Finite Group Databasebeta

← #30606557

Subgroups — #30606557

Order 15616.

500 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 102 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×#16840672C212yesmaximal
2#21461572C212yesmaximal
3#21460916C212yesmaximal
4#21448388C211yesmaximal, characteristic
5C2×#14519838C2214yes—
6C4×#11758217—22no—
7#16840672C418yescomplemented
8#16840642—22no—
9C2×#14519775C2211yescharacteristic
10C2×Q8×Dic61C411yescharacteristic
11C2×#14519742C2211yescharacteristic
12#16839668C2211yescharacteristic
13#16839659—22no—
14#16839631C411yescharacteristic
15#16839613—22no—
16C42×Dic61C411yescharacteristic
17C61×#391C411yescharacteristic
18C2×#11758217—24no—
19#14519838—24no—
20#14519838C2×C418yes—
21#14519832—42no—
22C4×#92420—42no—
23C22×Dic122C2311yescharacteristic
24#14519775—22no—
25#14519775C2×C414yes—
26Q8×Dic61—41no—
27Q8×Dic61—41no—
28#14519742—41no—
29#14519742—41no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—22no—
33C2×#11758196—22no—
34C2×#11758196D412yes—
35C2×C4×Dic61—21no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61D412yes—
41#14519684—22no—
42C22×Q8×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45#95×C61—22no—
46C2×Q8×C61—21no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C2×Q8×C61C4212yes—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61C22⋊C412yes—
53C22×C4×C61C22×C411yescharacteristic
54C22×Dic61—21no—
55C22×Dic61—21no—
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C2×D412yes—
59C2×Dic122—41no—
60C2×Dic122—41no—
61C2×Dic122C22×C412yes—
62C2×Dic122#4112yes—
63#11758217—28no—
64#11758217—44no—
65C2×#92420—44no—
66C4⋊C4×C61—41no—
67C42×C61—41no—
68C4⋊Dic61—42no—
69C4⋊Dic61—41no—
70#11758196—28no—
71#11758196—42no—
72#11758196—44no—
73C4×Dic61—24no—
74C4×Dic61—21no—
75C4×Dic61—22no—
76C4×Dic61—22no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61—42no—
80C4×Dic61—41no—
81C4×Dic61—41no—
82C4×Dic61C4212yes—
83C23×C61C2×C22⋊C411yescharacteristic
84Q8×C61—42no—
85Q8×C61—42no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—42no—
96C2×C4×C61C2×C4211yescharacteristic
97C2×C4×C61#11711yescharacteristic
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—42no—
107C2×Dic61—41no—
108C2×Dic61#9911yescharacteristic
109C2×Dic61#9911yescharacteristic
110C2×Dic61C4×D414yes—
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—21no—
121C4×C61—21no—
122C4×C61—42no—
123C4×C61—42no—
124C4×C61—42no—
125Dic61—24no—
126Dic61—21no—
127Dic61—24no—
128Dic61—41no—
129Dic61—81no—
130Dic61#35612yescomplemented
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#692311yescharacteristic
147#389—1222no—
148#384—611no—
149C4×C4⋊C4—1222no—
150C43—611no—
151#356—618no—
152#343—1222no—
153C61C4×#35611yescharacteristic, complemented, Sylow
154C22×Q8—611no—
155C22×Q8C2×#692311yescharacteristic
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—1222no—
166C2×C4⋊C4—1221no—
167C2×C4⋊C4—1222no—
168C2×C4⋊C4C2×#692311yescharacteristic
169C2×C42—611no—
170C2×C42—612no—
171C2×C42—611no—
172C2×C42—1221no—
173C2×C42—1221no—
174C2×C42—1221no—
175C2×C42C2×#692311yescharacteristic
176#101—618no—
177#101—1224no—
178#97—2442no—
179C4×C8—2442no—
180#95—22no—
181#95—1222no—
182C2×Q8—21no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—612no—
186C2×Q8—612no—
187C2×Q8—2441no—
188C2×Q8—2441no—
189C2×Q8C4×#692312yes—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—612no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4C22⋊#692312yes—
198C22×C4C22×#692311yescharacteristic
199M16—1228no—
200M16—2444no—
201C2×C8—2444no—
202C4⋊C4—41no—
203C4⋊C4—1228no—
204C4⋊C4—2442no—
205C4⋊C4—2441no—
206C4⋊C4—2444no—
207C4⋊C4—2442no—
208C42—41no—
209C42—612no—
210C42—1222no—
211C42—1222no—
212C42—1221no—
213C42—1221no—
214C42—1224no—
215C42—1221no—
216C42—2441no—
217C42—2441no—
218C42—2442no—
219C23C2×C22⋊#692311yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—2442no—
223Q8—2442no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—611no—
235C2×C4—611no—
236C2×C4—614no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—1221no—
244C2×C4—2442no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4C2×C4×#692311yescharacteristic
248C2×C4#1451985611yescharacteristic
249C8—2448no—
250C22—21no—
251C22—21no—
252C22C4×C22⋊#692311yescharacteristic
253C22D61⋊#9911yescharacteristic
254C22#1684074211yescharacteristic
255C4—21no—
256C4—21no—
257C4—42no—
258C4—42no—
259C4—42no—
260C4—612no—
261C4—1224no—
262C4—1224no—
263C4—1221no—
264C4—4881no—
265C4—2441no—
266C2—21no—
267C2—21no—
268C2#2146156611yescharacteristic
269C2D61⋊#35611yescharacteristic
270C2#2146211311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC22×Dic122C23
hypercenter#391#6923
hypocenterC61C4×#356
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #391

Complements

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

NH ≅ G/Ntype
7. #16840672C4semidirect
130. Dic61#356semidirect
153. C61C4×#356semidirect

Maximal subgroups

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

subgroupindex
C2×#168406722
#214615722
#214609162
#214483882
C4×#35661