Finite Group Databasebeta

← #16948265

Subgroups — #16948265

Order 4352.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#14531020C211yesmaximal, characteristic
2#14530936C211yesmaximal, characteristic, complemented
3#14528302C211yesmaximal, characteristic, complemented
4#14526827C211yesmaximal, characteristic
5#14526766C211yesmaximal, characteristic, complemented
6#14526754C211yesmaximal, characteristic, complemented
7C17×#3402C211yesmaximal, characteristic
8#11763214C2211yescharacteristic
9#11763019—21no—
10#11762634—21no—
11C4⋊#63214C2211yescharacteristic
12#11762613—21no—
13#11762613—21no—
14#11762610—21no—
15#11762585C2211yescharacteristic
16#11762560C2211yescharacteristic
17#11762554—21no—
18C17×#556—21no—
19C17×#497—21no—
20C17×#495C2211yescharacteristic
21C17×#464—21no—
22C17×#463—21no—
23C17×#462—21no—
24C17×#446C2211yescharacteristic
25C17×#440—21no—
26C4×Q16×C17C2211yescharacteristic
27C2×Q16×C17—21no—
28C2×Q16×C17D411yescharacteristic
29C2×Q16×C17D411yescharacteristic
30C2×SD16×C17—21no—
31C2×SD16×C17—21no—
32C2×D8×C17D411yescharacteristic
33C17×C4⋊Q8—21no—
34C17×#126—41no—
35C17×#126—41no—
36C17×#124—21no—
37C17×#124—21no—
38C17×C22⋊Q8—41no—
39C4×Q8×C17—21no—
40C4×Q8×C17—21no—
41C4×Q8×C17D411yescharacteristic
42C4×D4×C17—21no—
43C17×#117—41no—
44C2×#63231—41no—
45#10587555—21no—
46C17×#107D411yescharacteristic
47C17×C4⋊C8—21no—
48C17×C4⋊C8D411yescharacteristic
49C17×#103—21no—
50C17×#103—21no—
51C17×#102—21no—
52C17×#97—21no—
53C4×C8×C17C2311yescharacteristic
54#10587489—21no—
55#10587489—21no—
56C2×#63214—21no—
57C2×#63214—21no—
58#10587481—41no—
59C4⋊#3622—21no—
60C2×Q8×C17—21no—
61C2×Q8×C17—21no—
62C2×Q8×C17D811yescharacteristic
63C2×D4×C17—21no—
64C22×C4×C17—41no—
65C2×Dic34—41no—
66Q16×C17—21no—
67Q16×C17—21no—
68Q16×C17—41no—
69Q16×C17—81no—
70SD16×C17—41no—
71SD16×C17—41no—
72SD16×C17—81no—
73D8×C17—41no—
74C2×C8×C17—21no—
75C2×C8×C17C2×D411yescharacteristic
76C2×C8×C17C2×D411yescharacteristic
77C4⋊C4×C17—21no—
78C4⋊C4×C17—21no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C4⋊C4×C17—41no—
83C4⋊C4×C17D811yescharacteristic
84C22⋊C4×C17—41no—
85C22⋊C4×C17—41no—
86C22⋊C4×C17—41no—
87C22⋊C4×C17—41no—
88C22⋊C4×C17—41no—
89C42×C17—21no—
90C42×C17—41no—
91C42×C17—41no—
92C42×C17C2×D411yescharacteristic
93#63231—82no—
94C4⋊Dic17—41no—
95C4⋊Dic17—41no—
96C2×#3622—41no—
97#63214—41no—
98#63214—41no—
99#12391—171nomaximal, Sylow
100C23×C17—41no—
101Q8×C17—41no—
102Q8×C17—41no—
103Q8×C17—41no—
104Q8×C17—41no—
105Q8×C17—41no—
106D4×C17—41no—
107D4×C17—41no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—82no—
114C2×C4×C17#12011yescharacteristic
115C2×C4×C17C2×D811yescharacteristic
116C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
117C2×Dic17—81no—
118Dic34—81no—
119Dic34—81no—
120C8×C17—21no—
121C8×C17—41no—
122C8×C17#13511yescharacteristic
123C8×C17#13711yescharacteristic
124#3622—81no—
125#3402D1711yescharacteristic
126#2243—171no—
127#2227—171no—
128#1694—171no—
129#1360—171no—
130#1338—171no—
131#1334—171no—
132C22×C17—81no—
133C22×C17—81no—
134C22×C17—81no—
135C22×C17#44711yescharacteristic
136C4×C17—21no—
137C4×C17—21no—
138C4×C17—41no—
139C4×C17—41no—
140C4×C17—81no—
141C4×C17—81no—
142C4×C17—81no—
