Finite Group Databasebeta

← C2×#21462006 #30616479

Subgroups — C2×#21462006 #30616479

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840766C211yesmaximal, characteristic
2C2×#16840698C211yesmaximal, characteristic
3#21462006C218yesmaximal, direct product factor
4C2×#16840632C214yesmaximal
5C2×#16840318C211yesmaximal, characteristic
6C22×#11758213C2212yes—
7C22×C4×#6923C2212yes—
8#16840766—22no—
9#16840766C2214yes—
10C2×C4⋊#92420—22no—
11#16840698—22no—
12#16840698C2214yes—
13C2×(C2×#6923)⋊C4—22no—
14#16840632C22116yes—
15#16840318—22no—
16#16840318—22no—
17#16840318C414yescomplemented
18#16840318C2214yes—
19C2×#14519776C412yescomplemented
20C2×#14519769C411yescharacteristic, complemented
21C2×#14519755—22no—
22C2×#14519742—22no—
23C2×#14519735C2212yes—
24C2×C42×D61C2211yescharacteristic
25C2×#125×C61C411yescharacteristic, complemented
26C23×#6923—22no—
27C2×#11758213—28no—
28C2×#11758213—22no—
29C2×#11758213C2314yes—
30C22×#92420—22no—
31C2×C4×#6923—22no—
32C2×C4×#6923—24no—
33C2×C4×#6923Q818yescomplemented
34C2×C4×#6923C2314yes—
35C4⋊#92420—28no—
36(C2×#6923)⋊C4—28no—
37C22×Dic122—22no—
38C22×C4×D61D412yes—
39C22×C4×D61C2311yescharacteristic
40#14519776—24no—
41#14519776C2×C418yescomplemented
42#14519769—22no—
43#14519769C2×C414yescomplemented
44#14519755—28no—
45#14519755—28no—
46#14519742—28no—
47#14519742—28no—
48#14519735—22no—
49#14519735—22no—
50#14519735C2×C414yes—
51#14519735C2314yes—
52C2×C4⋊Dic61C2×C412yes—
53C2×#11758196—22no—
54C2×#11758196—22no—
55C2×#11758198—22no—
56C2×C4×Dic61—22no—
57C2×C4×Dic61C2×C411yescharacteristic
58C2×C4×Dic61D412yes—
59C42×D61C2×C412yes—
60C42×D61D412yes—
61C42×D61D412yes—
62C42×D61C2312yes—
63#125×C61—22no—
64#125×C61C2×C414yescomplemented
65C2×C4⋊C4×C61—22no—
66C2×C4⋊C4×C61C2×C412yes—
67C2×C42×C61C2×C411yescharacteristic
68C23×D61C2×D411yescharacteristic
69C22×#6923—28no—
70C22×#6923—24no—
71C22×#6923—48no—
72C22×C4×C61—22no—
73C22×C4×C61C22⋊C412yes—
74C22×C4×C61C22×C411yescharacteristic
75C22×Dic61—22no—
76C22×Dic61C22⋊C412yes—
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—44no—
79C2×C4×D61C22⋊C414yes—
80C2×C4×D61C22×C411yescharacteristic
81C2×C4×D61C2×D414yes—
82C2×C4×D61C2×D411yescharacteristic
83C2×C4×D61C2×D411yescharacteristic
84C2×C4×D61C2×Q814yes—
85C2×C4×D61#4114yes—
86C2×C4×D61C2411yescharacteristic
87C2×Dic122—28no—
88C2×Dic122—48no—
89C2×#92420—24no—
90C2×#92420—44no—
91C4×#6923—28no—
92C4×#6923—24no—
93C4×#6923C2×Q818yescomplemented
94#11758213—28no—
95#11758213—44no—
96C4⋊C4×C61—28no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61C22×C414yes—
99C42×C61C22⋊C412yes—
100C42×C61C22×C412yes—
101#11758198—24no—
102#11758198—24no—
103C4⋊Dic61—22no—
104C4⋊Dic61C22×C414yes—
