Finite Group Databasebeta

← #13071471

Subgroups — #13071471

Order 1408.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66945C211yesmaximal, characteristic
2C11×#387C211yesmaximal, characteristic, complemented
3#10622602C211yesmaximal, characteristic
4#10622594C211yesmaximal, characteristic, complemented
5C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#10622545C211yesmaximal, characteristic, complemented
8#10622281C211yesmaximal, characteristic
9#10622279C211yesmaximal, characteristic
10#10622277C211yesmaximal, characteristic
11D11×#95C211yesmaximal, characteristic
12#10622267C211yesmaximal, characteristic, complemented
13#10622266C211yesmaximal, characteristic, complemented
14#10622264C211yesmaximal, characteristic, complemented
15#10622263C211yesmaximal, characteristic, complemented
16C22×C4×D11C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C42×C11C2211yescharacteristic
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31C2×C4×Dic11C2211yescharacteristic
32C2×C4×Dic11C2211yescharacteristic
33C2×C4×Dic11C2211yescharacteristic
34C2×C4×Dic11C2211yescharacteristic
35#66945C418yescomplemented
36C11×#95C2211yescharacteristic
37C11×#95C2211yescharacteristic
38C11×#95C2211yescharacteristic
39C11×#95C2211yescharacteristic
40C11⋊#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C11⋊#95C2211yescharacteristic
52C23×D11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C2×C4×D11—22no—
68C2×C4×D11—22no—
69C2×C4×D11—22no—
70C2×C4×D11—22no—
71C2×C4×D11—22no—
72C2×C4×D11—22no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C2×C4×D11C2×C414yes—
76C11×C4⋊C4—22no—
77C11×C4⋊C4C2×C414yescomplemented
78C42×C11—22no—
79(C2×D11)⋊C4—22no—
80(C2×D11)⋊C4—22no—
81(C2×D11)⋊C4C2×C414yes—
82(C2×D11)⋊C4C2×C414yes—
83C4⋊Dic11—22no—
84C4⋊Dic11C2×C414yescomplemented
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87C4×Dic11—22no—
88C4×Dic11—41no—
89C4×Dic11—41no—
90C4×Dic11C2×C414yescomplemented
91C4×Dic11C2×C414yescomplemented
92#2343—111nomaximal, Sylow
93C23×C11C2411yescharacteristic
94C22×D11—21no—
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11C22×C412yes—
99C22×D11#4112yes—
100C22×D11#4112yes—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C22×C412yes—
119C2×C4×C11C22×C412yes—
120C2×C4×C11C22×C412yes—
121C2×C4×C11#4112yes—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11C22×C412yes—
140C2×Dic11C22×C412yes—
141C2×Dic11C22×C412yes—
142C2×Dic11#4112yes—
143C4×D11—28no—
144C4×D11—44no—
145C4×D11—44no—
146C2×#117—111no—
147#387—111no—
148#387—111no—
149#387—111no—
150#387D1111yescharacteristic, complemented
151#385—111no—
152#385—111no—
153#383—111no—
154#382—111no—
155#381—111no—
156C4×C4⋊C4—111no—
157C4×C22⋊C4—111no—
158C4×C22⋊C4—111no—
159#376—111no—
160C2×#95—111no—
161C22×C11C23×C411yescharacteristic
162C22×C11C2×#4111yescharacteristic
163C22×C11C2×#4111yescharacteristic
164C22×C11C2×#4111yescharacteristic
165C22×C11C2×#4111yescharacteristic
166C22×C11H(5,𝔽2)11yescharacteristic
167C22×C112−1+411yescharacteristic
168C2×D11—22no—
169C2×D11—22no—
170C2×D11—22no—
171C2×D11—22no—
172C2×D11—22no—
173C2×D11—22no—
174C2×D11#11714yes—
175C4×C11—22no—
176C4×C11—22no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—41no—
180C4×C11—41no—
181C4×C11—41no—
182Dic11—22no—
183Dic11—22no—
184Dic11—22no—
185Dic11—22no—
186Dic11—41no—
187Dic11—41no—
188Dic11—41no—
189C23×C4—111no—
190C23×C4—111no—
191C23×C4—111no—
192#117—118no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4C2×D1111yescharacteristic
198C2×C4⋊C4C2×D1111yescharacteristic
199C2×C22⋊C4—111no—
200C2×C22⋊C4—111no—
