Finite Group Databasebeta

← #30604048

Subgroups — #30604048

Order 15616.

356 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 86 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#21462181C212yesmaximal, complemented
2#21460742C212yesmaximal, complemented
3#21460741C212yesmaximal, complemented
4#21454529C211yesmaximal, characteristic
5#16840683—22no—
6C22⋊#11758187C2214yes—
7#16840651—22no—
8C2×#14519783C411yescharacteristic
9#16840308C411yescharacteristic
10#16839838—22no—
11C8×C22⋊D61—22no—
12#16839785C411yescharacteristic
13#16839730C2211yescharacteristic
14#16839729C2211yescharacteristic
15C2×C8×Dic61C2211yescharacteristic
16C2×#131×C61C411yescharacteristic
17C2×#11758187—24no—
18C2×#11758222C2×C411yescharacteristic
19#14519783—42no—
20C2×#11758194C2×C411yescharacteristic
21C2×#11758189—21no—
22C22×#92418C2311yescharacteristic
23C2×C8×D61—21no—
24#14519775C811yescharacteristic
25#14519773C811yescharacteristic
26#14519766C811yescharacteristic
27#14519764C811yescharacteristic
28#14519749—22no—
29C4×C22⋊D61—22no—
30C2×C4×Dic61C2×C411yescharacteristic
31#14519706—22no—
32C22⋊#92418—22no—
33#14519689—22no—
34C8×Dic61D412yes—
35C8×Dic61D412yes—
36C2×#41×C61C2×C411yescharacteristic
37#131×C61—42no—
38C2×M16×C61—21no—
39C2×M16×C61C2×C411yescharacteristic
40C22×C8×C61—21no—
41C22×C8×C61C2×C411yescharacteristic
42#41×C61—41no—
43#41×C61—41no—
44C2×Q8×C61C2×C811yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61C2×C811yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61C22×C411yescharacteristic
49C2×C22⋊D61—21no—
50C2×C22⋊D61—22no—
51C22×Dic61M1612yes—
52#11758222—41no—
53#11758222—41no—
54C2×D244C2×C811yescharacteristic
55C2×C4×D61—21no—
56C2×Dic122C2×C811yescharacteristic
57M16×C61—42no—
58M16×C61—41no—
59C2×C8×C61—22no—
60C2×C8×C61—21no—
61C2×C8×C61—42no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22⋊C411yescharacteristic
64C22⋊Dic61—22no—
65#11758198—22no—
66#11758196—22no—
67C4×Dic61C22⋊C412yes—
68C4×Dic61C2×C811yescharacteristic
69C4×Dic61C2×C811yescharacteristic
70#11758194—41no—
71C2×#92418—21no—
72C2×#92418—41no—
73C2×#92418C2×D412yes—
74#11758189—42no—
75C8×D61—42no—
76#11758187—44no—
77C23×C61—21no—
78C23×C61C2×M1611yescharacteristic
79C22×D61—21no—
80Q8×C61—41no—
81D4×C61—41no—
82D4×C61—42no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61C22×C811yescharacteristic
90C22⋊D61—44no—
91C22⋊D61—42no—
92C2×Dic61—21no—
93C2×Dic61—42no—
94C2×Dic61C22⋊C812yes—
95C2×Dic61C22⋊C812yes—
96D244—41no—
97C4×D61—41no—
98C4×D61—41no—
99Dic122—41no—
100C8×C61—21no—
101C8×C61—41no—
102C8×C61#10012yes—
103#92418—22no—
104#92418—41no—
105#11491—611nomaximal, Sylow
106C22×C61—22no—
107C22×C61—21no—
108C22×C61—42no—
109C22×C61—41no—
110C22×C61C2×C22⋊C811yescharacteristic
111C2×D61—42no—
112C2×D61—41no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61#41011yescharacteristic
116C4×C61C2×#10011yescharacteristic
