Finite Group Databasebeta

← C2×#13077245 #15617494

Subgroups — C2×#13077245 #15617494

Order 2816.

2806 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic11C211yesmaximal, characteristic
2#13077245C2116yesmaximal, direct product factor
3C2×#10622332C214yesmaximal, complemented
4C2×#10622331C214yesmaximal, complemented
5C2×#10622731C212yesmaximal, complemented
6C2×#10622820C211yesmaximal, characteristic
7C2×M16×Dic11C212yesmaximal, complemented
8C2×C11×#407C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C24×Dic11C412yes—
11C22×C11×M16C2212yes—
12C22×C4×Dic11C418yes—
13C22×C4×Dic11C412yes—
14C22×C4×Dic11C412yes—
15C22×C4×Dic11C412yes—
16C22×C4×Dic11C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2218yes—
21C22×#4318C2212yes—
22C11×#407C2218yes—
23C2×C11×C22⋊C8C2214yes—
24#10622820C2218yes—
25C2×C22⋊(C11⋊C8)C2214yes—
26#10622731C22116yescomplemented
27M16×Dic11C22116yescomplemented
28C2×#66879C2214yescomplemented
29C2×Dic11⋊C8C2218yescomplemented
30C2×C8×Dic11C2214yescomplemented
31#10622332C22132yescomplemented
32#10622331C22132yescomplemented
33C25×C11C2×C411yescharacteristic
34C23×C4×C11—28no—
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11C2×C414yes—
37C23×C4×C11C2×C412yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2314yes—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—216no—
42C23×Dic11C2×C412yes—
43C23×Dic11C2×C412yes—
44C23×Dic11C2×C412yes—
45C23×Dic11C2×C412yes—
46C23×Dic11C2×C4116yes—
47C23×Dic11C2×C412yes—
48C23×Dic11C2×C412yes—
49C2×C11×M16—28no—
50C2×C11×M16C2318yes—
51C22×C8×C11C2314yes—
52C2×C4×Dic11C2×C412yes—
53C2×C4×Dic11C2×C418yes—
54C2×C4×Dic11C2×C4116yes—
55C2×C4×Dic11C2×C4116yes—
56C2×C4×Dic11C2×C414yes—
57C2×C4×Dic11C2×C411yescharacteristic
58C2×C4×Dic11C2×C414yes—
59C2×C4×Dic11C2×C412yes—
60C2×C4×Dic11C2×C412yes—
61C2×C4×Dic11C2×C412yes—
62C2×C4×Dic11C2×C418yes—
63C2×C4×Dic11C2×C4116yes—
64C2×C4×Dic11C2×C412yes—
65C2×C4×Dic11C2×C411yescharacteristic
66C2×C4×Dic11C2314yes—
67C2×C4×Dic11C2314yes—
68C2×C4×Dic11C2318yes—
69C2×C4×Dic11C2318yes—
70C2×C4×Dic11C2311yescharacteristic
71C2×C4×Dic11C2312yes—
72C2×C4×Dic11C2311yescharacteristic
73C2×#4318—28no—
74C2×#4318C2318yes—
75C22×C11⋊C8C2314yes—
76C11×C22⋊C8C23116yes—
77C22⋊(C11⋊C8)C23116yes—
78#66879C23116yescomplemented
79Dic11⋊C8C23132yescomplemented
80C8×Dic11C23116yescomplemented
81C2×#2920—111nomaximal, Sylow
82C24×C11—24no—
83C24×C11—28no—
84C24×C11C22×C414yes—
85C24×C11C22×C411yescharacteristic
86C24×C11C22×C412yes—
87C22×C4×C11—24no—
88C22×C4×C11—216no—
89C22×C4×C11—28no—
90C22×C4×C11—28no—
91C22×C4×C11—216no—
92C22×C4×C11C22×C414yes—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C22×C414yes—
95C22×C4×C11C22×C418yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11#4118yes—
99C22×C4×C11C2414yes—
100C22×C4×C11C2412yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—28no—
103C22×Dic11—28no—
104C22×Dic11—28no—
105C22×Dic11—28no—
106C22×Dic11—264no—
107C22×Dic11—28no—
108C22×Dic11M16116yescomplemented
109C22×Dic11C22×C418yes—
110C22×Dic11C22×C418yes—
111C22×Dic11C22×C418yes—
112C22×Dic11C22×C418yes—
113C22×Dic11C22×C418yes—
114C22×Dic11C22×C412yes—
115C22×Dic11C22×C412yes—
116C22×Dic11C22×C412yes—
117C22×Dic11C22×C412yes—
118C22×Dic11C22×C418yes—
119C11×M16—216no—
120C2×C8×C11—28no—
