Finite Group Databasebeta

← #16938677

Subgroups — #16938677

Order 4352.

448 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 79 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#14539559C211yesmaximal, characteristic
2#14529252C212yesmaximal
3#14527303C212yesmaximal
4#14526661C211yesmaximal, characteristic
5C17×#1851C211yesmaximal, characteristic
6C2×#10587610C2212yes—
7#11763145—22no—
8#11763050—21no—
9#11763050—21no—
10#11762967—22no—
11C2×#10587495—22no—
12#11762773C2212yes—
13#11762577—22no—
14#11762545—22no—
15#11762545—22no—
16C22×M16×C17C2211yescharacteristic
17C2×C17×C4⋊C8—21no—
18C2×C17×C22⋊C8C2211yescharacteristic
19C4×C22⋊C4×C17C2211yescharacteristic
20C17×#336—21no—
21C23×C4×C17C2311yescharacteristic
22C22×Dic34D412yes—
23C2×M16×C17—22no—
24C2×M16×C17—42no—
25C22×C8×C17—21no—
26C22×C8×C17D411yescharacteristic
27C22×C8×C17D411yescharacteristic
28C2×C22⋊C4×C17—21no—
29C2×C42×C17—21no—
30C2×C22⋊Dic17—22no—
31C2×C4⋊Dic17D412yes—
32#10587610—22no—
33#10587610—22no—
34#10587610—22no—
35#10587610—22no—
36C2×#63225—22no—
37C2×#63223—22no—
38C2×Dic68—21no—
39C2×Dic68—21no—
40C17×C4⋊C8—42no—
41C17×C22⋊C8—22no—
42C17×#95D411yescharacteristic
43C17×#95D411yescharacteristic
44C22⋊#3622—22no—
45C22⋊#3622—22no—
46#10587495—44no—
47#10587489—21no—
48#10587489—21no—
49#10587487—22no—
50#10587487—22no—
51C24×C17#4111yescharacteristic
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—41no—
55C22×C4×C17—41no—
56C22×C4×C17C2×D411yescharacteristic
57C22×C4×C17C2×D412yes—
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17#4112yes—
60C22×Dic17—22no—
61C22×Dic17—22no—
62C2×Dic34—22no—
63C2×Dic34—22no—
64C2×Dic34—42no—
65C2×Dic34—42no—
66M16×C17—24no—
67M16×C17—42no—
68C2×C8×C17—22no—
69C2×C8×C17—21no—
70C2×C8×C17—21no—
71C2×C8×C17—41no—
72C2×C8×C17—41no—
73C2×C8×C17—41no—
74C2×C8×C17—41no—
75C22⋊C4×C17—42no—
76C42×C17—41no—
77C42×C17—41no—
78C22⋊Dic17—42no—
79C22⋊Dic17—42no—
80C4⋊Dic17—22no—
81C4⋊Dic17—22no—
82#63225—42no—
83#63225—42no—
84#63223—42no—
85#63223—42no—
86C2×#3622—42no—
87Dic68—81no—
88Dic68—81no—
89#10559—171nomaximal, Sylow
90C23×C17—21no—
91C23×C17—21no—
92C23×C17—41no—
93C23×C17—41no—
94C23×C17#12111yescharacteristic
95C23×C17#12312yes—
96C2×C4×C17—21no—
97C2×C4×C17—22no—
98C2×C4×C17—21no—
99C2×C4×C17—22no—
100C2×C4×C17—22no—
101C2×C4×C17—41no—
102C2×C4×C17—42no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17#12011yescharacteristic
109C2×C4×C17#12112yes—
110C2×C4×C17#12411yescharacteristic
111C2×Dic17—44no—
112C2×Dic17—42no—
113C2×Dic17—42no—
114C2×Dic17—82no—
115Dic34—42no—
116Dic34—42no—
117Dic34—82no—
118C8×C17—42no—
119C8×C17—41no—
120C8×C17—41no—
121#3622—82no—
122#3189—171no—
123#1901—172no—
124#1851D1711yescharacteristic
125#1508—172no—
126#1293—171no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17—22no—
130C22×C17—22no—
131C22×C17—22no—
132C22×C17—81no—
133C22×C17—81no—
134C22×C17#39411yescharacteristic
135C22×C17#47311yescharacteristic
136C22×C17#47311yescharacteristic
137C4×C17—22no—
138C4×C17—21no—
139C4×C17—42no—
140C4×C17—81no—
