Finite Group Databasebeta

← #30594981

Subgroups — #30594981

Order 15616.

224 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460760C211yesmaximal, characteristic, complemented
2#21460695C211yesmaximal, characteristic, complemented
3#21447049C211yesmaximal, characteristic
4C2×#14519832—21no—
5#16840607—21no—
6#16840343C411yescharacteristic
7C2×#14519703—21no—
8#16839764—21no—
9#16839627C2211yescharacteristic
10C61×#343C411yescharacteristic
11C22×#92420—41no—
12C22⋊#92420—41no—
13#14519832—22no—
14#14519832—41no—
15C2×#11758222—21no—
16#14519757—41no—
17#14519752—41no—
18#14519751—41no—
19C2×C4⋊Dic61D411yescharacteristic
20C2×C4×Dic61D411yescharacteristic
21#14519703—41no—
22#14519703—41no—
23#14519702—41no—
24#14519699—41no—
25#14519684—41no—
26C2×M16×C61—21no—
27C2×C4⋊C4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61C22⋊C411yescharacteristic
30C2×C22⋊D61—41no—
31C22×Dic61—21no—
32C22×Dic61—21no—
33#11758222—41no—
34#11758222—41no—
35#11758222—41no—
36#11758222—41no—
37C2×D244—21no—
38C2×D244—41no—
39C2×C4×D61—41no—
40C2×Dic122—21no—
41C2×#92420—42no—
42C2×#92420—42no—
43C2×#92420—42no—
44C2×#92420—81no—
45M16×C61—41no—
46M16×C61—41no—
47C2×C8×C61—41no—
48C4⋊C4×C61—41no—
49#11758198—42no—
50C4⋊Dic61—41no—
51C4⋊Dic61—41no—
52C4×Dic61—21no—
53C4×Dic61D811yescharacteristic
54C4×Dic61SD1611yescharacteristic
55C23×C61#9911yescharacteristic
56C22×D61—41no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—41no—
60C2×C4×C61—81no—
61C2×C4×C61#10211yescharacteristic
62C2×C4×C61#10411yescharacteristic
63C22⋊D61—81no—
64C22⋊D61—81no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—81no—
72D244—41no—
73D244—41no—
74D244—161no—
75C4×D61—81no—
76C4×D61—81no—
77Dic122—41no—
78Dic122—41no—
79#92420—44no—
80#92420—161no—
81C8×C61—81no—
82#7416—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61#32711yescharacteristic
86C22×C61AΣL(1,𝔽16)11yescharacteristic
87C22×C61#35511yescharacteristic
88C2×D61—81no—
89C2×D61—81no—
90C2×D61—81no—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—81no—
94Dic61—41no—
95Dic61—41no—
96Dic61—81no—
97Dic61—81no—
98#2040—611no—
99#1324—611no—
100#1295—611no—
101C2×C61—21no—
102C2×C61—21no—
103C2×C61#134511yescharacteristic
104C2×C61#140311yescharacteristic
105C2×C61#140411yescharacteristic
106D61—161no—
107#537—611no—
108C2×#104—1221no—
109#417—1221no—
110C2×#97—1221no—
111#382—611no—
112#343#692311yescharacteristic
113#324—1221no—
114C61#741611yescharacteristic, complemented, Sylow
115C2×#41—1221no—
116C2×M16—21no—
117C22×C8—2441no—
118C22⋊Q8—2441no—
119#121—2441no—
120#121—2441no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4C2×#692311yescharacteristic
123C2×C42—611no—
124#104—2441no—
125#104—2441no—
126#103—2441no—
127#102—2441no—
128C22⋊C8—2441no—
129#97—1222no—
130#97—2441no—
131#95—2441no—
132#41—2441no—
133#41—2441no—
134#41—2441no—
135#41—2441no—
136C2×Q8—1221no—
137C2×D4—1221no—
138C2×D4—2441no—
139C2×D4—2441no—
140C22×C4—21no—
141C22×C4—1221no—
142C22×C4—1221no—
143C22×C4—2441no—
144C22×C4C22⋊#692311yescharacteristic
145M16—41no—
146M16—41no—
147C2×C8—41no—
148C2×C8—4881no—
149C2×C8—2442no—
150C2×C8—2442no—
151C2×C8—2442no—
152C4⋊C4—41no—
153C4⋊C4—2441no—
154C4⋊C4—2441no—
155C22⋊C4—2442no—
156C42—611no—
157C42—611no—
158C42—1221no—
159C23—2441no—
160C23#1451983611yescharacteristic
161Q8—2441no—
162Q8—2441no—
163D4—9761no—
164D4—4881no—
165D4—4881no—
166D4—2441no—
167D4—2441no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—81no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—4881no—
175C2×C4—4881no—
176C2×C4—4881no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4#1451983911yescharacteristic
182C2×C4#1451984211yescharacteristic
183C8—81no—
184C8—9761no—
185C8—2444no—
186C22—21no—
187C22—21no—
188C22—4881no—
189C22—4881no—
190C22—4881no—
191C22#1684061411yescharacteristic
192C22#1684066311yescharacteristic
193C22#1684067111yescharacteristic
194C4—21no—
195C4—21no—
196C4—81no—
197C4—4881no—
198C4—4881no—
199C4—2441no—
200C4—2441no—
201C2—21no—
202C2—21no—
203C2—9761no—
204C2#2146080211yescharacteristic
205C2#2146094111yescharacteristic
206C2#2146094311yescharacteristic
subgroupG/H
centerC22#16840663
commutatorC2×C4⋊C4×C61C2×C4
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#343C4
socleC22×C61AΣL(1,𝔽16)
prime radical#16840343C4
cosocle#16839627C22
hypercenter#343#6923
hypocenterC61#7416
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. #21460760C2semidirect
2. #21460695C2semidirect
114. C61#7416semidirect

Maximal subgroups

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

subgroupindex
#214607602
#214606952
#214470492
#741661