Finite Group Databasebeta

← #14670849

Subgroups — #14670849

Order 2816.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66893C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic
3C2×#10622141C211yesmaximal, characteristic
4#13069475C211yesmaximal, characteristic
5#13066707C211yesmaximal, characteristic
6#13066693C211yesmaximal, characteristic
7C2×C11×#358C211yesmaximal, characteristic
8C22×C11×Q16C2211yescharacteristic
9C2×Q8×Dic11—21no—
10C22×Dic44C2211yescharacteristic
11C22×C11×C16C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C2×#66899—21no—
14Q16×Dic11—22no—
15Q16×Dic11—22no—
16C2×#66893—22no—
17C2×#66893—22no—
18C2×#66893C414yescomplemented
19C2×#66882C2211yescharacteristic
20C2×C8×Dic11C2211yescharacteristic
21C22×C11⋊C16C2211yescharacteristic
22#10622587—21no—
23C2×#66874—21no—
24C11×#358—22no—
25#10622141—22no—
26C22×Q8×C11—21no—
27C22×Dic22—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16C2×C412yes—
32C2×C11×Q16D412yes—
33C2×C11×Q16D412yes—
34C22×C8×C11C2311yescharacteristic
35C2×C11×C4⋊C4—21no—
36Q8×Dic11—24no—
37Q8×Dic11—42no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—41no—
40C2×C4×Dic11—41no—
41C2×C4×Dic11D411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43C2×Dic44—21no—
44C2×Dic44—21no—
45C2×Dic44—21no—
46C2×Dic44—21no—
47C2×Dic44—21no—
48C2×Dic44C2×C412yes—
49C2×C11×C16—21no—
50C2×C11×C16—21no—
51C2×C11×C16—21no—
52C11×#107—21no—
53C11×#107—21no—
54#66899—24no—
55C11⋊#95—41no—
56C11⋊#95—41no—
57#66893—28no—
58#66882—21no—
59#66882D412yes—
60C8×Dic11—21no—
61C8×Dic11—21no—
62C2×C11⋊C16—21no—
63C2×C11⋊C16—21no—
64C2×C11⋊C16C2×C412yes—
65#66874—42no—
66#13015—111nomaximal, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11—22no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—41no—
77C22×Dic11—41no—
78C22×Dic11D811yescharacteristic
79C22×Dic11D811yescharacteristic
80C2×Dic22—22no—
81C2×Dic22—41no—
82C2×Dic22—41no—
83C2×Dic22—41no—
84C2×Dic22—41no—
85C2×Dic22—41no—
86C11×Q16—22no—
87C11×Q16—22no—
88C11×Q16—22no—
89C11×Q16C22⋊C414yes—
90C2×C8×C11C22×C411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11#4111yescharacteristic
95C2×C8×C11#4111yescharacteristic
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C4⋊Dic11—22no—
99C4⋊Dic11—44no—
100C4⋊Dic11—41no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—44no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107Dic44—22no—
108Dic44—22no—
109Dic44—41no—
110Dic44—41no—
111C11×C16—41no—
112C11⋊C16—22no—
113C22×Q32—111no—
114C2×C4×Q16—111no—
115C2×#358—111no—
116C2×#358D1111yescharacteristic
117#1969—111no—
118#1380—111no—
119#1374—111no—
120C23×C11C2×D811yescharacteristic
121Q8×C11—24no—
122Q8×C11—42no—
123Q8×C11—42no—
124Q8×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11—81no—
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—81no—
145C2×Dic11—81no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148C2×Dic11Q3212yescomplemented
149Dic22—42no—
150Dic22—42no—
151Dic22—81no—
152Dic22—81no—
153C8×C11C2×C22⋊C411yescharacteristic
154C8×C11C4×D411yescharacteristic
155C8×C11#12111yescharacteristic
156C8×C11#12311yescharacteristic
157C11⋊C8—41no—
158C22×Q16—111no—
159C22×Q16C2×D1111yescharacteristic
160C2×C4×Q8—221no—
161C2×Q32—114no—
162C2×Q32—222no—
163C2×Q32—222no—
164C22×C16—111no—
165C22×C16C2×D1111yescharacteristic
166C4×Q16—222no—
167C4×Q16—222no—
168C2×#107—111no—
169C2×#107C2×D1111yescharacteristic
170C2×#103—221no—
171C2×#103—221no—
172C2×C4×C8—111no—
173#391—221no—
174#358—22no—
175#358—222no—
176C22×C11C4×D811yescharacteristic
177C22×C11#44711yescharacteristic
178C22×C11#45911yescharacteristic
179C22×C11C2×Q3211yescharacteristic
180C22×C11#50811yescharacteristic
181C22×C11#51011yescharacteristic
182C22×C11#51011yescharacteristic
183C4×C11—44no—
184C4×C11—161no—
185C4×C11#38611yescharacteristic
