Finite Group Databasebeta

← #29581306

Subgroups — #29581306

Order 15616.

552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16840127C212yesmaximal
2#21453887C211yesmaximal, characteristic, complemented
3#21446642C211yesmaximal, characteristic
4C2×#16839503C212yesmaximal, complemented
5C61×#1295C211yesmaximal, characteristic, complemented
6C2×#14519774C2211yescharacteristic
7C2×#14519769C2212yes—
8#16840127—24no—
9#16840127—24no—
10C2×#14519699—22no—
11C2×#14519699—22no—
12C2×#14519697—22no—
13C2×#14519688C2211yescharacteristic
14#16839702—22no—
15#16839694—22no—
16#16839692—22no—
17#16839503—24no—
18C2×#97×C61C2212yes—
19C61×#382C2211yescharacteristic
20C22×D244—21no—
21C22×D244—22no—
22C22×#92418—21no—
23#14519774—22no—
24#14519774—21no—
25#14519774D412yes—
26#14519769—22no—
27#14519769—22no—
28#14519769—22no—
29#14519769—22no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61D412yes—
32C2×C4⋊Dic61D412yes—
33C2×#11758196—22no—
34C2×#11758196—22no—
35#14519699—28no—
36#14519699—28no—
37#14519697—44no—
38#14519688—22no—
39#14519684—24no—
40#14519684—22no—
41C22×C8×C61—22no—
42C2×C4⋊C4×C61D412yes—
43C2×C42×C61C2311yescharacteristic
44#97×C61—22no—
45#97×C61D414yes—
46#95×C61—22no—
47C23×D61—41no—
48C22×C4×C61—22no—
49C22×C4×C61C2×D412yes—
50C22×C4×C61C2×D411yescharacteristic
51C22×Dic61—22no—
52C22×Dic61—22no—
53C2×D244—24no—
54C2×D244—22no—
55C2×D244—42no—
56C2×D244—48no—
57C2×D244—42no—
58C2×D244—42no—
59C2×D244—41no—
60C2×C8×C61—24no—
61C2×C8×C61—44no—
62C4⋊C4×C61—42no—
63C42×C61C2×D411yescharacteristic
64C42×C61C2×D412yes—
65C42×C61#4111yescharacteristic
66C4⋊Dic61—22no—
67C4⋊Dic61—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—22no—
70C4⋊Dic61—82no—
71#11758196—42no—
72#11758196—42no—
73#11758196—42no—
74#11758196—42no—
75C2×#92418—22no—
76C2×#92418—41no—
77C2×#92418—41no—
78C23×C61#12011yescharacteristic
79C22×D61—42no—
80C22×D61—81no—
81C22×D61—84no—
82C22×D61—81no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—24no—
86C2×C4×C61—42no—
87C2×C4×C61—44no—
88C2×C4×C61#12012yes—
89C2×C4×C61#12111yescharacteristic
90C2×C4×C61#12112yes—
91C2×C4×C61#12711yescharacteristic
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—44no—
96C2×Dic61—42no—
97D244—48no—
98D244—44no—
99D244—84no—
100D244—82no—
101C8×C61—44no—
102#92418—42no—
103#10080—611nomaximal, Sylow
104C22×C61#39211yescharacteristic
105C22×C61#45311yescharacteristic
106C22×C61#45414yes—
107C22×C61#45411yescharacteristic
108C2×D61—84no—
109C2×D61—82no—
110C2×D61—162no—
111C2×D61—162no—
112C4×C61—22no—
113C4×C61—22no—
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—82no—
117Dic61—82no—
118Dic61—82no—
119C2×#490—612no—
120#2822—611no—
121#1961—611no—
122C2×#330—612no—
123#1295D6111yescharacteristic, complemented
124C2×C61#165712yes—
125C2×C61#165812yes—
126C2×C61#200312yes—
127C2×C61#200611yescharacteristic
128D61—162no—
129C2×#127—611no—
130C2×#125—612no—
131#490—1224no—
132#490—1224no—
133C2×#102—1222no—
134C2×#102—1222no—
135C2×#102—1222no—
136C2×#97—611no—
137C2×#97C2×D6112yes—
138#400—1222no—
139#398—1222no—
140#398—1222no—
141#382C2×D6111yescharacteristic
142#330—1224no—
143C61#1008011yescharacteristic, complemented, Sylow
144C22×D4—1221no—
145C22×D4—1222no—
146C22×C8—22no—
147C22×C8—1221no—
148#127—612no—
149#127—1222no—
150#127—1221no—
151#125—1222no—
152#125—1222no—
153#125—1222no—
154#125—1222no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—1222no—
158C2×C4⋊C4—1222no—
159C2×C4⋊C4—1222no—
160C2×C4⋊C4D24412yes—
161C2×C42C22×D6111yescharacteristic
162#102—1228no—
163#102—1228no—
164#102—2444no—
165#97—22no—
166#97—1222no—
167#97D24414yes—
168#95—22no—
169#95—1224no—
170#95—1222no—
171C24—2441no—
172C2×D4—1224no—
173C2×D4—1222no—
174C2×D4—2442no—
175C2×D4—2448no—
176C2×D4—2442no—
177C2×D4—2442no—
178C2×D4—2441no—
179C22×C4—22no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4C2×D24411yescharacteristic
183C22×C4D4×D6112yes—
184C2×C8—24no—
185C2×C8—44no—
186C2×C8—1222no—
187C2×C8—2441no—
188C2×C8—2441no—
189C4⋊C4—42no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4—1222no—
194C4⋊C4—4882no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C4⋊C4—2442no—
198C4⋊C4—2442no—
199C42C2×D24412yes—
200C42D4×D6111yescharacteristic
201C42#1175822611yescharacteristic
202C23—4884no—
203C23—4881no—
204C23—4881no—
205C23—2442no—
206C23#1451974711yescharacteristic
207D4—4884no—
208D4—4882no—
209D4—2448no—
210D4—2444no—
211C2×C4—24no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—2444no—
217C2×C4—2442no—
218C2×C4—2442no—
219C2×C4—2442no—
220C2×C4—2442no—
221C2×C4#1451974712yes—
222C2×C4#1451975212yes—
223C2×C4#1451975211yescharacteristic
224C2×C4#1451977411yescharacteristic
225C8—44no—
226C8—2442no—
227C22—9762no—
228C22—9762no—
229C22—4884no—
230C22—4882no—
231C22#1683967211yescharacteristic
232C22#1683993211yescharacteristic
233C22#1683993614yes—
234C22#1683993711yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—4882no—
241C4—4882no—
242C2—9762no—
243C2#2144511812yes—
244C2#2144512212yes—
245C2#2144684412yes—
246C2#2144686311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61#120
prime radicalC2×#14519774C22
hypercenter#1295D61
hypocenterC61#10080
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #21453887C2semidirect
4. C2×#16839503C2semidirect
5. C61×#1295C2semidirect
123. #1295D61semidirect
143. C61#10080semidirect

Maximal subgroups

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

subgroupindex
C2×#168401272
#214538872
#214466422
C2×#168395032
C61×#12952
#1008061