Finite Group Databasebeta

← #14669883

Subgroups — #14669883

Order 2816.

400 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622508C211yesmaximal, characteristic
2C2×#10622149C211yesmaximal, characteristic, complemented
3#13070366C211yesmaximal, characteristic
4#13070363C211yesmaximal, characteristic
5#13068786C211yesmaximal, characteristic, complemented
6#13066719C211yesmaximal, characteristic, complemented
7C11×#1385C211yesmaximal, 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#10622155—21no—
24#10622154—21no—
25#10622149—21no—
26#10622149—21no—
27#10622134—21no—
28#10622133—21no—
29C2×#4339—21no—
30C2×C11×M16—21no—
31C2×C11×M16—21no—
32C22×C8×C11C2311yescharacteristic
33C2×C4×Dic11D411yescharacteristic
34C2×#4318—21no—
35C22×C11⋊C8D411yescharacteristic
36#66960—22no—
37#66960—22no—
38#66960—41no—
39#66960—41no—
40C2×Dic44D411yescharacteristic
41#66957—21no—
42#66957—21no—
43#66957C2×C412yes—
44#66957Q812yes—
45C2×D88D411yescharacteristic
46C2×#4314—21no—
47C2×#4313—41no—
48C2×C8×D11—41no—
49C11×M32—21no—
50C11×M32—21no—
51C2×C11×C16—21no—
52C11×#108—21no—
53C11×#108—21no—
54C11×#108—21no—
55C11×#108C2×C412yes—
56#66889—22no—
57#66889—22no—
58#66886—41no—
59#66886—41no—
60#66883—21no—
61#66883—21no—
62Dic11⋊C8—42no—
63C8×Dic11C2×C411yescharacteristic
64C8×Dic11C2×C411yescharacteristic
65C8×Dic11D411yescharacteristic
66C8×Dic11D411yescharacteristic
67#66876—21no—
68#66876—21no—
69C2×C11⋊C16—21no—
70#12825—111nomaximal, Sylow
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—41no—
73C22×Dic11—21no—
74#4339—22no—
75#4339—22no—
76#4339—41no—
77#4339—41no—
78C2×D44—21no—
79C2×C4×D11—41no—
80C2×Dic22—21no—
81C11×M16—22no—
82C11×M16—41no—
83C11×M16—41no—
84C11×M16—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11C22×C411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×Q811yescharacteristic
91C2×C8×C11#4111yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C4×Dic11—21no—
94C4×Dic11C22⋊C411yescharacteristic
95C4×Dic11C22⋊C411yescharacteristic
96#4318—41no—
97#4318—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8C22⋊C411yescharacteristic
100C2×C11⋊C8C22⋊C411yescharacteristic
101C2×C11⋊C8D811yescharacteristic
102C2×C11⋊C8D811yescharacteristic
103C2×C11⋊C8SD1611yescharacteristic
104C2×C11⋊C8SD1611yescharacteristic
105Dic44—21no—
106Dic44C4⋊C412yes—
107D88—21no—
108D88C4⋊C412yes—
109#4314—22no—
110#4314—22no—
111#4313—42no—
112#4313—42no—
113C8×D11—42no—
114C8×D11—42no—
115C11×C16—41no—
116C11⋊C16—41no—
117C2×#443—111no—
118C2×#364—111no—
119#2148—111no—
120#2148—111no—
121#1848—111no—
122#1385—111no—
123#1385D1111yescharacteristic, complemented
124C23×C11#13711yescharacteristic
125C22×D11—41no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11C2×D811yescharacteristic
130C2×C4×C11C2×SD1611yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C22⋊D11—42no—
133C22⋊D11—42no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—42no—
137C2×Dic11—41no—
138D44—22no—
139D44—41no—
140C4×D11—42no—
141C4×D11—42no—
142Dic22—22no—
143Dic22—41no—
144C8×C11—42no—
145C8×C11—81no—
146C8×C11C2×C4⋊C411yescharacteristic
147C8×C11#11711yescharacteristic
148C8×C11#12111yescharacteristic
149C8×C11C22⋊Q811yescharacteristic
150C11⋊C8—81no—
151C11⋊C8#10211yescharacteristic
152C11⋊C8#10211yescharacteristic
153C11⋊C8#10211yescharacteristic
154C11⋊C8#10211yescharacteristic
155C2×#135—111no—
156C2×#131—221no—
157C2×M32—111no—
158C2×M32C2×D1111yescharacteristic
159#443—112no—
160#443—112no—
161#443—221no—
162#443—221no—
163C2×#108—111no—
164C2×#108—221no—
165C2×#108C2×D1111yescharacteristic
166C2×#108C2×D1111yescharacteristic
167#423—221no—
168C2×#104—221no—
169C2×C4×C8—111no—
170#364—221no—
171#364—221no—
172#362—221no—
173#362—221no—
