Finite Group Databasebeta

← #16932018

Subgroups — #16932018

Order 4352.

448 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 107 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#14533989C211yesmaximal, characteristic
2#14527500C212yesmaximal
3#14527128C211yesmaximal, characteristic
4#14526641C212yesmaximal
5C17×#2983C211yesmaximal, characteristic
6C2×#10587555C2211yescharacteristic
7#11762866C2212yes—
8#11762729—21no—
9#11762729—21no—
10#11762716C412yes—
11#11762707—21no—
12#11762707—21no—
13#11762678C412yes—
14C4×C4⋊Dic17C2211yescharacteristic
15#11762554—24no—
16#11762535—21no—
17#11762535—21no—
18C2×C4×Q8×C17C2211yescharacteristic
19C17×#446—24no—
20C17×#432—21no—
21C17×#432C2212yes—
22C17×#431—21no—
23C22×Q8×C17C2×C411yescharacteristic
24C22×Dic34—21no—
25C4×Q8×C17—22no—
26C4×Q8×C17—22no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17D411yescharacteristic
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C42×C17D411yescharacteristic
31C2×C42×C17D411yescharacteristic
32C2×C42×C17C2311yescharacteristic
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17C2×C412yes—
36C2×#63225—22no—
37C2×#63225—22no—
38C2×C4×Dic17C2×C412yes—
39#10587555—22no—
40#10587555—22no—
41C17×C4⋊C8—22no—
42C17×C4⋊C8—22no—
43C17×C4⋊C8D414yes—
44C17×C22⋊C8—22no—
45C17×#97—22no—
46C17×#97—22no—
47C4×C8×C17—22no—
48#10587502—22no—
49#10587502—22no—
50#10587502—21no—
51C22⋊#3622—22no—
52C4⋊#3622—22no—
53#10587474—22no—
54C2×Q8×C17—22no—
55C2×Q8×C17—22no—
56C2×Q8×C17—41no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22×C411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C22×Dic17—22no—
65C22×Dic17—22no—
66C2×Dic34—42no—
67C2×Dic34—82no—
68C2×C8×C17—24no—
69C4⋊C4×C17—22no—
70C4⋊C4×C17—22no—
71C4⋊C4×C17—22no—
72C42×C17—21no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—21no—
76C42×C17C2×D412yes—
77C42×C17#4112yes—
78C4⋊Dic17—24no—
79C4⋊Dic17—24no—
80C4⋊Dic17—41no—
81C4⋊Dic17—41no—
82#63225—82no—
83#63225—82no—
84C4×Dic17—42no—
85C2×#3622—42no—
86#9454—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88Q8×C17—44no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—22no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17#10112yes—
103C2×C4×C17C4×D412yes—
104C2×C4×C17#12011yescharacteristic
105C2×C4×C17#12112yes—
106C2×C4×C17#12311yescharacteristic
107C2×Dic17—24no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—42no—
112C2×Dic17—42no—
113Dic34—84no—
114C8×C17—44no—
115#3622—82no—
116#2983D1711yescharacteristic
117#2567—171no—
118#1556—172no—
119#1467—171no—
120#1285—172no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17#38611yescharacteristic
124C22×C17C2×#10111yescharacteristic
125C22×C17#41311yescharacteristic
126C4×C17—21no—
127C4×C17—22no—
128C4×C17—22no—
129C4×C17—22no—
130C4×C17—41no—
131C4×C17—41no—
132C4×C17—41no—
133C4×C17#45612yes—
134Dic17—44no—
135Dic17—82no—
136C2×C4⋊Q8—171no—
137C2×C4×Q8C2×D1711yescharacteristic
138#446—24no—
139#432—21no—
140#432—172no—
141#432C2×D1712yes—
142#431—21no—
143#395—341no—
144#395—341no—
145#391—172no—
146#389—341no—
147#389—341no—
148#384—172no—
149C4×C4⋊C4—171no—
150#332—344no—
151#324—341no—
152#324—341no—
153C2×C17—21no—
154C2×C17—21no—
155C2×C17#188611yescharacteristic
156C2×C17#190111yescharacteristic
157C2×C17#191011yescharacteristic
158C22×Q8—341no—
159C22×Q8C4×D1711yescharacteristic
160C4⋊Q8—342no—
161C4⋊Q8—342no—
162C4×Q8—22no—
163C4×Q8—22no—
164C2×C4⋊C4—172no—
165C2×C4⋊C4—341no—
166C2×C4⋊C4—341no—
167C2×C4⋊C4—342no—
168C2×C4⋊C4—342no—
169C2×C4⋊C4C4×D1711yescharacteristic
170C2×C4⋊C4D6811yescharacteristic
171C2×C4⋊C4D6811yescharacteristic
172C2×C42—172no—
173C2×C42C22⋊D1711yescharacteristic
174C2×C42C22⋊D1711yescharacteristic
175C2×C42C22×D1711yescharacteristic
176C4⋊C8—22no—
177C4⋊C8—22no—
178C4⋊C8—342no—
179C4⋊C8C22⋊D1714yes—
180C22⋊C8—22no—
181C22⋊C8—342no—
182#97—22no—
183#97—22no—
184#97—342no—
185C4×C8—22no—
186#95—341no—
187#95—342no—
188#95—342no—
189C17#945411yescharacteristic, complemented, Sylow
190C2×Q8—22no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—682no—
194C2×Q8—1362no—
195C22×C4—342no—
196C22×C4—342no—
197C22×C4#6322711yescharacteristic
198C22×C4#6322711yescharacteristic
199C22×C4#6322711yescharacteristic
200C22×C4#6322711yescharacteristic
201C22×C4C2×C4×D1711yescharacteristic
202C22×C4C2×D6811yescharacteristic
203C22×C4C2×C22⋊D1711yescharacteristic
204C2×C8—24no—
205C2×C8—682no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—22no—
209C4⋊C4—344no—
210C4⋊C4—344no—
211C4⋊C4—681no—
212C4⋊C4—681no—
213C4⋊C4—1362no—
214C4⋊C4—1362no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—682no—
220C42#6325212yes—
221C42C2×C22⋊D1712yes—
222C23C2×#6322711yescharacteristic
223Q8—44no—
224Q8—1364no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—344no—
239C2×C4—682no—
240C2×C4—682no—
241C2×C4—682no—
242C2×C4—682no—
243C2×C4—682no—
244C2×C4#1058749512yes—
245C2×C4C4×C22⋊D1712yes—
246C2×C4#1058761511yescharacteristic
247C2×C4#1058761612yes—
248C2×C4#1058763911yescharacteristic
249C8—44no—
250C8—1362no—
251C22—21no—
252C22—21no—
253C22#1176268811yescharacteristic
254C22C2×#1058749511yescharacteristic
255C22#1176279111yescharacteristic
256C4—22no—
257C4—21no—
258C4—22no—
259C4—22no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—684no—
264C4—1362no—
265C4#1176299212yes—
266C2—21no—
267C2—21no—
268C2#1452917711yescharacteristic
269C2#1452925211yescharacteristic
270C2#1452931111yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2983C2
socleC22×C17#386
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2983D17
hypocenterC17#9454
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
189. C17#9454semidirect

Maximal subgroups

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

subgroupindex
#145339892
#145275002
#145271282
#145266412
C17×#29832
#945417