Finite Group Databasebeta

← #16948887

Subgroups — #16948887

Order 4352.

212 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 63 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#14530831C211yesmaximal, characteristic
3#14528378C211yesmaximal, characteristic
4#14527680C211yesmaximal, characteristic
5#14526853C211yesmaximal, characteristic
6#14526843C211yesmaximal, characteristic
7C17×#1362C211yesmaximal, characteristic
8C2×#10587500—21no—
9#11763214C2211yescharacteristic
10#11763205—21no—
11#11763161—21no—
12#11762936—21no—
13C4×Dic68C2211yescharacteristic
14#11762635—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—42no—
41#10587479—41no—
42#10587479—41no—
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#12488—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—82no—
82C8×C17—21no—
83C8×C17—81no—
84C8×C17AGL(1,ℤ/8)11yescharacteristic
85C8×C17#13711yescharacteristic
86#3622—21no—
87#3622—41no—
88#3622Q3212yescomplemented
89#2227—171no—
90#2209—171no—
91#1707—171no—
92#1591—171no—
93#1370—171no—
94#1365—171no—
95#1362D1711yescharacteristic
96C22×C17#45911yescharacteristic
97C4×C17—21no—
98C4×C17—161no—
99C4×C17#46811yescharacteristic
100C4×C17#47111yescharacteristic
101C4×C17C2×Q3211yescharacteristic
102C4×C17#51011yescharacteristic
103Dic17—81no—
104Dic17—81no—
105Dic17—161no—
106C2×Q32—341no—
107#500—171no—
108#498—341no—
109#494C2×D1711yescharacteristic
110#487—341no—
111#446—341no—
112C4×Q16—171no—
113#366—341no—
114C4⋊C16—171no—
115C4⋊C16C2×D1711yescharacteristic
116#358—341no—
117#358—341no—
118#335C2×D1711yescharacteristic
119Q8⋊C8—341no—
120C82—171no—
121C2×C17#168511yescharacteristic
122C2×C17#220911yescharacteristic
123C2×C17#221211yescharacteristic
124C2×Q16—21no—
125C2×Q16—21no—
126C2×Q16—171no—
127C4⋊Q8—21no—
128C4⋊Q8—341no—
129C4×Q8—341no—
130Q32—682no—
131C2×C16—21no—
132C2×C16—341no—
133#107—171no—
134#107—341no—
135#107—341no—
136#106—681no—
137#106—681no—
138C4⋊C8—21no—
139C4⋊C8—681no—
140#103—341no—
141#103—682no—
142#97—681no—
143C4×C8—171no—
144C4×C8—171no—
145C4×C8C22×D1711yescharacteristic
146C17#1248811yescharacteristic, complemented, Sylow
147C2×Q8—41no—
148C2×Q8—341no—
149C2×Q8—681no—
150Q16—41no—
151Q16—41no—
152Q16—81no—
153Q16—341no—
154Q16—341no—
155C2×C8—41no—
156C2×C8—171no—
157C2×C8—171no—
158C2×C8—341no—
159C2×C8#6325211yescharacteristic
160C2×C8D4×D1711yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—41no—
163C4⋊C4—341no—
164C4⋊C4—681no—
165C4⋊C4—681no—
166C4⋊C4—681no—
167C42—681no—
168C42D4×D1711yescharacteristic
169C16—41no—
170C16—681no—
171Q8—81no—
172Q8—81no—
173Q8—681no—
174Q8—681no—
175Q8—1362no—
176C2×C4—81no—
177C2×C4—681no—
178C2×C4—681no—
179C2×C4—1361no—
180C2×C4#1058757011yescharacteristic
181C2×C4D8×D1711yescharacteristic
182C2×C4#1058760011yescharacteristic
183C8—21no—
184C8—81no—
185C8—172no—
186C8—341no—
187C8—681no—
188C8#1058759711yescharacteristic
189C8#1058760111yescharacteristic
190C22#1176300311yescharacteristic
191C4—21no—
192C4—161no—
193C4—2721no—
194C4—1361no—
195C4—1361no—
196C4#1176305411yescharacteristic
197C4#1176307111yescharacteristic
198C4Q32×D1711yescharacteristic
199C4#1176324811yescharacteristic
200C2#1452824811yescharacteristic
201C2#1453083311yescharacteristic
202C2#1453085611yescharacteristic
subgroupG/H
centerC22#11763003
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1362C2
socle, prime radicalC22×C17#459
hypercenter#1362D17
hypocenterC17#12488
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
88. #3622Q32semidirect
146. C17#12488semidirect

Maximal subgroups

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

subgroupindex
#145309372
#145308312
#145283782
#145276802
#145268532
#145268432
C17×#13622
#1248817