Finite Group Databasebeta

← C2×#21450102 #29849830

Subgroups — C2×#21450102 #29849830

Order 15616.

2918 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758196C211yesmaximal, characteristic
2#21450102C2116yesmaximal, direct product factor
3C2×#16839700C212yesmaximal, complemented
4C2×#16839693C212yesmaximal, complemented
5C2×#16839646C214yesmaximal, complemented
6C2×#16839634C212yesmaximal
7C2×#16839625C211yesmaximal, characteristic
8C2×#16839623C212yesmaximal
9C22×#117×C61C211yesmaximal, characteristic
10C24×Dic61C2211yescharacteristic
11C24×Dic61C2211yescharacteristic
12C22×#11758196—28no—
13C22×#11758196C2212yes—
14C22×#11758196C2212yes—
15C22×#11758196C2218yes—
16C22×#11758196C2214yes—
17C22×C22⋊Dic61C2212yes—
18#16839700C22116yescomplemented
19#16839693C22116yescomplemented
20#16839646C22132yescomplemented
21#16839634C22116yes—
22#16839625C2218yes—
23#16839623C22116yes—
24C2×#14519684C2214yes—
25C2×#14519684C2214yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2214yes—
29C24×C4×C61C2211yescharacteristic
30C2×#117×C61—28no—
31C2×#117×C61C2218yes—
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C22⋊C4×C61C2212yes—
35C22×C42×C61C2212yes—
36C23×Dic61—24no—
37C23×Dic61—28no—
38C23×Dic61—24no—
39C23×Dic61—28no—
40C23×Dic61C2314yes—
41C23×Dic61C2312yes—
42C23×Dic61C2314yes—
43C23×Dic61C2314yes—
44C23×Dic61C2312yes—
45C2×#11758196—28no—
46C2×#11758196—28no—
47C2×#11758196—232no—
48C2×#11758196—216no—
49C2×#11758196C2318yes—
50C2×#11758196C23116yes—
51C2×#11758196C2318yes—
52C2×C22⋊Dic61—28no—
53C2×C22⋊Dic61C2318yes—
54#14519684C2318yes—
55#14519684C23116yes—
56#14519684C23116yes—
57#14519684C23116yes—
58#14519684C2318yes—
59C25×C61C2311yescharacteristic
60C23×C4×C61—28no—
61C23×C4×C61D418yes—
62C23×C4×C61C2312yes—
63C23×C4×C61C2312yes—
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C23×C4×C61C2314yes—
67#117×C61—232no—
68C2×C4⋊C4×C61—24no—
69C2×C4⋊C4×C61—24no—
70C2×C4⋊C4×C61C2314yes—
71C2×C4⋊C4×C61C2314yes—
72C2×C22⋊C4×C61—28no—
73C2×C22⋊C4×C61C2318yes—
74C2×C42×C61—28no—
75C2×C42×C61C2318yes—
76C24×C61—24no—
77C24×C61—24no—
78C24×C61C2×D414yes—
79C24×C61#4118yes—
80C24×C61C2412yes—
81C24×C61C2411yescharacteristic
82C22×C4×C61—232no—
83C22×C4×C61—216no—
84C22×C4×C61—24no—
85C22×C4×C61—24no—
86C22×C4×C61—24no—
87C22×C4×C61—24no—
88C22×C4×C61—28no—
89C22×C4×C61—28no—
90C22×C4×C61C2×D414yes—
91C22×C4×C61C2×D414yes—
92C22×C4×C61C2×D4116yes—
93C22×C4×C61C2414yes—
94C22×C4×C61C2414yes—
95C22×C4×C61C2412yes—
96C22×C4×C61C2412yes—
97C22×Dic61—232no—
98C22×Dic61—28no—
99C22×Dic61—24no—
100C22×Dic61—24no—
101C22×Dic61—216no—
102C22×Dic61—28no—
103C22×Dic61—24no—
104C22×Dic61—216no—
105C22×Dic61—28no—
106C22×Dic61—28no—
107C22×Dic61—28no—
108C22×Dic61—28no—
109C22×Dic61—416no—
110C22×Dic61#4118yes—
111C22×Dic61C2414yes—
112C22×Dic61C2418yes—
113C22×Dic61C2414yes—
114C4⋊C4×C61—28no—
115C4⋊C4×C61—28no—
116C22⋊C4×C61—216no—
117C42×C61—216no—
