Finite Group Databasebeta

← #13079718

Subgroups — #13079718

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#10623213C211yesmaximal, characteristic, complemented
2#10623206C211yesmaximal, characteristic, complemented
3C11×#495C211yesmaximal, characteristic, complemented
4#10622799C211yesmaximal, characteristic, complemented
5#10622795C211yesmaximal, characteristic, complemented
6#10622786C211yesmaximal, characteristic, complemented
7#10622783C211yesmaximal, characteristic, complemented
8#10622779C211yesmaximal, characteristic, complemented
9#10622775C211yesmaximal, characteristic, complemented
10#10622771C211yesmaximal, characteristic
11#10622766C211yesmaximal, characteristic, complemented
12#10622673C211yesmaximal, characteristic, complemented
13#10622668C211yesmaximal, characteristic, complemented
14#10622303C211yesmaximal, characteristic, complemented
15#10622294C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4341C2211yescharacteristic
18C2×C11×Q16C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C2×C11×D8C2211yescharacteristic
22C11×#124C2211yescharacteristic
23C11×#124C2211yescharacteristic
24#66999C2211yescharacteristic
25Q8×Dic11C2211yescharacteristic
26#66997C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29#66991C2211yescharacteristic
30#66989C2211yescharacteristic
31D4×Dic11C2211yescharacteristic
32C2×#4324C2211yescharacteristic
33C2×#4324C2211yescharacteristic
34#66939—21no—
35#66938—21no—
36#66936—21no—
37#66936—21no—
38#66932—21no—
39#66931—21no—
40#66931—21no—
41#66931—21no—
42#66925C2211yescharacteristic
43#66922C2211yescharacteristic
44#66922C2211yescharacteristic
45C4×C8×C11C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57Dic11⋊C8C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C22×Dic11—21no—
66C22×Dic11—21no—
67Q8×D11—41no—
68Q8×D11—41no—
69#4341—41no—
70#4341—41no—
71C2×C4×D11—21no—
72C2×C4×D11C2311yescharacteristic
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22C2311yescharacteristic
76C2×Dic22C2311yescharacteristic
77C11×Q16—41no—
78C11×SD16—41no—
79C11×SD16—41no—
80C11×D8—41no—
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C42×C11C2311yescharacteristic
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91C22⋊Dic11—21no—
92#4326—41no—
93#4326—41no—
94#4324—41no—
95#4324—41no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4D411yescharacteristic
98(C2×D11)⋊C4D411yescharacteristic
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108Dic11⋊C4D411yescharacteristic
109Dic11⋊C4D411yescharacteristic
110C4×Dic11—21no—
111C4×Dic11C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113C2×C11⋊C8C2311yescharacteristic
114#3225—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C22×D11C2×D411yescharacteristic
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—42no—
132C22⋊D11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—42no—
138C2×Dic11—81no—
139C2×Dic11C2×D411yescharacteristic
140C2×Dic11C2×D411yescharacteristic
141C2×Dic11C2×D411yescharacteristic
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—42no—
145Dic22—21no—
146Dic22—21no—
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#495D1111yescharacteristic, complemented
159#489—111no—
160#487—111no—
161#464—111no—
162#463—111no—
163#462—111no—
164#461—111no—
165#452—111no—
166#451—111no—
167#449—111no—
168#448—111no—
169#433—111no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11C22×D411yescharacteristic
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11H(5,𝔽2)11yescharacteristic
185C4×C11H(5,𝔽2)11yescharacteristic
186Dic11—21no—
187Dic11—21no—
188Dic11—21no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41—111no—
194C22×Q8—111no—
195C2×Q16—111no—
196C2×Q16—111no—
197C2×Q16C2×D1111yescharacteristic
198C2×SD16—111no—
199C2×SD16—111no—
200C2×SD16C2×D1111yescharacteristic
201C2×SD16C2×D1111yescharacteristic
202C2×D8C2×D1111yescharacteristic
203C4⋊Q8—111no—
204C4⋊Q8—111no—
205C4⋊Q8—111no—
206#126—221no—
207#124—111no—
208#124—221no—
209#124C2×D1111yescharacteristic
210#124C2×D1111yescharacteristic
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×Q8—111no—
220C4×D4—111no—
221#117—111no—
222C4⋊C8—111no—
223C4⋊C8—111no—
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#103—111no—
229#103—111no—
230#102—111no—
231#102—111no—
232C22⋊C8—111no—
233C22⋊C8—111no—
234#97—111no—
235C4×C8C2×D1111yescharacteristic
236C2×C11—81no—
237C2×C11—81no—
238C2×C11#53511yescharacteristic
239C2×C11#57711yescharacteristic
240C2×C11#57811yescharacteristic
241D11—41no—
242#41—441no—
243#41—441no—
244C2×Q8—111no—
245C2×Q8—111no—
246C2×Q8—221no—
247C2×Q8—221no—
248C2×Q8—441no—
249C2×Q8—441no—
250C2×Q8C22×D1111yescharacteristic
251C2×Q8C22×D1111yescharacteristic
252C2×D4—221no—
253C2×D4—221no—
254C2×D4C22×D1111yescharacteristic
255C2×D4C22×D1111yescharacteristic
256C22×C4—111no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260Q16—41no—
261Q16—441no—
262Q16—441no—
263SD16—41no—
264SD16—41no—
265SD16—441no—
266SD16—441no—
267D8—41no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8C22×D1111yescharacteristic
271C2×C8C22×D1111yescharacteristic
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—111no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—111no—
288C22⋊C4—111no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C42—111no—
295C42—221no—
296C42C22×D1111yescharacteristic
297C11#322511yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23—111no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—221no—
306Q8—221no—
307Q8—221no—
308Q8—221no—
309Q8—442no—
310Q8—881no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—442no—
316D4—881no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—111no—
320C2×C4—111no—
321C2×C4—111no—
322C2×C4—221no—
323C2×C4—221no—
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—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—221no—
345C22—221no—
346C22—221no—
347C22C2×D4×D1111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—221no—
353C4—221no—
354C4—221no—
355C4—441no—
356C4—441no—
357C4—441no—
358C4—441no—
359C4#6703711yescharacteristic
360C4#6703711yescharacteristic
361C2—81no—
362C2—81no—
363C2—441no—
364C2#1062324611yescharacteristic
365C2#1062330111yescharacteristic
366C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#495C2
socleC22×C11C22×D4
prime radical#10622771C2
hypercenter#495D11
hypocenterC11#3225
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #10623213C2semidirect
2. #10623206C2semidirect
3. C11×#495C2semidirect
4. #10622799C2semidirect
5. #10622795C2semidirect
6. #10622786C2semidirect
7. #10622783C2semidirect
8. #10622779C2semidirect
9. #10622775C2semidirect
11. #10622766C2semidirect
12. #10622673C2semidirect
13. #10622668C2semidirect
14. #10622303C2semidirect
15. #10622294C2semidirect
158. #495D11semidirect
297. C11#3225semidirect

Maximal subgroups

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

subgroupindex
#106232132
#106232062
C11×#4952
#106227992
#106227952
#106227862
#106227832
#106227792
#106227752
#106227712
#106227662
#106226732
#106226682
#106223032
#106222942
#322511