Finite Group Databasebeta

← #14670367

Subgroups — #14670367

Order 2816.

490 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic11C211yesmaximal, characteristic
2C2×#10622142C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic
4#13069350C211yesmaximal, characteristic, complemented
5#13066707C211yesmaximal, characteristic, complemented
6#13066693C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic
8C22×C11×D8C2211yescharacteristic
9C2×D4×Dic11—21no—
10C22×C11×C16C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12C2×#66896—21no—
13D8×Dic11—22no—
14D8×Dic11—22no—
15C2×#66882C2211yescharacteristic
16C2×#66882C2211yescharacteristic
17C2×C8×Dic11C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19#10622598—21no—
20C11×#357C414yescomplemented
21#10622200—22no—
22#10622167—21no—
23#10622142—22no—
24C22×D4×C11—21no—
25C23×Dic11—41no—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C2×C11×D8—21no—
29C2×C11×D8C2×C412yes—
30C2×C11×D8D412yes—
31C2×C11×D8Q812yes—
32C22×C8×C11C2311yescharacteristic
33C2×C11×C4⋊C4—21no—
34C2×C22⋊Dic11—41no—
35D4×Dic11—24no—
36D4×Dic11—42no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—41no—
40C2×C4×Dic11D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42C2×C11×C16—21no—
43C2×C11×C16—21no—
44C2×C11×C16C2×C412yescomplemented
45C11×#107—21no—
46C11×#107C2×C412yescomplemented
47#66896—24no—
48C11⋊#95—41no—
49#66882—21no—
50#66882—21no—
51#66882—21no—
52#66882D412yes—
53C8×Dic11—21no—
54C8×Dic11—21no—
55C2×C11⋊C16—21no—
56C2×C11⋊C16—21no—
57C2×C11⋊C16—21no—
58#12935—111nomaximal, Sylow
59C24×C11—41no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—44no—
69C22×Dic11—41no—
70C22×Dic11—41no—
71C22×Dic11—82no—
72C22×Dic11—82no—
73C22×Dic11D811yescharacteristic
74C22×Dic11D811yescharacteristic
75C11×D8—22no—
76C11×D8—22no—
77C11×D8—22no—
78C11×D8C4⋊C414yescomplemented
79C2×C8×C11C22×C411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C2×C8×C11C2×D411yescharacteristic
82C2×C8×C11C2×Q811yescharacteristic
83C2×C8×C11#4111yescharacteristic
84C2×C8×C11#4111yescharacteristic
85C11×C4⋊C4—22no—
86C11×C4⋊C4—41no—
87C22⋊Dic11—44no—
88C4⋊Dic11—22no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—82no—
93C4×Dic11—21no—
94C4×Dic11—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—21no—
98C11×C16—22no—
99C11⋊C16—41no—
100C2×C4×D8—111no—
101C2×#366—111no—
102C2×#357—111no—
103C2×#357D1111yescharacteristic
104#1942—111no—
105#1380—111no—
106#1374—111no—
107C23×C11—42no—
108C23×C11—42no—
109C23×C11—42no—
110C23×C11—81no—
111C23×C11—81no—
112C23×C11—81no—
113C23×C11—81no—
114C23×C11C2×D811yescharacteristic
115D4×C11—24no—
116D4×C11—42no—
117D4×C11—42no—
118D4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—81no—
121C2×C4×C11—81no—
122C2×C4×C11C4×D411yescharacteristic
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—42no—
134C2×Dic11—88no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137C2×Dic11—81no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140C2×Dic11D1612yes—
141C8×C11C2×C4⋊C411yescharacteristic
142C8×C11C4×D411yescharacteristic
143C8×C11C22⋊Q811yescharacteristic
144C8×C11#12311yescharacteristic
145C11⋊C8—41no—
146C22×D8C2×D1111yescharacteristic
147C2×C4×D4—221no—
148C22×C16—111no—
149C22×C16C2×D1111yescharacteristic
150C4×D8—222no—
151C4×D8—222no—
152C2×#107—111no—
153C2×#107—111no—
154C2×#107C2×D1111yescharacteristic
155C2×#102—221no—
156C2×C4×C8—111no—
157#389—221no—
158#366—222no—
159#357—222no—
160#357Dic1114yescomplemented
161#340—221no—
162C22×C11—44no—
163C22×C11—82no—
164C22×C11—82no—
165C22×C11—82no—
166C22×C11—82no—
167C22×C11—82no—
168C22×C11—82no—
169C22×C11C4×D811yescharacteristic
170C22×C11#44711yescharacteristic
171C22×C11#47411yescharacteristic
172C22×C11C2×D1611yescharacteristic
173C22×C11#50811yescharacteristic
174C22×C11#50911yescharacteristic
175C22×C11#51011yescharacteristic
176C4×C11—82no—
177C4×C11#38511yescharacteristic
178C4×C11#44011yescharacteristic
179C4×C11#45211yescharacteristic