201C2×C22⋊C4—111no—
202C2×C22⋊C4—111no—
203C2×C42—111no—
204C2×C42—111no—
205C2×C42—111no—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42C2×D1111yescharacteristic
209#95—111no—
210#95—111no—
211#95—111no—
212#95—111no—
213#95—111no—
214#95—111no—
215#95—111no—
216#95—111no—
217#95—111no—
218#95—111no—
219#95—111no—
220#95—111no—
221#95C2×D1111yescharacteristic
222#95C2×D1111yescharacteristic
223#95C2×D1111yescharacteristic
224#95C2×D1111yescharacteristic
225C2×C11C2×#11711yescharacteristic
226C2×C11C4×#4111yescharacteristic
227C2×C11#52011yescharacteristic
228C2×C11#55111yescharacteristic
229C2×C11#55111yescharacteristic
230C2×C11#55211yescharacteristic
231C2×C11#55211yescharacteristic
232D11—24no—
233C24—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—114no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—111no—
242C22×C4—222no—
243C22×C4—222no—
244C22×C4—222no—
245C22×C4—222no—
246C22×C4—222no—
247C22×C4—222no—
248C22×C4—441no—
249C22×C4—441no—
250C22×C4C22×D1111yescharacteristic
251C22×C4C22×D1111yescharacteristic
252C22×C4C22×D1111yescharacteristic
253C22×C4C22×D1111yescharacteristic
254C22×C4C22×D1111yescharacteristic
255C22×C4C22×D1111yescharacteristic
256C22×C4C22×D1111yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—114no—
259C4⋊C4—222no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C4⋊C4C4×D1114yescomplemented
263C22⋊C4—114no—
264C22⋊C4—114no—
265C22⋊C4—222no—
266C22⋊C4—222no—
267C42—22no—
268C42—114no—
269C42—114no—
270C42—222no—
271C42—441no—
272C42—441no—
273C11#234311yescharacteristic, complemented, Sylow
274C23—112no—
275C23—112no—
276C23—112no—
277C23—221no—
278C23—221no—
279C23—221no—
280C23—221no—
281C23C23×D1111yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—112no—
300C2×C4—112no—
301C2×C4—112no—
302C2×C4—112no—
303C2×C4—228no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—444no—
322C2×C4—444no—
323C2×C4C2×C4×D1112yes—
324C2×C4C2×C4×D1112yes—
325C2×C4C2×C4×D1112yes—
326C2×C4#434112yes—
327C22—114no—
328C22—222no—
329C22—222no—
330C22—222no—
331C22—222no—
332C22—222no—
333C22—222no—
334C22C22×C4×D1111yescharacteristic
335C22C2×#434111yescharacteristic
336C22#6704011yescharacteristic
337C22#41×D1111yescharacteristic
338C22#41×D1111yescharacteristic
339C22#41×D1111yescharacteristic
340C22#6704211yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—222no—
349C4—222no—
350C4—222no—
351C4—222no—
352C4—441no—
353C4—441no—
354C4—441no—
355C2—224no—
356C2D11×#11711yescharacteristic
357C2C4×#434111yescharacteristic
358C2#1062310511yescharacteristic
359C2#1062317011yescharacteristic
360C2#1062318911yescharacteristic
361C2#1062322411yescharacteristic
362C2#1062323611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#387C2
socle, cosocleC23×C11C24
prime radicalC23×D11C23
hypercenter#387D11
hypocenterC11#2343
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C11×#387C2semidirect
4. #10622594C2semidirect
5. C4⋊C4×Dic11C2semidirect
7. #10622545C2semidirect
12. #10622267C2semidirect
13. #10622266C2semidirect
14. #10622264C2semidirect
15. #10622263C2semidirect
35. #66945C4semidirect
77. C11×C4⋊C4C2×C4semidirect
84. C4⋊Dic11C2×C4semidirect
90. C4×Dic11C2×C4semidirect
91. C4×Dic11C2×C4semidirect
150. #387D11semidirect
262. C4⋊C4C4×D11semidirect
273. C11#2343semidirect

Maximal subgroups

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

subgroupindex
C2×#669452
C11×#3872
#106226022
#106225942
C4⋊C4×Dic112
C4×(C2×D11)⋊C42
#106225452
#106222812
#106222792
#106222772
D11×#952
#106222672
#106222662
#106222642
#106222632
#234311