Finite Group Databasebeta

← #16950331

Subgroups — #16950331

Order 4352.

480 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 119 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×#11762606C212yesmaximal
2#14528780C212yesmaximal, complemented
3#14526911C212yesmaximal, complemented
4C17×#2326C211yesmaximal, characteristic
5#11762833—22no—
6C2×#10587507C2214yes—
7#11762606—24no—
8#11762578—22no—
9C2×C17×#124C2211yescharacteristic
10C2×C4×Q8×C17C2211yescharacteristic
11C2×C4×D4×C17C411yescharacteristic
12C17×#391C2211yescharacteristic
13C17×#390C411yescharacteristic
14C17×#388—22no—
15C17×#385—22no—
16C17×#384C411yescharacteristic
17C17×#376C411yescharacteristic
18C22×Q8×C17C2311yescharacteristic
19C22×D4×C17C2×C411yescharacteristic
20C23×C4×C17—21no—
21C17×#124—22no—
22C17×#124D412yes—
23C17×#124Q812yes—
24C4×Q8×C17—42no—
25C4×D4×C17—42no—
26C2×C4⋊C4×C17—22no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C4⋊C4×C17D412yes—
30C2×C22⋊C4×C17—22no—
31C2×C22⋊C4×C17—21no—
32C2×C22⋊C4×C17—22no—
33C2×C42×C17C2×C411yescharacteristic
34C2×C42×C17C2×C411yescharacteristic
35C2×C42×C17C2×C411yescharacteristic
36C2×C42×C17D412yes—
37C2×#63223—24no—
38C17×#95—21no—
39C17×#95—21no—
40C17×#95—22no—
41#10587507—24no—
42#10587507—24no—
43C4⋊#3622—44no—
44C24×C17—21no—
45C2×Q8×C17—41no—
46C2×Q8×C17—41no—
47C2×Q8×C17C2×D411yescharacteristic
48C2×Q8×C17C2×Q811yescharacteristic
49C2×Q8×C17#4112yes—
50C2×D4×C17—21no—
51C2×D4×C17—41no—
52C2×D4×C17—41no—
53C2×D4×C17C4⋊C412yes—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—42no—
58C22×C4×C17—82no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C412yes—
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22×C411yescharacteristic
63C22×C4×C17C2×D412yes—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—42no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—82no—
68C22⋊C4×C17—24no—
69C22⋊C4×C17—24no—
70C22⋊C4×C17—42no—
71C22⋊C4×C17—82no—
72C42×C17—24no—
73C42×C17—22no—
74C42×C17—21no—
75C42×C17—41no—
76C42×C17C4⋊C412yes—
77#63223—44no—
78#63223—44no—
79C2×#3622—44no—
80#12803—171nomaximal, Sylow
81C23×C17—22no—
82C23×C17—42no—
83C23×C17—42no—
84C23×C17—41no—
85C23×C17—41no—
86C23×C17C2×C22⋊C411yescharacteristic
87Q8×C17—41no—
88Q8×C17—41no—
89Q8×C17—42no—
90D4×C17—42no—
91D4×C17—42no—
92C2×C4×C17—21no—
93C2×C4×C17—22no—
94C2×C4×C17—21no—
95C2×C4×C17—22no—
96C2×C4×C17—22no—
97C2×C4×C17—21no—
98C2×C4×C17—22no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—42no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—84no—
110C2×C4×C17#9912yes—
111C2×C4×C17C2×C4⋊C411yescharacteristic
112C2×C4×C17#11711yescharacteristic
113C2×C4×C17#12112yes—
114C2×C4×C17C22⋊Q812yes—
115#3622—84no—
116#2326D1711yescharacteristic
117C2×#355—172no—
118#1801—172no—
119#1394—172no—
120C22×C17—21no—
121C22×C17—21no—
122C22×C17—44no—
123C22×C17—42no—
124C22×C17—82no—
125C22×C17—81no—
126C22×C17—81no—
127C22×C17#38011yescharacteristic
128C22×C17C2×#9911yescharacteristic
129C22×C17#41011yescharacteristic
130C4×C17—22no—
131C4×C17—21no—
132C4×C17—21no—
133C4×C17—22no—
134C4×C17—22no—
135C4×C17—42no—
136C4×C17—42no—
137C4×C17—41no—
138C4×C17—81no—
139C4×C17—81no—
140C2×#124C2×D1711yescharacteristic
