Finite Group Databasebeta

← #16947682

Subgroups — #16947682

Order 4352.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#14540223C211yesmaximal, characteristic
2#14530998C212yesmaximal, complemented
3#14526774C212yesmaximal, complemented
4#14526737C211yesmaximal, characteristic, complemented
5C17×#2103C211yesmaximal, characteristic, complemented
6#11763414—21no—
7#11763110—22no—
8#11763062C2212yes—
9#11763045—21no—
10#11763005—22no—
11#11762633—22no—
12#11762621—22no—
13#11762591C2212yes—
14C17×#430C2211yescharacteristic
15C17×#424C2211yescharacteristic
16C17×#344—21no—
17C17×#341—21no—
18C17×#338C2211yescharacteristic
19C2×M16×C17—21no—
20C2×M16×C17—21no—
21C2×M16×C17C2311yescharacteristic
22C22×C8×C17D411yescharacteristic
23C17×#117D411yescharacteristic
24#10587616—22no—
25C2×D136—21no—
26C2×D136D412yes—
27#10587580—42no—
28#10587570—42no—
29#10587560—21no—
30C4×D68—22no—
31#10587556—21no—
32C17×#108—22no—
33C17×C4⋊C8—22no—
34#10587492—22no—
35#10587492—22no—
36#10587489—21no—
37#10587488D412yes—
38#10587483—22no—
39C22×C4×C17C2×D411yescharacteristic
40C2×C22⋊D17—42no—
41C2×D68—22no—
42C2×D68—42no—
43C2×C4×D17—42no—
44M16×C17—41no—
45M16×C17—41no—
46M16×C17—41no—
47M16×C17—41no—
48M16×C17—41no—
49C2×C8×C17—21no—
50C2×C8×C17—41no—
51C2×C8×C17—41no—
52C2×C8×C17—41no—
53C2×C8×C17C2×D412yes—
54C4⋊C4×C17—21no—
55C22⋊C4×C17SD1612yes—
56C42×C17—21no—
57#63227—42no—
58#63227—42no—
59C4⋊Dic17—22no—
60#63225—42no—
61D136—42no—
62D136—81no—
63#63214—42no—
64#12304—171nomaximal, Sylow
65C23×C17C2×SD1611yescharacteristic
66C22×D17—42no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—22no—
70C2×C4×C17#12011yescharacteristic
71C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
72C22⋊D17—162no—
73C2×Dic17—42no—
74D68—42no—
75D68—42no—
76D68—162no—
77C4×D17—162no—
78C8×C17—22no—
79C8×C17—41no—
80C8×C17—81no—
81C8×C17—81no—
82#3259—171no—
83#2238—172no—
84#2103D1711yescharacteristic, complemented
85#1341—172no—
86#1328—171no—
87C22×C17—21no—
88C22×C17—41no—
89C22×C17#45011yescharacteristic
90C2×D17—82no—
91C2×D17—82no—
92C2×D17—82no—
93C4×C17—21no—
94C4×C17—42no—
95C4×C17#45411yescharacteristic
96C4×C17#45811yescharacteristic
97Dic17—82no—
98#540—341no—
99#478—342no—
100#469—172no—
101#466—341no—
102#459—342no—
103#430C2×D1711yescharacteristic
104#424C2×D1711yescharacteristic
105#365—342no—
106#361—342no—
107#349—172no—
108#344—21no—
109#341—21no—
110#338C2×D1711yescharacteristic
111C2×C17—21no—
112C2×C17—41no—
113C2×C17#161611yescharacteristic
114D17—162no—
115C2×D8—172no—
116C2×D8—341no—
117C2×M16—21no—
118C2×M16—21no—
119C2×M16C22×D1711yescharacteristic
120C22×C8C22⋊D1711yescharacteristic
121#127—341no—
122#125—341no—
123#123—682no—
124#121—342no—
125#121—682no—
126C4×D4—342no—
127#117C22⋊D1711yescharacteristic
128M32—342no—
129#108—22no—
130#107—341no—
131#106—172no—
132C4⋊C8—22no—
133#102—342no—
134#102—342no—
135C17#1230411yescharacteristic, complemented, Sylow
136C2×D4—342no—
137C2×D4—682no—
138C2×D4—682no—
139C22×C4—682no—
140C22×C4C2×C22⋊D1711yescharacteristic
141D8—682no—
142D8—1361no—
143M16—41no—
144M16—41no—
145M16—41no—
146M16—41no—
147M16—41no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8D4×D1712yes—
153C4⋊C4—21no—
154C4⋊C4—342no—
155C4⋊C4—682no—
156C22⋊C4—682no—
157C22⋊C4—682no—
158C22⋊C4#6323012yes—
159C42—21no—
160C16—682no—
161C23—682no—
162C23C2×#6323011yescharacteristic
163D4—2722no—
164D4—2722no—
165D4—682no—
166D4—682no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—2722no—
171C2×C4—682no—
172C2×C4#1058762311yescharacteristic
173C2×C4#1058763511yescharacteristic
174C8—22no—
175C8—41no—
176C8—81no—
177C8—81no—
178C22—21no—
179C22—41no—
180C22—1362no—
181C22—1362no—
182C22—1362no—
183C22#1176295911yescharacteristic
184C4—21no—
185C4—42no—
186C4—1362no—
187C4#1176298111yescharacteristic
188C4#1176299811yescharacteristic
189C2—21no—
190C2—41no—
191C2—2722no—
192C2#1452782011yescharacteristic
subgroupG/H
centerC2#14527820
commutator, cosocleC2×M16×C17C23
FrattiniC2×M16C22×D17
FittingC17×#2103C2
socleC2×C17#1616
prime radical#14540223C2
hypercenter#2103D17
hypocenterC17#12304
LCSG ▷ C2×M16×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2103

Complements

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

NH ≅ G/Ntype
2. #14530998C2semidirect
3. #14526774C2semidirect
4. #14526737C2semidirect
5. C17×#2103C2semidirect
84. #2103D17semidirect
135. C17#12304semidirect

Maximal subgroups

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

subgroupindex
#145402232
#145309982
#145267742
#145267372
C17×#21032
#1230417