Finite Group Databasebeta

← #16938396

Subgroups — #16938396

Order 4352.

388 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 81 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#14528903C211yesmaximal, characteristic, complemented
2#14527479C212yesmaximal, complemented
3#14527292C212yesmaximal, complemented
4#14526654C211yesmaximal, characteristic, complemented
5C17×#3245C211yesmaximal, characteristic
6#11762866C2212yes—
7C2×C4⋊#3622C2211yescharacteristic
8#11762655C2211yescharacteristic
9#11762563—22no—
10#11762558—22no—
11#11762553—22no—
12#11762543—24no—
13C17×#532C2212yes—
14C17×#474—22no—
15C17×#466—22no—
16C17×#459—22no—
17C2×C17×C4⋊C8C2211yescharacteristic
18C2×#41×C17—22no—
19C2×D8×C17—22no—
20C22×C8×C17D412yes—
21C17×C4⋊Q8D412yes—
22C17×#127D412yes—
23C17×#124—22no—
24C17×#121—22no—
25C17×#121—22no—
26C4×D4×C17—22no—
27C4×D4×C17—22no—
28C2×C42×C17C2311yescharacteristic
29C2×C4×Dic17—21no—
30C22×#3622—21no—
31C17×#107—22no—
32C17×C4⋊C8—22no—
33C17×#102—24no—
34#10587502—21no—
35#10587502D412yes—
36C22⋊#3622—22no—
37C4⋊#3622—22no—
38C4⋊#3622—22no—
39#10587474—22no—
40#41×C17—84no—
41C2×Q8×C17—22no—
42C2×D4×C17—22no—
43C2×D4×C17—22no—
44C2×D4×C17—22no—
45C2×D4×C17—42no—
46C22×C4×C17—42no—
47C22×C4×C17C2×D411yescharacteristic
48C22×C4×C17C2×D411yescharacteristic
49C22×C4×C17#4111yescharacteristic
50C22×Dic17—22no—
51D8×C17—82no—
52C2×C8×C17—22no—
53C2×C8×C17—42no—
54C4⋊C4×C17—22no—
55C4⋊C4×C17—22no—
56C22⋊C4×C17—42no—
57C22⋊C4×C17—42no—
58C42×C17C2×D412yes—
59C42×C17#4112yes—
60C4×Dic17—41no—
61C4×Dic17—41no—
62C2×#3622—42no—
63C2×#3622—41no—
64C2×#3622—42no—
65#10513—171nomaximal, Sylow
66C23×C17—42no—
67C23×C17#12111yescharacteristic
68Q8×C17—82no—
69D4×C17—42no—
70D4×C17—42no—
71D4×C17—82no—
72D4×C17—82no—
73D4×C17—84no—
74C2×C4×C17—22no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—41no—
78C2×C4×C17—42no—
79C2×C4×C17—84no—
80C2×C4×C17#12011yescharacteristic
81C2×C4×C17#12112yes—
82C2×C4×C17#12312yes—
83C2×C4×C17#12411yescharacteristic
84C2×Dic17—42no—
85C2×Dic17—42no—
86C2×Dic17—42no—
87C8×C17—42no—
88#3622—82no—
89#3622—81no—
90#3245D1711yescharacteristic
91#1832—171no—
92#1551—172no—
93#1505—172no—
94#1290—171no—
95C22×C17—21no—
96C22×C17—21no—
97C22×C17—82no—
98C22×C17—82no—
99C22×C17—82no—
100C22×C17#39411yescharacteristic
101C22×C17#47212yes—
102C4×C17—22no—
103C4×C17—21no—
104C4×C17—22no—
105C4×C17—82no—
106C4×C17#45411yescharacteristic
107C4×C17#45511yescharacteristic
108Dic17—82no—
109#532C2×D1712yes—
110#474—22no—
111#466—22no—
112#459—22no—
113#432—172no—
114C2×C4⋊C8—171no—
115C2×C4⋊C8C2×D1711yescharacteristic
116#376—171no—
117#336—342no—
118#333—342no—
119#331—342no—
120#327—344no—
121C2×C17—22no—
122C2×C17—162no—
123C2×C17#204011yescharacteristic
124C2×C17#204511yescharacteristic
125C2×C17#205311yescharacteristic
126C2×#41—22no—
127C2×D8—22no—
128C22×C8—341no—
129C22×C8C22⋊D1712yes—
130C4⋊Q8C22⋊D1712yes—
131#127C22⋊D1712yes—
132#124—22no—
133#121—22no—
134#121—22no—
135C4×D4—22no—
136C4×D4—22no—
137C2×C42—341no—
138C2×C42C22×D1711yescharacteristic
139#107—22no—
140C4⋊C8—22no—
141C4⋊C8—342no—
142C4⋊C8—342no—
143#102—24no—
144C22⋊C8—342no—
145#97—342no—
146#95—172no—
147#95—341no—
148C17#1051311yescharacteristic, complemented, Sylow
149#41—84no—
150C2×Q8—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—42no—
155C22×C4—42no—
156C22×C4—342no—
157C22×C4D4×D1711yescharacteristic
158C22×C4#6325411yescharacteristic
159C22×C4C2×C22⋊D1711yescharacteristic
160D8—82no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—682no—
164C2×C8—682no—
165C2×C8—681no—
166C4⋊C4—22no—
167C4⋊C4—22no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C42—681no—
171C42—681no—
172C42#6325412yes—
173C42C2×C22⋊D1712yes—
174C23—42no—
175C23#1058762411yescharacteristic
176Q8—82no—
177D4—42no—
178D4—42no—
179D4—82no—
180D4—82no—
181D4—84no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—84no—
188C2×C4—682no—
189C2×C4—682no—
190C2×C4—682no—
191C2×C4#1058762112yes—
192C2×C4#1058762211yescharacteristic
193C2×C4#1058762512yes—
194C2×C4#1058763911yescharacteristic
195C8—42no—
196C8—1362no—
197C8—1361no—
198C22—21no—
199C22—21no—
200C22—82no—
201C22—82no—
202C22—82no—
203C22#1176272311yescharacteristic
204C22#1176307612yes—
205C4—22no—
206C4—21no—
207C4—22no—
208C4—82no—
209C4—1362no—
210C4#1176298211yescharacteristic
211C4#1176298711yescharacteristic
212C2—22no—
213C2—162no—
214C2#1453001011yescharacteristic
215C2#1453003711yescharacteristic
216C2#1453008711yescharacteristic
subgroupG/H
centerC22#11762723
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
Fitting, prime radicalC17×#3245C2
socleC22×C17#394
hypercenter#3245D17
hypocenterC17#10513
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #14528903C2semidirect
2. #14527479C2semidirect
3. #14527292C2semidirect
4. #14526654C2semidirect
148. C17#10513semidirect

Maximal subgroups

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

subgroupindex
#145289032
#145274792
#145272922
#145266542
C17×#32452
#1051317