Finite Group Databasebeta

← #13077458

Subgroups — #13077458

Order 1408.

470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66971C211yesmaximal, characteristic
2#10623105C211yesmaximal, characteristic
3#10623103C211yesmaximal, characteristic, complemented
4C11×#441C211yesmaximal, characteristic, complemented
5Q16×Dic11C211yesmaximal, characteristic, complemented
6C4×#4326C211yesmaximal, characteristic, complemented
7C4×#4325C211yesmaximal, characteristic, complemented
8#10622474C211yesmaximal, characteristic, complemented
9#10622465C211yesmaximal, characteristic, complemented
10#10622430C211yesmaximal, characteristic, complemented
11#10622417C211yesmaximal, characteristic
12D11×#103C211yesmaximal, characteristic, complemented
13#10622402C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622321C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×Q8×C11C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23C2×#4326C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25#66971C418yescomplemented
26C2×#4314C2211yescharacteristic
27C2×#4313C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29#66946—21no—
30#66946C2211yescharacteristic
31#66945—21no—
32#66945C2211yescharacteristic
33C4⋊C4×D11—21no—
34C4⋊C4×D11C2211yescharacteristic
35#66940—21no—
36#66940C2211yescharacteristic
37C4×D44—21no—
38C4×D44C2211yescharacteristic
39#66925—21no—
40#66925—21no—
41#66925C2211yescharacteristic
42C4×Dic22—21no—
43C4×Dic22C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#97C2211yescharacteristic
48#66899C2211yescharacteristic
49#66899C2211yescharacteristic
50#66885C2211yescharacteristic
51#66882C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C4×C11⋊C8C2211yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62#4343—22no—
63#4343C2×C414yes—
64Q8×D11—22no—
65Q8×D11C2×C414yescomplemented
66C2×D44—21no—
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11C2311yescharacteristic
74C2×Dic22—21no—
75C2×Dic22C2311yescharacteristic
76C11×Q16C2×C414yescomplemented
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C42×C11—21no—
84C42×C11—21no—
85C42×C11C2311yescharacteristic
86#4326C2×C414yescomplemented
87#4325C2×C414yescomplemented
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4D411yescharacteristic
92(C2×D11)⋊C4D411yescharacteristic
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4314C2×C414yescomplemented
111#4313C2×C414yescomplemented
112C8×D11—22no—
113#2947—111nomaximal, Sylow
114C22×D11—21no—
115C22×D11C2×D411yescharacteristic
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11C22×C412yes—
119Q8×C11C22×C412yes—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133D44—24no—
134D44—21no—
135D44C22×C412yes—
136C4×D11—24no—
137C4×D11—24no—
138C4×D11—81no—
139C4×D11—81no—
140C4×D11—81no—
141C4×D11C22×C412yes—
142C4×D11#4112yes—
143Dic22—21no—
144Dic22—24no—
145Dic22C22×C412yes—
146C8×C11—21no—
147C8×C11C22×C412yes—
148C11⋊C8—21no—
149C11⋊C8C22×C412yes—
150C2×#137—111no—
151#520—111no—
152#519—111no—
153#441—111no—
154#441D1111yescharacteristic, complemented
155#440—111no—
156#440—111no—
157C4×Q16—111no—
158C4×Q16—111no—
159C4×SD16—111no—
160C4×SD16—111no—
161#428—111no—
162#416—111no—
163C2×#103—111no—
164#405—111no—
165C22×C11C22×D411yescharacteristic
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—22no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11C4×D412yes—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11C23×C411yescharacteristic
179C4×C11C2×#4111yescharacteristic
180Dic11—22no—
181Dic11—21no—
182Dic11—21no—
183Dic11—41no—
184Dic11—41no—
185Dic11C4×D412yes—
186C2×#41—111no—
187C22×Q8—111no—
188#137—118no—
189C2×Q16—111no—
190C2×Q16C2×D1111yescharacteristic
191C2×SD16—111no—
192C2×SD16—111no—
193C2×M16—111no—
194C22×C8—111no—
