Finite Group Databasebeta

← #29585039

Subgroups — #29585039

Order 15616.

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

normal subgroups only

This group has 296 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#21446800C211yesmaximal, characteristic
2#21445939C211yesmaximal, characteristic
3#21444594C211yesmaximal, characteristic
4#21444590C211yesmaximal, characteristic
5#21444223C211yesmaximal, characteristic
6#21444223C211yesmaximal, characteristic
7C61×#1274C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16839786C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12#16839522—22no—
13#16839517—22no—
14#16839515—22no—
15#16839513—22no—
16#16839494—22no—
17#16839494—22no—
18C61×#431C2211yescharacteristic
19C61×#431C2211yescharacteristic
20C61×#376C2211yescharacteristic
21C2×#11758194—21no—
22C22×#92418—21no—
23C22×#92418—21no—
24#14519777Q811yescharacteristic
25#14519777Q811yescharacteristic
26#14519769—21no—
27#14519756—21no—
28#14519756—21no—
29C4×Dic122—21no—
30C4×Dic122—21no—
31#14519736—21no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38C2×C42×C61D412yes—
39C2×C42×C61C2311yescharacteristic
40C4⋊C8×C61—21no—
41C4⋊C8×C61—21no—
42C22⋊C8×C61—21no—
43C22⋊C8×C61—21no—
44C4×C8×C61D412yes—
45C4×C8×C61D412yes—
46#95×C61—21no—
47#95×C61—21no—
48C22×C4×C61—22no—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61#4111yescharacteristic
51C22×C4×C61#4111yescharacteristic
52C2×Dic122—21no—
53C2×Dic122—21no—
54C2×C8×C61—22no—
55C2×C8×C61—22no—
56C42×C61—22no—
57C42×C61—22no—
58C42×C61C2×D411yescharacteristic
59C42×C61C2×D411yescharacteristic
60C42×C61C2×Q811yescharacteristic
61C42×C61#4111yescharacteristic
62C22⋊Dic61—41no—
63C4⋊Dic61—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67#11758196—41no—
68#11758196—41no—
69C4×Dic61—41no—
70#11758194—42no—
71C2×#92418—41no—
72C2×#92418—41no—
73C2×#92418—41no—
74C2×#92418—42no—
75C2×#92418—42no—
76C23×C61#12311yescharacteristic
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61—42no—
82C2×C4×C61C22⋊Q811yescharacteristic
83C2×C4×C61C22⋊Q811yescharacteristic
84C2×C4×C61C22⋊Q811yescharacteristic
85C2×C4×C61#12311yescharacteristic
86C2×C4×C61#12311yescharacteristic
87C2×C4×C61#12711yescharacteristic
88C2×C4×C61#13512yes—
89C2×C4×C61#13712yes—
90C2×Dic61—41no—
91C2×Dic61—41no—
92Dic122—42no—
93Dic122—42no—
94C8×C61—42no—
95C8×C61—42no—
96#92418—81no—
97#92418—81no—
98#92418—81no—
99#10669—611nomaximal, Sylow
100C22×C61—21no—
101C22×C61—21no—
102C22×C61#39911yescharacteristic
103C22×C61#48512yes—
104C4×C61—21no—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—82no—
109C4×C61#47912yes—
110C4×C61#49511yescharacteristic
111C4×C61#49711yescharacteristic
112Dic61—81no—
113Dic61—81no—
114#1995—611no—
115#1832—611no—
116#1571—611no—
117#1570—611no—
118#1481—611no—
119#1481—611no—
120#1274D6111yescharacteristic
121C2×C61—22no—
122C2×C61#209711yescharacteristic
123C2×C61#209811yescharacteristic
124C2×C61#209811yescharacteristic
125#533—611no—
126#431C2×D6111yescharacteristic
127#431C2×D6111yescharacteristic
128#423—611no—
129C2×C4⋊C8—611no—
130C2×C4⋊C8—611no—
131#376C2×D6111yescharacteristic
132#339—1222no—
133#336—1222no—
134#335—1222no—
135#334—1222no—
136Q8⋊C8—1222no—
137Q8⋊C8—1222no—
138C61#1066911yescharacteristic, complemented, Sylow
139C2×M16—1221no—
140C22×C8—1221no—
141C22×C8—1221no—
142C4⋊Q8—611no—
143C4⋊Q8—611no—
144#125—1221no—
145C22⋊Q8—1221no—
146C22⋊Q8—1221no—
147C4×Q8—1221no—
148C4×Q8—1221no—
149#117—1221no—
150C2×C42D24412yes—
151C2×C42C22×D6111yescharacteristic
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—1221no—
155C4⋊C8—1221no—
156C4⋊C8—1221no—
157C4⋊C8—1221no—
158C4⋊C8—1221no—
159C4⋊C8—1221no—
160C22⋊C8—21no—
161C22⋊C8—21no—
162C4×C8D24412yes—
163C4×C8D24412yes—
164#95—21no—
165#95—21no—
166C2×Q8—1221no—
167C2×Q8—1221no—
168C22×C4—22no—
169C22×C4C2×D24411yescharacteristic
170C22×C4#1175822411yescharacteristic
171C22×C4#1175822411yescharacteristic
172M16—2442no—
173C2×C8—22no—
174C2×C8—22no—
175C2×C8—2442no—
176C2×C8—2441no—
177C2×C8—2441no—
178C2×C8—2441no—
179C2×C8—2442no—
180C4⋊C4—1221no—
181C4⋊C4—1221no—
182C4⋊C4—1221no—
183C4⋊C4—1221no—
184C4⋊C4—2441no—
185C4⋊C4—2441no—
186C22⋊C4—2441no—
187C42—22no—
188C42—22no—
189C42—2441no—
190C42C2×D24411yescharacteristic
191C42C2×D24411yescharacteristic
192C42#1175822411yescharacteristic
193C42Q8×D6111yescharacteristic
194C23#1451976111yescharacteristic
195Q8—2442no—
196Q8—2442no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—2441no—
203C2×C4—2441no—
204C2×C4#1451975711yescharacteristic
205C2×C4#1451975711yescharacteristic
206C2×C4#1451975711yescharacteristic
207C2×C4#1451976111yescharacteristic
208C2×C4#1451976111yescharacteristic
209C2×C4#1451977411yescharacteristic
210C2×C4#1451979912yes—
211C2×C4#1451981012yes—
212C8—42no—
213C8—42no—
214C8—4881no—
215C8—4881no—
216C8—4881no—
217C22—21no—
218C22—21no—
219C22#1683969911yescharacteristic
220C22#1684010412yes—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—82no—
226C4—4881no—
227C4—4881no—
228C4#1684007012yes—
229C4#1684014611yescharacteristic
230C4#1684015611yescharacteristic
231C2—22no—
232C2#2144736611yescharacteristic
233C2#2144737311yescharacteristic
234C2#2144737311yescharacteristic
subgroupG/H
centerC2×C4#14519774
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#399
prime radicalC23×C61#123
hypercenter#1274D61
hypocenterC61#10669
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
138. C61#10669semidirect

Maximal subgroups

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

subgroupindex
#214468002
#214459392
#214445942
#214445902
#214442232
C61×#12742
#1066961