Finite Group Databasebeta

← #16938605

Subgroups — #16938605

Order 4352.

364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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#14539308C211yesmaximal, characteristic
2#14529507C211yesmaximal, characteristic
3#14527439C212yesmaximal
4#14527284C212yesmaximal
5C17×#1275C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763218—22no—
8#11763218—22no—
9#11762847—21no—
10#11762847—21no—
11C2×C4⋊#3622C2211yescharacteristic
12C2×#10587485—21no—
13C4×C4⋊Dic17C2211yescharacteristic
14#11762563—21no—
15#11762557—22no—
16#11762556—22no—
17#11762547—22no—
18#11762547—22no—
19C17×#431C2212yes—
20C2×C17×#97C2211yescharacteristic
21C22×C8×C17D411yescharacteristic
22C22×C8×C17D411yescharacteristic
23C2×C42×C17C2311yescharacteristic
24#10587612—22no—
25C2×C4⋊Dic17—21no—
26#10587610—22no—
27#10587610—22no—
28C2×C4×Dic17—21no—
29C22×#3622—21no—
30#10587556—22no—
31#10587555D412yes—
32#10587555D412yes—
33C4×Dic34—22no—
34C4×Dic34—22no—
35C17×C4⋊C8—22no—
36C17×C22⋊C8—22no—
37C17×#97—22no—
38C4×C8×C17—22no—
39#10587502D411yescharacteristic
40#10587502D411yescharacteristic
41#10587489—21no—
42#10587489—21no—
43#10587489—21no—
44#10587489—21no—
45#10587488—22no—
46#10587488—22no—
47#10587485—42no—
48C4⋊#3622—22no—
49C22×C4×C17C2×D411yescharacteristic
50C22×C4×C17C2×D411yescharacteristic
51C22×C4×C17#4111yescharacteristic
52C22×Dic17—21no—
53C22×Dic17—21no—
54C2×Dic34—22no—
55C2×Dic34—22no—
56C2×C8×C17—21no—
57C2×C8×C17—21no—
58C2×C8×C17—21no—
59C2×C8×C17—21no—
60C2×C8×C17—42no—
61C2×C8×C17SD1612yes—
62C2×C8×C17Q1612yes—
63C42×C17C2×D412yes—
64C42×C17#4112yes—
65C22⋊Dic17—42no—
66C4⋊Dic17—22no—
67C4⋊Dic17—22no—
68C4⋊Dic17—22no—
69C4⋊Dic17—22no—
70C4⋊Dic17—42no—
71#63225—42no—
72#63225—42no—
73C4×Dic17—42no—
74C4×Dic17—41no—
75C4×Dic17—41no—
76C2×#3622—41no—
77C2×#3622—41no—
78C2×#3622—41no—
79#10548—171nomaximal, Sylow
80C23×C17#12111yescharacteristic
81C2×C4×C17—41no—
82C2×C4×C17—41no—
83C2×C4×C17#12011yescharacteristic
84C2×C4×C17#12112yes—
85C2×C4×C17#12312yes—
86C2×C4×C17#12411yescharacteristic
87C2×C4×C17C2×SD1611yescharacteristic
88C2×C4×C17C2×Q1611yescharacteristic
89C2×C4×C17#13711yescharacteristic
90C2×C4×C17#13711yescharacteristic
91C2×Dic17—22no—
92C2×Dic17—41no—
93C2×Dic17—41no—
94C2×Dic17—41no—
95C2×Dic17—41no—
96C2×Dic17—42no—
97C2×Dic17—42no—
98C2×Dic17—41no—
99Dic34—82no—
100Dic34—82no—
101C8×C17—22no—
102C8×C17—22no—
103C8×C17—82no—
104#3622—81no—
105#3162—171no—
106#1940—171no—
107#1542—172no—
108#1503—172no—
109#1275D1711yescharacteristic
110C22×C17—21no—
111C22×C17—21no—
112C22×C17#39411yescharacteristic
113C22×C17#46111yescharacteristic
114C22×C17#46211yescharacteristic
115C4×C17—22no—
116C4×C17—22no—
117C4×C17#44811yescharacteristic
118C4×C17#45111yescharacteristic
119C4×C17#48711yescharacteristic
120C4×C17#49111yescharacteristic
121Dic17—42no—
122Dic17—81no—
123Dic17—82no—
124Dic17—82no—
