Finite Group Databasebeta

← #13072054

Subgroups — #13072054

Order 1408.

788 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66948C212yesmaximal, complemented
2C2×#66948C211yesmaximal, characteristic, complemented
3C2×#66948C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
5C2×C4×D44C211yesmaximal, characteristic, complemented
6C11×#389C211yesmaximal, characteristic, complemented
7#10622607C212yesmaximal, complemented
8#10622600C211yesmaximal, characteristic, complemented
9#10622552C211yesmaximal, characteristic, complemented
10#10622285C212yesmaximal, complemented
11#10622278C212yesmaximal, complemented
12C22×D44C2212yes—
13C22×D44C2211yescharacteristic
14C22×D44C2212yes—
15C22×D44C2211yescharacteristic
16C22×C4×D11C2211yescharacteristic
17C22×C4×D11C2212yes—
18C22×C4×D11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2212yes—
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C42×C11C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×(C2×D11)⋊C4C2212yes—
29C2×(C2×D11)⋊C4C2212yes—
30C2×C4⋊Dic11C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×Dic11⋊C4C2212yes—
33#66948—28no—
34#66948—24no—
35#66948—24no—
36C4⋊C4×D11—24no—
37C4×D44—24no—
38C11×#95C2212yes—
39C11⋊#95C2212yes—
40C23×D11C2312yes—
41C23×D11C2311yescharacteristic
42C23×D11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×C4×C11C2311yescharacteristic
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C2×D44—22no—
52C2×D44—24no—
53C2×D44—24no—
54C2×D44—24no—
55C2×D44—22no—
56C2×D44—24no—
57C2×D44—24no—
58C2×D44—22no—
59C2×D44—22no—
60C2×D44—22no—
61C2×D44—42no—
62C2×D44D414yescomplemented
63C2×C4×D11—24no—
64C2×C4×D11—22no—
65C2×C4×D11—22no—
66C2×C4×D11—24no—
67C2×C4×D11—22no—
68C2×C4×D11—22no—
69C2×C4×D11—22no—
70C2×C4×D11—42no—
71C2×C4×D11D414yescomplemented
72C11×C4⋊C4—24no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4D414yescomplemented
75C42×C11—22no—
76(C2×D11)⋊C4—22no—
77(C2×D11)⋊C4—24no—
78(C2×D11)⋊C4—22no—
79(C2×D11)⋊C4—24no—
80(C2×D11)⋊C4—24no—
81(C2×D11)⋊C4—24no—
82(C2×D11)⋊C4—42no—
83C4⋊Dic11—22no—
84C4⋊Dic11—22no—
85Dic11⋊C4—24no—
86#2416—111nomaximal, Sylow
87C23×C11C2411yescharacteristic
88C22×D11—21no—
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11—21no—
93C22×D11—21no—
94C22×D11—21no—
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—22no—
99C22×D11—22no—
100C22×D11—22no—
101C22×D11—22no—
102C22×D11—22no—
103C22×D11—22no—
104C22×D11—22no—
105C22×D11C2×D412yes—
106C22×D11C2×D412yes—
107C22×D11C2×D412yes—
108C22×D11#4112yes—
109C2×C4×C11—21no—
110C2×C4×C11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11C2×D414yes—
120C2×C4×C11C2×D412yes—
121C2×C4×C11C2×D412yes—
122C2×C4×C11C2×D412yes—
123C2×C4×C11#4112yes—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—22no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—22no—
130C2×Dic11—21no—
131C2×Dic11—22no—
132C2×Dic11C2×D412yes—
133D44—28no—
134D44—48no—
135D44—48no—
136D44—44no—
137C4×D11—28no—
138C4×D11—48no—
139C4×D11—44no—
140C2×#121—112no—
141C2×#121—111no—
142C2×#121—111no—
143C2×C4×D4—111no—
144C22×C4⋊C4—111no—
145#396—112no—
146#394—112no—
147#390—111no—
148#389D1111yescharacteristic, complemented
149#386—112no—
150#380—111no—
151C22×C11C22×D411yescharacteristic
152C22×C11C22×D411yescharacteristic
153C22×C11C22×D411yescharacteristic
154C22×C11C2×#4111yescharacteristic
155C22×C11C2×#4111yescharacteristic
156C22×C11H(5,𝔽2)11yescharacteristic
157C22×C112−1+411yescharacteristic
158C2×D11—22no—
159C2×D11—22no—
160C2×D11—22no—
161C2×D11—22no—
162C2×D11—22no—
163C2×D11—22no—
164C2×D11—22no—
165C2×D11—22no—
166C2×D11—22no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—42no—
172C2×D11—42no—
173C2×D11—42no—
174C2×D11—42no—
175C2×D11—42no—
176C2×D11—42no—
177C2×D11—42no—
178C2×D11#12114yescomplemented
179C4×C11—22no—
180C4×C11—24no—
181C4×C11—42no—
182C4×C11—41no—
183C4×C11#12114yescomplemented
184Dic11—22no—
185Dic11—41no—
186Dic11—42no—
187C22×D4—111no—
188C22×D4—112no—
189C22×D4—111no—
190C22×D4—112no—
191C23×C4—111no—
192C23×C4—111no—
193C23×C4—112no—
194#121—224no—
