Finite Group Databasebeta

← #17948701

Subgroups — #17948701

Order 4352.

364 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C4×#10587553C211yesmaximal, characteristic
2#14544019C211yesmaximal, characteristic
3#14529074C211yesmaximal, characteristic
4C2×#10587553C412yes—
5#11763777—21no—
6C4×#63247—21no—
7#11763689—21no—
8#11763655—21no—
9#11763652C412yes—
10C23×#3622C411yescharacteristic
11C2×C4×C22⋊D17C2211yescharacteristic
12C2×#10587491—21no—
13#11762563—21no—
14C2×C17×C22⋊C8C411yescharacteristic
15C23×C4×C17C2×C411yescharacteristic
16C22×C22⋊D17C2×C411yescharacteristic
17C22×C4×D17D411yescharacteristic
18C2×#63247—22no—
19C2×#63242—41no—
20C22×C8×C17—21no—
21C2×C22⋊Dic17C2×C411yescharacteristic
22C4×C22⋊D17—41no—
23C4×C22⋊D17—41no—
24C2×#63227Q811yescharacteristic
25C2×#63225D411yescharacteristic
26C2×C4×Dic17D411yescharacteristic
27C22×#3622—21no—
28C22×#3622—41no—
29C22×#3622—42no—
30#10587553—22no—
31#10587553C814yescomplemented
32C22⋊#3624—22no—
33#10587543—41no—
34#10587542—41no—
35C4×#3624—41no—
36C17×C22⋊C8—41no—
37#10587491—42no—
38C24×C17C4211yescharacteristic
39C23×D17C4⋊C411yescharacteristic
40C22×C4×C17—21no—
41C22×C4×C17—21no—
42C22×C4×C17—41no—
43C22×C4×C17—41no—
44C22×C4×C17C22⋊C411yescharacteristic
45C22×C4×C17C4⋊C411yescharacteristic
46C2×C22⋊D17—41no—
47C2×C22⋊D17—41no—
48C2×C22⋊D17C2×C812yes—
49C2×C22⋊D17M1612yes—
50C22×Dic17C22⋊C411yescharacteristic
51C22×Dic17C22⋊C411yescharacteristic
52C22×Dic17C4⋊C411yescharacteristic
53C2×C4×D17—21no—
54C2×C4×D17—21no—
55C2×C4×D17—41no—
56C2×C4×D17—41no—
57#63247—24no—
58#63247—42no—
59C2×#3624—42no—
60C2×#3624—42no—
61#63242—81no—
62#63242—81no—
63C2×C8×C17—41no—
64C2×C8×C17—41no—
65C2×C8×C17—41no—
66C22⋊Dic17—41no—
67#63227—41no—
68#63225—41no—
69C4×Dic17—21no—
70C4×Dic17—21no—
71C2×#3622—22no—
72C2×#3622—41no—
73C2×#3622—42no—
74C2×#3622—41no—
75C2×#3622—42no—
76#7203—171nomaximal, Sylow
77C23×C17—21no—
78C23×C17—21no—
79C23×C17—41no—
80C23×C17—41no—
81C23×C17#9511yescharacteristic
82C23×C17C4×C811yescharacteristic
83C23×C17#9711yescharacteristic
84C22×D17—21no—
85C22×D17—21no—
86C22×D17—41no—
87C22×D17—41no—
88C22×D17C4⋊C812yes—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—42no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17#9911yescharacteristic
97C2×C4×C17#9911yescharacteristic
98C22⋊D17—42no—
99C22⋊D17—42no—
100C2×Dic17—21no—
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—41no—
105C2×Dic17—41no—
106C2×Dic17C22⋊C812yes—
107C4×D17—41no—
108C4×D17—41no—
109C4×D17—81no—
110#3624—44no—
111#3624—82no—
112C8×C17—81no—
113#3622—42no—
114#1869—171no—
115C4×#100—171no—
116#1459—171no—
117C22×C17—21no—
118C22×C17—21no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17—41no—
122C22×C17—41no—
123C22×C17—42no—
124C22×C17—41no—
125C22×C17—41no—
126C22×C17#33611yescharacteristic
127C22×C17#34211yescharacteristic
128C22×C17#34411yescharacteristic
129C2×D17—22no—
130C2×D17—41no—
131C2×D17—41no—
132C2×D17—42no—
133C2×D17—81no—
134C4×C17—21no—
135C4×C17—41no—
136C4×C17AΣL(1,𝔽16)11yescharacteristic
137C4×C17#35211yescharacteristic
138Dic17—22no—
139Dic17—41no—
