Finite Group Databasebeta

← #29589326

Subgroups — #29589326

Order 15616.

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

normal subgroups only

This group has 364 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#21454536C211yesmaximal, characteristic
2#21447438C212yesmaximal, complemented
3#21443770C211yesmaximal, characteristic, complemented
4#21443756C212yesmaximal, complemented
5C61×#1327C211yesmaximal, characteristic, complemented
6C2×#14519785C411yescharacteristic
7C2×#14519785C2211yescharacteristic
8#16840312C411yescharacteristic
9M32×D61—22no—
10#16839832—22no—
11#16839832—22no—
12#16839730C411yescharacteristic
13#16839730C2211yescharacteristic
14C2×#14519688C411yescharacteristic
15#16839544C2212yes—
16#16839543—22no—
17C61×#423C2211yescharacteristic
18C61×#349C2212yes—
19C2×#11758222C2×C411yescharacteristic
20C2×#11758222C2×C411yescharacteristic
21#14519785—42no—
22#14519785—42no—
23C2×#11758189—21no—
24C2×#11758189D412yes—
25C22×#92418C2×C411yescharacteristic
26C22×#92418C2×C411yescharacteristic
27C2×C8×D61—21no—
28C2×C8×D61D412yes—
29#14519777C811yescharacteristic
30#14519774C811yescharacteristic
31#14519765C811yescharacteristic
32#14519765C811yescharacteristic
33#14519751—22no—
34C4×D244—22no—
35#14519717—22no—
36#14519716—42no—
37C16×D61—42no—
38#14519689—22no—
39#14519689—22no—
40#14519688—21no—
41#14519688—21no—
42C2×M16×C61C2×C411yescharacteristic
43C2×M16×C61C2311yescharacteristic
44C2×C42×C61C2×C411yescharacteristic
45M32×C61—22no—
46C4⋊C8×C61—22no—
47C22×C4×C61—21no—
48C22×C4×C61C22×C411yescharacteristic
49C2×C22⋊D61—21no—
50C2×C22⋊D61M1612yes—
51#11758222—41no—
52#11758222—41no—
53#11758222—41no—
54#11758222—41no—
55C2×D244—22no—
56C2×D244C2×C811yescharacteristic
57C2×D244C2×C811yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61C22⋊C412yes—
60C2×Dic122C2×C811yescharacteristic
61C2×Dic122C2×C811yescharacteristic
62M16×C61—41no—
63M16×C61—41no—
64C2×C8×C61—21no—
65C2×C8×C61C2×D412yes—
66C42×C61—21no—
67C42×C61C2×C811yescharacteristic
68C42×C61C2×C811yescharacteristic
69#11758198—22no—
70#11758198—22no—
71C4⋊Dic61—22no—
72C2×#92418—22no—
73C2×#92418—21no—
74C2×#92418—41no—
75C2×#92418C22⋊C411yescharacteristic
76C2×#92418C22⋊C411yescharacteristic
77#11758189—42no—
78#11758189—42no—
79C8×D61—22no—
80C8×D61—22no—
81C8×D61—42no—
82C16×C61—42no—
83#11758185—42no—
84C23×C61C2×M1611yescharacteristic
85C22×D61—21no—
86C22×D61C22⋊C812yes—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—81no—
92C2×C4×C61C2×C22⋊C411yescharacteristic
93C2×C4×C61C22×C811yescharacteristic
94C22⋊D61—42no—
95C22⋊D61—42no—
96C2×Dic61—21no—
97C2×Dic61C22⋊C812yes—
98D244—41no—
99D244—41no—
100D244—82no—
101C4×D61—22no—
102C4×D61—22no—
103C4×D61—41no—
104C4×D61—41no—
105Dic122—41no—
106Dic122—41no—
107C8×C61—22no—
108C8×C61—41no—
109#92418—21no—
110#92418—41no—
111#92418#9912yes—
112#11486—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—41no—
115C22×C61C2×C22⋊C811yescharacteristic
116C2×D61—22no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—41no—
120C4×C61—21no—
121C4×C61—41no—
122C4×C61—41no—
