Finite Group Databasebeta

← #16923509

Subgroups — #16923509

Order 4352.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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#14530327C211yesmaximal, characteristic, complemented
2#14530187C212yesmaximal, complemented
3#14526610C211yesmaximal, characteristic, complemented
4#14526605C212yesmaximal, complemented
5C17×#2733C211yesmaximal, characteristic
6C2×#10587479—21no—
7C2×#10587506—21no—
8C2×#10587503—22no—
9#11762679C2211yescharacteristic
10#11762571—22no—
11#11762564C2211yescharacteristic
12#11762564C2212yes—
13C2×C17×#124—21no—
14C17×#394—21no—
15C17×#392—22no—
16C17×#391C2211yescharacteristic
17C17×#390C2212yes—
18C17×#388—22no—
19C22×Q8×C17D411yescharacteristic
20C22×D4×C17—21no—
21C22×D4×C17—21no—
22C22×D4×C17D412yes—
23C17×#124—42no—
24C17×#124—42no—
25C2×C4⋊C4×C17D412yes—
26C2×C4⋊C4×C17D411yescharacteristic
27C2×C22⋊C4×C17—22no—
28C2×C22⋊C4×C17—22no—
29C2×C22⋊C4×C17—22no—
30C2×C22⋊C4×C17—22no—
31C2×C42×C17—21no—
32C2×C42×C17C2311yescharacteristic
33C2×C4⋊Dic17—22no—
34C2×C4⋊Dic17—21no—
35C22×#3622—21no—
36C22×#3622—22no—
37C17×#95—21no—
38C17×#95—22no—
39#10587506—42no—
40#10587503—44no—
41#10587479—42no—
42C24×C17—22no—
43C2×Q8×C17—21no—
44C2×Q8×C17—41no—
45C2×Q8×C17—41no—
46C2×Q8×C17SD1612yes—
47C2×D4×C17—22no—
48C2×D4×C17—22no—
49C2×D4×C17—42no—
50C2×D4×C17—42no—
51C2×D4×C17—42no—
52C2×D4×C17—81no—
53C2×D4×C17—81no—
54C2×D4×C17—81no—
55C2×D4×C17—82no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—22no—
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17C2×D412yes—
61C22×Dic17—41no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—42no—
64C22⋊C4×C17—44no—
65C22⋊C4×C17—42no—
66C22⋊C4×C17—42no—
67C22⋊C4×C17—42no—
68C22⋊C4×C17—42no—
69C22⋊C4×C17—82no—
70C42×C17—41no—
71C42×C17—42no—
72C4⋊Dic17—41no—
73C4⋊Dic17—41no—
74C4⋊Dic17—42no—
75C4⋊Dic17—42no—
76C2×#3622—22no—
77C2×#3622—41no—
78C2×#3622—41no—
79C2×#3622—42no—
80C2×#3622—42no—
81C2×#3622—42no—
82#7810—171nomaximal, Sylow
83C23×C17—42no—
84C23×C17—42no—
85C23×C17—42no—
86C23×C17—42no—
87C23×C17—42no—
88C23×C17—42no—
89C23×C17—42no—
90C23×C17#12011yescharacteristic
91Q8×C17—42no—
92Q8×C17—81no—
93D4×C17—44no—
94D4×C17—82no—
95D4×C17—84no—
96D4×C17—84no—
97C2×C4×C17—21no—
98C2×C4×C17—22no—
99C2×C4×C17—22no—
100C2×C4×C17—21no—
101C2×C4×C17—22no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—41no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17C2×SD1611yescharacteristic
110C2×C4×C17#13512yes—
111C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C17AGL(1,ℤ/8)12yes—
113C2×Dic17—82no—
114C2×Dic17—81no—
115#3622—42no—
116#3622—82no—
117#2733D1711yescharacteristic
118#2096—171no—
119#2071—172no—
120#1272—171no—
121#1270—172no—
122C22×C17—82no—
123C22×C17—82no—
124C22×C17—82no—
125C22×C17—82no—
126C22×C17—82no—
127C22×C17—82no—
128C22×C17—82no—
129C22×C17#44912yes—
130C22×C17#45011yescharacteristic
131C22×C17#45311yescharacteristic
132C22×C17#45512yes—
133C22×C17#45811yescharacteristic
