Finite Group Databasebeta

← #30597847

Subgroups — #30597847

Order 15616.

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

normal subgroups only

This group has 452 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
1#21461322C211yesmaximal, characteristic
2#21461273C211yesmaximal, characteristic
3C8×#11758217C212yesmaximal, complemented
4#21460703C212yesmaximal, complemented
5#21454529C211yesmaximal, characteristic
6#16840779C2212yes—
7C4×#11758217C2212yes—
8#16840622C412yes—
9#16840620C412yes—
10#16840618C412yes—
11#16840617C412yes—
12#92420⋊C8—22no—
13C8×#92420—22no—
14C2×#14519783C411yescharacteristic
15#16840308C2211yescharacteristic
16#16839838—22no—
17C8×C22⋊D61—22no—
18#16839785C2211yescharacteristic
19#16839730C411yescharacteristic
20#16839729C411yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C2×#131×C61C411yescharacteristic
23C2×#11758217—22no—
24#14519844C2×C414yes—
25C22⋊#92420—22no—
26#14519832C2×C414yes—
27C4×#92420—22no—
28C4×#92420—22no—
29C2×#11758222C2×C411yescharacteristic
30#14519783—42no—
31C2×#11758194C2×C411yescharacteristic
32C2×#11758189—21no—
33C22×#92418C2×C411yescharacteristic
34C2×C8×D61—21no—
35#14519775C2×C411yescharacteristic
36#14519773C2×C411yescharacteristic
37#14519766C2×C411yescharacteristic
38#14519764C2×C411yescharacteristic
39#14519749—22no—
40C4×C22⋊D61—22no—
41C2×C4×Dic61C2311yescharacteristic
42#14519706—22no—
43C22⋊#92418—22no—
44#14519689—22no—
45C8×Dic61D412yes—
46C8×Dic61D412yes—
47C2×#41×C61C2×C411yescharacteristic
48#131×C61—42no—
49C2×M16×C61—21no—
50C2×M16×C61C2×C411yescharacteristic
51C22×C8×C61—21no—
52C22×C8×C61C2×C411yescharacteristic
53#41×C61—41no—
54#41×C61—41no—
55C2×Q8×C61C4211yescharacteristic
56C2×D4×C61—21no—
57C2×D4×C61C4211yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61C22×C411yescharacteristic
60C2×C22⋊D61—21no—
61C2×C22⋊D61—22no—
62C22×Dic61#4112yes—
63#11758222—41no—
64#11758222—41no—
65C2×D244C4211yescharacteristic
66C2×C4×D61—21no—
67C2×Dic122C4211yescharacteristic
68#11758217—28no—
69C2×#92420—24no—
70C2×#92420—24no—
71M16×C61—42no—
72M16×C61—41no—
73C2×C8×C61—22no—
74C2×C8×C61—21no—
75C2×C8×C61—42no—
76C2×C8×C61C22⋊C411yescharacteristic
77C2×C8×C61C22⋊C411yescharacteristic
78C22⋊Dic61—22no—
79#11758198—22no—
80#11758196—22no—
81C4×Dic61C22×C411yescharacteristic
82C4×Dic61C22×C411yescharacteristic
83C4×Dic61C2×D412yes—
84#11758194—41no—
85C2×#92418—21no—
86C2×#92418—41no—
87C2×#92418C22⋊C412yes—
88#11758189—42no—
89C8×D61—42no—
90C23×C61—21no—
91C23×C61#11711yescharacteristic
92C22×D61—21no—
93Q8×C61—41no—
94D4×C61—41no—
95D4×C61—42no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61C2×C4211yescharacteristic
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C22⋊D61—42no—
104C22⋊D61—44no—
105C2×Dic61—24no—
106C2×Dic61—21no—
107C2×Dic61C4×D412yes—
108C2×Dic61C4×D412yes—
109D244—41no—
110C4×D61—41no—
111C4×D61—41no—
112Dic122—41no—
113#92420—28no—
114#92420—44no—
115C8×C61—21no—
116C8×C61—41no—
117C8×C61#10012yes—
118#92418—22no—
119#92418—41no—
120#8241—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—22no—
123C22×C61—41no—
124C22×C61—42no—
125C22×C61C4×C22⋊C411yescharacteristic
126C2×D61—41no—
127C2×D61—42no—
128C4×C61—21no—
129C4×C61—41no—
