Finite Group Databasebeta

← #13079725

Subgroups — #13079725

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
1C11×#536C211yesmaximal, characteristic, complemented
2#10623065C211yesmaximal, characteristic, complemented
3#10622852C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic
5#10622841C211yesmaximal, characteristic, complemented
6#10622840C211yesmaximal, characteristic, complemented
7#10622703C211yesmaximal, characteristic, complemented
8#10622699C211yesmaximal, characteristic, complemented
9#10622696C211yesmaximal, characteristic, complemented
10#10622694C211yesmaximal, characteristic, complemented
11#10622672C211yesmaximal, characteristic, complemented
12#10622670C211yesmaximal, characteristic, complemented
13#10622668C211yesmaximal, characteristic, complemented
14#10622667C211yesmaximal, characteristic, complemented
15#10622613C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C22×Q8×C11C2211yescharacteristic
18C11×C4⋊Q8C2211yescharacteristic
19C11×C4⋊Q8C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C11×#124C2211yescharacteristic
22C11×#123—21no—
23C11×#123—21no—
24C11×C22⋊Q8—21no—
25C11×C22⋊Q8—21no—
26C11×#117C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28C2×#4326C2211yescharacteristic
29C2×#4326C2211yescharacteristic
30C2×#4325C2211yescharacteristic
31C2×#4325C2211yescharacteristic
32C2×#4325C2211yescharacteristic
33C2×#4324C2211yescharacteristic
34C2×#4323C2211yescharacteristic
35#66983C2211yescharacteristic
36#66977C2211yescharacteristic
37#66951—21no—
38#66949—21no—
39#66938—21no—
40#66936—21no—
41#66928C2211yescharacteristic
42C4×D44C2211yescharacteristic
43#66922C2211yescharacteristic
44C4×Dic22C2211yescharacteristic
45#66899C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66899C2211yescharacteristic
49#66899C2211yescharacteristic
50#66899C2211yescharacteristic
51#66896C2211yescharacteristic
52#66896C2211yescharacteristic
53C22⋊(C11⋊C8)C2211yescharacteristic
54C22⋊(C11⋊C8)C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56C4⋊(C11⋊C8)C2211yescharacteristic
57#66867C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C11×#41—41no—
60C11×#41—41no—
61C2×Q8×C11—21no—
62C2×Q8×C11—41no—
63C2×Q8×C11—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×Q8×C11C2311yescharacteristic
66C2×Q8×C11C2311yescharacteristic
67C2×D4×C11—21no—
68C2×D4×C11C2311yescharacteristic
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11C2311yescharacteristic
72C2×C22⋊D11—21no—
73C2×D44C2311yescharacteristic
74C2×C4×D11—21no—
75C2×Dic22—21no—
76C2×Dic22C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4D411yescharacteristic
82C11×C4⋊C4D411yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4—21no—
86C11×C22⋊C4—21no—
87C11×C22⋊C4D411yescharacteristic
88C11×C22⋊C4D411yescharacteristic
89C42×C11C2311yescharacteristic
90C42×C11C2311yescharacteristic
91C22⋊Dic11—21no—
92#4326—41no—
93#4326—41no—
94#4326—41no—
95#4325—41no—
96#4325—41no—
97#4325—41no—
98#4324—41no—
99#4323—41no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11C2311yescharacteristic
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113C2×C11⋊C8C2311yescharacteristic
114#3225—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C22×D11—21no—
118Q8×C11—21no—
119Q8×C11—21no—
120Q8×C11—21no—
121Q8×C11—21no—
122Q8×C11—21no—
123Q8×C11—21no—
124Q8×C11—42no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—42no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C2×D411yescharacteristic
136C2×C4×C11C2×D411yescharacteristic
137C2×C4×C11C2×D411yescharacteristic
138C2×C4×C11C2×D411yescharacteristic
139C2×C4×C11C2×D411yescharacteristic
140C2×C4×C11C2411yescharacteristic
141C22⋊D11—81no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145D44—21no—
146D44—21no—
147C4×D11—81no—
148Dic22—21no—
149Dic22—21no—
150Dic22—81no—
151C11⋊C8—21no—
152C11⋊C8—21no—
153C11⋊C8—21no—
154C11⋊C8—21no—
155#542—111no—
