Finite Group Databasebeta

← #14670244

Subgroups — #14670244

Order 2816.

420 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×M32C211yesmaximal, characteristic
2C2×#10622101C211yesmaximal, characteristic, complemented
3C2×#10622149C211yesmaximal, characteristic, complemented
4#13070226C211yesmaximal, characteristic
5C8×(C2×D11)⋊C4C211yesmaximal, characteristic
6#13066697C211yesmaximal, characteristic, complemented
7C11×#1376C211yesmaximal, characteristic, complemented
8C22×C8×D11C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C2×C11×M32C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C2×(C2×D11)⋊C8C411yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14C2×#66876C2211yescharacteristic
15C2×#66876C2211yescharacteristic
16C4×(C2×D11)⋊C4C411yescharacteristic
17D11×M32—22no—
18D11×M32—22no—
19C2×#66862—21no—
20C2×C16×D11—21no—
21#10622188C411yescharacteristic
22#10622162C411yescharacteristic
23#10622149—22no—
24(C2×D11)⋊C16—21no—
25(C2×D11)⋊C16—21no—
26#10622101—22no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C8×C11C2×C411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×(C2×D11)⋊C4—21no—
32C2×C4×Dic11C2×C411yescharacteristic
33C22×C11⋊C8C2×C411yescharacteristic
34C22×C11⋊C8C2×C411yescharacteristic
35C2×C8×D11—21no—
36C2×C8×D11—21no—
37C2×C8×D11—21no—
38C2×C8×D11—21no—
39C2×C8×D11D411yescharacteristic
40C2×C8×D11D411yescharacteristic
41C2×C8×D11Q811yescharacteristic
42C2×C8×D11Q811yescharacteristic
43C11×M32—21no—
44C11×M32—21no—
45C11×M32—21no—
46C11×M32D412yes—
47C2×C11×C16—21no—
48C2×C11×C16—21no—
49C4×C8×C11—21no—
50C4×C8×C11—21no—
51C11⋊#95—21no—
52(C2×D11)⋊C8C812yes—
53(C2×D11)⋊C8C812yes—
54C8×Dic11—21no—
55C8×Dic11—21no—
56#66876—21no—
57#66876—21no—
58#66876—21no—
59#66876D412yes—
60C2×C11⋊C16—21no—
61C2×C11⋊C16—21no—
62#66862—24no—
63C16×D11—24no—
64#12914—111nomaximal, Sylow
65C23×D11M1611yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11C22×C411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11M1611yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11C4⋊C411yescharacteristic
75C2×C4×D11C4⋊C411yescharacteristic
76C2×C4×D11C2×C811yescharacteristic
77C2×C4×D11C2×C811yescharacteristic
78C2×C8×C11—21no—
79C2×C8×C11—21no—
80C2×C8×C11C2×C812yes—
81C2×C8×C11C2×D411yescharacteristic
82C2×C8×C11C2×D411yescharacteristic
83C2×C8×C11C2×D411yescharacteristic
84C2×C8×C11C2×Q811yescharacteristic
85C2×C8×C11#4111yescharacteristic
86C2×C8×C11#4111yescharacteristic
87C42×C11—21no—
88C42×C11—21no—
89(C2×D11)⋊C4—24no—
90C4×Dic11—21no—
91C4×Dic11—21no—
92C2×C11⋊C8—21no—
93C2×C11⋊C8—21no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8C4⋊C411yescharacteristic
97C2×C11⋊C8C4⋊C411yescharacteristic
98C2×C11⋊C8C2×C812yes—
99C8×D11—21no—
100C8×D11—21no—
101C8×D11—21no—
102C8×D11—21no—
103C8×D11—21no—
104C8×D11—21no—
105C8×D11—21no—
106C8×D11—21no—
107C11×C16—22no—
108C11×C16—41no—
109C11⋊C16—22no—
110C11⋊C16—41no—
111C22×M32—111no—
112C2×#364—111no—
113C2×#364—111no—
114#2112—111no—
115C8×C22⋊C4—111no—
116#1376—111no—
117#1376D1111yescharacteristic, complemented
118C23×C11C2×M1611yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—22no—
122C22×D11—41no—
123C22×D11C4⋊C811yescharacteristic
124C22×D11C4⋊C811yescharacteristic
125C2×C4×C11—22no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11C2×C4⋊C411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11C22×C811yescharacteristic
132C2×C4×C11#13111yescharacteristic
133C2×C4×C11#13111yescharacteristic
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—22no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11C4⋊C811yescharacteristic
140C2×Dic11C4⋊C811yescharacteristic
141C4×D11—21no—
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—21no—
148C4×D11—21no—
149C8×C11—22no—
150C8×C11#12011yescharacteristic
151C8×C11C22⋊Q811yescharacteristic
152C8×C11C22⋊Q811yescharacteristic
153C8×C11#12311yescharacteristic
154C11⋊C8—21no—
155C11⋊C8—21no—
156C11⋊C8—22no—
157C23×C8—111no—
158C2×M32—111no—
159C2×M32—111no—
160C2×M32—221no—
161C2×M32—222no—
162C2×M32—222no—
163C2×M32C2×D1111yescharacteristic
164C2×M32C2×D1111yescharacteristic
165C22×C16—221no—
166C2×C22⋊C8—111no—
167C2×C4×C8—111no—
168C2×C4×C8C2×D1111yescharacteristic
169C4×C22⋊C4—111no—
170#364—222no—
