Finite Group Databasebeta

← #16943752

Subgroups — #16943752

Order 4352.

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

normal subgroups only

This group has 418 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#14531404C211yesmaximal, characteristic
2#14527118C211yesmaximal, characteristic
3#14526733C214yesmaximal
4C17×#1464C211yesmaximal, characteristic
5C2×#10587612C411yescharacteristic
6C22×C4⋊Dic17C411yescharacteristic
7#11762866—21no—
8#11762707—21no—
9#11762707—21no—
10#11762681C412yes—
11#11762681C2212yes—
12#11762678—21no—
13#11762674—21no—
14#11762535—21no—
15#11762533C2212yes—
16C2×C17×#117C2211yescharacteristic
17C17×#432—21no—
18C17×#324—21no—
19C17×#323C2212yes—
20C23×C4×C17C2×C411yescharacteristic
21C23×Dic17C2×C412yes—
22C17×#117—41no—
23C17×#117—41no—
24C2×C4⋊C4×C17D411yescharacteristic
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C22⋊C4×C17C2×C411yescharacteristic
27C2×C22⋊C4×C17C2311yescharacteristic
28C2×C42×C17D411yescharacteristic
29C2×C42×C17D411yescharacteristic
30C2×C22⋊Dic17C2×C412yes—
31#10587612—24no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—41no—
36C2×C4⋊Dic17—41no—
37C2×#63225—22no—
38C2×#63225—22no—
39C2×C4×Dic17—21no—
40C17×C4⋊C8—41no—
41C17×C22⋊C8—22no—
42C17×#97—41no—
43#10587502—22no—
44#10587502—22no—
45C22⋊#3622—22no—
46C4⋊#3622—41no—
47#10587474—41no—
48C24×C17C22×C411yescharacteristic
49C22×C4×C17—22no—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—22no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×Dic17—22no—
60C22×Dic17—22no—
61C22×Dic17—42no—
62C22×Dic17—82no—
63C2×C8×C17—42no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C22⋊C4×C17—41no—
67C22⋊C4×C17—41no—
68C42×C17—21no—
69C42×C17—21no—
70C42×C17—21no—
71C42×C17—21no—
72C22⋊Dic17—22no—
73C22⋊Dic17M1614yes—
74C4⋊Dic17—24no—
75C4⋊Dic17—42no—
76C4⋊Dic17—41no—
77C4⋊Dic17—41no—
78#63225—82no—
79#63225—82no—
80C4×Dic17—24no—
81C2×#3622—42no—
82#11520—171nomaximal, Sylow
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—41no—
86C23×C17—41no—
87C23×C17C2×C22⋊C411yescharacteristic
88C23×C17C2×M1612yes—
89C2×C4×C17—24no—
90C2×C4×C17—24no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17#9911yescharacteristic
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17#10112yes—
106C2×Dic17—24no—
107C2×Dic17—42no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—42no—
112C2×Dic17—84no—
113C8×C17—82no—
114#3622—82no—
115#2317—171no—
116#1464—171no—
117#1464D1711yescharacteristic
118#1326—174no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17—22no—
122C22×C17—42no—
123C22×C17—42no—
124C22×C17—41no—
125C22×C17—41no—
126C22×C17#40711yescharacteristic
127C22×C17C2×#9911yescharacteristic
128C22×C17C2×#10111yescharacteristic
129C4×C17—21no—
130C4×C17—21no—
131C4×C17—22no—
132C4×C17—41no—
133C4×C17—41no—
134C4×C17—41no—
135C4×C17—41no—
136Dic17—44no—
137Dic17—82no—
138C2×#117—171no—
139C2×#117C2×D1711yescharacteristic
140C22×C4⋊C4—171no—
141#432—21no—
142#432—341no—
143#389—341no—
144#389—341no—
145#385—172no—
146#385—172no—
147#384—341no—
148#382—341no—
149#324—21no—
150#324—341no—
151#323—172no—
152#323C2×D1712yes—
153C2×C17—21no—
154C2×C17—21no—
155C2×C17—42no—
156C2×C17#146311yescharacteristic
157C2×C17#212211yescharacteristic
158C2×C17#212311yescharacteristic
159C23×C4—172no—
160C23×C4C4×D1711yescharacteristic
161#117—41no—
162#117—41no—
163#117—344no—
164C2×C4⋊C4—341no—
165C2×C4⋊C4—341no—
166C2×C4⋊C4—341no—
167C2×C4⋊C4—342no—
168C2×C4⋊C4—342no—
169C2×C4⋊C4—681no—
170C2×C4⋊C4—681no—
171C2×C4⋊C4D6811yescharacteristic
172C2×C4⋊C4C22⋊D1711yescharacteristic
173C2×C22⋊C4—172no—
174C2×C22⋊C4C4×D1711yescharacteristic
175C2×C22⋊C4C22×D1711yescharacteristic
176C2×C42—341no—
177C2×C42D6811yescharacteristic
178C2×C42C22⋊D1711yescharacteristic
179C4⋊C8—41no—
180C4⋊C8—681no—
181C22⋊C8—22no—
182C22⋊C8—342no—
183#97—41no—
184#97—681no—
185#95—342no—
186#95—342no—
187C17#1152011yescharacteristic, complemented, Sylow
188C24C2×C4×D1711yescharacteristic
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—342no—
194C22×C4—342no—
195C22×C4—682no—
196C22×C4—1362no—
197C22×C4#6322711yescharacteristic
198C22×C4#6322711yescharacteristic
199C22×C4#6322711yescharacteristic
200C22×C4#6322711yescharacteristic
201C22×C4C2×D6811yescharacteristic
202C22×C4C2×C22⋊D1711yescharacteristic
203C2×C8—42no—
204C2×C8—682no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—344no—
208C4⋊C4—682no—
209C4⋊C4—681no—
210C4⋊C4—681no—
211C4⋊C4—1362no—
212C4⋊C4—1362no—
213C22⋊C4—41no—
214C22⋊C4—41no—
215C22⋊C4—174no—
216C22⋊C4—342no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—344no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23M16×D1712yes—
227C23C2×#6322711yescharacteristic
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—344no—
243C2×C4—682no—
244C2×C4—682no—
245C2×C4—682no—
246C2×C4—682no—
247C2×C4—682no—
248C2×C4—1364no—
249C2×C4#1058747711yescharacteristic
250C2×C4#1058747711yescharacteristic
251C2×C4#1058749512yes—
252C8—82no—
253C8—1362no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22#1176277211yescharacteristic
262C22C2×#1058747711yescharacteristic
263C22C2×#1058749511yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—41no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—684no—
272C4—1362no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#1452711311yescharacteristic
277C2#1453043511yescharacteristic
278C2#1453043711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutator, prime radicalC24×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#1464C2
socleC22×C17C2×#99
cosocleC2×C22⋊C4×C17C23
hypercenter#1464D17
hypocenterC17#11520
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
187. C17#11520semidirect

Maximal subgroups

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

subgroupindex
#145314042
#145271182
#145267332
C17×#14642
#1152017