134C4×C17—22no—
135C4×C17—22no—
136C4×C17—21no—
137C4×C17—21no—
138C4×C17—42no—
139C4×C17—82no—
140C4×C17—81no—
141Dic17—161no—
142C2×#124—21no—
143C2×#106—341no—
144C2×#103—341no—
145C2×#102—342no—
146#394—21no—
147#392—22no—
148#391C2×D1711yescharacteristic
149#390C2×D1712yes—
150#388—22no—
151#384—171no—
152#340—342no—
153#336—172no—
154#336—171no—
155C2×C17—162no—
156C2×C17#161212yes—
157C2×C17#161311yescharacteristic
158C2×C17#162411yescharacteristic
159C2×C17#164212yes—
160C2×C17#165911yescharacteristic
161C22×Q8C22⋊D1711yescharacteristic
162C22×D4—21no—
163C22×D4—21no—
164C22×D4C22⋊D1712yes—
165C22×C8—341no—
166C22×C8—342no—
167#124—42no—
168#124—42no—
169C2×C4⋊C4—342no—
170C2×C4⋊C4—341no—
171C2×C4⋊C4C22⋊D1712yes—
172C2×C4⋊C4C22⋊D1711yescharacteristic
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C42—21no—
178C2×C42C22×D1711yescharacteristic
179#106—682no—
180#103—682no—
181#102—684no—
182#95—21no—
183#95—22no—
184C17#781011yescharacteristic, complemented, Sylow
185C24—22no—
186C2×Q8—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8#6322912yes—
190C2×D4—22no—
191C2×D4—22no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—42no—
195C2×D4—81no—
196C2×D4—81no—
197C2×D4—81no—
198C2×D4—82no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—681no—
203C22×C4C2×C22⋊D1711yescharacteristic
204C22×C4C2×C22⋊D1712yes—
205C2×C8—342no—
206C2×C8—681no—
207C2×C8—681no—
208C2×C8—682no—
209C2×C8—682no—
210C2×C8—682no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—681no—
214C4⋊C4—681no—
215C4⋊C4—682no—
216C4⋊C4—682no—
217C22⋊C4—44no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—82no—
223C42—41no—
224C42—42no—
225C23—42no—
226C23—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23#1058763911yescharacteristic
233Q8—42no—
234Q8—81no—
235D4—44no—
236D4—82no—
237D4—84no—
238D4—84no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—1362no—
252C2×C4—1361no—
253C2×C4#1058761811yescharacteristic
254C2×C4C2×#6322911yescharacteristic
255C2×C4#1058763512yes—
256C2×C4#1058763612yes—
257C8—682no—
258C8—1362no—
259C22—82no—
260C22—82no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22#1176295412yes—
267C22#1176296011yescharacteristic
268C22#1176297711yescharacteristic
269C22#1176298712yes—
270C22#1176299911yescharacteristic
271C4—22no—
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—81no—
277C4—82no—
278C4—2721no—
279C2—162no—
280C2#1452779812yes—
281C2#1452780411yescharacteristic
282C2#1452786711yescharacteristic
283C2#1452798412yes—
284C2#1452809011yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
Fitting, prime radicalC17×#2733C2
socleC23×C17#120
hypercenter#2733D17
hypocenterC17#7810
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #14530327C2semidirect
2. #14530187C2semidirect
3. #14526610C2semidirect
4. #14526605C2semidirect
184. C17#7810semidirect

Maximal subgroups

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

subgroupindex
#145303272
#145301872
#145266102
#145266052
C17×#27332
#781017