Finite Group Databasebeta

← #14737820

Subgroups — #14737820

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078711C212yesmaximal
2C2×#10622301C211yesmaximal, characteristic
3#13068160C214yesmaximal, complemented
4#13068126C212yesmaximal, complemented
5#13068102C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067316C212yesmaximal, complemented
8C11×#3170C211yesmaximal, characteristic, complemented
9C11×#533C2212yes—
10C22×#4313—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#500C2211yescharacteristic, complemented
13C11×#494C2211yescharacteristic, complemented
14C11×#487C2212yescomplemented
15C11×#467—21no—
16C11×#467—21no—
17C4×C11×Q16—21no—
18C4×C11×Q16—21no—
19C2×C4×C8×C11C2211yescharacteristic
20C2×(C2×D11)⋊C8—21no—
21#10622700C2214yes—
22#10622696C2214yes—
23#10622659—22no—
24#10622657—22no—
25#10622639—24no—
26#10622539C2212yes—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622301—21no—
29#10622301—21no—
30#10622301C2212yes—
31#10622301C2212yes—
32#10622185C2214yescomplemented
33#10622185C2214yescomplemented
34#10622096C2212yescomplemented
35#10622095C2212yescomplemented
36C22×D44D411yescharacteristic
37C22×C4×D11—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16—21no—
40C22×C8×C11D411yescharacteristic
41C22×C8×C11D411yescharacteristic
42C11×C4⋊Q8C2312yes—
43C11×C4⋊Q8C2312yes—
44C11×#125—22no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—22no—
47C4×Q8×C11—22no—
48C4×Q8×C11—22no—
49C11×#117—22no—
50C2×C42×C11C2311yescharacteristic
51C2×#4325—24no—
52C2×(C2×D11)⋊C4—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C22×C11⋊C8—21no—
55C2×#4313—22no—
56C2×#4313—22no—
57C2×#4313—44no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44D412yes—
61C4×D44C2312yes—
62C11×#107—21no—
63C11×#107—21no—
64C11×#103—22no—
65C11×#103—22no—
66C4×C8×C11D411yescharacteristic
67C4×C8×C11D411yescharacteristic
68C4×C8×C11C2311yescharacteristic
69C4×C8×C11C2311yescharacteristic
70#66899—24no—
71C22⋊(C11⋊C8)—22no—
72(C2×D11)⋊C8—22no—
73(C2×D11)⋊C8—22no—
74#66873—24no—
75#66871—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)C2312yes—
78C4⋊(C11⋊C8)C2314yes—
79#66867—22no—
80#19284—111nomaximal, Sylow
81C23×D11—21no—
82C2×Q8×C11—22no—
83C2×Q8×C11—22no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×Dic11—21no—
88C2×D44—21no—
89C2×D44—42no—
90C2×D44C2×D412yes—
91C2×C4×D11—22no—
92C2×C4×D11—22no—
93C2×C4×D11—42no—
94C2×C4×D11—42no—
95C11×Q16—42no—
96C11×Q16—42no—
97C2×C8×C11—22no—
98C2×C8×C11—41no—
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4—42no—
109C11×C22⋊C4—42no—
110C42×C11—42no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11C2411yescharacteristic
115#4325—48no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11C2×D412yes—
120C2×C11⋊C8—24no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—42no—
123#4313—44no—
124#4313—44no—
125#3170D1111yescharacteristic, complemented
126#3110—112no—
127C2×#436—111no—
128#1699—114no—
129#1693—112no—
130#1689—112no—
131#1568—111no—
132#1552—112no—
133C23×C11#12111yescharacteristic
134C22×D11—22no—
135C22×D11—42no—
136C22×D11—42no—
137C22×D11—42no—
138Q8×C11—42no—
139Q8×C11—44no—
140Q8×C11—42no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C22×D411yescharacteristic
152C2×C4×C11C2×#4111yescharacteristic
153C2×Dic11—22no—
154C2×Dic11—42no—
155D44—24no—
156D44—42no—
157C4×D11—44no—
158C4×D11—42no—
159C4×D11—42no—
160C8×C11—21no—
161C8×C11—21no—
162C8×C11—21no—
163C8×C11AGL(1,ℤ/8)12yes—
164C11⋊C8—42no—
165C11⋊C8—44no—
166C22×M16—221no—
167#533C2×D1112yes—
168C2×C4×D4—111no—
169#500C2×D1111yescharacteristic, complemented
170#494C2×D1111yescharacteristic, complemented
171#487C2×D1112yescomplemented
172#484—222no—
173#474—114no—
174#467—21no—
175#467—21no—
176#461—114no—
177#450—222no—
178#440—224no—
179C4×Q16—21no—
180C4×Q16—21no—
181#436—112no—
182#436—112no—
183#436—221no—
184#436—221no—
185#432—112no—
186C2×C4⋊C8—111no—
187C2×C22⋊C8—221no—
188C2×C4×C8C2×D1111yescharacteristic
189#335—112no—
190#334—112no—
191#332—114no—
192#332—114no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#47312yes—
