Finite Group Databasebeta

← #14644442

Subgroups — #14644442

Order 2816.

574 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#13071081C211yesmaximal, characteristic
2C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
3#13068361C211yesmaximal, characteristic, complemented
4C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic
5#13066456C211yesmaximal, characteristic, complemented
6#13066455C211yesmaximal, characteristic, complemented
7C2×C11×D4⋊C8C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66979—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12#10622834C412yes—
13C4×C22⋊Dic11—21no—
14C2×C8×Dic11—21no—
15#10622598C412yes—
16#10622564—22no—
17C4×C4⋊Dic11C2211yescharacteristic
18C42×Dic11C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×D4⋊C8C414yescomplemented
22#10622188—22no—
23#10622188—21no—
24D4⋊(C11⋊C8)C414yescomplemented
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C4×D4×C11—21no—
30C4×D4×C11—21no—
31C4×D4×C11C2×C412yes—
32C4×D4×C11C2×C412yes—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36C2×C22⋊Dic11—22no—
37C2×C22⋊Dic11—22no—
38#66979—42no—
39#66979—42no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11C2×C412yes—
42C2×C4×Dic11—21no—
43C2×C4×Dic11C2×C412yes—
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D412yes—
46C2×C4×Dic11D411yescharacteristic
47C22×C11⋊C8—21no—
48C22×C11⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8C2×C412yes—
51C4×C8×C11—21no—
52C4×C8×C11C2×C412yes—
53C11⋊#95—21no—
54C11⋊#95—22no—
55C8×Dic11—42no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)C2×C412yes—
58C4×C11⋊C8—21no—
59C4×C11⋊C8C2×C412yes—
60#8183—111nomaximal, Sylow
61C24×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11C4212yes—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—22no—
77C22×Dic11C22⋊C412yes—
78C22×Dic11C22⋊C412yes—
79C2×C8×C11—22no—
80C2×C8×C11—22no—
81C2×C8×C11—42no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4C4212yes—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C42×C11C22×C411yescharacteristic
89C42×C11C22×C411yescharacteristic
90C42×C11#4111yescharacteristic
91C42×C11#4111yescharacteristic
92C22⋊Dic11—44no—
93C22⋊Dic11—44no—
94C4⋊Dic11—22no—
95C4⋊Dic11—22no—
96C4⋊Dic11—44no—
97C4×Dic11—22no—
98C4×Dic11—22no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—42no—
102C4×Dic11—41no—
103C4×Dic11—41no—
104C4×Dic11D812yes—
105C4×Dic11SD1612yes—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—42no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2293—111no—
112C4×C4⋊C8—111no—
113#1744—111no—
114C2×D4⋊C8—111no—
115C2×D4⋊C8D1111yescharacteristic
116#1279—111no—
117#1279—111no—
118C23×C11—22no—
119C23×C11—42no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—42no—
123C23×C11C2×C22⋊C411yescharacteristic
124D4×C11—22no—
125D4×C11—22no—
126D4×C11—42no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C2×C4211yescharacteristic
136C2×C4×C11#11711yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11#13112yes—
142C2×C4×C11#13112yes—
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—22no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11#10214yes—
156C8×C11—42no—
157C8×C11—42no—
158C11⋊C8—42no—
159C11⋊C8—42no—
160C2×C4×D4C2×D1111yescharacteristic
161C2×#117—221no—
162C2×C4⋊C8—111no—
163C2×C4⋊C8C2×D1111yescharacteristic
164C2×C4×C8—111no—
165C2×C4×C8—221no—
166C2×C4×C8C2×D1111yescharacteristic
167#390—112no—
168#389—112no—
169#388—222no—
170C4×C4⋊C4—111no—
171C4×C22⋊C4—221no—
172C43—111no—
173#336—222no—
174#336—221no—
175D4⋊C8—114no—
176D4⋊C8Dic1114yescomplemented
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—82no—
181C22×C11—82no—
182C22×C11C4×C22⋊C411yescharacteristic
183C22×C11#40812yes—
184C22×C11C2×#10211yescharacteristic
185C22×C11#41611yescharacteristic
186C22×C11#42112yes—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11#40511yescharacteristic