141C2×C4×Q8C2×D1711yescharacteristic
142C2×C4×D4Dic1711yescharacteristic
143#423—342no—
144C2×#101—174no—
145#391C2×D1711yescharacteristic
146#390Dic1711yescharacteristic
147#388—22no—
148#385—22no—
149#384Dic1711yescharacteristic
150#376Dic1711yescharacteristic
151#355—344no—
152#343—342no—
153C2×C17—21no—
154C2×C17—21no—
155C2×C17—82no—
156C2×C17#179911yescharacteristic
157C2×C17#213311yescharacteristic
158C2×C17#213411yescharacteristic
159C22×Q8C22×D1711yescharacteristic
160C22×D4C2×Dic1711yescharacteristic
161C23×C4—21no—
162C2×M16—344no—
163#124—22no—
164#124Dic3412yes—
165#124D6812yes—
166C4×Q8—42no—
167C4×D4—42no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4C2×Dic1711yescharacteristic
170C2×C4⋊C4C2×Dic1711yescharacteristic
171C2×C4⋊C4C22⋊D1712yes—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—22no—
175C2×C42C2×Dic1711yescharacteristic
176C2×C42C2×Dic1711yescharacteristic
177C2×C42C2×Dic1711yescharacteristic
178C2×C42C22⋊D1712yes—
179C4⋊C8—684no—
180#101—344no—
181#101—344no—
182#95—21no—
183#95—21no—
184#95—22no—
185C17#1280311yescharacteristic, complemented, Sylow
186C24—21no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8C2×Dic3411yescharacteristic
190C2×Q8C2×D6811yescharacteristic
191C2×Q8#6325212yes—
192C2×D4—21no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4C4⋊Dic1712yes—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—42no—
200C22×C4—82no—
201C22×C4C22⋊Dic1711yescharacteristic
202C22×C4C22⋊Dic1712yes—
203C22×C4C22⋊Dic1711yescharacteristic
204C22×C4C22×Dic1711yescharacteristic
205C22×C4C2×C22⋊D1712yes—
206M16—684no—
207M16—684no—
208C2×C8—684no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—82no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—24no—
218C42—22no—
219C42—21no—
220C42—41no—
221C42C4⋊Dic1712yes—
222C23—22no—
223C23—42no—
224C23—42no—
225C23—41no—
226C23—41no—
227C23C2×C22⋊Dic1711yescharacteristic
228Q8—41no—
229Q8—41no—
230Q8—42no—
231D4—42no—
232D4—42no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—84no—
251C2×C4#1058750512yes—
252C2×C4#1058761012yes—
253C2×C4C2×C4⋊Dic1711yescharacteristic
254C2×C4#1058761211yescharacteristic
255C2×C4#1058761612yes—
256C8—1364no—
257C22—21no—
258C22—21no—
259C22—44no—
260C22—42no—
261C22—82no—
262C22—81no—
263C22—81no—
264C22#1176266911yescharacteristic
265C22C2×#1058750511yescharacteristic
266C22#1176278311yescharacteristic
267C4—22no—
268C4—22no—
269C4—21no—
270C4—21no—
271C4—22no—
272C4—42no—
273C4—41no—
274C4—42no—
275C4—81no—
276C4—81no—
277C2—21no—
278C2—21no—
279C2—82no—
280C2#1452877211yescharacteristic
281C2#1453047311yescharacteristic
282C2#1453047611yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC22×Q8C22×D17
FittingC17×#2326C2
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC22×Q8×C17C23
hypercenter#2326D17
hypocenterC17#12803
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2326

Complements

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

NH ≅ G/Ntype
2. #14528780C2semidirect
3. #14526911C2semidirect
185. C17#12803semidirect

Maximal subgroups

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

subgroupindex
C2×#117626062
#145287802
#145269112
C17×#23262
#1280317