Finite Group Databasebeta

← #16937578

Subgroups — #16937578

Order 4352.

542 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 73 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#14537037C211yesmaximal, characteristic
2#14528856C211yesmaximal, characteristic
3#14528856C212yesmaximal
4#14526688C212yesmaximal
5C17×#1304C211yesmaximal, characteristic
6C22×C22⋊Dic17C2211yescharacteristic
7#11762721—22no—
8#11762721—24no—
9#11762665C2211yescharacteristic
10#11762665C2212yes—
11#11762575—22no—
12#11762575—24no—
13C17×#379C2212yes—
14C17×#379C2211yescharacteristic
15C25×C17C2311yescharacteristic
16C23×Dic17Q812yescomplemented
17C22×Dic34—22no—
18C2×C22⋊C4×C17—22no—
19C2×C22⋊C4×C17—22no—
20C2×C22⋊C4×C17—22no—
21C2×C22⋊C4×C17—22no—
22C2×C22⋊C4×C17D412yes—
23C2×C22⋊Dic17—21no—
24C2×C22⋊Dic17—22no—
25C2×C22⋊Dic17—22no—
26C2×C22⋊Dic17—21no—
27C2×C22⋊Dic17—21no—
28C2×C22⋊Dic17—22no—
29C2×C22⋊Dic17—22no—
30C2×C22⋊Dic17—22no—
31C2×C22⋊Dic17D414yes—
32#10587502—26no—
33C24×C17—42no—
34C24×C17—82no—
35C24×C17C2×D411yescharacteristic
36C24×C17C2×D412yes—
37C24×C17C2×Q811yescharacteristic
38C24×C17#4112yes—
39C24×C17#4111yescharacteristic
40C22×C4×C17—22no—
41C22×C4×C17—42no—
42C22×Dic17—24no—
43C22×Dic17—22no—
44C22×Dic17—22no—
45C22×Dic17—22no—
46C22×Dic17—41no—
47C22×Dic17—82no—
48C2×Dic34—84no—
49C2×Dic34—82no—
50C22⋊C4×C17—42no—
51C22⋊C4×C17—44no—
52C22⋊C4×C17—82no—
53C22⋊C4×C17—82no—
54C22⋊C4×C17—82no—
55C22⋊Dic17—41no—
56C22⋊Dic17—41no—
57C22⋊Dic17—42no—
58C22⋊Dic17—44no—
59C22⋊Dic17—42no—
60C22⋊Dic17—82no—
61C22⋊Dic17—82no—
62C22⋊Dic17—82no—
63#10391—171nomaximal, Sylow
64C23×C17—22no—
65C23×C17—24no—
66C23×C17—42no—
67C23×C17—41no—
68C23×C17—42no—
69C23×C17—42no—
70C23×C17—42no—
71C23×C17—42no—
72C23×C17—42no—
73C23×C17—42no—
74C23×C17—42no—
75C23×C17—41no—
76C23×C17—88no—
77C23×C17#12011yescharacteristic
78C23×C17C22⋊Q812yes—
79C23×C17C22⋊Q811yescharacteristic
80C23×C17#12411yescharacteristic
81C23×C17#12412yes—
82C2×C4×C17—44no—
83C2×C4×C17—42no—
84C2×C4×C17—82no—
85C2×C4×C17—82no—
86C2×C4×C17—82no—
87C2×Dic17—44no—
88C2×Dic17—44no—
89C2×Dic17—42no—
90C2×Dic17—44no—
91C2×Dic17—82no—
92C2×Dic17—82no—
93C2×Dic17—82no—
94C2×Dic17—81no—
95C2×Dic17—82no—
96Dic34—88no—
97#2840—171no—
98#1819—172no—
99#1819—171no—
100#1304—172no—
101#1304D1711yescharacteristic
102C22×C17—22no—
103C22×C17—21no—
104C22×C17—22no—
105C22×C17—22no—
106C22×C17—21no—
107C22×C17—22no—
108C22×C17—22no—
109C22×C17—22no—
110C22×C17—22no—
111C22×C17—22no—
112C22×C17—22no—
113C22×C17—44no—
114C22×C17—82no—
115C22×C17—84no—
116C22×C17—84no—
117C22×C17—82no—
118C22×C17#39311yescharacteristic
119C22×C17#45812yes—
120C4×C17—82no—
121C4×C17—162no—
122Dic17—84no—
123Dic17—82no—
