Finite Group Databasebeta

← #29583103

Subgroups — #29583103

Order 15616.

416 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 101 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#21446796C211yesmaximal, characteristic
2#21444382C212yesmaximal
3#21443677C212yesmaximal
4#21443652C211yesmaximal, characteristic
5C61×#2862C211yesmaximal, characteristic
6#16840319C2211yescharacteristic
7#16839815C2212yes—
8#16839786C2211yescharacteristic
9#16839522—21no—
10#16839522—21no—
11#16839498—24no—
12C2×C4⋊Q8×C61—21no—
13C61×#391—24no—
14C61×#382—21no—
15C61×#382C2212yes—
16C43×C61C2211yescharacteristic
17C2×#11758194—21no—
18#14519777Q812yescomplemented
19#14519769—21no—
20#14519756—22no—
21C4×Dic122—22no—
22#14519736—21no—
23C4⋊#92418—22no—
24C4⋊#92418—22no—
25C22⋊#92418—22no—
26C4×#92418—22no—
27C22×Q8×C61—22no—
28C4⋊Q8×C61—42no—
29C4⋊Q8×C61—42no—
30C2×C4⋊C4×C61—22no—
31C2×C4⋊C4×C61—22no—
32C2×C42×C61—22no—
33C2×C42×C61D411yescharacteristic
34C2×C42×C61D411yescharacteristic
35C2×C42×C61C2311yescharacteristic
36#95×C61—24no—
37#95×C61—22no—
38#95×C61D414yes—
39C2×Q8×C61—44no—
40C2×Q8×C61—48no—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61—24no—
44C22×C4×C61C2×D412yes—
45C22×C4×C61C2×D411yescharacteristic
46C2×Dic122—22no—
47C4⋊C4×C61—44no—
48C4⋊C4×C61—42no—
49C4⋊C4×C61—42no—
50C42×C61—21no—
51C42×C61—21no—
52C42×C61—44no—
53C42×C61SD1612yes—
54C42×C61Q1612yes—
55C42×C61C2×Q811yescharacteristic
56C42×C61#4111yescharacteristic
57C42×C61#4112yes—
58C22⋊Dic61—41no—
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61#11758196—42no—
62C4×Dic61—41no—
63#11758194—41no—
64#11758194—41no—
65C2×#92418—42no—
66C2×#92418—41no—
67C23×C61#12011yescharacteristic
68Q8×C61—88no—
69C2×C4×C61—24no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—48no—
75C2×C4×C61—44no—
76C2×C4×C61C22⋊Q812yes—
77C2×C4×C61C22⋊Q811yescharacteristic
78C2×C4×C61#12412yes—
79C2×C4×C61#12411yescharacteristic
80C2×C4×C61C2×SD1611yescharacteristic
81C2×C4×C61C2×Q1611yescharacteristic
82C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
83C2×C4×C61#13711yescharacteristic
84C2×Dic61—42no—
85Dic122—82no—
86#92418—82no—
87#92418—81no—
88#10363—611nomaximal, Sylow
89C22×C61—22no—
90C22×C61#39311yescharacteristic
91C22×C61#45011yescharacteristic
92C22×C61#45111yescharacteristic
93C4×C61—24no—
94C4×C61—22no—
95C4×C61—22no—
96C4×C61—42no—
97C4×C61—84no—
98C4×C61#47511yescharacteristic
99C4×C61#47711yescharacteristic
100C4×C61#48711yescharacteristic
101C4×C61#48911yescharacteristic
102Dic61—82no—
103#2862D6111yescharacteristic
104#1994—611no—
105#1518—612no—
106#1286—612no—
107#1276—611no—
108C2×C61—21no—
109C2×C61—21no—
110C2×C61#202411yescharacteristic
111C2×C61#203112yes—
112#533—611no—
113C2×C4⋊Q8—21no—
114#431—612no—
115#423—611no—
116#391—24no—
117#382—21no—
118#382C2×D6112yes—
119C43C2×D6111yescharacteristic
120#339—1221no—
121#339—1221no—
122#328—1224no—
123C61#1036311yescharacteristic, complemented, Sylow
124C22×Q8—22no—
125C2×M16—1221no—
126C4⋊Q8—42no—
127C4⋊Q8—42no—
128C4⋊Q8—612no—
129#125—1221no—
130C22⋊Q8—1222no—
131C4×Q8—1222no—
132#117—1221no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C42—22no—
136C2×C42C22⋊D6111yescharacteristic
137C2×C42C22⋊D6111yescharacteristic
138C2×C42C22×D6111yescharacteristic
139C4⋊C8—1222no—
140C4⋊C8—1222no—
141C22⋊C8—1222no—
142C4×C8—1222no—
143#95—24no—
144#95—22no—
145#95C22⋊D6114yes—
146C2×Q8—44no—
147C2×Q8—48no—
148C2×Q8—1222no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—24no—
152C22×C4C2×C22⋊D6112yes—
153C22×C4C2×C22⋊D6111yescharacteristic
154M16—2441no—
155M16—2441no—
156C2×C8—2442no—
157C2×C8—2441no—
158C4⋊C4—44no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—1222no—
162C4⋊C4—1222no—
163C4⋊C4—2442no—
164C22⋊C4—2441no—
165C42—21no—
166C42—21no—
167C42—44no—
168C42—2441no—
169C42#1175820012yes—
170C42#1175820212yes—
171C42Q8×D6111yescharacteristic
172C42#1175822611yescharacteristic
173C42#1175822612yes—
174C23#1451974611yescharacteristic
175Q8—88no—
176Q8—4882no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—48no—
183C2×C4—44no—
184C2×C4—2442no—
185C2×C4#1451975312yes—
186C2×C4#1451975311yescharacteristic
187C2×C4#1451976612yes—
188C2×C4#1451976611yescharacteristic
189C2×C4C2×#1175820011yescharacteristic
190C2×C4C2×#1175820211yescharacteristic
191C2×C4#1451980311yescharacteristic
192C2×C4#1451980811yescharacteristic
193C8—4882no—
194C8—4881no—
195C22—22no—
196C22#1683967311yescharacteristic
197C22#1683991311yescharacteristic
198C22#1683991811yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—84no—
204C4—4882no—
205C4#1684004411yescharacteristic
206C4#1684005411yescharacteristic
207C4#1684011411yescharacteristic
208C4#1684012411yescharacteristic
209C2—21no—
210C2—21no—
211C2#2144695711yescharacteristic
212C2#2144698812yes—
subgroupG/H
centerC22#16839673
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2862C2
socleC22×C61#393
prime radicalC23×C61#120
hypercenter#2862D61
hypocenterC61#10363
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

Complements

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

NH ≅ G/Ntype
18. #14519777Q8semidirect
123. C61#10363semidirect

Maximal subgroups

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

subgroupindex
#214467962
#214443822
#214436772
#214436522
C61×#28622
#1036361