Finite Group Databasebeta

← #16930342

Subgroups — #16930342

Order 4352.

458 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 115 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#14534605C211yesmaximal, characteristic
2#14527470C212yesmaximal, complemented
3#14527098C211yesmaximal, characteristic
4#14526644C212yesmaximal, complemented
5C17×#2921C211yesmaximal, characteristic
6C2×#10587555C2211yescharacteristic
7#11762862C2212yes—
8#11762748C412yes—
9#11762745C412yes—
10#11762729—21no—
11#11762721—21no—
12#11762707—21no—
13#11762675C2211yescharacteristic
14#11762669—21no—
15#11762554—24no—
16#11762535—21no—
17#11762533—21no—
18C2×C17×#117C2211yescharacteristic
19C17×#433—24no—
20C17×#423C2212yes—
21C17×#407—21no—
22C4×M16×C17—21no—
23C23×C4×C17D411yescharacteristic
24C22×Dic34—21no—
25C2×M16×C17—22no—
26C17×#117—22no—
27C17×#117—22no—
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17D411yescharacteristic
30C2×C22⋊C4×C17C2×C411yescharacteristic
31C2×C22⋊C4×C17D411yescharacteristic
32C2×C42×C17D411yescharacteristic
33C2×C42×C17C2311yescharacteristic
34C2×C22⋊Dic17—22no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17C2×C412yes—
38C2×#63225—22no—
39#10587555—22no—
40#10587555—22no—
41C17×C4⋊C8—22no—
42C17×C4⋊C8D414yes—
43C17×C22⋊C8—24no—
44C17×#97—22no—
45C4×C8×C17—22no—
46#10587502—22no—
47#10587502—22no—
48#10587502—21no—
49#10587502C2×C412yes—
50C22⋊#3622—22no—
51C4⋊#3622—22no—
52C4×#3622—22no—
53C24×C17C22⋊C411yescharacteristic
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—22no—
57C22×C4×C17—22no—
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—
68M16×C17—42no—
69M16×C17—42no—
70C2×C8×C17—24no—
71C4⋊C4×C17—22no—
72C4⋊C4×C17—22no—
73C22⋊C4×C17—22no—
74C22⋊C4×C17—22no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17C2×D412yes—
78C42×C17#4112yes—
79C22⋊Dic17—82no—
80C4⋊Dic17—24no—
81C4⋊Dic17—41no—
82C4⋊Dic17—41no—
83C4⋊Dic17—42no—
84#63225—82no—
85C2×#3622—42no—
86#9194—171nomaximal, Sylow
87C23×C17—21no—
88C23×C17—21no—
89C23×C17—21no—
90C23×C17—41no—
91C23×C17—41no—
92C23×C17C2×C22⋊C411yescharacteristic
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17C4×D412yes—
105C2×C4×C17#12011yescharacteristic
106C2×C4×C17#12112yes—
107C2×C4×C17#12311yescharacteristic
108C2×C4×C17#13512yes—
109C2×C4×C17#13712yes—
110C2×Dic17—42no—
111C2×Dic17—42no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17—42no—
115C2×Dic17—42no—
116Dic34—84no—
117C8×C17—44no—
118#3622—82no—
119#2921D1711yescharacteristic
120#2628—171no—
121#1549—172no—
122#1458—171no—
123#1286—172no—
124C22×C17—21no—
125C22×C17—21no—
126C22×C17—42no—
127C22×C17—41no—
128C22×C17—41no—
129C22×C17—41no—
130C22×C17—81no—
131C22×C17#38611yescharacteristic
132C22×C17#41611yescharacteristic
133C22×C17#41911yescharacteristic
134C4×C17—22no—
135C4×C17—22no—
136C4×C17—41no—
137C4×C17—41no—
138C4×C17—41no—
139C4×C17#45212yes—
140C4×C17#48512yes—
141Dic17—82no—
142Dic17—82no—
143C2×C4⋊Q8—171no—
144C2×#117C2×D1711yescharacteristic
145#433—24no—
146#431—172no—
147#423C2×D1712yes—
148#407—21no—
