Finite Group Databasebeta

← #14669848

Subgroups — #14669848

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622485C211yesmaximal, characteristic
2#13070371C211yesmaximal, characteristic, complemented
3C2×#10622154C211yesmaximal, characteristic
4C2×#10622133C211yesmaximal, characteristic
5#13068786C211yesmaximal, characteristic, complemented
6#13066724C211yesmaximal, characteristic, complemented
7C11×#1387C211yesmaximal, characteristic, complemented
8C22×D88C2211yescharacteristic
9C2×#66946—21no—
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C2×#66886—21no—
14#10622731—21no—
15C2×#66883C2211yescharacteristic
16C2×C8×Dic11C2211yescharacteristic
17C2×#66876C2211yescharacteristic
18C2×#66873—21no—
19#10622485—21no—
20#10622485—21no—
21#10622485C412yes—
22#10622485C412yes—
23#10622154—22no—
24Dic11⋊C16—21no—
25Dic11⋊C16—21no—
26#10622133—22no—
27C22×D44—21no—
28C22×C4×D11—41no—
29C2×C11×M16—21no—
30C22×C8×C11C2311yescharacteristic
31C2×C11×C4⋊C4—21no—
32C2×(C2×D11)⋊C4—41no—
33C2×C4×Dic11D411yescharacteristic
34C2×#4318—21no—
35C22×C11⋊C8D411yescharacteristic
36C2×D88—21no—
37C2×D88—21no—
38C2×D88—21no—
39C2×D88C2×C412yes—
40C2×D88D412yes—
41C2×D88Q812yes—
42#66946—22no—
43#66946—22no—
44#66946—41no—
45#66946—41no—
46C11×M32—21no—
47C11×M32—21no—
48C2×C11×C16—21no—
49C11×#108—21no—
50C11×#108—21no—
51C11×#107—21no—
52C11×#107C2×C412yes—
53#66886—42no—
54#66883—21no—
55#66883—21no—
56Dic11⋊C8—41no—
57Dic11⋊C8—41no—
58C8×Dic11C2×C411yescharacteristic
59C8×Dic11C2×C411yescharacteristic
60C8×Dic11D411yescharacteristic
61C8×Dic11D411yescharacteristic
62#66876—21no—
63#66876—21no—
64C2×C11⋊C16—21no—
65#66873—22no—
66#66873—22no—
67#12818—111nomaximal, Sylow
68C23×D11—41no—
69C22×C4×C11—41no—
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11SD1611yescharacteristic
72C22×Dic11SD1611yescharacteristic
73C2×D44—22no—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—41no—
79C2×C4×D11—42no—
80C2×C4×D11—42no—
81C2×C4×D11—84no—
82C11×M16—41no—
83C11×M16—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
91C11×C4⋊C4—22no—
92C11×C4⋊C4—41no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95C4×Dic11C22⋊C411yescharacteristic
96C4×Dic11C22⋊C411yescharacteristic
97C4×Dic11D811yescharacteristic
98C4×Dic11D811yescharacteristic
99#4318—41no—
100#4318—41no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8C22⋊C411yescharacteristic
105C2×C11⋊C8C22⋊C411yescharacteristic
106D88—22no—
107D88—22no—
108D88—22no—
109D88C4⋊C414yes—
110C11×C16—41no—
111C11⋊C16—41no—
112C2×C4×D8—111no—
113#2150—111no—
114C2×#361—111no—
115C2×#361—111no—
116#1848—111no—
117#1387—111no—
118#1387D1111yescharacteristic, complemented
119C23×C11C2×SD1611yescharacteristic
120C22×D11—42no—
121C22×D11—42no—
122C22×D11—42no—
123C22×D11—82no—
124C22×D11—82no—
125C2×C4×C11—42no—
126C2×C4×C11—82no—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11#12111yescharacteristic
129C2×C4×C11C22⋊Q811yescharacteristic
130C2×C4×C11C2×D811yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C11#13711yescharacteristic
133C2×Dic11—22no—
134C2×Dic11—41no—
135C2×Dic11#10211yescharacteristic
136C2×Dic11#10211yescharacteristic
137C2×Dic11#10211yescharacteristic
138C2×Dic11#10211yescharacteristic
139D44—24no—
140D44—42no—
141D44—42no—
142D44—42no—
143C4×D11—84no—
144C4×D11—84no—
145C8×C11—81no—
146C8×C11C2×C4⋊C411yescharacteristic
147C8×C11#11711yescharacteristic
148C8×C11#12111yescharacteristic
149C8×C11C22⋊Q811yescharacteristic
150C11⋊C8—21no—
151C11⋊C8—21no—
152C11⋊C8—81no—
153C22×D8—111no—
154C2×C4×D4—221no—
155C2×M32—111no—
156C2×M32C2×D1111yescharacteristic
157C4×D8—112no—
158C4×D8—112no—
159C4×D8—221no—
160C4×D8—221no—
161C2×#108—111no—
162C2×#108—221no—
163C2×#108C2×D1111yescharacteristic
164C2×#107C2×D1111yescharacteristic
165#423—221no—
166C2×#102—221no—
167C2×C4×C8—111no—
168C4⋊C16—221no—
169C4⋊C16—221no—
170#361—222no—
