Finite Group Databasebeta

← #16947683

Subgroups — #16947683

Order 4352.

286 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 59 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#14530996C212yesmaximal, complemented
2#14530364C211yesmaximal, characteristic, complemented
3#14526775C212yesmaximal, complemented
4#14526737C211yesmaximal, characteristic, complemented
5C17×#3259C211yesmaximal, characteristic
6#11762858C2211yescharacteristic
7#11762631—22no—
8#11762622—22no—
9#11762591C2212yes—
10#11762579—21no—
11#11762574—21no—
12#11762567C2211yescharacteristic
13C17×#540—21no—
14C17×#478—22no—
15C17×#469C2212yes—
16C17×#466—21no—
17C17×#459—22no—
18C17×#424C2211yescharacteristic
19C2×D8×C17—21no—
20C2×D8×C17D412yes—
21C2×M16×C17C2311yescharacteristic
22C22×C8×C17D411yescharacteristic
23C17×#127—21no—
24C17×#125—21no—
25C17×#123—42no—
26C17×#121—22no—
27C17×#121—42no—
28C4×D4×C17—22no—
29C17×#117D411yescharacteristic
30C2×#63223—21no—
31C2×#63223—21no—
32C17×#107—21no—
33C17×#106D412yes—
34C17×C4⋊C8—22no—
35C17×#102—22no—
36C17×#102—22no—
37#10587490—22no—
38#10587483—22no—
39C2×D4×C17—22no—
40C2×D4×C17—42no—
41C2×D4×C17—42no—
42C22×C4×C17—42no—
43C22×C4×C17C2×D411yescharacteristic
44D8×C17—42no—
45D8×C17—81no—
46M16×C17—41no—
47C2×C8×C17—21no—
48C2×C8×C17—41no—
49C2×C8×C17C2×D412yes—
50C4⋊C4×C17—21no—
51C4⋊C4×C17—22no—
52C4⋊C4×C17—42no—
53C22⋊C4×C17—42no—
54C22⋊C4×C17—42no—
55C22⋊C4×C17SD1612yes—
56C42×C17—21no—
57#63223—41no—
58#63223—41no—
59#63223—41no—
60#63223—41no—
61C2×#3622—41no—
62C2×#3622—41no—
63#63214—42no—
64#12304—171nomaximal, Sylow
65C23×C17—42no—
66C23×C17C2×SD1611yescharacteristic
67D4×C17—42no—
68D4×C17—42no—
69D4×C17—162no—
70D4×C17—162no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—22no—
74C2×C4×C17—42no—
75C2×C4×C17—162no—
76C2×C4×C17#12011yescharacteristic
77C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
78C8×C17—22no—
79C8×C17—41no—
80#3622—81no—
81#3622—81no—
82#3259D1711yescharacteristic
83#2238—172no—
84#2103—171no—
85#1341—172no—
86#1328—171no—
87C22×C17—21no—
88C22×C17—41no—
89C22×C17—82no—
90C22×C17—82no—
91C22×C17—82no—
92C22×C17#45011yescharacteristic
93C4×C17—21no—
94C4×C17—42no—
95C4×C17—82no—
96C4×C17#45411yescharacteristic
97C4×C17#45811yescharacteristic
98#540—21no—
99#478—22no—
100#469C2×D1712yes—
101#466—21no—
102#459—22no—
103#430—171no—
104#424C2×D1711yescharacteristic
105#365—342no—
106#361—342no—
107#349—172no—
108#344—341no—
109#341—341no—
110#338—171no—
111C2×C17—21no—
112C2×C17—41no—
113C2×C17—162no—
114C2×C17#161611yescharacteristic
115C2×D8—21no—
116C2×D8C22⋊D1712yes—
117C2×M16—341no—
118C2×M16—341no—
119C2×M16C22×D1711yescharacteristic
120C22×C8C22⋊D1711yescharacteristic
121#127—21no—
122#125—21no—
123#123—42no—
124#121—22no—
125#121—42no—
126C4×D4—22no—
127#117C22⋊D1711yescharacteristic
128M32—342no—
129#108—342no—
130#107—21no—
131#106C22⋊D1712yes—
132C4⋊C8—22no—
133#102—22no—
134#102—22no—
135C17#1230411yescharacteristic, complemented, Sylow
136C2×D4—22no—
137C2×D4—42no—
138C2×D4—42no—
139C22×C4—42no—
140C22×C4C2×C22⋊D1711yescharacteristic
141D8—42no—
142D8—81no—
143M16—41no—
144M16—681no—
145M16—681no—
146M16—681no—
147M16—681no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—681no—
151C2×C8—681no—
152C2×C8C2×C22⋊D1712yes—
153C4⋊C4—21no—
154C4⋊C4—22no—
155C4⋊C4—42no—
156C22⋊C4—42no—
157C22⋊C4—42no—
158C22⋊C4#6322912yes—
159C42—21no—
160C16—682no—
161C23—42no—
162C23C2×#6322911yescharacteristic
163D4—42no—
164D4—42no—
165D4—162no—
166D4—162no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—162no—
172C2×C4#1058761811yescharacteristic
173C2×C4#1058763911yescharacteristic
174C8—22no—
175C8—41no—
176C8—1361no—
177C8—1361no—
178C22—21no—
179C22—41no—
180C22—82no—
181C22—82no—
182C22—82no—
183C22#1176296011yescharacteristic
184C4—21no—
185C4—42no—
186C4—82no—
187C4#1176298211yescharacteristic
188C4#1176299911yescharacteristic
189C2—21no—
190C2—41no—
191C2—162no—
192C2#1452782111yescharacteristic
subgroupG/H
centerC2#14527821
commutator, cosocleC2×M16×C17C23
FrattiniC2×M16C22×D17
Fitting, prime radicalC17×#3259C2
socleC2×C17#1616
hypercenter#3259D17
hypocenterC17#12304
LCSG ▷ C2×M16×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3259

Complements

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

NH ≅ G/Ntype
1. #14530996C2semidirect
2. #14530364C2semidirect
3. #14526775C2semidirect
4. #14526737C2semidirect
135. C17#12304semidirect

Maximal subgroups

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

subgroupindex
#145309962
#145303642
#145267752
#145267372
C17×#32592
#1230417