Finite Group Databasebeta

← #14739034

Subgroups — #14739034

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078711C211yesmaximal, characteristic
2#13078620C211yesmaximal, characteristic
3#13077639C211yesmaximal, characteristic
4#13068064C212yesmaximal, complemented
5#13068036C212yesmaximal, complemented
6#13068002C212yesmaximal, complemented
7#13067988C212yesmaximal, complemented
8#13067396C211yesmaximal, characteristic, complemented
9#13067326C211yesmaximal, characteristic, complemented
10#13067281C211yesmaximal, characteristic, complemented
11C11×#3231C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C11×#533C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C11×#500C2211yescharacteristic, complemented
16C11×#498C2211yescharacteristic, complemented
17C11×#487C2211yescharacteristic, complemented
18C11×#487C2211yescharacteristic, complemented
19C11×#485—22no—
20C11×#479—22no—
21C11×#431C2211yescharacteristic
22#10622700C2212yes—
23#10622697C2212yes—
24#10622696C2212yes—
25#10622696C2212yes—
26#10622659—21no—
27#10622659—21no—
28#10622657—21no—
29#10622656—21no—
30#10622639—22no—
31C4×#4325—22no—
32#10622539C2211yescharacteristic
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622447—22no—
36D11×C22⋊C8—22no—
37C8×D44C2212yes—
38C8×D44C2212yes—
39#10622185C2212yescomplemented
40#10622185C2212yescomplemented
41#10622185C2212yescomplemented
42#10622184C2212yescomplemented
43#10622096C2212yescomplemented
44#10622095C2212yescomplemented
45C22×D44D411yescharacteristic
46C22×C4×D11—21no—
47C11×C4⋊Q8C2311yescharacteristic
48C11×C4⋊Q8C2311yescharacteristic
49C11×C4⋊Q8C2311yescharacteristic
50C11×C4⋊Q8C2311yescharacteristic
51C11×#125—21no—
52C11×#125—21no—
53C11×C22⋊Q8—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C4×Q8×C11—21no—
58C4×Q8×C11—21no—
59C4×Q8×C11—21no—
60C4×Q8×C11—21no—
61C11×#117—21no—
62C11×#117—21no—
63C2×C42×C11C2311yescharacteristic
64C2×#4325—22no—
65C2×#4325—22no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C8×D11—22no—
69C2×C8×D11—22no—
70C4×D44—21no—
71C4×D44—21no—
72C4×D44D412yes—
73C4×D44C2312yes—
74C11×#107—22no—
75C11×#106—22no—
76C11×C4⋊C8D412yes—
77C11×#103—22no—
78C11×#103—22no—
79C11×C22⋊C8D412yes—
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66899—22no—
83#66899—22no—
84C22⋊(C11⋊C8)—21no—
85C22⋊(C11⋊C8)—21no—
86C22⋊(C11⋊C8)—21no—
87(C2×D11)⋊C8—22no—
88(C2×D11)⋊C8—22no—
89#66873—22no—
90#66873—22no—
91#66872—22no—
92#66871—22no—
93C4⋊(C11⋊C8)C2312yes—
94C4⋊(C11⋊C8)C2312yes—
95C4⋊(C11⋊C8)C2312yes—
96#66867—21no—
97C4×C11⋊C8—21no—
98C4×C11⋊C8—21no—
99#19395—111nomaximal, Sylow
100C23×D11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×Dic11—21no—
109C2×D44—24no—
110C2×D44—21no—
111C2×D44C2×D412yes—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—82no—
115C2×C8×C11C2×D412yes—
116C2×C8×C11C2×D412yes—
117C11×C4⋊C4—21no—
118C11×C4⋊C4—21no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—41no—
131C42×C11—41no—
132C42×C11—41no—
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11#4111yescharacteristic
136C42×C11C2411yescharacteristic
137#4325—44no—
138#4325—44no—
139(C2×D11)⋊C4—22no—
140(C2×D11)⋊C4—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11C2×D412yes—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C8×D11—82no—
147C8×D11—82no—
148#3231D1111yescharacteristic, complemented
149#3110—111no—
150#3101—111no—
151#2972—111no—
152#1683—112no—
153#1679—112no—
154#1673—112no—
155#1671—112no—
156#1572—111no—
157#1554—111no—
158#1544—111no—
159C23×C11#12111yescharacteristic
160C22×D11—22no—
161C22×D11—24no—
162C22×D11—81no—
163C22×D11—81no—
164Q8×C11—42no—
165Q8×C11—42no—
166Q8×C11—42no—
167Q8×C11—81no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×Dic11—22no—
182C2×Dic11—81no—
183D44—24no—
184D44—22no—
185D44#13514yes—
186C4×D11—42no—
187C4×D11—42no—
188C4×D11—82no—
189C8×C11—22no—
190C8×C11—22no—
191C11⋊C8—42no—
192C11⋊C8—42no—
193C11⋊C8—42no—
194#533C2×D1111yescharacteristic
195#533C2×D1111yescharacteristic
196C2×C4×D4—111no—
197#500C2×D1111yescharacteristic, complemented
198#498C2×D1111yescharacteristic, complemented
199#487C2×D1111yescharacteristic, complemented
200#487C2×D1111yescharacteristic, complemented
201#485—22no—
202#484—221no—
203#483—221no—
204#479—22no—
205#476—112no—
206#474—112no—
207#461—112no—
208#461—112no—
209#450—221no—
210#450—221no—
211#440—222no—
212C4×SD16—222no—
213C8×D4—112no—
