Finite Group Databasebeta

← #14736845

Subgroups — #14736845

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079536C212yesmaximal, complemented
2C2×#10622308C211yesmaximal, characteristic, complemented
3#13077329C211yesmaximal, characteristic, complemented
4#13068096C214yesmaximal, complemented
5#13067972C214yesmaximal, complemented
6#13067283C212yesmaximal, complemented
7C11×#1564C211yesmaximal, characteristic, complemented
8C22×D88—21no—
9C22×D88—21no—
10C2×#66954—21no—
11#10623008C2211yescharacteristic
12C2×#66927C2212yes—
13C11×#431C2212yes—
14C2×C4×C8×C11C2211yescharacteristic
15#10622723—21no—
16#10622537C2211yescharacteristic
17#10622456C2218yescomplemented
18#10622345—24no—
19#10622308—22no—
20#10622308—21no—
21#10622308—21no—
22#10622308C2212yes—
23#10622308C2212yes—
24#10622307—22no—
25#10622301—21no—
26#10622301C2212yescomplemented
27C8×D44—21no—
28C8×D44C2212yescomplemented
29C11×#335C2212yescomplemented
30C11×#334C2212yescomplemented
31#10622123C2218yescomplemented
32C2×#4339—21no—
33C22×D44—22no—
34C22×D44—22no—
35C22×D44—22no—
36C22×C8×C11D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38C2×C42×C11C2311yescharacteristic
39#66983—21no—
40#66983D412yes—
41C2×#4318—21no—
42C2×D88—22no—
43C2×D88—22no—
44C2×D88—22no—
45C2×D88—22no—
46C2×D88—28no—
47C2×D88—44no—
48C2×D88—44no—
49#66954—44no—
50C2×#4313—22no—
51C2×C8×D11—22no—
52#66928—21no—
53#66927—22no—
54#66927—22no—
55#66927—22no—
56#66927D411yescharacteristic
57#66927C2314yes—
58C4×D44—21no—
59C4×D44C2312yes—
60#66922D411yescharacteristic
61C11×C4⋊C8C2314yes—
62C11×C22⋊C8—22no—
63C4×C8×C11—22no—
64C4×C8×C11D411yescharacteristic
65C4×C8×C11D411yescharacteristic
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2311yescharacteristic
68#66885—28no—
69(C2×D11)⋊C8—22no—
70(C2×D11)⋊C8—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)C2312yes—
73#19187—111nomaximal, Sylow
74C23×D11—42no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×C22⋊D11—22no—
79#4339—42no—
80#4339—42no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44—24no—
84C2×D44—24no—
85C2×D44—24no—
86C2×D44—42no—
87C2×D44—42no—
88C2×D44—42no—
89C2×D44—44no—
90C2×D44—44no—
91C2×D44—84no—
92C2×D44—84no—
93C2×D44C2×D412yes—
94C2×C4×D11—22no—
95C2×Dic22—21no—
96C2×C8×C11—22no—
97C2×C8×C11—24no—
98C2×C8×C11D814yescomplemented
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2×D411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11C2411yescharacteristic
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109C4⋊Dic11—21no—
110C4⋊Dic11C2×D412yes—
111#4318—42no—
112C2×C11⋊C8—22no—
113D88—44no—
114D88—44no—
115D88—44no—
116D88—44no—
117D88—88no—
118#4313—44no—
119C8×D11—44no—
120#3205—112no—
121C2×#493—111no—
122#2931—111no—
123#1687—114no—
124#1667—114no—
125#1564D1111yescharacteristic, complemented
126#1545—112no—
127C23×C11#12111yescharacteristic
128C22×D11—22no—
129C22×D11—44no—
130C22×D11—84no—
131C22×D11—84no—
132C22×D11—84no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11C2×D812yes—
139C2×C4×C11AGL(1,ℤ/8)12yes—
140C2×C4×C11C22×D411yescharacteristic
141C2×C4×C11C22×D411yescharacteristic
142C2×C4×C11C2×#4111yescharacteristic
143C22⋊D11—44no—
144C2×Dic11—22no—
145D44—24no—
146D44—44no—
147D44—44no—
148D44—48no—
149D44—42no—
150D44—42no—
151D44—84no—
152D44—84no—
153D44—84no—
154D44—84no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—42no—
158C8×C11—21no—
159C8×C11—21no—
160C8×C11—44no—
161C8×C11C2×D812yes—
162C8×C11C2×D812yes—
163C11⋊C8—42no—
164C22×D8—221no—
165C22×D8—221no—
166C2×#131—221no—
167#532—111no—
168C2×#127—112no—
169#493—112no—
170#493—112no—
171#493—222no—
172#493—221no—
173#493—221no—
174#486—222no—
175#459—118no—
176#447—224no—
177#436—112no—
178#436—221no—
179C8×D4—112no—
180C8×D4—221no—
181#431C2×D1112yes—
182#423—111no—
183#408—221no—
184C2×C4×C8C2×D1111yescharacteristic
185#335C2×D1112yescomplemented
186#334C2×D1112yescomplemented
187#331—118no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#45912yes—
191C22×C11C2×#12111yescharacteristic
192C2×D11—42no—
193C2×D11—42no—
194C2×D11—42no—
195C2×D11—84no—
196C2×D11—84no—
197C2×D11—84no—