171#361—222no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11C2×#10211yescharacteristic
175C22×C11#46111yescharacteristic
176C22×C11#47611yescharacteristic
177C2×D11—44no—
178C2×D11—84no—
179C2×D11—84no—
180C2×D11—82no—
181C2×D11—82no—
182C4×C11—82no—
183C4×C11#38011yescharacteristic
184C4×C11#41711yescharacteristic
185C4×C11#45911yescharacteristic
186C4×C11#47411yescharacteristic
187Dic11—21no—
188Dic11—21no—
189Dic11—21no—
190Dic11#36112yescomplemented
191C22×D4—221no—
192C23×C4—441no—
193C2×D8—112no—
194C2×D8—112no—
195C2×D8—112no—
196C2×D8—221no—
197C2×D8—221no—
198C2×D8—221no—
199C2×M16—21no—
200C2×M16—221no—
201C22×C8—111no—
202C22×C8C22×D1111yescharacteristic
203C4×D4—222no—
204C4×D4—222no—
205C4×D4—441no—
206C4×D4—441no—
207C2×C4⋊C4—21no—
208C2×C22⋊C4—441no—
209C2×C42—111no—
210M32—21no—
211M32—21no—
212M32—221no—
213M32—221no—
214C2×C16—21no—
215C2×C16—221no—
216#108—21no—
217#108—21no—
218#108—221no—
219#108—221no—
220#108—442no—
221#107—21no—
222#107C4×D1112yes—
223C4⋊C8—441no—
224C4⋊C8—441no—
225#102—222no—
226#102—222no—
227C4×C8—111no—
228C4×C8—111no—
229C4×C8—111no—
230C4×C8—111no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#180211yescharacteristic
234C2×C11C2×#36111yescharacteristic
235C2×C11#214811yescharacteristic
236D11—84no—
237C24—441no—
238C2×D4—222no—
239C2×D4—222no—
240C2×D4—222no—
241C2×D4—441no—
242C2×D4—441no—
243C2×D4—441no—
244C22×C4—41no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—442no—
248C22×C4—442no—
249C22×C4—884no—
250C22×C4D4×D1111yescharacteristic
251D8—114no—
252D8—222no—
253D8—222no—
254D8—222no—
255M16—41no—
256M16—41no—
257M16—441no—
258M16—441no—
259C2×C8—41no—
260C2×C8—111no—
261C2×C8—111no—
262C2×C8—221no—
263C2×C8—221no—
264C2×C8—441no—
265C2×C8C2×C4×D1111yescharacteristic
266C2×C8#433911yescharacteristic
267C2×C8#433911yescharacteristic
268C2×C8D4×D1111yescharacteristic
269C2×C8D4×D1111yescharacteristic
270C2×C8Q8×D1111yescharacteristic
271C4⋊C4—22no—
272C4⋊C4—41no—
273C22⋊C4—442no—
274C22⋊C4—442no—
275C42—111no—
276C42—111no—
277C42—111no—
278C42—111no—
279C16—41no—
280C16—441no—
281C11#1281811yescharacteristic, complemented, Sylow
282C23—442no—
283C23—442no—
284C23—442no—
285C23—882no—
286C23—882no—
287C23SD16×D1111yescharacteristic
288D4—224no—
289D4—442no—
290D4—442no—
291D4—442no—
292C2×C4—42no—
293C2×C4—82no—
294C2×C4—111no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—222no—
299C2×C4—441no—
300C2×C4—884no—
301C2×C4—884no—
302C2×C4C22⋊C4×D1111yescharacteristic
303C2×C4#6693711yescharacteristic
304C2×C4#6694911yescharacteristic
305C2×C4D8×D1111yescharacteristic
306C2×C4#6696711yescharacteristic
307C2×C4#6697111yescharacteristic
308C8—81no—
309C8—221no—
310C8—221no—
311C8—881no—
312C8#6692511yescharacteristic
313C8#6693711yescharacteristic
314C8C4⋊C4×D1111yescharacteristic
315C8#6694911yescharacteristic
316C22—21no—
317C22—21no—
318C22—444no—
319C22—884no—
320C22—884no—
321C22—882no—
322C22—882no—
323C22D11×#10211yescharacteristic
324C22#1062243111yescharacteristic
325C22#1062248311yescharacteristic
326C4—82no—
327C4—112no—
328C4—221no—
329C4—221no—
330C4—221no—
331C4#1062228011yescharacteristic
332C4#1062239911yescharacteristic
333C4#1062241611yescharacteristic
334C4#1062250311yescharacteristic
335C2—21no—
336C2—21no—
337C2—884no—
338C2#1306861511yescharacteristic
339C2D11×#36111yescharacteristic
340C2#1307036411yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1387C2
socleC22×C11C2×#102
prime radicalC22×D88C22
cosocleC22×C8×C11C23
hypercenter#1387D11
hypocenterC11#12818
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
2. #13070371C2semidirect
5. #13068786C2semidirect
6. #13066724C2semidirect
7. C11×#1387C2semidirect
118. #1387D11semidirect
190. Dic11#361semidirect
281. C11#12818semidirect

Maximal subgroups

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

subgroupindex
C2×#106224852
#130703712
C2×#106221542
C2×#106221332
#130687862
#130667242
C11×#13872
#1281811