Finite Group Databasebeta

← #14673125

Subgroups — #14673125

Order 2816.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622309C211yesmaximal, characteristic
2C2×#10622141C211yesmaximal, characteristic, complemented
3C2×#10622141C211yesmaximal, characteristic, complemented
4C2×#10622147C211yesmaximal, characteristic
5C2×#10622147C211yesmaximal, characteristic
6#13069349C211yesmaximal, characteristic, complemented
7C11×#1374C211yesmaximal, characteristic, complemented
8C22×Dic44C2211yescharacteristic
9C22×D88C2211yescharacteristic
10C22×#4314—21no—
11C2×#66928—21no—
12C22×C11×C16C2211yescharacteristic
13C22×C11×C16C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C2×#66882C2211yescharacteristic
16C2×#66882C2211yescharacteristic
17#10622541—21no—
18#10622309—22no—
19#10622309—22no—
20#10622189—21no—
21#10622147—22no—
22#10622147—22no—
23#10622141—22no—
24#10622141—22no—
25C22×D44—21no—
26C22×Dic22—21no—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×(C2×D11)⋊C4—41no—
31C2×(C2×D11)⋊C4—41no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×Dic11⋊C4—41no—
35C2×Dic44—21no—
36C2×Dic44—21no—
37C2×Dic44—21no—
38C2×Dic44—21no—
39C2×Dic44—21no—
40C2×Dic44D412yes—
41C2×D88—21no—
42C2×D88—21no—
43C2×D88—21no—
44C2×D88—21no—
45C2×D88—21no—
46C2×D88D412yes—
47C2×#4314—24no—
48C2×#4314—42no—
49C2×#4314—42no—
50#66928—24no—
51#66928—42no—
52C2×C11×C16—21no—
53C2×C11×C16—21no—
54C2×C11×C16—21no—
55C2×C11×C16—21no—
56C2×C11×C16—21no—
57C2×C11×C16—21no—
58C4×C8×C11—21no—
59C4×C8×C11—21no—
60C11⋊#95—41no—
61#66882—21no—
62#66882—21no—
63#66882—21no—
64#66882D412yes—
65#13408—111nomaximal, Sylow
66C23×D11—41no—
67C22×C4×C11D811yescharacteristic
68C22×C4×C11D811yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—41no—
71C22×Dic11—41no—
72C22×Dic11—41no—
73C2×D44—22no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—41no—
79C2×Dic22—22no—
80C2×Dic22—41no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11SD1612yes—
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11#4111yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C2×C8×C11#4111yescharacteristic
94C42×C11—21no—
95C42×C11—21no—
96(C2×D11)⋊C4—44no—
97(C2×D11)⋊C4—44no—
98C4⋊Dic11—22no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102Dic11⋊C4—82no—
103Dic44—22no—
104Dic44—22no—
105Dic44—41no—
106Dic44—41no—
107D88—22no—
108D88—22no—
109D88—41no—
110D88—41no—
111#4314—48no—
112C11×C16—41no—
113C11×C16—41no—
114C2×#495—111no—
115C2×#358—111no—
116C2×#358—111no—
117C2×#357—111no—
118C2×#357—111no—
119#1942—111no—
120#1374D1111yescharacteristic, complemented
121C23×C11C2×D811yescharacteristic
122C22×D11—42no—
123C22×D11—81no—
124C22×D11—81no—
125C22×D11—81no—
126C22×D11—81no—
127C22×D11—81no—
128C22×D11—81no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C2×C4×C11C2×SD1611yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—81no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150D44—42no—
151D44—42no—
152D44—81no—
153D44—81no—
154Dic22—42no—
155Dic22—42no—
156Dic22—81no—
157Dic22—81no—
158C8×C11—22no—
159C8×C11#12111yescharacteristic
160C8×C11#12111yescharacteristic
161C8×C11#12311yescharacteristic
162C8×C11#12311yescharacteristic
163C22×Q16—111no—
164C22×SD16—221no—
165C22×D8—111no—
166C2×#124—221no—
167C22×C16C2×D1111yescharacteristic
168C22×C16C2×D1111yescharacteristic
169#495—222no—
170#495—222no—
171C2×#107—111no—
172C2×#107—111no—
173C2×C4×C8C2×D1111yescharacteristic
174#389—221no—
175#358—222no—
176#358—222no—
177#357—222no—
178#357—222no—
179#340—221no—
180C22×C11#44711yescharacteristic
181C22×C11#45911yescharacteristic
182C22×C11#48611yescharacteristic
183C22×C11#50811yescharacteristic
184C22×C11#50811yescharacteristic
185C22×C11#50911yescharacteristic
186C22×C11#51011yescharacteristic
187C2×D11—82no—
188C2×D11—82no—
189C2×D11—82no—
190C2×D11—161no—
191C2×D11—161no—
192C2×D11—161no—
193C2×D11—161no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11#39411yescharacteristic
197C4×C11#45011yescharacteristic
