Finite Group Databasebeta

← C2×#10622574 #13071821

Subgroups — C2×#10622574 #13071821

Order 1408.

1252 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊D11C211yesmaximal, characteristic
2C22×C11×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic11C211yesmaximal, characteristic, complemented
4C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6C22×C4⋊Dic11C211yesmaximal, characteristic, complemented
7C2×C11⋊#95C211yesmaximal, characteristic, complemented
8#10622574C218yesmaximal, direct product factor
9C25×C11C2211yescharacteristic
10C24×D11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C23×C4×C11C2211yescharacteristic
13C22×C22⋊D11—24no—
14C22×C22⋊D11—24no—
15C22×C22⋊D11—24no—
16C22×C22⋊D11C2214yes—
17C23×Dic11C2211yescharacteristic
18C23×Dic11C2211yescharacteristic
19C23×Dic11C2211yescharacteristic
20C2×C11×C22⋊C4—24no—
21C2×C11×C22⋊C4C2214yescomplemented
22C2×C22⋊Dic11—24no—
23C2×C22⋊Dic11C2214yescomplemented
24C2×(C2×D11)⋊C4—24no—
25C2×(C2×D11)⋊C4—24no—
26C2×(C2×D11)⋊C4C2214yescomplemented
27C2×(C2×D11)⋊C4C2214yescomplemented
28C2×C4⋊Dic11—24no—
29C2×C4⋊Dic11C2214yescomplemented
30C11⋊#95C2214yescomplemented
31C24×C11—22no—
32C24×C11—22no—
33C24×C11—22no—
34C24×C11—22no—
35C24×C11—22no—
36C24×C11—22no—
37C24×C11D414yes—
38C24×C11C2312yes—
39C24×C11C2311yescharacteristic
40C23×D11—22no—
41C23×D11—22no—
42C23×D11—22no—
43C23×D11—22no—
44C23×D11—22no—
45C23×D11—22no—
46C23×D11D414yes—
47C23×D11C2312yes—
48C22×C4×C11—22no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11D414yescomplemented
54C22×C4×C11C2312yes—
55C22×C4×C11C2312yes—
56C2×C22⋊D11—232no—
57C2×C22⋊D11—28no—
58C2×C22⋊D11—28no—
59C2×C22⋊D11—28no—
60C22×Dic11—22no—
61C22×Dic11—22no—
62C22×Dic11—22no—
63C22×Dic11—22no—
64C22×Dic11—22no—
65C22×Dic11—22no—
66C22×Dic11—22no—
67C22×Dic11—22no—
68C22×Dic11D414yes—
69C22×Dic11C2312yes—
70C22×Dic11C2312yes—
71C22×Dic11C2312yes—
72C11×C22⋊C4—28no—
73C22⋊Dic11—28no—
74(C2×D11)⋊C4—28no—
75(C2×D11)⋊C4—28no—
76C4⋊Dic11—28no—
77C2×#394—111nomaximal, Sylow
78C23×C11—28no—
79C23×C11—28no—
80C23×C11—28no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—22no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—44no—
88C23×C11—44no—
89C23×C11—44no—
90C23×C11—44no—
91C23×C11C2×D414yes—
92C23×C11C2×D412yes—
93C23×C11C2×D412yes—
94C23×C11C2×D412yes—
95C23×C11C2×D412yes—
96C23×C11#4112yes—
97C23×C11#4112yes—
98C23×C11#4112yes—
99C23×C11C2411yescharacteristic
100C22×D11—28no—
101C22×D11—28no—
102C22×D11—28no—
103C22×D11—22no—
104C22×D11—22no—
105C22×D11—22no—
106C22×D11—22no—
107C22×D11—22no—
108C22×D11—22no—
109C22×D11—44no—
110C22×D11—44no—
111C22×D11—44no—
112C22×D11—44no—
113C22×D11C2×D414yes—
114C2×C4×C11—28no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—44no—
121C2×C4×C11C2×D414yescomplemented
