Finite Group Databasebeta

← #29580969

Subgroups — #29580969

Order 15616.

520 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 83 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#21457164C211yesmaximal, characteristic, complemented
2#21455918C212yesmaximal
3#21444433C212yesmaximal, complemented
4#21443689C211yesmaximal, characteristic, complemented
5C61×#1955C211yesmaximal, characteristic
6#16840319C2212yes—
7#16840097—22no—
8#16840058—22no—
9#16840042—22no—
10#16840003—22no—
11#16839973—22no—
12#16839967—22no—
13#16839913—22no—
14#16839862—24no—
15#16839819C2212yes—
16#16839503—24no—
17C2×C4×D4×C61C2211yescharacteristic
18C2×C4⋊C8×C61C2211yescharacteristic
19C2×C22⋊C8×C61—22no—
20C2×#97×C61C2211yescharacteristic
21C2×Dic244—22no—
22C2×#11758200—24no—
23#14519777D412yes—
24#14519777D412yes—
25#14519769—22no—
26#14519756—22no—
27#14519756—22no—
28C4×Dic122—22no—
29C4×Dic122—22no—
30#14519736—22no—
31#14519711—22no—
32#14519710—24no—
33C4⋊#92418—22no—
34#14519702—24no—
35#14519700—24no—
36#14519698—24no—
37C22⋊#92418—22no—
38#14519688D414yes—
39C22×D4×C61D411yescharacteristic
40C23×C4×C61—21no—
41C22×C8×C61—21no—
42C22×C8×C61D412yes—
43C4×D4×C61—22no—
44C4×D4×C61—22no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C22⋊C4×C61—21no—
47C2×C42×C61C2311yescharacteristic
48C4⋊C8×C61—22no—
49C22⋊C8×C61—44no—
50#97×C61—22no—
51C24×C61—21no—
52C2×D4×C61—22no—
53C2×D4×C61—42no—
54C22×C4×C61—21no—
55C22×C4×C61—42no—
56C22×C4×C61—42no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61#4111yescharacteristic
62C2×Dic122—22no—
63C2×Dic122—22no—
64C2×C8×C61—22no—
65C2×C8×C61—22no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61—42no—
69C4⋊C4×C61—22no—
70C22⋊C4×C61—42no—
71C42×C61C2×D412yes—
72C42×C61C2×D412yes—
73C22⋊Dic61—42no—
74#11758200—48no—
75C4⋊Dic61—22no—
76C4⋊Dic61—22no—
77C4⋊Dic61—22no—
78C4⋊Dic61—22no—
79#11758196—42no—
80#11758196—42no—
81C4×Dic61—42no—
82C2×#92418—24no—
83Dic244—82no—
84C23×C61—22no—
85C23×C61—42no—
86C23×C61—41no—
87C23×C61—41no—
88C23×C61—42no—
89C23×C61#12111yescharacteristic
90D4×C61—24no—
91D4×C61—42no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61—82no—
99C2×C4×C61—81no—
100C2×C4×C61—81no—
101C2×C4×C61#12012yes—
102C2×C4×C61#12011yescharacteristic
103C2×C4×C61#12112yes—
104C2×C4×C61#12711yescharacteristic
105C2×Dic61—42no—
106C2×Dic61—42no—
107Dic122—44no—
108Dic122—42no—
109Dic122—42no—
110C8×C61—42no—
111C8×C61—42no—
112#92418—44no—
113#10030—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—21no—
116C22×C61—44no—
117C22×C61—42no—
118C22×C61—82no—
119C22×C61—81no—
120C22×C61—81no—
121C22×C61#39211yescharacteristic
122C22×C61#47312yes—
123C4×C61—21no—
124C4×C61—22no—
125C4×C61—22no—
126C4×C61—81no—
127C4×C61#45311yescharacteristic
128C4×C61#45411yescharacteristic
129Dic61—82no—
130Dic61—82no—
131#3249—611no—
132#3110—612no—
133#1955D6111yescharacteristic
