Finite Group Databasebeta

← #16938458

Subgroups — #16938458

Order 4352.

382 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 95 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#14529760C212yesmaximal
3#14528900C211yesmaximal, characteristic
4#14527475C212yesmaximal
5C17×#1292C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763105—22no—
8#11763050—22no—
9#11763020—22no—
10C2×C4⋊#3622C2211yescharacteristic
11C42×Dic17C2211yescharacteristic
12#11762570—22no—
13#11762570—22no—
14#11762563—22no—
15#11762557—22no—
16#11762554—22no—
17C17×#423C2212yes—
18C2×C17×C4⋊C8C2211yescharacteristic
19C2×M16×C17—22no—
20C22×C8×C17D412yes—
21C2×C42×C17C2311yescharacteristic
22#10587612—22no—
23#10587610—22no—
24#10587610—22no—
25C2×C4×Dic17—21no—
26C2×C4×Dic17—21no—
27C2×C4×Dic17D411yescharacteristic
28C2×C4×Dic17D411yescharacteristic
29C22×#3622—21no—
30C2×Dic68—22no—
31#10587556—22no—
32#10587555D412yes—
33#10587555D412yes—
34C4×Dic34—22no—
35C4×Dic34—22no—
36C17×C4⋊C8—22no—
37C17×C4⋊C8—22no—
38C17×C4⋊C8—22no—
39#10587489—22no—
40#10587487—24no—
41C4⋊#3622—22no—
42C22×C4×C17C2×D411yescharacteristic
43C22×C4×C17C2×D411yescharacteristic
44C22×C4×C17#4111yescharacteristic
45C22×Dic17—21no—
46C22×Dic17—21no—
47C2×Dic34—22no—
48C2×Dic34—22no—
49M16×C17—42no—
50M16×C17—42no—
51C2×C8×C17—22no—
52C2×C8×C17—42no—
53C2×C8×C17—42no—
54C42×C17C2×D412yes—
55C42×C17#4112yes—
56C22⋊Dic17—42no—
57C4⋊Dic17—22no—
58C4⋊Dic17—22no—
59C4⋊Dic17—22no—
60C4⋊Dic17—22no—
61#63225—42no—
62#63225—42no—
63C4×Dic17—21no—
64C4×Dic17—22no—
65C4×Dic17—42no—
66C4×Dic17—41no—
67C4×Dic17—41no—
68C4×Dic17—42no—
69C4×Dic17Q1612yescomplemented
70C2×#3622—42no—
71C2×#3622—41no—
72Dic68—82no—
73#10523—171nomaximal, Sylow
74C23×C17#12111yescharacteristic
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—41no—
78C2×C4×C17#12011yescharacteristic
79C2×C4×C17#12112yes—
80C2×C4×C17#12312yes—
81C2×C4×C17#12411yescharacteristic
82C2×C4×C17C2×Q1611yescharacteristic
83C2×C4×C17#13511yescharacteristic
84C2×C4×C17#13712yes—
85C2×Dic17—22no—
86C2×Dic17—22no—
87C2×Dic17—41no—
88C2×Dic17—41no—
89C2×Dic17—41no—
90C2×Dic17—41no—
91C2×Dic17—42no—
92C2×Dic17—42no—
93Dic34—42no—
94Dic34—42no—
95Dic34—82no—
96C8×C17—42no—
97C8×C17—82no—
98#3622—81no—
99#3249—171no—
100#1994—172no—
101#1831—171no—
102#1550—172no—
103#1292D1711yescharacteristic
104C22×C17—21no—
105C22×C17—21no—
106C22×C17#39411yescharacteristic
107C22×C17#46711yescharacteristic
108C22×C17#47011yescharacteristic
109C4×C17—22no—
110C4×C17—21no—
111C4×C17#45411yescharacteristic
112C4×C17#45511yescharacteristic
113C4×C17#46212yes—
114C4×C17#46412yes—
115Dic17—42no—
116Dic17—42no—
117Dic17—82no—
118Dic17—82no—
119#533—172no—
120#477—342no—
121#467—342no—
122#462—342no—
123#423C2×D1712yes—
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—342no—
138C2×M16—22no—
139C22×C8—341no—
140C22×C8D6812yes—
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—171no—
150C2×C42—171no—
151C2×C42—341no—
152C2×C42—341no—
153C2×C42C22×D1711yescharacteristic
154#107—342no—
155C4⋊C8—22no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—342no—
159#103—344no—
160C17#1052311yescharacteristic, complemented, Sylow
161C2×Q8—342no—
162C2×Q8—342no—
163C22×C4—341no—
164C22×C4—341no—
165C22×C4C2×D6811yescharacteristic
166C22×C4D4×D1711yescharacteristic
167C22×C4#6325611yescharacteristic
168Q16—1362no—
169M16—42no—
170M16—42no—
171C2×C8—22no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—682no—
175C2×C8—681no—
176C4⋊C4—342no—
177C4⋊C4—342no—
178C4⋊C4—342no—
179C4⋊C4—342no—
180C4⋊C4—682no—
181C4⋊C4—682no—
182C22⋊C4—682no—
183C42—172no—
184C42—341no—
185C42—342no—
186C42—681no—
187C42—681no—
188C42—682no—
189C42—682no—
190C42#6325212yes—
191C42D4×D1712yes—
192C23#1058758111yescharacteristic
193Q8—682no—
194Q8—682no—
195Q8—1362no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—342no—
200C2×C4—342no—
201C2×C4—681no—
202C2×C4—681no—
203C2×C4—681no—
204C2×C4—681no—
205C2×C4—682no—
206C2×C4—682no—
207C2×C4#1058756111yescharacteristic
208C2×C4#1058756811yescharacteristic
209C2×C4#1058757012yes—
210C2×C4#1058758012yes—
211C2×C4#1058759811yescharacteristic
212C2×C4#1058760112yes—
213C2×C4Q16×D1711yescharacteristic
214C8—42no—
215C8—82no—
216C8—1361no—
217C22—21no—
218C22—21no—
219C22#1176272711yescharacteristic
220C22#1176305111yescharacteristic
221C22#1176306811yescharacteristic
222C4—22no—
223C4—21no—
224C4—682no—
225C4—682no—
226C4—1362no—
227C4—1362no—
228C4#1176298411yescharacteristic
229C4#1176298911yescharacteristic
230C4#1176301812yes—
231C4#1176303012yes—
232C2—21no—
233C2—21no—
234C2#1453001411yescharacteristic
235C2#1453007211yescharacteristic
236C2#1453010811yescharacteristic
subgroupG/H
centerC22#11762727
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1292C2
socleC22×C17#394
prime radicalC23×C17#121
hypercenter#1292D17
hypocenterC17#10523
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
69. 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
#145401292
#145297602
#145289002
#145274752
C17×#12922
#1052317