122C22⋊D11—232no—
123C2×Dic11—28no—
124C2×Dic11—22no—
125C2×Dic11—22no—
126C2×Dic11—22no—
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—44no—
133C2×Dic11—44no—
134C2×Dic11C2×D414yes—
135C23×D4—111no—
136C22×C4⋊C4—111no—
137C22×C22⋊C4—111no—
138C22×C22⋊C4—111no—
139C22×C22⋊C4—111no—
140C22×C22⋊C4D1111yescharacteristic, complemented
141#394—118no—
142C2×#95—111no—
143C22×C11—24no—
144C22×C11—24no—
145C22×C11—24no—
146C22×C11—42no—
147C22×C11—42no—
148C22×C11—42no—
149C22×C11—42no—
150C22×C11—416no—
151C22×C11#12014yes—
152C22×C11#12114yes—
153C22×C11#12114yes—
154C22×C11#12114yes—
155C22×C11#12314yes—
156C22×C11#12314yes—
157C22×C11#12414yes—
158C22×C11C22×D411yescharacteristic
159C22×C11C22×D411yescharacteristic
160C22×C11C22×D411yescharacteristic
161C22×C11C22×D411yescharacteristic
162C22×C11C2×#4111yescharacteristic
163C22×C11C2×#4111yescharacteristic
164C22×C11C2×#4111yescharacteristic
165C2×D11—24no—
166C2×D11—24no—
167C2×D11—24no—
168C2×D11—42no—
169C2×D11—42no—
170C2×D11—42no—
171C2×D11—42no—
172C2×D11—416no—
173C4×C11—24no—
174C4×C11—42no—
175Dic11—24no—
176Dic11—42no—
177Dic11—42no—
178C25—111no—
179C25C2×D1111yescharacteristic
180C22×D4—114no—
181C22×D4—224no—
182C22×D4—224no—
183C22×D4—224no—
184C23×C4—111no—
185C23×C4—111no—
186C23×C4—111no—
187C23×C4C2×D1111yescharacteristic
188C23×C4C2×D1111yescharacteristic
189C2×C4⋊C4—114no—
190C2×C4⋊C4—224no—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—114no—
193C2×C22⋊C4—114no—
194C2×C22⋊C4—114no—
195C2×C22⋊C4—224no—
196C2×C22⋊C4—224no—
197C2×C22⋊C4—224no—
198C2×C22⋊C4C2×D1114yescomplemented
199#95—114no—
200C2×C11—44no—
201C2×C11#39418yescomplemented
202C2×C11C2×#12011yescharacteristic
203C2×C11C2×#12111yescharacteristic
204C2×C11C2×#12111yescharacteristic
205C2×C11C2×#12111yescharacteristic
206C2×C11C2×#12311yescharacteristic
207C2×C11C2×#12311yescharacteristic
208C2×C11C2×#12411yescharacteristic
209D11—44no—
210C24—22no—
211C24—22no—
212C24—22no—
213C24—22no—
214C24—22no—
215C24—22no—
216C24—114no—
217C24—112no—
218C24—222no—
219C24—222no—
220C24—222no—
221C24—222no—
222C24—222no—
223C24—222no—
224C24D4414yes—
225C24C22×D1112yes—
226C24C22×D1111yescharacteristic
227C2×D4—228no—
228C2×D4—228no—
229C2×D4—2232no—
230C2×D4—228no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—114no—
237C22×C4—112no—
238C22×C4—112no—
239C22×C4—112no—
240C22×C4—222no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4—222no—
244C22×C4—222no—
245C22×C4—222no—
246C22×C4—222no—
247C22×C4—222no—
248C22×C4C22⋊D1114yescomplemented
249C22×C4C22×D1112yes—
250C22×C4C22×D1112yes—
251C4⋊C4—228no—
252C22⋊C4—28no—
253C22⋊C4—228no—
254C22⋊C4—228no—
255C22⋊C4—228no—
256C11C2×#39411yescharacteristic, complemented, Sylow
257C23—28no—
258C23—28no—
