Finite Group Databasebeta

← #16932168

Subgroups — #16932168

Order 4352.

474 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 131 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#14534146C211yesmaximal, characteristic
2#14528780C211yesmaximal, characteristic
3#14527214C212yesmaximal
4#14526643C212yesmaximal
5C17×#2982C211yesmaximal, characteristic
6C2×C4×Dic34C2211yescharacteristic
7#11762833C2212yes—
8C2×#10587507—21no—
9#11762748C412yes—
10#11762729C412yes—
11#11762716—21no—
12#11762705—21no—
13#11762693—22no—
14#11762675C2211yescharacteristic
15#11762578—21no—
16#11762541—24no—
17C2×C4×Q8×C17C2211yescharacteristic
18C8×Q8×C17—24no—
19C17×#431—22no—
20C17×#431C2212yes—
21C22×Q8×C17D411yescharacteristic
22C22×Dic34C2×C411yescharacteristic
23C4×Q8×C17—22no—
24C4×Q8×C17—22no—
25C2×C4⋊C4×C17C2×C412yes—
26C2×C4⋊C4×C17D411yescharacteristic
27C2×C42×C17D412yes—
28C2×C42×C17C2311yescharacteristic
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×#63225—22no—
32C2×#63225—21no—
33C2×C4×Dic17—21no—
34C2×#63223—22no—
35C4×Dic34—22no—
36C4×Dic34—22no—
37C17×C4⋊C8—24no—
38C17×C4⋊C8—22no—
39C17×C22⋊C8—22no—
40C4×C8×C17—24no—
41C4×C8×C17D414yes—
42#10587507—42no—
43#10587502—22no—
44#10587502—22no—
45#10587502—22no—
46#10587502—21no—
47#10587502C2×C412yes—
48C4⋊#3622—22no—
49C4⋊#3622—22no—
50C2×Q8×C17—22no—
51C2×Q8×C17—22no—
52C2×Q8×C17SD1612yes—
53C2×Q8×C17Q1612yes—
54C22×C4×C17C22⋊C412yes—
55C22×C4×C17C22⋊C412yes—
56C22×C4×C17C22×C411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×Dic17—21no—
60C22×Dic17—22no—
61C22×Dic17—21no—
62C2×Dic34—22no—
63C2×Dic34—42no—
64C2×C8×C17—24no—
65C4⋊C4×C17—24no—
66C4⋊C4×C17—22no—
67C42×C17—22no—
68C42×C17—22no—
69C42×C17C2×D412yes—
70C42×C17#4112yes—
71C4⋊Dic17—22no—
72C4⋊Dic17—42no—
73#63225—44no—
74#63225—41no—
75#63225—41no—
76C4×Dic17—42no—
77#63223—42no—
78#63223—42no—
79C2×#3622—42no—
80#9484—171nomaximal, Sylow
81C23×C17C2×C22⋊C411yescharacteristic
82Q8×C17—24no—
83Q8×C17—24no—
84C2×C4×C17—22no—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—42no—
90C2×C4×C17#10314yes—
91C2×C4×C17C4×D412yes—
92C2×C4×C17#12011yescharacteristic
93C2×C4×C17#12112yes—
94C2×C4×C17#12311yescharacteristic
95C2×C4×C17C2×SD1611yescharacteristic
96C2×C4×C17C2×Q1611yescharacteristic
97C2×C4×C17#13512yes—
98C2×Dic17—22no—
99C2×Dic17—41no—
100C2×Dic17—41no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103C2×Dic17—42no—
104C2×Dic17—41no—
105C2×Dic17—42no—
106Dic34—24no—
107Dic34—42no—
108C8×C17—44no—
109#3622—82no—
110#2982D1711yescharacteristic
111#2581—171no—
112#1801—171no—
113#1487—172no—
114#1286—172no—
115C22×C17—21no—
116C22×C17—21no—
117C22×C17#38611yescharacteristic
118C22×C17C2×#10311yescharacteristic
119C22×C17#41611yescharacteristic
120C4×C17—22no—
121C4×C17—24no—
122C4×C17—21no—
123C4×C17—21no—
124C4×C17—42no—
125C4×C17#46512yes—
126C4×C17#46712yes—
127Dic17—42no—
128Dic17—82no—
