Finite Group Databasebeta

← #17958638

Subgroups — #17958638

Order 4352.

394 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 74 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#14544046C211yesmaximal, characteristic
2#14544026C211yesmaximal, characteristic
3#14543715C214yesmaximal
4#14533772C211yesmaximal, characteristic
5#11763830—21no—
6#11763826—21no—
7#11763655—21no—
8#11763655—21no—
9#11763654C2212yes—
10#11763654C2212yes—
11C2×#10587555C412yes—
12C2×#10587555C411yescharacteristic
13C2×C4×Dic34C2211yescharacteristic
14#11762741—21no—
15#11762741—21no—
16#11762715C2212yes—
17#11762708—21no—
18#11762708—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Dic34C2×C411yescharacteristic
21C22×Dic34C2×C412yes—
22C2×C4⋊C4×C17—21no—
23C2×C42×C17C2×C411yescharacteristic
24C2×C42×C17C2×C412yes—
25C2×C4⋊Dic17—21no—
26C2×C4⋊Dic17—21no—
27C2×C4⋊Dic17—22no—
28C2×C4⋊Dic17—22no—
29C2×C4⋊Dic17C2311yescharacteristic
30C2×#63225D411yescharacteristic
31C2×#63225D411yescharacteristic
32C2×C4×Dic17D411yescharacteristic
33C2×C4×Dic17D411yescharacteristic
34#10587555—41no—
35#10587555—41no—
36#10587555—44no—
37C4×Dic34—41no—
38C4×Dic34—41no—
39C22⋊#3624—22no—
40C22⋊#3624—22no—
41#10587544—41no—
42#10587542—41no—
43C4⋊#3624—41no—
44C4×#3624—41no—
45C17×#95—21no—
46#10587502—22no—
47#10587502—22no—
48C22×C4×C17—22no—
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22×C411yescharacteristic
52C22×Dic17—22no—
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C2×Dic34—22no—
58C2×Dic34—22no—
59C2×Dic34—24no—
60C2×Dic34—41no—
61C2×Dic34—42no—
62C2×Dic34—42no—
63C2×#3624—42no—
64C2×#3624—42no—
65C4⋊C4×C17—24no—
66C42×C17—21no—
67C42×C17—21no—
68C42×C17—42no—
69C4⋊Dic17—41no—
70C4⋊Dic17—44no—
71C4⋊Dic17—42no—
72C4⋊Dic17—41no—
73C4⋊Dic17—41no—
74C4⋊Dic17—44no—
75#63225—41no—
76#63225—41no—
77C4×Dic17—21no—
78C4×Dic17—21no—
79C4×Dic17—21no—
80C4×Dic17—21no—
81#11568—171nomaximal, Sylow
82C23×C17C2×C22⋊C411yescharacteristic
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—24no—
87C2×C4×C17—21no—
88C2×C4×C17—42no—
89C2×C4×C17—42no—
90C2×C4×C17—41no—
91C2×C4×C17#9911yescharacteristic
92C2×C4×C17#9911yescharacteristic
93C2×C4×C17#13112yes—
94C2×Dic17—21no—
95C2×Dic17—21no—
96C2×Dic17—21no—
97C2×Dic17—21no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17—42no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17#10012yes—
107Dic34—44no—
108Dic34—84no—
109#3624—82no—
110#3624—82no—
111#2546—171no—
112#1467—171no—
113#1461—171no—
114#1319—174no—
115C22×C17—21no—
116C22×C17—21no—
117C22×C17#40811yescharacteristic
118C22×C17C2×#9911yescharacteristic
119C22×C17C2×#10011yescharacteristic
120C4×C17—21no—
121C4×C17—22no—
122C4×C17—44no—
123C4×C17—41no—
124C4×C17#35612yes—
125Dic17—22no—
126Dic17—41no—
127Dic17—41no—
128Dic17—41no—
129Dic17—82no—
130C2×C4⋊Q8—172no—
131C2×C4⋊Q8—171no—
132C2×C4×Q8—171no—
133#432—341no—
134#431—341no—
135#398—341no—
136#398—341no—
137#391—172no—
138#389—341no—
139#389—341no—
140C4×C4⋊C4#59511yescharacteristic
141#324—172no—
142#324—172no—
143#324—341no—
144#324—341no—
145C2×C17—21no—
146C2×C17—21no—
147C2×C17#147111yescharacteristic
148C2×C17#212911yescharacteristic
149C2×C17C2×#35611yescharacteristic
150C22×Q8—171no—
151C22×Q8—172no—
152C4⋊Q8—681no—
153C4⋊Q8—681no—
154C4⋊Q8—684no—
155C4×Q8—681no—
156C4×Q8—681no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—171no—
159C2×C4⋊C4—171no—
160C2×C4⋊C4—171no—
161C2×C4⋊C4—342no—
162C2×C4⋊C4—342no—
163C2×C4⋊C4—341no—
164C2×C4⋊C4—341no—
165C2×C42—171no—
166C2×C42—171no—
167C2×C42C2×#59512yes—
168C2×C42C2×#59511yescharacteristic
169C4⋊C8—681no—
170C4⋊C8—681no—
171C22⋊C8—342no—
172C22⋊C8—342no—
173#97—681no—
174C4×C8—681no—
175#95—21no—
176#95—342no—
177#95—342no—
178C17#1156811yescharacteristic, complemented, Sylow
179C2×Q8—342no—
180C2×Q8—342no—
181C2×Q8—344no—
182C2×Q8—681no—
183C2×Q8—682no—
184C2×Q8—682no—
185C22×C4—22no—
186C22×C4—171no—
187C22×C4—171no—
188C22×C4—171no—
189C22×C4—171no—
190C22×C4—342no—
191C22×C4C22⋊#59511yescharacteristic
192C22×C4C22⋊#59511yescharacteristic
193C22×C4C22×#59511yescharacteristic
194C2×C8—682no—
195C2×C8—682no—
196C4⋊C4—24no—
197C4⋊C4—681no—
198C4⋊C4—681no—
199C4⋊C4—681no—
200C4⋊C4—682no—
201C4⋊C4—684no—
202C4⋊C4—684no—
203C4⋊C4—681no—
204C4⋊C4—681no—
205C42—21no—
206C42—21no—
207C42—42no—
208C42—341no—
209C42—341no—
210C42—341no—
211C42—341no—
212C23C2×C22⋊#59511yescharacteristic
213Q8—684no—
214Q8—1364no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—172no—
224C2×C4—341no—
225C2×C4—341no—
226C2×C4—341no—
227C2×C4—341no—
228C2×C4—341no—
229C2×C4—341no—
230C2×C4—341no—
231C2×C4—681no—
232C2×C4—681no—
233C2×C4—682no—
234C2×C4—682no—
235C2×C4—682no—
236C2×C4#1058753911yescharacteristic
237C2×C4#1058753911yescharacteristic
238C2×C4#1058768012yes—
239C8—1362no—
240C8—1362no—
241C22—21no—
242C22—21no—
243C22#1176378411yescharacteristic
244C22C2×#1058753911yescharacteristic
245C22D17⋊#10011yescharacteristic
246C4—21no—
247C4—22no—
248C4—44no—
249C4—41no—
250C4—342no—
251C4—681no—
252C4—681no—
253C4—681no—
254C4—1362no—
255C4#1176372012yes—
256C2—21no—
257C2—21no—
258C2#1454406111yescharacteristic
259C2#1454506811yescharacteristic
260C2C2×#1176372011yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#11568
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
178. C17#11568semidirect

Maximal subgroups

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

subgroupindex
#145440462
#145440262
#145437152
#145337722
#1156817