121C2×C8×C11C2418yes—
122C4×Dic11C22×C418yes—
123C4×Dic11C22×C418yes—
124C4×Dic11C22×C418yes—
125C4×Dic11C22×C418yes—
126C4×Dic11C22×C414yes—
127C4×Dic11C22×C412yes—
128C4×Dic11C22×C418yes—
129C4×Dic11C22×C414yes—
130C4×Dic11C22×C414yes—
131C4×Dic11C22×C412yes—
132C4×Dic11C2412yes—
133C4×Dic11C2414yes—
134C4×Dic11C2412yes—
135#4318—216no—
136C2×C11⋊C8—28no—
137C2×C11⋊C8C2418yes—
138C23×C42—111no—
139#2920—1116no—
140C2×#432—114no—
141C2×#431—114no—
142C2×#423—112no—
143C2×#407—111no—
144C2×#407D1111yescharacteristic
145C2×C4×M16—112no—
146C23×C11—232no—
147C23×C11—28no—
148C23×C11—24no—
149C23×C11—216no—
150C23×C11—24no—
151C23×C11—24no—
152C23×C11#11714yes—
153C23×C11C2×M1618yes—
154C23×C11C23×C412yes—
155C23×C11C23×C414yes—
156C23×C11C23×C411yescharacteristic
157C2×C4×C11—28no—
158C2×C4×C11—24no—
159C2×C4×C11—28no—
160C2×C4×C11—216no—
161C2×C4×C11—28no—
162C2×C4×C11#11718yes—
163C2×C4×C11#11714yes—
164C2×C4×C11C23×C414yes—
165C2×C4×C11C23×C412yes—
166C2×C4×C11C23×C411yescharacteristic
167C2×C4×C11C2×#4114yes—
168C2×C4×C11C2×#4118yes—
169C2×C4×C11C2511yescharacteristic
170C2×Dic11—216no—
171C2×Dic11—24no—
172C2×Dic11—24no—
173C2×Dic11—216no—
174C2×Dic11—216no—
175C2×Dic11—216no—
176C2×Dic11—216no—
177C2×Dic11C2×M1618yes—
178C2×Dic11C2×M1618yes—
179C2×Dic11C2×M16132yescomplemented
180C2×Dic11C23×C414yes—
181C2×Dic11C23×C414yes—
182C2×Dic11C23×C414yes—
183C2×Dic11C23×C414yes—
184C8×C11—28no—
185C11⋊C8—28no—
186C24×C4—112no—
187C24×C4C2×D1111yescharacteristic
188C22×M16—112no—
189C22×M16C2×D1112yes—
190C22×C42—111no—
191C22×C42—111no—
192C22×C42—112no—
193C22×C42—112no—
194C22×C42—118no—
195C22×C42—112no—
196C22×C42—112no—
197C22×C42—118no—
198C22×C42—112no—
199#432—1132no—
200#431—1132no—
201#423—1116no—
202C2×C4⋊C8—118no—
203#407—118no—
204#407C2×D1118yes—
205C2×C22⋊C8—114no—
206C2×C22⋊C8C2×D1114yes—
207C4×M16—1116no—
208C2×#97—114no—
209C2×C4×C8—114no—
210C22×C11—232no—
211C22×C11—24no—
212C22×C11—28no—
213C22×C11—216no—
214C22×C11—24no—
215C22×C11—24no—
216C22×C11C2×#11714yes—
217C22×C11C2×#11712yes—
218C22×C11C22×M1618yes—
219C22×C11C22×M1614yes—
220C22×C11C24×C411yescharacteristic
221C4×C11—24no—
222C4×C11C2×#11712yes—
223C4×C11C2×#11714yes—
224C4×C11C22×#4112yes—
225Dic11—24no—
226Dic11—24no—
227Dic11C22×M1618yes—
228Dic11C22×M1618yes—
229C25C4×D1111yescharacteristic
230C23×C4—28no—
231C23×C4—112no—
232C23×C4—1116no—
233C23×C4—112no—
234C23×C4—112no—
235C23×C4—112no—
236C23×C4—112no—
237C23×C4—112no—
238C23×C4—2216no—
239C23×C4C4×D1111yescharacteristic
240C23×C4C4×D1114yes—
241C23×C4C4×D1112yes—
242C23×C4C22×D1114yes—
243C23×C4C22×D1112yes—
244C23×C4C22×D1111yescharacteristic
245C2×M16—28no—
246C2×M16—118no—
247C2×M16—228no—
248C2×M16C22×D1118yes—
249C22×C8—114no—
250C22×C8C22×D1114yes—
251C2×C42—112no—
252C2×C42—111no—
253C2×C42—118no—
254C2×C42—112no—
255C2×C42—112no—
256C2×C42—1116no—
257C2×C42—112no—
258C2×C42—118no—
259C2×C42—112no—
260C2×C42—1116no—
261C2×C42—1116no—
262C2×C42—114no—
263C2×C42—114no—
264C2×C42—111no—
265C2×C42—114no—
266C2×C42—114no—
267C2×C42—118no—
268C2×C42—118no—
269C2×C42—111no—
270C2×C42—111no—
271C2×C42—112no—
272C4⋊C8—1132no—
273C22⋊C8—1116no—
274C22⋊C8C22×D11116yes—
275#97—1116no—
276C4×C8—1116no—
277C2×C11—24no—
278C2×C11—28no—
279C2×C11#292014yescomplemented
