Finite Group Databasebeta

← #16938604

Subgroups — #16938604

Order 4352.

364 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 99 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#14539308C211yesmaximal, characteristic
2#14527442C212yesmaximal
3#14527282C212yesmaximal
4#14526615C211yesmaximal, characteristic
5C17×#1940C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763218—22no—
8#11763218—22no—
9#11762862C2212yes—
10#11762847—21no—
11#11762847—21no—
12#11762557—22no—
13#11762554—22no—
14#11762545—22no—
15#11762545—22no—
16C2×C17×C4⋊C8—21no—
17C2×C17×C4⋊C8C2211yescharacteristic
18C2×C17×#97C2211yescharacteristic
19C4×C4⋊C4×C17C2211yescharacteristic
20C17×#336—21no—
21C22×C8×C17—21no—
22C22×C8×C17D411yescharacteristic
23C22×C8×C17D411yescharacteristic
24C2×C4⋊C4×C17—21no—
25C2×C42×C17—21no—
26C2×C42×C17C2311yescharacteristic
27#10587612—22no—
28#10587610—22no—
29#10587610—22no—
30#10587556—22no—
31#10587555D412yes—
32#10587555D412yes—
33C4×Dic34—22no—
34C4×Dic34—22no—
35C17×C4⋊C8—22no—
36C17×C4⋊C8—42no—
37C17×#97—22no—
38C17×#95D411yescharacteristic
39C17×#95D411yescharacteristic
40C22⋊#3622—22no—
41#10587489—21no—
42#10587489—21no—
43#10587489—21no—
44#10587489—21no—
45#10587488—22no—
46#10587488—22no—
47C4⋊#3622—22no—
48C4×#3622—22no—
49C22×C4×C17—21no—
50C22×C4×C17—21no—
51C22×C4×C17C2×D411yescharacteristic
52C22×C4×C17C2×D411yescharacteristic
53C22×C4×C17#4111yescharacteristic
54C2×Dic34—22no—
55C2×Dic34—22no—
56C2×C8×C17—21no—
57C2×C8×C17—21no—
58C2×C8×C17—21no—
59C2×C8×C17—21no—
60C2×C8×C17—41no—
61C2×C8×C17—41no—
62C2×C8×C17—41no—
63C2×C8×C17SD1612yes—
64C2×C8×C17Q1612yes—
65C4⋊C4×C17—42no—
66C42×C17—41no—
67C42×C17—41no—
68C42×C17C2×D412yes—
69C42×C17#4112yes—
70C22⋊Dic17—42no—
71C4⋊Dic17—22no—
72C4⋊Dic17—22no—
73C4⋊Dic17—22no—
74C4⋊Dic17—22no—
75#63225—42no—
76#63225—42no—
77C4×Dic17—42no—
78C2×#3622—42no—
79#10548—171nomaximal, Sylow
80C23×C17#12111yescharacteristic
81C2×C4×C17—22no—
82C2×C4×C17—41no—
83C2×C4×C17—41no—
84C2×C4×C17—41no—
85C2×C4×C17—41no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17#12011yescharacteristic
90C2×C4×C17#12112yes—
91C2×C4×C17#12312yes—
92C2×C4×C17#12411yescharacteristic
93C2×C4×C17C2×SD1611yescharacteristic
94C2×C4×C17C2×Q1611yescharacteristic
95C2×C4×C17#13711yescharacteristic
96C2×C4×C17#13711yescharacteristic
97C2×Dic17—42no—
98C2×Dic17—42no—
99Dic34—82no—
100Dic34—82no—
101C8×C17—22no—
102C8×C17—22no—
103C8×C17—81no—
104#3622—82no—
105#3162—171no—
106#1940D1711yescharacteristic
107#1542—172no—
108#1503—172no—
109#1275—171no—
110C22×C17—21no—
111C22×C17—21no—
112C22×C17#39411yescharacteristic
113C22×C17#46111yescharacteristic
114C22×C17#46211yescharacteristic
115C4×C17—22no—
116C4×C17—22no—
117C4×C17—42no—
118C4×C17—81no—
119C4×C17#44811yescharacteristic
120C4×C17#45111yescharacteristic
121C4×C17#48711yescharacteristic
122C4×C17#49111yescharacteristic
123Dic17—82no—
124Dic17—82no—
125#533—172no—
