Finite Group Databasebeta

← #16948602

Subgroups — #16948602

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#14531036C211yesmaximal, characteristic
2#14530689C211yesmaximal, characteristic
3#14528155C211yesmaximal, characteristic
4#14528151C211yesmaximal, characteristic
5#14526857C211yesmaximal, characteristic
6#14526834C211yesmaximal, characteristic
7C17×#1362C211yesmaximal, characteristic
8C2×#10587500—21no—
9C2×#10587500—21no—
10#11763189C2211yescharacteristic
11#11763095—21no—
12#11763091—21no—
13C8×Dic34C2211yescharacteristic
14#11762627—21no—
15#11762584—21no—
16C4×#63214C2211yescharacteristic
17#11762562C2211yescharacteristic
18#11762555—21no—
19#11762554—21no—
20C17×#494C2211yescharacteristic
21C17×C4⋊C16C2211yescharacteristic
22C17×#335C2211yescharacteristic
23C2×Q16×C17—21no—
24C2×Q16×C17—21no—
25C17×C4⋊Q8—21no—
26C2×Dic68—21no—
27C2×Dic68—21no—
28#10587555—21no—
29C4×Dic34D411yescharacteristic
30C2×C16×C17—21no—
31C17×C4⋊C8—21no—
32C4×C8×C17C2311yescharacteristic
33#10587500—42no—
34#10587500—42no—
35#10587488—41no—
36#10587487—41no—
37#10587485—21no—
38C8×Dic17—21no—
39C2×#63214D411yescharacteristic
40C2×#63214D411yescharacteristic
41#10587481—41no—
42#10587479—41no—
43C4⋊#3622—21no—
44C4⋊#3622D411yescharacteristic
45C2×Q8×C17—41no—
46C2×Dic34—41no—
47C2×Dic34D811yescharacteristic
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—41no—
58C4⋊Dic17—41no—
59C4⋊Dic17D811yescharacteristic
60#63225—21no—
61C4×Dic17—21no—
62C2×#3622—21no—
63C2×#3622—41no—
64Dic68—41no—
65Dic68—41no—
66Dic68—81no—
67C16×C17—41no—
68#63214—21no—
69#63214SD1612yes—
70#12443—171nomaximal, Sylow
71Q8×C17—81no—
72Q8×C17—81no—
73C2×C4×C17—81no—
74C2×C4×C17#12111yescharacteristic
75C2×C4×C17C2×D811yescharacteristic
76C2×C4×C17#13511yescharacteristic
77C2×Dic17—21no—
78C2×Dic17—21no—
79C2×Dic17—81no—
80Dic34—21no—
81Dic34—21no—
82Dic34—81no—
83Dic34—81no—
84C8×C17—21no—
85C8×C17—81no—
86C8×C17C2×SD1611yescharacteristic
87C8×C17AGL(1,ℤ/8)11yescharacteristic
88#3622—41no—
89#3622—81no—
90#2247—171no—
91#2183—171no—
92#1670—171no—
93#1670—171no—
94#1372—171no—
95#1362—171no—
96#1362D1711yescharacteristic
97C22×C17#46611yescharacteristic
98C4×C17—21no—
99C4×C17—161no—
100C4×C17#46011yescharacteristic
101C4×C17#47211yescharacteristic
102C4×C17#51011yescharacteristic
103C4×C17#51011yescharacteristic
104Dic17—41no—
105Dic17—41no—
106Dic17—161no—
107C2×Q32—341no—
108C2×Q32—341no—
109#494—171no—
110#494C2×D1711yescharacteristic
111#475—341no—
112#475—341no—
113C8×Q8—171no—
114C4⋊C16—341no—
115C4⋊C16C2×D1711yescharacteristic
116#346—341no—
117C4×C16—171no—
118#335—171no—
119#335C2×D1711yescharacteristic
120#332—341no—
121#332—341no—
122C2×C17#166811yescharacteristic
123C2×C17#221911yescharacteristic
124C2×C17#222211yescharacteristic
125C2×Q16—21no—
126C2×Q16—21no—
127C2×Q16—341no—
128C2×Q16—341no—
129C4⋊Q8—21no—
130C4⋊Q8—341no—
131C4×Q8—171no—
132Q32—682no—
133Q32—682no—
134C2×C16—21no—
135C2×C16—171no—
136C2×C16—171no—
137#106—681no—
138#106—681no—
139C4⋊C8—21no—
140C4⋊C8—171no—
141C4⋊C8—341no—
142C4⋊C8—341no—
143#103—681no—
144#103—681no—
145C4×C8—341no—
146C4×C8C22×D1711yescharacteristic
147C17#1244311yescharacteristic, complemented, Sylow
148C2×Q8—41no—
149C2×Q8—171no—
150C2×Q8—681no—
151Q16—41no—
152Q16—41no—
153Q16—81no—
154Q16—681no—
155Q16—681no—
156Q16—1361no—
157C2×C8—41no—
158C2×C8—341no—
159C2×C8—681no—
160C2×C8#6325211yescharacteristic
161C2×C8D4×D1711yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—171no—
165C4⋊C4—341no—
166C4⋊C4—681no—
167C4⋊C4—681no—
168C42—341no—
169C42D4×D1711yescharacteristic
170C16—41no—
171C16—172no—
172C16—341no—
173Q8—81no—
174Q8—81no—
175Q8—341no—
176Q8—341no—
177Q8—1361no—
178Q8—1361no—
179C2×C4—81no—
180C2×C4—341no—
181C2×C4—341no—
182C2×C4—1361no—
183C2×C4#1058757011yescharacteristic
184C2×C4D8×D1711yescharacteristic
185C2×C4#1058760211yescharacteristic
186C8—21no—
187C8—81no—
188C8—681no—
189C8—1361no—
190C8#1058759711yescharacteristic
191C8SD16×D1711yescharacteristic
192C22#1176304411yescharacteristic
193C4—21no—
194C4—161no—
195C4—2721no—
196C4—681no—
197C4—681no—
198C4#1176300811yescharacteristic
199C4#1176307811yescharacteristic
200C4#1176324811yescharacteristic
201C4#1176325111yescharacteristic
202C2#1452814311yescharacteristic
203C2#1453089111yescharacteristic
204C2#1453090811yescharacteristic
subgroupG/H
centerC22#11763044
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1362C2
socle, prime radicalC22×C17#466
hypercenter#1362D17
hypocenterC17#12443
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#12443semidirect

Maximal subgroups

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

subgroupindex
#145310362
#145306892
#145281552
#145281512
#145268572
#145268342
C17×#13622
#1244317