⋊C8—114no—
310C22⋊C8C22×D1112yes—
311C22⋊C8C22×D1112yes—
312#97—224no—
313#97—222no—
314C4×C8—22no—
315C4×C8—224no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11#288011yescharacteristic
319C2×C11#288411yescharacteristic
320C2×C11C2×#41311yescharacteristic
321D11—82no—
322C24—112no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—41no—
326C2×Q8—112no—
327C2×Q8—112no—
328C2×Q8—221no—
329C2×Q8—221no—
330C2×Q8—442no—
331C2×Q8—442no—
332C2×D4—221no—
333C2×D4—221no—
334C2×D4—442no—
335C22×C4—112no—
336C22×C4—112no—
337C22×C4—112no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—224no—
341C22×C4—442no—
342C22×C4C2×C4×D1111yescharacteristic
343C22×C4C2×C4×D1111yescharacteristic
344C22×C4C2×C4×D1111yescharacteristic
345C22×C4C2×C4×D1111yescharacteristic
346C22×C4C2×C4×D1111yescharacteristic
347C22×C4C2×C4×D1111yescharacteristic
348C22×C4C23×D1111yescharacteristic
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—224no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—112no—
356C4⋊C4—111no—
357C4⋊C4—111no—
358C4⋊C4—114no—
359C4⋊C4—114no—
360C4⋊C4—224no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—224no—
364C22⋊C4—224no—
365C22⋊C4—222no—
366C22⋊C4—222no—
367C22⋊C4—224no—
368C22⋊C4—224no—
369C22⋊C4—224no—
370C42—21no—
371C42—21no—
372C42—21no—
373C42—21no—
374C42—114no—
375C42—114no—
376C42—222no—
377C42—222no—
378C42D4×D1112yes—
379C42D4×D1112yes—
380C11#1742811yescharacteristic, complemented, Sylow
381C23—222no—
382C23—222no—
383C23—222no—
384C23—442no—
385C23—442no—
386C23C22×C4×D1111yescharacteristic
387Q8—44no—
388Q8—224no—
389Q8—442no—
390Q8—442no—
391Q8—442no—
392D4—442no—
393D4—442no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—112no—
408C2×C4—112no—
409C2×C4—114no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—444no—
414C2×C4—444no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4C22⋊C4×D1111yescharacteristic
418C2×C4C22⋊C4×D1112yes—
419C2×C4C22⋊C4×D1111yescharacteristic
420C2×C4#6695412yes—
421C2×C4C2×D4×D1112yes—
422C8—42no—
423C8—42no—
424C8—444no—
425C22—21no—
426C22—21no—
427C22—442no—
428C22—442no—
429C22—442no—
430C22—882no—
431C22—882no—
432C22C2×C22⋊C4×D1111yescharacteristic
433C22C2×#6695411yescharacteristic
434C22#1062327611yescharacteristic
435C4—22no—
436C4—22no—
437C4—22no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4—222no—
443C4—222no—
444C4—224no—
445C4—442no—
446C4#1062236412yes—
447C2—21no—
448C2—21no—
449C2—882no—
450C2#1307706211yescharacteristic
451C2#1307707811yescharacteristic
452C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1461C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1461D11
hypocenterC11#17428
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
2. #13077703C2semidirect
3. #13066984C2semidirect
5. #13066960C2semidirect
6. #13066949C2semidirect
7. #13066929C2semidirect
8. C11×#1461C2semidirect
161. #1461D11semidirect
380. C11#17428semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
#130777032
#130669842
#130669672
#130669602
#130669492
#130669292
C11×#14612
#1742811