174#361—221no—
175#361—221no—
176C22×C11—41no—
177C22×C11#41711yescharacteristic
178C22×C11#46111yescharacteristic
179C22×C11#47411yescharacteristic
180C2×D11—42no—
181C2×D11—82no—
182C4×C11#38011yescharacteristic
183C4×C11C2×#10211yescharacteristic
184C4×C11#45911yescharacteristic
185C4×C11#47611yescharacteristic
186Dic11—22no—
187Dic11—41no—
188Dic11—42no—
189C2×#41—221no—
190#135—112no—
191#135—112no—
192#135—221no—
193#135—221no—
194C2×Q16—111no—
195C2×SD16—221no—
196C2×D8—111no—
197#131—222no—
198#131—222no—
199#131—441no—
200#131—441no—
201C2×M16—21no—
202C2×M16—21no—
203C2×M16—221no—
204C2×M16—441no—
205C22×C8—111no—
206C22×C8—441no—
207C22×C8C22×D1111yescharacteristic
208C2×C42—111no—
209M32—21no—
210M32—21no—
211M32—221no—
212M32—221no—
213C2×C16—21no—
214C2×C16—221no—
215#108—21no—
216#108—21no—
217#108—21no—
218#108—221no—
219#108—221no—
220#108—441no—
221#108—441no—
222#108C4×D1112yes—
223C4⋊C8—442no—
224#104—222no—
225#104—222no—
226C4×C8—111no—
227C4×C8—111no—
228C4×C8—111no—
229C4×C8—111no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#180211yescharacteristic
234D11—82no—
235#41—222no—
236#41—222no—
237#41—441no—
238#41—441no—
239C2×Q8—221no—
240C2×D4—221no—
241C2×D4—441no—
242C22×C4—221no—
243C22×C4—441no—
244C22×C4D4×D1111yescharacteristic
245Q16—112no—
246Q16—221no—
247SD16—222no—
248SD16—222no—
249D8—112no—
250D8—221no—
251M16—22no—
252M16—41no—
253M16—41no—
254M16—41no—
255M16—442no—
256M16—442no—
257M16—441no—
258M16—441no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—111no—
262C2×C8—111no—
263C2×C8—111no—
264C2×C8—111no—
265C2×C8—111no—
266C2×C8—111no—
267C2×C8—442no—
268C2×C8—442no—
269C2×C8—441no—
270C2×C8C2×C4×D1111yescharacteristic
271C2×C8#433911yescharacteristic
272C2×C8#433911yescharacteristic
273C2×C8D4×D1111yescharacteristic
274C2×C8D4×D1111yescharacteristic
275C2×C8Q8×D1111yescharacteristic
276C42—111no—
277C42—111no—
278C42—221no—
279C16—41no—
280C16—441no—
281C11#1282511yescharacteristic, complemented, Sylow
282C23—441no—
283C23#6697111yescharacteristic
284Q8—222no—
285Q8—441no—
286D4—222no—
287D4—442no—
288D4—442no—
289D4—441no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—442no—
293C2×C4—441no—
294C2×C4—442no—
295C2×C4—442no—
296C2×C4C22⋊C4×D1111yescharacteristic
297C2×C4#6693711yescharacteristic
298C2×C4#6694911yescharacteristic
299C2×C4D8×D1111yescharacteristic
300C2×C4SD16×D1111yescharacteristic
301C2×C4#6696711yescharacteristic
302C8—42no—
303C8—81no—
304C8—111no—
305C8—111no—
306C8—111no—
307C8—111no—
308C8—881no—
309C8#6692511yescharacteristic
310C8#6693711yescharacteristic
311C8C4⋊C4×D1111yescharacteristic
312C8#6694911yescharacteristic
313C22—41no—
314C22—442no—
315C22—882no—
316C22#1062241611yescharacteristic
317C22#1062243111yescharacteristic
318C22#1062250311yescharacteristic
319C4—222no—
320C4—441no—
321C4—442no—
322C4#1062228011yescharacteristic
323C4D11×#10211yescharacteristic
324C4#1062239911yescharacteristic
325C4#1062248311yescharacteristic
326C2—21no—
327C2—21no—
328C2—21no—
329C2—882no—
330C2#1306861511yescharacteristic
subgroupG/H
centerC4#10622483
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1385C2
socleC2×C11#1802
prime radicalC2×#66957C22
cosocleC22×C8×C11C23
hypercenter#1385D11
hypocenterC11#12825
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1385

Complements

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

NH ≅ G/Ntype
2. C2×#10622149C2semidirect
5. #13068786C2semidirect
6. #13066719C2semidirect
7. C11×#1385C2semidirect
123. #1385D11semidirect
281. C11#12825semidirect

Maximal subgroups

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

subgroupindex
C2×#106225082
C2×#106221492
#130703662
#130703632
#130687862
#130667192
C11×#13852
#1282511