180C4×C11#47811yescharacteristic
181Dic11—22no—
182Dic11—41no—
183Dic11—82no—
184Dic11—161no—
185C22×D4—21no—
186C23×C4—441no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8Dic2212yes—
191C2×D8D4412yes—
192C2×D8C2×Dic1112yes—
193C22×C8—111no—
194C22×C8C22×D1111yescharacteristic
195C4×D4—224no—
196C4×D4—442no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—441no—
201C2×C22⋊C4—441no—
202C2×C42—111no—
203C2×C16—21no—
204C2×C16—21no—
205C2×C16—221no—
206C2×C16—221no—
207C2×C16—221no—
208C2×C16C2×Dic1112yescomplemented
209#107—21no—
210#107—112no—
211#107—221no—
212#107—221no—
213#107—221no—
214#107C2×Dic1112yescomplemented
215#102—224no—
216C4×C8—221no—
217C4×C8—221no—
218#95—441no—
219C2×C11—84no—
220C2×C11#186211yescharacteristic
221C2×C11C4×D1611yescharacteristic
222C2×C11#217511yescharacteristic
223C2×C11#218411yescharacteristic
224C2×C11#218911yescharacteristic
225C2×C11#222411yescharacteristic
226C2×C11#222811yescharacteristic
227C24—41no—
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C22×C4—41no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—444no—
238C22×C4—441no—
239C22×C4—441no—
240C22×C4—882no—
241C22×C4—882no—
242C22×C4D4×D1111yescharacteristic
243D8—22no—
244D8—22no—
245D8—22no—
246D8C4⋊Dic1114yescomplemented
247C2×C8—221no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8C2×Dic2211yescharacteristic
251C2×C8C2×D4411yescharacteristic
252C2×C8D4×D1111yescharacteristic
253C2×C8#434111yescharacteristic
254C2×C8#434111yescharacteristic
255C2×C8C22×Dic1111yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—222no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4—882no—
263C22⋊C4—444no—
264C42—221no—
265C42—221no—
266C16—22no—
267C16—441no—
268C11#1293511yescharacteristic, complemented, Sylow
269C23—42no—
270C23—42no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23D8×D1111yescharacteristic
277D4—24no—
278D4—42no—
279D4—42no—
280D4—42no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—112no—
285C2×C4—221no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—221no—
289C2×C4—221no—
290C2×C4—442no—
291C2×C4—888no—
292C2×C4—881no—
293C2×C4—881no—
294C2×C4—881no—
295C2×C4—881no—
296C2×C4—881no—
297C2×C4#6693111yescharacteristic
298C2×C4#6693511yescharacteristic
299C2×C4#6696511yescharacteristic
300C2×C4#6696711yescharacteristic
301C2×C4#6696811yescharacteristic
302C2×C4D4×Dic1111yescharacteristic
303C8—441no—
304C8#6693111yescharacteristic
305C8#6693911yescharacteristic
306C8C2×C4⋊Dic1111yescharacteristic
307C8D4×Dic1111yescharacteristic
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22#1062237211yescharacteristic
316C22#1062238611yescharacteristic
317C22D11×D1611yescharacteristic
318C22#1062252511yescharacteristic
319C22#1062252711yescharacteristic
320C22#1062252811yescharacteristic
321C22D8×Dic1111yescharacteristic
322C4—82no—
323C4—222no—
324C4—441no—
325C4—882no—
326C4—1761no—
327C4#1062237911yescharacteristic
328C4#1062239611yescharacteristic
329C4#1062256311yescharacteristic
330C4#1062277711yescharacteristic
331C2—84no—
332C2#1306886511yescharacteristic
333C2D16×Dic1111yescharacteristic
334C2#1307048111yescharacteristic
335C2#1307052911yescharacteristic
336C2#1307055711yescharacteristic
337C2#1307075111yescharacteristic
338C2#1307077111yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#357C2
socleC23×C11C2×D8
prime radicalC22×C11×D8C22
cosocleC22×C8×C11C23
hypercenterC2×#357D11
hypocenterC11#12935
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#10622142C2semidirect
4. #13069350C2semidirect
5. #13066707C2semidirect
6. #13066693C2semidirect
20. C11×#357C4semidirect
44. C2×C11×C16C2×C4semidirect
46. C11×#107C2×C4semidirect
78. C11×D8C4⋊C4semidirect
160. #357Dic11semidirect
208. C2×C16C2×Dic11semidirect
214. #107C2×Dic11semidirect
246. D8C4⋊Dic11semidirect
268. C11#12935semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic112
C2×#106221422
C2×#106222002
#130693502
#130667072
#130666932
C2×C11×#3572
#1293511