Finite Group Databasebeta

← #13078886

Subgroups — #13078886

Order 1408.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623358C211yesmaximal, characteristic, complemented
2#10623174C211yesmaximal, characteristic, complemented
3C11×#452C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic
5#10622798C211yesmaximal, characteristic, complemented
6#10622797C211yesmaximal, characteristic, complemented
7#10622778C211yesmaximal, characteristic, complemented
8SD16×Dic11C211yesmaximal, characteristic, complemented
9#10622656C211yesmaximal, characteristic, complemented
10#10622404C211yesmaximal, characteristic, complemented
11#10622401C211yesmaximal, characteristic, complemented
12#10622398C211yesmaximal, characteristic, complemented
13#10622374C211yesmaximal, characteristic, complemented
14#10622348C211yesmaximal, characteristic, complemented
15#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×Q16C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20#67000C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25D4×Dic11—21no—
26D4×Dic11—21no—
27D4×Dic11C2211yescharacteristic
28D4×Dic11C2211yescharacteristic
29C2×#4323C2211yescharacteristic
30#66983C2211yescharacteristic
31#66979—21no—
32#66979C2211yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2211yescharacteristic
35#66951—21no—
36#66950—21no—
37#66946C2211yescharacteristic
38#66941C2211yescharacteristic
39#66938—21no—
40#66936—21no—
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66881C2211yescharacteristic
52#66881C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56C8×Dic11C2211yescharacteristic
57#66872C2211yescharacteristic
58#66872C2211yescharacteristic
59C11×#41—22no—
60C11×#41—22no—
61C2×Q8×C11C2311yescharacteristic
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C2×D44C2311yescharacteristic
72C2×C4×D11—21no—
73C2×Dic22—21no—
74C11×Q16—22no—
75C11×SD16—22no—
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11D411yescharacteristic
84C22⋊Dic11D411yescharacteristic
85#4325—22no—
86#4323—22no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11D411yescharacteristic
96C4⋊Dic11D411yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3125—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112Q8×C11—21no—
113Q8×C11—21no—
114Q8×C11—21no—
115Q8×C11#4112yes—
116D4×C11—24no—
117D4×C11—21no—
118D4×C11#4112yes—
119C2×C4×C11—24no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—81no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138D44—21no—
139D44—21no—
140C4×D11—81no—
141Dic22—81no—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#542—111no—
147#520—111no—
148#483—111no—
149#481—111no—
150#476—111no—
151#475—111no—
152#464—111no—
153#463—111no—
154#452D1111yescharacteristic, complemented
155#449—111no—
156#442—111no—
157#441—111no—
158C4×SD16—111no—
159C4×SD16—111no—
160#433—111no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11C22×D411yescharacteristic
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C11C2×#4111yescharacteristic
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—21no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184C2×#41C2×D1111yescharacteristic
185C2×Q16C2×D1111yescharacteristic
186C2×SD16—111no—
187C2×SD16C2×D1111yescharacteristic
188C2×D8—111no—
189C4⋊Q8—111no—
190#126—221no—
191#124—111no—
192#124—221no—
193#123—221no—
194C22⋊Q8—221no—
195C22⋊Q8C2×D1111yescharacteristic
196#121—111no—
197C4×Q8—111no—
198C4×Q8—111no—
199C4×Q8—111no—
200C4×D4—111no—
201C4×D4—111no—
202C4×D4—111no—
203C4×D4—221no—
204C4×D4—221no—
205#117—111no—
206#117—221no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4—221no—
209#106—111no—
210#106—111no—
211#106—111no—
212#106—111no—
213C4⋊C8—111no—
214C4⋊C8—111no—
215#103—111no—
216#103—111no—
217#103—111no—
218#103C2×D1111yescharacteristic
219#102—111no—
220#102—111no—
221#102—111no—
222#102C2×D1111yescharacteristic
223C22⋊C8—111no—
224C22⋊C8C2×D1111yescharacteristic
225#97—111no—
226C4×C8—111no—
227C2×C11—41no—
228C2×C11—42no—
229C2×C11#52511yescharacteristic
230C2×C11#57711yescharacteristic
231C2×C11#57711yescharacteristic
232D11—81no—
233#41—22no—
234#41—22no—
235C2×Q8—221no—
236C2×Q8C22×D1111yescharacteristic
237C2×Q8C22×D1111yescharacteristic
238C2×D4—21no—
239C2×D4—111no—
240C2×D4—221no—
241C2×D4C22×D1111yescharacteristic
242C22×C4—21no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4C22×D1111yescharacteristic
248Q16—22no—
249SD16—22no—
250SD16—222no—
251D8—222no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8C22×D1111yescharacteristic
255C2×C8C22×D1111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4C22×D1111yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—111no—
270C22⋊C4—111no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C42—111no—
278C42—111no—
279C42—221no—
280C42—221no—
281C42—221no—
282C11#312511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—221no—
285C23D4×D1111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—881no—
290Q8#434112yes—
291D4—24no—
292D4—21no—
293D4—221no—
294D4—221no—
295D4—881no—
296D4#434112yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—111no—
306C2×C4—111no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—881no—
311C2×C4—881no—
312C2×C4—881no—
313C2×C4—881no—
314C2×C4D4×D1111yescharacteristic
315C2×C4C23×D1111yescharacteristic
316C8—21no—
317C8—21no—
318C8—221no—
319C8—221no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—441no—
327C22—441no—
328C22—441no—
329C22C2×D4×D1111yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—221no—
335C4—221no—
336C4—221no—
337C4—221no—
338C4—441no—
339C4—441no—
340C4—441no—
341C4C2×#434111yescharacteristic
342C4C2×#434111yescharacteristic
343C2—41no—
344C2—42no—
345C2—881no—
346C2#1062311711yescharacteristic
347C2#1062330111yescharacteristic
348C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
prime radical#10622851C2
hypercenter#452D11
hypocenterC11#3125
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #10623358C2semidirect
2. #10623174C2semidirect
3. C11×#452C2semidirect
5. #10622798C2semidirect
6. #10622797C2semidirect
7. #10622778C2semidirect
8. SD16×Dic11C2semidirect
9. #10622656C2semidirect
10. #10622404C2semidirect
11. #10622401C2semidirect
12. #10622398C2semidirect
13. #10622374C2semidirect
14. #10622348C2semidirect
15. #10622333C2semidirect
154. #452D11semidirect
282. C11#3125semidirect

Maximal subgroups

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

subgroupindex
#106233582
#106231742
C11×#4522
#106228512
#106227982
#106227972
#106227782
SD16×Dic112
#106226562
#106224042
#106224012
#106223982
#106223742
#106223482
#106223332
#312511