Finite Group Databasebeta

← #16945382

Subgroups — #16945382

Order 4352.

408 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 107 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#14528780C211yesmaximal, characteristic
2#14527108C211yesmaximal, characteristic
3#14526790C214yesmaximal
4C17×#2546C211yesmaximal, characteristic
5#11762862—21no—
6#11762833—21no—
7C2×#10587507—21no—
8#11762578C2212yes—
9#11762535—21no—
10#11762535C2212yes—
11C2×C17×C4⋊Q8—21no—
12C2×C17×C4⋊Q8C411yescharacteristic
13C2×C4×Q8×C17C2211yescharacteristic
14C17×#398C412yes—
15C17×#398C2212yes—
16C17×#391—21no—
17C17×#389—21no—
18C17×#389—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Q8×C17—21no—
21C22×Q8×C17D411yescharacteristic
22C17×C4⋊Q8—41no—
23C17×C4⋊Q8—41no—
24C17×C4⋊Q8—42no—
25C17×C4⋊Q8—42no—
26C4×Q8×C17—41no—
27C4×Q8×C17—41no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—22no—
32C2×C4⋊C4×C17C2×C412yes—
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C4⋊C4×C17D411yescharacteristic
35C2×C4⋊C4×C17C2311yescharacteristic
36C2×C42×C17—21no—
37C2×C42×C17C2×C411yescharacteristic
38C2×C42×C17D411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C2×#63223—22no—
41C17×#95—22no—
42C17×#95—22no—
43C17×#95C2×C412yes—
44#10587507—42no—
45C22⋊#3622—22no—
46C4⋊#3622—41no—
47C4⋊#3622—41no—
48C4⋊#3622—41no—
49C4×#3622—41no—
50C2×Q8×C17—41no—
51C2×Q8×C17—41no—
52C2×Q8×C17—42no—
53C2×Q8×C17—42no—
54C2×Q8×C17—42no—
55C2×Q8×C17D812yes—
56C2×Q8×C17SD1612yes—
57C22×C4×C17—22no—
58C22×C4×C17—22no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22×C411yescharacteristic
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C4⋊C4×C17—24no—
67C4⋊C4×C17—41no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—42no—
71C4⋊C4×C17—41no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—44no—
74C4⋊C4×C17—42no—
75C4⋊C4×C17—42no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—21no—
79C42×C17—21no—
80C42×C17—21no—
81C42×C17—21no—
82C42×C17—42no—
83#63223—42no—
84#63223—42no—
85C2×#3622—42no—
86C2×#3622—42no—
87#11883—171nomaximal, Sylow
88C23×C17C2×C22⋊C411yescharacteristic
89Q8×C17—42no—
90Q8×C17—42no—
91Q8×C17—84no—
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—22no—
99C2×C4×C17—24no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17#9911yescharacteristic
112C2×C4×C17#9911yescharacteristic
113C2×C4×C17#10212yes—
114C2×C4×C17#10212yes—
115C2×C4×C17C2×D811yescharacteristic
116C2×C4×C17C2×SD1611yescharacteristic
117#3622—82no—
118#3622—82no—
119#2546D1711yescharacteristic
120#1801—171no—
121#1461—171no—
122#1346—174no—
123C22×C17—21no—
124C22×C17—21no—
125C22×C17C2×#9911yescharacteristic
126C22×C17C2×#10211yescharacteristic
127C22×C17#42111yescharacteristic
128C4×C17—21no—
129C4×C17—21no—
130C4×C17—22no—
131C4×C17—22no—
132C4×C17—21no—
133C4×C17—44no—
134C4×C17—41no—
135C4×C17—41no—
136C4×C17—41no—
137C4×C17—82no—
138C4×C17#35612yes—
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8Dic1711yescharacteristic
141C2×C4×Q8C2×D1711yescharacteristic
142#431—341no—
143#423—341no—
144C2×#101—341no—
145#398Dic1712yes—
146#398C2×D1712yes—
147#391—21no—
148#389—21no—
149#389—21no—
150C4×C4⋊C4Dic1711yescharacteristic
151#343—172no—
152#324—172no—
153#324—341no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17#151911yescharacteristic
157C2×C17#212311yescharacteristic
158C2×C17C2×#35611yescharacteristic
159C22×Q8—21no—
160C22×Q8C22⋊D1711yescharacteristic
161C2×M16—342no—
162C4⋊Q8—41no—
163C4⋊Q8—41no—
164C4⋊Q8—42no—
165C4⋊Q8—42no—
166C4×Q8—41no—
167C4×Q8—41no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4C2×Dic1712yes—
173C2×C4⋊C4C2×Dic1711yescharacteristic
174C2×C4⋊C4C22⋊D1711yescharacteristic
175C2×C4⋊C4C22×D1711yescharacteristic
176C2×C42—21no—
177C2×C42C2×Dic1711yescharacteristic
178C2×C42C22⋊D1711yescharacteristic
179C2×C42C22⋊D1711yescharacteristic
180C4⋊C8—681no—
181C4⋊C8—681no—
182C4⋊C8—681no—
183#101—682no—
184C22⋊C8—342no—
185C4×C8—681no—
186#95—22no—
187#95—22no—
188#95C2×Dic1712yes—
189C17#1188311yescharacteristic, complemented, Sylow
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—42no—
195C2×Q8#6322812yes—
196C2×Q8#6322912yes—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4C22⋊Dic1711yescharacteristic
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—24no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—44no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—42no—
227C23C2×C22⋊Dic1711yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—84no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4#1058750312yes—
251C2×C4#1058750312yes—
252C2×C4#1058750511yescharacteristic
253C2×C4#1058750511yescharacteristic
254C2×C4C2×#6322811yescharacteristic
255C2×C4C2×#6322911yescharacteristic
256C8—1362no—
257C8—1362no—
258C22—21no—
259C22—21no—
260C22C2×#1058750511yescharacteristic
261C22C2×#1058750311yescharacteristic
262C22#1176282611yescharacteristic
263C4—21no—
264C4—22no—
265C4—22no—
266C4—21no—
267C4—21no—
268C4—44no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4#1176260812yes—
274C2—21no—
275C2—21no—
276C2#1452735211yescharacteristic
277C2#1453043811yescharacteristic
278C2C2×#1176260811yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2546C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2546D17
hypocenterC17#11883
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
189. C17#11883semidirect

Maximal subgroups

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

subgroupindex
#145287802
#145271082
#145267902
C17×#25462
#1188317