Finite Group Databasebeta

← #30601578

Subgroups — #30601578

Order 15616.

290 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461933C212yesmaximal
2#21461377C211yesmaximal, characteristic
3#21461029C211yesmaximal, characteristic
4#21460711C212yesmaximal
5#334×D61C211yesmaximal, characteristic
6#16840781C2211yescharacteristic
7C2×#14519848—22no—
8#16840766C2212yes—
9C4×#11758213C2211yescharacteristic
10#16840638—22no—
11#16840625—21no—
12#16840625—21no—
13#92420⋊C8—21no—
14#16840603—21no—
15C4⋊C8×D61C2212yes—
16C4×C8×D61C2211yescharacteristic
17#16839513C411yescharacteristic
18#16839512C412yes—
19C61×#334C411yescharacteristic
20C2×#11758213—22no—
21C2×#11758213D411yescharacteristic
22C2×#11758213D411yescharacteristic
23#14519848—44no—
24C4⋊#92420—22no—
25C4⋊#92420—21no—
26C4⋊#92420—22no—
27#14519834Q812yes—
28#14519832—21no—
29C4×#92420—21no—
30C4×#92420—21no—
31C2×C8×D61—22no—
32C2×C8×D61Q811yescharacteristic
33C2×C8×D61Q811yescharacteristic
34C42×D61C2311yescharacteristic
35C4⋊#92418C2×C412yes—
36#14519706—22no—
37C4×#92418C2×C411yescharacteristic
38C8×Dic61D411yescharacteristic
39C8×Dic61D411yescharacteristic
40C4⋊C8×C61C2×C412yes—
41C4×C8×C61C2×C411yescharacteristic
42C2×C4×D61C2×D411yescharacteristic
43C2×C4×D61C2×Q811yescharacteristic
44C2×C4×D61C2×Q811yescharacteristic
45C2×#92420—21no—
46C2×#92420—21no—
47C2×#92420—22no—
48C2×#92420—42no—
49#11758213—22no—
50#11758213—22no—
51#11758213—42no—
52#11758213—42no—
53C2×C8×C61—22no—
54C2×C8×C61C4⋊C411yescharacteristic
55C2×C8×C61C4⋊C411yescharacteristic
56C42×C61C22×C411yescharacteristic
57C4×Dic61C2×D411yescharacteristic
58C4×Dic61#4111yescharacteristic
59C4×Dic61#4111yescharacteristic
60C2×#92418—22no—
61C2×#92418C4⋊C411yescharacteristic
62C2×#92418C4⋊C411yescharacteristic
63C8×D61—22no—
64C8×D61—41no—
65C8×D61—42no—
66C8×D61—42no—
67C22×D61C4⋊Q811yescharacteristic
68C2×C4×C61C2×C4⋊C411yescharacteristic
69C2×C4×C61C4×D411yescharacteristic
70C2×C4×C61C4×Q811yescharacteristic
71C2×Dic61#12111yescharacteristic
72C2×Dic61C22⋊Q811yescharacteristic
73C2×Dic61#12511yescharacteristic
74C4×D61—21no—
75C4×D61—21no—
76C4×D61—41no—
77C4×D61AGL(1,ℤ/8)12yes—
78C4×D61#13712yes—
79#92420—42no—
80#92420—41no—
81#92420—41no—
82#92420—82no—
83C8×C61—21no—
84C8×C61—42no—
85C8×C61#10812yescomplemented
86#92418—21no—
87#92418—21no—
88#92418—42no—
89#9626—611nomaximal, Sylow
90C22×C61#38911yescharacteristic
91C2×D61—21no—
92C2×D61—21no—
93C2×D61#50112yes—
94C4×C61—21no—
95C4×C61C2×#10811yescharacteristic
96C4×C61#43011yescharacteristic
97C4×C61#44012yes—
98Dic61—21no—
99Dic61—21no—
100Dic61#46911yescharacteristic
101Dic61#47011yescharacteristic
102#1950—612no—
103#1567—611no—
104C2×#334—611no—
105#1451—611no—
106#1301—612no—
107C2×C61#194411yescharacteristic
108C2×C61#195011yescharacteristic
109C2×C61#195311yescharacteristic
110D61—22no—
111#431—611no—
112C2×#108—1222no—
113#423—612no—
114C2×C4⋊C8—612no—
115C4×M16—611no—
116C2×C4×C8—611no—
117#341—1222no—
118#335—1221no—
119#335—1221no—
120#334—612no—
121#334—611no—
122#334#692311yescharacteristic
123#322—1221no—
124#322—1221no—
125C61#962611yescharacteristic, complemented, Sylow
126C2×M16—611no—
127C2×M16—611no—
128C2×M16—1222no—
129C22×C8—611no—
130C22×C8—611no—
131C22×C8—1222no—
132C2×C42—611no—
133#108—2444no—
134C4⋊C8—612no—
135C4⋊C8—1222no—
136C4⋊C8—1221no—
137C4⋊C8—1222no—
138C4⋊C8—1222no—
139C4⋊C8C2×#692312yes—
140C22⋊C8—612no—
141#97—1221no—
142C4×C8—611no—
143C4×C8—611no—
144C4×C8—611no—
145C4×C8—1221no—
146C4×C8—1221no—
147C4×C8C2×#692311yescharacteristic
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—611no—
151M16—1222no—
152M16—1222no—
153M16—2442no—
154M16—2442no—
155C2×C8—22no—
156C2×C8—611no—
157C2×C8—611no—
158C2×C8—1222no—
159C2×C8—1221no—
160C2×C8—1221no—
161C2×C8—1222no—
162C2×C8—1222no—
163C2×C8—2441no—
164C2×C8—2442no—
165C2×C8—2442no—
166C2×C8—2442no—
167C2×C8C4⋊#692311yescharacteristic
168C2×C8C4⋊#692311yescharacteristic
169C42—611no—
170C42—611no—
171C42—611no—
172C42C22×#692311yescharacteristic
173C23—611no—
174C2×C4—611no—
175C2×C4—612no—
176C2×C4—612no—
177C2×C4—611no—
178C2×C4—611no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4—2441no—
182C2×C4C2×C4⋊#692311yescharacteristic
183C2×C4D4×#692311yescharacteristic
184C2×C4Q8×#692311yescharacteristic
185C8—21no—
186C8—42no—
187C8—1221no—
188C8—1221no—
189C8—4882no—
190C8—2441no—
191C8—2441no—
192C8—2442no—
193C8—2442no—
194C8#1451984812yescomplemented
195C22—612no—
196C22—1221no—
197C22—1221no—
198C22#1684071311yescharacteristic
199C4—21no—
200C4—611no—
201C4—611no—
202C4—1221no—
203C4—1221no—
204C4C2×#1451984811yescharacteristic
205C4#1684077711yescharacteristic
206C4#1684080112yes—
207C2—1222no—
208C2#2146192511yescharacteristic
209C2#2146193311yescharacteristic
210C2#2146193911yescharacteristic
subgroupG/H
centerC22#16840713
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#334C4
socleC22×C61#389
prime radicalC22×D61C4⋊Q8
cosocleC42×D61C23
hypercenter#334#6923
hypocenterC61#9626
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
85. C8×C61#108semidirect
125. C61#9626semidirect
194. C8#14519848semidirect

Maximal subgroups

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

subgroupindex
#214619332
#214613772
#214610292
#214607112
#334×D612
#962661