Finite Group Databasebeta

← #14670282

Subgroups — #14670282

Order 2816.

442 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622493C211yesmaximal, characteristic
2C2×#10622127C211yesmaximal, characteristic, complemented
3C2×(C2×D11)⋊C16C211yesmaximal, characteristic
4#13068642C211yesmaximal, characteristic
5#13066708C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C2×C11×#367C211yesmaximal, characteristic, complemented
8C22×C8×D11C2211yescharacteristic
9C2×#66945—21no—
10C22×C11×C16C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C2×#66882C2211yescharacteristic
14C2×#66882C2211yescharacteristic
15C22×C11⋊C16C2211yescharacteristic
16#10622600—21no—
17C2×#66872—21no—
18#10622493—22no—
19#10622493—22no—
20C11×#367—22no—
21#10622167—21no—
22(C2×D11)⋊C16C414yescomplemented
23#10622127—22no—
24C22×C4×D11D411yescharacteristic
25C22×C8×C11C2311yescharacteristic
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×(C2×D11)⋊C4—41no—
29C2×(C2×D11)⋊C4—41no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4×Dic11—41no—
33C22×C11⋊C8D411yescharacteristic
34C2×C8×D11—21no—
35C2×C8×D11—21no—
36C2×C8×D11—21no—
37C2×C8×D11—21no—
38C2×C8×D11C2×C412yes—
39C2×C8×D11Q812yes—
40#66945—24no—
41#66945—42no—
42C2×C11×C16—21no—
43C2×C11×C16—21no—
44C2×C11×C16C2×C412yes—
45C11×#107—21no—
46C11×#107—21no—
47C11×#107—21no—
48C11×#107D412yes—
49C11⋊#95—41no—
50#66882—21no—
51#66882—21no—
52#66882—21no—
53#66882D412yes—
54C2×C11⋊C16—21no—
55C2×C11⋊C16—21no—
56C2×C11⋊C16C2×C412yes—
57#66872—24no—
58#12921—111nomaximal, Sylow
59C23×D11D811yescharacteristic
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—41no—
64C22×Dic11—41no—
65C22×Dic11D811yescharacteristic
66C2×C4×D11—21no—
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11C4⋊C412yes—
71C2×C4×D11Q1612yes—
72C2×C8×C11C22×C411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C2×C8×C11C2×D411yescharacteristic
75C2×C8×C11C2×Q811yescharacteristic
76C2×C8×C11#4111yescharacteristic
77C2×C8×C11#4111yescharacteristic
78C11×C4⋊C4—22no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82(C2×D11)⋊C4—44no—
83(C2×D11)⋊C4—82no—
84C4⋊Dic11—22no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87C4⋊Dic11—41no—
88C4×Dic11—44no—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8C4⋊C412yes—
92C8×D11—22no—
93C8×D11—22no—
94C8×D11—22no—
95C8×D11—22no—
96C11×C16—22no—
97C11⋊C16—22no—
98C2×#427—111no—
99C2×#367D1111yescharacteristic, complemented
100C2×#366—111no—
101C2×C22⋊C16—111no—
102#1808—111no—
103#1380—111no—
104#1380—111no—
105C23×C11C2×D811yescharacteristic
106C22×D11—21no—
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11#10712yes—
113C2×C4×C11—42no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11—81no—
119C2×C4×C11C2×C4⋊C411yescharacteristic
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12311yescharacteristic
122C2×C4×C11C2×Q1611yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C11#13711yescharacteristic
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—42no—
128C2×Dic11—81no—
129C2×Dic11—81no—
130C2×Dic11—81no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133C2×Dic11#10712yes—
134C4×D11—22no—
135C4×D11—22no—
136C4×D11—22no—
137C4×D11—22no—
138C8×C11C4×D411yescharacteristic
139C8×C11C4×D411yescharacteristic
140C8×C11C22⋊Q811yescharacteristic
141C8×C11C22⋊Q811yescharacteristic
142C11⋊C8—22no—
143C23×C8—111no—
144C2×#117—221no—
145C22×C16—111no—
146C22×C16C2×D1111yescharacteristic
147#427—222no—
148#427—222no—
149C2×#107—111no—
150C2×#107—111no—
151C2×#107C2×D1111yescharacteristic
152C2×#107C2×D1111yescharacteristic
153C2×#106—221no—
154#380—221no—
155#367—22no—
156#366—222no—
157C22⋊C16—114no—
158#340—221no—
159C22×C11C2×#10711yescharacteristic
160C22×C11#44711yescharacteristic
161C22×C11#48011yescharacteristic
162C22×C11#50811yescharacteristic
163C22×C11#50811yescharacteristic
164C22×C11#50911yescharacteristic
165C22×C11#51011yescharacteristic
166C2×D11—22no—
167C2×D11—22no—
168C2×D11—22no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C4×C11—82no—
174C4×C11—161no—
