Finite Group Databasebeta

← #13081679

Subgroups — #13081679

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#10623212C211yesmaximal, characteristic, complemented
2#10623073C211yesmaximal, characteristic, complemented
3C11×#463C211yesmaximal, characteristic, complemented
4#10622781C211yesmaximal, characteristic, complemented
5#10622779C211yesmaximal, characteristic, complemented
6#10622767C211yesmaximal, characteristic
7#10622766C211yesmaximal, characteristic, complemented
8#10622673C211yesmaximal, characteristic, complemented
9#10622627C211yesmaximal, characteristic, complemented
10#10622454C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622411C211yesmaximal, characteristic, complemented
13#10622402C211yesmaximal, characteristic, complemented
14#10622375C211yesmaximal, characteristic, complemented
15#10622371C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×D8C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#67000C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23C2×#4326C2211yescharacteristic
24#66993C2211yescharacteristic
25#66989C2211yescharacteristic
26#66989C2211yescharacteristic
27D4×Dic11C2211yescharacteristic
28C2×#4324C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66979—21no—
32#66977—21no—
33C2×#4314C2211yescharacteristic
34C2×#4314C2211yescharacteristic
35#66940C2211yescharacteristic
36#66940C2211yescharacteristic
37#66939—21no—
38#66938—21no—
39#66936—21no—
40(C22⋊D11)⋊C4—21no—
41#66932—21no—
42#66932—21no—
43C4×D44C2211yescharacteristic
44#66922C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#102C2211yescharacteristic
49#66896C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C22×Dic11—21no—
66C2×D44C2311yescharacteristic
67C2×C4×D11—21no—
68C2×Dic22D411yescharacteristic
69C2×Dic22C2311yescharacteristic
70C2×Dic22C2311yescharacteristic
71C11×SD16—41no—
72C11×D8—41no—
73C2×C8×C11C2311yescharacteristic
74C2×C8×C11C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C42×C11C2311yescharacteristic
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85#4326—22no—
86#4326—41no—
87#4324—22no—
88#4324—41no—
89#4323—22no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11D411yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4D411yescharacteristic
101Dic11⋊C4D411yescharacteristic
102C4×Dic11—21no—
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—
113C23×C11—21no—
114C22×D11—21no—
115Q8×C11—21no—
116Q8×C11—21no—
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—42no—
128C22⋊D11—81no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—81no—
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137D44—21no—
138D44—21no—
139C4×D11—81no—
140Dic22—21no—
141Dic22—21no—
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#464—111no—
156#463—111no—
157#463D1111yescharacteristic, complemented
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×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11C22×D411yescharacteristic
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11C2×#4111yescharacteristic
179C4×C11H(5,𝔽2)11yescharacteristic
180Dic11—21no—
181Dic11—21no—
182Dic11—21no—
183Dic11—21no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187C2×Q16—111no—
188C2×Q16—111no—
189C2×SD16—111no—
190C2×SD16—111no—
191C2×SD16—111no—
192C2×SD16—111no—
193C2×SD16C2×D1111yescharacteristic
194C2×D8—111no—
195C2×D8C2×D1111yescharacteristic
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×Q8—111no—
212C4×D4—111no—
213C4×D4—111no—
214C4×D4—221no—
215C4×D4C2×D1111yescharacteristic
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—81no—
232C2×C11#55011yescharacteristic
233C2×C11#57511yescharacteristic
234C2×C11#57711yescharacteristic
235D11—81no—
236C2×Q8—111no—
237C2×Q8—111no—
238C2×Q8—111no—
239C2×Q8C22×D1111yescharacteristic
240C2×D4—111no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4C22×D1111yescharacteristic
244C2×D4C22×D1111yescharacteristic
245C22×C4—21no—
246C22×C4—221no—
247C22×C4—221no—
248Q16—222no—
249Q16—441no—
250SD16—41no—
251SD16—222no—
252SD16—441no—
253SD16—441no—
254SD16—441no—
255D8—41no—
256D8—222no—
257C2×C8—111no—
258C2×C8—111no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4C22×D1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
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—111no—
283C42—111no—
284C42—221no—
285C42—221no—
286C42—221no—
287C42C22×D1111yescharacteristic
288C11#340111yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—221no—
292Q8—21no—
293Q8—21no—
294Q8—221no—
295Q8—221no—
296Q8—221no—
297Q8—221no—
298Q8—441no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—221no—
304D4—221no—
305D4—442no—
306D4—881no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—111no—
313C2×C4—111no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
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—41no—
330C22—41no—
331C22—41no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22C2×D4×D1111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—221no—
341C4—221no—
342C4—221no—
343C4—221no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4#6703711yescharacteristic
348C4#41×D1111yescharacteristic
349C2—81no—
350C2—81no—
351C2—881no—
352C2#1062313011yescharacteristic
353C2#1062330111yescharacteristic
354C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
prime radical#10622767C2
hypercenter#463D11
hypocenterC11#3401
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #10623212C2semidirect
2. #10623073C2semidirect
3. C11×#463C2semidirect
4. #10622781C2semidirect
5. #10622779C2semidirect
7. #10622766C2semidirect
8. #10622673C2semidirect
9. #10622627C2semidirect
10. #10622454C2semidirect
11. #10622441C2semidirect
12. #10622411C2semidirect
13. #10622402C2semidirect
14. #10622375C2semidirect
15. #10622371C2semidirect
157. #463D11semidirect
288. C11#3401semidirect

Maximal subgroups

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

subgroupindex
#106232122
#106230732
C11×#4632
#106227812
#106227792
#106227672
#106227662
#106226732
#106226272
#106224542
#106224412
#106224112
#106224022
#106223752
#106223712
#340111