Finite Group Databasebeta

← #30605357

Subgroups — #30605357

Order 15616.

300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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#21462182C211yesmaximal, characteristic
2#21461744C211yesmaximal, characteristic
3#21460812C214yesmaximal
4#21456406C211yesmaximal, characteristic
5#16840767—21no—
6#16840683—21no—
7#16840657C2212yes—
8#16840650—21no—
9#16840638—21no—
10#16840638C2212yes—
11#16840317—21no—
12#16840142C411yescharacteristic
13#16840114—21no—
14#16840004—21no—
15#16840004C2212yes—
16#16839856—21no—
17#16839856C412yes—
18C4×C8×D61C2211yescharacteristic
19C61×#500C411yescharacteristic
20C2×#11758213—22no—
21C2×#11758187—22no—
22#14519844—41no—
23#14519844—41no—
24C2×Dic244—21no—
25C2×Dic244C2×C412yes—
26C2×C8×D61D411yescharacteristic
27C2×C8×D61C2311yescharacteristic
28#14519777—21no—
29#14519768—41no—
30#14519757—22no—
31#14519753—41no—
32Q8×Dic61—41no—
33#14519742—22no—
34#14519735—41no—
35C42×D61D411yescharacteristic
36#14519700—22no—
37#14519700—22no—
38C4×#92418D411yescharacteristic
39C8×Dic61C2×C411yescharacteristic
40C8×Dic61D411yescharacteristic
41C4⋊Q8×C61—21no—
42#107×C61—21no—
43#107×C61C2×C412yes—
44C4×C8×C61C2×C411yescharacteristic
45C2×Q8×C61—41no—
46C2×C4×D61SD1611yescharacteristic
47C2×C4×D61SD1611yescharacteristic
48C2×C4×D61C2×D411yescharacteristic
49C2×Dic122—22no—
50C2×#92420—42no—
51#11758213—42no—
52#11758213—42no—
53C2×C8×C61C22⋊C411yescharacteristic
54C2×C8×C61C22×C411yescharacteristic
55C4⋊C4×C61—22no—
56C4⋊C4×C61—41no—
57C42×C61C22⋊C411yescharacteristic
58#11758198—42no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61C4⋊Dic61—42no—
62#11758196—42no—
63C4×Dic61—42no—
64C4×Dic61C22⋊C411yescharacteristic
65C4×Dic61D811yescharacteristic
66C4×Dic61D811yescharacteristic
67C2×#92418C22⋊C411yescharacteristic
68C2×#92418C2×D411yescharacteristic
69Dic244—42no—
70Dic244—42no—
71C8×D61—41no—
72C8×D61—41no—
73#11758187—42no—
74C22×D61C2×SD1611yescharacteristic
75Q8×C61—82no—
76C2×C4×C61—42no—
77C2×C4×C61#10211yescharacteristic
78C2×C4×C61#10211yescharacteristic
79C2×C4×C61C2×C22⋊C411yescharacteristic
80C2×Dic61—42no—
81C2×Dic61#10211yescharacteristic
82C2×Dic61#10211yescharacteristic
83C2×Dic61C2×D811yescharacteristic
84C4×D61—21no—
85C4×D61—21no—
86C4×D61—22no—
87C4×D61—41no—
88Dic122—42no—
89Dic122—42no—
90#92420—82no—
91C8×C61—21no—
92C8×C61—21no—
93#92418—21no—
94#92418—21no—
95#11865—611nomaximal, Sylow
96C22×C61C2×#10211yescharacteristic
97C2×D61—21no—
98C2×D61—21no—
99C2×D61—21no—
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—82no—
103C4×C61#41011yescharacteristic
104C4×C61#42111yescharacteristic
105Dic61—21no—
106Dic61—21no—
107Dic61—82no—
108Dic61#36212yes—
109#3170—611no—
110#2163—611no—
111#1837—611no—
112#1350—614no—
113C2×C61#151711yescharacteristic
114C2×C61#214311yescharacteristic
115C2×C61C2×#36211yescharacteristic
116D61—41no—
117#533—1221no—
118#500#692311yescharacteristic
119#494—611no—
120#487—1221no—
121#467—612no—
122#467—1221no—
123C4×Q16—612no—
124C4×Q16—1221no—
125#423—1221no—
126C2×C4×C8—611no—
127C4⋊C16—1221no—
128C22⋊C16—612no—
129#346—1221no—
130#341—612no—
131#341—1221no—
132C61#1186511yescharacteristic, complemented, Sylow
133C2×Q16—612no—
134C2×Q16—1221no—
135C2×M16—1222no—
136C22×C8—611no—
137C22×C8—611no—
138C4⋊Q8—21no—
139C4⋊Q8—1221no—
140#125—2441no—
141C22⋊Q8—1222no—
142C22⋊Q8—2441no—
143C4×Q8—1222no—
144C4×Q8—2441no—
145#117—2441no—
146C2×C42—611no—
147C2×C16—1222no—
148#107—21no—
149#107C2×#692312yes—
150C4⋊C8—2441no—
151C4⋊C8—2441no—
152#103—1222no—
153#103—1222no—
154C4×C8—611no—
155C4×C8—611no—
156C4×C8—611no—
157C4×C8C2×#692311yescharacteristic
158C2×Q8—41no—
159C2×Q8—1222no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163Q16—2442no—
164Q16—2442no—
165M16—2442no—
166M16—2442no—
167C2×C8—611no—
168C2×C8—611no—
169C2×C8—2441no—
170C2×C8—2441no—
171C2×C8—2442no—
172C2×C8C22⋊#692311yescharacteristic
173C2×C8C22×#692311yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—41no—
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C22⋊C4—2442no—
181C42—611no—
182C42—611no—
183C42—611no—
184C42—2442no—
185C42C22⋊#692311yescharacteristic
186C16—2442no—
187C23—611no—
188Q8—82no—
189Q8—2442no—
190Q8—2442no—
191C2×C4—42no—
192C2×C4—611no—
193C2×C4—611no—
194C2×C4—611no—
195C2×C4—1222no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—2441no—
199C2×C4—2442no—
200C2×C4#1451983911yescharacteristic
201C2×C4#1451983911yescharacteristic
202C2×C4C2×C22⋊#692311yescharacteristic
203C8—21no—
204C8—21no—
205C8—1221no—
206C8—1221no—
207C8—4882no—
208C22—1221no—
209C22—1221no—
210C22—1221no—
211C22C2×#1451983911yescharacteristic
212C4—21no—
213C4—21no—
214C4—82no—
215C4—612no—
216C4—1221no—
217C4—1221no—
218C4—4882no—
219C4#1684074311yescharacteristic
220C4#1684076111yescharacteristic
221C2—2441no—
222C2#2146125011yescharacteristic
223C2#2146213411yescharacteristic
224C2D61⋊#36211yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#500C4
socleC22×C61C2×#102
prime radicalC22×D61C2×SD16
cosocleC2×C8×D61C23
hypercenter#500#6923
hypocenterC61#11865
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
132. C61#11865semidirect

Maximal subgroups

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

subgroupindex
#214621822
#214617442
#214608122
#214564062
#1186561