Finite Group Databasebeta

← #29585010

Subgroups — #29585010

Order 15616.

304 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 93 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#21446759C211yesmaximal, characteristic
2#21445960C211yesmaximal, characteristic
3#21444594C211yesmaximal, characteristic
4#21444590C211yesmaximal, characteristic
5#21444249C211yesmaximal, characteristic
6#21444249C211yesmaximal, characteristic
7C61×#1275C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16839786C2211yescharacteristic
10#16839786C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12#16839527—22no—
13#16839516—22no—
14#16839515—22no—
15#16839513—22no—
16#16839494—22no—
17#16839494—22no—
18C61×#431C2211yescharacteristic
19C61×#431C2211yescharacteristic
20C2×#97×C61C2211yescharacteristic
21C22×Dic122Q811yescharacteristic
22C2×#11758194—21no—
23C2×#11758194—21no—
24C22×#92418—21no—
25C4×Dic122—21no—
26C4×Dic122—21no—
27C4×Dic122—21no—
28C4×Dic122—21no—
29C2×C4⋊Dic61Q811yescharacteristic
30C2×#11758196—21no—
31C2×C4×Dic61—21no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38C22×C8×C61D412yes—
39C2×C42×C61C2311yescharacteristic
40C4⋊C8×C61—21no—
41C4⋊C8×C61—21no—
42C22⋊C8×C61—21no—
43C22⋊C8×C61—21no—
44#97×C61—21no—
45#97×C61—21no—
46C4×C8×C61D412yes—
47C4×C8×C61D412yes—
48C22×C4×C61C2×D411yescharacteristic
49C22×C4×C61C2×Q811yescharacteristic
50C22×C4×C61#4111yescharacteristic
51C22×Dic61—21no—
52C22×Dic61—21no—
53C2×Dic122—21no—
54C2×Dic122—21no—
55C2×Dic122—42no—
56C2×C8×C61—22no—
57C2×C8×C61—22no—
58C2×C8×C61—22no—
59C2×C8×C61—22no—
60C2×C8×C61—22no—
61C42×C61C2×D411yescharacteristic
62C42×C61C2×D411yescharacteristic
63C42×C61#4111yescharacteristic
64C42×C61#4111yescharacteristic
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67#11758196—41no—
68#11758196—41no—
69C4×Dic61—41no—
70C4×Dic61—41no—
71#11758194—42no—
72#11758194—42no—
73C2×#92418—41no—
74C2×#92418—41no—
75C2×#92418—41no—
76C2×#92418—42no—
77C23×C61C22⋊Q811yescharacteristic
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61C22⋊Q811yescharacteristic
81C2×C4×C61C22⋊Q811yescharacteristic
82C2×C4×C61#12311yescharacteristic
83C2×C4×C61#12311yescharacteristic
84C2×C4×C61#12311yescharacteristic
85C2×C4×C61#12711yescharacteristic
86C2×C4×C61#13512yes—
87C2×C4×C61#13712yes—
88C2×Dic61—22no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—42no—
92C2×Dic61—41no—
93Dic122—22no—
94Dic122—22no—
95Dic122—41no—
96Dic122—41no—
97C8×C61—42no—
98C8×C61—42no—
99C8×C61—42no—
100#92418—81no—
101#92418—81no—
102#92418—81no—
103#10664—611nomaximal, Sylow
104C22×C61—21no—
105C22×C61—21no—
106C22×C61#39911yescharacteristic
107C22×C61#47912yes—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—21no—
112C4×C61#48512yes—
113C4×C61#49511yescharacteristic
114C4×C61#49711yescharacteristic
115Dic61—42no—
116Dic61—81no—
117#1985—611no—
118#1838—611no—
119#1571—611no—
120#1570—611no—
121#1487—611no—
122#1487—611no—
123#1275D6111yescharacteristic
124C2×C61—22no—
125C2×C61#209111yescharacteristic
126C2×C61#209711yescharacteristic
127C2×C61#209811yescharacteristic
128C2×C4×Q8—611no—
129#431C2×D6111yescharacteristic
130#431C2×D6111yescharacteristic
131#423—611no—
132#423—611no—
133C2×C4⋊C8—611no—
134C2×#97C2×D6111yescharacteristic
135#341—1222no—
136#336—1222no—
137#335—1222no—
138#334—1222no—
139Q8⋊C8—1222no—
140Q8⋊C8—1222no—
141C61#1066411yescharacteristic, complemented, Sylow
142C22×Q8—611no—
143C2×M16—1221no—
144C2×M16—1221no—
145C22×C8—1221no—
146C22×C8D24412yes—
147C4×Q8—1221no—
148C4×Q8—1221no—
149C4×Q8—1221no—
150C4×Q8—1221no—
151C2×C4⋊C4—611no—
152C2×C4⋊C4—1221no—
153C2×C42—1221no—
154C2×C42C22×D6111yescharacteristic
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—1221no—
158C4⋊C8—1221no—
159C4⋊C8—1221no—
160C4⋊C8—1221no—
161C4⋊C8—1221no—
162C4⋊C8—1221no—
163C22⋊C8—21no—
164C22⋊C8—21no—
165#97—21no—
166#97—21no—
167C4×C8D24412yes—
168C4×C8D24412yes—
169C2×Q8—1221no—
170C2×Q8—1221no—
171C2×Q8—2442no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4C2×D24411yescharacteristic
175C22×C4#1175822411yescharacteristic
176C22×C4Q8×D6111yescharacteristic
177M16—2442no—
178M16—2442no—
179C2×C8—22no—
180C2×C8—22no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—22no—
184C2×C8—2441no—
185C2×C8—2441no—
186C2×C8—2441no—
187C2×C8—2442no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4—2441no—
191C4⋊C4—2441no—
192C42—2441no—
193C42—2441no—
194C42C2×D24411yescharacteristic
195C42C2×D24411yescharacteristic
196C42#1175822411yescharacteristic
197C42#1175822411yescharacteristic
198C23#1451975711yescharacteristic
199Q8—1222no—
200Q8—1222no—
201Q8—2441no—
202Q8—2441no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—1222no—
206C2×C4—2442no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4#1451975711yescharacteristic
211C2×C4#1451975711yescharacteristic
212C2×C4#1451976111yescharacteristic
213C2×C4#1451976111yescharacteristic
214C2×C4#1451976111yescharacteristic
215C2×C4#1451977411yescharacteristic
216C2×C4#1451979912yes—
217C2×C4#1451981012yes—
218C8—42no—
219C8—42no—
220C8—42no—
221C8—4881no—
222C8—4881no—
223C8—4881no—
224C22—21no—
225C22—21no—
226C22#1683969911yescharacteristic
227C22#1684007012yes—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—4881no—
233C4—2442no—
234C4#1684010412yes—
235C4#1684014611yescharacteristic
236C4#1684015611yescharacteristic
237C2—22no—
238C2#2144733611yescharacteristic
239C2#2144736611yescharacteristic
240C2#2144737311yescharacteristic
subgroupG/H
centerC2×C4#14519774
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1275C2
socleC22×C61#399
prime radicalC23×C61C22⋊Q8
hypercenter#1275D61
hypocenterC61#10664
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
141. C61#10664semidirect

Maximal subgroups

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

subgroupindex
#214467592
#214459602
#214445942
#214445902
#214442492
C61×#12752
#1066461