Finite Group Databasebeta

← #13077488

Subgroups — #13077488

Order 1408.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66969C211yesmaximal, characteristic
2#10623105C211yesmaximal, characteristic, complemented
3#10623077C211yesmaximal, characteristic, complemented
4C11×#440C211yesmaximal, characteristic, complemented
5#10622777C211yesmaximal, characteristic, complemented
6C4×#4326C211yesmaximal, characteristic, complemented
7C4×#4323C211yesmaximal, characteristic, complemented
8#10622502C211yesmaximal, characteristic, complemented
9D11×#107C211yesmaximal, characteristic, complemented
10#10622416C211yesmaximal, characteristic, complemented
11#10622403C211yesmaximal, characteristic, complemented
12#10622384C211yesmaximal, characteristic, complemented
13#10622369C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622321C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23D4×Dic11C2211yescharacteristic
24C2×#4323C2211yescharacteristic
25C4×C22⋊D11—21no—
26C2×Dic11⋊C4—21no—
27#66969C418yescomplemented
28C2×#4314C2211yescharacteristic
29C2×#4313C2211yescharacteristic
30C2×C8×D11C2211yescharacteristic
31#66946—21no—
32#66946C2211yescharacteristic
33C4⋊C4×D11—21no—
34C4⋊C4×D11C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66940C2211yescharacteristic
37(C22⋊D11)⋊C4—21no—
38#66930—21no—
39C4×D44—21no—
40C4×D44C2211yescharacteristic
41#66925—21no—
42#66925C2211yescharacteristic
43C4×Dic22C2211yescharacteristic
44C11×#107C2211yescharacteristic
45C11×#103C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C11×#97C2211yescharacteristic
48#66899C2211yescharacteristic
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51#66882C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54C8×Dic11C2211yescharacteristic
55#66874C2211yescharacteristic
56#66873C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C4×C11⋊C8C2211yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65C22×Dic11—21no—
66#4343—22no—
67#4343C2×C414yescomplemented
68#4341—22no—
69#4341C2×C414yescomplemented
70C2×D44—21no—
71C2×D44C2311yescharacteristic
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11C2311yescharacteristic
78C2×Dic22C2311yescharacteristic
79C11×SD16C2×C414yescomplemented
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C11×C4⋊C4—21no—
83C11×C4⋊C4C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C42×C11—21no—
87C42×C11C2311yescharacteristic
88C22⋊Dic11—21no—
89#4326C2×C414yescomplemented
90#4323C2×C414yescomplemented
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4D411yescharacteristic
94(C2×D11)⋊C4D411yescharacteristic
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103Dic11⋊C4D411yescharacteristic
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4314C2×C414yescomplemented
111#4313—22no—
112C8×D11C2×C414yescomplemented
113#2951—111nomaximal, Sylow
114C23×C11—21no—
115C22×D11—21no—
116C22×D11C2×D411yescharacteristic
117Q8×C11—21no—
118Q8×C11C22×C412yes—
119D4×C11—21no—
120D4×C11C22×C412yes—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—81no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—24no—
129C2×Dic11—21no—
130C2×Dic11—24no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—81no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137D44—24no—
138D44—21no—
139D44C22×C412yes—
140C4×D11—24no—
141C4×D11—81no—
142C4×D11—81no—
143C4×D11—81no—
144C4×D11—81no—
145C4×D11C22×C412yes—
146C4×D11#4112yes—
147Dic22—21no—
148Dic22C22×C412yes—
149C8×C11—21no—
150C8×C11C22×C412yes—
151C11⋊C8—21no—
152C11⋊C8C22×C412yes—
153C2×#135—111no—
154#520—111no—
155#520—111no—
156#440—111no—
157#440—111no—
158#440—111no—
159#440D1111yescharacteristic, complemented
160C4×Q16—111no—
161C4×Q16—111no—
162C4×D8—111no—
163C4×D8—111no—
164C2×#107—111no—
165#417—111no—
166#417—111no—
167#405—111no—
168C22×C11—22no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11C22×D411yescharacteristic
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—22no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11C4×D412yes—
178C4×C11—22no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11C23×C411yescharacteristic
184C4×C11C2×#4111yescharacteristic
185Dic11—22no—
