Finite Group Databasebeta

← #16923629

Subgroups — #16923629

Order 4352.

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

normal subgroups only

This group has 494 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#14530322C211yesmaximal, characteristic, complemented
2#14530317C212yesmaximal, complemented
3#14526610C211yesmaximal, characteristic, complemented
4#14526605C212yesmaximal, complemented
5C17×#2733C211yesmaximal, characteristic
6C2×#10587478—21no—
7C2×#10587479—22no—
8C2×#10587506—21no—
9C2×#10587503—22no—
10#11762679C2211yescharacteristic
11#11762564C2212yes—
12#11762564C2211yescharacteristic
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—22no—
36C22×#3622—21no—
37C17×#95—21no—
38C17×#95—22no—
39#10587506—42no—
40#10587503—44no—
41#10587479—44no—
42#10587478—42no—
43C24×C17—22no—
44C2×Q8×C17—21no—
45C2×Q8×C17—41no—
46C2×Q8×C17—41no—
47C2×Q8×C17SD1612yes—
48C2×D4×C17—22no—
49C2×D4×C17—22no—
50C2×D4×C17—42no—
51C2×D4×C17—42no—
52C2×D4×C17—42no—
53C2×D4×C17—81no—
54C2×D4×C17—81no—
55C2×D4×C17—82no—
56C2×D4×C17—81no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17—22no—
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17C2×D412yes—
62C22×Dic17—41no—
63C4⋊C4×C17—41no—
64C4⋊C4×C17—42no—
65C22⋊C4×C17—44no—
66C22⋊C4×C17—42no—
67C22⋊C4×C17—42no—
68C22⋊C4×C17—42no—
69C22⋊C4×C17—42no—
70C22⋊C4×C17—82no—
71C42×C17—41no—
72C42×C17—42no—
73C4⋊Dic17—41no—
74C4⋊Dic17—42no—
75C4⋊Dic17—42no—
76C4⋊Dic17—41no—
77C2×#3622—22no—
78C2×#3622—24no—
79C2×#3622—42no—
80C2×#3622—41no—
81C2×#3622—42no—
82C2×#3622—41no—
83#7830—171nomaximal, Sylow
84C23×C17—42no—
85C23×C17—42no—
86C23×C17—42no—
87C23×C17—42no—
88C23×C17—42no—
89C23×C17—42no—
90C23×C17—42no—
91C23×C17#12011yescharacteristic
92Q8×C17—42no—
93Q8×C17—81no—
94D4×C17—44no—
95D4×C17—82no—
96D4×C17—84no—
97D4×C17—84no—
98C2×C4×C17—22no—
99C2×C4×C17—21no—
100C2×C4×C17—22no—
101C2×C4×C17—21no—
102C2×C4×C17—22no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—41no—
110C2×C4×C17C2×SD1611yescharacteristic
111C2×C4×C17#13512yes—
112C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C17#13712yes—
114C2×Dic17—81no—
115C2×Dic17—82no—
116#3622—42no—
117#3622—44no—
118#2733D1711yescharacteristic
119#2095—171no—
120#2094—172no—
121#1272—171no—
122#1270—172no—
123C22×C17—82no—
124C22×C17—82no—
125C22×C17—82no—
126C22×C17—82no—
127C22×C17—82no—
128C22×C17—82no—
129C22×C17—82no—
130C22×C17#45011yescharacteristic
131C22×C17#45212yes—
132C22×C17#45311yescharacteristic
133C22×C17#45312yes—
134C22×C17#45811yescharacteristic
135C4×C17—21no—
136C4×C17—21no—
137C4×C17—22no—
138C4×C17—22no—
139C4×C17—42no—
140C4×C17—82no—
141C4×C17—81no—
142Dic17—161no—
143C2×#124—21no—
144C2×#107—341no—
145C2×#106—342no—
146C2×#103—341no—
147C2×#102—342no—
148#394—21no—
149#392—22no—
150#391C2×D1711yescharacteristic
151#390C2×D1712yes—
152#388—22no—
153#384—171no—
154#336—172no—
155#336—171no—
156C2×C17—162no—
157C2×C17#161311yescharacteristic
158C2×C17#161812yes—
159C2×C17#163112yes—
160C2×C17#163411yescharacteristic
161C2×C17#165511yescharacteristic
162C22×Q8C22⋊D1711yescharacteristic
163C22×D4—21no—
164C22×D4—21no—
165C22×D4C22⋊D1712yes—
166C22×C8—342no—
167C22×C8—341no—
168#124—42no—
169#124—42no—
170C2×C4⋊C4—342no—
171C2×C4⋊C4—341no—
172C2×C4⋊C4C22⋊D1712yes—
173C2×C4⋊C4C22⋊D1711yescharacteristic
174C2×C22⋊C4—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C42—21no—
179C2×C42C22×D1711yescharacteristic
180#107—682no—
181#106—684no—
182#103—682no—
183#102—684no—
184#95—21no—
185#95—22no—
186C17#783011yescharacteristic, complemented, Sylow
187C24—22no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8#6322912yes—
192C2×D4—22no—
193C2×D4—22no—
194C2×D4—42no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—81no—
198C2×D4—81no—
199C2×D4—82no—
200C2×D4—81no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—681no—
205C22×C4C2×C22⋊D1711yescharacteristic
206C22×C4C2×C22⋊D1712yes—
207C2×C8—344no—
208C2×C8—342no—
209C2×C8—682no—
210C2×C8—681no—
211C2×C8—681no—
212C2×C8—682no—
213C4⋊C4—42no—
214C4⋊C4—41no—
215C4⋊C4—682no—
216C4⋊C4—681no—
217C4⋊C4—682no—
218C4⋊C4—681no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—82no—
225C42—41no—
226C42—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23#1058763911yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—44no—
238D4—82no—
239D4—84no—
240D4—84no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—1361no—
254C2×C4—1362no—
255C2×C4#1058761811yescharacteristic
256C2×C4C2×#6322911yescharacteristic
257C2×C4#1058763612yes—
258C2×C4#1058763712yes—
259C8—682no—
260C8—684no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22#1176296011yescharacteristic
269C22#1176297112yes—
270C22#1176297711yescharacteristic
271C22#1176297712yes—
272C22#1176299911yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—81no—
279C4—82no—
280C4—2721no—
281C2—162no—
282C2#1452780411yescharacteristic
283C2#1452783212yes—
284C2#1452791112yes—
285C2#1452792911yescharacteristic
286C2#1452807311yescharacteristic
subgroupG/H
centerC23#10587639
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
Fitting, prime radicalC17×#2733C2
socleC23×C17#120
hypercenter#2733D17
hypocenterC17#7830
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. #14530322C2semidirect
2. #14530317C2semidirect
3. #14526610C2semidirect
4. #14526605C2semidirect
186. C17#7830semidirect

Maximal subgroups

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

subgroupindex
#145303222
#145303172
#145266102
#145266052
C17×#27332
#783017