Finite Group Databasebeta

← #30607500

Subgroups — #30607500

Order 15616.

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

normal subgroups only

This group has 488 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#21462788C211yesmaximal, characteristic, complemented
2#21462057C211yesmaximal, characteristic, complemented
3#21462048C212yesmaximal, complemented
4#21460869C212yesmaximal, complemented
5#21454512C211yesmaximal, characteristic
6#16840821—24no—
7D61⋊M32—22no—
8C2×#14519851C2212yes—
9C2×#14519851C2212yes—
10#16840659—22no—
11#16840657—24no—
12C2×#14519785C2211yescharacteristic
13C22×C8×D61C2211yescharacteristic
14#16840274C411yescharacteristic
15#16839832—22no—
16#16839827—22no—
17#16839728C411yescharacteristic
18#16839725C411yescharacteristic
19#16839718C2211yescharacteristic
20C61×#424C411yescharacteristic
21#14519852—24no—
22#14519851—22no—
23#14519851—22no—
24#14519851—22no—
25#14519851—22no—
26D61⋊C16—24no—
27C2×#11758187—22no—
28C2×#11758187D414yescomplemented
29C2×#11758222C2×C411yescharacteristic
30C22×C4×D61C2×C411yescharacteristic
31#14519785—22no—
32#14519785—22no—
33C2×#11758194C2×C411yescharacteristic
34C2×#11758189D412yes—
35C22×#92418C2311yescharacteristic
36C2×C8×D61—21no—
37C2×C8×D61—21no—
38C2×C8×D61—22no—
39C2×C8×D61—22no—
40C2×C8×D61D412yes—
41#14519761C812yes—
42#14519757—21no—
43#14519752—21no—
44#14519747C812yes—
45C4×D244—22no—
46#14519689—22no—
47#14519689—22no—
48#14519688—21no—
49C4×#92418—21no—
50C2×M16×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52#117×C61C2×C411yescharacteristic
53C4⋊C8×C61—22no—
54C23×D61C2×C811yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C2×C22⋊D61C2×C812yes—
57C22×Dic61C2×C811yescharacteristic
58#11758222—22no—
59#11758222—22no—
60C2×D244—22no—
61C2×D244M1611yescharacteristic
62C2×C4×D61—21no—
63C2×C4×D61—22no—
64C2×C4×D61—21no—
65C2×C4×D61—22no—
66C2×C4×D61C22⋊C412yes—
67C2×Dic122M1611yescharacteristic
68M16×C61—22no—
69C2×C8×C61—21no—
70C2×C8×C61—22no—
71C2×C8×C61C22⋊C412yes—
72C4⋊C4×C61—21no—
73C22⋊C4×C61C2×C812yes—
74C42×C61—21no—
75#11758198—22no—
76#11758198—22no—
77C4⋊Dic61—22no—
78#11758194—22no—
79C2×#92418—21no—
80C2×#92418C2×D412yes—
81C2×#92418C2×D411yescharacteristic
82C2×#92418C2×D411yescharacteristic
83C2×#92418#4112yes—
84#11758189—24no—
85C8×D61—22no—
86C8×D61—22no—
87C8×D61—41no—
88C8×D61—42no—
89C8×D61—41no—
90#11758187—24no—
91#11758187—42no—
92C23×C61C22×C811yescharacteristic
93C22×D61—21no—
94C22×D61—22no—
95C22×D61—42no—
96C22×D61C22⋊C812yes—
97C2×C4×C61—22no—
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C2×C4×C61C4×D412yes—
100C2×C4×C61C2×M1611yescharacteristic
101C2×C4×C61#13112yes—
102C22⋊D61—24no—
103C2×Dic61—21no—
104C2×Dic61—22no—
105C2×Dic61C22⋊C812yes—
106D244—22no—
107D244—44no—
108C4×D61—22no—
109C4×D61—22no—
110C4×D61—41no—
111C4×D61—41no—
112C4×D61—42no—
113Dic122—22no—
114C8×C61—22no—
115C8×C61—41no—
116#92418—41no—
117#92418#12011yescharacteristic
118#92418#12112yes—
119#92418#12311yescharacteristic
120#12981—611nomaximal, Sylow
121C22×C61—41no—
122C22×C61C2×C22⋊C811yescharacteristic
123C22×C61C8×D412yes—
124C2×D61—22no—
125C2×D61—24no—
126C2×D61—22no—
127C2×D61—41no—
128C2×D61—42no—
129C2×D61—41no—
130C2×D61—42no—
131C4×C61—42no—
