Finite Group Databasebeta

← #29600652

Subgroups — #29600652

Order 15616.

334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 71 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×#16839597C212yesmaximal, complemented
2#21447905C211yesmaximal, characteristic, complemented
3#21443997C212yesmaximal, complemented
4C22⋊#14519683C211yesmaximal, characteristic, complemented
5C22×D16×C61C211yesmaximal, characteristic, complemented
6C2×D976C2211yescharacteristic, complemented
7#16839998—21no—
8#16839597—24no—
9C2×#14519683C2212yescomplemented
10#16839588C2211yescharacteristic, complemented
11#16839564—21no—
12C22×D8×C61—21no—
13C2×D16×C61—24no—
14C2×D16×C61—21no—
15C2×D16×C61C2212yes—
16C22×C16×C61C2211yescharacteristic
17C2×D488—21no—
18#14519751—41no—
19D976—22no—
20#14519711—21no—
21#14519699—41no—
22#14519683—22no—
23C22×D4×C61—41no—
24C2×D8×C61—24no—
25C2×D8×C61—22no—
26C2×D8×C61—42no—
27C2×D8×C61—41no—
28C22×C8×C61D411yescharacteristic
29D16×C61—24no—
30D16×C61—22no—
31D16×C61D414yescomplemented
32C2×C16×C61—22no—
33C2×C16×C61D411yescharacteristic
34C2×C16×C61C2311yescharacteristic
35C24×C61—81no—
36C2×D4×C61—44no—
37C2×D4×C61—42no—
38C2×D4×C61—82no—
39C2×D4×C61—81no—
40C22×C4×C61D811yescharacteristic
41C2×C22⋊D61—81no—
42C2×D244—41no—
43D8×C61—24no—
44D8×C61—44no—
45D8×C61—42no—
46C2×C8×C61—21no—
47C2×C8×C61—21no—
48C2×C8×C61D811yescharacteristic
49C2×C8×C61C2×D411yescharacteristic
50#11758198—81no—
51C4⋊Dic61—41no—
52D488—41no—
53D488—41no—
54C16×C61—21no—
55C16×C61C2×D412yes—
56C23×C61—84no—
57C23×C61—82no—
58C23×C61—162no—
59C23×C61—162no—
60C23×C61D1611yescharacteristic
61C22×D61—81no—
62D4×C61—44no—
63D4×C61—84no—
64D4×C61—82no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61D1611yescharacteristic
68C2×C4×C61C2×D811yescharacteristic
69C22⋊D61—162no—
70C2×Dic61—81no—
71D244—81no—
72D244—81no—
73C8×C61—21no—
74C8×C61#12011yescharacteristic
75C8×C61AGL(1,ℤ/8)11yescharacteristic
76#13661—611nomaximal, Sylow
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—84no—
80C22×C61—168no—
81C22×C61—162no—
82C22×C61—162no—
83C22×C61D3212yescomplemented
84C22×C61C2×D1611yescharacteristic
85C2×D61—161no—
86C2×D61—161no—
87C2×D61—161no—
88C4×C61—21no—
89C4×C61#44711yescharacteristic
90C4×C61#50911yescharacteristic
91Dic61—161no—
92C22×D16D6111yescharacteristic, complemented
93C2×D32—612no—
94#2215—611no—
95#1415—612no—
96C22⋊C32—611no—
97C2×C61—22no—
98C2×C61—164no—
99C2×C61#218411yescharacteristic
100C2×C61C2×D3211yescharacteristic
101C2×C61#226311yescharacteristic
102D61—321no—
103C22×D8—21no—
104C2×D16—24no—
105C2×D16—21no—
106C2×D16—611no—
107C2×D16C2×D6112yes—
108C22×C16C2×D6111yescharacteristic
109#466—1221no—
110D32—1224no—
111C2×C32—612no—
112#366—611no—
113#357—1221no—
114C61#1366111yescharacteristic, complemented, Sylow
115C22×D4—41no—
116C2×D8—24no—
117C2×D8—22no—
118C2×D8—42no—
119C2×D8—41no—
120C2×D8—1221no—
121C22×C8C22⋊D6111yescharacteristic
122#121—2441no—
123D16—24no—
124D16—22no—
125D16—1222no—
126D16C22⋊D6114yescomplemented
127C2×C16—22no—
128C2×C16C22⋊D6111yescharacteristic
129C2×C16C22×D6111yescharacteristic
130#107—1221no—
131#102—2441no—
132C32—1222no—
133C24—81no—
134C2×D4—44no—
135C2×D4—42no—
136C2×D4—82no—
137C2×D4—81no—
138C2×D4—4881no—
139C2×D4—2441no—
140C22×C4#1175819911yescharacteristic
141D8—24no—
142D8—44no—
143D8—42no—
144D8—2441no—
145D8—2441no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8#1175819911yescharacteristic
149C2×C8C2×C22⋊D6111yescharacteristic
150C4⋊C4—2441no—
151C22⋊C4—4881no—
152C16—21no—
153C16C2×C22⋊D6112yes—
154C23—84no—
155C23—82no—
156C23—162no—
157C23—162no—
158C23—4881no—
159C23#1451971811yescharacteristic
160D4—44no—
161D4—84no—
162D4—82no—
163D4—9762no—
164D4—4881no—
165D4—4881no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—4881no—
169C2×C4#1451971811yescharacteristic
170C2×C4C2×#1175819911yescharacteristic
171C8—21no—
172C8#1451974611yescharacteristic
173C8#1451980311yescharacteristic
174C22—21no—
175C22—21no—
176C22—84no—
177C22—168no—
178C22—162no—
179C22—162no—
180C22—9761no—
181C22—9761no—
182C22—9761no—
183C22#1683959712yescomplemented
184C22C2×#1451971811yescharacteristic
185C4—21no—
186C4—9761no—
187C4#1683989611yescharacteristic
188C4#1684019811yescharacteristic
189C2—22no—
190C2—164no—
191C2—19521no—
192C2#2144773111yescharacteristic
193C2C2×#1683959711yescharacteristic
194C2#2144813211yescharacteristic
subgroupG/H
centerC22C2×#14519718
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC22×D16×C61C2
socleC22×C61C2×D16
hypercenterC22×D16D61
hypocenterC61#13661
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22×D16

Complements

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

NH ≅ G/Ntype
1. C2×#16839597C2semidirect
2. #21447905C2semidirect
3. #21443997C2semidirect
4. C22⋊#14519683C2semidirect
5. C22×D16×C61C2semidirect
6. C2×D976C22semidirect
9. C2×#14519683C22semidirect
10. #16839588C22semidirect
31. D16×C61D4semidirect
83. C22×C61D32semidirect
92. C22×D16D61semidirect
114. C61#13661semidirect
126. D16C22⋊D61semidirect
183. C22#16839597semidirect

Maximal subgroups

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

subgroupindex
C2×#168395972
#214479052
#214439972
C22⋊#145196832
C22×D16×C612
#1366161