Finite Group Databasebeta

← #14669868

Subgroups — #14669868

Order 2816.

400 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622508C211yesmaximal, characteristic
2C2×#10622149C211yesmaximal, characteristic, complemented
3#13070345C211yesmaximal, characteristic
4#13070343C211yesmaximal, characteristic
5#13068786C211yesmaximal, characteristic, complemented
6#13066729C211yesmaximal, characteristic, complemented
7C11×#1388C211yesmaximal, characteristic, complemented
8C2×#66960—21no—
9C2×#66957C2211yescharacteristic
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#108C2211yescharacteristic
13C2×#66889—21no—
14C2×#66886—21no—
15#10622731—21no—
16C2×#66883C2211yescharacteristic
17C2×C8×Dic11C2211yescharacteristic
18C2×#66876C2211yescharacteristic
19#10622508—21no—
20#10622508—21no—
21#10622508C412yes—
22#10622508C412yes—
23#10622149—21no—
24#10622149—21no—
25#10622148—22no—
26#10622135—22no—
27C2×#4339—21no—
28C2×C11×M16—21no—
29C2×C11×M16—21no—
30C22×C8×C11C2311yescharacteristic
31C2×C4×Dic11D411yescharacteristic
32C2×#4318—21no—
33C22×C11⋊C8D411yescharacteristic
34#66960—22no—
35#66960—22no—
36#66960—41no—
37#66960—41no—
38C2×Dic44Q811yescharacteristic
39#66957—21no—
40#66957—21no—
41#66957C2×C412yes—
42#66957D412yes—
43C2×D88Q811yescharacteristic
44C2×#4314—21no—
45C2×#4313—41no—
46C2×C8×D11—41no—
47C11×M32—21no—
48C11×M32—21no—
49C2×C11×C16—21no—
50C11×#108—21no—
51C11×#108—21no—
52C11×#108—21no—
53C11×#108C2×C412yes—
54#66889—22no—
55#66889—22no—
56#66886—41no—
57#66886—41no—
58#66883—21no—
59#66883—21no—
60Dic11⋊C8—42no—
61C8×Dic11C2×C411yescharacteristic
62C8×Dic11C2×C411yescharacteristic
63C8×Dic11D411yescharacteristic
64C8×Dic11D411yescharacteristic
65#66876—21no—
66#66876—21no—
67C2×C11⋊C16—21no—
68#12822—111nomaximal, Sylow
69C22×C4×C11C2×D411yescharacteristic
70C2×C22⋊D11—41no—
71C22×Dic11—21no—
72#4339—22no—
73#4339—22no—
74#4339—41no—
75#4339—41no—
76C2×D44—21no—
77C2×C4×D11—41no—
78C2×Dic22—21no—
79C11×M16—22no—
80C11×M16—41no—
81C11×M16—41no—
82C11×M16—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11C22×C411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×Q811yescharacteristic
89C2×C8×C11#4111yescharacteristic
90C2×C8×C11#4111yescharacteristic
91C4×Dic11—21no—
92C4×Dic11C22⋊C411yescharacteristic
93C4×Dic11C22⋊C411yescharacteristic
94#4318—41no—
95#4318—41no—
96C2×C11⋊C8—41no—
97C2×C11⋊C8C22⋊C411yescharacteristic
98C2×C11⋊C8C22⋊C411yescharacteristic
99C2×C11⋊C8D811yescharacteristic
100C2×C11⋊C8D811yescharacteristic
101C2×C11⋊C8SD1611yescharacteristic
102C2×C11⋊C8SD1611yescharacteristic
103Dic44—21no—
104Dic44C4⋊C412yes—
105D88—21no—
106D88C4⋊C412yes—
107#4314—22no—
108#4314—22no—
109#4313—42no—
110#4313—42no—
111C8×D11—42no—
112C8×D11—42no—
113C11×C16—41no—
114C11⋊C16—41no—
115C2×#443—111no—
116C2×#364—111no—
117#2143—111no—
118#2143—111no—
119#1848—111no—
120#1388—111no—
121#1388D1111yescharacteristic, complemented
122C23×C11#13711yescharacteristic
123C22×D11—41no—
124C2×C4×C11C2×C22⋊C411yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C2×D811yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C22⋊D11—42no—
131C22⋊D11—42no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—42no—
135C2×Dic11—41no—
136D44—22no—
137D44—41no—
138C4×D11—42no—
139C4×D11—42no—
140Dic22—22no—
141Dic22—41no—
142C8×C11—42no—
143C8×C11—81no—
144C8×C11C2×C4⋊C411yescharacteristic
145C8×C11#11711yescharacteristic
146C8×C11#12111yescharacteristic
147C8×C11C22⋊Q811yescharacteristic
148C11⋊C8—81no—
149C11⋊C8#10211yescharacteristic
150C11⋊C8#10211yescharacteristic
151C11⋊C8#10211yescharacteristic
152C11⋊C8#10211yescharacteristic
153C2×#135—111no—
154C2×#131—221no—
155C2×M32—111no—
156C2×M32C2×D1111yescharacteristic
157#443—112no—
158#443—112no—
159#443—221no—
160#443—221no—
161C2×#108—111no—
162C2×#108—221no—
163C2×#108C2×D1111yescharacteristic
164C2×#108C2×D1111yescharacteristic