118C22⋊Dic61—216no—
119#11758196—216no—
120#11758196—216no—
121#11758196—232no—
122C23×C61—28no—
123C23×C61—28no—
124C23×C61—232no—
125C23×C61—24no—
126C23×C61—24no—
127C23×C61#123116yes—
128C23×C61C22×D414yes—
129C23×C61C22×D412yes—
130C23×C61C2×#4118yes—
131C23×C61C2×#4114yes—
132C23×C61C2×#4114yes—
133C23×C612−1+414yes—
134C23×C61C2511yescharacteristic
135C2×C4×C61—232no—
136C2×C4×C61—28no—
137C2×C4×C61—28no—
138C2×C4×C61—24no—
139C2×C4×C61—24no—
140C2×C4×C61—24no—
141C2×C4×C61—24no—
142C2×C4×C61—28no—
143C2×C4×C61—28no—
144C2×C4×C61—48no—
145C2×C4×C61—48no—
146C2×C4×C61C22×D414yes—
147C2×C4×C61C22×D414yes—
148C2×Dic61—232no—
149C2×Dic61—216no—
150C2×Dic61—24no—
151C2×Dic61—24no—
152C2×Dic61—24no—
153C2×Dic61—28no—
154C2×Dic61—28no—
155C2×Dic61—28no—
156C2×Dic61—28no—
157C2×Dic61—416no—
158C2×Dic61—48no—
159C2×Dic61—416no—
160C2×Dic61C2×#4118yes—
161C2×#2484—611nomaximal, Sylow
162C22×C61—24no—
163C22×C61—24no—
164C22×C61—216no—
165C22×C61—232no—
166C22×C61C2×#12318yes—
167C22×C61C2×#12314yes—
168C22×C61#52514yes—
169C22×C61#53614yes—
170C22×C61#552116yes—
171C22×C61C23×D411yescharacteristic
172C22×C61C22×#4112yes—
173C22×C61C22×#4112yes—
174C22×C61C2×2−1+412yes—
175C4×C61—24no—
176C4×C61—24no—
177C4×C61—44no—
178C4×C61—44no—
179Dic61—28no—
180Dic61—44no—
181Dic61—48no—
182C22×#117D6111yescharacteristic
183C23×C4⋊C4—611no—
184#2484—6116no—
185C2×#400—612no—
186C2×#398—612no—
187C2×#387—614no—
188C2×#385—612no—
189C2×#381—611no—
190C2×#381—612no—
191C2×C61—28no—
192C2×C61#248418yescomplemented
193C2×C61C22×#12311yescharacteristic
194C2×C61C2×#52511yescharacteristic
195C2×C61C2×#53611yescharacteristic
196C2×C61C2×#55214yes—
197C24×C4—611no—
198C24×C4—611no—
199C24×C4C2×D6111yescharacteristic
200C2×#117—28no—
201C2×#117C2×D6118yes—
202C22×C4⋊C4—612no—
203C22×C4⋊C4—614no—
204C22×C4⋊C4—618no—
205C22×C4⋊C4—612no—
206C22×C4⋊C4—1228no—
207C22×C4⋊C4C2×D6111yescharacteristic
208C22×C4⋊C4C2×D6111yescharacteristic
209C22×C22⋊C4—612no—
210C22×C22⋊C4C2×D6112yes—
211C22×C42C2×D6112yes—
212#400—6116no—
213#398—6116no—
214#387—6132no—
215#385—6116no—
216#381—618no—
217#381—6116no—
218C2×#95—612no—
219C2×#95—614no—
220C2×#95—614no—
221C2×#95—614no—
222C2×#95—612no—
223C61C2×#248411yescharacteristic, complemented, Sylow
224C25C22×D6111yescharacteristic
225C23×C4—28no—
226C23×C4—612no—
227C23×C4—614no—
228C23×C4—614no—
229C23×C4—614no—
230C23×C4—612no—
231C23×C4—1228no—
232C23×C4—1224no—
233C23×C4—1228no—
234C23×C4—1224no—
235C23×C4C22⋊D6118yes—
236C23×C4C22×D6112yes—
237C23×C4C22×D6112yes—
238C23×C4C22×D6114yes—
239C23×C4C22×D6111yescharacteristic
240C23×C4C22×D6111yescharacteristic
241#117—232no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—618no—
245C2×C4⋊C4—618no—
246C2×C4⋊C4—6116no—
247C2×C4⋊C4—12216no—
248C2×C4⋊C4—1228no—
249C2×C4⋊C4—1228no—
250C2×C4⋊C4—12232no—
251C2×C4⋊C4C22×D6114yes—
252C2×C4⋊C4C22×D6114yes—
253C2×C22⋊C4—28no—
254C2×C22⋊C4—618no—
