Finite Group Databasebeta

← #14725522

Subgroups — #14725522

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077742C212yesmaximal, complemented
2C4×#66957C211yesmaximal, characteristic
3#13067524C212yesmaximal, complemented
4#13067451C214yesmaximal, complemented
5#13067439C212yesmaximal, complemented
6#13067053C212yesmaximal, complemented
7#13066905C211yesmaximal, characteristic, complemented
8C11×#1566C211yesmaximal, characteristic, complemented
9C2×#66957C411yescharacteristic
10C4×#4339C2212yes—
11C11×#423C2212yes—
12C2×C4×C8×C11C2211yescharacteristic
13#10622740—24no—
14#10622726C412yes—
15#10622719C411yescharacteristic
16#10622538C2211yescharacteristic
17C4×#4318C2211yescharacteristic
18#10622448—22no—
19#10622447C2214yes—
20D11×C4⋊C8—22no—
21#10622444C2214yes—
22C4×Dic44C411yescharacteristic
23C4×Dic44C2211yescharacteristic
24C4×D88C411yescharacteristic
25C4×D88C2211yescharacteristic
26C4×#4314C412yes—
27C4×#4314C2212yes—
28C11×#334C2212yes—
29C11×#334C2212yes—
30#10622122C2214yes—
31#10622121C2214yes—
32#10622093C2212yes—
33#10622092C2212yes—
34C2×#4339C2×C412yes—
35C2×C11×M16—22no—
36C22×C8×C11C2×C411yescharacteristic
37C22×C8×C11C2×C411yescharacteristic
38C2×C42×C11C2311yescharacteristic
39C4×C22⋊D11—22no—
40C4×C22⋊D11—22no—
41#66979C2×C412yes—
42C2×#4318—21no—
43C2×Dic44C2×C411yescharacteristic
44#66957—24no—
45C2×D88C2×C411yescharacteristic
46C2×#4314C2×C412yes—
47C2×C8×D11—24no—
48C4×D44C2×C412yes—
49C4×D44C2312yes—
50#66925—22no—
51C42×D11—22no—
52C4×Dic22C2×C412yes—
53C4×Dic22C2312yes—
54C11×C4⋊C8—22no—
55C11×C4⋊C8C2314yes—
56C4×C8×C11C2×C411yescharacteristic
57C4×C8×C11C2×C411yescharacteristic
58C4×C8×C11C2311yescharacteristic
59C4×C8×C11C2311yescharacteristic
60C22⋊(C11⋊C8)D412yes—
61#66885C2×C412yes—
62#66885C2×C412yes—
63(C2×D11)⋊C8—24no—
64#66882C2×C411yescharacteristic
65#66882C2×C411yescharacteristic
66#66881C2×C412yes—
67#66880C2×C412yes—
68#66880C2×C412yes—
69#66879—24no—
70Dic11⋊C8—24no—
71C4⋊(C11⋊C8)D412yes—
72#66867—21no—
73C4×C11⋊C8C2312yes—
74C4×C11⋊C8C2312yes—
75#18065—111nomaximal, Sylow
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C2×C22⋊D11—22no—
80#4339—24no—
81#4339—42no—
82C2×D44C22×C412yes—
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—22no—
86C2×Dic22C22×C412yes—
87C11×M16—82no—
88C2×C8×C11—22no—
89C2×C8×C11—24no—
90C2×C8×C11—41no—
91C2×C8×C11C22×C411yescharacteristic
92C2×C8×C11C22×C411yescharacteristic
93C2×C8×C11C22×C411yescharacteristic
94C2×C8×C11C22×C411yescharacteristic
95C42×C11C22×C411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11C2411yescharacteristic
99C22⋊Dic11—22no—
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—22no—
102C4⋊Dic11C22×C412yes—
103C4⋊Dic11C22×C412yes—
104Dic11⋊C4—22no—
105Dic11⋊C4—22no—
106C4×Dic11—22no—
107C4×Dic11—22no—
108C4×Dic11—22no—
109#4318—42no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8C2×D414yes—
112Dic44—22no—
113D88M1614yescomplemented
114#4314—24no—
115C8×D11—84no—
116#2990—112no—
117C4×#135—111no—
118#1593—112no—
119#1582—114no—
120#1580—112no—
121#1566D1111yescharacteristic, complemented
122#1489—112no—
123#1451—111no—
124C23×C11C4×D411yescharacteristic
125C22×D11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11C23×C411yescharacteristic
134C2×C4×C11C22×D411yescharacteristic
135C2×C4×C11C2×#4111yescharacteristic
136C22⋊D11—44no—
137C2×Dic11—22no—
138C2×Dic11—22no—
139C2×Dic11—22no—
140D44—22no—
141D44C2×M1614yes—
142C4×D11—44no—
143C4×D11—42no—
144C4×D11—42no—
145C4×D11—44no—
146Dic22—22no—
147Dic22—22no—
148C8×C11—21no—
149C8×C11—21no—
150C8×C11—21no—
151C8×C11—44no—
152C8×C11C2×M1612yes—
153C11⋊C8—24no—
154C11⋊C8—42no—
155C2×#135—111no—
156C4×#41—112no—
157#446—114no—
158C4×Q16—111no—
159C4×Q16—111no—
160C4×SD16—112no—
161C4×SD16—112no—
162C4×D8—111no—
163C4×D8—111no—
164#435—224no—
165C8×D4—114no—
166#432—222no—
167#431—111no—
168#427—111no—
169#423C2×D1112yes—
170C2×C4⋊C8—222no—
171#416—112no—
172C4×M16—111no—