141C4×C17B(4,𝔽2)11yescharacteristic
142C4×C17#45811yescharacteristic
143Dic17—82no—
144Dic17—82no—
145C22×M16C2×D1711yescharacteristic
146C2×C22⋊Q8—172no—
147#484—342no—
148#467—341no—
149#467—341no—
150#451—342no—
151C2×C4⋊C8—21no—
152C2×#101—342no—
153#407—172no—
154C2×C22⋊C8C2×D1711yescharacteristic
155C4×C22⋊C4C2×D1711yescharacteristic
156#343—342no—
157#336—21no—
158#328—342no—
159#328—342no—
160C2×C17—21no—
161C2×C17—21no—
162C2×C17—42no—
163C2×C17#204411yescharacteristic
164C2×C17#204711yescharacteristic
165C2×C17#205011yescharacteristic
166C22×Q8—172no—
167C23×C4C22×D1711yescharacteristic
168C2×Q16—341no—
169C2×Q16—341no—
170C2×M16—22no—
171C2×M16—42no—
172C2×M16—342no—
173C22×C8—21no—
174C22×C8C22⋊D1711yescharacteristic
175C22×C8C22⋊D1711yescharacteristic
176C22⋊Q8—342no—
177C22⋊Q8—342no—
178C22⋊Q8—342no—
179C22⋊Q8—342no—
180C2×C4⋊C4—172no—
181C2×C4⋊C4—342no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—342no—
184C2×C42—21no—
185#107—341no—
186#107—341no—
187C4⋊C8—42no—
188#103—342no—
189#103—342no—
190#101—684no—
191C22⋊C8—22no—
192C22⋊C8—342no—
193C22⋊C8—342no—
194#95D6811yescharacteristic
195#95D6811yescharacteristic
196C17#1055911yescharacteristic, complemented, Sylow
197C24#6325211yescharacteristic
198C2×Q8—342no—
199C2×Q8—342no—
200C2×Q8—682no—
201C2×Q8—682no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—342no—
207C22×C4—342no—
208C22×C4C2×D6811yescharacteristic
209C22×C4D4×D1712yes—
210C22×C4#6325612yes—
211C22×C4C2×C22⋊D1711yescharacteristic
212Q16—1361no—
213Q16—1361no—
214M16—24no—
215M16—42no—
216M16—682no—
217M16—682no—
218C2×C8—22no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—682no—
226C4⋊C4—342no—
227C4⋊C4—342no—
228C4⋊C4—682no—
229C4⋊C4—682no—
230C22⋊C4—42no—
231C22⋊C4—682no—
232C22⋊C4—682no—
233C42—41no—
234C42—41no—
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23#1058758012yes—
240C23#1058761611yescharacteristic
241Q8—682no—
242Q8—682no—
243Q8—1362no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—684no—
257C2×C4—682no—
258C2×C4—682no—
259C2×C4—1362no—
260C2×C4#1058758112yes—
261C2×C4#1058762311yescharacteristic
262C2×C4#1058763311yescharacteristic
263C8—42no—
264C8—41no—
265C8—41no—
266C8—1362no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—81no—
273C22—81no—
274C22#1176272611yescharacteristic
275C22#1176308411yescharacteristic
276C22#1176308411yescharacteristic
277C4—22no—
278C4—21no—
279C4—42no—
280C4—81no—
281C4—1362no—
282C4—1362no—
283C4#1176299511yescharacteristic
284C4#1176299811yescharacteristic
285C2—21no—
286C2—21no—
287C2—42no—
288C2#1453003511yescharacteristic
289C2#1453005211yescharacteristic
290C2#1453007111yescharacteristic
subgroupG/H
centerC22#11762726
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1851C2
socleC22×C17#394
prime radicalC24×C17#41
hypercenter#1851D17
hypocenterC17#10559
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
196. C17#10559semidirect

Maximal subgroups

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

subgroupindex
#145395592
#145292522
#145273032
#145266612
C17×#18512
#1055917