156#536D1111yescharacteristic, complemented
157#497—111no—
158#495—111no—
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—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11C22×D411yescharacteristic
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11H(5,𝔽2)11yescharacteristic
189C4×C11H(5,𝔽2)11yescharacteristic
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193C2×#41C2×D1111yescharacteristic
194C22×Q8C2×D1111yescharacteristic
195C2×Q16—111no—
196C2×Q16—111no—
197C2×Q16—111no—
198C2×SD16—111no—
199C2×SD16—111no—
200C2×SD16—111no—
201C2×SD16—111no—
202C2×D8—111no—
203C4⋊Q8—111no—
204C4⋊Q8C2×D1111yescharacteristic
205C4⋊Q8C2×D1111yescharacteristic
206#126—221no—
207#124—111no—
208#124—221no—
209#124C2×D1111yescharacteristic
210#124C2×D1111yescharacteristic
211#123—21no—
212#123—21no—
213#123—221no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—111no—
217C22⋊Q8—221no—
218#121—111no—
219C4×Q8—111no—
220C4×D4—111no—
221#117C2×D1111yescharacteristic
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×C8—111no—
236C2×C11—41no—
237C2×C11—81no—
238C2×C11#53511yescharacteristic
239C2×C11#57711yescharacteristic
240C2×C11#57811yescharacteristic
241D11—81no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—111no—
248C2×Q8—221no—
249C2×Q8C22×D1111yescharacteristic
250C2×Q8C22×D1111yescharacteristic
251C2×Q8C22×D1111yescharacteristic
252C2×D4—21no—
253C2×D4—111no—
254C2×D4—221no—
255C2×D4C22×D1111yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—221no—
259C22×C4C22×D1111yescharacteristic
260Q16—441no—
261Q16—441no—
262Q16—441no—
263SD16—441no—
264SD16—441no—
265SD16—441no—
266SD16—441no—
267D8—441no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—111no—
271C2×C8—111no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—111no—
277C4⋊C4—111no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4C22⋊D1111yescharacteristic
282C4⋊C4C22⋊D1111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4C22⋊D1111yescharacteristic
293C22⋊C4C22⋊D1111yescharacteristic
294C42—221no—
295C42C22×D1111yescharacteristic
296C42C22×D1111yescharacteristic
297C11#322511yescharacteristic, complemented, Sylow
298C23—21no—
299C23—221no—
300C23C2×C22⋊D1111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—221no—
309Q8—221no—
310Q8—881no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—221no—
315D4—221no—
316D4—881no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—881no—
328C2×C4C2×C22⋊D1111yescharacteristic
329C2×C4C2×C22⋊D1111yescharacteristic
330C2×C4C2×C22⋊D1111yescharacteristic
331C2×C4C2×C22⋊D1111yescharacteristic
332C2×C4C2×C22⋊D1111yescharacteristic
333C2×C4C23×D1111yescharacteristic
334C8—221no—
335C8—221no—
336C8—221no—
337C8—221no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22C22×C22⋊D1111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—441no—
357C4—441no—
358C4—441no—
359C4#6703711yescharacteristic
360C4#6703711yescharacteristic
361C2—41no—
362C2—81no—
363C2—881no—
364C2#1062333611yescharacteristic
365C2#1062336811yescharacteristic
366C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#536C2
socleC22×C11C22×D4
prime radical#10622851C2
hypercenter#536D11
hypocenterC11#3225
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C11×#536C2semidirect
2. #10623065C2semidirect
3. #10622852C2semidirect
5. #10622841C2semidirect
6. #10622840C2semidirect
7. #10622703C2semidirect
8. #10622699C2semidirect
9. #10622696C2semidirect
10. #10622694C2semidirect
11. #10622672C2semidirect
12. #10622670C2semidirect
13. #10622668C2semidirect
14. #10622667C2semidirect
15. #10622613C2semidirect
156. #536D11semidirect
297. C11#3225semidirect

Maximal subgroups

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

subgroupindex
C11×#5362
#106230652
#106228522
#106228512
#106228412
#106228402
#106227032
#106226992
#106226962
#106226942
#106226722
#106226702
#106226682
#106226672
#106226132
#322511