Finite Group Databasebeta

← C4×#16839503 #29570932

Subgroups — C4×#16839503 #29570932

Order 15616.

532 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519769C211yesmaximal, characteristic
2C4×#14519688C211yesmaximal, characteristic
3C2×#16839503C212yesmaximal
4#21443701C212yesmaximal
5C4×#97×C61C211yesmaximal, characteristic
6C2×#14519769C2211yescharacteristic
7C2×#14519688—21no—
8C2×#14519688C2212yes—
9C2×C4×#92418—21no—
10#16839660C411yescharacteristic
11#16839660C411yescharacteristic
12#16839646—21no—
13#16839646—21no—
14#16839628C2211yescharacteristic
15C4×#11758196—21no—
16C4×#11758196—21no—
17C4×C4⋊Dic61C411yescharacteristic
18C4×C4⋊Dic61C411yescharacteristic
19#16839503C418yesdirect product factor
20C2×#97×C61—21no—
21C2×#97×C61C2212yes—
22C2×C4×C8×C61—21no—
23C43×C61C2211yescharacteristic
24C22×#92418—22no—
25#14519769—22no—
26#14519769C2×C414yes—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37#14519688—24no—
38#14519688—22no—
39#14519688C2×C414yes—
40C4×#92418—24no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C22×C8×C61—22no—
48C2×C42×C61C2×C411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61D411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61C2311yescharacteristic
55#97×C61—24no—
56#97×C61—22no—
57#97×C61C2×C414yes—
58C4×C8×C61—24no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C2×C8×C61—24no—
71C2×C8×C61—24no—
72C2×C8×C61—24no—
73C42×C61—22no—
74C42×C61—22no—
75C42×C61—22no—
76C42×C61—22no—
77C42×C61—22no—
78C42×C61—41no—
79C42×C61C22×C412yes—
80C42×C61#4112yes—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85C4⋊Dic61C4212yes—
86C4⋊Dic61C4212yes—
87#11758196—24no—
88#11758196—24no—
89#11758196—42no—
90#11758196—42no—
91C4×Dic61—42no—
92C4×Dic61—42no—
93C2×#92418—24no—
94C2×#92418—24no—
95C2×#92418—24no—
96C23×C61C2×C22⋊C411yescharacteristic
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61#10112yes—
111C2×C4×C61#10412yes—
112C2×C4×C61#10412yes—
113C2×C4×C61#10412yes—
114C2×C4×C61#10412yes—
115C2×C4×C61C2×C4211yescharacteristic
116C2×C4×C61#11711yescharacteristic
117C2×C4×C61C4×D412yes—
118C2×C4×C61C4×D412yes—
119C2×Dic61—22no—
120C2×Dic61—22no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C8×C61—28no—
132#92418—28no—
133C4×#330—611nomaximal, Sylow
134C22×C61C4×C22⋊C411yescharacteristic
135C22×C61C2×#10111yescharacteristic
136C22×C61#41311yescharacteristic
137C22×C61C2×#10411yescharacteristic
138C22×C61C2×#10411yescharacteristic
139C22×C61C2×#10411yescharacteristic
140C22×C61C2×#10411yescharacteristic
141C4×C61—21no—
142C4×C61—21no—
143C4×C61—22no—
144C4×C61—22no—
145C4×C61—22no—
146C4×C61—22no—
147C4×C61—41no—
148C4×C61#33014yescomplemented
149Dic61—42no—
150Dic61—42no—
151Dic61—81no—
152Dic61—81no—
153C4×#125—611no—
154C4×#97—611no—
155C4×#97D6111yescharacteristic
156C2×#330—612no—
157#1295—612no—
158C2×C61C2×#33011yescharacteristic
159C2×C61#152411yescharacteristic
160C2×C61#152411yescharacteristic
161C2×C61#152611yescharacteristic
162C2×C61C4×#10111yescharacteristic
163C2×C61C4×#10411yescharacteristic
164C2×C61C4×#10411yescharacteristic
165C2×#125—611no—
166C2×#97—21no—
167C2×#97—612no—
168C2×#97—1221no—
