Finite Group Databasebeta

← #16949510

Subgroups — #16949510

Order 4352.

464 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×#11762608C212yesmaximal
2C4×#10587507C212yesmaximal
3#14526911C212yesmaximal
4C17×#2327C211yesmaximal, characteristic
5C2×#10587507C2214yes—
6C4×#63223—22no—
7#11762608C418yescomplemented
8#11762578—22no—
9C2×C17×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C17C411yescharacteristic
11C2×C4×Q8×C17C2211yescharacteristic
12C17×#391C411yescharacteristic
13C17×#391C2211yescharacteristic
14C17×#387—22no—
15C17×#387—22no—
16C17×#382C411yescharacteristic
17C17×#376C411yescharacteristic
18C22×Q8×C17C2×C411yescharacteristic
19C22×Q8×C17C2311yescharacteristic
20C17×C4⋊Q8—22no—
21C17×C4⋊Q8C2×C414yes—
22C4×Q8×C17—42no—
23C4×Q8×C17—42no—
24C2×C4⋊C4×C17—22no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17D412yes—
29C2×C42×C17—21no—
30C2×C42×C17C2×C411yescharacteristic
31C2×C42×C17C2×C411yescharacteristic
32C2×C42×C17C2×C411yescharacteristic
33C2×C42×C17D412yes—
34C2×#63223—24no—
35C17×#95—21no—
36C17×#95—21no—
37C17×#95—22no—
38C17×#95—22no—
39C17×#95—22no—
40#10587507—24no—
41#10587507C2×C418yes—
42#10587474—42no—
43C4×#3622—42no—
44C2×Q8×C17—21no—
45C2×Q8×C17—41no—
46C2×Q8×C17—41no—
47C2×Q8×C17—41no—
48C2×Q8×C17—41no—
49C2×Q8×C17C4212yes—
50C2×Q8×C17C22×C412yes—
51C2×Q8×C17#4112yes—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17C22⋊C412yes—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22×C411yescharacteristic
60C22×C4×C17C2×D412yes—
61C4⋊C4×C17—28no—
62C4⋊C4×C17—41no—
63C4⋊C4×C17—42no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—42no—
66C42×C17—22no—
67C42×C17—22no—
68C42×C17—22no—
69C42×C17—21no—
70C42×C17—41no—
71C42×C17—42no—
72C42×C17C4212yes—
73#63223—28no—
74#63223—44no—
75C2×#3622—44no—
76#12631—171nomaximal, Sylow
77C23×C17C2×C22⋊C411yescharacteristic
78Q8×C17—42no—
79Q8×C17—42no—
80Q8×C17—42no—
81Q8×C17—42no—
82C2×C4×C17—21no—
83C2×C4×C17—22no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—22no—
88C2×C4×C17—21no—
89C2×C4×C17—22no—
90C2×C4×C17—41no—
91C2×C4×C17—41no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—42no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—42no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17#9912yes—
103C2×C4×C17C2×C4211yescharacteristic
104C2×C4×C17#11711yescharacteristic
105C2×C4×C17C4×D414yes—
106#3622—48no—
107#2327D1711yescharacteristic
108C2×#356—172no—
109C4×#101—172no—
110#1394—172no—
111C22×C17—21no—
112C22×C17—21no—
113C22×C17C4×C22⋊C411yescharacteristic
114C22×C17C2×#9911yescharacteristic
115C22×C17#41011yescharacteristic
116C4×C17—22no—
117C4×C17—24no—
118C4×C17—21no—
119C4×C17—21no—
120C4×C17—42no—
121C4×C17—41no—
122C4×C17—42no—
123C4×C17—42no—
124C4×C17—81no—
125C4×C17—81no—
126C2×C4⋊Q8C2×D1711yescharacteristic
127C2×C4×Q8Dic1711yescharacteristic
128C2×C4×Q8C2×D1711yescharacteristic
129C2×#101—174no—
130C4×M16—342no—
131#391Dic1711yescharacteristic
132#391C2×D1711yescharacteristic
133#387—22no—
134#387—22no—
135#382Dic1711yescharacteristic
136#376Dic1711yescharacteristic
137#356—178no—
138#343—342no—
139C2×C17—21no—
140C2×C17—21no—
141C2×C17C4×#9911yescharacteristic
142C2×C17#213311yescharacteristic
143C2×C17#213511yescharacteristic
144C22×Q8C2×Dic1711yescharacteristic
145C22×Q8C22×D1711yescharacteristic
146C2×M16—344no—
147C4⋊Q8—22no—
148C4⋊Q8C4×D1714yes—
149C4×Q8—42no—
150C4×Q8—42no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4C2×Dic1711yescharacteristic
154C2×C4⋊C4C2×Dic1711yescharacteristic
155C2×C4⋊C4C22⋊D1712yes—
156C2×C42—21no—
157C2×C42C2×Dic1711yescharacteristic
158C2×C42C2×Dic1711yescharacteristic
159C2×C42C2×Dic1711yescharacteristic
160C2×C42C22⋊D1712yes—
161#101—178no—
162#101—344no—
163#97—682no—
164C4×C8—682no—
165#95—21no—
166#95—22no—
167#95—22no—
168#95—21no—
169#95—22no—
170C17#1263111yescharacteristic, complemented, Sylow
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8C4×Dic1712yes—
177C2×Q8C2×C4×D1712yes—
178C2×Q8#6325212yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4C22⋊Dic1712yes—
184C22×C4C22⋊Dic1711yescharacteristic
185C22×C4C22⋊Dic1711yescharacteristic
186C22×C4C22×Dic1711yescharacteristic
187C22×C4C2×C22⋊D1712yes—
188M16—348no—
189M16—684no—
190C2×C8—684no—
191C4⋊C4—28no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C42—22no—
197C42—22no—
198C42—22no—
199C42—21no—
200C42—41no—
201C42—42no—
202C42C4×Dic1712yes—
203C23C2×C22⋊Dic1711yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—42no—
207Q8—42no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4#1058750512yes—
229C2×C4C2×C4×Dic1711yescharacteristic
230C2×C4#1058761211yescharacteristic
231C2×C4C4×C22⋊D1714yes—
232C8—688no—
233C22—21no—
234C22—21no—
235C22C4×C22⋊Dic1711yescharacteristic
236C22C2×#1058750511yescharacteristic
237C22#1176278311yescharacteristic
238C4—24no—
239C4—21no—
240C4—21no—
241C4—22no—
242C4—42no—
243C4—42no—
244C4—41no—
245C4—42no—
246C4—81no—
247C4—81no—
248C2—21no—
249C2—21no—
250C2C4×#1058750511yescharacteristic
251C2#1453047311yescharacteristic
252C2#1453047911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC2×C4×C17C2×C42
FrattiniC22×Q8C22×D17
FittingC17×#2327C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Q8×C17C23
hypercenter#2327D17
hypocenterC17#12631
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2327

Complements

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

NH ≅ G/Ntype
7. #11762608C4semidirect
170. C17#12631semidirect

Maximal subgroups

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

subgroupindex
C2×#117626082
C4×#105875072
#145269112
C17×#23272
#1263117