195#121—228no—
196#121—224no—
197C4×D4—224no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—112no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—224no—
202C2×C4⋊C4C2×D1111yescharacteristic
203C2×C4⋊C4C2×D1112yes—
204C2×C4⋊C4C2×D1111yescharacteristic
205C2×C22⋊C4—111no—
206C2×C22⋊C4—111no—
207C2×C22⋊C4—112no—
208C2×C22⋊C4—112no—
209C2×C22⋊C4—112no—
210C2×C22⋊C4—112no—
211C2×C22⋊C4—112no—
212C2×C42C2×D1111yescharacteristic
213#95—112no—
214#95C2×D1112yes—
215C2×C11C2×#12111yescharacteristic
216C2×C11C2×#12111yescharacteristic
217C2×C11#53711yescharacteristic
218C2×C11D4211yescharacteristic
219C2×C11#54711yescharacteristic
220C2×C11#54811yescharacteristic
221C2×C11#55311yescharacteristic
222D11—24no—
223D11—42no—
224D11—82no—
225C24—111no—
226C24—111no—
227C24—112no—
228C2×D4—114no—
229C2×D4—222no—
230C2×D4—222no—
231C2×D4—224no—
232C2×D4—224no—
233C2×D4—224no—
234C2×D4—224no—
235C2×D4—224no—
236C2×D4—222no—
237C2×D4—222no—
238C2×D4—222no—
239C2×D4—442no—
240C22×C4—111no—
241C22×C4—114no—
242C22×C4—111no—
243C22×C4—112no—
244C22×C4—224no—
245C22×C4—222no—
246C22×C4—222no—
247C22×C4—224no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4—222no—
251C22×C4—442no—
252C22×C4C22×D1112yes—
253C22×C4C22×D1111yescharacteristic
254C22×C4C22×D1112yes—
255C22×C4C22×D1111yescharacteristic
256C22×C4C22×D1111yescharacteristic
257C4⋊C4—24no—
258C4⋊C4—22no—
259C4⋊C4—222no—
260C4⋊C4—224no—
261C4⋊C4—222no—
262C4⋊C4D4414yescomplemented
263C22⋊C4—222no—
264C22⋊C4—224no—
265C22⋊C4—222no—
266C22⋊C4—224no—
267C22⋊C4—224no—
268C22⋊C4—224no—
269C22⋊C4—442no—
270C42—22no—
271C11#241611yescharacteristic, complemented, Sylow
272C23—112no—
273C23—112no—
274C23—112no—
275C23—112no—
276C23—221no—
277C23—221no—
278C23—221no—
279C23—221no—
280C23—221no—
281C23—221no—
282C23—221no—
283C23—221no—
284C23—221no—
285C23—221no—
286C23—222no—
287C23—222no—
288C23—222no—
289C23—222no—
290C23—222no—
291C23—222no—
292C23—222no—
293C23C23×D1111yescharacteristic
294D4—228no—
295D4—448no—
296D4—448no—
297D4—444no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—112no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—228no—
312C2×C4—221no—
313C2×C4—222no—
314C2×C4—222no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—222no—
318C2×C4—448no—
319C2×C4—444no—
320C2×C4C2×D4414yes—
321C2×C4C2×D4412yes—
322C2×C4D4×D1112yes—
323C2×C4D4×D1112yes—
324C2×C4#434312yes—
325C22—114no—
326C22—222no—
327C22—222no—
328C22—222no—
329C22—222no—
330C22—222no—
331C22—222no—
332C22—222no—
333C22—222no—
334C22—222no—
335C22—441no—
336C22—441no—
337C22—441no—
338C22—441no—
339C22—442no—
340C22—442no—
341C22—442no—
342C22—442no—
343C22—442no—
344C22—442no—
345C22—442no—
346C22C22×D4411yescharacteristic
347C22C2×D4×D1111yescharacteristic
348C22C2×D4×D1111yescharacteristic
349C22C2×#434311yescharacteristic
350C22#6704011yescharacteristic
351C22#41×D1111yescharacteristic
352C22#6704211yescharacteristic
353C4—24no—
354C4—22no—
355C4—42no—
356C4—41no—
357C4—222no—
358C4—441no—
359C4—442no—
360C4#6694814yescomplemented
361C2—224no—
362C2—442no—
363C2—882no—
364C2C2×#6694811yescharacteristic
365C2D4×D4411yescharacteristic
366C2#1062310711yescharacteristic
367C2D11×#12111yescharacteristic
368C2#1062316011yescharacteristic
369C2#1062322611yescharacteristic
370C2#1062325711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#389C2
hypercenter#389D11
hypocenterC11#2416
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×#66948C2semidirect
3. C2×#66948C2semidirect
4. C2×C4⋊C4×D11C2semidirect
5. C2×C4×D44C2semidirect
6. C11×#389C2semidirect
7. #10622607C2semidirect
8. #10622600C2semidirect
9. #10622552C2semidirect
10. #10622285C2semidirect
11. #10622278C2semidirect
62. C2×D44D4semidirect
71. C2×C4×D11D4semidirect
74. C11×C4⋊C4D4semidirect
148. #389D11semidirect
178. C2×D11#121semidirect
183. C4×C11#121semidirect
262. C4⋊C4D44semidirect
271. C11#2416semidirect
360. C4#66948semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×C4⋊C4×D112
C2×C4×D442
C11×#3892
#106226072
#106226002
#106225522
#106222852
#106222782
#241611