105#11758196—28no—
106#11758196—28no—
107C4×Dic61—24no—
108C4×Dic61—24no—
109C4×Dic61C22⋊C414yes—
110C4×Dic61C22⋊C412yes—
111C4×Dic61C22×C412yes—
112C4×Dic61C2×D414yes—
113C23×C61C2×C22⋊C411yescharacteristic
114C22×D61—24no—
115C22×D61C2×C22⋊C411yescharacteristic
116C22×D61C22⋊Q814yes—
117C22×D61C22×D411yescharacteristic
118C2×#6923—28no—
119C2×#6923—48no—
120C2×#6923—416no—
121C2×C4×C61—24no—
122C2×C4×C61—24no—
123C2×C4×C61—44no—
124C2×C4×C61C2×C22⋊C414yes—
125C2×C4×C61C2×C22⋊C411yescharacteristic
126C2×C4×C61C4×Q814yes—
127C2×C4×C61C23×C411yescharacteristic
128C2×Dic61—24no—
129C2×Dic61—24no—
130C2×Dic61—44no—
131C2×Dic61C2×C22⋊C414yes—
132C2×Dic61C2×C22⋊C411yescharacteristic
133C2×Dic61#12412yes—
134C2×Dic61C4⋊Q812yes—
135C2×Dic61C22×D411yescharacteristic
136C4×D61—44no—
137C4×D61—44no—
138C4×D61C4×Q814yes—
139C4×D61C22⋊Q814yes—
140C4×D61#12412yes—
141C4×D61C4⋊Q812yes—
142C4×D61C22×Q812yes—
143C4×D61C2×#4112yes—
144Dic122—416no—
145#92420—44no—
146C2×#1995—611nomaximal, Sylow
147C22×C61#39112yes—
148C22×C61#42114yes—
149C22×C61C22×C22⋊C411yescharacteristic
150C2×D61—22no—
151C2×D61—22no—
152C2×D61—28no—
153C2×D61#39112yes—
154C2×D61C2×C22⋊Q812yes—
155#6923—48no—
156C4×C61—24no—
157C4×C61—44no—
158C4×C61#39112yes—
159C4×C61C2×C4×Q812yes—
160Dic61—24no—
161Dic61—44no—
162Dic61#39112yes—
163Dic61C2×#12411yescharacteristic
164Dic61C2×C4⋊Q811yescharacteristic
165C2×#533—611no—
166C2×#423—611no—
167C2×#376—611no—
168#1995—618no—
169C2×#339—614no—
170C2×C61#199514yescomplemented
171C2×C61C2×#39111yescharacteristic
172C2×C61C2×#42112yes—
173D61—22no—
174D61—22no—
175C22×M16—612no—
176#533—614no—
177#533—614no—
178#533—1222no—
179#533—1222no—
180C2×C4⋊Q8—612no—
181C2×#125—611no—
182C2×#125#692311yescharacteristic, complemented
183C2×C22⋊Q8—1222no—
184C2×C4×Q8—1222no—
185C2×#117—612no—
186C22×C42—611no—
187C22×C42—612no—
188#423—614no—
189#423—1222no—
190C2×C4⋊C8—1222no—
191#376—614no—
192#376—1222no—
193C2×#95—1222no—
194#339—6116no—
195C61C2×#199511yescharacteristic, complemented, Sylow
196C22×Q8—1222no—
197C23×C4—611no—
198C23×C4—612no—
199C23×C4—1222no—
200C2×M16—614no—
201C2×M16—1222no—
202C2×M16—1228no—
203C22×C8—1222no—
204C4⋊Q8—618no—
205C4⋊Q8—1224no—
206#125—22no—
207#125—614no—
208#125—1222no—
209#125C2×#692314yescomplemented
210C22⋊Q8—1228no—
211C22⋊Q8—1228no—
212C4×Q8—1228no—
213C4×Q8—1228no—
214#117—614no—
215#117—614no—
216#117—1222no—
217#117—1222no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—612no—
220C2×C4⋊C4—1222no—
221C2×C4⋊C4—1222no—
222C2×C4⋊C4C2×#692312yes—
223C2×C22⋊C4—1222no—
224C2×C42—612no—
225C2×C42—611no—
226C2×C42—612no—
227C2×C42—612no—
228C2×C42—612no—
229C2×C42—612no—
230C2×C42—618no—
231C2×C42—614no—
232C2×C42—1222no—