134#1531—612no—
135#1290—611no—
136C2×C61—22no—
137C2×C61—82no—
138C2×C61#200611yescharacteristic
139C2×C61#201011yescharacteristic
140C2×C61#202011yescharacteristic
141#533—612no—
142C2×C4×D4C2×D6111yescharacteristic
143#484—1222no—
144#477—1222no—
145#474—1222no—
146#467—1222no—
147#462—1222no—
148#461—1222no—
149#450—1222no—
150#440—1224no—
151#432—612no—
152C2×C4⋊C8C2×D6111yescharacteristic
153C2×C22⋊C8—22no—
154C2×#97C2×D6111yescharacteristic
155#330—1224no—
156C61#1003011yescharacteristic, complemented, Sylow
157C22×D4D24411yescharacteristic
158C23×C4—21no—
159C2×Q16—1222no—
160C2×SD16—1224no—
161C22×C8—21no—
162C22×C8C22⋊D6112yes—
163C4⋊Q8—612no—
164C4⋊Q8—612no—
165#125—1222no—
166C22⋊Q8—1222no—
167C22⋊Q8—1222no—
168C4×Q8—1222no—
169C4×Q8—1222no—
170C4×D4—22no—
171C4×D4—22no—
172#117—1222no—
173C2×C4⋊C4D24411yescharacteristic
174C2×C22⋊C4—21no—
175C2×C42C22×D6111yescharacteristic
176#107—1224no—
177#107—1222no—
178C4⋊C8—22no—
179C4⋊C8—1222no—
180#103—1224no—
181#103—1224no—
182#102—1224no—
183C22⋊C8—44no—
184C22⋊C8—1222no—
185#97—22no—
186#97—614no—
187C24—21no—
188C2×Q8—1222no—
189C2×Q8—1222no—
190C2×D4—22no—
191C2×D4—42no—
192C22×C4—21no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4C2×D24411yescharacteristic
198C22×C4#1175822211yescharacteristic
199C22×C4C2×C22⋊D6111yescharacteristic
200Q16—4882no—
201SD16—2448no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—42no—
207C2×C8—1224no—
208C4⋊C4—22no—
209C4⋊C4—1222no—
210C4⋊C4—1222no—
211C4⋊C4—1222no—
212C4⋊C4—1222no—
213C4⋊C4—2442no—
214C4⋊C4—2442no—
215C22⋊C4—42no—
216C22⋊C4—2442no—
217C42—2442no—
218C42D4×D6112yes—
219C42D4×D6112yes—
220C23—22no—
221C23—42no—
222C23—41no—
223C23—42no—
224C23—41no—
225C23#1451975111yescharacteristic
226Q8—2444no—
227Q8—2442no—
228Q8—2442no—
229D4—24no—
230D4—42no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—82no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4#1451974511yescharacteristic
243C2×C4#1451974712yes—
244C2×C4#1451975012yes—
245C2×C4#1451977311yescharacteristic
246C8—42no—
247C8—42no—
248C8—2444no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22#1683967111yescharacteristic
257C22#1684003712yes—
258C4—22no—
259C4—21no—
260C4—22no—
261C4—81no—
262C4—4882no—
263C4—4882no—
264C4#1683992911yescharacteristic
265C4#1683993411yescharacteristic
266C2—22no—
267C2—82no—
268C2#2144686011yescharacteristic
269C2#2144688611yescharacteristic
270C2#2144694011yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1955C2
socleC22×C61#392
prime radicalC22×D4×C61D4
hypercenter#1955D61
hypocenterC61#10030
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #21457164C2semidirect
3. #21444433C2semidirect
4. #21443689C2semidirect
156. C61#10030semidirect

Maximal subgroups

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

subgroupindex
#214571642
#214559182
#214444332
#214436892
C61×#19552
#1003061