123C4×C61C2×#9911yescharacteristic
124C4×C61#41311yescharacteristic
125Dic61—22no—
126Dic61—41no—
127#2932—611no—
128#2115—612no—
129#1327—611no—
130#1327D6111yescharacteristic, complemented
131#1321—612no—
132C2×C61—21no—
133C2×C61—41no—
134C2×C61#145911yescharacteristic
135D61—42no—
136D61—81no—
137C2×#131—611no—
138C2×#131—611no—
139#532—611no—
140C2×M32—1222no—
141#435—1222no—
142#435—1222no—
143#423C2×D6111yescharacteristic
144#408—611no—
145#408—611no—
146C2×#97—611no—
147#349—612no—
148#349—1222no—
149#349C2×D6112yes—
150C61#1148611yescharacteristic, complemented, Sylow
151C2×#41—611no—
152C2×#41—611no—
153#131—2442no—
154#131—2442no—
155C2×M16—612no—
156C2×M16—1221no—
157C2×M16C4×D6111yescharacteristic
158C2×M16C22×D6111yescharacteristic
159C22×C8—611no—
160C22×C8—612no—
161C22×C8—611no—
162C22×C8—1221no—
163C4⋊Q8—611no—
164#127—611no—
165#124—611no—
166#124—611no—
167#121—1222no—
168C4×D4—1222no—
169C2×C42C4×D6111yescharacteristic
170M32—22no—
171M32—1222no—
172M32—2442no—
173C2×C16—2442no—
174C4⋊C8—22no—
175C22⋊C8—1222no—
176C22⋊C8—1222no—
177#97—1221no—
178#97—1221no—
179#41—2441no—
180#41—2441no—
181#41—2441no—
182#41—2441no—
183C2×Q8—611no—
184C2×Q8—611no—
185C2×D4—612no—
186C2×D4—611no—
187C2×D4—611no—
188C2×D4—1222no—
189C2×D4—1221no—
190C22×C4—21no—
191C22×C4—612no—
192C22×C4—1221no—
193C22×C4C2×C4×D6111yescharacteristic
194M16—41no—
195M16—41no—
196M16—2442no—
197M16—2442no—
198C2×C8—21no—
199C2×C8—611no—
200C2×C8—611no—
201C2×C8—1222no—
202C2×C8—1222no—
203C2×C8—1222no—
204C2×C8—1221no—
205C2×C8—2442no—
206C2×C8—2441no—
207C2×C8D4×D6112yes—
208C4⋊C4—1222no—
209C22⋊C4—1222no—
210C22⋊C4—1222no—
211C42—21no—
212C42C8×D6111yescharacteristic
213C42C8×D6111yescharacteristic
214C16—42no—
215C16—2442no—
216C23—612no—
217C23—1221no—
218C23M16×D6111yescharacteristic
219Q8—2441no—
220Q8—2441no—
221D4—4882no—
222D4—2441no—
223D4—2441no—
224D4—2442no—
225D4—2442no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—81no—
231C2×C4—612no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1221no—
235C2×C4—2441no—
236C2×C4—2441no—
237C2×C4C22⋊C4×D6111yescharacteristic
238C2×C4C2×C8×D6111yescharacteristic
239C8—22no—
240C8—41no—
241C8—612no—
242C8—1221no—
243C8—2441no—
244C22—21no—
245C22—41no—
246C22—1222no—
247C22—2442no—
248C22—2442no—
249C22—2441no—
250C22C22⋊C8×D6111yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—1222no—
255C4—2441no—
256C4#99×D6111yescharacteristic
257C4#1683974511yescharacteristic
258C2—21no—
259C2—41no—
260C2—4881no—
261C2—2442no—
262C2#2144413611yescharacteristic
subgroupG/H
centerC4#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×M16C22×D61
FittingC61×#1327C2
socleC2×C61#1459
prime radical#16840312C4
cosocleC2×M16×C61C23
hypercenter#1327D61
hypocenterC61#11486
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #21447438C2semidirect
3. #21443770C2semidirect
4. #21443756C2semidirect
5. C61×#1327C2semidirect
130. #1327D61semidirect
150. C61#11486semidirect

Maximal subgroups

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

subgroupindex
#214545362
#214474382
#214437702
#214437562
C61×#13272
#1148661