214C8×D4—112no—
215C8×D4—222no—
216#432—111no—
217#431—111no—
218#431—111no—
219#431C2×D1111yescharacteristic
220C2×C22⋊C8—222no—
221#335—112no—
222#334—112no—
223#333—112no—
224#332—112no—
225#332—112no—
226#332—112no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11C2×#12111yescharacteristic
231C2×D11—24no—
232C2×D11—42no—
233C2×D11—42no—
234C2×D11—84no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11—81no—
243C4×C11C2×#13512yes—
244C4×C11#57712yes—
245Dic11—42no—
246C22×D4—111no—
247C23×C4—221no—
248C2×SD16—222no—
249C2×SD16—222no—
250C22×C8—222no—
251C22×C8—222no—
252C4⋊Q8C22×D1111yescharacteristic
253C4⋊Q8C22×D1111yescharacteristic
254C4⋊Q8C22×D1111yescharacteristic
255C4⋊Q8C22×D1111yescharacteristic
256#125—21no—
257#125—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C22⋊Q8—21no—
262C4×Q8—21no—
263C4×Q8—21no—
264C4×Q8—21no—
265C4×Q8—21no—
266C4×D4—112no—
267C4×D4—112no—
268C4×D4—221no—
269C4×D4—221no—
270#117—21no—
271#117—21no—
272C2×C4⋊C4—111no—
273C2×C22⋊C4—221no—
274C2×C42C22×D1111yescharacteristic
275#107—22no—
276#107—222no—
277#106—22no—
278#106—222no—
279C4⋊C8—112no—
280C4⋊C8—112no—
281C4⋊C8—112no—
282C4⋊C8C22⋊D1112yes—
283#103—22no—
284#103—22no—
285#103—222no—
286#103—222no—
287#102—222no—
288#102—222no—
289C22⋊C8—221no—
290C22⋊C8—221no—
291C22⋊C8—221no—
292C22⋊C8—222no—
293C22⋊C8—222no—
294C22⋊C8C22⋊D1112yes—
295#97—221no—
296C4×C8—221no—
297C4×C8—221no—
298C4×C8C22×D1111yescharacteristic
299C4×C8C22×D1111yescharacteristic
300C2×C11—41no—
301C2×C11#304211yescharacteristic
302C2×C11#305011yescharacteristic
303C2×C11#306911yescharacteristic
304D11—44no—
305C24—221no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×D4—112no—
311C2×D4—224no—
312C2×D4—221no—
313C22×C4—221no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—882no—
317C22×C4D4×D1111yescharacteristic
318C22×C4#434111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320SD16—444no—
321SD16—444no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—882no—
326C2×C8—882no—
327C2×C8C2×C22⋊D1112yes—
328C2×C8C2×C22⋊D1112yes—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—112no—
342C4⋊C4—221no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—222no—
346C22⋊C4—222no—
347C42—41no—
348C42—41no—
349C42D4×D1111yescharacteristic
350C42#434111yescharacteristic
351C42C2×C22⋊D1111yescharacteristic
352C42C23×D1111yescharacteristic
353C11#1939511yescharacteristic, complemented, Sylow
354C23—224no—
355C23—222no—
356C23—881no—
357C23—881no—
358C23#6699111yescharacteristic
359Q8—42no—
360Q8—42no—
361Q8—42no—
362Q8—81no—
363D4—114no—
364D4—224no—
365D4—222no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—222no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—882no—
377C2×C4—881no—
378C2×C4#6699111yescharacteristic
379C2×C4#6699111yescharacteristic
380C2×C4#6699111yescharacteristic
381C2×C4C2×D4×D1111yescharacteristic
382C2×C4C2×#434111yescharacteristic
383C2×C4C22×C22⋊D1111yescharacteristic
384C8—22no—
385C8—22no—
386C8—442no—
387C8—442no—
388C8—442no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—224no—
393C22—442no—
394C22—442no—
395C22—884no—
396C22C2×#6699111yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—81no—
405C4—442no—
406C4D11×#13512yes—
407C4#1062336812yes—
408C2—41no—
409C2—444no—
410C2#1307812411yescharacteristic
411C2#1307819311yescharacteristic
412C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3231C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#3231D11
hypocenterC11#19395
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
4. #13068064C2semidirect
5. #13068036C2semidirect
6. #13068002C2semidirect
7. #13067988C2semidirect
8. #13067396C2semidirect
9. #13067326C2semidirect
10. #13067281C2semidirect
11. C11×#3231C2semidirect
15. C11×#500C22semidirect
16. C11×#498C22semidirect
17. C11×#487C22semidirect
18. C11×#487C22semidirect
39. #10622185C22semidirect
40. #10622185C22semidirect
41. #10622185C22semidirect
42. #10622184C22semidirect
43. #10622096C22semidirect
44. #10622095C22semidirect
148. #3231D11semidirect
197. #500C2×D11semidirect
198. #498C2×D11semidirect
199. #487C2×D11semidirect
200. #487C2×D11semidirect
353. C11#19395semidirect

Maximal subgroups

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

subgroupindex
#130787112
#130786202
#130776392
#130680642
#130680362
#130680022
#130679882
#130673962
#130673262
#130672812
C11×#32312
#1939511