Finite Group Databasebeta

← #14648050

Subgroups — #14648050

Order 2816.

388 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077748C211yesmaximal, characteristic
2#13068787C211yesmaximal, characteristic, complemented
3#13067407C211yesmaximal, characteristic, complemented
4#13066998C211yesmaximal, characteristic
5#13066506C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1489C211yesmaximal, characteristic
8C4×C11×#41C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C4×C11×M16C2211yescharacteristic
11C2×#66886—22no—
12Q8×C11⋊C8—21no—
13#10622625—21no—
14#10622625—22no—
15#10622538—21no—
16#10622538C2211yescharacteristic
17#10622538C2211yescharacteristic
18#10622537—21no—
19#10622537C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21C11×Q8⋊C8—21no—
22C11×D4⋊C8—21no—
23Q8⋊(C11⋊C8)C411yescharacteristic
24Q8⋊(C11⋊C8)C411yescharacteristic
25D4⋊(C11⋊C8)C411yescharacteristic
26D4⋊(C11⋊C8)C411yescharacteristic
27#10622118—21no—
28#10622117—21no—
29C2×C11×#41Q811yescharacteristic
30C2×C11×M16—21no—
31C2×C11×M16—21no—
32C4×Q8×C11C2×C411yescharacteristic
33C4×Q8×C11D411yescharacteristic
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11C2×C411yescharacteristic
37C4×D4×C11D411yescharacteristic
38C11×#117—21no—
39C11×#117Q811yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4318—22no—
43C2×#4318D412yes—
44C22×C11⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×#97—21no—
48C4×C8×C11—21no—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—21no—
51C22⋊(C11⋊C8)—21no—
52#66886—44no—
53C4⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)C2×C411yescharacteristic
57C4⋊(C11⋊C8)C2×C411yescharacteristic
58C4⋊(C11⋊C8)D411yescharacteristic
59C4⋊(C11⋊C8)D411yescharacteristic
60C4×C11⋊C8—22no—
61C4×C11⋊C8—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64C4×C11⋊C8C2×C411yescharacteristic
65C4×C11⋊C8C2×C411yescharacteristic
66#8899—111nomaximal, Sylow
67C11×#41—22no—
68C11×#41—41no—
69C2×Q8×C11C4⋊C411yescharacteristic
70C2×D4×C11—21no—
71C2×D4×C11C4⋊C411yescharacteristic
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×Q811yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C11×M16—22no—
79C11×M16—41no—
80C11×M16—42no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4C4⋊C411yescharacteristic
86C11×C4⋊C4C4⋊C411yescharacteristic
87C11×C22⋊C4—21no—
88C11×C22⋊C4—21no—
89C11×C22⋊C4—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11C22×C411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97#4318—42no—
98#4318—82no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—21no—
108#2991—111no—
109#1848—111no—
110#1574—111no—
111#1489D1111yescharacteristic
112#1476—111no—
113#1299—111no—
114#1278—111no—
115C23×C11—21no—
116C23×C11C22⋊Q811yescharacteristic
117Q8×C11—21no—
118Q8×C11#10812yescomplemented
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—42no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—42no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11C2×C4⋊C411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11C22⋊Q811yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C8×C11—42no—
143C8×C11—81no—
144C11⋊C8—22no—
145C11⋊C8—22no—
146C11⋊C8—41no—
147C11⋊C8—41no—
148C11⋊C8—42no—
149C11⋊C8—41no—
150C11⋊C8—41no—
151C4×#41C2×D1111yescharacteristic
152C8×Q8—221no—
153#436—222no—
154#436—221no—
155#431—111no—
156#431—111no—
157#431—221no—
158C2×#108—222no—
159#423—111no—
160#423—221no—
161#423C2×D1111yescharacteristic
162C4×M16C2×D1111yescharacteristic
163C2×C4×C8—111no—
164#335—221no—
165#334—221no—
166Q8⋊C8—21no—
167Q8⋊C8—111no—
168Q8⋊C8—111no—
169D4⋊C8—21no—
170D4⋊C8—111no—
