Finite Group Databasebeta

← #29585044

Subgroups — #29585044

Order 15616.

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

normal subgroups only

This group has 316 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#21446799C211yesmaximal, characteristic
2#21445972C211yesmaximal, characteristic
3#21444591C211yesmaximal, characteristic
4#21444223C211yesmaximal, characteristic
5#21444221C211yesmaximal, characteristic
6#21443647C211yesmaximal, characteristic
7C61×#1570C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16839815C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519706—22no—
12#16839608C2211yescharacteristic
13#16839523—22no—
14#16839512—22no—
15#16839494—22no—
16#16839492—22no—
17C61×#431C2211yescharacteristic
18C61×#423C2211yescharacteristic
19C2×C4⋊C8×C61C2211yescharacteristic
20C61×#334—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—
34#14519706—44no—
35C22⋊#92418—21no—
36C4×#92418D412yes—
37#14519684—21no—
38#14519684—21no—
39C2×M16×C61—21no—
40C22×C8×C61—21no—
41C2×C42×C61C2311yescharacteristic
42C4⋊C8×C61—21no—
43C4⋊C8×C61—21no—
44C4⋊C8×C61—21no—
45C4⋊C8×C61—21no—
46C4⋊C8×C61—21no—
47C22⋊C8×C61—21no—
48C4×C8×C61D412yes—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61#4111yescharacteristic
51C22×C4×C61#4111yescharacteristic
52C22×Dic61—22no—
53C2×Dic122—21no—
54C2×Dic122—21no—
55M16×C61—42no—
56C2×C8×C61—22no—
57C2×C8×C61—41no—
58C2×C8×C61—41no—
59C2×C8×C61—42no—
60C42×C61C2×D411yescharacteristic
61C42×C61C2×D411yescharacteristic
62C42×C61C2×Q811yescharacteristic
63C42×C61#4111yescharacteristic
64C22⋊Dic61—41no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—21no—
69#11758196—41no—
70#11758196—41no—
71C4×Dic61—22no—
72C4×Dic61—41no—
73C4×Dic61SD1614yes—
74C2×#92418—22no—
75C2×#92418—41no—
76C2×#92418—42no—
77C23×C61#12311yescharacteristic
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61C22⋊Q811yescharacteristic
81C2×C4×C61C22⋊Q811yescharacteristic
82C2×C4×C61C22⋊Q811yescharacteristic
83C2×C4×C61#12311yescharacteristic
84C2×C4×C61#12311yescharacteristic
85C2×C4×C61#12711yescharacteristic
86C2×C4×C61C2×SD1612yes—
87C2×C4×C61#13712yes—
88C2×Dic61—24no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93Dic122—42no—
94Dic122—42no—
95C8×C61—42no—
96C8×C61—81no—
97C8×C61—81no—
98#92418—42no—
99#92418—81no—
100#10670—611nomaximal, Sylow
101C22×C61—21no—
102C22×C61—21no—
103C22×C61#39911yescharacteristic
104C22×C61#48312yes—
105C4×C61—21no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—21no—
109C4×C61#47512yes—
110C4×C61#49211yescharacteristic
111C4×C61#49711yescharacteristic
112Dic61—44no—
113Dic61—81no—
114Dic61—81no—
115#1995—611no—
116#1843—611no—
117#1570—611no—
118#1570D6111yescharacteristic
119#1481—611no—
120#1481—611no—
121#1274—611no—
122C2×C61—22no—
123C2×C61#209611yescharacteristic
124C2×C61#209811yescharacteristic
125C2×C61#209811yescharacteristic
126#533—611no—
127#431—611no—
128#431C2×D6111yescharacteristic
129#423C2×D6111yescharacteristic
130C2×C4⋊C8—611no—
131C2×C4⋊C8—1222no—
132C2×C4⋊C8C2×D6111yescharacteristic
133#376—611no—
134#339—1222no—
135#334—22no—
136#334—1222no—
137Q8⋊C8—1222no—
138Q8⋊C8—1222no—
139C61#1067011yescharacteristic, complemented, Sylow
140C2×M16—21no—
141C22×C8—21no—
142C22×C8—1221no—
143C4⋊Q8—611no—
144C4⋊Q8—611no—
145#125—1221no—
146C22⋊Q8—1221no—
147C22⋊Q8—1221no—
148C4×Q8—1221no—
149C4×Q8—1221no—
150#117—1221no—
151C2×C42—612no—
152C2×C42C22×D6111yescharacteristic
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—21no—
157C4⋊C8—21no—
158C4⋊C8—1221no—
159C4⋊C8—1221no—
160C4⋊C8—1221no—
161C4⋊C8—2444no—
162C22⋊C8—21no—
163C22⋊C8—1221no—
164C4×C8—612no—
165C4×C8C22⋊D6112yes—
166#95—1221no—
167#95—1221no—
168C2×Q8—1221no—
169C2×Q8—1221no—
170C22×C4—1222no—
171C22×C4#1175822211yescharacteristic
172C22×C4D4×D6111yescharacteristic
173C22×C4#1175822611yescharacteristic
174M16—42no—
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—1222no—
180C2×C8—2441no—
181C2×C8—2442no—
182C4⋊C4—1221no—
183C4⋊C4—1221no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—2441no—
187C4⋊C4—2441no—
188C22⋊C4—2441no—
189C42—614no—
190C42—1222no—
191C42—2441no—
192C42#1175822211yescharacteristic
193C42D4×D6111yescharacteristic
194C42Q8×D6111yescharacteristic
195C42C2×C22⋊D6111yescharacteristic
196C23#1451976211yescharacteristic
197Q8—2442no—
198Q8—2442no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—1224no—
202C2×C4—2441no—
203C2×C4—2441no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4#1451975311yescharacteristic
207C2×C4#1451975511yescharacteristic
208C2×C4#1451975511yescharacteristic
209C2×C4#1451976011yescharacteristic
210C2×C4#1451976211yescharacteristic
211C2×C4#1451977311yescharacteristic
212C2×C4SD16×D6112yes—
213C2×C4#1451980612yes—
214C8—42no—
215C8—81no—
216C8—81no—
217C8—4881no—
218C8—2442no—
219C22—21no—
220C22—21no—
221C22#1683969711yescharacteristic
222C22#1684009412yes—
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—4881no—
228C4—4881no—
229C4—2444no—
230C4#1684004612yes—
231C4#1684013311yescharacteristic
232C4#1684015311yescharacteristic
233C2—22no—
234C2#2144735911yescharacteristic
235C2#2144737111yescharacteristic
236C2#2144737511yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1570C2
socleC22×C61#399
prime radicalC23×C61#123
hypercenter#1570D61
hypocenterC61#10670
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
139. C61#10670semidirect

Maximal subgroups

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

subgroupindex
#214467992
#214459722
#214445912
#214442232
#214442212
#214436472
C61×#15702
#1067061