175C4×C11#38511yescharacteristic
176C4×C11#42811yescharacteristic
177C4×C11#45111yescharacteristic
178C4×C11#48411yescharacteristic
179Dic11—22no—
180Dic11—82no—
181Dic11—161no—
182C23×C4—111no—
183C22×C8—111no—
184C22×C8—112no—
185C22×C8—112no—
186C22×C8—221no—
187C22×C8—221no—
188C22×C8—221no—
189C22×C8—221no—
190C22×C8C22×D1111yescharacteristic
191#117—224no—
192#117—442no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C22⋊C4—441no—
198C2×C22⋊C4—441no—
199C2×C42—441no—
200C2×C16—21no—
201C2×C16—21no—
202C2×C16—112no—
203C2×C16—221no—
204C2×C16—221no—
205C2×C16C4×D1112yes—
206#107—21no—
207#107—21no—
208#107—21no—
209#107—112no—
210#107—221no—
211#107—221no—
212#107—221no—
213#107C22⋊D1112yes—
214#106—224no—
215#95—441no—
216C2×C11#185211yescharacteristic
217C2×C11#215811yescharacteristic
218C2×C11#215911yescharacteristic
219C2×C11#218611yescharacteristic
220C2×C11#218911yescharacteristic
221C2×C11#223411yescharacteristic
222C2×C11#223711yescharacteristic
223D11—42no—
224C24—111no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—111no—
228C22×C4—112no—
229C22×C4—112no—
230C22×C4—221no—
231C22×C4—221no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—441no—
235C22×C4—441no—
236C22×C4D4×D1111yescharacteristic
237C2×C8—112no—
238C2×C8—221no—
239C2×C8—221no—
240C2×C8—222no—
241C2×C8—222no—
242C2×C8—222no—
243C2×C8—222no—
244C2×C8C2×C4×D1111yescharacteristic
245C2×C8#433911yescharacteristic
246C2×C8D4×D1111yescharacteristic
247C2×C8Q8×D1111yescharacteristic
248C2×C8#434311yescharacteristic
249C2×C8C2×C22⋊D1111yescharacteristic
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—222no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C22⋊C4—444no—
259C22⋊C4—882no—
260C42—444no—
261C16—22no—
262C16—222no—
263C11#1292111yescharacteristic, complemented, Sylow
264C23—112no—
265C23—221no—
266C23—221no—
267C23—221no—
268C23—221no—
269C23—221no—
270C23—221no—
271C23D8×D1111yescharacteristic
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—112no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—222no—
282C2×C4—222no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—442no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4—881no—
289C2×C4—881no—
290C2×C4—881no—
291C2×C4C4⋊C4×D1111yescharacteristic
292C2×C4#6694711yescharacteristic
293C2×C4#6696411yescharacteristic
294C2×C4Q16×D1111yescharacteristic
295C2×C4#6697111yescharacteristic
296C2×C4#6699011yescharacteristic
297C8—222no—
298C8#6694611yescharacteristic
299C8#6694911yescharacteristic
300C8C4×C22⋊D1111yescharacteristic
301C8#6699911yescharacteristic
302C22—222no—
303C22—222no—
304C22—222no—
305C22—441no—
306C22—441no—
307C22—441no—
308C22—441no—
309C22D11×#10711yescharacteristic
310C22#1062249511yescharacteristic
311C22#1062252711yescharacteristic
312C22#1062252811yescharacteristic
313C22#1062252911yescharacteristic
314C22#1062252911yescharacteristic
315C22#1062276911yescharacteristic
316C4—82no—
317C4—161no—
318C4—222no—
319C4—882no—
320C4—1761no—
321C4#1062249411yescharacteristic
322C4#1062249711yescharacteristic
323C4#1062260211yescharacteristic
324C4#1062279911yescharacteristic
325C2—442no—
326C2#1306880211yescharacteristic
327C2#1307039911yescharacteristic
328C2#1307040311yescharacteristic
329C2#1307053811yescharacteristic
330C2#1307055311yescharacteristic
331C2#1307080911yescharacteristic
332C2#1307082711yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#367C2
socleC23×C11C2×D8
prime radicalC23×D11D8
cosocleC22×C8×C11C23
hypercenterC2×#367D11
hypocenterC11#12921
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#367

Complements

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

NH ≅ G/Ntype
2. C2×#10622127C2semidirect
5. #13066708C2semidirect
6. #13066707C2semidirect
7. C2×C11×#367C2semidirect
22. (C2×D11)⋊C16C4semidirect
99. C2×#367D11semidirect
263. C11#12921semidirect

Maximal subgroups

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

subgroupindex
C2×#106224932
C2×#106221272
C2×(C2×D11)⋊C162
#130686422
#130667082
#130667072
C2×C11×#3672
#1292111