171D4⋊C8—111no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11#38511yescharacteristic
179C4×C11—21no—
180C4×C11—22no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#10811yescharacteristic
186C4×C11#43011yescharacteristic
187C4×C11#44311yescharacteristic
188C4×C11#44411yescharacteristic
189C4×C11#45311yescharacteristic
190C4×C11#45611yescharacteristic
191C2×#41Dic2211yescharacteristic
192C2×M16—21no—
193C2×M16—21no—
194C2×M16—112no—
195C2×M16—222no—
196C22×C8—221no—
197C4×Q8C4×D1111yescharacteristic
198C4×Q8C22⋊D1111yescharacteristic
199C4×D4—21no—
200C4×D4—21no—
201C4×D4C4×D1111yescharacteristic
202C4×D4C22⋊D1111yescharacteristic
203#117—21no—
204#117Dic2211yescharacteristic
205C2×C42—21no—
206C2×C42C22×D1111yescharacteristic
207#108—444no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—111no—
211C4⋊C8—111no—
212C4⋊C8—111no—
213C4⋊C8—111no—
214C4⋊C8—222no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217C22⋊C8—222no—
218C22⋊C8—221no—
219C22⋊C8—221no—
220#97—21no—
221C4×C8—21no—
222C4×C8—111no—
223C4×C8—111no—
224C4×C8—222no—
225C4×C8—221no—
226C4×C8—221no—
227C4×C8—221no—
228C2×C11—41no—
229C2×C11—81no—
230C2×C11#185511yescharacteristic
231C2×C11#185911yescharacteristic
232C2×C11#186611yescharacteristic
233#41—22no—
234#41—41no—
235C2×Q8Dic11⋊C411yescharacteristic
236C2×D4—21no—
237C2×D4Dic11⋊C411yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C2×Dic2211yescharacteristic
242C22×C4D4×D1111yescharacteristic
243C22×C4#434111yescharacteristic
244M16—22no—
245M16—41no—
246M16—42no—
247M16—442no—
248M16—882no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—222no—
252C2×C8—222no—
253C2×C8—221no—
254C2×C8—221no—
255C2×C8—221no—
256C2×C8—221no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—222no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4Dic11⋊C411yescharacteristic
263C4⋊C4Dic11⋊C411yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42C2×C4×D1111yescharacteristic
271C42D4×D1111yescharacteristic
272C42#434111yescharacteristic
273C42C2×C22⋊D1111yescharacteristic
274C11#889911yescharacteristic, complemented, Sylow
275C23—21no—
276C23#6693111yescharacteristic
277Q8—21no—
278Q8#6688612yescomplemented
279D4—21no—
280D4—21no—
281D4—42no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4#6693111yescharacteristic
297C2×C4(C22⋊D11)⋊C411yescharacteristic
298C2×C4(C22⋊D11)⋊C411yescharacteristic
299C2×C4C2×Dic11⋊C411yescharacteristic
300C2×C4#6698811yescharacteristic
301C2×C4#6699011yescharacteristic
302C8—42no—
303C8—81no—
304C8—222no—
305C8—222no—
306C8—442no—
307C8—441no—
308C8—441no—
309C8—441no—
310C8—441no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1062255911yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4#1062243611yescharacteristic
325C4#1062243711yescharacteristic
326C4C2×#6688611yescharacteristic
327C4#1062273711yescharacteristic
328C4#1062281111yescharacteristic
329C4#1062281811yescharacteristic
330C2—41no—
331C2—81no—
332C2#1306882011yescharacteristic
333C2#1306884011yescharacteristic
334C2#1306888911yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1489C2
socleC22×C11#385
prime radicalC2×C11×#41Q8
cosocleC2×C42×C11C23
hypercenter#1489D11
hypocenterC11#8899
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #13068787C2semidirect
3. #13067407C2semidirect
5. #13066506C2semidirect
6. #13066454C2semidirect
118. Q8×C11#108semidirect
274. C11#8899semidirect
278. Q8#66886semidirect

Maximal subgroups

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

subgroupindex
#130777482
#130687872
#130674072
#130669982
#130665062
#130664542
C11×#14892
#889911