Finite Group Databasebeta

← #16945028

Subgroups — #16945028

Order 4352.

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

normal subgroups only

This group has 388 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#14528867C211yesmaximal, characteristic
2#14527118C211yesmaximal, characteristic
3#14526790C214yesmaximal, complemented
4C17×#2621C211yesmaximal, characteristic
5#11762866—21no—
6#11762773—21no—
7#11762578—21no—
8#11762578C2212yes—
9#11762535C2212yes—
10#11762533—21no—
11C2×C17×C4⋊Q8C411yescharacteristic
12C2×C17×C22⋊Q8—21no—
13C2×C17×#117C2211yescharacteristic
14C17×#398—21no—
15C17×#398C2212yes—
16C17×#397—21no—
17C17×#397C412yes—
18C17×#391—21no—
19C17×#382C411yescharacteristic
20C22×Q8×C17—21no—
21C23×C4×C17D411yescharacteristic
22C17×C4⋊Q8—41no—
23C17×C4⋊Q8—41no—
24C17×C22⋊Q8—44no—
25C17×#117—41no—
26C17×#117—41no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17C2×C412yes—
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C4⋊C4×C17C2311yescharacteristic
33C2×C22⋊C4×C17—22no—
34C2×C22⋊C4×C17C2×C411yescharacteristic
35C2×C22⋊C4×C17D411yescharacteristic
36C2×C42×C17C2×C411yescharacteristic
37C2×C42×C17D411yescharacteristic
38C2×#63223—22no—
39C17×#95—21no—
40C17×#95—22no—
41C17×#95—22no—
42C17×#95C2×C412yes—
43C22⋊#3622—22no—
44C22⋊#3622—41no—
45C22⋊#3622—41no—
46C4⋊#3622—41no—
47#10587474—41no—
48C24×C17C22⋊C411yescharacteristic
49C2×Q8×C17—42no—
50C2×Q8×C17—42no—
51C2×Q8×C17—41no—
52C2×Q8×C17—41no—
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17—22no—
58C22×C4×C17—41no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22×C411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17C2×D411yescharacteristic
65C4⋊C4×C17—41no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—42no—
68C4⋊C4×C17—42no—
69C4⋊C4×C17—42no—
70C4⋊C4×C17—44no—
71C22⋊C4×C17—41no—
72C22⋊C4×C17—41no—
73C22⋊C4×C17—44no—
74C42×C17—21no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17—21no—
78#63223—42no—
79#63223—42no—
80C2×#3622—42no—
81C2×#3622—42no—
82#11807—171nomaximal, Sylow
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—21no—
86C23×C17—41no—
87C23×C17—41no—
88C23×C17C2×C22⋊C411yescharacteristic
89Q8×C17—82no—
90Q8×C17—82no—
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—42no—
100C2×C4×C17—42no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17#9911yescharacteristic
112C2×C4×C17#9911yescharacteristic
113C2×C4×C17AGL(1,ℤ/8)12yes—
114#3622—82no—
115#3622—82no—
116#2621D1711yescharacteristic
117#1822—171no—
118#1464—171no—
119#1346—174no—
120C22×C17—21no—
121C22×C17—21no—
122C22×C17—42no—
123C22×C17—41no—
124C22×C17—41no—
125C22×C17—41no—
126C22×C17—81no—
127C22×C17C2×#9911yescharacteristic
128C22×C17#41811yescharacteristic
129C22×C17#42111yescharacteristic
130C4×C17—22no—
131C4×C17—21no—
132C4×C17—21no—
133C4×C17—41no—
134C4×C17—41no—
135C4×C17—41no—
136C4×C17—41no—
137C4×C17—82no—
138C4×C17—82no—
139C2×C4⋊Q8Dic1711yescharacteristic
140C2×C22⋊Q8—21no—
141C2×#117C2×D1711yescharacteristic
142#432—341no—
143#407—341no—
144#398—21no—
145#398C2×D1712yes—
146#397—21no—
147#397Dic1712yes—
148#391—21no—
149#382Dic1711yescharacteristic
150#343—172no—
151#343—341no—
152#324—172no—
153#323—341no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17—81no—
157C2×C17#151011yescharacteristic
158C2×C17#212311yescharacteristic
159C2×C17#213511yescharacteristic
160C22×Q8—21no—
161C23×C4C22⋊D1711yescharacteristic
162C2×M16—342no—
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165C22⋊Q8—44no—
166#117—41no—
167#117—41no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C2×Dic1712yes—
172C2×C4⋊C4C22⋊D1711yescharacteristic
173C2×C4⋊C4C22×D1711yescharacteristic
174C2×C22⋊C4—22no—
175C2×C22⋊C4C2×Dic1711yescharacteristic
176C2×C22⋊C4C22⋊D1711yescharacteristic
177C2×C42C2×Dic1711yescharacteristic
178C2×C42C22⋊D1711yescharacteristic
179C4⋊C8—681no—
180C22⋊C8—342no—
181C22⋊C8—681no—
182C22⋊C8—681no—
183#97—681no—
184#95—21no—
185#95—22no—
186#95—22no—
187#95C2×Dic1712yes—
188C17#1180711yescharacteristic, complemented, Sylow
189C24C22⋊Dic1711yescharacteristic
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—41no—
193C2×Q8—41no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—41no—
200C22×C4C22⋊Dic1711yescharacteristic
201C22×C4C22⋊Dic1711yescharacteristic
202C22×C4C22⋊Dic1711yescharacteristic
203C22×C4C22×Dic1711yescharacteristic
204C22×C4C2×C22⋊D1711yescharacteristic
205C22×C4C2×C22⋊D1711yescharacteristic
206M16—682no—
207M16—682no—
208C2×C8—682no—
209C2×C8—682no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—44no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—44no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23C2×C22⋊Dic1711yescharacteristic
229Q8—82no—
230Q8—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4#1058750511yescharacteristic
252C2×C4#1058750511yescharacteristic
253C2×C4#1058761812yes—
254C8—1362no—
255C8—1362no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22C2×#1058750511yescharacteristic
264C22#1176281411yescharacteristic
265C22#1176282611yescharacteristic
266C4—22no—
267C4—21no—
268C4—21no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—82no—
274C4—82no—
275C2—21no—
276C2—21no—
277C2—81no—
278C2#1452731311yescharacteristic
279C2#1453043811yescharacteristic
280C2#1453047911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2621C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2621D17
hypocenterC17#11807
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2621

Complements

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

NH ≅ G/Ntype
3. #14526790C2semidirect
188. C17#11807semidirect

Maximal subgroups

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

subgroupindex
#145288672
#145271182
#145267902
C17×#26212
#1180717