186C4×C11#44211yescharacteristic
187C4×C11#44911yescharacteristic
188C4×C11#46311yescharacteristic
189Dic11—22no—
190Dic11—41no—
191Dic11—82no—
192Dic11—82no—
193C22×Q8—21no—
194C22×Q8—221no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—112no—
199C2×Q16—221no—
200C2×Q16—221no—
201C2×Q16—221no—
202C2×Q16—221no—
203C2×Q16—221no—
204C2×Q16C4×D1112yes—
205C2×Q16D4412yes—
206C2×Q16C22⋊D1112yes—
207C22×C8—111no—
208C22×C8C22×D1111yescharacteristic
209C4×Q8—224no—
210C4×Q8—442no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—441no—
214C2×C42—111no—
215C2×C42—441no—
216Q32—228no—
217C2×C16—21no—
218C2×C16—21no—
219C2×C16—21no—
220C2×C16—112no—
221C2×C16—221no—
222C2×C16—221no—
223#107—21no—
224#107—21no—
225#107—112no—
226#107—221no—
227#103—224no—
228#103—442no—
229C4×C8—221no—
230C4×C8—221no—
231#95—441no—
232#95—441no—
233C2×C11#187911yescharacteristic
234C2×C11C4×Q3211yescharacteristic
235C2×C11#217611yescharacteristic
236C2×C11#218811yescharacteristic
237C2×C11#218911yescharacteristic
238C2×C11#220911yescharacteristic
239C2×C11#221111yescharacteristic
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—222no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×Q8—441no—
251C2×Q8—441no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—111no—
255C22×C4—111no—
256C22×C4—441no—
257C22×C4—441no—
258C22×C4D4×D1111yescharacteristic
259Q16—22no—
260Q16—22no—
261Q16—22no—
262Q16—222no—
263Q16—222no—
264Q16—441no—
265Q16—441no—
266Q16(C2×D11)⋊C414yes—
267C2×C8—221no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8C2×C4×D1111yescharacteristic
271C2×C8C2×D4411yescharacteristic
272C2×C8D4×D1111yescharacteristic
273C2×C8#434111yescharacteristic
274C2×C8#434111yescharacteristic
275C2×C8C2×C22⋊D1111yescharacteristic
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—222no—
279C4⋊C4—444no—
280C4⋊C4—441no—
281C42—221no—
282C42—221no—
283C42—444no—
284C16—41no—
285C16—222no—
286C11#1301511yescharacteristic, complemented, Sylow
287C23D8×D1111yescharacteristic
288Q8—24no—
289Q8—42no—
290Q8—42no—
291Q8—42no—
292Q8—442no—
293Q8—442no—
294Q8—881no—
295Q8—881no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—112no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—881no—
311C2×C4—881no—
312C2×C4—881no—
313C2×C4—881no—
314C2×C4(C22⋊D11)⋊C411yescharacteristic
315C2×C4#6693511yescharacteristic
316C2×C4#6696411yescharacteristic
317C2×C4#6696711yescharacteristic
318C2×C4#6696911yescharacteristic
319C2×C4#6699211yescharacteristic
320C8—441no—
321C8(C22⋊D11)⋊C411yescharacteristic
322C8#6693911yescharacteristic
323C8C2×(C2×D11)⋊C411yescharacteristic
324C8#6699211yescharacteristic
325C22#1062236911yescharacteristic
326C22#1062238611yescharacteristic
327C22#1062252811yescharacteristic
328C22#1062252911yescharacteristic
329C22D11×Q3211yescharacteristic
330C22#1062253111yescharacteristic
331C22#1062276311yescharacteristic
332C4—44no—
333C4—161no—
334C4—222no—
335C4—441no—
336C4—882no—
337C4—882no—
338C4#1062239411yescharacteristic
339C4#1062239811yescharacteristic
340C4#1062257111yescharacteristic
341C4#1062277811yescharacteristic
342C2#1306896211yescharacteristic
343C2#1307047211yescharacteristic
344C2#1307048411yescharacteristic
345C2#1307055111yescharacteristic
346C2#1307055911yescharacteristic
347C2#1307066411yescharacteristic
348C2#1307067611yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#358C2
socle, prime radicalC23×C11C2×D8
cosocleC22×C8×C11C23
hypercenterC2×#358D11
hypocenterC11#13015
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
18. C2×#66893C4semidirect
148. C2×Dic11Q32semidirect
286. C11#13015semidirect

Maximal subgroups

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

subgroupindex
C22×#668932
C2×Q16×Dic112
C2×#106221412
#130694752
#130667072
#130666932
C2×C11×#3582
#1301511