Finite Group Databasebeta

← #17948969

Subgroups — #17948969

Order 4352.

324 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 58 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#14544023C211yesmaximal, characteristic
2#14544019C211yesmaximal, characteristic
3#14529079C211yesmaximal, characteristic
4#11763826—21no—
5#11763777—21no—
6#11763655C412yes—
7#11763653C412yes—
8#11763652—21no—
9#11763652—21no—
10C22×#63223C411yescharacteristic
11C2×C4×C22⋊D17C2211yescharacteristic
12C2×#10587491—21no—
13#11762563—21no—
14C2×C17×C22⋊C8C411yescharacteristic
15C23×C4×C17C2×C411yescharacteristic
16C22×C22⋊D17Q811yescharacteristic
17C22×C4×D17D411yescharacteristic
18C2×#63242—41no—
19C22×C8×C17—21no—
20C2×C22⋊Dic17D411yescharacteristic
21C4×C22⋊D17—41no—
22C4×C22⋊D17—41no—
23C2×#63227C2×C411yescharacteristic
24C2×#63225C2×C411yescharacteristic
25C2×C4×Dic17D411yescharacteristic
26C2×#63223—41no—
27C2×#63223—42no—
28C22×#3622—21no—
29C22⋊#3624—22no—
30C22⋊#3624—22no—
31#10587544—41no—
32#10587543—41no—
33C4×#3624—41no—
34C17×C22⋊C8—41no—
35#10587491—42no—
36C24×C17C4⋊C411yescharacteristic
37C23×D17C4⋊C411yescharacteristic
38C22×C4×C17—21no—
39C22×C4×C17—21no—
40C22×C4×C17—41no—
41C22×C4×C17—41no—
42C22×C4×C17C4211yescharacteristic
43C22×C4×C17C22⋊C411yescharacteristic
44C2×C22⋊D17—22no—
45C2×C22⋊D17—22no—
46C2×C22⋊D17—41no—
47C22×Dic17C22⋊C411yescharacteristic
48C22×Dic17C22⋊C411yescharacteristic
49C22×Dic17C4⋊C411yescharacteristic
50C2×C4×D17—21no—
51C2×C4×D17—21no—
52C2×C4×D17—41no—
53C2×C4×D17—41no—
54C2×#3624—42no—
55C2×#3624—42no—
56#63242—81no—
57#63242—81no—
58C2×C8×C17—41no—
59C2×C8×C17—41no—
60C2×C8×C17—41no—
61C22⋊Dic17—41no—
62#63227—41no—
63#63225—41no—
64C4×Dic17—21no—
65C4×Dic17—21no—
66#63223—42no—
67#63223—42no—
68C2×#3622—22no—
69C2×#3622—41no—
70C2×#3622—41no—
71#7285—171nomaximal, Sylow
72C23×C17—21no—
73C23×C17—21no—
74C23×C17—21no—
75C23×C17—41no—
76C23×C17—41no—
77C23×C17#9511yescharacteristic
78C22×D17—21no—
79C22×D17—21no—
80C22×D17—41no—
81C22×D17—41no—
82C22×D17#10812yes—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—42no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17#9911yescharacteristic
91C2×C4×C17#9911yescharacteristic
92C22⋊D17—44no—
93C2×Dic17—21no—
94C2×Dic17—21no—
95C2×Dic17—21no—
96C2×Dic17—21no—
97C2×Dic17—41no—
98C2×Dic17—41no—
99C2×Dic17#10812yes—
100C4×D17—41no—
101C4×D17—41no—
102C4×D17—81no—
103#3624—82no—
104#3624—82no—
105C8×C17—81no—
106#3622—42no—
107#1870—171no—
108#1460—171no—
109#1459—171no—
110C22×C17—21no—
111C22×C17—21no—
112C22×C17—41no—
113C22×C17—41no—
114C22×C17—41no—
115C22×C17—81no—
116C22×C17—81no—
117C22×C17#34111yescharacteristic
118C22×C17#34111yescharacteristic
119C22×C17#34211yescharacteristic
120C2×D17—22no—
121C2×D17—41no—
122C2×D17—41no—
123C2×D17—42no—
124C2×D17—81no—
125C4×C17—21no—
126C4×C17—41no—
127C4×C17AΣL(1,𝔽16)11yescharacteristic
128C4×C17#35211yescharacteristic
129Dic17—22no—
