Finite Group Databasebeta

← #13079732

Subgroups — #13079732

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623255C211yesmaximal, characteristic, complemented
2#10623113C211yesmaximal, characteristic, complemented
3C11×#462C211yesmaximal, characteristic, complemented
4#10622804C211yesmaximal, characteristic, complemented
5#10622803C211yesmaximal, characteristic, complemented
6#10622800C211yesmaximal, characteristic, complemented
7#10622799C211yesmaximal, characteristic, complemented
8#10622696C211yesmaximal, characteristic, complemented
9#10622641C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622424C211yesmaximal, characteristic
13#10622419C211yesmaximal, characteristic, complemented
14#10622408C211yesmaximal, characteristic, complemented
15#10622405C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×Q16C2211yescharacteristic
20C11×C4⋊Q8C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic
22#67000C2211yescharacteristic
23#67000C2211yescharacteristic
24#66999C2211yescharacteristic
25#66997C2211yescharacteristic
26C2×#4326C2211yescharacteristic
27C2×#4325C2211yescharacteristic
28C2×#4325C2211yescharacteristic
29C2×#4325C2211yescharacteristic
30C2×D88C2211yescharacteristic
31C2×#4314C2211yescharacteristic
32#66949—21no—
33#66949—21no—
34#66949—21no—
35#66948C2211yescharacteristic
36#66947—21no—
37#66947—21no—
38#66947—21no—
39#66941C2211yescharacteristic
40#66929—21no—
41#66928—21no—
42#66928C2211yescharacteristic
43C4×D44C2211yescharacteristic
44#66925C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#103C2211yescharacteristic
47C11×#103C2211yescharacteristic
48#66899C2211yescharacteristic
49#66899C2211yescharacteristic
50#66885C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic
53#66880C2211yescharacteristic
54#66879C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66874C2211yescharacteristic
57#66873C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62#4343—41no—
63#4343—41no—
64Q8×D11—41no—
65Q8×D11—41no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44C2311yescharacteristic
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11C2311yescharacteristic
74C2×Dic22—21no—
75C2×Dic22—21no—
76C2×Dic22C2311yescharacteristic
77C11×Q16—41no—
78C11×Q16—41no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4C2311yescharacteristic
85C42×C11—21no—
86C42×C11C2311yescharacteristic
87#4326—41no—
88#4325—41no—
89#4325—41no—
90#4325—41no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4D411yescharacteristic
101(C2×D11)⋊C4D411yescharacteristic
102C4⋊Dic11C2311yescharacteristic
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4D411yescharacteristic
108Dic11⋊C4D411yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112D88—41no—
113#4314—41no—
114#3225—111nomaximal, Sylow
115C22×D11—21no—
116C22×D11—21no—
117C22×D11C2×D411yescharacteristic
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
123Q8×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136D44—21no—
137D44—21no—
138D44—21no—
139D44—21no—
140D44—42no—
141D44—81no—
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—42no—
145C4×D11—42no—
146C4×D11—81no—
147Dic22—21no—
148Dic22—21no—
149Dic22—42no—
150Dic22—81no—
151C8×C11—21no—
152C8×C11—21no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155#542—111no—
156#536—111no—
157#497—111no—
158#495—111no—
159#489—111no—
160#487—111no—
161#464—111no—
162#463—111no—
163#462D1111yescharacteristic, complemented
164#461—111no—
165#452—111no—
166#451—111no—
167#449—111no—
168#448—111no—
169#433—111no—
170C22×C11C22×D411yescharacteristic
171C2×D11—21no—
172C2×D11—21no—
173C2×D11—21no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—41no—
