Finite Group Databasebeta

← #16938775

Subgroups — #16938775

Order 4352.

406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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#14529547C212yesmaximal
2#14528943C211yesmaximal, characteristic
3#14526667C211yesmaximal, characteristic
4#14526625C212yesmaximal
5C17×#2571C211yesmaximal, characteristic
6C2×#10587478—22no—
7C2×#10587479—22no—
8C2×C4⋊#3622C2212yes—
9C2×C4×#3622C2211yescharacteristic
10#11762679C2211yescharacteristic
11#11762571—22no—
12C17×#400—22no—
13C17×#389—22no—
14C17×#384C2211yescharacteristic
15C17×#382—22no—
16C4×C4⋊C4×C17C2212yes—
17C2×C4⋊C4×C17—22no—
18C2×C4⋊C4×C17—22no—
19C2×C4⋊C4×C17D412yes—
20C2×C4⋊C4×C17D412yes—
21C2×C4⋊C4×C17D412yes—
22C2×C42×C17—22no—
23C2×C42×C17C2311yescharacteristic
24C2×C4⋊Dic17—22no—
25C2×C4⋊Dic17—21no—
26C22×#3622—21no—
27C22×#3622—22no—
28C17×#95—22no—
29C17×#95—24no—
30C17×#95—22no—
31#10587479—44no—
32#10587478—44no—
33C4⋊#3622—22no—
34C4⋊#3622Q814yes—
35C4×#3622—21no—
36C4×#3622Q812yes—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17C2×D411yescharacteristic
41C22×C4×C17C2×D412yes—
42C22×Dic17—41no—
43C4⋊C4×C17—22no—
44C4⋊C4×C17—22no—
45C4⋊C4×C17—22no—
46C4⋊C4×C17—22no—
47C4⋊C4×C17—42no—
48C4⋊C4×C17—42no—
49C4⋊C4×C17—42no—
50C4⋊C4×C17—82no—
51C42×C17—42no—
52C42×C17—42no—
53C42×C17C2×Q811yescharacteristic
54C42×C17C2×Q812yes—
55C42×C17#4111yescharacteristic
56C4⋊Dic17—42no—
57C4⋊Dic17—42no—
58C4⋊Dic17—42no—
59C2×#3622—22no—
60C2×#3622—22no—
61C2×#3622—22no—
62C2×#3622—24no—
63C2×#3622—42no—
64C2×#3622—42no—
65#10576—171nomaximal, Sylow
66C23×C17#12011yescharacteristic
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—42no—
70C2×C4×C17—44no—
71C2×C4×C17—42no—
72C2×C4×C17—42no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17C22⋊Q811yescharacteristic
78C2×C4×C17C22⋊Q812yes—
79C2×C4×C17C4⋊Q811yescharacteristic
80C2×C4×C17C4⋊Q812yes—
81C2×C4×C17#13512yes—
82C2×C4×C17#13512yes—
83C2×C4×C17AGL(1,ℤ/8)12yes—
84C2×C4×C17#13712yes—
85C2×Dic17—82no—
86C2×Dic17—81no—
87#3622—24no—
88#3622—44no—
89#2571D1711yescharacteristic
90#1948—172no—
91#1845—171no—
92#1296—171no—
93#1279—172no—
94C22×C17#39511yescharacteristic
95C22×C17#44912yes—
96C22×C17#45212yes—
97C22×C17#45311yescharacteristic
98C22×C17#45611yescharacteristic
99C4×C17—21no—
100C4×C17—21no—
101C4×C17—82no—
102C4×C17—82no—
103C4×C17—82no—
104C4×C17#47812yes—
105C4×C17#47912yes—
106C4×C17#49912yes—
107C4×C17#50112yes—
108Dic17—161no—
109C2×#107—342no—
110C2×#106—342no—
111C2×C4⋊C8—172no—
112C2×C4×C8—171no—
113#400—22no—
114#389—22no—
115#384—171no—
116#384C2×D1711yescharacteristic
117#382—22no—
118C4×C4⋊C4C2×D1712yes—
119#340—342no—
120C2×C17#162011yescharacteristic
121C2×C17#163411yescharacteristic
122C2×C17#165012yes—
123C2×C17#205912yes—
124C2×C17#206011yescharacteristic
125C22×C8—341no—
126C22×C8—342no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—342no—
130C2×C4⋊C4—341no—
131C2×C4⋊C4C22⋊D1712yes—
132C2×C4⋊C4C22⋊D1712yes—
133C2×C4⋊C4C22⋊D1712yes—
134C2×C42—22no—
135C2×C42C22×D1711yescharacteristic
136#107—684no—
137#106—684no—
138C4⋊C8—174no—
139C4⋊C8—342no—
140C4×C8—172no—
141C4×C8—341no—
142#95—22no—
143#95—24no—
144#95—22no—
145C17#1057611yescharacteristic, complemented, Sylow
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—681no—
150C22×C4C2×C22⋊D1711yescharacteristic
151C22×C4C2×C22⋊D1712yes—
152C2×C8—342no—
153C2×C8—342no—
154C2×C8—342no—
155C2×C8—344no—
156C2×C8—682no—
157C2×C8—682no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—82no—
166C4⋊C4—682no—
167C4⋊C4—682no—
168C4⋊C4—682no—
169C42—42no—
170C42—42no—
171C42Q8×D1711yescharacteristic
172C42Q8×D1712yes—
173C42#6325611yescharacteristic
174C23#1058763911yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—1362no—
186C2×C4—1361no—
187C2×C4#1058763011yescharacteristic
188C2×C4#1058763012yes—
189C2×C4#1058763211yescharacteristic
190C2×C4#1058763212yes—
191C2×C4#1058763512yes—
192C2×C4#1058763612yes—
193C2×C4#1058763612yes—
194C2×C4#1058763712yes—
195C8—344no—
196C8—684no—
197C22#1176272811yescharacteristic
198C22#1176295412yes—
199C22#1176297112yes—
200C22#1176297711yescharacteristic
201C22#1176299211yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—2721no—
208C4#1176310612yes—
209C4#1176311312yes—
210C4#1176320812yes—
211C4#1176321912yes—
212C2#1452784311yescharacteristic
213C2#1452792911yescharacteristic
214C2#1452804012yes—
215C2#1453011912yes—
216C2#1453012611yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2571C2
socle, prime radicalC23×C17#120
hypercenter#2571D17
hypocenterC17#10576
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
145. C17#10576semidirect

Maximal subgroups

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

subgroupindex
#145295472
#145289432
#145266672
#145266252
C17×#25712
#1057617