Finite Group Databasebeta

← #29589223

Subgroups — #29589223

Order 15616.

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

normal subgroups only

This group has 314 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#21454462C211yesmaximal, characteristic
2#21447615C212yesmaximal, complemented
3#21443761C211yesmaximal, characteristic, complemented
4#21443744C212yesmaximal
5C61×#1323C211yesmaximal, characteristic, complemented
6#16840230C411yescharacteristic
7#16839822—22no—
8#16839814—22no—
9#16839789C411yescharacteristic
10#16839730C411yescharacteristic
11#16839728C2211yescharacteristic
12M16×Dic61C411yescharacteristic
13C2×C8×Dic61C2211yescharacteristic
14#16839580—22no—
15C22⋊#11758185C2212yes—
16C16×Dic61—22no—
17C61×#424C2211yescharacteristic
18C61×C22⋊C16C2212yes—
19C2×#11758222C2×C411yescharacteristic
20C2×#11758194C2×C411yescharacteristic
21C22×#92418C2×C411yescharacteristic
22#14519742C812yes—
23#14519739C812yes—
24#14519737—22no—
25#14519734—21no—
26C2×C4×Dic61C2×C411yescharacteristic
27C42×D61—21no—
28C2×#11758185—22no—
29C4⋊#92418—22no—
30#14519689—22no—
31#14519689—22no—
32#14519687—21no—
33C8×Dic61—21no—
34C8×Dic61D412yes—
35C8×Dic61D412yes—
36C2×M16×C61C2×C411yescharacteristic
37C22×C8×C61C2311yescharacteristic
38#117×C61C2×C411yescharacteristic
39C2×C16×C61—22no—
40C4⋊C8×C61—22no—
41C22×C4×C61C22×C411yescharacteristic
42C2×C22⋊D61—21no—
43C22×Dic61M1612yes—
44#11758222—41no—
45#11758222—41no—
46C2×D244C2×C811yescharacteristic
47C2×C4×D61—21no—
48C2×C4×D61—22no—
49C2×Dic122C2×C811yescharacteristic
50M16×C61—41no—
51C2×C8×C61—21no—
52C2×C8×C61—41no—
53C2×C8×C61C2×D412yes—
54C4⋊C4×C61C2×C812yes—
55C22⋊C4×C61—21no—
56C42×C61—21no—
57#11758198—22no—
58#11758196—22no—
59C4×Dic61—22no—
60C4×Dic61C22⋊C411yescharacteristic
61C4×Dic61C22⋊C411yescharacteristic
62C4×Dic61C2×C812yes—
63#11758194—41no—
64C2×#92418—21no—
65C2×#92418—41no—
66C2×#92418C22⋊C412yes—
67C16×C61—42no—
68#11758185—42no—
69C23×C61C2×M1611yescharacteristic
70C22×D61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—22no—
74C2×C4×C61C2×C22⋊C411yescharacteristic
75C2×C4×C61C22×C811yescharacteristic
76C22⋊D61—42no—
77C2×Dic61—24no—
78C2×Dic61—21no—
79C2×Dic61C22⋊C812yes—
80C2×Dic61C22⋊C812yes—
81D244—41no—
82C4×D61—41no—
83C4×D61—41no—
84C4×D61—44no—
85Dic122—41no—
86C8×C61—22no—
87C8×C61—41no—
88#92418—22no—
89#92418—41no—
90#11462—611nomaximal, Sylow
91C22×C61—22no—
92C22×C61—21no—
93C22×C61C2×C22⋊C811yescharacteristic
94C2×D61—42no—
95C2×D61—41no—
96C4×C61—21no—
97C4×C61—42no—
98C4×C61#41011yescharacteristic
99C4×C61#41311yescharacteristic
100Dic61—22no—
101Dic61—41no—
102Dic61#35014yes—
103#2922—611no—
104#2162—612no—
105#1323—611no—
106#1323D6111yescharacteristic, complemented
107#1315—612no—
108C2×C61—41no—
109C2×C61#145811yescharacteristic
110C2×C61C2×#35012yes—
111D61—81no—
112C4×#41—611no—
113#433—1222no—
114#431—1222no—
115#424—611no—
116#424C2×D6111yescharacteristic
117#408—611no—
118#408—611no—
119C4×M16—611no—
120C2×C4×C8—611no—
121C4⋊C16—1222no—
122C22⋊C16—612no—
123C22⋊C16C2×D6112yes—
124C4×C16—1222no—
125C61#1146211yescharacteristic, complemented, Sylow
126C2×#41—611no—
127C2×M16—611no—
128C2×M16C4×D6111yescharacteristic
129C22×C8—611no—
130C22×C8C22×D6111yescharacteristic
131C4×Q8—612no—
132C4×D4—612no—
133C4×D4—1222no—
134#117—1221no—
135#117C4×D6111yescharacteristic
136C2×C42—611no—
137C2×C42—1221no—
138C2×C16—22no—
139C2×C16—1222no—
140C4⋊C8—22no—
141C4⋊C8—1222no—
142C22⋊C8—1222no—
143C22⋊C8—1222no—
144#97—1221no—
145C4×C8—612no—
146C4×C8—612no—
147C4×C8—1221no—
148#41—2441no—
149#41—2441no—
150C2×Q8—611no—
151C2×D4—611no—
152C2×D4—1221no—
153C22×C4—612no—
154C22×C4—1222no—
155C22×C4—1221no—
156C22×C4C2×C4×D6111yescharacteristic
157M16—41no—
158M16—2441no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—612no—
162C2×C8—1221no—
163C2×C8—2441no—
164C2×C8D4×D6112yes—
165C4⋊C4—1222no—
166C4⋊C4C8×D6112yes—
167C22⋊C4—21no—
168C22⋊C4—1222no—
169C42—21no—
170C42—611no—
171C42—611no—
172C42—612no—
173C42—1222no—
174C16—42no—
175C16—2442no—
176C23—1221no—
177C23M16×D6111yescharacteristic
178Q8—2441no—
179D4—2441no—
180D4—2442no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—612no—
185C2×C4—612no—
186C2×C4—1224no—
187C2×C4—1221no—
188C2×C4—2444no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4C22⋊C4×D6111yescharacteristic
192C2×C4C2×C8×D6111yescharacteristic
193C8—22no—
194C8—41no—
195C8—1222no—
196C8—2441no—
197C22—22no—
198C22—21no—
199C22—2442no—
200C22—2441no—
201C22C22⋊C8×D6111yescharacteristic
202C4—21no—
203C4—42no—
204C4—614no—
205C4—1222no—
206C4—2441no—
207C4#1683973411yescharacteristic
208C4#1683974511yescharacteristic
209C2—41no—
210C2—4881no—
211C2#2144413211yescharacteristic
212C2#350×D6112yes—
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1323C2
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758222C2×C4
cosocleC22×C8×C61C23
hypercenter#1323D61
hypocenterC61#11462
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #21447615C2semidirect
3. #21443761C2semidirect
5. C61×#1323C2semidirect
106. #1323D61semidirect
125. C61#11462semidirect

Maximal subgroups

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

subgroupindex
#214544622
#214476152
#214437612
#214437442
C61×#13232
#1146261