186C4×C11H(5,𝔽2)11yescharacteristic
187C4×C11H(5,𝔽2)11yescharacteristic
188Dic11—21no—
189Dic11—21no—
190Dic11—21no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C22×Q8—111no—
195C2×Q16—111no—
196C2×Q16C2×D1111yescharacteristic
197C2×Q16C2×D1111yescharacteristic
198C2×SD16—111no—
199C2×SD16—111no—
200C2×SD16—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C4⋊Q8—111no—
204C4⋊Q8—111no—
205C4⋊Q8C2×D1111yescharacteristic
206#126—221no—
207#124—111no—
208#124—111no—
209#124—111no—
210#124—221no—
211#123—221no—
212#123—221no—
213#123—221no—
214C22⋊Q8—111no—
215C22⋊Q8—221no—
216C22⋊Q8—221no—
217C22⋊Q8—221no—
218#121—111no—
219C4×Q8C2×D1111yescharacteristic
220C4×D4—111no—
221#117—111no—
222C4⋊C8—111no—
223C4⋊C8C2×D1111yescharacteristic
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#103C2×D1111yescharacteristic
229#103C2×D1111yescharacteristic
230#102—111no—
231#102—111no—
232C22⋊C8—111no—
233C22⋊C8—111no—
234#97—111no—
235C4×C8—111no—
236C2×C11#53511yescharacteristic
237C2×C11#57711yescharacteristic
238C2×C11#57811yescharacteristic
239D11—41no—
240D11—81no—
241D11—81no—
242#41—441no—
243#41—441no—
244C2×Q8—111no—
245C2×Q8—221no—
246C2×Q8—221no—
247C2×Q8—441no—
248C2×Q8—441no—
249C2×Q8C22×D1111yescharacteristic
250C2×Q8C22×D1111yescharacteristic
251C2×Q8C22×D1111yescharacteristic
252C2×D4—111no—
253C2×D4—111no—
254C2×D4—221no—
255C2×D4—221no—
256C22×C4—111no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260Q16—41no—
261Q16—41no—
262Q16—441no—
263SD16—441no—
264SD16—441no—
265SD16—441no—
266SD16—441no—
267D8—441no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—111no—
276C4⋊C4—111no—
277C4⋊C4—111no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4C22×D1111yescharacteristic
283C22⋊C4—111no—
284C22⋊C4—111no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C42—21no—
295C42—111no—
296C42C22×D1111yescharacteristic
297C11#322511yescharacteristic, complemented, Sylow
298C23—111no—
299C23—221no—
300C23—221no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—221no—
308Q8—221no—
309Q8—442no—
310Q8—881no—
311D4—221no—
312D4—221no—
313D4—221no—
314D4—221no—
315D4—442no—
316D4—881no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—111no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—881no—
331C2×C4D4×D1111yescharacteristic
332C2×C4D4×D1111yescharacteristic
333C2×C4C23×D1111yescharacteristic
334C8—21no—
335C8—21no—
336C8—221no—
337C8—221no—
338C22—221no—
339C22—221no—
340C22—221no—
341C22—441no—
342C22—441no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22C2×D4×D1111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—221no—
355C4—221no—
356C4—221no—
357C4—441no—
358C4—441no—
359C4#6703711yescharacteristic
360C4#6704211yescharacteristic
361C2—441no—
362C2—881no—
363C2—881no—
364C2#1062313811yescharacteristic
365C2#1062329711yescharacteristic
366C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#462C2
socleC22×C11C22×D4
prime radical#10622424C2
hypercenter#462D11
hypocenterC11#3225
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #10623255C2semidirect
2. #10623113C2semidirect
3. C11×#462C2semidirect
4. #10622804C2semidirect
5. #10622803C2semidirect
6. #10622800C2semidirect
7. #10622799C2semidirect
8. #10622696C2semidirect
9. #10622641C2semidirect
10. #10622457C2semidirect
11. #10622453C2semidirect
13. #10622419C2semidirect
14. #10622408C2semidirect
15. #10622405C2semidirect
163. #462D11semidirect
297. C11#3225semidirect

Maximal subgroups

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

subgroupindex
#106232552
#106231132
C11×#4622
#106228042
#106228032
#106228002
#106227992
#106226962
#106226412
#106224572
#106224532
#106224242
#106224192
#106224082
#106224052
#322511