124Dic17—161no—
125C22×C22⋊C4—171no—
126#393—344no—
127#393—342no—
128#379—172no—
129#379—171no—
130#379C2×D1712yes—
131#379C2×D1711yescharacteristic
132#342—344no—
133#342—342no—
134C2×C17—22no—
135C2×C17—41no—
136C2×C17—42no—
137C2×C17—42no—
138C2×C17—41no—
139C2×C17#203011yescharacteristic
140C2×C17#203212yes—
141C25C22×D1711yescharacteristic
142C22×Q8—342no—
143C23×C4—172no—
144C2×C22⋊C4—22no—
145C2×C22⋊C4—22no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—22no—
148C2×C22⋊C4—174no—
149C2×C22⋊C4—341no—
150C2×C22⋊C4—342no—
151C2×C22⋊C4—342no—
152C2×C22⋊C4—341no—
153C2×C22⋊C4—341no—
154C2×C22⋊C4—342no—
155C2×C22⋊C4—342no—
156C2×C22⋊C4—342no—
157C2×C22⋊C4D6812yes—
158#95—346no—
159C17#1039111yescharacteristic, complemented, Sylow
160C24—42no—
161C24—82no—
162C24C2×D6811yescharacteristic
163C24#6325212yes—
164C24D4×D1712yes—
165C24#6325411yescharacteristic
166C24Q8×D1711yescharacteristic
167C2×Q8—1364no—
168C2×Q8—1362no—
169C22×C4—22no—
170C22×C4—42no—
171C22×C4—344no—
172C22×C4—342no—
173C22×C4—342no—
174C22×C4—342no—
175C22×C4—681no—
176C22×C4—1362no—
177C22⋊C4—42no—
178C22⋊C4—44no—
179C22⋊C4—82no—
180C22⋊C4—82no—
181C22⋊C4—82no—
182C22⋊C4—681no—
183C22⋊C4—681no—
184C22⋊C4—682no—
185C22⋊C4—684no—
186C22⋊C4—682no—
187C22⋊C4—1362no—
188C22⋊C4—1362no—
189C22⋊C4—1362no—
190C23—22no—
191C23—24no—
192C23—42no—
193C23—41no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—42no—
201C23—41no—
202C23—88no—
203C23#1058756111yescharacteristic
204C23#1058756811yescharacteristic
205C23#1058757112yes—
206C23#1058758212yes—
207C23#1058758311yescharacteristic
208Q8—1368no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4—684no—
215C2×C4—684no—
216C2×C4—682no—
217C2×C4—684no—
218C2×C4—1361no—
219C2×C4—1362no—
220C2×C4—1362no—
221C2×C4—1362no—
222C2×C4—1362no—
223C22—22no—
224C22—22no—
225C22—21no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—84no—
236C22—82no—
237C22—82no—
238C22—84no—
239C22#1176272211yescharacteristic
240C22#1176300012yes—
241C4—82no—
242C4—162no—
243C4—2721no—
244C4—1364no—
245C4—1362no—
246C2—22no—
247C2—42no—
248C2—41no—
249C2—42no—
250C2—41no—
251C2#1452995211yescharacteristic
252C2#1452996212yes—
subgroupG/H
centerC22#11762722
commutator, prime radical, cosocleC25×C17C23
FrattiniC25C22×D17
FittingC17×#1304C2
socleC22×C17#393
hypercenter#1304D17
hypocenterC17#10391
LCSG ▷ C25×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C25 ◁ #1304

Complements

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

NH ≅ G/Ntype
16. C23×Dic17Q8semidirect
159. C17#10391semidirect

Maximal subgroups

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

subgroupindex
#145370372
#145288562
#145266882
C17×#13042
#1039117