Finite Group Databasebeta

← #30595567

Subgroups — #30595567

Order 15616.

874 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461545C212yesmaximal, complemented
2#21460636C214yesmaximal, complemented
3C2×#16839663C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5C2×#14519832—22no—
6#16840628C2214yescomplemented
7C23×D244C411yescharacteristic
8C22×#11758198—22no—
9C22×C4×Dic61C2211yescharacteristic
10#16839663—22no—
11#16839663C412yes—
12#16839663C2212yes—
13C22×C4⋊C4×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—28no—
16#14519832—44no—
17C24×D61—21no—
18C22×D244—21no—
19C22×D244—24no—
20C22×D244—42no—
21C22×D244—42no—
22C22×D244C2×C412yes—
23C23×Dic61D412yes—
24C2×#11758198—24no—
25C2×#11758198—24no—
26C2×#11758198—48no—
27C2×C4×Dic61—42no—
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61D412yes—
30C2×C4×Dic61C2311yescharacteristic
31C23×C4×C61—21no—
32C23×C4×C61C2×C411yescharacteristic
33C2×C4⋊C4×C61—21no—
34C2×C4⋊C4×C61—42no—
35C2×C4⋊C4×C61C2×C412yes—
36C24×C61C22⋊C411yescharacteristic
37C23×D61—24no—
38C23×D61—22no—
39C23×D61—42no—
40C23×D61—44no—
41C23×D61—42no—
42C23×D61—44no—
43C22×C4×C61—22no—
44C22×C4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61—22no—
47C22×C4×C61—44no—
48C22×C4×C61—42no—
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—24no—
52C22×Dic61—24no—
53C22×Dic61—42no—
54C22×Dic61C22⋊C412yes—
55C22×Dic61C2×D412yes—
56C2×D244—24no—
57C2×D244—22no—
58C2×D244—416no—
59C2×D244—42no—
60C2×D244—42no—
61C2×D244—42no—
62C2×D244—42no—
63C2×D244M1614yes—
64C2×#92420—28no—
65C2×#92420—44no—
66C2×#92420—44no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—42no—
69#11758198—48no—
70#11758198—48no—
71C4×Dic61—24no—
72C4×Dic61—41no—
73C4×Dic61—41no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—22no—
77C23×C61#10012yes—
78C23×C61#10414yes—
79C23×C61C2×C22⋊C411yescharacteristic
80C22×D61—24no—
81C22×D61—48no—
82C22×D61—416no—
83C22×D61—42no—
84C22×D61—42no—
85C22×D61—44no—
86C22×D61—44no—
87C22×D61—84no—
88C22×D61—88no—
89C22×D61—84no—
90C2×C4×C61—28no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—42no—
96C2×C4×C61—44no—
97C2×C4×C61—84no—
98C2×C4×C61#9912yes—
99C2×C4×C61C2×M1612yes—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—48no—
106C2×Dic61AGL(1,ℤ/8)14yes—
107D244—44no—
108D244—48no—
109D244—44no—
110#92420—48no—
111#7626—611nomaximal, Sylow
112C22×C61—22no—
113C22×C61—22no—
114C22×C61—24no—
115C22×C61—24no—
116C22×C61#32914yes—
117C22×C61#40711yescharacteristic
118C22×C61C2×#9911yescharacteristic
119C22×C61C2×#10011yescharacteristic
120C22×C61#41812yes—
121C22×C61C2×#10412yes—
122C2×D61—44no—
123C2×D61—48no—
124C2×D61—816no—
125C2×D61—82no—
126C2×D61—84no—
127C2×D61—82no—
128C4×C61—22no—
129C4×C61—22no—
130C4×C61—82no—
131Dic61—24no—
132Dic61—42no—
133C2×#390—611no—
134#1749—612no—
135#1270—614no—
136C2×C61—24no—
137C2×C61#146211yescharacteristic
138C2×C61#149012yes—
139C2×C61#150712yes—
140C2×C61C2×#32911yescharacteristic
141C2×C61#155511yescharacteristic
142D61—84no—
143C23×D4—611no—
144C22×C4⋊C4#692311yescharacteristic
145C22×C22⋊C4—1222no—
146C22×C42—611no—
147C2×C22⋊C8—1222no—
148C2×#97—1222no—
149#390—612no—
150#390—612no—
151#390—1222no—
152#336—614no—
153C61#762611yescharacteristic, complemented, Sylow
154C25—1221no—
155C22×D4—612no—
156C22×D4—1224no—
157C22×D4—1221no—
158C22×D4—2442no—
159C22×D4—2442no—
160C23×C4—21no—
161C23×C4—612no—
162C23×C4C2×#692311yescharacteristic
163C22×C8—1224no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4C2×#692312yes—
167C2×C22⋊C4—1224no—
168C2×C22⋊C4—1224no—
169C2×C22⋊C4—2448no—
170C2×C42—612no—
171C2×C42—611no—
172C2×C42—611no—
173C2×C42—2442no—
174C22⋊C8—1228no—
175#97—2444no—
176C24—1224no—
177C24—1222no—
178C24—2444no—
179C24—2442no—
180C24—2442no—
181C24—2444no—
182C24C22⋊#692311yescharacteristic
183C2×D4—614no—
184C2×D4—1224no—
185C2×D4—1222no—
186C2×D4—2442no—
187C2×D4—2442no—
188C2×D4—24416no—
189C2×D4—2442no—
190C2×D4—2442no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—44no—
196C22×C4—42no—
197C22×C4—612no—
198C22×C4—612no—
199C22×C4—1224no—
200C22×C4—1224no—
201C22×C4—2442no—
202C22×C4C22⋊#692311yescharacteristic
203C22×C4C22×#692311yescharacteristic
204C2×C8—1228no—
205C2×C8—2444no—
206C2×C8—2444no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C22⋊C4—2448no—
210C22⋊C4—2448no—
211C42—1224no—
212C42—2441no—
213C42—2441no—
214C23—21no—
215C23—21no—
216C23—22no—
217C23—1224no—
218C23—4884no—
219C23—4888no—
220C23—4884no—
221C23—2448no—
222C23—24416no—
223C23—2442no—
224C23—2442no—
225C23—2444no—
226C23—2444no—
227C23#1451983712yes—
228C23#1451984214yes—
229C23C2×C22⋊#692311yescharacteristic
230D4—2444no—
231D4—2448no—
232D4—2444no—
233C2×C4—28no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—44no—
240C2×C4—84no—
241C2×C4—614no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—2448no—
248C2×C4#1451983612yes—
249C2×C4D61⋊M1612yes—
250C8—2448no—
251C22—22no—
252C22—22no—
253C22—24no—
254C22—24no—
255C22—48816no—
256C22—4882no—
257C22—4882no—
258C22—4884no—
259C22—2444no—
260C22—2448no—
261C22#1684061814yes—
262C22#1684073411yescharacteristic
263C22C2×#1451983611yescharacteristic
264C22C2×#1451983711yescharacteristic
265C22#1684075412yes—
266C22C2×#1451984212yes—
267C4—22no—
268C4—22no—
269C4—82no—
270C4—1224no—
271C4—2442no—
272C2—24no—
273C2—4884no—
274C2#2146106611yescharacteristic
275C2#2146116012yes—
276C2#2146121612yes—
277C2C2×#1684061811yescharacteristic
278C2#2146134611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D244C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#7626
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461545C2semidirect
2. #21460636C2semidirect
6. #16840628C22semidirect
153. C61#7626semidirect

Maximal subgroups

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

subgroupindex
#214615452
#214606362
C2×#168396632
#762661