165#423—221no—
166C2×#104—221no—
167C2×C4×C8—111no—
168#364—221no—
169#364—221no—
170#359—222no—
171#359—222no—
172C22×C11—41no—
173C22×C11#41711yescharacteristic
174C22×C11#46111yescharacteristic
175C22×C11#47411yescharacteristic
176C2×D11—42no—
177C2×D11—82no—
178C4×C11#38011yescharacteristic
179C4×C11C2×#10211yescharacteristic
180C4×C11#45911yescharacteristic
181C4×C11#47611yescharacteristic
182Dic11—22no—
183Dic11—41no—
184Dic11—42no—
185C2×#41—221no—
186#135—112no—
187#135—112no—
188#135—221no—
189#135—221no—
190C2×Q16—111no—
191C2×SD16—221no—
192C2×D8—111no—
193#131—222no—
194#131—222no—
195#131—441no—
196#131—441no—
197C2×M16—21no—
198C2×M16—21no—
199C2×M16—221no—
200C2×M16—441no—
201C22×C8—111no—
202C22×C8—441no—
203C22×C8C22×D1111yescharacteristic
204C2×C42—111no—
205M32—21no—
206M32—21no—
207M32—221no—
208M32—221no—
209C2×C16—21no—
210C2×C16—221no—
211#108—21no—
212#108—21no—
213#108—21no—
214#108—221no—
215#108—221no—
216#108—441no—
217#108—441no—
218#108C4×D1112yes—
219C4⋊C8—442no—
220#104—222no—
221#104—222no—
222C4×C8—111no—
223C4×C8—111no—
224C4×C8—111no—
225C4×C8—111no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11—21no—
229C2×C11#180211yescharacteristic
230D11—82no—
231#41—222no—
232#41—222no—
233#41—441no—
234#41—441no—
235C2×Q8—221no—
236C2×D4—221no—
237C2×D4—441no—
238C22×C4—221no—
239C22×C4—441no—
240C22×C4D4×D1111yescharacteristic
241Q16—112no—
242Q16—221no—
243SD16—222no—
244SD16—222no—
245D8—112no—
246D8—221no—
247M16—22no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16—442no—
252M16—442no—
253M16—441no—
254M16—441no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—111no—
258C2×C8—111no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8—111no—
262C2×C8—111no—
263C2×C8—442no—
264C2×C8—442no—
265C2×C8—441no—
266C2×C8C2×C4×D1111yescharacteristic
267C2×C8#433911yescharacteristic
268C2×C8#433911yescharacteristic
269C2×C8D4×D1111yescharacteristic
270C2×C8D4×D1111yescharacteristic
271C2×C8Q8×D1111yescharacteristic
272C42—111no—
273C42—111no—
274C42—221no—
275C16—41no—
276C16—441no—
277C11#1282211yescharacteristic, complemented, Sylow
278C23—441no—
279C23#6697111yescharacteristic
280Q8—222no—
281Q8—441no—
282D4—222no—
283D4—442no—
284D4—442no—
285D4—441no—
286C2×C4—221no—
287C2×C4—221no—
288C2×C4—442no—
289C2×C4—441no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4C22⋊C4×D1111yescharacteristic
293C2×C4#6693711yescharacteristic
294C2×C4#6694911yescharacteristic
295C2×C4D8×D1111yescharacteristic
296C2×C4SD16×D1111yescharacteristic
297C2×C4#6696711yescharacteristic
298C8—42no—
299C8—81no—
300C8—111no—
301C8—111no—
302C8—111no—
303C8—111no—
304C8—881no—
305C8#6692511yescharacteristic
306C8#6693711yescharacteristic
307C8C4⋊C4×D1111yescharacteristic
308C8#6694911yescharacteristic
309C22—41no—
310C22—442no—
311C22—882no—
312C22#1062241611yescharacteristic
313C22#1062243111yescharacteristic
314C22#1062250311yescharacteristic
315C4—222no—
316C4—441no—
317C4—442no—
318C4#1062228011yescharacteristic
319C4D11×#10211yescharacteristic
320C4#1062239911yescharacteristic
321C4#1062248311yescharacteristic
322C2—21no—
323C2—21no—
324C2—21no—
325C2—882no—
326C2#1306861511yescharacteristic
subgroupG/H
centerC4#10622399
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1388C2
socleC2×C11#1802
prime radicalC2×#66957C22
cosocleC22×C8×C11C23
hypercenter#1388D11
hypocenterC11#12822
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1388

Complements

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

NH ≅ G/Ntype
2. C2×#10622149C2semidirect
5. #13068786C2semidirect
6. #13066729C2semidirect
7. C11×#1388C2semidirect
121. #1388D11semidirect
277. C11#12822semidirect

Maximal subgroups

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

subgroupindex
C2×#106225082
C2×#106221492
#130703452
#130703432
#130687862
#130667292
C11×#13882
#1282211