Finite Group Databasebeta

← #16943817

Subgroups — #16943817

Order 4352.

376 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 75 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#14531502C211yesmaximal, characteristic
2#14527126C212yesmaximal
3#14526727C212yesmaximal
4#14526718C211yesmaximal, characteristic
5C17×#1319C211yesmaximal, characteristic
6C2×#10587630C411yescharacteristic
7C2×Q8×Dic17C411yescharacteristic
8C2×#10587573C2211yescharacteristic
9#11762863—22no—
10#11762715C411yescharacteristic
11#11762696—22no—
12#11762691—22no—
13#11762674C2211yescharacteristic
14#11762655C411yescharacteristic
15#11762535C2212yes—
16#11762534—22no—
17C17×#391C2211yescharacteristic
18C17×#324C2212yes—
19C22×Q8×C17C2×C411yescharacteristic
20C22×Dic34C2×C411yescharacteristic
21C2×C4⋊C4×C17C2311yescharacteristic
22C2×C42×C17C2×C411yescharacteristic
23Q8×Dic17—42no—
24#10587630—22no—
25#10587630—22no—
26C2×C4⋊Dic17—21no—
27C2×C4⋊Dic17C2×C411yescharacteristic
28C2×#63225—22no—
29C2×#63225D412yes—
30C2×C4×Dic17—21no—
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34#10587573—42no—
35C17×C22⋊C8—22no—
36C17×#95—22no—
37#10587502—22no—
38#10587502—21no—
39#10587502—22no—
40#10587502—21no—
41C22⋊#3622—22no—
42#10587486—42no—
43#10587485—42no—
44C2×Q8×C17—21no—
45C2×Q8×C17—41no—
46C2×Q8×C17—41no—
47C2×Q8×C17M1612yes—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17C22×C411yescharacteristic
51C22×C4×C17C2×D412yes—
52C22×Dic17—21no—
53C22×Dic17—21no—
54C22×Dic17C22⋊C412yes—
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C22⋊C411yescharacteristic
57C2×Dic34—21no—
58C2×Dic34—21no—
59C2×Dic34—41no—
60C2×Dic34—41no—
61C2×C8×C17—42no—
62C4⋊C4×C17—41no—
63C42×C17—41no—
64C4⋊Dic17—42no—
65C4⋊Dic17—41no—
66#63225—28no—
67#63225—42no—
68C4×Dic17—21no—
69C4×Dic17—22no—
70C4×Dic17—22no—
71C4×Dic17—22no—
72C4×Dic17—42no—
73C4×Dic17M1612yes—
74C2×#3622—42no—
75#11536—171nomaximal, Sylow
76C23×C17C2×C22⋊C411yescharacteristic
77Q8×C17—42no—
78Q8×C17—42no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—22no—
82C2×C4×C17—22no—
83C2×C4×C17—41no—
84C2×C4×C17—41no—
85C2×C4×C17—42no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17C2×M1611yescharacteristic
90C2×C4×C17C2×M1611yescharacteristic
91C2×Dic17—22no—
92C2×Dic17—22no—
93C2×Dic17—22no—
94C2×Dic17—21no—
95C2×Dic17—22no—
96C2×Dic17—41no—
97C2×Dic17—41no—
98C2×Dic17—41no—
99C2×Dic17—41no—
100C2×Dic17—42no—
101C2×Dic17—41no—
102C2×Dic17#9912yes—
103Dic34—42no—
104Dic34—42no—
105C8×C17—82no—
106#3622—82no—
107#2327—171no—
108#1467—172no—
109#1324—172no—
110#1319—171no—
111#1319D1711yescharacteristic
112C22×C17—21no—
113C22×C17—21no—
114C22×C17#40711yescharacteristic
115C22×C17C2×#9911yescharacteristic
116C22×C17#41311yescharacteristic
117C4×C17—21no—
118C4×C17—21no—
119C4×C17—42no—
120C4×C17—42no—
121C4×C17—81no—
122Dic17—22no—
123Dic17—42no—
124Dic17—41no—
125Dic17—42no—
126Dic17—81no—
127C2×C4⋊Q8—171no—
128C2×C4×Q8—171no—
129C2×C4×Q8—171no—
130#432—342no—
131#391—171no—
132#391C2×D1711yescharacteristic
133#387—342no—
134#387—342no—
135#382—171no—
136#376—171no—
137#324—172no—
138#324—342no—
139#324C2×D1712yes—
140C2×C17—21no—
141C2×C17—21no—
142C2×C17#146511yescharacteristic
143C2×C17#212911yescharacteristic
144C2×C17#213311yescharacteristic
145C22×Q8—171no—
146C22×Q8C4×D1711yescharacteristic
147C4⋊Q8—342no—
148C4⋊Q8—342no—
149C4×Q8—682no—
150C4×Q8—682no—
151C2×C4⋊C4—172no—
152C2×C4⋊C4—171no—
153C2×C4⋊C4—342no—
154C2×C4⋊C4—341no—
155C2×C4⋊C4C22×D1711yescharacteristic
156C2×C42—171no—
157C2×C42—171no—
158C2×C42—172no—
159C2×C42—341no—
160C2×C42C4×D1711yescharacteristic
161C4⋊C8—682no—
162C22⋊C8—22no—
163C22⋊C8—342no—
164#97—682no—
165#95—22no—
166#95—341no—
167#95—341no—
168#95—342no—
169#95—342no—
170C17#1153611yescharacteristic, complemented, Sylow
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—341no—
175C2×Q8—341no—
176C2×Q8—681no—
177C2×Q8—681no—
178C2×Q8#6321812yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—171no—
182C22×C4—172no—
183C22×C4—171no—
184C22×C4—341no—
185C22×C4—341no—
186C22×C4C2×C4×D1711yescharacteristic
187C22×C4D4×D1712yes—
188C2×C8—42no—
189C2×C8—682no—
190C4⋊C4—41no—
191C4⋊C4—348no—
192C4⋊C4—682no—
193C4⋊C4—681no—
194C4⋊C4—682no—
195C42—41no—
196C42—172no—
197C42—342no—
198C42—342no—
199C42—342no—
200C42—341no—
201C42—682no—
202C23C22⋊C4×D1711yescharacteristic
203Q8—42no—
204Q8—42no—
205Q8—682no—
206Q8—682no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—172no—
218C2×C4—342no—
219C2×C4—342no—
220C2×C4—341no—
221C2×C4—342no—
222C2×C4—342no—
223C2×C4—681no—
224C2×C4—681no—
225C2×C4—681no—
226C2×C4—681no—
227C2×C4—682no—
228C2×C4—681no—
229C2×C4C2×#6321811yescharacteristic
230C2×C4M16×D1711yescharacteristic
231C8—82no—
232C8—1362no—
233C22—21no—
234C22—21no—
235C22#1176277111yescharacteristic
236C22#99×D1711yescharacteristic
237C22#1176279011yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—342no—
244C4—682no—
245C4—682no—
246C4—681no—
247C4—1361no—
248C2—21no—
249C2—21no—
250C2#1452711911yescharacteristic
251C2#1453045711yescharacteristic
252C2#1453047211yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1319C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1319D17
hypocenterC17#11536
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
170. C17#11536semidirect

Maximal subgroups

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

subgroupindex
#145315022
#145271262
#145267272
#145267182
C17×#13192
#1153617