130C4×C61C2×#10011yescharacteristic
131C4×C61#41311yescharacteristic
132Dic61—22no—
133Dic61—41no—
134Dic61#44314yes—
135#2931—611no—
136#1543—611no—
137#1525—611no—
138C8×M16—612no—
139#1299—612no—
140C2×C61—41no—
141C2×C61—81no—
142C2×C61C4×#10011yescharacteristic
143C2×C61#176412yes—
144D61—81no—
145C2×#131—611no—
146C2×#131#692311yescharacteristic
147#532—611no—
148#436—1222no—
149C8×D4—1222no—
150#431—612no—
151#423—611no—
152#408—611no—
153#408—611no—
154C4×M16—612no—
155C2×C4×C8—611no—
156#333—612no—
157#331—612no—
158#329—612no—
159#329—612no—
160#322—1222no—
161C82—1222no—
162C61#824111yescharacteristic, complemented, Sylow
163C2×#41—611no—
164C2×#41C2×#692311yescharacteristic
165#131—42no—
166#131—2442no—
167C2×M16—21no—
168C2×M16—611no—
169C2×M16—1222no—
170C2×M16—1221no—
171C2×M16C2×#692311yescharacteristic
172C22×C8—21no—
173C22×C8—611no—
174C22×C8—1221no—
175C22×C8C2×#692311yescharacteristic
176C4⋊Q8—611no—
177#127—611no—
178#124—611no—
179#124—611no—
180#121—1222no—
181C4×D4—1222no—
182C2×C42—611no—
183C4⋊C8—614no—
184C4⋊C8—1222no—
185C22⋊C8—1222no—
186C22⋊C8—1222no—
187C22⋊C8—1222no—
188#97—614no—
189C4×C8—612no—
190C4×C8—612no—
191C4×C8—1222no—
192C4×C8—1222no—
193#41—41no—
194#41—41no—
195#41—2441no—
196#41—2441no—
197C2×Q8—611no—
198C2×Q8C4×#692311yescharacteristic
199C2×D4—21no—
200C2×D4—611no—
201C2×D4—1222no—
202C2×D4—1221no—
203C2×D4C4×#692311yescharacteristic
204C22×C4—21no—
205C22×C4—612no—
206C22×C4—1221no—
207C22×C4C22×#692311yescharacteristic
208M16—42no—
209M16—41no—
210M16—1228no—
211M16—2442no—
212M16—2441no—
213C2×C8—22no—
214C2×C8—21no—
215C2×C8—42no—
216C2×C8—612no—
217C2×C8—1224no—
218C2×C8—1224no—
219C2×C8—1221no—
220C2×C8—2441no—
221C2×C8—2442no—
222C2×C8C22⋊#692311yescharacteristic
223C2×C8C22⋊#692311yescharacteristic
224C4⋊C4—1222no—
225C22⋊C4—1222no—
226C22⋊C4—1222no—
227C42—611no—
228C42—611no—
229C42—612no—
230C23—21no—
231C23—1221no—
232C23#1451985611yescharacteristic
233Q8—41no—
234Q8—2441no—
235D4—41no—
236D4—42no—
237D4—2441no—
238D4—2444no—
239D4—2442no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—612no—
246C2×C4—612no—
247C2×C4—1224no—
248C2×C4—1221no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4C2×C4×#692311yescharacteristic
252C2×C4C2×C22⋊#692311yescharacteristic
253C8—21no—
254C8—41no—
255C8—1228no—
256C8—1222no—
257C8—2444no—
258C8—2441no—
259C8#1451983712yes—
260C22—21no—
261C22—22no—
262C22—41no—
263C22—42no—
264C22—2441no—
265C22—2442no—
266C22C4×C22⋊#692311yescharacteristic
267C4—21no—
268C4—41no—
269C4—614no—
270C4—1222no—
271C4—2441no—
272C4C2×#1451983711yescharacteristic
273C4#1684074811yescharacteristic
274C2—41no—
275C2—81no—
276C2—4881no—
277C2C4×#1451983711yescharacteristic
278C2#2146159312yes—
subgroupG/H
centerC2×C8C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#131×C61C4
socleC22×C61C4×C22⋊C4
prime radical#16840308C22
cosocleC2×C4×Dic61C23
hypercenterC2×#131#6923
hypocenterC61#8241
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
3. C8×#11758217C2semidirect
4. #21460703C2semidirect
162. C61#8241semidirect

Maximal subgroups

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

subgroupindex
#214613222
#214612732
C8×#117582172
#214607032
#214545292
#824161