169C2×#97C2×D6112yes—
170C2×C4×C8—21no—
171C2×C4×C8—1221no—
172#389—611no—
173#389—611no—
174#387—1221no—
175#387—1221no—
176#382—611no—
177C4×C4⋊C4—611no—
178C4×C4⋊C4—611no—
179C4×C4⋊C4—1221no—
180C4×C4⋊C4—1221no—
181C43C2×D6111yescharacteristic
182#330—618no—
183C61C4×#33011yescharacteristic, complemented, Sylow
184C22×C8—22no—
185C22×C8—1222no—
186#125—614no—
187#125—1222no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C42—1221no—
197C2×C42—1221no—
198C2×C42C4×D6111yescharacteristic
199C2×C42C4×D6111yescharacteristic
200C2×C42D24411yescharacteristic
201C2×C42D24411yescharacteristic
202C2×C42C22⋊D6111yescharacteristic
203C2×C42C22⋊D6111yescharacteristic
204C2×C42C22×D6111yescharacteristic
205#97—24no—
206#97—22no—
207#97—614no—
208#97—1224no—
209#97—1222no—
210#97C4×D6114yes—
211C4×C8—24no—
212C4×C8—1224no—
213#95—1221no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4#1175819811yescharacteristic
224C22×C4#1175819811yescharacteristic
225C22×C4#1175819811yescharacteristic
226C22×C4#1175819811yescharacteristic
227C22×C4C2×C4×D6111yescharacteristic
228C22×C4C2×D24411yescharacteristic
229C22×C4C2×C22⋊D6111yescharacteristic
230C2×C8—24no—
231C2×C8—24no—
232C2×C8—24no—
233C2×C8—1224no—
234C2×C8—1224no—
235C2×C8—1224no—
236C4⋊C4—612no—
237C4⋊C4—612no—
238C4⋊C4—1221no—
239C4⋊C4—1221no—
240C4⋊C4—1224no—
241C4⋊C4—1224no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2442no—
245C4⋊C4—2442no—
246C42—22no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—41no—
252C42—2442no—
253C42—2442no—
254C42C2×C4×D6112yes—
255C42#1175822212yes—
256C23C2×#1175819811yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4#1451969512yes—
283C2×C4#1451970312yes—
284C2×C4#1451970312yes—
285C2×C4#1451970512yes—
286C2×C4#1451970512yes—
287C2×C4C42×D6111yescharacteristic
288C2×C4#1451973411yescharacteristic
289C2×C4C4×C22⋊D6112yes—
290C2×C4C4×D24412yes—
291C8—28no—
292C8—1228no—
293C22C4×#1175819811yescharacteristic
294C22C2×#1451969511yescharacteristic
295C22#1683974411yescharacteristic
296C22C2×#1451970311yescharacteristic
297C22C2×#1451970311yescharacteristic
298C22C2×#1451970511yescharacteristic
299C22C2×#1451970511yescharacteristic
300C4—22no—
301C4—22no—
302C4—21no—
303C4—21no—
304C4—22no—
305C4—22no—
306C4—41no—
307C4—4881no—
308C4—4881no—
309C4—2442no—
310C4—2442no—
311C4#1683950314yesdirect product factor
312C2C2×#1683950311yescharacteristic
313C2#2144440511yescharacteristic
314C2#2144440811yescharacteristic
315C2#2144441311yescharacteristic
316C2C4×#1451969511yescharacteristic
317C2C4×#1451970511yescharacteristic
318C2C4×#1451970311yescharacteristic
subgroupG/H
centerC22×C4#11758198
commutatorC2×C4×C61C2×C42
FrattiniC2×C42C22×D61
FittingC4×#97×C61C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenterC4×#97D61
hypocenterC61C4×#330
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#97

Complements

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

NH ≅ G/Ntype
19. #16839503C4direct (N × H)
148. C4×C61#330semidirect
183. C61C4×#330semidirect
311. C4#16839503direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#145197692
C4×#145196882
C2×#168395032
#214437012
C4×#97×C612
C4×#33061