Finite Group Databasebeta

← #30597854

Subgroups — #30597854

Order 15616.

384 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 100 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#21462609C211yesmaximal, characteristic
2#21461325C211yesmaximal, characteristic
3#21461017C212yesmaximal
4#21460704C212yesmaximal
5#21444412C211yesmaximal, characteristic
6#16840814—22no—
7#16840811—22no—
8#16840780C2212yes—
9#16840769C412yes—
10#16840767C2211yescharacteristic
11#16840727C412yes—
12C4×D61⋊C8C2211yescharacteristic
13#16840621C414yes—
14#16840603—22no—
15C8×#92420—22no—
16#16840318C2211yescharacteristic
17#16839714C2212yes—
18#16839504C411yescharacteristic
19#16839503C412yes—
20C61×#330C411yescharacteristic
21C2×#11758213C2×C412yes—
22C2×D61⋊C8C2×C411yescharacteristic
23C2×D61⋊C8C2×C411yescharacteristic
24#14519844—22no—
25#14519844—22no—
26#14519844C2×C414yes—
27C4⋊#92420—22no—
28#14519834—22no—
29#14519832—22no—
30C4×#92420—22no—
31C4×#92420—22no—
32C4×#92420D412yes—
33C4×#92420D412yes—
34C2×#11758189—22no—
35#14519776C2×C412yes—
36#14519769C2×C411yescharacteristic
37#14519755—22no—
38#14519742—22no—
39#14519735C2×C412yes—
40C42×D61C2311yescharacteristic
41#14519688C2×C412yes—
42C8×Dic61—22no—
43#125×C61C2×C411yescharacteristic
44#97×C61C2×C412yes—
45C2×C4×D61C22×C411yescharacteristic
46C2×C4×D61#4112yes—
47C2×Dic122—22no—
48C2×#92420—22no—
49C2×#92420—24no—
50C2×#92420C22⋊C411yescharacteristic
51C2×#92420C22⋊C412yes—
52C2×#92420C22⋊C411yescharacteristic
53#11758213—42no—
54D61⋊C8—22no—
55D61⋊C8—41no—
56C2×C8×C61—22no—
57C4⋊C4×C61—22no—
58C4⋊C4×C61C4212yes—
59C42×C61C22×C411yescharacteristic
60#11758198—22no—
61C4⋊Dic61C4212yes—
62#11758196—22no—
63#11758196—22no—
64C4×Dic61—22no—
65C4×Dic61C22×C411yescharacteristic
66C4×Dic61C2×D412yes—
67C2×#92418—22no—
68#11758189—28no—
69C22×D61#11711yescharacteristic
70C2×C4×C61—22no—
71C2×C4×C61C2×C4211yescharacteristic
72C2×C4×C61C4×D412yes—
73C2×Dic61—22no—
74C2×Dic61C2×C22⋊C411yescharacteristic
75C2×Dic61C4×D412yes—
76C4×D61—21no—
77C4×D61—21no—
78C4×D61—24no—
79Dic122—44no—
80#92420—21no—
81#92420—22no—
82#92420—42no—
83#92420—44no—
84#92420#10112yes—
85C8×C61—24no—
86#92418—24no—
87#8242—611nomaximal, Sylow
88C22×C61C4×C22⋊C411yescharacteristic
89C2×D61—21no—
90C2×D61—22no—
91C4×C61—21no—
92C4×C61—22no—
93C4×C61—42no—
94Dic61—42no—
95Dic61C2×#10111yescharacteristic
96Dic61#41311yescharacteristic
97Dic61#44314yes—
98#2960—611no—
99#1544—611no—
100#1526—611no—
101C8×M16—612no—
102#1299—612no—
103C2×C61C4×#10111yescharacteristic
104C2×C61#176412yes—
105D61—41no—
106#533—611no—
107#446—1222no—
108C8×Q8—1222no—
109#431—612no—
110#424—612no—
111#423—611no—
112#405—612no—
113C4×M16—612no—
114C2×C4×C8—611no—
115#332—614no—
116#330—611no—
117#330—612no—
118#330#692311yescharacteristic
119#322—1222no—
120C82—1222no—
121C61#824211yescharacteristic, complemented, Sylow
122C2×M16—612no—
123C2×M16—1222no—
124C22×C8—611no—
125C22×C8—611no—
126C4⋊Q8—612no—
127#125—611no—
128#125C2×#692311yescharacteristic
129C22⋊Q8—1222no—
130C4×Q8—1222no—
131#117—612no—
132C2×C42—611no—
133C4⋊C8—614no—
134C4⋊C8—1222no—
135C4⋊C8—1222no—
136C4⋊C8—1222no—
137C22⋊C8—1222no—
138#97—612no—
139#97—1222no—
140#97C2×#692312yes—
141C4×C8—612no—
142C4×C8—612no—
143C4×C8—1222no—
144C4×C8—1222no—
145C4×C8—1222no—
146C2×Q8—1222no—
147C22×C4—611no—
148C22×C4—612no—
149M16—1228no—
150M16—2442no—
151C2×C8—22no—
152C2×C8—611no—
153C2×C8—611no—
154C2×C8—612no—
155C2×C8—1222no—
156C2×C8—1222no—
157C2×C8—1222no—
158C2×C8—1224no—
159C2×C8—2441no—
160C4⋊C4—22no—
161C4⋊C4—612no—
162C4⋊C4—1222no—
163C4⋊C4—1222no—
164C4⋊C4C4×#692312yes—
165C22⋊C4—1222no—
166C42—611no—
167C42—612no—
168C42—1222no—
169C42C22×#692311yescharacteristic
170C23—611no—
171Q8—2444no—
172C2×C4—22no—
173C2×C4—611no—
174C2×C4—612no—
175C2×C4—1221no—
176C2×C4—1221no—
177C2×C4—1224no—
178C2×C4—1222no—
179C2×C4C2×C4×#692311yescharacteristic
180C2×C4D4×#692312yes—
181C8—24no—
182C8—612no—
183C8—1224no—
184C8—1221no—
185C8—1222no—
186C8—2444no—
187C8—2442no—
188C22—1221no—
189C22—1222no—
190C22C22⋊C4×#692311yescharacteristic
191C4—21no—
192C4—22no—
193C4—42no—
194C4—611no—
195C4—611no—
196C4—614no—
197C4—2442no—
198C2—2441no—
199C2#101×#692311yescharacteristic
200C2#2146159512yes—
subgroupG/H
centerC22C22⋊C4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC42C22×#6923
FittingC61×#330C4
socleC22×C61C4×C22⋊C4
prime radicalC22×D61#117
cosocleC42×D61C23
hypercenter#330#6923
hypocenterC61#8242
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
121. C61#8242semidirect

Maximal subgroups

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

subgroupindex
#214626092
#214613252
#214610172
#214607042
#214444122
#824261