198C2×D11—168no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11#45912yes—
202C4×C11#47212yes—
203C4×C11C22×D811yescharacteristic
204C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
205C4×C11#57612yes—
206Dic11—42no—
207C2×#41—221no—
208C22×D4—222no—
209C22×D4—222no—
210C22×D4—222no—
211C2×D8—228no—
212C2×D8—222no—
213C2×D8—222no—
214C2×D8—222no—
215C2×D8—222no—
216C2×D8—444no—
217C2×D8—444no—
218#131—444no—
219C2×M16—221no—
220C2×M16—222no—
221C22×C8—222no—
222C22×C8D4411yescharacteristic
223C22×C8D4411yescharacteristic
224C4⋊Q8—111no—
225#127—111no—
226#127—114no—
227#127—222no—
228#127—222no—
229#127—222no—
230#124—221no—
231#121—112no—
232#121—221no—
233C4×D4—112no—
234C4×D4—221no—
235C2×C42C22×D1111yescharacteristic
236C4⋊C8—112no—
237C4⋊C8—221no—
238C4⋊C8C22×D1114yes—
239#102—228no—
240C22⋊C8—22no—
241C22⋊C8—222no—
242C22⋊C8—222no—
243C4×C8—22no—
244C4×C8D4411yescharacteristic
245C4×C8D4411yescharacteristic
246C4×C8C22×D1111yescharacteristic
247C4×C8C22×D1111yescharacteristic
248C2×C11—22no—
249C2×C11C2×#45911yescharacteristic
250C2×C11#305811yescharacteristic
251C2×C11C2×#47211yescharacteristic
252D11—82no—
253D11—164no—
254C24—442no—
255#41—442no—
256#41—442no—
257C2×Q8—221no—
258C2×D4—112no—
259C2×D4—222no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—224no—
263C2×D4—224no—
264C2×D4—224no—
265C2×D4—442no—
266C2×D4—442no—
267C2×D4—442no—
268C2×D4—444no—
269C2×D4—444no—
270C2×D4—884no—
271C2×D4—884no—
272C22×C4—222no—
273C22×C4C2×D4411yescharacteristic
274C22×C4D4×D1111yescharacteristic
275C22×C4#434311yescharacteristic
276D8—444no—
277D8—444no—
278D8—444no—
279D8—444no—
280D8—888no—
281M16—442no—
282M16—444no—
283C2×C8—22no—
284C2×C8—24no—
285C2×C8—222no—
286C2×C8—444no—
287C2×C8D8814yescomplemented
288C2×C8C2×D4411yescharacteristic
289C2×C8C2×D4411yescharacteristic
290C2×C8C2×D4411yescharacteristic
291C2×C8C2×D4411yescharacteristic
292C4⋊C4—112no—
293C4⋊C4—221no—
294C22⋊C4—222no—
295C22⋊C4—222no—
296C42C2×D4411yescharacteristic
297C42D4×D1111yescharacteristic
298C42#434311yescharacteristic
299C42C23×D1111yescharacteristic
300C11#1918711yescharacteristic, complemented, Sylow
301C23—222no—
302C23—444no—
303C23—884no—
304C23—884no—
305C23—884no—
306C23#6694811yescharacteristic
307Q8—442no—
308D4—224no—
309D4—444no—
310D4—444no—
311D4—444no—
312D4—442no—
313D4—448no—
314D4—442no—
315D4—884no—
316D4—884no—
317D4—884no—
318D4—884no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—222no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4#6694811yescharacteristic
325C2×C4#6694811yescharacteristic
326C2×C4#6694811yescharacteristic
327C2×C4C2×D8812yes—
328C2×C4#6696112yes—
329C2×C4C22×D4411yescharacteristic
330C2×C4C2×D4×D1111yescharacteristic
331C2×C4C2×#434311yescharacteristic
332C8—21no—
333C8—21no—
334C8—44no—
335C8—442no—
336C8C2×D8812yes—
337C8C2×D8812yes—
338C22—21no—
339C22—21no—
340C22—442no—
341C22—442no—
342C22—442no—
343C22—884no—
344C22—884no—
345C22—884no—
346C22—1768no—
347C22#1062245612yes—
348C22C2×#6694811yescharacteristic
349C4—21no—
350C4—21no—
351C4—442no—
352C4#1062245612yes—
353C4#1062251012yes—
354C4C22×D8811yescharacteristic
355C4C2×#6696111yescharacteristic
356C4#1062330012yes—
357C2—22no—
358C2—882no—
359C2—1764no—
360C2C2×#1062245611yescharacteristic
361C2#1307826511yescharacteristic
362C2C2×#1062251011yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1564C2
socleC22×C11C2×#121
hypercenter#1564D11
hypocenterC11#19187
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
1. #13079536C2semidirect
2. C2×#10622308C2semidirect
3. #13077329C2semidirect
4. #13068096C2semidirect
5. #13067972C2semidirect
6. #13067283C2semidirect
7. C11×#1564C2semidirect
17. #10622456C22semidirect
26. #10622301C22semidirect
28. C8×D44C22semidirect
29. C11×#335C22semidirect
30. C11×#334C22semidirect
31. #10622123C22semidirect
98. C2×C8×C11D8semidirect
125. #1564D11semidirect
185. #335C2×D11semidirect
186. #334C2×D11semidirect
287. C2×C8D88semidirect
300. C11#19187semidirect

Maximal subgroups

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

subgroupindex
#130795362
C2×#106223082
#130773292
#130680962
#130679722
#130672832
C11×#15642
#1918711