191C4×C11#40511yescharacteristic
192C4×C11#43312yes—
193C4×C11C4×D811yescharacteristic
194C4×C11C4×D811yescharacteristic
195C4×C11C4×SD1611yescharacteristic
196C4×C11C4×SD1611yescharacteristic
197Dic11—24no—
198Dic11—42no—
199Dic11—82no—
200C22×D4C4×D1111yescharacteristic
201C23×C4—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—221no—
205C22×C8—221no—
206C4×D4—21no—
207C4×D4—21no—
208C4×D4C4×D1112yes—
209C4×D4C2×Dic1112yes—
210#117—442no—
211#117—442no—
212C2×C4⋊C4—112no—
213C2×C4⋊C4—222no—
214C2×C4⋊C4C4×D1111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—222no—
217C2×C22⋊C4—222no—
218C2×C42—111no—
219C2×C42—112no—
220C2×C42—111no—
221C2×C42—112no—
222C2×C42—221no—
223C2×C42C22×D1111yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—112no—
226C4⋊C8—221no—
227C4⋊C8C2×Dic1112yes—
228C4×C8—21no—
229C4×C8—112no—
230C4×C8—221no—
231C4×C8—442no—
232C4×C8C2×Dic1112yes—
233#95—222no—
234#95—221no—
235C2×C11—82no—
236C2×C11#148012yes—
237C2×C11#148212yes—
238C2×C11#175011yescharacteristic
239C2×C11#175911yescharacteristic
240C2×C11C4×#10211yescharacteristic
241C24—21no—
242C2×D4—21no—
243C2×D4—22no—
244C2×D4—22no—
245C2×D4C4×Dic1112yes—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—112no—
254C22×C4—112no—
255C22×C4—222no—
256C22×C4C2×C4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—42no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—442no—
267C2×C8—441no—
268C2×C8—441no—
269C4⋊C4—21no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—444no—
273C4⋊C4C4×Dic1112yes—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—444no—
277C22⋊C4—444no—
278C42—112no—
279C42—112no—
280C42—222no—
281C42—222no—
282C42—221no—
283C42—221no—
284C42—442no—
285C42—441no—
286C42—441no—
287C42C2×C4×D1111yescharacteristic
288C42#434111yescharacteristic
289C42#434111yescharacteristic
290C42C22×Dic1111yescharacteristic
291C11#818311yescharacteristic, complemented, Sylow
292C23—22no—
293C23—42no—
294C23—41no—
295C23—41no—
296C23—42no—
297C23C22⋊C4×D1111yescharacteristic
298D4—22no—
299D4—22no—
300D4—42no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—114no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4—222no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4#6693011yescharacteristic
319C2×C4(C22⋊D11)⋊C411yescharacteristic
320C2×C4(C22⋊D11)⋊C411yescharacteristic
321C2×C4#6695412yes—
322C2×C4#6696012yes—
323C2×C4D8×D1111yescharacteristic
324C2×C4#6696511yescharacteristic
325C2×C4SD16×D1111yescharacteristic
326C2×C4#6696911yescharacteristic
327C2×C4C2×C4×Dic1111yescharacteristic
328C2×C4D4×Dic1111yescharacteristic
329C2×C4D4×Dic1111yescharacteristic
330C8—42no—
331C8—42no—
332C8—442no—
333C8—442no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—82no—
338C22—82no—
339C22#1062234012yes—
340C22D11×#10211yescharacteristic
341C22#1062238511yescharacteristic
342C22#1062243412yes—
343C22C22⋊C4×Dic1111yescharacteristic
344C4—21no—
345C4—21no—
346C4—42no—
347C4—224no—
348C4—442no—
349C4—882no—
350C4#1062233312yes—
351C4#1062236911yescharacteristic
352C4#1062237111yescharacteristic
353C4#1062271411yescharacteristic
354C4#1062273511yescharacteristic
355C4D8×Dic1111yescharacteristic
356C4SD16×Dic1111yescharacteristic
357C2—82no—
358C2#1306701312yes—
359C2#1306702112yes—
360C2#1306838411yescharacteristic
361C2#1306842811yescharacteristic
362C2#102×Dic1111yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenterC2×D4⋊C8D11
hypocenterC11#8183
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×Dic11C2semidirect
3. #13068361C2semidirect
5. #13066456C2semidirect
6. #13066455C2semidirect
21. C11×D4⋊C8C4semidirect
24. D4⋊(C11⋊C8)C4semidirect
176. D4⋊C8Dic11semidirect
291. C11#8183semidirect

Maximal subgroups

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

subgroupindex
#130710812
C4⋊C8×Dic112
#130683612
C2×D4⋊(C11⋊C8)2
#130664562
#130664552
C2×C11×D4⋊C82
#818311