Finite Group Databasebeta

← #16943763

Subgroups — #16943763

Order 4352.

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

normal subgroups only

This group has 280 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#14537434C211yesmaximal, characteristic
2#14530593C212yesmaximal, complemented
3#14526737C211yesmaximal, characteristic, complemented
4#14526721C212yesmaximal
5C17×#1328C211yesmaximal, characteristic, complemented
6#11763277C411yescharacteristic
7#11762869—22no—
8#11762865—22no—
9#11762836C411yescharacteristic
10#11762777C2211yescharacteristic
11#11762775C411yescharacteristic
12M16×Dic17C2211yescharacteristic
13C2×#10587486C411yescharacteristic
14#11762629—22no—
15#11762591C2212yes—
16#11762586—22no—
17C17×#424C2211yescharacteristic
18C17×#349C2212yes—
19C2×#63252C2×C411yescharacteristic
20C2×M16×C17C2311yescharacteristic
21C22×C8×C17C2×C411yescharacteristic
22C17×#117C2×C411yescharacteristic
23C2×C4×Dic17C2×C411yescharacteristic
24C2×#63223C2×C411yescharacteristic
25C22×#3622C2×C411yescharacteristic
26#10587579—21no—
27#10587573—21no—
28#10587567—22no—
29#10587558—21no—
30C42×D17—21no—
31C17×M32—22no—
32C17×C4⋊C8—22no—
33#10587491—22no—
34#10587491—22no—
35#10587486—21no—
36#10587486—21no—
37#10587486D412yes—
38C8×Dic17D412yes—
39#10587483—22no—
40C4⋊#3622—22no—
41C22×C4×C17C22×C411yescharacteristic
42C2×C22⋊D17—21no—
43C22×Dic17—21no—
44#63252—41no—
45#63252—41no—
46C2×D68M1611yescharacteristic
47C2×C4×D17—21no—
48C2×C4×D17—22no—
49C2×Dic34M1611yescharacteristic
50M16×C17—41no—
51C2×C8×C17—21no—
52C2×C8×C17—41no—
53C2×C8×C17C2×D412yes—
54C4⋊C4×C17—21no—
55C22⋊C4×C17M1612yes—
56C42×C17—21no—
57#63227—22no—
58#63225—22no—
59C4×Dic17—22no—
60C4×Dic17—21no—
61C4×Dic17C22⋊C411yescharacteristic
62C4×Dic17C22⋊C411yescharacteristic
63#63223—41no—
64C2×#3622—21no—
65C2×#3622—41no—
66C2×#3622C22⋊C412yes—
67C16×C17—42no—
68#63214—42no—
69#11523—171nomaximal, Sylow
70C23×C17C2×M1611yescharacteristic
71C22×D17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—22no—
75C2×C4×C17C2×C22⋊C411yescharacteristic
76C2×C4×C17C2×M1611yescharacteristic
77C22⋊D17—42no—
78C2×Dic17—21no—
79C2×Dic17—21no—
80C2×Dic17—21no—
81C2×Dic17—81no—
82D68—41no—
83C4×D17—41no—
84C4×D17—41no—
85C4×D17—82no—
86Dic34—41no—
87C8×C17—22no—
88C8×C17—41no—
89#3622—22no—
90#3622—41no—
91#2923—171no—
92#2165—172no—
93#1328—171no—
94#1328D1711yescharacteristic, complemented
95#1321—172no—
96C22×C17—21no—
97C22×C17—41no—
98C22×C17#40711yescharacteristic
99C2×D17—42no—
100C2×D17—41no—
101C4×C17—21no—
102C4×C17—42no—
103C4×C17#41011yescharacteristic
104C4×C17#41311yescharacteristic
105Dic17—41no—
106Dic17—41no—
107Dic17—41no—
108C4×#41—171no—
109#433—342no—
110#432—342no—
111#424—171no—
112#424C2×D1711yescharacteristic
113#408—171no—
114#408—171no—
115C4×M16—171no—
116C2×#97—171no—
117#364—342no—
118#349—172no—
119#349C2×D1712yes—
120#347—342no—
121C2×C17—21no—
122C2×C17—41no—
123C2×C17#146411yescharacteristic
124D17—81no—
125C2×#41—171no—
126C2×M16—171no—
127C2×M16C22×D1711yescharacteristic
128C22×C8—171no—
129C22×C8C4×D1711yescharacteristic
130C4×Q8—341no—
131C4×D4—341no—
132C4×D4—342no—
133#117—341no—
134#117C4×D1711yescharacteristic
135C2×C42—171no—
136C2×C42—341no—
137M32—22no—
138M32—342no—
139C4⋊C8—22no—
140C4⋊C8—342no—
141C22⋊C8—342no—
142C22⋊C8—342no—
143#97—172no—
144#97—341no—
145#97—341no—
146C4×C8—172no—
147C17#1152311yescharacteristic, complemented, Sylow
148#41—681no—
149#41—681no—
150C2×Q8—171no—
151C2×D4—171no—
152C2×D4—341no—
153C22×C4—342no—
154C22×C4—341no—
155C22×C4—341no—
156C22×C4C2×C4×D1711yescharacteristic
157M16—41no—
158M16—681no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—172no—
162C2×C8—341no—
163C2×C8—681no—
164C2×C8D4×D1712yes—
165C4⋊C4—21no—
166C4⋊C4—342no—
167C22⋊C4—342no—
168C22⋊C4#6321812yes—
169C42—21no—
170C42—171no—
171C42—171no—
172C42—342no—
173C42—341no—
174C16—42no—
175C16—682no—
176C23—341no—
177C23C2×#6321811yescharacteristic
178Q8—681no—
179D4—681no—
180D4—682no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—341no—
185C2×C4—341no—
186C2×C4—341no—
187C2×C4—681no—
188C2×C4—681no—
189C2×C4—1362no—
190C2×C4—1361no—
191C2×C4C22⋊C4×D1711yescharacteristic
192C2×C4M16×D1711yescharacteristic
193C8—22no—
194C8—41no—
195C8—342no—
196C8—681no—
197C22—21no—
198C22—41no—
199C22—682no—
200C22—681no—
201C22#1176277111yescharacteristic
202C4—21no—
203C4—42no—
204C4—681no—
205C4—681no—
206C4—681no—
207C4#1176278111yescharacteristic
208C4#1176279211yescharacteristic
209C2—21no—
210C2—41no—
211C2—1361no—
212C2#1452711711yescharacteristic
subgroupG/H
centerC4#11762781
commutatorC22×C4×C17C22×C4
FrattiniC2×M16C22×D17
FittingC17×#1328C2
socleC2×C17#1464
prime radicalC2×#63252C2×C4
cosocleC2×M16×C17C23
hypercenter#1328D17
hypocenterC17#11523
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
2. #14530593C2semidirect
3. #14526737C2semidirect
5. C17×#1328C2semidirect
94. #1328D17semidirect
147. C17#11523semidirect

Maximal subgroups

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

subgroupindex
#145374342
#145305932
#145267372
#145267212
C17×#13282
#1152317