Finite Group Databasebeta

← #16945491

Subgroups — #16945491

Order 4352.

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

normal subgroups only

This group has 388 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#14526814C214yesmaximal
4C17×#2567C211yesmaximal, characteristic
5#11762862—21no—
6#11762833—21no—
7C2×#10587507—21no—
8#11762578C2212yes—
9#11762535—21no—
10#11762535C2212yes—
11C2×C17×C4⋊Q8C411yescharacteristic
12C2×C4×Q8×C17C2211yescharacteristic
13C17×#395C412yes—
14C17×#395C2212yes—
15C17×#391—21no—
16C17×#389—21no—
17C17×#389—21no—
18C17×#384—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×Q8×C17C2×C412yes—
21C22×Q8×C17D411yescharacteristic
22C17×C4⋊Q8—41no—
23C17×C4⋊Q8—41no—
24C4×Q8×C17—41no—
25C4×Q8×C17—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17—22no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C4⋊C4×C17C2311yescharacteristic
34C2×C42×C17—21no—
35C2×C42×C17C2×C411yescharacteristic
36C2×C42×C17D411yescharacteristic
37C2×C42×C17D411yescharacteristic
38C2×#63223—22no—
39C17×#95—22no—
40C17×#95—22no—
41C17×#95C2×C412yes—
42#10587507—42no—
43C22⋊#3622—22no—
44C4⋊#3622—41no—
45C4⋊#3622—41no—
46C4⋊#3622—41no—
47C4×#3622—41no—
48C2×Q8×C17—41no—
49C2×Q8×C17—41no—
50C2×Q8×C17—42no—
51C2×Q8×C17—82no—
52C2×Q8×C17SD1612yes—
53C2×Q8×C17Q1612yes—
54C22×C4×C17—22no—
55C22×C4×C17—22no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C4⋊C4×C17—24no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—42no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—82no—
71C4⋊C4×C17—82no—
72C42×C17—21no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—42no—
79#63223—42no—
80#63223—42no—
81C2×#3622—42no—
82C2×#3622—42no—
83#11908—171nomaximal, Sylow
84C23×C17C2×C22⋊C411yescharacteristic
85Q8×C17—42no—
86Q8×C17—42no—
87Q8×C17—84no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—22no—
95C2×C4×C17—24no—
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—42no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17#9911yescharacteristic
108C2×C4×C17#9911yescharacteristic
109C2×C4×C17#10312yes—
110C2×C4×C17#10312yes—
111C2×C4×C17C2×SD1611yescharacteristic
112C2×C4×C17C2×Q1611yescharacteristic
113#3622—82no—
114#3622—82no—
115#2567D1711yescharacteristic
116#1801—171no—
117#1461—171no—
118#1354—174no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17C2×#9911yescharacteristic
122C22×C17C2×#10311yescharacteristic
123C22×C17#42111yescharacteristic
124C4×C17—21no—
125C4×C17—21no—
126C4×C17—22no—
127C4×C17—22no—
128C4×C17—21no—
129C4×C17—44no—
130C4×C17—41no—
131C4×C17—41no—
132C4×C17—41no—
133C4×C17—82no—
134C4×C17#35612yes—
135C2×C4⋊Q8Dic1711yescharacteristic
136C2×C4×Q8C2×D1711yescharacteristic
137#431—341no—
138#423—341no—
139C2×#101—341no—
140#395Dic1712yes—
141#395C2×D1712yes—
142#391—21no—
143#389—21no—
144#389—21no—
145#384—21no—
146C4×C4⋊C4Dic1711yescharacteristic
147#343—172no—
148#324—172no—
149#324—341no—
150C2×C17—21no—
151C2×C17—21no—
152C2×C17#152011yescharacteristic
153C2×C17#212211yescharacteristic
154C2×C17C2×#35611yescharacteristic
155C22×Q8C2×Dic1712yes—
156C22×Q8C22⋊D1711yescharacteristic
157C2×M16—342no—
158C4⋊Q8—41no—
159C4⋊Q8—41no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4C2×Dic1711yescharacteristic
168C2×C4⋊C4C22⋊D1711yescharacteristic
169C2×C4⋊C4C22×D1711yescharacteristic
170C2×C42—21no—
171C2×C42C2×Dic1711yescharacteristic
172C2×C42C22⋊D1711yescharacteristic
173C2×C42C22⋊D1711yescharacteristic
174C4⋊C8—681no—
175C4⋊C8—681no—
176C4⋊C8—681no—
177#101—682no—
178C22⋊C8—342no—
179C4×C8—681no—
180#95—22no—
181#95—22no—
182#95C2×Dic1712yes—
183C17#1190811yescharacteristic, complemented, Sylow
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—82no—
188C2×Q8#6323012yes—
189C2×Q8#6323112yes—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4C22⋊Dic1711yescharacteristic
193C22×C4C22⋊Dic1711yescharacteristic
194C22×C4C22⋊Dic1711yescharacteristic
195C22×C4C22⋊Dic1711yescharacteristic
196C22×C4C22×Dic1711yescharacteristic
197C22×C4C2×C22⋊D1711yescharacteristic
198C22×C4C2×C22⋊D1711yescharacteristic
199M16—682no—
200M16—682no—
201C2×C8—682no—
202C2×C8—682no—
203C4⋊C4—24no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—82no—
211C4⋊C4—82no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—42no—
219C23C2×C22⋊Dic1711yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—84no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—24no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4#1058750511yescharacteristic
243C2×C4#1058750511yescharacteristic
244C2×C4#1058750612yes—
245C2×C4#1058750612yes—
246C2×C4C2×#6323011yescharacteristic
247C2×C4C2×#6323111yescharacteristic
248C8—1362no—
249C8—1362no—
250C22—21no—
251C22—21no—
252C22C2×#1058750511yescharacteristic
253C22C2×#1058750611yescharacteristic
254C22#1176282611yescharacteristic
255C4—21no—
256C4—22no—
257C4—22no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4#1176260812yes—
266C2—21no—
267C2—21no—
268C2#1452735611yescharacteristic
269C2#1453043411yescharacteristic
270C2C2×#1176260811yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2567C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2567D17
hypocenterC17#11908
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
183. C17#11908semidirect

Maximal subgroups

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

subgroupindex
#145287802
#145271082
#145268142
C17×#25672
#1190817