233C2×C42—1222no—
234C2×C42—1224no—
235C2×C42C2×#692311yescharacteristic
236C4⋊C8—1228no—
237#95—1228no—
238C24—611no—
239C2×Q8—1228no—
240C2×Q8—2448no—
241C22×C4—22no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—614no—
246C22×C4—614no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—612no—
250C22×C4—614no—
251C22×C4—614no—
252C22×C4—1224no—
253C22×C4—1228no—
254C22×C4—1222no—
255C22×C4—2444no—
256C22×C4—2448no—
257C22×C4C22⋊#692312yes—
258C22×C4C22×#692311yescharacteristic
259M16—1228no—
260M16—2444no—
261C2×C8—1224no—
262C2×C8—2444no—
263C4⋊C4—28no—
264C4⋊C4—22no—
265C4⋊C4—614no—
266C4⋊C4—1228no—
267C4⋊C4—1222no—
268C4⋊C4—1228no—
269C4⋊C4C22×#692314yes—
270C22⋊C4—1224no—
271C22⋊C4—1224no—
272C42—614no—
273C42—614no—
274C42—612no—
275C42—612no—
276C42—618no—
277C42—1224no—
278C42—1224no—
279C42—1228no—
280C42—1224no—
281C42C22⋊#692312yes—
282C42C22×#692312yes—
283C23—614no—
284C23—611no—
285C23—611no—
286C23—1224no—
287C23C2×C22⋊#692311yescharacteristic
288Q8—24416no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—44no—
292C2×C4—612no—
293C2×C4—612no—
294C2×C4—611no—
295C2×C4—611no—
296C2×C4—614no—
297C2×C4—612no—
298C2×C4—612no—
299C2×C4—614no—
300C2×C4—612no—
301C2×C4—612no—
302C2×C4—614no—
303C2×C4—1224no—
304C2×C4—1228no—
305C2×C4—1224no—
306C2×C4—2444no—
307C2×C4—2444no—
308C2×C4—2448no—
309C2×C4—24416no—
310C2×C4—2444no—
311C2×C4C2×C22⋊#692314yes—
312C2×C4C2×C22⋊#692311yescharacteristic
313C2×C4Q8×#692314yes—
314C2×C4C23×#692311yescharacteristic
315C8—2444no—
316C22—612no—
317C22—612no—
318C22—1222no—
319C22—1222no—
320C22—1228no—
321C22(C2×#6923)⋊Q812yes—
322C22#1684075914yes—
323C22C22×C22⋊#692311yescharacteristic
324C4—24no—
325C4—44no—
326C4—611no—
327C4—611no—
328C4—612no—
329C4—1224no—
330C4—2448no—
331C4—2444no—
332C4(C2×#6923)⋊Q812yes—
333C4C2×Q8×#692312yes—
334C2—1222no—
335C2—1222no—
336C2#2146200614yesdirect product factor
337C2C2×(C2×#6923)⋊Q811yescharacteristic
338C2C2×#1684075912yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×#125×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenterC2×#125#6923
hypocenterC61C2×#1995
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
3. #21462006C2direct (N × H)
17. #16840318C4semidirect
19. C2×#14519776C4semidirect
20. C2×#14519769C4semidirect
25. C2×#125×C61C4semidirect
33. C2×C4×#6923Q8semidirect
41. #14519776C2×C4semidirect
43. #14519769C2×C4semidirect
64. #125×C61C2×C4semidirect
93. C4×#6923C2×Q8semidirect
170. C2×C61#1995semidirect
182. C2×#125#6923semidirect
195. C61C2×#1995semidirect
209. #125C2×#6923semidirect
336. C2#21462006direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407662
C2×#168406982
#214620062
C2×#168406322
C2×#168403182
C2×#199561