Finite Group Databasebeta

← #16945178

Subgroups — #16945178

Order 4352.

280 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 71 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#14539529C211yesmaximal, characteristic
2#14528933C211yesmaximal, characteristic
3#14526779C212yesmaximal
4#14526773C212yesmaximal
5C17×#2165C211yesmaximal, characteristic
6#11763366—21no—
7#11763207C411yescharacteristic, complemented
8#11763189C411yescharacteristic, complemented
9#11763160—21no—
10#11763067—21no—
11#11763067C2212yes—
12#11762917—21no—
13#11762917C412yescomplemented
14#11762580—21no—
15#11762569—21no—
16#11762567C2211yescharacteristic
17#11762566C2211yescharacteristic
18C4×M16×C17C2211yescharacteristic
19C17×#364—21no—
20C17×#349C2212yes—
21C17×#347—21no—
22C2×M16×C17D411yescharacteristic
23C2×M16×C17C2311yescharacteristic
24C2×C42×C17D411yescharacteristic
25#10587612—21no—
26#10587612—41no—
27#10587610—22no—
28#10587610—41no—
29C2×#63223—21no—
30C2×Dic68—21no—
31C2×Dic68C2×C412yes—
32#10587556—41no—
33#10587555—21no—
34#10587555—21no—
35C4×Dic34—22no—
36C4×Dic34—41no—
37C17×M32—22no—
38C17×#97C2×C411yescharacteristic
39C17×#97D411yescharacteristic
40C4×C8×C17C2×C411yescharacteristic
41C4×C8×C17D411yescharacteristic
42#10587488—21no—
43#10587488C2×C412yes—
44#10587487—22no—
45#10587487—22no—
46C22×C4×C17—21no—
47C22×C4×C17C2×D411yescharacteristic
48C2×Dic34—22no—
49C2×Dic34—41no—
50M16×C17—41no—
51M16×C17—41no—
52C2×C8×C17C22⋊C411yescharacteristic
53C2×C8×C17C22⋊C411yescharacteristic
54C2×C8×C17C22×C411yescharacteristic
55C2×C8×C17C2×D411yescharacteristic
56C42×C17—21no—
57C42×C17C22⋊C411yescharacteristic
58C42×C17C22⋊C411yescharacteristic
59C22⋊Dic17—42no—
60C22⋊Dic17—41no—
61C4⋊Dic17—22no—
62C4⋊Dic17—41no—
63C4⋊Dic17—41no—
64C4⋊Dic17—41no—
65C4⋊Dic17—41no—
66#63225—42no—
67#63225—42no—
68C4×Dic17—42no—
69C4×Dic17—41no—
70#63223—41no—
71#63223—41no—
72C2×#3622—41no—
73Dic68—42no—
74Dic68—42no—
75C16×C17—42no—
76#11838—171nomaximal, Sylow
77C23×C17AGL(1,ℤ/8)11yescharacteristic
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—42no—
83C2×C4×C17C2×C22⋊C411yescharacteristic
84C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
85C2×Dic17—42no—
86C2×Dic17—42no—
87C2×Dic17—81no—
88Dic34—42no—
89Dic34—42no—
90Dic34—82no—
91C8×C17—21no—
92C8×C17—21no—
93C8×C17—21no—
94C8×C17—21no—
95#3622—81no—
96#3185—171no—
97#2165D1711yescharacteristic
98#1841—171no—
99#1342—172no—
100#1340—172no—
101C22×C17—21no—
102C22×C17—41no—
103C22×C17#41811yescharacteristic
104C4×C17—22no—
105C4×C17—21no—
106C4×C17—41no—
107C4×C17#41011yescharacteristic
108C4×C17#42111yescharacteristic
109Dic17—82no—
110Dic17—82no—
111Dic17—161no—
112#533—341no—
113#498—171no—
114#494—171no—
115#487—341no—
116#470—172no—
117#470—341no—
118#441—172no—
119#441—341no—
120C4×M16C2×D1711yescharacteristic
121#364—21no—
122#349C2×D1712yes—
123#347—21no—
124#344—341no—
125#339—341no—
126#338—171no—
127H(3,ℤ/4)—171no—
128C2×C17—21no—
129C2×C17—41no—
130C2×C17#151411yescharacteristic
131C2×Q16—172no—
132C2×Q16—341no—
133C2×M16—341no—
134C2×M16D6811yescharacteristic
135C2×M16C22×D1711yescharacteristic
136C4⋊Q8—341no—
137C4⋊Q8—341no—
138#125—681no—
139C22⋊Q8—342no—
140C22⋊Q8—681no—
141C4×Q8—342no—
142C4×Q8—681no—
143#117—341no—
144#117—681no—
145C2×C42D6811yescharacteristic
146M32—22no—
147#106—172no—
148#106—341no—
149#103—342no—
150#103—342no—
151#97C4×D1711yescharacteristic
152#97C22⋊D1711yescharacteristic
153C4×C8C4×D1711yescharacteristic
154C4×C8C22⋊D1711yescharacteristic
155C17#1183811yescharacteristic, complemented, Sylow
156C2×Q8—342no—
157C2×Q8—681no—
158C22×C4—21no—
159C22×C4C2×D6811yescharacteristic
160Q16—682no—
161Q16—682no—
162M16—41no—
163M16—41no—
164M16—681no—
165M16—681no—
166C2×C8—681no—
167C2×C8#6322711yescharacteristic
168C2×C8#6322711yescharacteristic
169C2×C8C2×C4×D1711yescharacteristic
170C2×C8C2×C22⋊D1711yescharacteristic
171C4⋊C4—342no—
172C4⋊C4—681no—
173C4⋊C4—681no—
174C4⋊C4—682no—
175C4⋊C4—681no—
176C4⋊C4—681no—
177C4⋊C4—682no—
178C22⋊C4—682no—
179C22⋊C4—681no—
180C42—21no—
181C42—682no—
182C42—681no—
183C42#6322711yescharacteristic
184C42#6322711yescharacteristic
185C16—42no—
186C23#1058759411yescharacteristic
187Q8—682no—
188Q8—682no—
189Q8—1362no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—682no—
196C2×C4—682no—
197C2×C4—1361no—
198C2×C4#1058759411yescharacteristic
199C2×C4C2×#6322711yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—1361no—
205C22—21no—
206C22—41no—
207C22#1176281511yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—2721no—
212C4—1362no—
213C4—1362no—
214C4#1176278211yescharacteristic
215C4#1176282511yescharacteristic
216C2—21no—
217C2—41no—
218C2#1452733211yescharacteristic
subgroupG/H
centerC2#14527332
commutatorC2×C8×C17C22×C4
FrattiniC2×M16C22×D17
FittingC17×#2165C2
socleC2×C17#1514
prime radicalC23×C17AGL(1,ℤ/8)
cosocleC2×M16×C17C23
hypercenter#2165D17
hypocenterC17#11838
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
7. #11763207C4semidirect
8. #11763189C4semidirect
13. #11762917C4semidirect
155. C17#11838semidirect

Maximal subgroups

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

subgroupindex
#145395292
#145289332
#145267792
#145267732
C17×#21652
#1183817