198C4×C11#46011yescharacteristic
199C4×C11#49011yescharacteristic
200Dic11—82no—
201Dic11—82no—
202Dic11—161no—
203C22×Q8—221no—
204C22×D4—221no—
205C2×Q16—112no—
206C2×Q16—221no—
207C2×Q16—221no—
208C2×Q16—221no—
209C2×Q16—221no—
210C2×Q16—221no—
211C2×SD16—224no—
212C2×SD16—442no—
213C2×SD16—442no—
214C2×D8—112no—
215C2×D8—221no—
216C2×D8—221no—
217C2×D8—221no—
218C2×D8—221no—
219C2×D8—221no—
220C22×C8D4411yescharacteristic
221C22×C8C22×D1111yescharacteristic
222#124—224no—
223#124—442no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—441no—
227C2×C22⋊C4—441no—
228C2×C22⋊C4—441no—
229C2×C42D4411yescharacteristic
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16—21no—
236#107—112no—
237#107—221no—
238#107—221no—
239#107—221no—
240C4×C8—21no—
241C4×C8—21no—
242#95—441no—
243C2×C11#204111yescharacteristic
244C2×C11#218611yescharacteristic
245C2×C11#218911yescharacteristic
246C2×C11#221011yescharacteristic
247C2×C11#221111yescharacteristic
248C2×C11#224211yescharacteristic
249C2×C11#224311yescharacteristic
250D11—162no—
251C24—441no—
252C2×Q8—222no—
253C2×Q8—441no—
254C2×Q8—441no—
255C2×Q8—441no—
256C2×Q8—441no—
257C2×Q8—441no—
258C2×D4—222no—
259C2×D4—441no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—441no—
264C22×C4—441no—
265C22×C4—441no—
266C22×C4—441no—
267C22×C4D8811yescharacteristic
268C22×C4D8811yescharacteristic
269C22×C4C2×D4411yescharacteristic
270Q16—222no—
271Q16—222no—
272Q16—441no—
273Q16—441no—
274SD16—448no—
275D8—222no—
276D8—222no—
277D8—441no—
278D8—441no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8#431412yes—
282C2×C8#433911yescharacteristic
283C2×C8#433911yescharacteristic
284C2×C8D4×D1111yescharacteristic
285C2×C8D4×D1111yescharacteristic
286C2×C8D4×D1111yescharacteristic
287C2×C8#434311yescharacteristic
288C4⋊C4—222no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—882no—
293C22⋊C4—444no—
294C22⋊C4—444no—
295C42—21no—
296C42—21no—
297C16—41no—
298C16—41no—
299C11#1340811yescharacteristic, complemented, Sylow
300C23—442no—
301C23—881no—
302C23—881no—
303C23—881no—
304C23—881no—
305C23—881no—
306C23—881no—
307C23C2×D8811yescharacteristic
308Q8—442no—
309Q8—442no—
310Q8—881no—
311Q8—881no—
312D4—442no—
313D4—442no—
314D4—881no—
315D4—881no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4—881no—
328C2×C4—881no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4#6692811yescharacteristic
332C2×C4#6693511yescharacteristic
333C2×C4#6694811yescharacteristic
334C2×C4C2×#431411yescharacteristic
335C2×C4#6696111yescharacteristic
336C2×C4#6696111yescharacteristic
337C8—22no—
338C8#6693711yescharacteristic
339C8#6693711yescharacteristic
340C8#6694711yescharacteristic
341C8#6694711yescharacteristic
342C22—882no—
343C22—882no—
344C22—882no—
345C22—1761no—
346C22—1761no—
347C22—1761no—
348C22—1761no—
349C22#1062230711yescharacteristic
350C22#1062234511yescharacteristic
351C22#1062245611yescharacteristic
352C22#1062251711yescharacteristic
353C22#1062251711yescharacteristic
354C22#1062252111yescharacteristic
355C22#1062252211yescharacteristic
356C4—41no—
357C4—41no—
358C4—882no—
359C4—882no—
360C4—1761no—
361C4#1062228511yescharacteristic
362C4#1062232611yescharacteristic
363C4#1062234411yescharacteristic
364C4#1062246111yescharacteristic
365C2—1762no—
366C2#1306985111yescharacteristic
367C2#1307054111yescharacteristic
368C2#1307055811yescharacteristic
369C2#1307067211yescharacteristic
370C2#1307067911yescharacteristic
371C2#1307084811yescharacteristic
372C2#1307085311yescharacteristic
subgroupG/H
centerC23C2×D88
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1374C2
socleC23×C11C2×D8
prime radicalC22×D88C22
hypercenter#1374D11
hypocenterC11#13408
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
2. C2×#10622141C2semidirect
3. C2×#10622141C2semidirect
6. #13069349C2semidirect
7. C11×#1374C2semidirect
120. #1374D11semidirect
299. C11#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#106223092
C2×#106221412
C2×#106221472
#130693492
C11×#13742
#1340811