Finite Group Databasebeta

← #29600843

Subgroups — #29600843

Order 15616.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#16839597C211yesmaximal, characteristic, complemented
2C2×C32×D61C211yesmaximal, characteristic, complemented
3#21447906C211yesmaximal, characteristic, complemented
4#21447902C211yesmaximal, characteristic, complemented
5#21444018C211yesmaximal, characteristic, complemented
6#21443998C211yesmaximal, characteristic, complemented
7C61×#1415C211yesmaximal, characteristic, complemented
8C2×D976C2211yescharacteristic
9C2×C16×D61C2211yescharacteristic
10#16839999—21no—
11#16839995—21no—
12#16839597—22no—
13C2×#14519683C2211yescharacteristic
14C32×D61—22no—
15#16839588C2211yescharacteristic
16#16839563—21no—
17#16839562—21no—
18C2×D16×C61C2211yescharacteristic
19C2×C32×C61C2211yescharacteristic
20C61×#366C2211yescharacteristic
21C2×D488—21no—
22C2×C8×D61D411yescharacteristic
23#14519752—41no—
24#14519748—41no—
25D976—21no—
26D976—21no—
27C2×#11758185D411yescharacteristic
28C16×D61—21no—
29C16×D61—21no—
30#14519711—21no—
31#14519698—41no—
32#14519697—41no—
33#14519683D412yescomplemented
34C2×D8×C61—21no—
35D16×C61—21no—
36D16×C61—21no—
37C2×C16×C61C2311yescharacteristic
38#107×C61—21no—
39C32×C61—21no—
40C2×D4×C61—41no—
41C2×C22⋊D61—81no—
42C2×D244—41no—
43C2×D244—81no—
44C2×C4×D61D811yescharacteristic
45D8×C61—41no—
46D8×C61—41no—
47C2×C8×C61C2×D411yescharacteristic
48C4⋊C4×C61—41no—
49C22⋊Dic61—81no—
50#11758198—81no—
51C4⋊Dic61—41no—
52C2×#92418D811yescharacteristic
53D488—41no—
54D488—41no—
55C8×D61—21no—
56C8×D61—21no—
57C16×C61C2×D411yescharacteristic
58C16×C61#4111yescharacteristic
59#11758185—21no—
60C23×C61—81no—
61C22×D61—81no—
62C22×D61D1611yescharacteristic
63D4×C61—81no—
64D4×C61—81no—
65C2×C4×C61—81no—
66C2×C4×C61C2×D811yescharacteristic
67C22⋊D61—162no—
68C2×Dic61—81no—
69C2×Dic61D1611yescharacteristic
70D244—81no—
71D244—81no—
72D244—162no—
73C4×D61—21no—
74C4×D61—21no—
75C8×C61#12111yescharacteristic
76C8×C61#13511yescharacteristic
77#92418—21no—
78#13694—611nomaximal, Sylow
79C22×C61—161no—
80C22×C61—161no—
81C22×C61—161no—
82C22×C61C2×D1611yescharacteristic
83C2×D61—21no—
84C2×D61—21no—
85C2×D61—161no—
86C2×D61—161no—
87C2×D61—161no—
88C2×D61D3212yescomplemented
89C4×C61—161no—
90C4×C61#46611yescharacteristic
91C4×C61#50811yescharacteristic
92Dic61—21no—
93Dic61—161no—
94C2×D32—611no—
95C22×C32—611no—
96#2215—611no—
97#2215—611no—
98#1423—611no—
99#1415—611no—
100#1415D6111yescharacteristic, complemented
101C2×C61—321no—
102C2×C61#221511yescharacteristic
103C2×C61C2×D3211yescharacteristic
104C2×C61#226211yescharacteristic
105D61—22no—
106D61—321no—
107C2×D16—611no—
108C2×D16C2×D6111yescharacteristic
109C22×C16—611no—
110#466—1221no—
111#466—1221no—
112D32—1222no—
113C2×C32—611no—
114C2×C32—1222no—
115C2×C32C2×D6111yescharacteristic
116#366—611no—
117#366C2×D6111yescharacteristic
118#357—1221no—
119#357—1221no—
120C61#1369411yescharacteristic, complemented, Sylow
121C2×D8—21no—
122C2×D8—1221no—
123C22×C8—611no—
124#121—2441no—
125#121—2441no—
126D16—21no—
127D16—21no—
128D16—1221no—
129D16—1221no—
130C2×C16—611no—
131C2×C16—1221no—
132C2×C16—1221no—
133C2×C16C22×D6111yescharacteristic
134#107—21no—
135#107—1221no—
136#102—2441no—
137#102—2441no—
138C32—21no—
139C32—612no—
140C2×D4—41no—
141C2×D4—4881no—
142C2×D4—4881no—
143C2×D4—2441no—
144C22×C4—611no—
145D8—41no—
146D8—41no—
147D8—2441no—
148D8—2441no—
149C2×C8—611no—
150C2×C8—1221no—
151C2×C8—1221no—
152C2×C8D4×D6111yescharacteristic
153C4⋊C4—41no—
154C4⋊C4—2441no—
155C22⋊C4—4881no—
156C22⋊C4—4881no—
157C16—1221no—
158C16#1175822211yescharacteristic
159C16D4×D6111yescharacteristic
160C23—81no—
161C23—611no—
162C23—4881no—
163D4—81no—
164D4—81no—
165D4—9762no—
166D4—9762no—
167D4—4881no—
168D4—4881no—
169C2×C4—81no—
170C2×C4—611no—
171C2×C4—1221no—
172C2×C4—1221no—
173C2×C4—4881no—
174C2×C4D8×D6111yescharacteristic
175C8—1221no—
176C8#1451975011yescharacteristic
177C8#1451979811yescharacteristic
178C22—161no—
179C22—161no—
180C22—161no—
181C22—612no—
182C22—1221no—
183C22—1221no—
184C22—9761no—
185C22—9761no—
186C22—9761no—
187C22D16×D6111yescharacteristic
188C4—161no—
189C4—1221no—
190C4—9761no—
191C4#1683999711yescharacteristic
192C4#1684019311yescharacteristic
193C2—321no—
194C2—1222no—
195C2—19521no—
196C2#2144790411yescharacteristic
197C2D32×D6111yescharacteristic
198C2#2144812711yescharacteristic
subgroupG/H
centerC22D16×D61
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1415C2
socleC22×C61C2×D16
hypercenter#1415D61
hypocenterC61#13694
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#16839597C2semidirect
2. C2×C32×D61C2semidirect
3. #21447906C2semidirect
4. #21447902C2semidirect
5. #21444018C2semidirect
6. #21443998C2semidirect
7. C61×#1415C2semidirect
33. #14519683D4semidirect
88. C2×D61D32semidirect
100. #1415D61semidirect
120. C61#13694semidirect

Maximal subgroups

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

subgroupindex
C2×#168395972
C2×C32×D612
#214479062
#214479022
#214440182
#214439982
C61×#14152
#1369461