Finite Group Databasebeta

← #13081685

Subgroups — #13081685

Order 1408.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623202C211yesmaximal, characteristic, complemented
2#10623116C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic, complemented
4#10622803C211yesmaximal, characteristic, complemented
5#10622798C211yesmaximal, characteristic, complemented
6#10622781C211yesmaximal, characteristic, complemented
7#10622778C211yesmaximal, characteristic, complemented
8#10622671C211yesmaximal, characteristic
9#10622643C211yesmaximal, characteristic, complemented
10#10622461C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622431C211yesmaximal, characteristic, complemented
13#10622401C211yesmaximal, characteristic, complemented
14#10622400C211yesmaximal, characteristic, complemented
15#10622398C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20#67000C2211yescharacteristic
21#67000C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66997C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25C2×#4325C2211yescharacteristic
26C2×#4325C2211yescharacteristic
27#66989C2211yescharacteristic
28D4×Dic11C2211yescharacteristic
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31C2×#4314C2211yescharacteristic
32C2×#4314C2211yescharacteristic
33#66947—21no—
34#66947—21no—
35#66946C2211yescharacteristic
36#66946C2211yescharacteristic
37#66932—21no—
38#66932—21no—
39#66931—21no—
40#66930—21no—
41#66928—21no—
42#66927C2211yescharacteristic
43C4×D44—21no—
44C4×Dic22C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#102C2211yescharacteristic
49#66899C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52#66879C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×Dic11—21no—
63C2×D44—21no—
64C2×D44—21no—
65C2×D44C2311yescharacteristic
66C2×D44C2311yescharacteristic
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×Dic22D411yescharacteristic
70C2×Dic22C2311yescharacteristic
71C11×Q16—41no—
72C11×SD16—41no—
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4—21no—
76C11×C4⋊C4C2311yescharacteristic
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C42×C11—21no—
80C42×C11C2311yescharacteristic
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84#4326—22no—
85#4325—22no—
86#4325—41no—
87#4323—22no—
88#4323—41no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11D411yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4D411yescharacteristic
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11C2311yescharacteristic
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109#4314—41no—
110#4314—41no—
111#3401—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114C22×D11—21no—
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119D4×C11—21no—
120D4×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—42no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134D44—21no—
135D44—21no—
136D44—21no—
137D44—21no—
138D44—42no—
139D44—81no—
140C4×D11—81no—
141C4×D11—81no—
142Dic22—21no—
143Dic22—21no—
144Dic22—41no—
145C8×C11—21no—
146C8×C11—21no—
147C11⋊C8—21no—
148C11⋊C8#4112yes—
149#559—111no—
150#556—111no—
151#497—111no—
152#496—111no—
153#495—111no—
154#464—111no—
155#464D1111yescharacteristic, complemented
156#463—111no—
157#463—111no—
158#461—111no—
159#460—111no—
160#446—111no—
161#442—111no—
162#441—111no—
163C4×SD16—111no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11C22×D411yescharacteristic
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11C2×#4111yescharacteristic
180C4×C11H(5,𝔽2)11yescharacteristic
181Dic11—21no—
182Dic11—21no—
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187C2×Q16—111no—
188C2×Q16C2×D1111yescharacteristic
189C2×SD16—111no—
190C2×SD16—111no—
191C2×SD16—111no—
192C2×SD16—111no—
193C2×SD16C2×D1111yescharacteristic
194C2×D8—111no—
195C2×D8—111no—
196C4⋊Q8—111no—
197#127—111no—
198#126—221no—
199#126—221no—
200#124—111no—
201#124—111no—
202#124—111no—
203#124—221no—
204#124C2×D1111yescharacteristic
205#123—221no—
206#123—221no—
207C22⋊Q8—221no—
208C4×Q8—111no—
209C4×Q8—111no—
210C4×Q8—111no—
211C4×Q8C2×D1111yescharacteristic
212C4×D4—111no—
213C4×D4—111no—
214C4×D4—111no—
215C4×D4—221no—
216#117—221no—
217#106—111no—
218C4⋊C8—111no—
219C4⋊C8—111no—
220C4⋊C8C2×D1111yescharacteristic
221#103—111no—
222#103—111no—
223#103C2×D1111yescharacteristic
224#102—111no—
225#102—111no—
226#102C2×D1111yescharacteristic
227#97—111no—
228#97—111no—
229C4×C8—111no—
230C2×C11—81no—
231C2×C11#55011yescharacteristic
232C2×C11#57511yescharacteristic
233C2×C11#57711yescharacteristic
234D11—81no—
235D11—81no—
236C2×Q8—111no—
237C2×Q8—111no—
238C2×Q8C22×D1111yescharacteristic
239C2×Q8C22×D1111yescharacteristic
240C2×D4—111no—
241C2×D4—111no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4C22×D1111yescharacteristic
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248Q16—41no—
249Q16—222no—
250SD16—41no—
251SD16—222no—
252SD16—441no—
253SD16—441no—
254SD16—441no—
255D8—222no—
256D8—441no—
257C2×C8—111no—
258C2×C8—111no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4C22×D1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C42—21no—
283C42—111no—
284C42—111no—
285C42—221no—
286C42—221no—
287C42C22×D1111yescharacteristic
288C11#340111yescharacteristic, complemented, Sylow
289C23—21no—
290C23—221no—
291C23—221no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—221no—
297Q8—221no—
298Q8—441no—
299D4—21no—
300D4—21no—
301D4—221no—
302D4—221no—
303D4—221no—
304D4—221no—
305D4—442no—
306D4—881no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—111no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—442no—
317C2×C4—881no—
318C2×C4—881no—
319C2×C4D4×D1111yescharacteristic
320C2×C4D4×D1111yescharacteristic
321C2×C4C23×D1111yescharacteristic
322C8—21no—
323C8—21no—
324C8—112no—
325C8—221no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—441no—
330C22—441no—
331C22—441no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22C2×D4×D1111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—221no—
342C4—221no—
343C4—221no—
344C4—221no—
345C4—441no—
346C4—441no—
347C4#6703711yescharacteristic
348C4#41×D1111yescharacteristic
349C2—81no—
350C2—881no—
351C2—881no—
352C2#1062313011yescharacteristic
353C2#1062330111yescharacteristic
354C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radical#10622671C2
hypercenter#464D11
hypocenterC11#3401
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #10623202C2semidirect
2. #10623116C2semidirect
3. C11×#464C2semidirect
4. #10622803C2semidirect
5. #10622798C2semidirect
6. #10622781C2semidirect
7. #10622778C2semidirect
9. #10622643C2semidirect
10. #10622461C2semidirect
11. #10622441C2semidirect
12. #10622431C2semidirect
13. #10622401C2semidirect
14. #10622400C2semidirect
15. #10622398C2semidirect
155. #464D11semidirect
288. C11#3401semidirect

Maximal subgroups

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

subgroupindex
#106232022
#106231162
C11×#4642
#106228032
#106227982
#106227812
#106227782
#106226712
#106226432
#106224612
#106224412
#106224312
#106224012
#106224002
#106223982
#340111