126#501—342no—
127#501—342no—
128#431—172no—
129#427—341no—
130#427—341no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8C2×D1711yescharacteristic
133C2×#97C2×D1711yescharacteristic
134C4×C4⋊C4C2×D1711yescharacteristic
135#336—21no—
136#333—342no—
137#332—342no—
138#328—342no—
139#328—342no—
140C2×C17—21no—
141C2×C17—21no—
142C2×C17#204311yescharacteristic
143C2×C17#205011yescharacteristic
144C2×C17#205311yescharacteristic
145C22×C8—21no—
146C22×C8C22⋊D1711yescharacteristic
147C22×C8C22⋊D1711yescharacteristic
148C4⋊Q8—172no—
149C4⋊Q8—172no—
150#125—342no—
151C22⋊Q8—342no—
152C22⋊Q8—342no—
153C4×Q8—342no—
154C4×Q8—342no—
155#117—342no—
156C2×C4⋊C4—21no—
157C2×C42—21no—
158C2×C42C22×D1711yescharacteristic
159#107—341no—
160#107—341no—
161#107—341no—
162#107—341no—
163#106—342no—
164#106—342no—
165C4⋊C8—22no—
166C4⋊C8—42no—
167C4⋊C8—342no—
168C22⋊C8—342no—
169#97—22no—
170C4×C8—342no—
171#95D6811yescharacteristic
172#95D6811yescharacteristic
173C17#1054811yescharacteristic, complemented, Sylow
174C2×Q8—342no—
175C2×Q8—342no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4C2×D6811yescharacteristic
179C22×C4#6325211yescharacteristic
180C22×C4C2×C22⋊D1711yescharacteristic
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—682no—
189C2×C8#6322912yes—
190C2×C8#6323112yes—
191C4⋊C4—42no—
192C4⋊C4—342no—
193C4⋊C4—342no—
194C4⋊C4—342no—
195C4⋊C4—342no—
196C4⋊C4—682no—
197C4⋊C4—682no—
198C22⋊C4—682no—
199C42—41no—
200C42—41no—
201C42—682no—
202C42D4×D1712yes—
203C42#6325612yes—
204C23#1058761611yescharacteristic
205Q8—1362no—
206Q8—1362no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—682no—
216C2×C4—682no—
217C2×C4#1058758012yes—
218C2×C4#1058758112yes—
219C2×C4C2×#6322911yescharacteristic
220C2×C4#1058762311yescharacteristic
221C2×C4C2×#6323111yescharacteristic
222C2×C4#1058763311yescharacteristic
223C2×C4#1058763711yescharacteristic
224C2×C4#1058763711yescharacteristic
225C8—22no—
226C8—22no—
227C8—81no—
228C8—1362no—
229C22—21no—
230C22—21no—
231C22#1176272611yescharacteristic
232C22#1176301411yescharacteristic
233C22#1176301911yescharacteristic
234C4—22no—
235C4—22no—
236C4—42no—
237C4—81no—
238C4—1362no—
239C4—1362no—
240C4#1176294711yescharacteristic
241C4#1176296411yescharacteristic
242C4#1176316111yescharacteristic
243C4#1176317911yescharacteristic
244C2—21no—
245C2—21no—
246C2#1453003011yescharacteristic
247C2#1453007111yescharacteristic
248C2#1453009011yescharacteristic
subgroupG/H
centerC2×C4#10587633
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1940C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#1940D17
hypocenterC17#10548
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1940

Complements

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

NH ≅ G/Ntype
173. C17#10548semidirect

Maximal subgroups

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

subgroupindex
#145393082
#145274422
#145272822
#145266152
C17×#19402
#1054817