Finite Group Databasebeta

← #16938454

Subgroups — #16938454

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#14529762C212yesmaximal
2#14528900C211yesmaximal, characteristic
3#14527474C212yesmaximal
4#14526659C211yesmaximal, characteristic
5C17×#3249C211yesmaximal, characteristic
6#11762833C2212yes—
7C2×C4⋊#3622C2211yescharacteristic
8C42×Dic17C2211yescharacteristic
9#11762568—22no—
10#11762568—22no—
11#11762563—22no—
12#11762558—22no—
13#11762555—22no—
14C17×#533C2212yes—
15C17×#477—22no—
16C17×#467—22no—
17C17×#462—22no—
18C2×C17×C4⋊C8C2211yescharacteristic
19C2×Q16×C17—22no—
20C22×C8×C17D412yes—
21C17×C4⋊Q8D412yes—
22C17×C4⋊Q8D412yes—
23C17×#125—22no—
24C17×C22⋊Q8—22no—
25C17×C22⋊Q8—22no—
26C4×Q8×C17—22no—
27C4×Q8×C17—22no—
28C17×#117—22no—
29C2×C42×C17C2311yescharacteristic
30C2×C4×Dic17—21no—
31C2×C4×Dic17—21no—
32C2×C4×Dic17D411yescharacteristic
33C2×C4×Dic17D411yescharacteristic
34C2×#63223—22no—
35C22×#3622—21no—
36C17×#107—22no—
37C17×C4⋊C8—22no—
38C17×#103—24no—
39C4⋊#3622—22no—
40C4⋊#3622—22no—
41C4⋊#3622—22no—
42C2×Q8×C17—22no—
43C2×Q8×C17—22no—
44C22×C4×C17C2×D411yescharacteristic
45C22×C4×C17C2×D411yescharacteristic
46C22×C4×C17#4111yescharacteristic
47C22×Dic17—21no—
48C22×Dic17—21no—
49Q16×C17—82no—
50C2×C8×C17—22no—
51C2×C8×C17—42no—
52C4⋊C4×C17—22no—
53C4⋊C4×C17—22no—
54C4⋊C4×C17—22no—
55C4⋊C4×C17—22no—
56C4⋊C4×C17—42no—
57C4⋊C4×C17—42no—
58C22⋊C4×C17—42no—
59C42×C17—42no—
60C42×C17C2×D412yes—
61C42×C17#4112yes—
62C4×Dic17—21no—
63C4×Dic17—22no—
64C4×Dic17—42no—
65C4×Dic17—41no—
66C4×Dic17—41no—
67C4×Dic17Q1612yescomplemented
68#63223—42no—
69#63223—42no—
70C2×#3622—42no—
71C2×#3622—41no—
72C2×#3622—42no—
73#10523—171nomaximal, Sylow
74C23×C17#12111yescharacteristic
75Q8×C17—42no—
76Q8×C17—42no—
77Q8×C17—82no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—41no—
81C2×C4×C17—42no—
82C2×C4×C17—42no—
83C2×C4×C17#12011yescharacteristic
84C2×C4×C17#12112yes—
85C2×C4×C17#12312yes—
86C2×C4×C17#12411yescharacteristic
87C2×C4×C17C2×Q1611yescharacteristic
88C2×C4×C17#13511yescharacteristic
89C2×C4×C17#13712yes—
90C2×Dic17—22no—
91C2×Dic17—22no—
92C2×Dic17—41no—
93C2×Dic17—41no—
94C2×Dic17—41no—
95C2×Dic17—41no—
96C8×C17—42no—
97#3622—81no—
98#3622—82no—
99#3249D1711yescharacteristic
100#1994—172no—
101#1831—171no—
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—82no—
112C4×C17—82no—
113C4×C17#45411yescharacteristic
114C4×C17#45511yescharacteristic
115C4×C17#46212yes—
116C4×C17#46412yes—
117Dic17—42no—
118Dic17—42no—
119#533C2×D1712yes—
120#477—22no—
121#467—22no—
122#462—22no—
123#423—172no—
124C2×C4⋊C8—171no—
125C2×C4⋊C8C2×D1711yescharacteristic
126C43—171no—
127#339—342no—
128#339—342no—
129#336—342no—
130#333—342no—
131#332—342no—
132C2×C17—21no—
133C2×C17—21no—
134C2×C17#204011yescharacteristic
135C2×C17#205011yescharacteristic
136C2×C17#205611yescharacteristic
137C2×Q16—22no—
138C2×M16—342no—
139C22×C8—341no—
140C22×C8C22⋊D1712yes—
141C4⋊Q8C22⋊D1712yes—
142C4⋊Q8C22⋊D1712yes—
143#125—22no—
144C22⋊Q8—22no—
145C22⋊Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148#117—22no—
149C2×C42—171no—
150C2×C42—171no—
151C2×C42—341no—
152C2×C42—341no—
153C2×C42C22×D1711yescharacteristic
154#107—22no—
155C4⋊C8—22no—
156C4⋊C8—342no—
157C4⋊C8—342no—
158C4⋊C8—342no—
159#103—24no—
160C17#1052311yescharacteristic, complemented, Sylow
161C2×Q8—22no—
162C2×Q8—22no—
163C22×C4—341no—
164C22×C4—341no—
165C22×C4D4×D1711yescharacteristic
166C22×C4#6325411yescharacteristic
167C22×C4C2×C22⋊D1711yescharacteristic
168Q16—82no—
169M16—682no—
170M16—682no—
171C2×C8—22no—
172C2×C8—42no—
173C2×C8—682no—
174C2×C8—682no—
175C2×C8—681no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C22⋊C4—42no—
183C42—42no—
184C42—172no—
185C42—341no—
186C42—342no—
187C42—681no—
188C42—681no—
189C42—682no—
190C42#6325412yes—
191C42C2×C22⋊D1712yes—
192C23#1058762411yescharacteristic
193Q8—42no—
194Q8—42no—
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—342no—
202C2×C4—342no—
203C2×C4—681no—
204C2×C4—681no—
205C2×C4—681no—
206C2×C4—681no—
207C2×C4Q16×D1711yescharacteristic
208C2×C4#1058760412yes—
209C2×C4#1058760511yescharacteristic
210C2×C4#1058762112yes—
211C2×C4#1058762211yescharacteristic
212C2×C4#1058762512yes—
213C2×C4#1058763911yescharacteristic
214C8—42no—
215C8—1361no—
216C8—1362no—
217C22—21no—
218C22—21no—
219C22#1176272311yescharacteristic
220C22#1176304711yescharacteristic
221C22#1176306411yescharacteristic
222C4—22no—
223C4—21no—
224C4—82no—
225C4—82no—
226C4—682no—
227C4—682no—
228C4#1176298211yescharacteristic
229C4#1176298711yescharacteristic
230C4#1176301712yes—
231C4#1176303312yes—
232C2—21no—
233C2—21no—
234C2#1453001011yescharacteristic
235C2#1453006811yescharacteristic
236C2#1453010411yescharacteristic
subgroupG/H
centerC22#11762723
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#3249C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#3249D17
hypocenterC17#10523
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
67. C4×Dic17Q16semidirect
160. C17#10523semidirect

Maximal subgroups

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

subgroupindex
#145297622
#145289002
#145274742
#145266592
C17×#32492
#1052317