117Dic61—22no—
118Dic61—22no—
119Dic61—41no—
120#2931—611no—
121#2163—612no—
122#1315—612no—
123#1315—612no—
124C2×C61—41no—
125C2×C61—81no—
126C2×C61#146011yescharacteristic
127C2×C61#211712yes—
128D61—81no—
129C2×#131—611no—
130C2×#131#692311yescharacteristic
131#532—611no—
132#436—1222no—
133C8×D4—1222no—
134#423—611no—
135#408—611no—
136#408—611no—
137C2×C4×C8—611no—
138C4⋊C16—1222no—
139C22⋊C16—614no—
140#346—1222no—
141C61#1149111yescharacteristic, complemented, Sylow
142C2×#41—611no—
143C2×#41C2×#692311yescharacteristic
144#131—42no—
145#131—2442no—
146C2×M16—21no—
147C2×M16—611no—
148C2×M16—1221no—
149C2×M16C2×#692311yescharacteristic
150C22×C8—21no—
151C22×C8—611no—
152C22×C8—1221no—
153C22×C8C2×#692311yescharacteristic
154C4⋊Q8—611no—
155#127—611no—
156#124—611no—
157#124—611no—
158#121—1222no—
159C4×D4—1222no—
160C2×C42—611no—
161C2×C16—1224no—
162C4⋊C8—1222no—
163C22⋊C8—1222no—
164C22⋊C8—1222no—
165C4×C8—612no—
166C4×C8—612no—
167#41—41no—
168#41—41no—
169#41—2441no—
170#41—2441no—
171C2×Q8—611no—
172C2×Q8D61⋊C811yescharacteristic
173C2×D4—21no—
174C2×D4—611no—
175C2×D4—1222no—
176C2×D4—1221no—
177C2×D4D61⋊C811yescharacteristic
178C22×C4—21no—
179C22×C4—612no—
180C22×C4—1221no—
181C22×C4C22×#692311yescharacteristic
182M16—42no—
183M16—41no—
184M16—2442no—
185M16—2441no—
186C2×C8—22no—
187C2×C8—21no—
188C2×C8—42no—
189C2×C8—612no—
190C2×C8—1221no—
191C2×C8—2441no—
192C2×C8—2442no—
193C2×C8C22⋊#692311yescharacteristic
194C2×C8C22⋊#692311yescharacteristic
195C4⋊C4—1222no—
196C22⋊C4—1222no—
197C22⋊C4—1222no—
198C42—612no—
199C42—611no—
200C42—611no—
201C16—2444no—
202C23—21no—
203C23—1221no—
204C23D61⋊M1611yescharacteristic
205Q8—41no—
206Q8—2441no—
207D4—41no—
208D4—42no—
209D4—2441no—
210D4—2444no—
211D4—2442no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—612no—
218C2×C4—612no—
219C2×C4—1221no—
220C2×C4—2442no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4C2×C22⋊#692311yescharacteristic
224C2×C4C2×D61⋊C811yescharacteristic
225C8—21no—
226C8—41no—
227C8—1222no—
228C8—2441no—
229C8#1451983712yes—
230C22—22no—
231C22—21no—
232C22—42no—
233C22—41no—
234C22—2442no—
235C22—2441no—
236C22D61⋊(C22⋊C8)11yescharacteristic
237C4—21no—
238C4—41no—
239C4—1222no—
240C4—1222no—
241C4—2441no—
242C4#1684074111yescharacteristic
243C4C2×#1451983711yescharacteristic
244C2—41no—
245C2—81no—
246C2—4881no—
247C2#2146105811yescharacteristic
248C2#2146206212yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#131×C61C4
socleC22×C61C2×C22⋊C8
prime radical#16840308C4
cosocleC22×#92418C23
hypercenterC2×#131#6923
hypocenterC61#11491
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #21462181C2semidirect
2. #21460742C2semidirect
3. #21460741C2semidirect
141. C61#11491semidirect

Maximal subgroups

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

subgroupindex
#214621812
#214607422
#214607412
#214545292
#1149161