259C23—28no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—44no—
267C23—44no—
268C23—44no—
269C23—44no—
270C23—114no—
271C23—228no—
272C23—228no—
273C23—228no—
274C23—222no—
275C23—222no—
276C23—222no—
277C23—222no—
278C23—222no—
279C23—222no—
280C23—444no—
281C23—444no—
282C23—444no—
283C23—444no—
284C23C2×D4414yes—
285C23C2×D4412yes—
286C23#433912yes—
287C23D4×D1112yes—
288C23D4×D1112yes—
289C23#434112yes—
290C23#434112yes—
291C23C2×C22⋊D1112yes—
292C23C23×D1111yescharacteristic
293D4—2232no—
294C2×C4—28no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—44no—
301C2×C4—114no—
302C2×C4—228no—
303C2×C4—222no—
304C2×C4—222no—
305C2×C4—222no—
306C2×C4—222no—
307C2×C4—222no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—444no—
312C2×C4—444no—
313C2×C4C2×C22⋊D1114yescomplemented
314C22—24no—
315C22—24no—
316C22—24no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—416no—
322C22—224no—
323C22—224no—
324C22—224no—
325C22—442no—
326C22—442no—
327C22—442no—
328C22—442no—
329C22—4416no—
330C22#6693514yes—
331C22#6693614yes—
332C22#6693814yes—
333C22#6693914yes—
334C22#6698314yes—
335C22#6699114yes—
336C22#6699214yes—
337C22C22×D4411yescharacteristic
338C22C2×#433911yescharacteristic
339C22C2×D4×D1111yescharacteristic
340C22C2×D4×D1111yescharacteristic
341C22C2×#434111yescharacteristic
342C22C2×#434111yescharacteristic
343C22C22×C22⋊D1111yescharacteristic
344C4—24no—
345C4—42no—
346C4—224no—
347C4—442no—
348C4—442no—
349C2—44no—
350C2—444no—
351C2#1062257418yesdirect product factor
352C2C2×#6693511yescharacteristic
353C2C2×#6693611yescharacteristic
354C2C2×#6693811yescharacteristic
355C2C2×#6693911yescharacteristic
356C2C2×#6698311yescharacteristic
357C2C2×#6699111yescharacteristic
358C2C2×#6699211yescharacteristic
subgroupG/H
centerC24C22×D11
commutator, cosocleC23×C11C24
FrattiniC23C23×D11
FittingC22×C11×C22⋊C4C2
socleC24×C11C23
prime radicalC23×C22⋊D11C2
hypercenterC22×C22⋊C4D11
hypocenterC11C2×#394
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C11×C22⋊C4C2semidirect
3. C22×C22⋊Dic11C2semidirect
4. C22×(C2×D11)⋊C4C2semidirect
5. C22×(C2×D11)⋊C4C2semidirect
6. C22×C4⋊Dic11C2semidirect
7. C2×C11⋊#95C2semidirect
8. #10622574C2direct (N × H)
21. C2×C11×C22⋊C4C22semidirect
23. C2×C22⋊Dic11C22semidirect
26. C2×(C2×D11)⋊C4C22semidirect
27. C2×(C2×D11)⋊C4C22semidirect
29. C2×C4⋊Dic11C22semidirect
30. C11⋊#95C22semidirect
53. C22×C4×C11D4semidirect
121. C2×C4×C11C2×D4semidirect
140. C22×C22⋊C4D11semidirect
198. C2×C22⋊C4C2×D11semidirect
201. C2×C11#394semidirect
248. C22×C4C22⋊D11semidirect
256. C11C2×#394semidirect
313. C2×C4C2×C22⋊D11semidirect
351. C2#10622574direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D112
C22×C11×C22⋊C42
C22×C22⋊Dic112
C22×(C2×D11)⋊C42
C22×C4⋊Dic112
C2×C11⋊#952
#106225742
C2×#39411