Finite Group Databasebeta

← #13078871

Subgroups — #13078871

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#10623134C211yesmaximal, characteristic, complemented
3C11×#449C211yesmaximal, characteristic
4#10622852C211yesmaximal, characteristic, complemented
5#10622779C211yesmaximal, characteristic, complemented
6#10622777C211yesmaximal, characteristic, complemented
7#10622766C211yesmaximal, characteristic, complemented
8D8×Dic11C211yesmaximal, characteristic, complemented
9#10622646C211yesmaximal, characteristic, complemented
10#10622407C211yesmaximal, characteristic, complemented
11#10622403C211yesmaximal, characteristic, complemented
12#10622372C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622335C211yesmaximal, characteristic, complemented
15#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C11×#121C2211yescharacteristic
20Q8×Dic11C2211yescharacteristic
21Q8×Dic11C2211yescharacteristic
22C2×#4326C2211yescharacteristic
23#66989—21no—
24#66989C2211yescharacteristic
25#66988—21no—
26D4×Dic11—21no—
27D4×Dic11—21no—
28D4×Dic11C2211yescharacteristic
29D4×Dic11C2211yescharacteristic
30D4×Dic11C2211yescharacteristic
31C2×#4324C2211yescharacteristic
32#66979—21no—
33#66979C2211yescharacteristic
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11C2211yescharacteristic
36#66977C2211yescharacteristic
37#66941C2211yescharacteristic
38#66940C2211yescharacteristic
39#66932—21no—
40#66931—21no—
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44#66899C2211yescharacteristic
45#66896C2211yescharacteristic
46#66896C2211yescharacteristic
47#66896C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66879C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56C8×Dic11C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C11×#41—22no—
60C11×#41—22no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C22×C4×C11C2311yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C2×Dic22—21no—
73C2×Dic22C2311yescharacteristic
74C11×SD16—22no—
75C11×D8—22no—
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11D411yescharacteristic
87C22⋊Dic11D411yescharacteristic
88#4326—22no—
89#4324—22no—
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11D411yescharacteristic
94C4⋊Dic11D411yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3124—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11—21no—
111C23×C11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11#4112yes—
114D4×C11—24no—
115D4×C11—21no—
116D4×C11—21no—
117D4×C11—21no—
118D4×C11—81no—
119D4×C11#4112yes—
120C2×C4×C11—24no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133C2×Dic11—81no—
134C2×Dic11—81no—
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139Dic22—21no—
140Dic22—21no—
141Dic22—81no—
142C8×C11—21no—
143C8×C11—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#542—111no—
147#520—111no—
148#484—111no—
149#480—111no—
150#477—111no—
151#474—111no—
152#464—111no—
153#463—111no—
154#452—111no—
155#449D1111yescharacteristic
156#440—111no—
157#440—111no—
158C4×Q16—111no—
159C4×D8—111no—
160#433—111no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11C22×D411yescharacteristic
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—41no—
174C4×C11C2×#4111yescharacteristic
175C4×C11C2×#4111yescharacteristic
176Dic11—21no—
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184C2×#41C2×D1111yescharacteristic
185C2×Q16—111no—
186C2×SD16—111no—
187C2×SD16C2×D1111yescharacteristic
188C2×D8C2×D1111yescharacteristic
189C4⋊Q8—111no—
190#126—221no—
191#124—111no—
192#124—221no—
193#123—221no—
194C22⋊Q8—111no—
195C22⋊Q8—221no—
196#121C2×D1111yescharacteristic
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#107—111no—
210#107—111no—
211#107—111no—
212#107—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—81no—
230C2×C11#52511yescharacteristic
231C2×C11#57611yescharacteristic
232C2×C11#57811yescharacteristic
233#41—22no—
234#41—22no—
235C2×Q8—111no—
236C2×Q8—221no—
237C2×Q8C22×D1111yescharacteristic
238C2×D4—21no—
239C2×D4—21no—
240C2×D4C22×D1111yescharacteristic
241C2×D4C22×D1111yescharacteristic
242C22×C4—21no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4C22×D1111yescharacteristic
248Q16—222no—
249SD16—22no—
250SD16—222no—
251D8—22no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8C22×D1111yescharacteristic
255C2×C8C22×D1111yescharacteristic
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—221no—
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#312411yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23D4×D1111yescharacteristic
286Q8—21no—
287Q8—221no—
288Q8—221no—
289Q8—881no—
290Q8#434112yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#434112yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—111no—
306C2×C4—221no—
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—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D1111yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—221no—
334C4—221no—
335C4—221no—
336C4—221no—
337C4—441no—
338C4—441no—
339C4—441no—
340C4—441no—
341C4C2×#434111yescharacteristic
342C4C2×#434111yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#1062311711yescharacteristic
347C2#1062330211yescharacteristic
348C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#449C2
socleC22×C11C22×D4
hypercenter#449D11
hypocenterC11#3124
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #10623358C2semidirect
2. #10623134C2semidirect
4. #10622852C2semidirect
5. #10622779C2semidirect
6. #10622777C2semidirect
7. #10622766C2semidirect
8. D8×Dic11C2semidirect
9. #10622646C2semidirect
10. #10622407C2semidirect
11. #10622403C2semidirect
12. #10622372C2semidirect
13. #10622370C2semidirect
14. #10622335C2semidirect
15. #10622333C2semidirect
282. C11#3124semidirect

Maximal subgroups

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

subgroupindex
#106233582
#106231342
C11×#4492
#106228522
#106227792
#106227772
#106227662
D8×Dic112
#106226462
#106224072
#106224032
#106223722
#106223702
#106223352
#106223332
#312411