Finite Group Databasebeta

← #16938391

Subgroups — #16938391

Order 4352.

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

normal subgroups only

This group has 408 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#14528937C211yesmaximal, characteristic, complemented
2#14527479C212yesmaximal, complemented
3#14527292C212yesmaximal, complemented
4#14526654C211yesmaximal, characteristic, complemented
5C17×#3245C211yesmaximal, characteristic
6#11762866C2212yes—
7C2×C4⋊#3622C2211yescharacteristic
8C2×#10587485—22no—
9#11762655C2211yescharacteristic
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—
37#10587485—44no—
38C4⋊#3622—22no—
39C4⋊#3622—22no—
40#10587474—22no—
41#41×C17—84no—
42C2×Q8×C17—22no—
43C2×D4×C17—22no—
44C2×D4×C17—22no—
45C2×D4×C17—22no—
46C2×D4×C17—42no—
47C22×C4×C17—42no—
48C22×C4×C17C2×D411yescharacteristic
49C22×C4×C17C2×D411yescharacteristic
50C22×C4×C17#4111yescharacteristic
51C22×Dic17—22no—
52D8×C17—82no—
53C2×C8×C17—22no—
54C2×C8×C17—42no—
55C4⋊C4×C17—22no—
56C4⋊C4×C17—22no—
57C22⋊C4×C17—42no—
58C22⋊C4×C17—42no—
59C42×C17C2×D412yes—
60C42×C17#4112yes—
61C4×Dic17—22no—
62C4×Dic17—22no—
63C2×#3622—42no—
64C2×#3622—41no—
65C2×#3622—42no—
66#10512—171nomaximal, Sylow
67C23×C17—42no—
68C23×C17#12111yescharacteristic
69Q8×C17—82no—
70D4×C17—42no—
71D4×C17—42no—
72D4×C17—82no—
73D4×C17—82no—
74D4×C17—84no—
75C2×C4×C17—22no—
76C2×C4×C17—21no—
77C2×C4×C17—21no—
78C2×C4×C17—41no—
79C2×C4×C17—42no—
80C2×C4×C17—84no—
81C2×C4×C17#12011yescharacteristic
82C2×C4×C17#12112yes—
83C2×C4×C17#12312yes—
84C2×C4×C17#12411yescharacteristic
85C2×Dic17—24no—
86C2×Dic17—42no—
87C2×Dic17—42no—
88C8×C17—42no—
89#3622—82no—
90#3622—81no—
91#3245D1711yescharacteristic
92#1843—171no—
93#1551—172no—
94#1505—172no—
95#1290—171no—
96C22×C17—21no—
97C22×C17—21no—
98C22×C17—82no—
99C22×C17—82no—
100C22×C17—82no—
101C22×C17#39411yescharacteristic
102C22×C17#47212yes—
103C4×C17—22no—
104C4×C17—21no—
105C4×C17—22no—
106C4×C17—82no—
107C4×C17#45311yescharacteristic
108C4×C17#45611yescharacteristic
109Dic17—44no—
110#532C2×D1712yes—
111#474—22no—
112#466—22no—
113#459—22no—
114#432—172no—
115C2×C4⋊C8—171no—
116C2×C4⋊C8—342no—
117C2×C4⋊C8C2×D1711yescharacteristic
118#376—171no—
119#333—342no—
120#331—342no—
121#327—344no—
122C2×C17—22no—
123C2×C17—162no—
124C2×C17#203911yescharacteristic
125C2×C17#204511yescharacteristic
126C2×C17#205311yescharacteristic
127C2×#41—22no—
128C2×D8—22no—
129C22×C8—341no—
130C22×C8C22⋊D1712yes—
131C4⋊Q8C22⋊D1712yes—
132#127C22⋊D1712yes—
133#124—22no—
134#121—22no—
135#121—22no—
136C4×D4—22no—
137C4×D4—22no—
138C2×C42—341no—
139C2×C42C22×D1711yescharacteristic
140#107—22no—
141C4⋊C8—22no—
142C4⋊C8—342no—
143C4⋊C8—342no—
144C4⋊C8—684no—
145#102—24no—
146C22⋊C8—342no—
147#97—342no—
148#95—172no—
149#95—341no—
150C17#1051211yescharacteristic, complemented, Sylow
151#41—84no—
152C2×Q8—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—42no—
157C22×C4—42no—
158C22×C4—342no—
159C22×C4D4×D1711yescharacteristic
160C22×C4#6325411yescharacteristic
161C22×C4C2×C22⋊D1711yescharacteristic
162D8—82no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—682no—
166C2×C8—682no—
167C2×C8—681no—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C42—342no—
173C42—342no—
174C42#6325412yes—
175C42C2×C22⋊D1712yes—
176C23—42no—
177C23#1058762411yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—82no—
182D4—82no—
183D4—84no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—84no—
190C2×C4—344no—
191C2×C4—682no—
192C2×C4—682no—
193C2×C4#1058762112yes—
194C2×C4#1058762211yescharacteristic
195C2×C4#1058762512yes—
196C2×C4#1058763911yescharacteristic
197C8—42no—
198C8—1362no—
199C8—1361no—
200C22—21no—
201C22—21no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#1176272311yescharacteristic
206C22#1176307612yes—
207C4—22no—
208C4—21no—
209C4—22no—
210C4—82no—
211C4—684no—
212C4#1176297711yescharacteristic
213C4#1176299211yescharacteristic
214C2—22no—
215C2—162no—
216C2#1453000511yescharacteristic
217C2#1453003711yescharacteristic
218C2#1453008711yescharacteristic
subgroupG/H
centerC22#11762723
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
Fitting, prime radicalC17×#3245C2
socleC22×C17#394
hypercenter#3245D17
hypocenterC17#10512
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. #14528937C2semidirect
2. #14527479C2semidirect
3. #14527292C2semidirect
4. #14526654C2semidirect
150. C17#10512semidirect

Maximal subgroups

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

subgroupindex
#145289372
#145274792
#145272922
#145266542
C17×#32452
#1051217