196C22×C11C2×#12111yescharacteristic
197C2×D11—42no—
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—84no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—82no—
206C4×C11—82no—
207C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
208C4×C11#57512yes—
209C4×C11#57511yescharacteristic
210Dic11—42no—
211C22×D4—111no—
212C23×C4—221no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×SD16—224no—
216C2×M16—222no—
217C2×M16—222no—
218C2×M16—444no—
219C22×C8—221no—
220C22×C8C22⋊D1111yescharacteristic
221C22×C8C22⋊D1111yescharacteristic
222C4⋊Q8C22×D1112yes—
223C4⋊Q8C22×D1112yes—
224#125—22no—
225C22⋊Q8—22no—
226C22⋊Q8—22no—
227C4×Q8—22no—
228C4×Q8—22no—
229C4×D4—112no—
230C4×D4—112no—
231C4×D4—221no—
232C4×D4—221no—
233#117—22no—
234C2×C4⋊C4—111no—
235C2×C22⋊C4—221no—
236C2×C42C22×D1111yescharacteristic
237#107—21no—
238#107—21no—
239#107—224no—
240C4⋊C8—112no—
241C4⋊C8—114no—
242C4⋊C8—221no—
243#103—22no—
244#103—22no—
245#103—224no—
246#102—224no—
247C22⋊C8—222no—
248C22⋊C8—222no—
249C22⋊C8—222no—
250#97—222no—
251C4×C8C22⋊D1111yescharacteristic
252C4×C8C22⋊D1111yescharacteristic
253C4×C8C22×D1111yescharacteristic
254C4×C8C22×D1111yescharacteristic
255C2×C11—22no—
256C2×C11#303611yescharacteristic
257C2×C11#305411yescharacteristic
258C2×C11C2×#47311yescharacteristic
259D11—82no—
260C24—221no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×D4—112no—
264C2×D4—221no—
265C2×D4—442no—
266C22×C4—221no—
267C22×C4—222no—
268C22×C4—222no—
269C22×C4—442no—
270C22×C4—442no—
271C22×C4D4×D1111yescharacteristic
272C22×C4#434111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274Q16—42no—
275Q16—42no—
276SD16—448no—
277M16—444no—
278M16—444no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—224no—
282C2×C8—222no—
283C2×C8—442no—
284C2×C8C2×C22⋊D1111yescharacteristic
285C2×C8C2×C22⋊D1111yescharacteristic
286C2×C8C2×C22⋊D1111yescharacteristic
287C2×C8C2×C22⋊D1111yescharacteristic
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—112no—
295C4⋊C4—221no—
296C22⋊C4—42no—
297C22⋊C4—222no—
298C22⋊C4—222no—
299C42—42no—
300C42D4×D1111yescharacteristic
301C42#434111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C42C23×D1111yescharacteristic
304C11#1928411yescharacteristic, complemented, Sylow
305C23—222no—
306C23—442no—
307C23—442no—
308C23—442no—
309C23#6699111yescharacteristic
310Q8—44no—
311Q8—42no—
312Q8—42no—
313D4—224no—
314D4—442no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—222no—
322C2×C4—444no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4#6699111yescharacteristic
327C2×C4#6699111yescharacteristic
328C2×C4#6699111yescharacteristic
329C2×C4C2×D4×D1111yescharacteristic
330C2×C4C2×#434111yescharacteristic
331C2×C4C22×C22⋊D1111yescharacteristic
332C8—21no—
333C8—21no—
334C8—21no—
335C8—444no—
336C8—442no—
337C8#6700212yes—
338C22—21no—
339C22—21no—
340C22—442no—
341C22—442no—
342C22—442no—
343C22—884no—
344C22#1062280512yes—
345C22C2×#6699111yescharacteristic
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—82no—
351C4—82no—
352C4—442no—
353C4#1062329912yes—
354C4C2×#6700211yescharacteristic
355C4#1062335311yescharacteristic
356C2—22no—
357C2—882no—
358C2#1307807611yescharacteristic
359C2#1307822111yescharacteristic
360C2C2×#1062280511yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3170C2
socleC22×C11C2×#121
prime radicalC22×D44D4
hypercenter#3170D11
hypocenterC11#19284
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13068160C2semidirect
4. #13068126C2semidirect
5. #13068102C2semidirect
6. #13067379C2semidirect
7. #13067316C2semidirect
8. C11×#3170C2semidirect
12. C11×#500C22semidirect
13. C11×#494C22semidirect
14. C11×#487C22semidirect
32. #10622185C22semidirect
33. #10622185C22semidirect
34. #10622096C22semidirect
35. #10622095C22semidirect
125. #3170D11semidirect
169. #500C2×D11semidirect
170. #494C2×D11semidirect
171. #487C2×D11semidirect
304. C11#19284semidirect

Maximal subgroups

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

subgroupindex
#130787112
C2×#106223012
#130681602
#130681262
#130681022
#130673792
#130673162
C11×#31702
#1928411