143C4×C17#45211yescharacteristic
144C4×C17#45511yescharacteristic
145Dic17—161no—
146#556—21no—
147#500—171no—
148#497—21no—
149#495C2×D1711yescharacteristic
150#464—21no—
151#463—21no—
152#462—21no—
153#462—341no—
154#446C2×D1711yescharacteristic
155#440—21no—
156C4×Q16C2×D1711yescharacteristic
157#366—341no—
158C4⋊C16—171no—
159#358—341no—
160#358—341no—
161#357—341no—
162#346—171no—
163#334—171no—
164#332—341no—
165C2×C17—161no—
166C2×C17#164111yescharacteristic
167C2×C17#219011yescharacteristic
168C2×C17#219511yescharacteristic
169C2×Q16—21no—
170C2×Q16—681no—
171C2×Q16C22⋊D1711yescharacteristic
172C2×Q16C22⋊D1711yescharacteristic
173C2×SD16—21no—
174C2×SD16—21no—
175C2×D8C22⋊D1711yescharacteristic
176C4⋊Q8—21no—
177C4⋊Q8—341no—
178#126—41no—
179#126—41no—
180#124—21no—
181#124—21no—
182C22⋊Q8—41no—
183C4×Q8—21no—
184C4×Q8—21no—
185C4×Q8C22⋊D1711yescharacteristic
186C4×D4—21no—
187#117—41no—
188C2×C16—341no—
189C2×C16—341no—
190#107—341no—
191#107—341no—
192#107C22⋊D1711yescharacteristic
193C4⋊C8—21no—
194C4⋊C8—341no—
195C4⋊C8C22⋊D1711yescharacteristic
196#103—21no—
197#103—21no—
198#103—681no—
199#102—21no—
200#97—21no—
201C4×C8C22×D1711yescharacteristic
202C17#1239111yescharacteristic, complemented, Sylow
203C2×Q8—21no—
204C2×Q8—21no—
205C2×Q8—681no—
206C2×Q8#6322811yescharacteristic
207C2×D4—21no—
208C22×C4—41no—
209Q16—21no—
210Q16—21no—
211Q16—41no—
212Q16—81no—
213Q16—1362no—
214SD16—41no—
215SD16—41no—
216SD16—81no—
217D8—41no—
218C2×C8—21no—
219C2×C8—681no—
220C2×C8C2×C22⋊D1711yescharacteristic
221C2×C8C2×C22⋊D1711yescharacteristic
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—681no—
229C4⋊C4—681no—
230C4⋊C4#6322811yescharacteristic
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C42—21no—
237C42—41no—
238C42—41no—
239C42C2×C22⋊D1711yescharacteristic
240C16—681no—
241C16—681no—
242C23—41no—
243Q8—41no—
244Q8—41no—
245Q8—41no—
246Q8—41no—
247Q8—41no—
248Q8—1361no—
249Q8—1361no—
250D4—41no—
251D4—41no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—1361no—
259C2×C4C2×#6322811yescharacteristic
260C2×C4#1058761811yescharacteristic
261C2×C4#1058763911yescharacteristic
262C8—21no—
263C8—41no—
264C8—1361no—
265C8#1058763611yescharacteristic
266C8#1058763711yescharacteristic
267C22—81no—
268C22—81no—
269C22—81no—
270C22#1176294311yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—81no—
276C4—81no—
277C4—81no—
278C4—2721no—
279C4#1176297111yescharacteristic
280C4#1176298711yescharacteristic
281C2—161no—
282C2#1452797711yescharacteristic
283C2#1453073011yescharacteristic
284C2#1453076211yescharacteristic
subgroupG/H
centerC22#11762943
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#3402C2
socleC22×C17#447
prime radicalC2×D8×C17D4
hypercenter#3402D17
hypocenterC17#12391
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #3402

Complements

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

NH ≅ G/Ntype
2. #14530936C2semidirect
3. #14528302C2semidirect
5. #14526766C2semidirect
6. #14526754C2semidirect
202. C17#12391semidirect

Maximal subgroups

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

subgroupindex
#145310202
#145309362
#145283022
#145268272
#145267662
#145267542
C17×#34022
#1239117