195C4×Q8—111no—
196C4×Q8—111no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—221no—
200C4×Q8—221no—
201C4×Q8C2×D1111yescharacteristic
202C4×Q8C2×D1111yescharacteristic
203C4×D4—111no—
204C4×D4—111no—
205C4×D4—221no—
206C4×D4—221no—
207#117—111no—
208#117—111no—
209#117—221no—
210#117—221no—
211#117—221no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214#107—111no—
215#107—111no—
216#106—111no—
217#106C2×D1111yescharacteristic
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103C2×D1111yescharacteristic
223#103C2×D1111yescharacteristic
224#102—111no—
225#102—111no—
226#97—111no—
227#97C2×D1111yescharacteristic
228C4×C8—111no—
229C4×C8—111no—
230C2×C11C2×C4×D411yescharacteristic
231C2×C11#57711yescharacteristic
232C2×C11#57811yescharacteristic
233D11—22no—
234D11—42no—
235#41—114no—
236#41—222no—
237C2×Q8—114no—
238C2×Q8—111no—
239C2×Q8—221no—
240C2×Q8—222no—
241C2×Q8C22×D1111yescharacteristic
242C2×Q8C22×D1111yescharacteristic
243C2×D4—111no—
244C2×D4—221no—
245C22×C4—111no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251Q16—114no—
252Q16C4×D1114yescomplemented
253SD16—114no—
254SD16—114no—
255M16—114no—
256C2×C8—111no—
257C2×C8—111no—
258C2×C8—222no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—111no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4C22×D1111yescharacteristic
273C4⋊C4C22×D1111yescharacteristic
274C22⋊C4—111no—
275C22⋊C4—111no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C42—21no—
280C42—21no—
281C42—111no—
282C42—221no—
283C42—221no—
284C42—221no—
285C42—221no—
286C42—221no—
287C42C22×D1111yescharacteristic
288C11#294711yescharacteristic, complemented, Sylow
289C23—111no—
290C23—221no—
291Q8—21no—
292Q8—21no—
293Q8—112no—
294Q8—224no—
295Q8—221no—
296Q8C2×C4×D1112yes—
297Q8C2×C4×D1112yes—
298D4—112no—
299D4—224no—
300D4—221no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—111no—
306C2×C4—112no—
307C2×C4—112no—
308C2×C4—111no—
309C2×C4—111no—
310C2×C4—224no—
311C2×C4—224no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—881no—
316C2×C4—881no—
317C2×C4—881no—
318C2×C4D4×D1111yescharacteristic
319C2×C4D4×D1111yescharacteristic
320C2×C4C23×D1111yescharacteristic
321C8—21no—
322C8—112no—
323C8—221no—
324C8C2×C4×D1112yes—
325C22—112no—
326C22—221no—
327C22—221no—
328C22—222no—
329C22—441no—
330C22—441no—
331C22C2×D4×D1111yescharacteristic
332C4—21no—
333C4—21no—
334C4—22no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—112no—
339C4—221no—
340C4—221no—
341C4—222no—
342C4—441no—
343C4—441no—
344C4C22×C4×D1111yescharacteristic
345C4#41×D1111yescharacteristic
346C2—222no—
347C2—442no—
348C2C4×D4×D1111yescharacteristic
349C2#1062330911yescharacteristic
350C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutatorC4×C11C23×C4
FrattiniC2×C4C23×D11
FittingC11×#441C2
socleC22×C11C22×D4
prime radicalC2×#4343C22
cosocleC2×C4×C11C24
hypercenter#441D11
hypocenterC11#2947
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. #10623103C2semidirect
4. C11×#441C2semidirect
5. Q16×Dic11C2semidirect
6. C4×#4326C2semidirect
7. C4×#4325C2semidirect
8. #10622474C2semidirect
9. #10622465C2semidirect
10. #10622430C2semidirect
12. D11×#103C2semidirect
13. #10622402C2semidirect
14. #10622323C2semidirect
15. #10622321C2semidirect
25. #66971C4semidirect
65. Q8×D11C2×C4semidirect
76. C11×Q16C2×C4semidirect
86. #4326C2×C4semidirect
87. #4325C2×C4semidirect
110. #4314C2×C4semidirect
111. #4313C2×C4semidirect
154. #441D11semidirect
252. Q16C4×D11semidirect
288. C11#2947semidirect

Maximal subgroups

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

subgroupindex
C2×#669712
#106231052
#106231032
C11×#4412
Q16×Dic112
C4×#43262
C4×#43252
#106224742
#106224652
#106224302
#106224172
D11×#1032
#106224022
#106223232
#106223212
#294711