Finite Group Databasebeta

← #16936616

Subgroups — #16936616

Order 4352.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#14539925C212yesmaximal
2#14529604C211yesmaximal, characteristic
3#14527348C212yesmaximal
4#14526629C211yesmaximal, characteristic
5C17×#3162C211yesmaximal, characteristic
6C2×#10587555C2211yescharacteristic
7#11763205—22no—
8#11763159—22no—
9#11763137—24no—
10#11763094—24no—
11#11762862C2212yes—
12C2×#10587487—22no—
13#11762675C2211yescharacteristic
14#11762546—24no—
15C17×#533C2212yes—
16C17×#501—22no—
17C17×#501—22no—
18C17×#427—22no—
19C2×C17×#97C2211yescharacteristic
20C22×Dic34—21no—
21C22×C8×C17D412yes—
22C17×C4⋊Q8D412yes—
23C17×C4⋊Q8D412yes—
24C17×#125—22no—
25C17×C22⋊Q8—22no—
26C17×C22⋊Q8—22no—
27C4×Q8×C17—22no—
28C4×Q8×C17—22no—
29C17×#117—22no—
30C2×C42×C17C2311yescharacteristic
31C2×C4⋊Dic17—22no—
32C2×C4⋊Dic17—21no—
33#10587555—22no—
34#10587555—21no—
35#10587555D412yes—
36C17×#107—24no—
37C17×#106—22no—
38C17×#106—22no—
39C17×#97—22no—
40#10587506—28no—
41#10587502—22no—
42C22⋊#3622D414yes—
43#10587487—44no—
44#10587479—28no—
45C4⋊#3622—22no—
46C4×#3622—22no—
47C2×Q8×C17—22no—
48C2×Q8×C17—22no—
49C22×C4×C17C2×D412yes—
50C22×C4×C17C2×D411yescharacteristic
51C22×Dic17—41no—
52C22×Dic17—41no—
53C2×Dic34—22no—
54C2×Dic34—42no—
55C2×Dic34—42no—
56C2×Dic34—41no—
57C2×C8×C17—22no—
58C2×C8×C17—22no—
59C2×C8×C17SD1614yes—
60C4⋊C4×C17—22no—
61C4⋊C4×C17—22no—
62C4⋊C4×C17—22no—
63C4⋊C4×C17—22no—
64C4⋊C4×C17—42no—
65C4⋊C4×C17—42no—
66C22⋊C4×C17—42no—
67C42×C17—42no—
68C42×C17C2×D411yescharacteristic
69C42×C17C2×D412yes—
70C42×C17#4111yescharacteristic
71C4⋊Dic17—24no—
72C4⋊Dic17—42no—
73C4⋊Dic17—42no—
74C2×#3622—24no—
75#10227—171nomaximal, Sylow
76C23×C17#12711yescharacteristic
77Q8×C17—44no—
78Q8×C17—82no—
79C2×C4×C17—42no—
80C2×C4×C17—42no—
81C2×C4×C17—42no—
82C2×C4×C17#12012yes—
83C2×C4×C17#12011yescharacteristic
84C2×C4×C17#12111yescharacteristic
85C2×C4×C17#12112yes—
86C2×C4×C17C2×SD1612yes—
87C2×C4×C17#13712yes—
88C2×Dic17—42no—
89C2×Dic17—81no—
90C2×Dic17—81no—
91C2×Dic17—82no—
92C2×Dic17—81no—
93Dic34—44no—
94Dic34—82no—
95C8×C17—24no—
96#3622—44no—
97#3229—172no—
98#3162D1711yescharacteristic
99#1960—171no—
100#1518—172no—
101#1281—171no—
102C22×C17—22no—
103C22×C17#39211yescharacteristic
104C22×C17#49211yescharacteristic
105C22×C17#49711yescharacteristic
106C4×C17—22no—
107C4×C17—22no—
108C4×C17—82no—
109C4×C17—82no—
110C4×C17#44812yes—
111C4×C17#46112yes—
112Dic17—82no—
113Dic17—161no—
114#533C2×D1712yes—
115C2×C4⋊Q8—171no—
116#501—22no—
117#501—22no—
118#498—342no—
119#487—342no—
120#483—344no—
121#475—344no—
122#431—172no—
123#427—22no—
124C2×#103—342no—
125C2×#97C2×D1711yescharacteristic
126#382—171no—
127#328—344no—
128C2×C17—21no—
129C2×C17—21no—
130C2×C17#200912yes—
131C2×C17#201311yescharacteristic
132C22×Q8—341no—
133C22×C8C22⋊D1712yes—
134C4⋊Q8—172no—
135C4⋊Q8—341no—
136C4⋊Q8—342no—
137C4⋊Q8C22⋊D1712yes—
138C4⋊Q8C22⋊D1712yes—
139#125—22no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144#117—22no—
145C2×C4⋊C4—342no—
146C2×C4⋊C4—341no—
147C2×C42C22×D1711yescharacteristic
148#107—24no—
149#106—22no—
150#106—22no—
151#106—348no—
152C4⋊C8—342no—
153#103—348no—
154#103—684no—
155C22⋊C8—174no—
156#97—22no—
157C4×C8—342no—
158#95—342no—
159C17#1022711yescharacteristic, complemented, Sylow
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—342no—
163C2×Q8—681no—
164C2×Q8—682no—
165C2×Q8—682no—
166C22×C4—681no—
167C22×C4—681no—
168C22×C4D4×D1712yes—
169C22×C4C2×C22⋊D1711yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—344no—
173C2×C8#6323014yes—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—344no—
181C4⋊C4—682no—
182C4⋊C4—682no—
183C22⋊C4—42no—
184C42—42no—
185C42D4×D1711yescharacteristic
186C42#6325411yescharacteristic
187C42C2×C22⋊D1712yes—
188C23#1058762611yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—684no—
192Q8—1362no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—682no—
197C2×C4—1362no—
198C2×C4—1361no—
199C2×C4—1361no—
200C2×C4—1361no—
201C2×C4#1058762312yes—
202C2×C4#1058762411yescharacteristic
203C2×C4#1058762512yes—
204C2×C4C2×#6323012yes—
205C2×C4#1058762812yes—
206C2×C4#1058763911yescharacteristic
207C8—24no—
208C8—684no—
209C22—22no—
210C22#1176271711yescharacteristic
211C22#1176318311yescharacteristic
212C22#1176320111yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—82no—
217C4—2721no—
218C4—1362no—
219C4#1176294812yes—
220C4#1176301112yes—
221C2—21no—
222C2—21no—
223C2#1452984112yes—
224C2#1452986711yescharacteristic
subgroupG/H
centerC22#11762717
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#3162C2
socleC22×C17#392
prime radicalC23×C17#127
hypercenter#3162D17
hypocenterC17#10227
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
159. C17#10227semidirect

Maximal subgroups

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

subgroupindex
#145399252
#145296042
#145273482
#145266292
C17×#31622
#1022717