Finite Group Databasebeta

← #16932189

Subgroups — #16932189

Order 4352.

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

normal subgroups only

This group has 454 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
1#14537869C211yesmaximal, characteristic
2#14528780C211yesmaximal, characteristic
3#14527213C212yesmaximal
4#14526642C212yesmaximal
5C17×#2581C211yesmaximal, characteristic
6#11762940—24no—
7#11762866—22no—
8#11762862C2212yes—
9#11762833C2212yes—
10C2×#10587507—21no—
11#11762578—21no—
12Q8⋊#3622—24no—
13C2×C4×Q8×C17C2211yescharacteristic
14C2×C4×Q8×C17C2211yescharacteristic
15C17×#400C412yes—
16C17×#395C412yes—
17C17×#391—21no—
18C17×#389—21no—
19C17×#387—22no—
20C17×#382C2211yescharacteristic
21C22×Q8×C17C2×C411yescharacteristic
22C22×Q8×C17D411yescharacteristic
23C4×Q8×C17—22no—
24C4×Q8×C17—22no—
25C4×Q8×C17—22no—
26C4×Q8×C17—22no—
27C2×C4⋊C4×C17—22no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17C2×C411yescharacteristic
31C2×C4⋊C4×C17C2×C412yes—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C42×C17—21no—
34C2×C42×C17D412yes—
35C2×C42×C17C2311yescharacteristic
36C2×#63223—22no—
37C17×#95—22no—
38C17×#95—22no—
39C17×#95—22no—
40C17×#95—21no—
41C17×#95C2×C412yes—
42#10587507—42no—
43C22⋊#3622—22no—
44C4⋊#3622—24no—
45C4⋊#3622—22no—
46C4⋊#3622—22no—
47C4⋊#3622—22no—
48#10587474—24no—
49C4×#3622D414yes—
50C2×Q8×C17—22no—
51C2×Q8×C17—21no—
52C2×Q8×C17—22no—
53C2×Q8×C17—21no—
54C2×Q8×C17—22no—
55C2×Q8×C17—42no—
56C22×C4×C17—21no—
57C22×C4×C17—22no—
58C22×C4×C17—21no—
59C22×C4×C17C22⋊C412yes—
60C22×C4×C17C22⋊C412yes—
61C22×C4×C17C22×C411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C4⋊C4×C17—24no—
65C4⋊C4×C17—22no—
66C4⋊C4×C17—22no—
67C4⋊C4×C17—44no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17—41no—
72C42×C17—22no—
73C42×C17—22no—
74C42×C17—42no—
75C42×C17C2×D412yes—
76C42×C17#4112yes—
77#63223—42no—
78#63223—42no—
79C2×#3622—24no—
80C2×#3622—42no—
81#9488—171nomaximal, Sylow
82C23×C17C2×C22⋊C411yescharacteristic
83Q8×C17—24no—
84Q8×C17—42no—
85Q8×C17—42no—
86Q8×C17—42no—
87C2×C4×C17—22no—
88C2×C4×C17—22no—
89C2×C4×C17—22no—
90C2×C4×C17—22no—
91C2×C4×C17—22no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17—42no—
97C2×C4×C17—42no—
98C2×C4×C17—42no—
99C2×C4×C17—42no—
100C2×C4×C17—41no—
101C2×C4×C17—42no—
102C2×C4×C17C4×D412yes—
103C2×C4×C17#12011yescharacteristic
104C2×C4×C17#12112yes—
105C2×C4×C17#12311yescharacteristic
106C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
107C2×C4×C17#13712yes—
108C2×C4×C17#13711yescharacteristic
109#3622—44no—
110#3622—82no—
111#2983—171no—
112#2581D1711yescharacteristic
113#1801—171no—
114#1487—172no—
115#1286—172no—
116C22×C17—21no—
117C22×C17—21no—
118C22×C17#38611yescharacteristic
119C22×C17#41711yescharacteristic
120C22×C17#41911yescharacteristic
121C4×C17—22no—
122C4×C17—21no—
123C4×C17—21no—
124C4×C17—42no—
125C4×C17—42no—
126C4×C17—42no—
127C4×C17—82no—
128C4×C17—81no—
129C4×C17#46812yes—
130C4×C17#47012yes—
131C2×C4×Q8C2×D1711yescharacteristic
132C2×C4×Q8C2×D1711yescharacteristic
133#446—344no—
134#432—342no—
135#431—172no—
136#423—172no—
137C2×#101—341no—
138#400Dic1712yes—
139#395Dic1712yes—
140#391—21no—
141#389—21no—
142#387—22no—
143#382C2×D1711yescharacteristic
144#343—341no—
145Q8⋊C8—344no—
146C2×C17—21no—
147C2×C17—21no—
148C2×C17#189111yescharacteristic
149C2×C17#189411yescharacteristic
150C2×C17#191211yescharacteristic
151C22×Q8C2×Dic1711yescharacteristic
152C22×Q8C22⋊D1711yescharacteristic
153C2×M16—342no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4C2×Dic1711yescharacteristic
162C2×C4⋊C4C2×Dic1712yes—
163C2×C4⋊C4C22⋊D1711yescharacteristic
164C2×C42—21no—
165C2×C42C22⋊D1712yes—
166C2×C42C22×D1711yescharacteristic
167C4⋊C8—344no—
168C4⋊C8—342no—
169C4⋊C8—342no—
170C4⋊C8—342no—
171#101—682no—
172C22⋊C8—342no—
173#97—344no—
174C4×C8—174no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—21no—
179#95C2×Dic1712yes—
180C17#948811yescharacteristic, complemented, Sylow
181C2×Q8—22no—
182C2×Q8—22no—
183C2×Q8—21no—
184C2×Q8—21no—
185C2×Q8—22no—
186C2×Q8—42no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4C22⋊Dic1712yes—
191C22×C4C22⋊Dic1712yes—
192C22×C4C22×Dic1711yescharacteristic
193C22×C4C2×C22⋊D1711yescharacteristic
194C22×C4C2×C22⋊D1711yescharacteristic
195M16—682no—
196M16—682no—
197C2×C8—344no—
198C2×C8—682no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—44no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C42—22no—
208C42—22no—
209C42—42no—
210C42D4×D1712yes—
211C42#6325412yes—
212C23C2×C22⋊Dic1711yescharacteristic
213Q8—24no—
214Q8—42no—
215Q8—42no—
216Q8—42no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4D4×Dic1712yes—
233C2×C4#1058762111yescharacteristic
234C2×C4#1058762311yescharacteristic
235C2×C4#1058762512yes—
236C2×C4#1058762812yes—
237C2×C4#1058763511yescharacteristic
238C2×C4#1058763711yescharacteristic
239C8—684no—
240C8—1362no—
241C22—21no—
242C22—21no—
243C22#1176268911yescharacteristic
244C22#1176281011yescharacteristic
245C22#1176281811yescharacteristic
246C4—21no—
247C4—21no—
248C4—22no—
249C4—42no—
250C4—42no—
251C4—42no—
252C4—82no—
253C4—81no—
254C4#1176305712yes—
255C4#1176306512yes—
256C2—21no—
257C2—21no—
258C2#1452920311yescharacteristic
259C2#1452921811yescharacteristic
260C2#1452932211yescharacteristic
subgroupG/H
centerC22#11762689
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2581C2
socleC22×C17#386
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2581D17
hypocenterC17#9488
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2581

Complements

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

NH ≅ G/Ntype
180. C17#9488semidirect

Maximal subgroups

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

subgroupindex
#145378692
#145287802
#145272132
#145266422
C17×#25812
#948817