149C4×M16—21no—
150#400—172no—
151#399—172no—
152#395—341no—
153#393—341no—
154#389—341no—
155#382—171no—
156#380—341no—
157#332—344no—
158#324—341no—
159#323—341no—
160C2×C17—21no—
161C2×C17—21no—
162C2×C17—81no—
163C2×C17#187311yescharacteristic
164C2×C17#191011yescharacteristic
165C2×C17#191511yescharacteristic
166C22×Q8—341no—
167C23×C4C22⋊D1711yescharacteristic
168C2×M16—22no—
169C4⋊Q8—342no—
170C4⋊Q8—342no—
171#117—22no—
172#117—22no—
173C2×C4⋊C4—172no—
174C2×C4⋊C4—341no—
175C2×C4⋊C4—341no—
176C2×C4⋊C4—342no—
177C2×C4⋊C4C4×D1711yescharacteristic
178C2×C4⋊C4D6811yescharacteristic
179C2×C22⋊C4—342no—
180C2×C22⋊C4C4×D1711yescharacteristic
181C2×C22⋊C4D6811yescharacteristic
182C2×C42C22⋊D1711yescharacteristic
183C2×C42C22×D1711yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—342no—
186C4⋊C8C22⋊D1714yes—
187C22⋊C8—24no—
188C22⋊C8—342no—
189#97—22no—
190C4×C8—22no—
191C4×C8—342no—
192#95—172no—
193#95—341no—
194#95—342no—
195#95—342no—
196C17#919411yescharacteristic, complemented, Sylow
197C24#6322711yescharacteristic
198C2×Q8—682no—
199C2×Q8—1362no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—342no—
205C22×C4—342no—
206C22×C4#6322711yescharacteristic
207C22×C4#6322711yescharacteristic
208C22×C4#6322711yescharacteristic
209C22×C4C2×C4×D1711yescharacteristic
210C22×C4C2×D6811yescharacteristic
211C22×C4C2×C22⋊D1711yescharacteristic
212M16—42no—
213M16—42no—
214C2×C8—24no—
215C2×C8—682no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—344no—
219C4⋊C4—681no—
220C4⋊C4—682no—
221C4⋊C4—681no—
222C4⋊C4—1362no—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—1362no—
226C42—21no—
227C42—21no—
228C42#6325212yes—
229C42C2×C22⋊D1712yes—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C2×#6322711yescharacteristic
236Q8—1364no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—682no—
249C2×C4—682no—
250C2×C4—682no—
251C2×C4—682no—
252C2×C4—682no—
253C2×C4—682no—
254C2×C4C4×C22⋊D1712yes—
255C2×C4#1058761511yescharacteristic
256C2×C4#1058761612yes—
257C2×C4#1058763612yes—
258C2×C4#1058763712yes—
259C2×C4#1058763911yescharacteristic
260C8—44no—
261C8—1362no—
262C22—21no—
263C22—21no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22#1176268811yescharacteristic
270C22#1176280311yescharacteristic
271C22#1176281711yescharacteristic
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—1362no—
278C4—1362no—
279C4#1176297112yes—
280C4#1176315012yes—
281C2—21no—
282C2—21no—
283C2—81no—
284C2#1452909611yescharacteristic
285C2#1452931111yescharacteristic
286C2#1452933611yescharacteristic
subgroupG/H
centerC22#11762688
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2921C2
socleC22×C17#386
prime radicalC24×C17C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2921D17
hypocenterC17#9194
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #14527470C2semidirect
4. #14526644C2semidirect
196. C17#9194semidirect

Maximal subgroups

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

subgroupindex
#145346052
#145274702
#145270982
#145266442
C17×#29212
#919417