125#533—172no—
126#501—342no—
127#501—342no—
128#431C2×D1712yes—
129#427—341no—
130#427—341no—
131C2×C4⋊C8—171no—
132C2×C4⋊C8—341no—
133C2×#97C2×D1711yescharacteristic
134C4×C4⋊C4—171no—
135#336—341no—
136#333—342no—
137#332—342no—
138#328—342no—
139#328—342no—
140C2×C17—21no—
141C2×C17—21no—
142C2×C17#204311yescharacteristic
143C2×C17#205011yescharacteristic
144C2×C17#205311yescharacteristic
145C22×C8—341no—
146C22×C8D6811yescharacteristic
147C22×C8D6811yescharacteristic
148C4⋊Q8—172no—
149C4⋊Q8—172no—
150#125—342no—
151C22⋊Q8—342no—
152C22⋊Q8—342no—
153C4×Q8—342no—
154C4×Q8—342no—
155#117—342no—
156C2×C4⋊C4—341no—
157C2×C42—341no—
158C2×C42C22×D1711yescharacteristic
159#107—341no—
160#107—341no—
161#107—341no—
162#107—341no—
163#106—342no—
164#106—342no—
165C4⋊C8—22no—
166C4⋊C8—342no—
167C4⋊C8—682no—
168C22⋊C8—22no—
169#97—22no—
170C4×C8—22no—
171#95—171no—
172#95—171no—
173C17#1054811yescharacteristic, complemented, Sylow
174C2×Q8—342no—
175C2×Q8—342no—
176C22×C4—341no—
177C22×C4—341no—
178C22×C4C2×D6811yescharacteristic
179C22×C4D4×D1711yescharacteristic
180C22×C4#6325611yescharacteristic
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—42no—
186C2×C8—681no—
187C2×C8—681no—
188C2×C8—681no—
189C2×C8#6321912yes—
190C2×C8Dic6812yes—
191C4⋊C4—342no—
192C4⋊C4—342no—
193C4⋊C4—342no—
194C4⋊C4—342no—
195C4⋊C4—682no—
196C4⋊C4—682no—
197C4⋊C4—682no—
198C22⋊C4—682no—
199C42—682no—
200C42—681no—
201C42—681no—
202C42#6325212yes—
203C42D4×D1712yes—
204C23#1058758111yescharacteristic
205Q8—1362no—
206Q8—1362no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—342no—
210C2×C4—681no—
211C2×C4—681no—
212C2×C4—681no—
213C2×C4—681no—
214C2×C4—682no—
215C2×C4—682no—
216C2×C4—681no—
217C2×C4#1058756111yescharacteristic
218C2×C4#1058756811yescharacteristic
219C2×C4#1058757012yes—
220C2×C4#1058758012yes—
221C2×C4C2×#6321911yescharacteristic
222C2×C4C2×Dic6811yescharacteristic
223C2×C4#1058759511yescharacteristic
224C2×C4#1058759511yescharacteristic
225C8—22no—
226C8—22no—
227C8—82no—
228C8—1361no—
229C22—21no—
230C22—21no—
231C22#1176272711yescharacteristic
232C22#1176301511yescharacteristic
233C22#1176302011yescharacteristic
234C4—22no—
235C4—22no—
236C4—682no—
237C4—1361no—
238C4—1362no—
239C4—1362no—
240C4#1176295011yescharacteristic
241C4#1176296711yescharacteristic
242C4#1176316011yescharacteristic
243C4#1176317811yescharacteristic
244C2—21no—
245C2—21no—
246C2#1453003111yescharacteristic
247C2#1453007211yescharacteristic
248C2#1453009111yescharacteristic
subgroupG/H
centerC2×C4#10587561
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1275C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#1275D17
hypocenterC17#10548
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
173. C17#10548semidirect

Maximal subgroups

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

subgroupindex
#145393082
#145295072
#145274392
#145272842
C17×#12752
#1054817