Finite Group Databasebeta

← #16948901

Subgroups — #16948901

Order 4352.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#14530927C211yesmaximal, characteristic
2#14530831C211yesmaximal, characteristic
3#14528378C211yesmaximal, characteristic
4#14527680C211yesmaximal, characteristic
5#14526853C211yesmaximal, characteristic
6#14526840C211yesmaximal, characteristic
7C17×#1362C211yesmaximal, characteristic
8C2×#10587500—21no—
9#11763214C2211yescharacteristic
10#11763205—21no—
11#11763161—21no—
12#11762936—21no—
13C4×Dic68C2211yescharacteristic
14#11762637—21no—
15C4⋊#63214C2211yescharacteristic
16#11762614—21no—
17#11762613—21no—
18#11762539—21no—
19C8×#3622C2211yescharacteristic
20C17×#494C2211yescharacteristic
21C17×C4⋊C16C2211yescharacteristic
22C17×#335C2211yescharacteristic
23C2×Q16×C17—21no—
24C2×Q16×C17—21no—
25C17×C4⋊Q8—21no—
26C2×Dic68D411yescharacteristic
27#10587555—21no—
28C4×Dic34—21no—
29C2×C16×C17—21no—
30C17×C4⋊C8—21no—
31C4×C8×C17C2311yescharacteristic
32#10587500—42no—
33#10587489—21no—
34#10587489—21no—
35#10587489D411yescharacteristic
36#10587487—21no—
37#10587486—41no—
38#10587485—41no—
39C2×#63214—21no—
40#10587481—41no—
41#10587481—41no—
42#10587479—42no—
43C4×#3622D411yescharacteristic
44C4×#3622D411yescharacteristic
45C2×Q8×C17—41no—
46C2×Dic34—21no—
47C2×Dic34—41no—
48Q16×C17—41no—
49Q16×C17—41no—
50Q16×C17—81no—
51C2×C8×C17—41no—
52C2×C8×C17C2×D411yescharacteristic
53C2×C8×C17#4111yescharacteristic
54C4⋊C4×C17—41no—
55C4⋊C4×C17—41no—
56C42×C17C2×D411yescharacteristic
57C4⋊Dic17—21no—
58C4⋊Dic17—41no—
59C4⋊Dic17—41no—
60#63225—41no—
61C4×Dic17—41no—
62C2×#3622—21no—
63C2×#3622D811yescharacteristic
64C2×#3622D811yescharacteristic
65Dic68—21no—
66Dic68—21no—
67C16×C17—41no—
68#63214—41no—
69#12490—171nomaximal, Sylow
70Q8×C17—81no—
71Q8×C17—81no—
72C2×C4×C17—81no—
73C2×C4×C17#12111yescharacteristic
74C2×C4×C17C2×D811yescharacteristic
75C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
76C2×Dic17—41no—
77C2×Dic17—41no—
78C2×Dic17—81no—
79Dic34—41no—
80Dic34—41no—
81Dic34—81no—
82Dic34—81no—
83C8×C17—21no—
84C8×C17—81no—
85C8×C17AGL(1,ℤ/8)11yescharacteristic
86C8×C17#13711yescharacteristic
87#3622—22no—
88#3622—21no—
89#3622—21no—
90#2225—171no—
91#2209—171no—
92#1707—171no—
93#1591—171no—
94#1370—171no—
95#1364—171no—
96#1362D1711yescharacteristic
97C22×C17#45911yescharacteristic
98C4×C17—21no—
99C4×C17—161no—
100C4×C17#46811yescharacteristic
101C4×C17#47111yescharacteristic
102C4×C17#50811yescharacteristic
103C4×C17#51011yescharacteristic
104Dic17—81no—
105Dic17—81no—
106Dic17—161no—
107C2×Q32—341no—
108#500—171no—
109#498—341no—
110#494C2×D1711yescharacteristic
111#487—341no—
112#446—341no—
113C4×Q16—171no—
114#367—341no—
115C4⋊C16—171no—
116C4⋊C16C2×D1711yescharacteristic
117#358—341no—
118#358—341no—
119#335C2×D1711yescharacteristic
120Q8⋊C8—341no—
121C82—171no—
122C2×C17#168511yescharacteristic
123C2×C17#221111yescharacteristic
124C2×C17#221411yescharacteristic
125C2×Q16—21no—
126C2×Q16—21no—
127C2×Q16—171no—
128C4⋊Q8—21no—
129C4⋊Q8—341no—
130C4×Q8—341no—
131Q32—682no—
132C2×C16—21no—
133C2×C16—341no—
134#107—171no—
135#107—341no—
136#107—341no—
137#106—682no—
138C4⋊C8—21no—
139C4⋊C8—681no—
140#103—341no—
141#103—681no—
142#103—681no—
143#97—681no—
144C4×C8—171no—
145C4×C8—171no—
146C4×C8C22×D1711yescharacteristic
147C17#1249011yescharacteristic, complemented, Sylow
148C2×Q8—41no—
149C2×Q8—341no—
150C2×Q8—681no—
151Q16—41no—
152Q16—41no—
153Q16—81no—
154Q16—341no—
155Q16—341no—
156C2×C8—41no—
157C2×C8—171no—
158C2×C8—171no—
159C2×C8—341no—
160C2×C8#6325211yescharacteristic
161C2×C8D4×D1711yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—341no—
165C4⋊C4—681no—
166C4⋊C4—681no—
167C4⋊C4—681no—
168C42—681no—
169C42D4×D1711yescharacteristic
170C16—41no—
171C16—681no—
172Q8—81no—
173Q8—81no—
174Q8—681no—
175Q8—681no—
176Q8—1361no—
177Q8—1361no—
178C2×C4—81no—
179C2×C4—681no—
180C2×C4—681no—
181C2×C4—1361no—
182C2×C4#1058757011yescharacteristic
183C2×C4D8×D1711yescharacteristic
184C2×C4#1058760011yescharacteristic
185C8—21no—
186C8—81no—
187C8—342no—
188C8—341no—
189C8—341no—
190C8#1058759711yescharacteristic
191C8#1058760111yescharacteristic
192C22#1176300311yescharacteristic
193C4—21no—
194C4—161no—
195C4—2721no—
196C4—1361no—
197C4—1361no—
198C4#1176305411yescharacteristic
199C4#1176307111yescharacteristic
200C4#1176324011yescharacteristic
201C4#1176325111yescharacteristic
202C2#1452824811yescharacteristic
203C2#1453084911yescharacteristic
204C2#1453086411yescharacteristic
subgroupG/H
centerC22#11763003
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1362C2
socle, prime radicalC22×C17#459
hypercenter#1362D17
hypocenterC17#12490
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
147. C17#12490semidirect

Maximal subgroups

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

subgroupindex
#145309272
#145308312
#145283782
#145276802
#145268532
#145268402
C17×#13622
#1249017