140Dic17—41no—
141C23×C8—171no—
142C2×C4×D4—171no—
143C2×#100—172no—
144C2×C22⋊C8—341no—
145C2×C22⋊C8—341no—
146C2×C22⋊C8#59511yescharacteristic
147C4×M16—341no—
148#343—341no—
149#336—341no—
150#324—341no—
151#323—172no—
152C2×C17—21no—
153C2×C17—21no—
154C2×C17—41no—
155C2×C17—41no—
156C2×C17#128211yescharacteristic
157C2×C17#139011yescharacteristic
158C2×C17#139211yescharacteristic
159D17—42no—
160C22×D4—171no—
161C23×C4—171no—
162C23×C4C2×#59511yescharacteristic
163C2×M16—342no—
164C22×C8—21no—
165C22×C8—341no—
166C22×C8—682no—
167C22×C8—681no—
168C22×C8—681no—
169C4×D4—681no—
170C4×D4—681no—
171C2×C4⋊C4—171no—
172C2×C22⋊C4—171no—
173C2×C22⋊C4—171no—
174C2×C42—171no—
175#100—174no—
176#100—342no—
177C22⋊C8—41no—
178C22⋊C8—342no—
179C22⋊C8—682no—
180C22⋊C8—681no—
181#97—681no—
182C4×C8—681no—
183C17#720311yescharacteristic, complemented, Sylow
184C24—171no—
185C24C4×#59511yescharacteristic
186C2×D4—172no—
187C2×D4—172no—
188C2×D4—681no—
189C2×D4—681no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—171no—
195C22×C4—171no—
196C22×C4—171no—
197C22×C4—341no—
198C22×C4—341no—
199C22×C4—681no—
200C22×C4—681no—
201C22×C4C4⋊#59511yescharacteristic
202C22×C4C22⋊#59511yescharacteristic
203M16—344no—
204M16—682no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—342no—
209C2×C8—681no—
210C2×C8—682no—
211C2×C8—682no—
212C2×C8—681no—
213C2×C8—682no—
214C2×C8—682no—
215C2×C8—1361no—
216C2×C8—1361no—
217C4⋊C4—681no—
218C22⋊C4—681no—
219C22⋊C4—681no—
220C42—341no—
221C42—341no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23—172no—
227C23—341no—
228C23—341no—
229C23—681no—
230C23—681no—
231C23C8×#59511yescharacteristic
232C23#1058753211yescharacteristic
233C23(C2×#595)⋊C411yescharacteristic
234D4—682no—
235D4—682no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—172no—
244C2×C4—341no—
245C2×C4—341no—
246C2×C4—341no—
247C2×C4—341no—
248C2×C4—681no—
249C2×C4—681no—
250C2×C4—681no—
251C2×C4—681no—
252C2×C4—1361no—
253C2×C4#1058753911yescharacteristic
254C2×C4#1058755111yescharacteristic
255C8—81no—
256C8—684no—
257C8—682no—
258C8—1362no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—41no—
268C22—342no—
269C22—682no—
270C22—681no—
271C22—681no—
272C22—1361no—
273C22#1176367411yescharacteristic
274C22#1176368711yescharacteristic
275C22#1176369111yescharacteristic
276C4—21no—
277C4—41no—
278C4—342no—
279C4—681no—
280C4—681no—
281C4#1176371011yescharacteristic
282C4#1176371211yescharacteristic
283C2—21no—
284C2—21no—
285C2—41no—
286C2—41no—
287C2—682no—
288C2#1454362611yescharacteristic
289C2#1454386911yescharacteristic
290C2#1454387611yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC23×C17C4×C8
FrattiniC23×C4C2×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17#342
prime radicalC22×C22⋊D17C2×C4
cosocleC2×C4×C22⋊D17C22
hypercenterC2×C22⋊C8#595
hypocenterC17#7203
LCSG ▷ C23×C17 ▷ C22×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
31. #10587553C8semidirect
183. C17#7203semidirect

Maximal subgroups

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

subgroupindex
C4×#105875532
#145440192
#145290742
#720317