Finite Group Databasebeta

← #16948889

Subgroups — #16948889

Order 4352.

212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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#14530937C211yesmaximal, characteristic
2#14530835C211yesmaximal, characteristic
3#14528381C211yesmaximal, characteristic
4#14527682C211yesmaximal, characteristic
5#14526841C211yesmaximal, characteristic
6#14526834C211yesmaximal, characteristic
7C17×#1370C211yesmaximal, characteristic
8C2×Dic136—21no—
9#11763214C2211yescharacteristic
10#11763207—21no—
11#11763189C2211yescharacteristic
12#11763160—21no—
13#11762939—21no—
14C4×Dic68C2211yescharacteristic
15#11762635—21no—
16#11762614—21no—
17#11762614—21no—
18#11762562C2211yescharacteristic
19#11762541—21no—
20C17×C4⋊C16C2211yescharacteristic
21C17×C4⋊C16C2211yescharacteristic
22C82×C17C2211yescharacteristic
23C2×Dic68—21no—
24C2×Dic68—21no—
25C2×Dic68D411yescharacteristic
26#10587555—21no—
27#10587555—21no—
28C4×Dic34—21no—
29C2×C16×C17—21no—
30C2×C16×C17—21no—
31C4×C8×C17D411yescharacteristic
32C4×C8×C17D411yescharacteristic
33C4×C8×C17C2311yescharacteristic
34#10587489—21no—
35#10587489—21no—
36#10587489D411yescharacteristic
37#10587488—41no—
38#10587488—41no—
39#10587487—21no—
40#10587487—42no—
41#10587486—41no—
42#10587485—41no—
43C4⋊#3622—21no—
44Dic136—42no—
45C2×Dic34—21no—
46C2×Dic34—41no—
47C2×Dic34—41no—
48C2×C8×C17—21no—
49C2×C8×C17D811yescharacteristic
50C2×C8×C17D811yescharacteristic
51C2×C8×C17C2×D411yescharacteristic
52C2×C8×C17#4111yescharacteristic
53C42×C17C2×D411yescharacteristic
54C4⋊Dic17—21no—
55C4⋊Dic17—41no—
56C4⋊Dic17—41no—
57C4⋊Dic17—41no—
58C4⋊Dic17—41no—
59#63225—41no—
60C4×Dic17—41no—
61C2×#3622—41no—
62Dic68—21no—
63Dic68—21no—
64Dic68—41no—
65Dic68—41no—
66Dic68—81no—
67C16×C17—41no—
68C16×C17—41no—
69#12488—171nomaximal, Sylow
70C2×C4×C17#12111yescharacteristic
71C2×C4×C17C2×D811yescharacteristic
72C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
73C2×Dic17—41no—
74C2×Dic17—41no—
75C2×Dic17—81no—
76C2×Dic17—81no—
77Dic34—41no—
78Dic34—41no—
79Dic34—82no—
80Dic34—81no—
81Dic34—81no—
82C8×C17—21no—
83C8×C17—21no—
84C8×C17—41no—
85C8×C17Q3212yescomplemented
86C8×C17AGL(1,ℤ/8)11yescharacteristic
87C8×C17#13711yescharacteristic
88#3622—81no—
89#2227—171no—
90#2209—171no—
91#1707—171no—
92#1591—171no—
93#1370D1711yescharacteristic
94#1365—171no—
95#1362—171no—
96C22×C17#45911yescharacteristic
97C4×C17—21no—
98C4×C17#46811yescharacteristic
99C4×C17#47111yescharacteristic
100C4×C17C2×Q3211yescharacteristic
101C4×C17#51011yescharacteristic
102Dic17—81no—
103Dic17—81no—
104Dic17—161no—
105Dic17—161no—
106C2×Q32—341no—
107#500—171no—
108#498—341no—
109#494—171no—
110#487—341no—
111#446—341no—
112C4×Q16—171no—
113#366—341no—
114C4⋊C16C2×D1711yescharacteristic
115C4⋊C16C2×D1711yescharacteristic
116#358—341no—
117#358—341no—
118#335—171no—
119Q8⋊C8—341no—
120C82C2×D1711yescharacteristic
121C2×C17#168511yescharacteristic
122C2×C17#220911yescharacteristic
123C2×C17#221211yescharacteristic
124C2×Q16—171no—
125C2×Q16—341no—
126C2×Q16—341no—
127C4⋊Q8—341no—
128C4⋊Q8—341no—
129C4×Q8—341no—
130Q32—682no—
131C2×C16—21no—
132C2×C16—21no—
133#107—171no—
134#107—341no—
135#107—341no—
136#106—681no—
137#106—681no—
138C4⋊C8—341no—
139C4⋊C8—681no—
140#103—341no—
141#103—682no—
142#97—681no—
143C4×C8D6811yescharacteristic
144C4×C8D6811yescharacteristic
145C4×C8C22×D1711yescharacteristic
146C17#1248811yescharacteristic, complemented, Sylow
147C2×Q8—341no—
148C2×Q8—681no—
149C2×Q8—681no—
150Q16—341no—
151Q16—341no—
152Q16—681no—
153Q16—681no—
154Q16—1361no—
155C2×C8—21no—
156C2×C8—681no—
157C2×C8D13611yescharacteristic
158C2×C8D13611yescharacteristic
159C2×C8D4×D1711yescharacteristic
160C2×C8#6325611yescharacteristic
161C4⋊C4—341no—
162C4⋊C4—681no—
163C4⋊C4—681no—
164C4⋊C4—681no—
165C4⋊C4—681no—
166C4⋊C4—681no—
167C42—681no—
168C42C2×D6811yescharacteristic
169C16—41no—
170C16—41no—
171Q8—681no—
172Q8—681no—
173Q8—1362no—
174Q8—1361no—
175Q8—1361no—
176C2×C4—681no—
177C2×C4—681no—
178C2×C4—1361no—
179C2×C4—1361no—
180C2×C4#1058758111yescharacteristic
181C2×C4C2×D13611yescharacteristic
182C2×C4#1058759411yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—1361no—
187C8Dic13612yescomplemented
188C8#1058759711yescharacteristic
189C8#1058760411yescharacteristic
190C22#1176300511yescharacteristic
191C4—21no—
192C4—2721no—
193C4—2721no—
194C4—1361no—
195C4—1361no—
196C4#1176305611yescharacteristic
197C4#1176307311yescharacteristic
198C4C2×Dic13611yescharacteristic
199C4#1176325211yescharacteristic
200C2#1452825011yescharacteristic
201C2#1453083511yescharacteristic
202C2#1453085411yescharacteristic
subgroupG/H
centerC22#11763005
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1370C2
socle, prime radicalC22×C17#459
hypercenter#1370D17
hypocenterC17#12488
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1370

Complements

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

NH ≅ G/Ntype
85. C8×C17Q32semidirect
146. C17#12488semidirect
187. C8Dic136semidirect

Maximal subgroups

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

subgroupindex
#145309372
#145308352
#145283812
#145276822
#145268412
#145268342
C17×#13702
#1248817