Finite Group Databasebeta

← #16937353

Subgroups — #16937353

Order 4352.

416 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 125 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#14529732C212yesmaximal
2#14529585C211yesmaximal, characteristic
3#14526667C211yesmaximal, characteristic
4#14526625C212yesmaximal
5C17×#2571C211yesmaximal, characteristic
6C2×#10587555C2211yescharacteristic
7C2×C4⋊#3622C2212yes—
8C2×#10587481—22no—
9C2×C4×#3622C2211yescharacteristic
10#11762571—22no—
11#11762571—22no—
12C17×#400—22no—
13C17×#389—22no—
14C17×#384C2211yescharacteristic
15C17×#382—22no—
16C4×C4⋊C4×C17C2212yes—
17C22×Dic34—21no—
18C2×C4⋊C4×C17—22no—
19C2×C4⋊C4×C17—22no—
20C2×C4⋊C4×C17D412yes—
21C2×C4⋊C4×C17D412yes—
22C2×C4⋊C4×C17D412yes—
23C2×C42×C17—22no—
24C2×C42×C17C2311yescharacteristic
25C2×C4⋊Dic17—22no—
26C22×#3622—21no—
27C22×#3622—22no—
28#10587555—21no—
29#10587555—22no—
30#10587555Q812yes—
31C17×#95—22no—
32C17×#95—24no—
33C17×#95—22no—
34#10587481—44no—
35C4⋊#3622—22no—
36C4⋊#3622—22no—
37C4×#3622—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—22no—
41C22×C4×C17C2×D411yescharacteristic
42C22×C4×C17C2×D412yes—
43C22×Dic17—41no—
44C2×Dic34—22no—
45C2×Dic34—42no—
46C2×Dic34—42no—
47C2×Dic34—41no—
48C4⋊C4×C17—22no—
49C4⋊C4×C17—22no—
50C4⋊C4×C17—22no—
51C4⋊C4×C17—22no—
52C4⋊C4×C17—42no—
53C4⋊C4×C17—42no—
54C4⋊C4×C17—42no—
55C4⋊C4×C17—82no—
56C42×C17—42no—
57C42×C17—42no—
58C42×C17C2×Q811yescharacteristic
59C42×C17#4112yes—
60C42×C17#4111yescharacteristic
61C4⋊Dic17—24no—
62C4⋊Dic17—42no—
63C2×#3622—22no—
64C2×#3622—41no—
65C2×#3622—41no—
66C2×#3622—42no—
67C2×#3622—42no—
68C2×#3622—42no—
69#10352—171nomaximal, Sylow
70C23×C17#12011yescharacteristic
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17—44no—
78C2×C4×C17—42no—
79C2×C4×C17—42no—
80C2×C4×C17—42no—
81C2×C4×C17C22⋊Q811yescharacteristic
82C2×C4×C17C22⋊Q812yes—
83C2×C4×C17#12411yescharacteristic
84C2×C4×C17#12412yes—
85C2×C4×C17#13512yes—
86C2×C4×C17#13512yes—
87C2×C4×C17#13712yes—
88C2×C4×C17#13712yes—
89C2×Dic17—42no—
90C2×Dic17—81no—
91C2×Dic17—81no—
92Dic34—44no—
93Dic34—82no—
94#3622—42no—
95#3622—82no—
96#2571D1711yescharacteristic
97#1987—172no—
98#1956—171no—
99#1296—171no—
100#1279—172no—
101C22×C17#39311yescharacteristic
102C22×C17#45212yes—
103C22×C17#45212yes—
104C22×C17#45311yescharacteristic
105C22×C17#45411yescharacteristic
106C4×C17—21no—
107C4×C17—21no—
108C4×C17—82no—
109C4×C17—82no—
110C4×C17—82no—
111C4×C17#47912yes—
112C4×C17#47912yes—
113C4×C17#48812yes—
114C4×C17#49112yes—
115Dic17—82no—
116C2×C4⋊Q8—171no—
117C2×C4⋊C8—172no—
118C2×#103—342no—
119C2×C4×C8—171no—
120#400—22no—
121#389—22no—
122#384C2×D1711yescharacteristic
123#382—22no—
124C4×C4⋊C4C2×D1712yes—
125#340—342no—
126#340—342no—
127C2×C17#163011yescharacteristic
128C2×C17#163411yescharacteristic
129C2×C17#163812yes—
130C2×C17#202612yes—
131C2×C17#202711yescharacteristic
132C22×Q8—341no—
133C22×C8—341no—
134C22×C8—342no—
135C4⋊Q8—172no—
136C4⋊Q8—342no—
137C4⋊Q8—341no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—342no—
141C2×C4⋊C4C22⋊D1712yes—
142C2×C4⋊C4C22⋊D1712yes—
143C2×C4⋊C4C22⋊D1712yes—
144C2×C42—22no—
145C2×C42C22×D1711yescharacteristic
146C4⋊C8—342no—
147C4⋊C8—342no—
148#103—684no—
149C4×C8—342no—
150#95—22no—
151#95—24no—
152#95—22no—
153C17#1035211yescharacteristic, complemented, Sylow
154C2×Q8—342no—
155C2×Q8—682no—
156C2×Q8—682no—
157C2×Q8—681no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—681no—
162C22×C4C2×C22⋊D1711yescharacteristic
163C22×C4C2×C22⋊D1712yes—
164C2×C8—342no—
165C2×C8—681no—
166C2×C8—681no—
167C2×C8—682no—
168C2×C8—682no—
169C2×C8—682no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—82no—
178C4⋊C4—344no—
179C4⋊C4—682no—
180C42—42no—
181C42—42no—
182C42Q8×D1711yescharacteristic
183C42#6325612yes—
184C42#6325611yescharacteristic
185C23#1058763911yescharacteristic
186Q8—684no—
187Q8—1362no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—682no—
199C2×C4—1361no—
200C2×C4—1361no—
201C2×C4#1058763211yescharacteristic
202C2×C4#1058763212yes—
203C2×C4#1058763311yescharacteristic
204C2×C4#1058763312yes—
205C2×C4#1058763612yes—
206C2×C4#1058763612yes—
207C2×C4#1058763712yes—
208C2×C4#1058763712yes—
209C8—682no—
210C8—1362no—
211C22#1176272011yescharacteristic
212C22#1176297112yes—
213C22#1176297112yes—
214C22#1176297711yescharacteristic
215C22#1176298211yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4—82no—
221C4—1362no—
222C4#1176311312yes—
223C4#1176311312yes—
224C4#1176316612yes—
225C4#1176317912yes—
226C2#1452790511yescharacteristic
227C2#1452792911yescharacteristic
228C2#1452795612yes—
229C2#1452993212yes—
230C2#1452993711yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2571C2
socle, prime radicalC23×C17#120
hypercenter#2571D17
hypocenterC17#10352
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2571

Complements

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

NH ≅ G/Ntype
153. C17#10352semidirect

Maximal subgroups

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

subgroupindex
#145297322
#145295852
#145266672
#145266252
C17×#25712
#1035217