255C2×C22⋊C4—1228no—
256C2×C22⋊C4C22×D6118yes—
257C2×C42—28no—
258C2×C42C22×D6118yes—
259#95—618no—
260#95—6116no—
261#95—6116no—
262#95—618no—
263#95—6116no—
264C24—24no—
265C24—24no—
266C24#1175822218yes—
267C24C2×C22⋊D6114yes—
268C24C23×D6112yes—
269C24C23×D6111yescharacteristic
270C22×C4—216no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—232no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—28no—
277C22×C4—28no—
278C22×C4—618no—
279C22×C4—614no—
280C22×C4—618no—
281C22×C4—614no—
282C22×C4—12216no—
283C22×C4—12232no—
284C22×C4—1228no—
285C22×C4—1224no—
286C22×C4—1224no—
287C22×C4—1228no—
288C22×C4—1224no—
289C22×C4—1228no—
290C22×C4—1228no—
291C22×C4—12216no—
292C22×C4—1228no—
293C22×C4—1228no—
294C22×C4—24416no—
295C22×C4C2×C22⋊D6114yes—
296C22×C4C2×C22⋊D6114yes—
297C22×C4C2×C22⋊D61116yes—
298C22×C4C23×D6114yes—
299C22×C4C23×D6114yes—
300C22×C4C23×D6112yes—
301C22×C4C23×D6112yes—
302C4⋊C4—28no—
303C4⋊C4—28no—
304C4⋊C4—12232no—
305C4⋊C4—12216no—
306C4⋊C4—12216no—
307C22⋊C4—216no—
308C22⋊C4—12216no—
309C42—216no—
310C23—28no—
311C23—24no—
312C23—28no—
313C23—24no—
314C23—232no—
315C23#14519760116yes—
316C23C22×C22⋊D6114yes—
317C23C22×C22⋊D6112yes—
318C23#41×D6114yes—
319C23C2×#1175822218yes—
320C23C2×#1175822214yes—
321C23#1451982414yes—
322C23C24×D6111yescharacteristic
323C2×C4—232no—
324C2×C4—28no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—48no—
333C2×C4—48no—
334C2×C4—618no—
335C2×C4—12232no—
336C2×C4—12216no—
337C2×C4—1224no—
338C2×C4—1224no—
339C2×C4—1224no—
340C2×C4—1228no—
341C2×C4—1228no—
342C2×C4—1228no—
343C2×C4—1228no—
344C2×C4—24416no—
345C2×C4—2448no—
346C2×C4—24416no—
347C2×C4C22×C22⋊D6114yes—
348C2×C4C22×C22⋊D6114yes—
349C22—24no—
350C22—232no—
351C22—216no—
352C22—24no—
353C22C2×#1451976018yes—
354C22C2×#1451976014yes—
355C22#1684026914yes—
356C22#1684033314yes—
357C22#16840445116yes—
358C22C23×C22⋊D6111yescharacteristic
359C22C2×#41×D6112yes—
360C22C22×#1175822212yes—
361C22C2×#1451982412yes—
362C4—24no—
363C4—24no—
364C4—44no—
365C4—44no—
366C4—1228no—
367C4—2444no—
368C4—2448no—
369C2—28no—
370C2#2145010218yesdirect product factor
371C2C22×#1451976011yescharacteristic
372C2C2×#1684026911yescharacteristic
373C2C2×#1684033311yescharacteristic
374C2C2×#1684044514yes—
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×#117×C61C2
socleC24×C61C24
prime radicalC25×C61C23
hypercenterC22×#117D61
hypocenterC61C2×#2484
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #21450102C2direct (N × H)
3. C2×#16839700C2semidirect
4. C2×#16839693C2semidirect
5. C2×#16839646C2semidirect
18. #16839700C22semidirect
19. #16839693C22semidirect
20. #16839646C22semidirect
192. C2×C61#2484semidirect
223. C61C2×#2484semidirect
370. C2#21450102direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117581962
#214501022
C2×#168397002
C2×#168396932
C2×#168396462
C2×#168396342
C2×#168396252
C2×#168396232
C22×#117×C612
C2×#248461