129Dic17—81no—
130C2×C4×Q8—171no—
131C2×C4×Q8C2×D1711yescharacteristic
132C8×Q8—24no—
133#431—22no—
134#431C2×D1712yes—
135#423—172no—
136C2×#101—341no—
137#400—172no—
138#395—172no—
139#391—341no—
140#389—341no—
141#387—342no—
142#382—171no—
143#343—341no—
144Q8⋊C8—344no—
145C2×C17—21no—
146C2×C17—21no—
147C2×C17#189111yescharacteristic
148C2×C17#189211yescharacteristic
149C2×C17#191211yescharacteristic
150C22×Q8—171no—
151C22×Q8D6811yescharacteristic
152C2×M16—342no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—342no—
156C4×Q8—342no—
157C2×C4⋊C4—171no—
158C2×C4⋊C4—341no—
159C2×C4⋊C4—341no—
160C2×C4⋊C4—342no—
161C2×C4⋊C4C4×D1712yes—
162C2×C4⋊C4D6811yescharacteristic
163C2×C42—341no—
164C2×C42C22⋊D1712yes—
165C2×C42C22×D1711yescharacteristic
166C4⋊C8—24no—
167C4⋊C8—22no—
168C4⋊C8—342no—
169C4⋊C8—342no—
170#101—682no—
171C22⋊C8—22no—
172C4×C8—24no—
173C4×C8C22⋊D1714yes—
174#95—172no—
175#95—341no—
176#95—342no—
177#95—342no—
178#95—342no—
179C17#948411yescharacteristic, complemented, Sylow
180C2×Q8—22no—
181C2×Q8—22no—
182C2×Q8—342no—
183C2×Q8—682no—
184C2×Q8#6321912yes—
185C2×Q8Dic6812yes—
186C22×C4—341no—
187C22×C4—342no—
188C22×C4—341no—
189C22×C4#6322712yes—
190C22×C4#6322712yes—
191C22×C4C2×C4×D1711yescharacteristic
192C22×C4C2×D6811yescharacteristic
193C22×C4C2×C22⋊D1711yescharacteristic
194M16—682no—
195M16—682no—
196C2×C8—24no—
197C2×C8—682no—
198C4⋊C4—24no—
199C4⋊C4—22no—
200C4⋊C4—342no—
201C4⋊C4—684no—
202C4⋊C4—682no—
203C4⋊C4—681no—
204C4⋊C4—681no—
205C42—22no—
206C42—22no—
207C42—682no—
208C42#6325212yes—
209C42C2×C22⋊D1712yes—
210C23C2×#6322711yescharacteristic
211Q8—24no—
212Q8—24no—
213Q8—344no—
214Q8—682no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—42no—
221C2×C4—342no—
222C2×C4—681no—
223C2×C4—681no—
224C2×C4—682no—
225C2×C4—682no—
226C2×C4—682no—
227C2×C4—681no—
228C2×C4—682no—
229C2×C4#1058748714yes—
230C2×C4C2×#6321911yescharacteristic
231C2×C4#1058759012yes—
232C2×C4C2×Dic6811yescharacteristic
233C2×C4C4×C22⋊D1712yes—
234C2×C4#1058761511yescharacteristic
235C2×C4#1058761612yes—
236C2×C4#1058763911yescharacteristic
237C8—44no—
238C8—1362no—
239C22—21no—
240C22—21no—
241C22#1176268811yescharacteristic
242C22C2×#1058748711yescharacteristic
243C22#1176280611yescharacteristic
244C4—21no—
245C4—21no—
246C4—22no—
247C4—24no—
248C4—42no—
249C4—682no—
250C4—1362no—
251C4—1361no—
252C4#1176303812yes—
253C4#1176305012yes—
254C2—21no—
255C2—21no—
256C2#1452920211yescharacteristic
257C2#1452920711yescharacteristic
258C2#1452932111yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2982C2
socleC22×C17#386
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2982D17
hypocenterC17#9484
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
179. C17#9484semidirect

Maximal subgroups

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

subgroupindex
#145341462
#145287802
#145272142
#145266432
C17×#29822
#948417