Finite Group Databasebeta

← #13080888

Subgroups — #13080888

Order 1408.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623348C211yesmaximal, characteristic
2#10623170C211yesmaximal, characteristic, complemented
3C11×#451C211yesmaximal, characteristic, complemented
4#10622838C211yesmaximal, characteristic, complemented
5#10622802C211yesmaximal, characteristic, complemented
6#10622800C211yesmaximal, characteristic, complemented
7#10622798C211yesmaximal, characteristic, complemented
8Q16×Dic11C211yesmaximal, characteristic, complemented
9#10622662C211yesmaximal, characteristic, complemented
10#10622422C211yesmaximal, characteristic, complemented
11#10622416C211yesmaximal, characteristic, complemented
12#10622413C211yesmaximal, characteristic, complemented
13#10622412C211yesmaximal, characteristic, complemented
14#10622350C211yesmaximal, characteristic, complemented
15#10622342C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C11×C22⋊Q8C2211yescharacteristic
21#67000—21no—
22#67000C2211yescharacteristic
23#66999—21no—
24#66999C2211yescharacteristic
25#66999C2211yescharacteristic
26Q8×Dic11C2211yescharacteristic
27Q8×Dic11C2211yescharacteristic
28C2×#4325C2211yescharacteristic
29#66983—21no—
30#66983C2211yescharacteristic
31C4×C22⋊D11—21no—
32C4×C22⋊D11C2211yescharacteristic
33#66979C2211yescharacteristic
34C2×#4318C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36#66945—21no—
37C4⋊C4×D11C2211yescharacteristic
38#66943C2211yescharacteristic
39#66942—21no—
40#66936—21no—
41#66932—21no—
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66899C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66882C2211yescharacteristic
54#66881C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56C8×Dic11C2211yescharacteristic
57#66873C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×Q8×C11C2311yescharacteristic
64C2×Q8×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11C2311yescharacteristic
67C2×C22⋊D11—21no—
68C2×C22⋊D11D411yescharacteristic
69#4343—22no—
70#4343—41no—
71C2×D44—21no—
72C2×D44C2311yescharacteristic
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×C4×D11C2311yescharacteristic
76C11×Q16—22no—
77C11×Q16—41no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C4⋊C4—21no—
81C11×C4⋊C4C2311yescharacteristic
82C11×C22⋊C4—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11D411yescharacteristic
85#4325—41no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4D411yescharacteristic
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107#4318—41no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110#4313—41no—
111#3327—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C22×D11—21no—
114C22×D11C2×D411yescharacteristic
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—42no—
121Q8×C11#4112yes—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—42no—
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—41no—
132C22⋊D11—42no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139D44—21no—
140D44—21no—
141D44—42no—
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—42no—
145C4×D11—42no—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#552—111no—
151#548—111no—
152#488—111no—
153#484—111no—
154#482—111no—
155#479—111no—
156#470—111no—
157#468—111no—
158#464—111no—
159#452—111no—
160#451D1111yescharacteristic, complemented
161C4×Q16—111no—
162#436—111no—
163#419—111no—
164#417—111no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11C22×D411yescharacteristic
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—21no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C4×C11—21no—
176C4×C11—22no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180C4×C11C2×#4111yescharacteristic
181C4×C11H(5,𝔽2)11yescharacteristic
182Dic11—21no—
183Dic11—21no—
184Dic11—21no—
185Dic11—41no—
186Dic11—41no—
187Dic11—41no—
188C2×#41—111no—
189C22×Q8C2×D1111yescharacteristic
190C2×Q16C2×D1111yescharacteristic
191C2×Q16C2×D1111yescharacteristic
192C2×SD16—111no—
193C2×M16—111no—
194C2×M16—111no—
195#126—221no—
196#125—111no—
197#125—221no—
198#124—111no—
199#124—221no—
200#123—221no—
201C22⋊Q8—111no—
202C22⋊Q8—111no—
203C22⋊Q8—221no—
204C22⋊Q8C2×D1111yescharacteristic
205#121—111no—
206#121—221no—
207C4×Q8—111no—
208C4×Q8—111no—
209C4×D4—111no—
210C4×D4—221no—
211#117—111no—
212#117—221no—
213C2×C4⋊C4—111no—
214#107—111no—
215#107—111no—
216#106—111no—
217C4⋊C8—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103—111no—
223#103C2×D1111yescharacteristic
224#103C2×D1111yescharacteristic
225#102—111no—
226#102—111no—
227#102—111no—
228C22⋊C8—111no—
229C22⋊C8C2×D1111yescharacteristic
230C4×C8—111no—
231C2×C11—41no—
232C2×C11#54611yescharacteristic
233C2×C11#57511yescharacteristic
234C2×C11#57811yescharacteristic
235D11—41no—
236D11—81no—
237#41—222no—
238#41—441no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8C22×D1111yescharacteristic
243C2×Q8C22×D1111yescharacteristic
244C2×Q8C22×D1111yescharacteristic
245C2×D4—111no—
246C2×D4—111no—
247C2×D4—221no—
248C2×D4—221no—
249C22×C4—21no—
250C22×C4—111no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4C22×D1111yescharacteristic
254Q16—22no—
255Q16—41no—
256SD16—441no—
257M16—441no—
258M16—441no—
259C2×C8—111no—
260C2×C8—111no—
261C2×C8C22×D1111yescharacteristic
262C2×C8C22×D1111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—111no—
267C4⋊C4—111no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4C22×D1111yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—111no—
278C22⋊C4—111no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C42—111no—
286C42—221no—
287C42—221no—
288C42—221no—
289C11#332711yescharacteristic, complemented, Sylow
290C23—111no—
291C23—221no—
292C23D4×D1111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8#434112yes—
300D4—221no—
301D4—221no—
302D4—442no—
303D4—441no—
304D4—442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—111no—
313C2×C4—111no—
314C2×C4—111no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—442no—
321C2×C4—442no—
322C2×C4D4×D1111yescharacteristic
323C2×C4C23×D1111yescharacteristic
324C8—21no—
325C8—21no—
326C8—221no—
327C8—221no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—221no—
332C22—221no—
333C22—221no—
334C22—441no—
335C22—441no—
336C22—441no—
337C22C2×D4×D1111yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—221no—
344C4—221no—
345C4—221no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4C2×#434111yescharacteristic
350C4#6703711yescharacteristic
351C2—41no—
352C2—441no—
353C2—881no—
354C2#1062312211yescharacteristic
355C2#1062329711yescharacteristic
356C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#451C2
socleC22×C11C22×D4
prime radical#10623348C2
hypercenter#451D11
hypocenterC11#3327
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #10623170C2semidirect
3. C11×#451C2semidirect
4. #10622838C2semidirect
5. #10622802C2semidirect
6. #10622800C2semidirect
7. #10622798C2semidirect
8. Q16×Dic11C2semidirect
9. #10622662C2semidirect
10. #10622422C2semidirect
11. #10622416C2semidirect
12. #10622413C2semidirect
13. #10622412C2semidirect
14. #10622350C2semidirect
15. #10622342C2semidirect
160. #451D11semidirect
289. C11#3327semidirect

Maximal subgroups

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

subgroupindex
#106233482
#106231702
C11×#4512
#106228382
#106228022
#106228002
#106227982
Q16×Dic112
#106226622
#106224222
#106224162
#106224132
#106224122
#106223502
#106223422
#332711