Finite Group Databasebeta

← #16949086

Subgroups — #16949086

Order 4352.

306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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#14531033C211yesmaximal, characteristic
2#14531011C211yesmaximal, characteristic, complemented
3#14531008C211yesmaximal, characteristic, complemented
4#14528391C211yesmaximal, characteristic, complemented
5#14528373C211yesmaximal, characteristic, complemented
6#14526703C211yesmaximal, characteristic, complemented
7C17×#2248C211yesmaximal, characteristic, complemented
8C2×#10587497—22no—
9#11763214C2211yescharacteristic
10#11763186C2211yescharacteristic
11#11763181—21no—
12#11763157—21no—
13#11763157—21no—
14#11763155—21no—
15#11762613—22no—
16#11762611—22no—
17C4×#63214C2211yescharacteristic
18C8×#3622C2211yescharacteristic
19C2×C17×SD32—22no—
20C17×#494C2211yescharacteristic
21C17×#493C2211yescharacteristic
22C4×C16×C17C2211yescharacteristic
23C2×Q16×C17—21no—
24C2×Q16×C17—21no—
25C2×D8×C17—21no—
26C2×D8×C17—21no—
27C17×C4⋊Q8—21no—
28C17×#127—21no—
29C2×#63229—42no—
30C2×D136—21no—
31C2×D136—21no—
32#10587560—21no—
33#10587555—21no—
34C17×SD32—44no—
35C2×C16×C17D412yes—
36C4×C8×C17C2311yescharacteristic
37#10587503—42no—
38#10587497—44no—
39#10587489—21no—
40#10587489—21no—
41C2×#63214D412yes—
42#10587480—42no—
43#10587480—42no—
44C4×#3622D411yescharacteristic
45C4×#3622D411yescharacteristic
46C2×Q8×C17—41no—
47C2×D4×C17—41no—
48C2×D4×C17—41no—
49C2×D4×C17—41no—
50C2×D68—41no—
51C2×D68—41no—
52C2×D68—41no—
53C2×Dic34—41no—
54Q16×C17—42no—
55Q16×C17—42no—
56D8×C17—42no—
57D8×C17—42no—
58C2×C8×C17C2×D411yescharacteristic
59C2×C8×C17C2×D411yescharacteristic
60C4⋊C4×C17—41no—
61C4⋊C4×C17—41no—
62C42×C17C2×D411yescharacteristic
63#63229—84no—
64C4⋊Dic17—41no—
65C4⋊Dic17—41no—
66C2×#3622D812yes—
67C2×#3622D812yes—
68D136—42no—
69D136—42no—
70C16×C17—22no—
71#63214—22no—
72#12527—171nomaximal, Sylow
73C23×C17—81no—
74C22×D17—81no—
75Q8×C17—81no—
76Q8×C17—81no—
77D4×C17—81no—
78D4×C17—81no—
79D4×C17—82no—
80D4×C17—82no—
81C2×C4×C17—81no—
82C2×C4×C17#12711yescharacteristic
83C2×C4×C17C2×D811yescharacteristic
84C2×C4×C17C2×D811yescharacteristic
85C2×Dic17—81no—
86D68—81no—
87D68—81no—
88D68—82no—
89D68—82no—
90Dic34—82no—
91C8×C17AGL(1,ℤ/8)12yes—
92C8×C17AGL(1,ℤ/8)12yes—
93#3622—22no—
94#3622—22no—
95#2248D1711yescharacteristic, complemented
96#2246—171no—
97#2241—171no—
98#2240—171no—
99#1709—171no—
100#1706—171no—
101#1312—171no—
102C22×C17—161no—
103C22×C17—161no—
104C22×C17—161no—
105C22×C17#49311yescharacteristic
106C2×D17—161no—
107C2×D17—161no—
108C2×D17—161no—
109C4×C17—161no—
110C4×C17#49611yescharacteristic
111C4×C17#49611yescharacteristic
112C4×C17#50812yes—
113C4×C17#50912yes—
114Dic17—161no—
115C2×SD32—22no—
116C2×D16—342no—
117#500—171no—
118#494C2×D1711yescharacteristic
119#493—171no—
120#493C2×D1711yescharacteristic
121#492—341no—
122#486—341no—
123#486—341no—
124#486—341no—
125#358—342no—
126#357—342no—
127C4×C16—171no—
128C4×C16C2×D1711yescharacteristic
129C82—171no—
130C2×C17—321no—
131C2×C17#172111yescharacteristic
132C2×C17#224911yescharacteristic
133C2×C17#225011yescharacteristic
134D17—321no—
135C2×Q16—21no—
136C2×Q16—21no—
137C2×SD16—682no—
138C2×D8—21no—
139C2×D8—21no—
140C2×D8—341no—
141C2×D8—341no—
142C4⋊Q8—21no—
143C4⋊Q8—341no—
144#127—21no—
145#127—341no—
146SD32—44no—
147D16—684no—
148C2×C16—172no—
149C2×C16C22⋊D1712yes—
150#107—341no—
151#107—341no—
152#102—682no—
153#102—682no—
154#102—682no—
155C4×C8—171no—
156C4×C8—171no—
157C4×C8C22×D1711yescharacteristic
158C17#1252711yescharacteristic, complemented, Sylow
159C2×Q8—41no—
160C2×Q8—681no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—681no—
165C2×D4—681no—
166C2×D4—681no—
167Q16—42no—
168Q16—42no—
169SD16—1364no—
170D8—42no—
171D8—42no—
172D8—682no—
173D8—682no—
174C2×C8—172no—
175C2×C8—172no—
176C2×C8D4×D1711yescharacteristic
177C2×C8C2×C22⋊D1711yescharacteristic
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—681no—
181C4⋊C4—681no—
182C42D4×D1711yescharacteristic
183C16—22no—
184C16—342no—
185C23—81no—
186C23—1361no—
187Q8—81no—
188Q8—81no—
189Q8—1362no—
190D4—82no—
191D4—82no—
192D4—81no—
193D4—81no—
194D4—1362no—
195D4—1362no—
196D4—1361no—
197D4—1361no—
198C2×C4—81no—
199C2×C4—1361no—
200C2×C4D8×D1711yescharacteristic
201C2×C4D8×D1711yescharacteristic
202C2×C4#1058762611yescharacteristic
203C8—342no—
204C8—342no—
205C8#1058759712yes—
206C8#1058761812yes—
207C22—161no—
208C22—161no—
209C22—161no—
210C22—2721no—
211C22—2721no—
212C22—2721no—
213C22#1176318411yescharacteristic
214C4—161no—
215C4—2721no—
216C4#1176319611yescharacteristic
217C4#1176319711yescharacteristic
218C4#1176324012yes—
219C4#1176324612yes—
220C2—321no—
221C2—5441no—
222C2#1452844911yescharacteristic
223C2#1453104411yescharacteristic
224C2#1453104911yescharacteristic
subgroupG/H
centerC22#11763184
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#2248C2
socleC22×C17#493
prime radical#14531033C2
hypercenter#2248D17
hypocenterC17#12527
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
2. #14531011C2semidirect
3. #14531008C2semidirect
4. #14528391C2semidirect
5. #14528373C2semidirect
6. #14526703C2semidirect
7. C17×#2248C2semidirect
95. #2248D17semidirect
158. C17#12527semidirect

Maximal subgroups

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

subgroupindex
#145310332
#145310112
#145310082
#145283912
#145283732
#145267032
C17×#22482
#1252717