Finite Group Databasebeta

← #17948959

Subgroups — #17948959

Order 4352.

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

normal subgroups only

This group has 388 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
1C4×#10587553C211yesmaximal, characteristic
2C4×#10587551C211yesmaximal, characteristic
3#14529079C211yesmaximal, characteristic
4C2×#10587553—21no—
5C2×#10587551—21no—
6C4×#63247—21no—
7C4×C22⋊#595—21no—
8#11763689C412yescomplemented
9#11763687C412yes—
10C22×#63223C411yescharacteristic, complemented
11C2×C4×C22⋊D17C2211yescharacteristic
12C2×#10587491—21no—
13#11762563—21no—
14C2×C17×C22⋊C8C411yescharacteristic, complemented
15C23×C4×C17C2×C411yescharacteristic
16C22×C22⋊D17D411yescharacteristic
17C22×C4×D17D411yescharacteristic
18C2×C22⋊#595—22no—
19C2×#63247—22no—
20C2×C4×#595—41no—
21C22×C8×C17—21no—
22C2×C22⋊Dic17Q811yescharacteristic
23C4×C22⋊D17—41no—
24C4×C22⋊D17—41no—
25C2×#63227C2×C411yescharacteristic
26C2×#63225C2×C411yescharacteristic
27C2×C4×Dic17D411yescharacteristic
28C2×#63223—41no—
29C2×#63223—42no—
30C22×#3622—21no—
31#10587553—24no—
32#10587551—24no—
33(C2×#595)⋊C4—41no—
34#10587542—41no—
35C4×#3624—41no—
36C17×C22⋊C8—41no—
37#10587491—42no—
38C24×C17C4⋊C411yescharacteristic
39C23×D17C22⋊C411yescharacteristic
40C22×#595—42no—
41C22×C4×C17—21no—
42C22×C4×C17—21no—
43C22×C4×C17—41no—
44C22×C4×C17—41no—
45C22×C4×C17C4211yescharacteristic
46C22×C4×C17C22⋊C411yescharacteristic
47C2×C22⋊D17—22no—
48C2×C22⋊D17—22no—
49C2×C22⋊D17—41no—
50C22×Dic17C22⋊C411yescharacteristic
51C22×Dic17C4⋊C411yescharacteristic
52C22×Dic17C4⋊C411yescharacteristic
53C2×C4×D17—21no—
54C2×C4×D17—21no—
55C2×C4×D17—41no—
56C2×C4×D17—41no—
57C22⋊#595—24no—
58C22⋊#595—42no—
59#63247—24no—
60#63247—42no—
61C2×#3624—42no—
62C4×#595—81no—
63C4×#595—81no—
64C2×C8×C17—41no—
65C2×C8×C17—41no—
66C2×C8×C17—41no—
67C22⋊Dic17—41no—
68#63227—41no—
69#63225—41no—
70C4×Dic17—21no—
71C4×Dic17—21no—
72#63223—42no—
73#63223—42no—
74C2×#3622—22no—
75C2×#3622—41no—
76C2×#3622—41no—
77#7282—171nomaximal, Sylow
78C23×C17—21no—
79C23×C17—21no—
80C23×C17—21no—
81C23×C17—41no—
82C23×C17—41no—
83C23×C17#9511yescharacteristic
84C22×D17—21no—
85C22×D17—21no—
86C22×D17—41no—
87C22×D17—41no—
88C22×D17#10412yes—
89C2×#595—44no—
90C2×#595—82no—
91C2×#595—82no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—42no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17#9911yescharacteristic
100C2×C4×C17#9911yescharacteristic
101C22⋊D17—44no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—21no—
106C2×Dic17—41no—
107C2×Dic17—41no—
108C2×Dic17#10412yes—
109C4×D17—41no—
110C4×D17—41no—
111C4×D17—81no—
112#3624—44no—
113C8×C17—81no—
114#3622—42no—
115#1870—171no—
116C4×#100—171no—
117C4×#99—171no—
118C22×C17—21no—
119C22×C17—21no—
120C22×C17—41no—
121C22×C17—41no—
122C22×C17—41no—
123C22×C17—81no—
124C22×C17—81no—
125C22×C17#33911yescharacteristic
126C22×C17#33911yescharacteristic
127C22×C17#34211yescharacteristic
128C2×D17—22no—
129C2×D17—41no—
130C2×D17—41no—
131C2×D17—42no—
132C2×D17—81no—
133#595—84no—
134C4×C17—21no—
135C4×C17—41no—
136C4×C17AΣL(1,𝔽16)11yescharacteristic
137C4×C17#35211yescharacteristic
138Dic17—22no—
139Dic17—41no—