186Dic11—21no—
187Dic11—21no—
188Dic11—41no—
189Dic11—41no—
190Dic11C4×D412yes—
191C2×#41—111no—
192C2×#41—111no—
193#135—118no—
194C2×Q16—111no—
195C2×SD16—111no—
196C2×SD16C2×D1111yescharacteristic
197C2×D8—111no—
198C2×M16—111no—
199C22×C8—111no—
200C4×Q8—111no—
201C4×Q8—111no—
202C4×Q8—111no—
203C4×Q8C2×D1111yescharacteristic
204C4×D4—111no—
205C4×D4—111no—
206C4×D4—111no—
207C4×D4—221no—
208C4×D4—221no—
209C4×D4—221no—
210C4×D4—221no—
211C4×D4C2×D1111yescharacteristic
212#117—111no—
213#117—221no—
214#117—221no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219#107—111no—
220#107—111no—
221#107—111no—
222#107C2×D1111yescharacteristic
223#103—111no—
224#103—111no—
225#103—111no—
226#103C2×D1111yescharacteristic
227#102—111no—
228#102—111no—
229#102—111no—
230#102C2×D1111yescharacteristic
231#97—111no—
232#97C2×D1111yescharacteristic
233C4×C8—111no—
234C4×C8—111no—
235C2×C11—42no—
236C2×C11C2×C4×D411yescharacteristic
237C2×C11#57611yescharacteristic
238C2×C11#57811yescharacteristic
239D11—22no—
240D11—42no—
241#41—114no—
242#41—114no—
243#41—222no—
244#41—222no—
245C2×Q8—111no—
246C2×Q8C22×D1111yescharacteristic
247C2×D4—111no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4C22×D1111yescharacteristic
251C22×C4—21no—
252C22×C4—111no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260Q16—114no—
261SD16—114no—
262SD16C4×D1114yescomplemented
263D8—114no—
264M16—222no—
265C2×C8—111no—
266C2×C8—114no—
267C2×C8—111no—
268C2×C8C22×D1111yescharacteristic
269C2×C8C22×D1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—111no—
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4C22×D1111yescharacteristic
281C4⋊C4C22×D1111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—111no—
284C22⋊C4—111no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C42—21no—
289C42—111no—
290C42—221no—
291C42—221no—
292C42—221no—
293C42C22×D1111yescharacteristic
294C11#295111yescharacteristic, complemented, Sylow
295C23—21no—
296C23—111no—
297C23—221no—
298Q8—21no—
299Q8—112no—
300Q8—221no—
301Q8C2×C4×D1112yes—
302D4—21no—
303D4—112no—
304D4—224no—
305D4—224no—
306D4—221no—
307D4C2×C4×D1112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—111no—
313C2×C4—112no—
314C2×C4—112no—
315C2×C4—111no—
316C2×C4—111no—
317C2×C4—224no—
318C2×C4—224no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—881no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4D4×D1111yescharacteristic
328C2×C4D4×D1111yescharacteristic
329C2×C4C23×D1111yescharacteristic
330C8—21no—
331C8—112no—
332C8—221no—
333C8C2×C4×D1112yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—112no—
338C22—221no—
339C22—221no—
340C22—222no—
341C22—441no—
342C22—441no—
343C22C2×D4×D1111yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—112no—
350C4—221no—
351C4—221no—
352C4—222no—
353C4—441no—
354C4—441no—
355C4C22×C4×D1111yescharacteristic
356C4#41×D1111yescharacteristic
357C2—42no—
358C2—222no—
359C2—442no—
360C2C4×D4×D1111yescharacteristic
361C2#1062330511yescharacteristic
362C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutatorC4×C11C23×C4
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
prime radicalC2×#66969C2
cosocleC2×C4×C11C24
hypercenter#440D11
hypocenterC11#2951
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #10623105C2semidirect
3. #10623077C2semidirect
4. C11×#440C2semidirect
5. #10622777C2semidirect
6. C4×#4326C2semidirect
7. C4×#4323C2semidirect
8. #10622502C2semidirect
9. D11×#107C2semidirect
10. #10622416C2semidirect
11. #10622403C2semidirect
12. #10622384C2semidirect
13. #10622369C2semidirect
14. #10622323C2semidirect
15. #10622321C2semidirect
27. #66969C4semidirect
67. #4343C2×C4semidirect
69. #4341C2×C4semidirect
79. C11×SD16C2×C4semidirect
89. #4326C2×C4semidirect
90. #4323C2×C4semidirect
110. #4314C2×C4semidirect
112. C8×D11C2×C4semidirect
159. #440D11semidirect
262. SD16C4×D11semidirect
294. C11#2951semidirect

Maximal subgroups

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

subgroupindex
C2×#669692
#106231052
#106230772
C11×#4402
#106227772
C4×#43262
C4×#43232
#106225022
D11×#1072
#106224162
#106224032
#106223842
#106223692
#106223232
#106223212
#295111