Finite Group Databasebeta

← #29585043

Subgroups — #29585043

Order 15616.

296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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#21446799C211yesmaximal, characteristic
2#21445938C211yesmaximal, characteristic
3#21444591C211yesmaximal, characteristic
4#21444223C211yesmaximal, characteristic
5#21444221C211yesmaximal, characteristic
6#21443647C211yesmaximal, characteristic
7C61×#1571C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16839815C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11#16839608C2211yescharacteristic
12#16839523—22no—
13#16839516—22no—
14#16839512—22no—
15#16839494—22no—
16#16839492—22no—
17C61×#431C2211yescharacteristic
18C61×#423C2211yescharacteristic
19C2×C4⋊C8×C61C2211yescharacteristic
20C61×#335—22no—
21C22×#92418—21no—
22#14519777Q811yescharacteristic
23#14519777Q811yescharacteristic
24#14519769—21no—
25#14519756—21no—
26#14519756—21no—
27C4×Dic122—21no—
28C4×Dic122—21no—
29#14519736—21no—
30C2×C4×Dic61D412yes—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33C4⋊#92418—21no—
34C22⋊#92418—21no—
35C4×#92418D412yes—
36#14519684—21no—
37#14519684—21no—
38C2×M16×C61—21no—
39C22×C8×C61—21no—
40C2×C42×C61C2311yescharacteristic
41C4⋊C8×C61—21no—
42C4⋊C8×C61—21no—
43C4⋊C8×C61—21no—
44C4⋊C8×C61—21no—
45C4⋊C8×C61—21no—
46C22⋊C8×C61—21no—
47C4×C8×C61D412yes—
48C22×C4×C61C2×D411yescharacteristic
49C22×C4×C61#4111yescharacteristic
50C22×C4×C61#4111yescharacteristic
51C22×Dic61—22no—
52C2×Dic122—21no—
53C2×Dic122—21no—
54M16×C61—42no—
55C2×C8×C61—22no—
56C2×C8×C61—41no—
57C2×C8×C61—41no—
58C2×C8×C61—42no—
59C42×C61C2×D411yescharacteristic
60C42×C61C2×D411yescharacteristic
61C42×C61C2×Q811yescharacteristic
62C42×C61#4111yescharacteristic
63C22⋊Dic61—41no—
64C4⋊Dic61—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61—21no—
68#11758196—41no—
69#11758196—41no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61—41no—
73C2×#92418—22no—
74C2×#92418—41no—
75C2×#92418—42no—
76C23×C61#12311yescharacteristic
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C22⋊Q811yescharacteristic
80C2×C4×C61C22⋊Q811yescharacteristic
81C2×C4×C61C22⋊Q811yescharacteristic
82C2×C4×C61#12311yescharacteristic
83C2×C4×C61#12311yescharacteristic
84C2×C4×C61#12711yescharacteristic
85C2×C4×C61#13512yes—
86C2×C4×C61#13712yes—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91C2×Dic61—42no—
92Dic122—42no—
93Dic122—42no—
94C8×C61—42no—
95C8×C61—81no—
96C8×C61—81no—
97#92418—42no—
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#47912yes—
109C4×C61#49511yescharacteristic
110C4×C61#49711yescharacteristic
111Dic61—82no—
112Dic61—81no—
113Dic61—81no—
114#1995—611no—
115#1832—611no—
116#1571D6111yescharacteristic
117#1570—611no—
118#1481—611no—
119#1481—611no—
120#1274—611no—
121C2×C61—22no—
122C2×C61#209711yescharacteristic
123C2×C61#209811yescharacteristic
124C2×C61#209811yescharacteristic
125#533—611no—
126#431—611no—
127#431C2×D6111yescharacteristic
128#423C2×D6111yescharacteristic
129C2×C4⋊C8—611no—
130C2×C4⋊C8C2×D6111yescharacteristic
131#376—611no—
132#339—1222no—
133#336—1222no—
134#335—22no—
135#334—1222no—
136Q8⋊C8—1222no—
137Q8⋊C8—1222no—
138C61#1066911yescharacteristic, complemented, Sylow
139C2×M16—21no—
140C22×C8—21no—
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×C42—612no—
151C2×C42C22×D6111yescharacteristic
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—1221no—
158C4⋊C8—1221no—
159C4⋊C8—1221no—
160C22⋊C8—21no—
161C22⋊C8—1221no—
162C4×C8—612no—
163C4×C8C22⋊D6112yes—
164#95—1221no—
165#95—1221no—
166C2×Q8—1221no—
167C2×Q8—1221no—
168C22×C4—1222no—
169C22×C4#1175822211yescharacteristic
170C22×C4D4×D6111yescharacteristic
171C22×C4#1175822611yescharacteristic
172M16—42no—
173C2×C8—22no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—42no—
177C2×C8—1222no—
178C2×C8—2442no—
179C2×C8—2441no—
180C4⋊C4—1221no—
181C4⋊C4—1221no—
182C4⋊C4—1221no—
183C4⋊C4—1221no—
184C4⋊C4—2441no—
185C4⋊C4—2441no—
186C22⋊C4—2441no—
187C42—1222no—
188C42—1222no—
189C42—2441no—
190C42#1175822211yescharacteristic
191C42D4×D6111yescharacteristic
192C42Q8×D6111yescharacteristic
193C42C2×C22⋊D6111yescharacteristic
194C23#1451976211yescharacteristic
195Q8—2442no—
196Q8—2442no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4—2441no—
202C2×C4—2441no—
203C2×C4—2442no—
204C2×C4#1451975311yescharacteristic
205C2×C4#1451975511yescharacteristic
206C2×C4#1451975511yescharacteristic
207C2×C4#1451976011yescharacteristic
208C2×C4#1451976211yescharacteristic
209C2×C4#1451977311yescharacteristic
210C2×C4#1451979612yes—
211C2×C4#1451980912yes—
212C8—42no—
213C8—81no—
214C8—81no—
215C8—4881no—
216C8—2442no—
217C22—21no—
218C22—21no—
219C22#1683969711yescharacteristic
220C22#1684010512yes—
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—4882no—
226C4—4881no—
227C4—4881no—
228C4#1684006812yes—
229C4#1684014511yescharacteristic
230C4#1684015511yescharacteristic
231C2—22no—
232C2#2144736411yescharacteristic
233C2#2144737111yescharacteristic
234C2#2144737511yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1571C2
socleC22×C61#399
prime radicalC23×C61#123
hypercenter#1571D61
hypocenterC61#10669
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1571

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
#214467992
#214459382
#214445912
#214442232
#214442212
#214436472
C61×#15712
#1066961