280C2×C11C22×#11711yescharacteristic
281C2×C11C23×M1612yes—
282C24—24no—
283C24—28no—
284C24C2×C4×D1114yes—
285C24C2×C4×D1111yescharacteristic
286C24C2×C4×D1112yes—
287C22×C4—24no—
288C22×C4—216no—
289C22×C4—28no—
290C22×C4—28no—
291C22×C4—216no—
292C22×C4—1116no—
293C22×C4—112no—
294C22×C4—112no—
295C22×C4—118no—
296C22×C4—118no—
297C22×C4—118no—
298C22×C4—118no—
299C22×C4—118no—
300C22×C4—118no—
301C22×C4—112no—
302C22×C4—112no—
303C22×C4—228no—
304C22×C4—228no—
305C22×C4—228no—
306C22×C4—228no—
307C22×C4—2264no—
308C22×C4—228no—
309C22×C4C2×C4×D1114yes—
310C22×C4C2×C4×D1112yes—
311C22×C4C2×C4×D1118yes—
312C22×C4C2×C4×D1114yes—
313C22×C4C2×C4×D1111yescharacteristic
314C22×C4C2×C4×D1112yes—
315C22×C4#434118yes—
316C22×C4C23×D1114yes—
317C22×C4C23×D1112yes—
318C22×C4C23×D1111yescharacteristic
319M16—216no—
320M16—2216no—
321C2×C8—28no—
322C2×C8—118no—
323C2×C8—228no—
324C2×C8C23×D1118yes—
325C42—118no—
326C42—114no—
327C42—112no—
328C42—118no—
329C42—118no—
330C42—118no—
331C42—114no—
332C42—118no—
333C42—114no—
334C42—112no—
335C42—112no—
336C42—112no—
337C42—114no—
338C11C2×#292011yescharacteristic, complemented, Sylow
339C23—232no—
340C23—28no—
341C23—24no—
342C23—216no—
343C23—24no—
344C23—24no—
345C23#6693014yes—
346C23M16×D1118yes—
347C23C22×C4×D1112yes—
348C23C22×C4×D1114yes—
349C23C22×C4×D1111yescharacteristic
350C2×C4—28no—
351C2×C4—24no—
352C2×C4—216no—
353C2×C4—28no—
354C2×C4—28no—
355C2×C4—118no—
356C2×C4—118no—
357C2×C4—1132no—
358C2×C4—114no—
359C2×C4—114no—
360C2×C4—114no—
361C2×C4—114no—
362C2×C4—2216no—
363C2×C4—2216no—
364C2×C4—2216no—
365C2×C4—2216no—
366C2×C4—2216no—
367C2×C4—224no—
368C2×C4—224no—
369C2×C4#6693018yes—
370C2×C4#6693014yes—
371C2×C4C22×C4×D1114yes—
372C2×C4C22×C4×D1112yes—
373C2×C4C22×C4×D1111yescharacteristic
374C2×C4C2×#434114yes—
375C2×C4C2×#434118yes—
376C2×C4C24×D1111yescharacteristic
377C8—28no—
378C8—228no—
379C22—232no—
380C22—24no—
381C22—24no—
382C22—24no—
383C22—28no—
384C22—216no—
385C22C2×#6693014yes—
386C22C2×#6693012yes—
387C22C2×M16×D1118yes—
388C22C2×M16×D1114yes—
389C22C23×C4×D1111yescharacteristic
390C4—24no—
391C4—118no—
392C4—118no—
393C4—224no—
394C4—224no—
395C4C2×#6693014yes—
396C4C2×#6693012yes—
397C4C22×#434112yes—
398C2—24no—
399C2—28no—
400C2#1307724514yesdirect product factor
401C2C22×#6693011yescharacteristic
402C2C22×M16×D1112yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#407C2
socleC23×C11C23×C4
prime radicalC25×C11C2×C4
cosocleC2×C4×C11C25
hypercenterC2×#407D11
hypocenterC11C2×#2920
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. #13077245C2direct (N × H)
3. C2×#10622332C2semidirect
4. C2×#10622331C2semidirect
5. C2×#10622731C2semidirect
7. C2×M16×Dic11C2semidirect
26. #10622731C22semidirect
27. M16×Dic11C22semidirect
28. C2×#66879C22semidirect
29. C2×Dic11⋊C8C22semidirect
30. C2×C8×Dic11C22semidirect
31. #10622332C22semidirect
32. #10622331C22semidirect
78. #66879C23semidirect
79. Dic11⋊C8C23semidirect
80. C8×Dic11C23semidirect
108. C22×Dic11M16semidirect
179. C2×Dic11C2×M16semidirect
279. C2×C11#2920semidirect
338. C11C2×#2920semidirect
400. C2#13077245direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×Dic112
#130772452
C2×#106223322
C2×#106223312
C2×#106227312
C2×#106228202
C2×M16×Dic112
C2×C11×#4072
C2×#292011