Finite Group Databasebeta

← #30597853

Subgroups — #30597853

Order 15616.

384 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461324C211yesmaximal, characteristic
2#21461276C211yesmaximal, characteristic
3C8×#11758217C212yesmaximal
4#21460703C212yesmaximal
5#21454752C211yesmaximal, characteristic
6#16840779C2212yes—
7C4×#11758217C2212yes—
8#16840621C414yes—
9#16840619C414yes—
10#92420⋊C8—22no—
11C8×#92420—22no—
12#16840315C2211yescharacteristic
13#16839891—22no—
14#16839886—22no—
15#16839788C411yescharacteristic
16#16839785C2211yescharacteristic
17#16839720C411yescharacteristic
18#16839718C411yescharacteristic
19C2×C8×Dic61C2211yescharacteristic
20C61×#424C411yescharacteristic
21C2×#11758217—22no—
22#14519844C2×C414yes—
23C22⋊#92420—22no—
24#14519832C2×C414yes—
25C4×#92420—22no—
26C4×#92420—22no—
27C2×#11758194C2×C411yescharacteristic
28C22×#92418C2×C411yescharacteristic
29#14519776C2×C412yes—
30#14519768C2×C412yes—
31#14519754—22no—
32C4×Dic122—22no—
33#14519736C2×C411yescharacteristic
34C2×C4×Dic61C2311yescharacteristic
35#14519706—22no—
36#14519706—22no—
37#14519688—21no—
38#14519687—21no—
39C4×#92418—21no—
40C8×Dic61—21no—
41C8×Dic61D412yes—
42C8×Dic61D412yes—
43C2×M16×C61C2×C411yescharacteristic
44C22×C8×C61C2×C411yescharacteristic
45#117×C61C2×C411yescharacteristic
46C4⋊C8×C61—22no—
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61#4112yes—
49C2×Dic122—22no—
50#11758217—28no—
51C2×#92420—24no—
52C2×#92420—24no—
53M16×C61—41no—
54C2×C8×C61—21no—
55C2×C8×C61—41no—
56C2×C8×C61C22⋊C412yes—
57C4⋊C4×C61C4212yes—
58C22⋊C4×C61—21no—
59C42×C61—21no—
60C22⋊Dic61—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61C4212yes—
63#11758196—22no—
64#11758196—22no—
65C4×Dic61—21no—
66C4×Dic61C22×C411yescharacteristic
67C4×Dic61C22×C411yescharacteristic
68C4×Dic61C2×D412yes—
69#11758194—41no—
70C2×#92418—22no—
71C2×#92418—21no—
72C2×#92418C22⋊C411yescharacteristic
73C2×#92418C22⋊C411yescharacteristic
74C23×C61#11711yescharacteristic
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61C2×C4211yescharacteristic
79C2×C4×C61C2×C22⋊C411yescharacteristic
80C2×Dic61—24no—
81C2×Dic61—22no—
82C2×Dic61C4×D412yes—
83C2×Dic61C4×D412yes—
84Dic122—44no—
85#92420—28no—
86#92420—44no—
87C8×C61—22no—
88C8×C61—41no—
89#92418—21no—
90#92418—41no—
91#92418#10112yes—
92#8242—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—22no—
95C22×C61C4×C22⋊C411yescharacteristic
96C4×C61—21no—
97C4×C61—42no—
98C4×C61C2×#10111yescharacteristic
99C4×C61#41311yescharacteristic
100Dic61—22no—
101Dic61—42no—
102Dic61#44314yes—
103#2960—611no—
104#1544—611no—
105#1526—611no—
106C8×M16—612no—
107#1299—612no—
108C2×C61—41no—
109C2×C61C4×#10111yescharacteristic
110C2×C61#176412yes—
111#533—611no—
112#446—1222no—
113C8×Q8—1222no—
114#431—612no—
115#424—611no—
116#424#692311yescharacteristic
117#423—611no—
118#405—611no—
119#405—611no—
120C4×M16—612no—
121C2×C4×C8—611no—
122#332—614no—
123#330—614no—
124#322—1222no—
125C82—1222no—
126C61#824211yescharacteristic, complemented, Sylow
127C2×M16—611no—
128C2×M16—1222no—
129C2×M16C2×#692311yescharacteristic
130C22×C8—611no—
131C22×C8C2×#692311yescharacteristic
132C4⋊Q8—612no—
133#125—612no—
134C22⋊Q8—1222no—
135C4×Q8—1222no—
136#117—611no—
137#117C2×#692311yescharacteristic
138C2×C42—611no—
139C4⋊C8—22no—
140C4⋊C8—614no—
141C4⋊C8—1222no—
142C4⋊C8—1222no—
143C22⋊C8—1222no—
144#97—614no—
145#97—1221no—
146#97—1221no—
147C4×C8—612no—
148C4×C8—612no—
149C4×C8—1221no—
150C4×C8—1222no—
151C4×C8—1222no—
152C4×C8—1221no—
153C2×Q8—1222no—
154C22×C4—612no—
155C22×C4C22×#692311yescharacteristic
156M16—41no—
157M16—1228no—
158M16—2441no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—611no—
162C2×C8—611no—
163C2×C8—1222no—
164C2×C8—1224no—
165C2×C8—1224no—
166C2×C8—1221no—
167C2×C8C22⋊#692312yes—
168C4⋊C4—612no—
169C4⋊C4—1222no—
170C4⋊C4—1222no—
171C4⋊C4—1222no—
172C4⋊C4C4×#692312yes—
173C22⋊C4—21no—
174C22⋊C4—1221no—
175C42—21no—
176C42—611no—
177C42—611no—
178C42—612no—
179C42—1221no—
180C23#1451985611yescharacteristic
181Q8—2444no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—612no—
186C2×C4—612no—
187C2×C4—1224no—
188C2×C4—1222no—
189C2×C4C2×C4×#692311yescharacteristic
190C2×C4C2×C22⋊#692311yescharacteristic
191C8—22no—
192C8—41no—
193C8—612no—
194C8—1228no—
195C8—1221no—
196C8—2444no—
197C8—2441no—
198C22—21no—
199C22—22no—
200C22C4×C22⋊#692311yescharacteristic
201C4—21no—
202C4—42no—
203C4—614no—
204C4—1222no—
205C4—2442no—
206C4D61⋊#10111yescharacteristic
207C4#1684074911yescharacteristic
208C2—41no—
209C2#2146157211yescharacteristic
210C2#2146159312yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC22×C61C4×C22⋊C4
prime radicalC23×C61#117
cosocleC2×C4×Dic61C23
hypercenter#424#6923
hypocenterC61#8242
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
126. C61#8242semidirect

Maximal subgroups

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

subgroupindex
#214613242
#214612762
C8×#117582172
#214607032
#214547522
#824261