130Dic17—41no—
131Dic17—41no—
132C22×M16—171no—
133C2×C4×D4—171no—
134#431—341no—
135C2×C22⋊C8—341no—
136C2×C22⋊C8—341no—
137C2×C22⋊C8#59511yescharacteristic
138#336—341no—
139#324—172no—
140#323—172no—
141#323—341no—
142#323—341no—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17—81no—
146C2×C17#129811yescharacteristic
147C2×C17#139011yescharacteristic
148C2×C17#139511yescharacteristic
149D17—42no—
150C22×D4—171no—
151C23×C4—171no—
152C23×C4C2×#59511yescharacteristic
153C2×M16—682no—
154C2×M16—681no—
155C22×C8—21no—
156C22×C8—341no—
157C22×C8—681no—
158C4×D4—681no—
159C4×D4—681no—
160C2×C4⋊C4—171no—
161C2×C22⋊C4—171no—
162C2×C22⋊C4—171no—
163C2×C42—171no—
164C4⋊C8—681no—
165C22⋊C8—41no—
166C22⋊C8—342no—
167C22⋊C8—342no—
168C22⋊C8—682no—
169C22⋊C8—681no—
170C4×C8—681no—
171C17#728511yescharacteristic, complemented, Sylow
172C24—171no—
173C24C4⋊#59511yescharacteristic
174C2×D4—342no—
175C2×D4—342no—
176C2×D4—681no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—171no—
182C22×C4—171no—
183C22×C4—171no—
184C22×C4—341no—
185C22×C4—341no—
186C22×C4—681no—
187C22×C4—681no—
188C22×C4C4×#59511yescharacteristic
189C22×C4C22⋊#59511yescharacteristic
190M16—682no—
191M16—682no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—342no—
196C2×C8—681no—
197C2×C8—681no—
198C2×C8—682no—
199C2×C8—682no—
200C2×C8—1361no—
201C2×C8—1361no—
202C4⋊C4—681no—
203C22⋊C4—681no—
204C22⋊C4—681no—
205C42—341no—
206C42—341no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—41no—
211C23—41no—
212C23—172no—
213C23—341no—
214C23—341no—
215C23—681no—
216C23—681no—
217C23(C2×#595)⋊C411yescharacteristic
218D4—684no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—172no—
227C2×C4—341no—
228C2×C4—341no—
229C2×C4—341no—
230C2×C4—341no—
231C2×C4—681no—
232C2×C4—681no—
233C2×C4—681no—
234C2×C4—681no—
235C2×C4—1361no—
236C2×C4#1058753911yescharacteristic
237C2×C4#1058755111yescharacteristic
238C8—81no—
239C8—682no—
240C8—1362no—
241C8—1362no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—81no—
248C22—81no—
249C22—342no—
250C22—682no—
251C22—681no—
252C22—681no—
253C22—1361no—
254C22#1176368411yescharacteristic
255C22#1176368411yescharacteristic
256C22#1176368711yescharacteristic
257C4—21no—
258C4—41no—
259C4—342no—
260C4—681no—
261C4—681no—
262C4#1176371011yescharacteristic
263C4#1176371211yescharacteristic
264C2—21no—
265C2—21no—
266C2—81no—
267C2—682no—
268C2#1454366611yescharacteristic
269C2#1454386911yescharacteristic
270C2#1454388411yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC22×C4×C17C42
FrattiniC23×C4C2×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17#342
prime radicalC22×C22⋊D17Q8
cosocleC2×C4×C22⋊D17C22
hypercenterC2×C22⋊C8#595
hypocenterC17#7285
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
171. C17#7285semidirect

Maximal subgroups

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

subgroupindex
#145440232
#145440192
#145290792
#728517