Finite Group Databasebeta

← #14672003

Subgroups — #14672003

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622764C211yesmaximal, characteristic
2C2×#10622147C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic, complemented
5C2×#10622140C211yesmaximal, characteristic, complemented
6#13068779C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×#66993—21no—
10C22×#4323—21no—
11C22×D88C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14#10622764—22no—
15#10622764C414yescomplemented
16C2×#66882C2211yescharacteristic
17C2×C8×Dic11C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19#10622590—21no—
20C2×#66872—21no—
21C11×#357—22no—
22#10622200—22no—
23#10622147—22no—
24#10622140—22no—
25#10622129—22no—
26C22×D4×C11—21no—
27C22×C22⋊D11—42no—
28C22×D44—21no—
29C2×C11×D8—21no—
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8—21no—
34C2×C11×D8C2×C412yes—
35C22×C8×C11C2311yescharacteristic
36C2×C11×C4⋊C4—21no—
37#66993—24no—
38#66993—42no—
39C2×#4323—24no—
40C2×#4323—42no—
41C2×#4323—42no—
42C2×C4⋊Dic11—21no—
43C2×C4×Dic11D411yescharacteristic
44C22×C11⋊C8D411yescharacteristic
45C2×D88—21no—
46C2×D88—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88—21no—
50C2×D88C2×C412yes—
51C2×C11×C16—21no—
52C2×C11×C16—21no—
53C2×C11×C16D412yescomplemented
54C11×#107—21no—
55C11×#107—21no—
56C11⋊#95—42no—
57#66882—21no—
58#66882—21no—
59C8×Dic11C2×C412yes—
60C8×Dic11D412yes—
61C2×C11⋊C16—21no—
62C2×C11⋊C16—21no—
63C2×C11⋊C16D412yescomplemented
64#66872—42no—
65#13206—111nomaximal, Sylow
66C24×C11—41no—
67C23×D11—41no—
68C2×D4×C11—22no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—48no—
77C2×C22⋊D11—84no—
78C2×C22⋊D11—84no—
79C22×Dic11—41no—
80C22×Dic11D812yes—
81C2×D44—22no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C11×D8—22no—
88C11×D8—22no—
89C11×D8—41no—
90C11×D8—41no—
91C2×C8×C11C22×C411yescharacteristic
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11#4111yescharacteristic
96C2×C8×C11#4111yescharacteristic
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99#4323—48no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4×Dic11C22⋊C412yes—
103C4×Dic11SD1612yes—
104C2×C11⋊C8C22⋊C412yes—
105C2×C11⋊C8D812yes—
106C2×C11⋊C8SD1612yes—
107D88—22no—
108D88—22no—
109D88—41no—
110D88—41no—
111C11×C16—22no—
112C11⋊C16—22no—
113C2×#493—111no—
114C2×#357—111no—
115C2×#357—111no—
116C2×#357—111no—
117C2×#357D1111yescharacteristic, complemented
118C2×#346—111no—
119#1846—111no—
120C23×C11—42no—
121C23×C11—81no—
122C23×C11—81no—
123C23×C11—82no—
124C23×C11—82no—
125C23×C11C2×D811yescharacteristic
126C22×D11—42no—
127C22×D11—81no—
128C22×D11—81no—
129C22×D11—82no—
130C22×D11—82no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—81no—
134D4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11—82no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11#12411yescharacteristic
139C2×C4×C11#12711yescharacteristic
140C2×C4×C11C2×D811yescharacteristic
141C2×C4×C11C2×SD1611yescharacteristic
142C2×C4×C11C2×SD1611yescharacteristic
143C22⋊D11—816no—
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—81no—
147C2×Dic11—82no—
148C2×Dic11#10214yes—
149D44—42no—
150D44—42no—
151D44—81no—
152D44—81no—
153C8×C11C4×D411yescharacteristic
154C8×C11C4×D411yescharacteristic
155C8×C11#12111yescharacteristic
156C8×C11#12111yescharacteristic
157C11⋊C8#10214yes—
158C22×D8—111no—
159C22×D8—221no—
160C22×D8C2×D1111yescharacteristic
161C2×#127—221no—
162C22×C16—111no—
163C22×C16C2×D1111yescharacteristic
164#493—114no—
165#493—222no—
166C2×#107—111no—
167C2×#107C2×D1111yescharacteristic
168C2×#106—221no—
169C2×C4×C8—111no—
170#382—221no—
171#357—22no—
172#357—222no—
173#357—222no—
174#357—222no—
175#346—222no—
176C22×C11—84no—
177C22×C11—82no—
178C22×C11—162no—
179C22×C11—161no—
180C22×C11—161no—
181C22×C11C2×#10211yescharacteristic
182C22×C11#48611yescharacteristic
183C22×C11#49311yescharacteristic
184C22×C11#50912yes—
185C22×C11#50912yes—
186C2×D11—84no—
187C2×D11—82no—
188C2×D11—162no—
189C2×D11—161no—