140Dic17—41no—
141C22×M16—171no—
142C2×C4×D4—171no—
143C2×#100—341no—
144C2×#99—341no—
145C2×C22⋊C8—341no—
146C2×C22⋊C8#59511yescharacteristic, complemented
147C4×M16—341no—
148C4×C22⋊C4—341no—
149#343—172no—
150#342—172no—
151#336—341no—
152C2×C17—21no—
153C2×C17—21no—
154C2×C17—81no—
155C2×C17#129711yescharacteristic
156C2×C17#139011yescharacteristic
157C2×C17#139511yescharacteristic
158D17—42no—
159C22×D4—171no—
160C23×C4—171no—
161C23×C4C2×#59511yescharacteristic
162C2×M16—342no—
163C2×M16—682no—
164C2×M16—681no—
165C22×C8—21no—
166C22×C8—341no—
167C4×D4—681no—
168C4×D4—681no—
169C2×C4⋊C4—171no—
170C2×C22⋊C4—171no—
171C2×C22⋊C4—171no—
172C2×C22⋊C4—342no—
173C2×C42—171no—
174C2×C42—681no—
175#100—344no—
176#99—344no—
177C22⋊C8—41no—
178C22⋊C8—682no—
179#97—681no—
180C4×C8—681no—
181#95—681no—
182C17#728211yescharacteristic, complemented, Sylow
183C24—171no—
184C24C4⋊#59511yescharacteristic
185C2×D4—342no—
186C2×D4—342no—
187C2×D4—681no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—171no—
193C22×C4—171no—
194C22×C4—171no—
195C22×C4—341no—
196C22×C4—341no—
197C22×C4—681no—
198C22×C4—681no—
199C22×C4—682no—
200C22×C4C4×#59511yescharacteristic
201C22×C4C22⋊#59511yescharacteristic
202M16—344no—
203M16—682no—
204M16—682no—
205M16—682no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—342no—
210C2×C8—681no—
211C2×C8—682no—
212C2×C8—681no—
213C4⋊C4—681no—
214C22⋊C4—344no—
215C22⋊C4—681no—
216C22⋊C4—681no—
217C22⋊C4—682no—
218C42—341no—
219C42—341no—
220C42—1361no—
221C42—1361no—
222C23—21no—
223C23—21no—
224C23—21no—
225C23—41no—
226C23—41no—
227C23—172no—
228C23—341no—
229C23—341no—
230C23—681no—
231C23—681no—
232C23(C2×#595)⋊C411yescharacteristic
233D4—684no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—172no—
242C2×C4—341no—
243C2×C4—341no—
244C2×C4—341no—
245C2×C4—341no—
246C2×C4—681no—
247C2×C4—681no—
248C2×C4—681no—
249C2×C4—681no—
250C2×C4—684no—
251C2×C4—1361no—
252C2×C4—1362no—
253C2×C4—1362no—
254C2×C4#1058753911yescharacteristic
255C2×C4#1058755111yescharacteristic
256C8—81no—
257C8—684no—
258C8—682no—
259C22—21no—
260C22—21no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—81no—
265C22—81no—
266C22—342no—
267C22—682no—
268C22—681no—
269C22—681no—
270C22—1361no—
271C22#1176368111yescharacteristic
272C22#1176368111yescharacteristic
273C22#1176368711yescharacteristic
274C4—21no—
275C4—41no—
276C4—342no—
277C4—681no—
278C4—681no—
279C4—1364no—
280C4#1176371011yescharacteristic
281C4#1176371211yescharacteristic
282C2—21no—
283C2—21no—
284C2—81no—
285C2—682no—
286C2#1454366411yescharacteristic
287C2#1454386911yescharacteristic
288C2#1454388411yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC22×C4×C17C42
FrattiniC23×C4C2×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17#342
prime radicalC22×C22⋊D17D4
cosocleC2×C4×C22⋊D17C22
hypercenterC2×C22⋊C8#595
hypocenterC17#7282
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
8. #11763689C4semidirect
10. C22×#63223C4semidirect
14. C2×C17×C22⋊C8C4semidirect
146. C2×C22⋊C8#595semidirect
182. C17#7282semidirect

Maximal subgroups

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

subgroupindex
C4×#105875532
C4×#105875512
#145290792
#728217