173C2×C4×C8C2×D1111yescharacteristic
174#334C2×D1112yes—
175#334C2×D1112yes—
176Q8⋊C8—114no—
177D4⋊C8—114no—
178#322—112no—
179#322—112no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11C2×C4×D411yescharacteristic
184C2×D11—24no—
185C2×D11—42no—
186C2×D11—42no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11#44412yes—
191C4×C11C22×M1611yescharacteristic
192C4×C11#56811yescharacteristic
193C4×C11#57712yes—
194Dic11—42no—
195Dic11—42no—
196Dic11—42no—
197C2×#41—112no—
198#135—224no—
199C2×Q16—111no—
200C2×SD16—112no—
201C2×D8—111no—
202C2×M16—22no—
203C2×M16—221no—
204C22×C8—224no—
205C22×C8C4×D1111yescharacteristic
206C22×C8C4×D1111yescharacteristic
207C4×Q8—112no—
208C4×Q8—112no—
209C4×D4—112no—
210C4×D4—112no—
211C4×D4—222no—
212C4×D4—222no—
213#117—112no—
214#117—222no—
215C2×C42—222no—
216C2×C42C22×D1111yescharacteristic
217#107—111no—
218#107—111no—
219#106—112no—
220C4⋊C8—22no—
221C4⋊C8—112no—
222C4⋊C8—224no—
223C4⋊C8C22×D1114yes—
224#103—112no—
225#103—112no—
226#102—112no—
227#102—112no—
228C22⋊C8—112no—
229C22⋊C8—224no—
230#97—224no—
231#97—221no—
232C4×C8—112no—
233C4×C8—112no—
234C4×C8C4×D1111yescharacteristic
235C4×C8C4×D1111yescharacteristic
236C4×C8C22×D1111yescharacteristic
237C4×C8C22×D1111yescharacteristic
238C2×C11—41no—
239C2×C11D4×M1611yescharacteristic
240C2×C11#295211yescharacteristic
241C2×C11C2×#44411yescharacteristic
242D11—44no—
243#41—224no—
244#41—442no—
245C2×Q8—112no—
246C2×D4—112no—
247C2×D4—222no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4—222no—
251C22×C4C2×C4×D1111yescharacteristic
252C22×C4D4×D1111yescharacteristic
253C22×C4#434311yescharacteristic
254Q16—222no—
255SD16—224no—
256D8—114no—
257M16—82no—
258M16—442no—
259C2×C8—22no—
260C2×C8—24no—
261C2×C8—41no—
262C2×C8—114no—
263C2×C8—222no—
264C2×C8—884no—
265C2×C8C2×C4×D1111yescharacteristic
266C2×C8C2×C4×D1111yescharacteristic
267C2×C8C2×C4×D1111yescharacteristic
268C2×C8C2×C4×D1111yescharacteristic
269C4⋊C4—112no—
270C4⋊C4—112no—
271C4⋊C4—222no—
272C4⋊C4—222no—
273C22⋊C4—222no—
274C22⋊C4—222no—
275C22⋊C4—222no—
276C42—222no—
277C42—222no—
278C42—222no—
279C42C2×C4×D1111yescharacteristic
280C42D4×D1111yescharacteristic
281C42#434311yescharacteristic
282C42C23×D1111yescharacteristic
283C11#1806511yescharacteristic, complemented, Sylow
284C23—222no—
285C23#6694611yescharacteristic
286Q8—222no—
287Q8—222no—
288D4—114no—
289D4—222no—
290D4—444no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—222no—
296C2×C4—222no—
297C2×C4—222no—
298C2×C4—444no—
299C2×C4—444no—
300C2×C4—442no—
301C2×C4—442no—
302C2×C4#6694611yescharacteristic
303C2×C4#6694611yescharacteristic
304C2×C4#6694611yescharacteristic
305C2×C4C22×C4×D1111yescharacteristic
306C2×C4C2×D4×D1111yescharacteristic
307C2×C4C2×#434311yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—44no—
312C8—224no—
313C8—442no—
314C8M16×D1112yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—224no—
319C22—442no—
320C22—442no—
321C22C2×#6694611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—442no—
326C4—442no—
327C4—442no—
328C4#1062250712yes—
329C4C2×M16×D1111yescharacteristic
330C4#1062327611yescharacteristic
331C4#1062329312yes—
332C2—41no—
333C2—444no—
334C2#1307735111yescharacteristic
335C2#1307749911yescharacteristic
336C2C2×#1062250711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1566C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C4
cosocleC42×C11C24
hypercenter#1566D11
hypocenterC11#18065
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
1. #13077742C2semidirect
3. #13067524C2semidirect
4. #13067451C2semidirect
5. #13067439C2semidirect
6. #13067053C2semidirect
7. #13066905C2semidirect
8. C11×#1566C2semidirect
113. D88M16semidirect
121. #1566D11semidirect
283. C11#18065semidirect

Maximal subgroups

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

subgroupindex
#130777422
C4×#669572
#130675242
#130674512
#130674392
#130670532
#130669052
C11×#15662
#1806511