Finite Group Databasebeta

← C4×#16840673 #30606556

Subgroups — C4×#16840673 #30606556

Order 15616.

500 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840673C212yesmaximal
2C4×#14519838C212yesmaximal
3#21460916C212yesmaximal
4C4×#14519777C211yesmaximal, characteristic
5C2×#14519838C2214yes—
6C4×#11758217—22no—
7#16840673C418yesdirect product factor
8#16840642—22no—
9C2×#14519777C2211yescharacteristic
10C2×C4×Dic122C411yescharacteristic
11C2×C4×Dic122C2211yescharacteristic
12#16839668C411yescharacteristic
13#16839668C2211yescharacteristic
14#16839660—22no—
15#16839632C411yescharacteristic
16C4×C4⋊Dic61—22no—
17C43×C61C411yescharacteristic
18C2×#11758217—24no—
19#14519838—24no—
20#14519838C2×C418yes—
21#14519832—42no—
22C4×#92420—42no—
23C22×Dic122C2×C411yescharacteristic
24C22×Dic122C2311yescharacteristic
25#14519777—22no—
26#14519777C2×C414yes—
27C4×Dic122—41no—
28C4×Dic122—41no—
29C4×Dic122—41no—
30C4×Dic122—41no—
31C2×C4⋊Dic61—22no—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196D412yes—
37C2×C4×Dic61—21no—
38C2×C4×Dic61D412yes—
39#14519684—22no—
40#14519684—22no—
41C2×C42×C61—21no—
42C2×C42×C61—21no—
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45C2×C42×C61C2×C411yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61C22⋊C412yes—
54C22×Dic61C2×D412yes—
55C2×Dic122—21no—
56C2×Dic122—41no—
57C2×Dic122—41no—
58C2×Dic122—41no—
59C2×Dic122—41no—
60C2×Dic122C4212yes—
61C2×Dic122C22×C412yes—
62C2×Dic122#4112yes—
63#11758217—28no—
64#11758217—44no—
65C2×#92420—44no—
66C42×C61—24no—
67C42×C61—21no—
68C42×C61—21no—
69C42×C61—21no—
70C42×C61—42no—
71C42×C61—41no—
72C42×C61C4212yes—
73C4⋊Dic61—28no—
74C4⋊Dic61—41no—
75C4⋊Dic61—44no—
76C4⋊Dic61—41no—
77#11758196—42no—
78#11758196—42no—
79C4×Dic61—22no—
80C4×Dic61—22no—
81C4×Dic61—41no—
82C4×Dic61—41no—
83C23×C61C2×C22⋊C411yescharacteristic
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61#9911yescharacteristic
96C2×C4×C61#9911yescharacteristic
97C2×C4×C61C2×C4211yescharacteristic
98C2×C4×C61#11711yescharacteristic
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—41no—
108C2×Dic61C4×D414yes—
109Dic122—42no—
110Dic122—42no—
111Dic122—42no—
112Dic122—42no—
113#92420—48no—
114C4×#356—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61C4×C22⋊C411yescharacteristic
118C22×C61C2×#9911yescharacteristic
119C22×C61#41011yescharacteristic
120C4×C61—24no—
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—42no—
125C4×C61—41no—
126C4×C61#35612yescomplemented
127Dic61—24no—
128Dic61—42no—
129Dic61—42no—
130Dic61—81no—
131C4×C4⋊Q8—611no—
132C2×#356—612no—
133C4×#101—612no—
134#1394—612no—
135C2×C61—21no—
136C2×C61—21no—
137C2×C61C4×#9911yescharacteristic
138C2×C61C2×#35611yescharacteristic
139C2×C61#213211yescharacteristic
140C2×C4⋊Q8—611no—
141C2×C4×Q8—611no—
142C2×C4×Q8—611no—
143C2×#101—614no—
144C4×M16—1222no—
145#391—611no—
146#391—611no—
147#389—1222no—
148#384—611no—
149C4×C4⋊C4—1222no—
150C43#692311yescharacteristic
151#356—618no—
152#343—1222no—
153C61C4×#35611yescharacteristic, complemented, Sylow
154C22×Q8—611no—
155C22×Q8—611no—
156C2×M16—1224no—
157C4⋊Q8—614no—
158C4⋊Q8—1222no—
159C4×Q8—2441no—
160C4×Q8—2441no—
161C4×Q8—2441no—
162C4×Q8—2441no—
163C2×C4⋊C4—612no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4—611no—
166C2×C4⋊C4—1222no—
167C2×C4⋊C4—1222no—
168C2×C4⋊C4—1221no—
169C2×C42—21no—
170C2×C42—21no—
171C2×C42—612no—
172C2×C42—1221no—
173C2×C42C2×#692311yescharacteristic
174C2×C42C2×#692311yescharacteristic
175C2×C42C2×#692311yescharacteristic
176#101—618no—
177#101—1224no—
178#97—2442no—
179C4×C8—2442no—
180#95—1222no—
181#95—1222no—
182C2×Q8—612no—
183C2×Q8—612no—
184C2×Q8—612no—
185C2×Q8—1221no—
186C2×Q8—2441no—
187C2×Q8—2441no—
188C2×Q8—2441no—
189C2×Q8—2441no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—612no—
193C22×C4—612no—
194C22×C4—1221no—
195C22×C4—1221no—
196C22×C4C22⋊#692311yescharacteristic
197C22×C4C22⋊#692311yescharacteristic
198C22×C4C22×#692311yescharacteristic
199M16—1228no—
200M16—2444no—
201C2×C8—2444no—
202C4⋊C4—1228no—
203C4⋊C4—2442no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2442no—
207C4⋊C4—2444no—
208C42—24no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—41no—
213C42—42no—
214C42—1222no—
215C42—1222no—
216C42—2441no—
217C42—2441no—
218C42C4×#692312yes—
219C23C2×C22⋊#692311yescharacteristic
220Q8—2442no—
221Q8—2442no—
222Q8—2442no—
223Q8—2442no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—614no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—2442no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4—2441no—
244C2×C4—2442no—
245C2×C4#1451983611yescharacteristic
246C2×C4#1451983611yescharacteristic
247C2×C4C2×C4×#692311yescharacteristic
248C2×C4#1451985611yescharacteristic
249C8—2448no—
250C22—21no—
251C22—21no—
252C22C4×C22⋊#692311yescharacteristic
253C22C2×#1451983611yescharacteristic
254C22#1684074111yescharacteristic
255C4—24no—
256C4—21no—
257C4—21no—
258C4—21no—
259C4—42no—
260C4—41no—
261C4—1224no—
262C4—4881no—
263C4—2442no—
264C4—2442no—
265C4#1684067312yesdirect product factor
266C2—21no—
267C2—21no—
268C2C4×#1451983611yescharacteristic
269C2C2×#1684067311yescharacteristic
270C2#2146211211yescharacteristic
subgroupG/H
centerC2×C4#14519836
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC43×C61C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Dic122C23
hypercenterC43#6923
hypocenterC61C4×#356
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
7. #16840673C4direct (N × H)
126. C4×C61#356semidirect
153. C61C4×#356semidirect
265. C4#16840673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406732
C4×#145198382
#214609162
C4×#145197772
C4×#35661