Finite Group Databasebeta

← #16932186

Subgroups — #16932186

Order 4352.

454 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 111 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#14534146C211yesmaximal, characteristic
3#14527212C212yesmaximal
4#14526644C212yesmaximal
5C17×#1801C211yesmaximal, characteristic
6C2×C4×Dic34C2211yescharacteristic
7#11762940—24no—
8#11762866—22no—
9#11762862C2212yes—
10#11762748C412yes—
11#11762729C412yes—
12#11762716—21no—
13#11762705—21no—
14#11762693—22no—
15#11762675C2211yescharacteristic
16#11762539—24no—
17C2×C4×Q8×C17C2211yescharacteristic
18C17×#423C2212yes—
19C2×C17×#101—21no—
20C17×#343—21no—
21C22×Q8×C17D411yescharacteristic
22C22×Dic34C2×C411yescharacteristic
23C2×M16×C17—22no—
24C4×Q8×C17—22no—
25C4×Q8×C17—22no—
26C2×C4⋊C4×C17C2×C412yes—
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C42×C17D412yes—
29C2×C42×C17C2311yescharacteristic
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×#63225—22no—
33C2×#63225—21no—
34C2×C4×Dic17—21no—
35C4×Dic34—22no—
36C4×Dic34—22no—
37C17×C4⋊C8—22no—
38C17×C4⋊C8—22no—
39C17×#101—42no—
40#10587502—22no—
41#10587502—22no—
42#10587502—22no—
43#10587502—21no—
44#10587502C2×C412yes—
45C22⋊#3622—22no—
46C4⋊#3622—24no—
47C4⋊#3622—22no—
48#10587474—24no—
49C4×#3622D414yes—
50C2×Q8×C17—22no—
51C2×Q8×C17—21no—
52C2×Q8×C17—21no—
53C2×Q8×C17—22no—
54C22×C4×C17C22⋊C412yes—
55C22×C4×C17C22⋊C412yes—
56C22×C4×C17C22×C411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×Dic17—21no—
60C22×Dic17—22no—
61C22×Dic17—21no—
62C2×Dic34—22no—
63C2×Dic34—42no—
64M16×C17—42no—
65M16×C17—42no—
66C2×C8×C17—42no—
67C4⋊C4×C17—24no—
68C4⋊C4×C17—22no—
69C42×C17—22no—
70C42×C17—22no—
71C42×C17C2×D412yes—
72C42×C17#4112yes—
73C4⋊Dic17—22no—
74C4⋊Dic17—41no—
75C4⋊Dic17—41no—
76#63225—44no—
77#63225—41no—
78#63225—41no—
79C4×Dic17—42no—
80C2×#3622—24no—
81#9488—171nomaximal, Sylow
82C23×C17C2×C22⋊C411yescharacteristic
83Q8×C17—42no—
84Q8×C17—42no—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—22no—
88C2×C4×C17—22no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17—42no—
92C2×C4×C17C4×D412yes—
93C2×C4×C17#12011yescharacteristic
94C2×C4×C17#12112yes—
95C2×C4×C17#12311yescharacteristic
96C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C17#13711yescharacteristic
98C2×C4×C17#13712yes—
99C2×Dic17—22no—
100C2×Dic17—41no—
101C2×Dic17—41no—
102C2×Dic17—42no—
103C2×Dic17—42no—
104C2×Dic17—42no—
105C2×Dic17—41no—
106C2×Dic17—42no—
107Dic34—24no—
108Dic34—42no—
109C8×C17—82no—
110#3622—44no—
111#2983—171no—
112#2581—171no—
113#1801D1711yescharacteristic
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#46812yes—
127C4×C17#47012yes—
128Dic17—42no—
129Dic17—82no—
130Dic17—81no—
131C2×C4×Q8—171no—
132C2×C4×Q8C2×D1711yescharacteristic
133#446—344no—
134#432—342no—
135#431—172no—
136#423C2×D1712yes—
137C2×#101—21no—
138#400—172no—
139#395—172no—
140#391—341no—
141#389—341no—
142#387—342no—
143#382—171no—
144#343—21no—
145Q8⋊C8—344no—
146C2×C17—21no—
147C2×C17—21no—
148C2×C17#189111yescharacteristic
149C2×C17#189411yescharacteristic
150C2×C17#191211yescharacteristic
151C22×Q8—171no—
152C22×Q8C22⋊D1711yescharacteristic
153C2×M16—22no—
154C4×Q8—22no—
155C4×Q8—22no—
156C4×Q8—342no—
157C4×Q8—342no—
158C2×C4⋊C4—171no—
159C2×C4⋊C4—341no—
160C2×C4⋊C4—341no—
161C2×C4⋊C4—342no—
162C2×C4⋊C4C4×D1712yes—
163C2×C4⋊C4C22⋊D1711yescharacteristic
164C2×C42—341no—
165C2×C42D6812yes—
166C2×C42C22×D1711yescharacteristic
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8—344no—
170C4⋊C8—342no—
171#101—42no—
172C22⋊C8—342no—
173#97—344no—
174C4×C8—174no—
175#95—172no—
176#95—341no—
177#95—342no—
178#95—342no—
179#95—342no—
180C17#948811yescharacteristic, complemented, Sylow
181C2×Q8—21no—
182C2×Q8—22no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8—342no—
186C2×Q8—682no—
187C22×C4—341no—
188C22×C4—342no—
189C22×C4—341no—
190C22×C4#6322712yes—
191C22×C4#6322712yes—
192C22×C4C2×C4×D1711yescharacteristic
193C22×C4C2×D6811yescharacteristic
194C22×C4C2×C22⋊D1711yescharacteristic
195M16—42no—
196M16—42no—
197C2×C8—42no—
198C2×C8—344no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—342no—
202C4⋊C4—684no—
203C4⋊C4—681no—
204C4⋊C4—681no—
205C4⋊C4—681no—
206C4⋊C4—681no—
207C42—22no—
208C42—22no—
209C42—682no—
210C42D4×D1712yes—
211C42#6325412yes—
212C23C2×#6322711yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—344no—
216Q8—682no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—342no—
225C2×C4—681no—
226C2×C4—681no—
227C2×C4—682no—
228C2×C4—682no—
229C2×C4—682no—
230C2×C4—682no—
231C2×C4—681no—
232C2×C4#1058756712yes—
233C2×C4#1058756811yescharacteristic
234C2×C4#1058757211yescharacteristic
235C2×C4#1058761811yescharacteristic
236C2×C4#1058762512yes—
237C2×C4#1058762811yescharacteristic
238C2×C4#1058763712yes—
239C8—82no—
240C8—684no—
241C22—21no—
242C22—21no—
243C22#1176268611yescharacteristic
244C22#1176280811yescharacteristic
245C22#1176281711yescharacteristic
246C4—21no—
247C4—21no—
248C4—22no—
249C4—42no—
250C4—42no—
251C4—682no—
252C4—1362no—
253C4—1361no—
254C4#1176305312yes—
255C4#1176306512yes—
256C2—21no—
257C2—21no—
258C2#1452920011yescharacteristic
259C2#1452921511yescharacteristic
260C2#1452931911yescharacteristic
subgroupG/H
centerC22#11762686
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1801C2
socleC22×C17#386
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenter#1801D17
hypocenterC17#9488
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

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
#145341462
#145272122
#145266442
C17×#18012
#948817