171#364—222no—
172C22⋊C16—221no—
173C22⋊C16—221no—
174#336—111no—
175#336—111no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11C2×C4⋊C811yescharacteristic
179C22×C11#43511yescharacteristic
180C22×C11#43511yescharacteristic
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—42no—
187C2×D11—42no—
188C2×D11#36412yescomplemented
189C4×C11—42no—
190C4×C11#38511yescharacteristic
191C4×C11#42411yescharacteristic
192C4×C11C8×D411yescharacteristic
193C4×C11C8×D411yescharacteristic
194Dic11—21no—
195Dic11—21no—
196Dic11—42no—
197C23×C4—111no—
198C22×C8—111no—
199C22×C8—111no—
200C22×C8—111no—
201C22×C8—111no—
202C22×C8—111no—
203C22×C8—111no—
204C22×C8—221no—
205C22×C8—221no—
206C22×C8—221no—
207C22×C8—221no—
208C22×C8C4×D1111yescharacteristic
209C22×C8C22×D1111yescharacteristic
210C2×C22⋊C4—221no—
211C2×C42—111no—
212C2×C42C4×D1111yescharacteristic
213M32—21no—
214M32—21no—
215M32—21no—
216M32—112no—
217M32—224no—
218M32—221no—
219M32—221no—
220M32—221no—
221M32D4412yes—
222C2×C16—21no—
223C2×C16—21no—
224C2×C16—224no—
225C2×C16—221no—
226C2×C16—221no—
227C22⋊C8—112no—
228C22⋊C8—112no—
229C4×C8—21no—
230C4×C8—21no—
231C4×C8—221no—
232C4×C8—221no—
233#95—221no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11#185011yescharacteristic
237C2×C11C2×#36411yescharacteristic
238C2×C11#215311yescharacteristic
239D11—22no—
240D11—41no—
241C24—111no—
242C22×C4—21no—
243C22×C4—111no—
244C22×C4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—111no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4C2×C4×D1111yescharacteristic
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—111no—
257C2×C8—111no—
258C2×C8—112no—
259C2×C8—221no—
260C2×C8—221no—
261C2×C8—221no—
262C2×C8—221no—
263C2×C8—221no—
264C2×C8—221no—
265C2×C8—221no—
266C2×C8—221no—
267C2×C8—221no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8C8×D1112yes—
272C2×C8C2×D4411yescharacteristic
273C2×C8#433911yescharacteristic
274C2×C8D4×D1111yescharacteristic
275C2×C8D4×D1111yescharacteristic
276C2×C8#434111yescharacteristic
277C2×C8Q8×D1111yescharacteristic
278C22⋊C4—224no—
279C42—21no—
280C42—21no—
281C42—221no—
282C42—221no—
283C16—22no—
284C16—41no—
285C16—222no—
286C16—441no—
287C11#1291411yescharacteristic, complemented, Sylow
288C23—111no—
289C23—111no—
290C23—222no—
291C23—221no—
292C23—221no—
293C23—441no—
294C23M16×D1111yescharacteristic
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—111no—
299C2×C4—111no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—222no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4C4×D4411yescharacteristic
314C2×C4(C22⋊D11)⋊C411yescharacteristic
315C2×C4C4⋊C4×D1111yescharacteristic
316C2×C4C2×C8×D1111yescharacteristic
317C2×C4#6695411yescharacteristic
318C2×C4#6696011yescharacteristic
319C8—22no—
320C8—221no—
321C8—221no—
322C8—222no—
323C8#6693511yescharacteristic
324C8#6693611yescharacteristic
325C8#6694911yescharacteristic
326C8#6695011yescharacteristic
327C22—21no—
328C22—21no—
329C22—112no—
330C22—221no—
331C22—221no—
332C22—221no—
333C22—221no—
334C22—221no—
335C22—442no—
336C22—442no—
337C22#1062231911yescharacteristic
338C22#1062234111yescharacteristic
339C22D11×C4⋊C811yescharacteristic
340C4—42no—
341C4—221no—
342C4—221no—
343C4—442no—
344C4#1062228111yescharacteristic
345C4C8×D4411yescharacteristic
346C4(C22⋊D11)⋊C811yescharacteristic
347C4#1062245211yescharacteristic
348C2—21no—
349C2—21no—
350C2—222no—
351C2—441no—
352C2#1306879511yescharacteristic
353C2D11×#36411yescharacteristic
354C2#1307038011yescharacteristic
subgroupG/H
centerC2×C8D4×D11
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#1376C2
socleC22×C11C2×C4⋊C8
prime radicalC23×D11M16
cosocleC22×C8×C11C23
hypercenter#1376D11
hypocenterC11#12914
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1376

Complements

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

NH ≅ G/Ntype
2. C2×#10622101C2semidirect
3. C2×#10622149C2semidirect
6. #13066697C2semidirect
7. C11×#1376C2semidirect
117. #1376D11semidirect
188. C2×D11#364semidirect
287. C11#12914semidirect

Maximal subgroups

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

subgroupindex
C2×D11×M322
C2×#106221012
C2×#106221492
#130702262
C8×(C2×D11)⋊C42
#130666972
C11×#13762
#1291411