Finite Group Databasebeta

← #16955166

Subgroups — #16955166

Order 4352.

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

normal subgroups only

This group has 204 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
1C2×#11762648C211yesmaximal, characteristic, complemented
2C2×C32×D17C211yesmaximal, characteristic, complemented
3#14530876C211yesmaximal, characteristic, complemented
4#14530871C211yesmaximal, characteristic
5#14526964C211yesmaximal, characteristic, complemented
6#14526961C211yesmaximal, characteristic, complemented
7C17×#1424C211yesmaximal, characteristic, complemented
8C2×Dic136C2211yescharacteristic
9C2×D272C2211yescharacteristic
10C2×C16×D17C2211yescharacteristic
11#11763051—21no—
12#11763046—21no—
13#11762648—22no—
14C2×#10587465C2211yescharacteristic
15C32×D17—22no—
16#11762612—21no—
17#11762609—21no—
18C2×C17×C32C2211yescharacteristic
19C17×#366C2211yescharacteristic
20C17×#366C2211yescharacteristic
21C2×Dic68—21no—
22C2×D136—21no—
23C2×C8×D17D411yescharacteristic
24#10587583—41no—
25#10587581—41no—
26C2×C16×C17C2311yescharacteristic
27C17×#107—21no—
28C17×#107—21no—
29C2×#63214D411yescharacteristic
30#10587481—41no—
31#10587480—41no—
32Dic136—21no—
33Dic136—21no—
34D272—21no—
35D272—21no—
36C16×D17—21no—
37C16×D17—21no—
38C17×C32D412yescomplemented
39#10587465—21no—
40C2×D68—41no—
41C2×D68—81no—
42C2×C4×D17D811yescharacteristic
43C2×Dic34—41no—
44C2×C8×C17C2×D411yescharacteristic
45C4⋊C4×C17—41no—
46C4⋊C4×C17—41no—
47#63227—81no—
48#63227—81no—
49C4⋊Dic17—81no—
50C2×#3622D811yescharacteristic
51Dic68—41no—
52Dic68—41no—
53D136—41no—
54D136—41no—
55C8×D17—21no—
56C8×D17—21no—
57C16×C17C2×D411yescharacteristic
58C16×C17#4111yescharacteristic
59#63214—21no—
60#13696—171nomaximal, Sylow
61C22×D17—81no—
62C22×D17D1611yescharacteristic
63C2×C4×C17—81no—
64C2×C4×C17—81no—
65C2×C4×C17C2×D811yescharacteristic
66C2×Dic17—81no—
67C2×Dic17D1611yescharacteristic
68D68—81no—
69D68—81no—
70D68—162no—
71C4×D17—21no—
72C4×D17—21no—
73Dic34—81no—
74Dic34—81no—
75C8×C17#12111yescharacteristic
76C8×C17#13511yescharacteristic
77#3622—21no—
78C2×SD64—171no—
79C22×C32—171no—
80#2216—171no—
81#2215—171no—
82#1424D1711yescharacteristic, complemented
83#1416—171no—
84#1415—171no—
85C22×C17C2×D1611yescharacteristic
86C2×D17—21no—
87C2×D17—21no—
88C2×D17—161no—
89C2×D17—161no—
90C2×D17—161no—
91C2×D17SD6412yescomplemented
92C4×C17—161no—
93C4×C17—161no—
94C4×C17#46611yescharacteristic
95C4×C17#50811yescharacteristic
96Dic17—21no—
97Dic17—161no—
98C2×Q32—171no—
99C2×D16—171no—
100C22×C16—171no—
101#467—341no—
102#466—341no—
103SD64—342no—
104C2×C32—171no—
105C2×C32—342no—
106C2×C32C2×D1711yescharacteristic
107#366C2×D1711yescharacteristic
108#366C2×D1711yescharacteristic
109#358—341no—
110#357—341no—
111C2×C17#221511yescharacteristic
112C2×C17C2×SD6411yescharacteristic
113C2×C17#226211yescharacteristic
114D17—22no—
115D17—321no—
116C2×Q16—341no—
117C2×D8—341no—
118C22×C8—171no—
119C22⋊Q8—681no—
120#121—681no—
121Q32—341no—
122Q32—341no—
123D16—341no—
124D16—341no—
125C2×C16—171no—
126C2×C16—341no—
127C2×C16—341no—
128C2×C16C22×D1711yescharacteristic
129#107—21no—
130#107—21no—
131#103—681no—
132#102—681no—
133C32—341no—
134C32D6812yescomplemented
135C17#1369611yescharacteristic, complemented, Sylow
136C2×Q8—681no—
137C2×D4—681no—
138C2×D4—1361no—
139C22×C4—171no—
140Q16—681no—
141Q16—681no—
142D8—681no—
143D8—681no—
144C2×C8—171no—
145C2×C8—341no—
146C2×C8—341no—
147C2×C8D4×D1711yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—1361no—
151C22⋊C4—1361no—
152C22⋊C4—1361no—
153C16—341no—
154C16C2×D6811yescharacteristic
155C16#6325611yescharacteristic
156C23—171no—
157C23—1361no—
158Q8—1361no—
159Q8—1361no—
160D4—2722no—
161D4—1361no—
162D4—1361no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—171no—
166C2×C4—341no—
167C2×C4—341no—
168C2×C4—1361no—
169C2×C4D8×D1711yescharacteristic
170C8—341no—
171C8#1058758111yescharacteristic
172C8#1058760511yescharacteristic
173C22—2721no—
174C22—2721no—
175C22—2721no—
176C22—172no—
177C22—341no—
178C22—341no—
179C22D16×D1711yescharacteristic
180C4—161no—
181C4—161no—
182C4—2721no—
183C4—341no—
184C4#1176304611yescharacteristic
185C4#1176324211yescharacteristic
186C2—5441no—
187C2—342no—
188C2#1453087111yescharacteristic
189C2D17×SD6411yescharacteristic
190C2#1453109211yescharacteristic
subgroupG/H
centerC22D16×D17
commutator, cosocleC2×C16×C17C23
FrattiniC2×C16C22×D17
FittingC17×#1424C2
socleC22×C17C2×D16
prime radical#14530871C2
hypercenter#1424D17
hypocenterC17#13696
LCSG ▷ C2×C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1424

Complements

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

NH ≅ G/Ntype
1. C2×#11762648C2semidirect
2. C2×C32×D17C2semidirect
3. #14530876C2semidirect
5. #14526964C2semidirect
6. #14526961C2semidirect
7. C17×#1424C2semidirect
38. C17×C32D4semidirect
82. #1424D17semidirect
91. C2×D17SD64semidirect
134. C32D68semidirect
135. C17#13696semidirect

Maximal subgroups

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

subgroupindex
C2×#117626482
C2×C32×D172
#145308762
#145308712
#145269642
#145269612
C17×#14242
#1369617