Finite Group Databasebeta

← #16938457

Subgroups — #16938457

Order 4352.

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

normal subgroups only

This group has 382 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#14540129C211yesmaximal, characteristic
2#14529761C212yesmaximal
3#14527472C212yesmaximal
4#14526659C211yesmaximal, characteristic
5C17×#1831C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763105—22no—
8#11763050—22no—
9#11763020—22no—
10#11762833C2212yes—
11#11762569—22no—
12#11762569—22no—
13#11762557—22no—
14#11762556—22no—
15C2×C17×C4⋊C8C2211yescharacteristic
16C2×C17×C4⋊C8C2211yescharacteristic
17C43×C17C2211yescharacteristic
18C17×#336—22no—
19C22×C8×C17—21no—
20C22×C8×C17D412yes—
21C2×C42×C17—21no—
22C2×C42×C17—21no—
23C2×C42×C17D411yescharacteristic
24C2×C42×C17D411yescharacteristic
25C2×C42×C17C2311yescharacteristic
26#10587612—22no—
27#10587610—22no—
28#10587610—22no—
29C2×#63223—22no—
30C2×Dic68—22no—
31#10587556—22no—
32#10587555D412yes—
33#10587555D412yes—
34C4×Dic34—22no—
35C4×Dic34—22no—
36C17×C4⋊C8—22no—
37C17×C4⋊C8—22no—
38#10587489—22no—
39#10587487—24no—
40C4⋊#3622—22no—
41C4⋊#3622—22no—
42C22×C4×C17—21no—
43C22×C4×C17—21no—
44C22×C4×C17C2×D411yescharacteristic
45C22×C4×C17C2×D411yescharacteristic
46C22×C4×C17#4111yescharacteristic
47C2×Dic34—22no—
48C2×Dic34—22no—
49C2×C8×C17—22no—
50C2×C8×C17—42no—
51C2×C8×C17—42no—
52C2×C8×C17—41no—
53C42×C17—21no—
54C42×C17—22no—
55C42×C17—41no—
56C42×C17—41no—
57C42×C17—42no—
58C42×C17Q1612yescomplemented
59C42×C17C2×D412yes—
60C42×C17#4112yes—
61C22⋊Dic17—42no—
62C4⋊Dic17—22no—
63C4⋊Dic17—22no—
64C4⋊Dic17—22no—
65C4⋊Dic17—22no—
66#63225—42no—
67#63225—42no—
68C4×Dic17—42no—
69#63223—42no—
70#63223—42no—
71C2×#3622—42no—
72Dic68—82no—
73#10523—171nomaximal, Sylow
74C23×C17#12111yescharacteristic
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—22no—
78C2×C4×C17—22no—
79C2×C4×C17—41no—
80C2×C4×C17—41no—
81C2×C4×C17—41no—
82C2×C4×C17—41no—
83C2×C4×C17—41no—
84C2×C4×C17#12011yescharacteristic
85C2×C4×C17#12112yes—
86C2×C4×C17#12312yes—
87C2×C4×C17#12411yescharacteristic
88C2×C4×C17C2×Q1611yescharacteristic
89C2×C4×C17#13511yescharacteristic
90C2×C4×C17#13712yes—
91C2×Dic17—42no—
92C2×Dic17—42no—
93Dic34—42no—
94Dic34—42no—
95Dic34—82no—
96C8×C17—42no—
97C8×C17—81no—
98#3622—82no—
99#3249—171no—
100#1994—172no—
101#1831D1711yescharacteristic
102#1550—172no—
103#1292—171no—
104C22×C17—21no—
105C22×C17—21no—
106C22×C17#39411yescharacteristic
107C22×C17#46711yescharacteristic
108C22×C17#47011yescharacteristic
109C4×C17—22no—
110C4×C17—21no—
111C4×C17—42no—
112C4×C17—42no—
113C4×C17#45411yescharacteristic
114C4×C17#45511yescharacteristic
115C4×C17#46212yes—
116C4×C17#46412yes—
117Dic17—82no—
118Dic17—82no—
119#533—172no—
120#477—342no—
121#467—342no—
122#462—342no—
123#423—172no—
124C2×C4⋊C8C2×D1711yescharacteristic
125C2×C4⋊C8C2×D1711yescharacteristic
126C43C2×D1711yescharacteristic
127#339—342no—
128#339—342no—
129#336—22no—
130#333—342no—
131#332—342no—
132C2×C17—21no—
133C2×C17—21no—
134C2×C17#204011yescharacteristic
135C2×C17#205011yescharacteristic
136C2×C17#205611yescharacteristic
137C2×Q16—342no—
138C2×M16—342no—
139C22×C8—21no—
140C22×C8C22⋊D1712yes—
141C4⋊Q8—172no—
142C4⋊Q8—172no—
143#125—342no—
144C22⋊Q8—342no—
145C22⋊Q8—342no—
146C4×Q8—342no—
147C4×Q8—342no—
148#117—342no—
149C2×C42—21no—
150C2×C42—21no—
151C2×C42D6811yescharacteristic
152C2×C42D6811yescharacteristic
153C2×C42C22×D1711yescharacteristic
154#107—342no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—342no—
158C4⋊C8—342no—
159#103—344no—
160C17#1052311yescharacteristic, complemented, Sylow
161C2×Q8—342no—
162C2×Q8—342no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C2×D6811yescharacteristic
166C22×C4#6325211yescharacteristic
167C22×C4C2×C22⋊D1711yescharacteristic
168Q16—1362no—
169M16—682no—
170M16—682no—
171C2×C8—22no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—41no—
175C2×C8—682no—
176C4⋊C4—342no—
177C4⋊C4—342no—
178C4⋊C4—342no—
179C4⋊C4—342no—
180C4⋊C4—682no—
181C4⋊C4—682no—
182C22⋊C4—682no—
183C42—21no—
184C42—22no—
185C42—41no—
186C42—41no—
187C42—42no—
188C42—682no—
189C42Dic6812yescomplemented
190C42D4×D1712yes—
191C42#6325612yes—
192C23#1058761611yescharacteristic
193Q8—682no—
194Q8—682no—
195Q8—1362no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—682no—
206C2×C4—682no—
207C2×C4#1058758012yes—
208C2×C4#1058758112yes—
209C2×C4#1058759011yescharacteristic
210C2×C4C2×Dic6811yescharacteristic
211C2×C4#1058759512yes—
212C2×C4#1058762311yescharacteristic
213C2×C4#1058763311yescharacteristic
214C8—42no—
215C8—81no—
216C8—1362no—
217C22—21no—
218C22—21no—
219C22#1176272611yescharacteristic
220C22#1176305011yescharacteristic
221C22#1176306711yescharacteristic
222C4—22no—
223C4—21no—
224C4—42no—
225C4—42no—
226C4—1362no—
227C4—1362no—
228C4#1176298111yescharacteristic
229C4#1176298611yescharacteristic
230C4#1176302012yes—
231C4#1176303212yes—
232C2—21no—
233C2—21no—
234C2#1453001311yescharacteristic
235C2#1453007111yescharacteristic
236C2#1453010711yescharacteristic
subgroupG/H
centerC22#11762726
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1831C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#1831D17
hypocenterC17#10523
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1831

Complements

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

NH ≅ G/Ntype
58. C42×C17Q16semidirect
160. C17#10523semidirect
189. C42Dic68semidirect

Maximal subgroups

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

subgroupindex
#145401292
#145297612
#145274722
#145266592
C17×#18312
#1052317