Finite Group Databasebeta

← #13081650

Subgroups — #13081650

Order 1408.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623202C211yesmaximal, characteristic
2#10623098C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic
4#10622795C211yesmaximal, characteristic, complemented
5#10622794C211yesmaximal, characteristic, complemented
6#10622780C211yesmaximal, characteristic
7#10622775C211yesmaximal, characteristic
8#10622673C211yesmaximal, characteristic
9#10622643C211yesmaximal, characteristic, complemented
10#10622462C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622406C211yesmaximal, characteristic, complemented
13#10622402C211yesmaximal, characteristic, complemented
14#10622380C211yesmaximal, characteristic
15#10622371C211yesmaximal, characteristic
16C2×C11×Q16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21#66997C2211yescharacteristic
22#66997C2211yescharacteristic
23#66997C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25C2×#4326C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27#66989C2211yescharacteristic
28D4×Dic11C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C2×Dic44C2211yescharacteristic
32C2×Dic44C2211yescharacteristic
33#66942—21no—
34#66942—21no—
35#66940C2211yescharacteristic
36#66940C2211yescharacteristic
37#66932—21no—
38#66932—21no—
39#66931—21no—
40#66930—21no—
41#66923—21no—
42#66922C2211yescharacteristic
43C4×Dic22—21no—
44C4×Dic22C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#102C2211yescharacteristic
49#66899C2211yescharacteristic
50#66880C2211yescharacteristic
51#66880C2211yescharacteristic
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×Dic22D411yescharacteristic
64C2×Dic22C2311yescharacteristic
65C2×Dic22C2311yescharacteristic
66C2×Dic22C2311yescharacteristic
67C11×Q16—41no—
68C11×SD16—41no—
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C22⋊C4—21no—
74C11×C22⋊C4—21no—
75C42×C11—21no—
76C42×C11C2311yescharacteristic
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80#4326—22no—
81#4326—22no—
82#4326—41no—
83#4324—22no—
84#4324—41no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11D411yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100Dic11⋊C4D411yescharacteristic
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11C2311yescharacteristic
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109Dic44—41no—
110Dic44—41no—
111#3398—111nomaximal, Sylow
112C23×C11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115Q8×C11—21no—
116Q8×C11—21no—
117D4×C11—21no—
118D4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—42no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134Dic22—22no—
135Dic22—21no—
136Dic22—21no—
137Dic22—21no—
138Dic22—21no—
139Dic22—21no—
140Dic22—21no—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8#4112yes—
145#557—111no—
146#556—111no—
147#497—111no—
148#497—111no—
149#494—111no—
150#464—111no—
151#464D1111yescharacteristic
152#462—111no—
153#462—111no—
154#462—111no—
155#461—111no—
156#446—111no—
157#441—111no—
158#441—111no—
159C4×SD16—111no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11C22×D411yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11C2×#4111yescharacteristic
170C4×C11H(5,𝔽2)11yescharacteristic
171Dic11—21no—
172Dic11—21no—
173Dic11—21no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177Dic11—41no—
178Dic11#13712yes—
179C2×Q16—111no—
180C2×Q16—111no—
181C2×Q16—111no—
182C2×Q16—111no—
183C2×Q16—111no—
184C2×Q16C2×D1111yescharacteristic
185C2×SD16—111no—
186C2×SD16—111no—
187C2×SD16C2×D1111yescharacteristic
188C4⋊Q8—111no—
189C4⋊Q8—111no—
190C4⋊Q8—111no—
191C4⋊Q8—111no—
192#126—221no—
193#126—221no—
194#125—221no—
195#125—221no—
196#125—221no—
197#124—111no—
198#124C2×D1111yescharacteristic
199C22⋊Q8—221no—
200C4×Q8—111no—
201C4×Q8—111no—
202C4×Q8—111no—
203C4×Q8—111no—
204C4×Q8—111no—
205C4×Q8—221no—
206C4×Q8C2×D1111yescharacteristic
207C4×D4—111no—
208#117—221no—
209#106—111no—
210C4⋊C8—111no—
211C4⋊C8—111no—
212C4⋊C8C2×D1111yescharacteristic
213#103—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#103C2×D1111yescharacteristic
218#102C2×D1111yescharacteristic
219#97—111no—
220#97—111no—
221C4×C8—111no—
222C2×C11—81no—
223C2×C11#55011yescharacteristic
224C2×C11C2×#13711yescharacteristic
225C2×C11#57811yescharacteristic
226C2×Q8—111no—
227C2×Q8—111no—
228C2×Q8—111no—
229C2×Q8—111no—
230C2×Q8C22×D1111yescharacteristic
231C2×Q8C22×D1111yescharacteristic
232C2×D4C22×D1111yescharacteristic
233C22×C4—221no—
234Q16—41no—
235Q16—222no—
236Q16—222no—
237Q16—441no—
238Q16—441no—
239Q16—441no—
240SD16—41no—
241SD16—222no—
242SD16—441no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—111no—
251C4⋊C4—111no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4C22×D1111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—221no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C42—21no—
271C42—111no—
272C42—111no—
273C42—221no—
274C42—221no—
275C42—221no—
276C42—221no—
277C42C22×D1111yescharacteristic
278C11#339811yescharacteristic, complemented, Sylow
279C23—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—222no—
285Q8—221no—
286Q8—221no—
287Q8—221no—
288Q8—221no—
289Q8—221no—
290Q8—221no—
291D4—21no—
292D4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—111no—
299C2×C4—111no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—442no—
305C2×C4D4×D1111yescharacteristic
306C2×C4D4×D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—21no—
309C8—21no—
310C8—112no—
311C8—221no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—112no—
322C4—221no—
323C4—221no—
324C4—221no—
325C4—441no—
326C4—441no—
327C4—441no—
328C4—441no—
329C4#6703711yescharacteristic
330C4#41×D1111yescharacteristic
331C2—81no—
332C2#1062313011yescharacteristic
333C2#1062330211yescharacteristic
334C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
prime radicalC2×D4×C11C23
hypercenter#464D11
hypocenterC11#3398
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
2. #10623098C2semidirect
4. #10622795C2semidirect
5. #10622794C2semidirect
9. #10622643C2semidirect
10. #10622462C2semidirect
11. #10622441C2semidirect
12. #10622406C2semidirect
13. #10622402C2semidirect
278. C11#3398semidirect

Maximal subgroups

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

subgroupindex
#106232022
#106230982
C11×#4642
#106227952
#106227942
#106227802
#106227752
#106226732
#106226432
#106224622
#106224412
#106224062
#106224022
#106223802
#106223712
#339811