190C2×D11—161no—
191C4×C11—161no—
192C4×C11#39011yescharacteristic
193C4×C11C2×#10211yescharacteristic
194C4×C11#48611yescharacteristic
195C4×C11#49211yescharacteristic
196Dic11—24no—
197Dic11—161no—
198C22×D4—21no—
199C22×D4—221no—
200C22×D4—442no—
201C2×D8—21no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—112no—
207C2×D8—224no—
208C2×D8—221no—
209C2×D8—221no—
210C2×D8—221no—
211C2×D8—221no—
212C2×D8—221no—
213C2×D8—442no—
214C2×D8—442no—
215C2×D8C4×D1112yes—
216C22×C8—111no—
217C22×C8C22×D1111yescharacteristic
218#127—224no—
219#127—442no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—221no—
222C2×C42—111no—
223C2×C16—21no—
224C2×C16—21no—
225C2×C16—112no—
226C2×C16—221no—
227C2×C16—221no—
228C2×C16C22⋊D1112yescomplemented
229#107—21no—
230#107—21no—
231#107—221no—
232#107—221no—
233#106—442no—
234C4×C8—112no—
235C4×C8—112no—
236#95—442no—
237C2×C11—162no—
238C2×C11#195711yescharacteristic
239C2×C11#214012yes—
240C2×C11#224412yes—
241C2×C11#225011yescharacteristic
242C2×C11#225011yescharacteristic
243D11—162no—
244C24—41no—
245C24—441no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—222no—
253C2×D4—448no—
254C2×D4—441no—
255C2×D4—441no—
256C2×D4—441no—
257C2×D4—441no—
258C2×D4—441no—
259C2×D4—884no—
260C2×D4—884no—
261C22×C4—41no—
262C22×C4—112no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265D8—22no—
266D8—22no—
267D8—41no—
268D8—41no—
269D8—222no—
270D8—222no—
271D8—448no—
272D8—441no—
273D8—441no—
274C2×C8—112no—
275C2×C8—112no—
276C2×C8—112no—
277C2×C8C2×C4×D1111yescharacteristic
278C2×C8#433911yescharacteristic
279C2×C8D4×D1111yescharacteristic
280C2×C8D4×D1111yescharacteristic
281C2×C8#434111yescharacteristic
282C2×C8C2×C22⋊D1111yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—441no—
286C4⋊C4—441no—
287C42—112no—
288C42—112no—
289C16—22no—
290C16—222no—
291C11#1320611yescharacteristic, complemented, Sylow
292C23—42no—
293C23—81no—
294C23—82no—
295C23—82no—
296C23—81no—
297C23—442no—
298C23—881no—
299C23—882no—
300C23—882no—
301C23—881no—
302C23D8×D1111yescharacteristic
303D4—42no—
304D4—42no—
305D4—81no—
306D4—81no—
307D4—442no—
308D4—442no—
309D4—8816no—
310D4—881no—
311D4—881no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4—114no—
315C2×C4—222no—
316C2×C4—222no—
317C2×C4—881no—
318C2×C4—882no—
319C2×C4C22⋊C4×D1111yescharacteristic
320C2×C4#6693811yescharacteristic
321C2×C4D8×D1111yescharacteristic
322C2×C4SD16×D1111yescharacteristic
323C2×C4SD16×D1111yescharacteristic
324C2×C4#6699311yescharacteristic
325C8—114no—
326C8(C22⋊D11)⋊C411yescharacteristic
327C8#6693711yescharacteristic
328C8C4×C22⋊D1111yescharacteristic
329C8#6699211yescharacteristic
330C22—82no—
331C22—84no—
332C22—162no—
333C22—161no—
334C22—161no—
335C22—882no—
336C22—884no—
337C22—1762no—
338C22—1761no—
339C22—1761no—
340C22#1062237311yescharacteristic
341C22D11×#10211yescharacteristic
342C22#1062252412yes—
343C22#1062252712yes—
344C22#1062276411yescharacteristic
345C4—161no—
346C4—224no—
347C4—1761no—
348C4#1062237311yescharacteristic
349C4D11×#10211yescharacteristic
350C4#1062257011yescharacteristic
351C4#1062278811yescharacteristic
352C2—162no—
353C2—1762no—
354C2#1306942011yescharacteristic
355C2#1307033012yes—
356C2#1307085612yes—
357C2#1307087911yescharacteristic
358C2#1307088111yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#357C2
socleC23×C11C2×D8
prime radicalC2×#10622764C2
cosocleC22×C8×C11C23
hypercenterC2×#357D11
hypocenterC11#13206
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×#10622147C2semidirect
3. C2×#10622200C2semidirect
4. C2×#10622129C2semidirect
5. C2×#10622140C2semidirect
6. #13068779C2semidirect
7. C2×C11×#357C2semidirect
15. #10622764C4semidirect
53. C2×C11×C16D4semidirect
63. C2×C11⋊C16D4semidirect
117. C2×#357D11semidirect
228. C2×C16C22⋊D11semidirect
291. C11#13206semidirect

Maximal subgroups

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

subgroupindex
C2×#106227642
C2×#106221472
C2×#106222002
C2×#106221292
C2×#106221402
#130687792
C2×C11×#3572
#1320611