132C4×C61#38611yescharacteristic
133C4×C61#40811yescharacteristic
134C4×C61#43512yes—
135Dic61—22no—
136Dic61—41no—
137#3407—611no—
138#2929—611no—
139#2115—611no—
140#2112—612no—
141#1378—612no—
142C2×C61—21no—
143C2×C61—22no—
144C2×C61#186911yescharacteristic
145D61—42no—
146D61—42no—
147C2×#131—611no—
148C23×C8—611no—
149#525—611no—
150#504—1224no—
151C2×M32—612no—
152C2×M32—612no—
153C2×M32—1222no—
154#435—1222no—
155C8×D4—1222no—
156#424#692311yescharacteristic
157#408—611no—
158#407—611no—
159#405—611no—
160#349—1222no—
161C22⋊C16—1224no—
162C61#1298111yescharacteristic, complemented, Sylow
163C2×#41—611no—
164C23×C4—611no—
165#131—1222no—
166#131—1222no—
167C2×M16—612no—
168C2×M16—611no—
169C2×M16C2×#692311yescharacteristic
170C22×C8—611no—
171C22×C8—612no—
172C22×C8—1222no—
173C22×C8—1221no—
174C22×C8—1221no—
175C22×C8—1222no—
176C22×C8C2×#692311yescharacteristic
177#123—612no—
178C22⋊Q8—1221no—
179#121—1221no—
180#120—612no—
181C4×D4—1222no—
182#117C2×#692311yescharacteristic
183M32—1222no—
184M32—1222no—
185M32—1224no—
186M32—1222no—
187M32—1222no—
188C2×C16—614no—
189C2×C16—1224no—
190C2×C16—1222no—
191C4⋊C8—22no—
192C22⋊C8—1222no—
193C22⋊C8—1222no—
194#97—1221no—
195C4×C8—1221no—
196C24—611no—
197#41—1222no—
198#41—1222no—
199C2×Q8—611no—
200C2×D4—612no—
201C2×D4—611no—
202C2×D4—1222no—
203C22×C4—612no—
204C22×C4—611no—
205C22×C4—1221no—
206C22×C4—1222no—
207C22×C4—1221no—
208C22×C4—1222no—
209C22×C4C22×#692311yescharacteristic
210M16—22no—
211M16—1224no—
212M16—1222no—
213C2×C8—21no—
214C2×C8—22no—
215C2×C8—611no—
216C2×C8—611no—
217C2×C8—612no—
218C2×C8—612no—
219C2×C8—1222no—
220C2×C8—1222no—
221C2×C8—1221no—
222C2×C8—2441no—
223C2×C8—2442no—
224C2×C8—2441no—
225C2×C8C22⋊#692312yes—
226C4⋊C4—21no—
227C4⋊C4—1222no—
228C22⋊C4—1222no—
229C22⋊C4—1222no—
230C22⋊C4D61⋊C812yes—
231C42—21no—
232C16—1224no—
233C16—2442no—
234C23—612no—
235C23—1221no—
236C23—1222no—
237C23—2442no—
238C23C2×D61⋊C811yescharacteristic
239Q8—1222no—
240D4—1224no—
241D4—1222no—
242D4—2444no—
243C2×C4—22no—
244C2×C4—612no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2442no—
252C2×C4C2×C22⋊#692311yescharacteristic
253C2×C4D4×#692312yes—
254C2×C4D61⋊M1611yescharacteristic
255C2×C4#1451986512yes—
256C8—22no—
257C8—41no—
258C8—611no—
259C8—612no—
260C8—611no—
261C8—2441no—
262C22—41no—
263C22—1222no—
264C22—1224no—
265C22—1222no—
266C22—2442no—
267C22—2441no—
268C22—2442no—
269C22—2441no—
270C22D61⋊(C22⋊C8)11yescharacteristic
271C22#1684079012yes—
272C4—42no—
273C4—1222no—
274C4—2441no—
275C4#1684071011yescharacteristic
276C4#1684073711yescharacteristic
277C4#1684079212yes—
278C2—21no—
279C2—22no—
280C2—2442no—
281C2—2442no—
282C2#2146179511yescharacteristic
subgroupG/H
centerC4#16840710
commutatorC23×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC2×C61#1869
prime radical#16840274C4
cosocleC22×#92418C23
hypercenter#424#6923
hypocenterC61#12981
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #21462788C2semidirect
2. #21462057C2semidirect
3. #21462048C2semidirect
4. #21460869C2semidirect
28. C2×#11758187D4semidirect
162. C61#12981semidirect

Maximal subgroups

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

subgroupindex
#214627882
#214620572
#214620482
#214608692
#214545122
#1298161