Finite Group Databasebeta

← #16943988

Subgroups — #16943988

Order 4352.

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

normal subgroups only

This group has 358 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#14533996C211yesmaximal, characteristic
2#14527128C211yesmaximal, characteristic
3#14526727C214yesmaximal
4C17×#1461C211yesmaximal, characteristic
5C2×#10587555C411yescharacteristic
6#11762866—21no—
7#11762748—21no—
8#11762748—21no—
9#11762716C412yes—
10#11762715—21no—
11#11762715—21no—
12#11762674C2212yes—
13C4×C4⋊Dic17C411yescharacteristic
14#11762535—21no—
15#11762535C2212yes—
16C2×C4×Q8×C17C2211yescharacteristic
17C17×#431—21no—
18C17×#324—21no—
19C17×#324C2212yes—
20C22×Q8×C17C2×C411yescharacteristic
21C22×Dic34—21no—
22C4×Q8×C17—41no—
23C4×Q8×C17—41no—
24C2×C4⋊C4×C17D411yescharacteristic
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C4⋊C4×C17C2311yescharacteristic
27C2×C42×C17C2×C411yescharacteristic
28C2×C42×C17D411yescharacteristic
29C2×C42×C17D411yescharacteristic
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17C2×C412yes—
33C2×C4×Dic17C2×C412yes—
34#10587555—41no—
35#10587555—41no—
36C17×C4⋊C8—41no—
37C17×C22⋊C8—22no—
38C4×C8×C17—41no—
39#10587502—22no—
40#10587502—22no—
41#10587502—21no—
42#10587502—22no—
43#10587502—22no—
44C22⋊#3622—22no—
45C4⋊#3622—41no—
46#10587474—41no—
47C2×Q8×C17—22no—
48C2×Q8×C17—22no—
49C2×Q8×C17—41no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×C4×C17C2×D411yescharacteristic
56C22×C4×C17C2×D411yescharacteristic
57C22×Dic17—22no—
58C22×Dic17—22no—
59C2×Dic34—44no—
60C2×Dic34—41no—
61C2×Dic34—41no—
62C2×C8×C17—42no—
63C4⋊C4×C17—41no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C42×C17—21no—
67C42×C17—21no—
68C42×C17—21no—
69C42×C17—21no—
70C42×C17—21no—
71C42×C17—21no—
72C4⋊Dic17—42no—
73C4⋊Dic17—42no—
74C4⋊Dic17—42no—
75C4×Dic17—24no—
76C2×#3622—42no—
77#11573—171nomaximal, Sylow
78C23×C17C2×C22⋊C411yescharacteristic
79Q8×C17—44no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17—21no—
84C2×C4×C17—22no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—41no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17#9911yescharacteristic
95C2×C4×C17#9911yescharacteristic
96C2×C4×C17#10112yes—
97C2×C4×C17#13112yes—
98C2×Dic17—44no—
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103Dic34—82no—
104Dic34—82no—
105C8×C17—82no—
106#3622—82no—
107#2568—171no—
108#1467—171no—
109#1461D1711yescharacteristic
110#1324—174no—
111C22×C17—21no—
112C22×C17—21no—
113C22×C17#40811yescharacteristic
114C22×C17C2×#9911yescharacteristic
115C22×C17C2×#10111yescharacteristic
116C4×C17—21no—
117C4×C17—22no—
118C4×C17—22no—
119C4×C17—41no—
120C4×C17—41no—
121C4×C17—41no—
122C4×C17—41no—
123C4×C17#35512yes—
124Dic17—82no—
125Dic17—82no—
126C2×C4⋊Q8—171no—
127C2×C4×Q8C2×D1711yescharacteristic
128#432—341no—
129#431—21no—
130#400—341no—
131#400—341no—
132#391—172no—
133#391—341no—
134#391—341no—
135#382—172no—
136C4×C4⋊C4—171no—
137#324—21no—
138#324—172no—
139#324—341no—
140#324C2×D1712yes—
141C2×C17—21no—
142C2×C17—21no—
143C2×C17#147211yescharacteristic
144C2×C17#212911yescharacteristic
145C2×C17C2×#35511yescharacteristic
146C22×Q8—341no—
147C22×Q8C4×D1711yescharacteristic
148C4⋊Q8—681no—
149C4⋊Q8—681no—
150C4×Q8—41no—
151C4×Q8—41no—
152C2×C4⋊C4—172no—
153C2×C4⋊C4—341no—
154C2×C4⋊C4—341no—
155C2×C4⋊C4D6811yescharacteristic
156C2×C4⋊C4C22⋊D1711yescharacteristic
157C2×C4⋊C4C22×D1711yescharacteristic
158C2×C42—172no—
159C2×C42C4×D1711yescharacteristic
160C2×C42D6811yescharacteristic
161C2×C42C22⋊D1711yescharacteristic
162C4⋊C8—41no—
163C4⋊C8—681no—
164C22⋊C8—22no—
165C22⋊C8—342no—
166#97—681no—
167C4×C8—41no—
168#95—342no—
169#95—342no—
170#95—341no—
171#95—342no—
172#95—342no—
173C17#1157311yescharacteristic, complemented, Sylow
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—684no—
178C2×Q8—681no—
179C2×Q8—681no—
180C22×C4—342no—
181C22×C4—342no—
182C22×C4#6322711yescharacteristic
183C22×C4#6322711yescharacteristic
184C22×C4#6322711yescharacteristic
185C22×C4#6322711yescharacteristic
186C22×C4C2×C4×D1711yescharacteristic
187C22×C4C2×D6811yescharacteristic
188C22×C4C2×C22⋊D1711yescharacteristic
189C2×C8—42no—
190C2×C8—682no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—682no—
195C4⋊C4—682no—
196C4⋊C4—682no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—344no—
204C23C2×#6322711yescharacteristic
205Q8—44no—
206Q8—1362no—
207Q8—1362no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—682no—
223C2×C4—684no—
224C2×C4—682no—
225C2×C4—682no—
226C2×C4—682no—
227C2×C4#1058747711yescharacteristic
228C2×C4#1058747711yescharacteristic
229C2×C4#1058749512yes—
230C2×C4#1058758712yes—
231C8—82no—
232C8—1362no—
233C22—21no—
234C22—21no—
235C22#1176277511yescharacteristic
236C22C2×#1058747711yescharacteristic
237C22C2×#1058749511yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—1362no—
246C4—1362no—
247C4#1176260512yes—
248C2—21no—
249C2—21no—
250C2#1452714711yescharacteristic
251C2#1453045811yescharacteristic
252C2C2×#1176260511yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1461C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1461D17
hypocenterC17#11573
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
173. C17#11573semidirect

Maximal subgroups

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

subgroupindex
#145339962
#145271282
#145267272
C17×#14612
#1157317