Finite Group Databasebeta

← #16947255

Subgroups — #16947255

Order 4352.

334 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 59 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#14530134C211yesmaximal, characteristic
2#14527791C211yesmaximal, characteristic
3#14527757C211yesmaximal, characteristic
4#14526814C211yesmaximal, characteristic
5#14526790C211yesmaximal, characteristic
6#14526728C211yesmaximal, characteristic
7C17×#2789C211yesmaximal, characteristic
8#11763440C2211yescharacteristic
9#11763139—21no—
10#11762965—21no—
11#11762849—21no—
12#11762578C2211yescharacteristic
13#11762569—21no—
14#11762545—21no—
15#11762545—21no—
16#11762535C2211yescharacteristic
17#11762535C2211yescharacteristic
18C17×#401—21no—
19C17×#400—21no—
20C17×#398C2211yescharacteristic
21C17×#395C2211yescharacteristic
22C17×#391—21no—
23C17×#387—21no—
24C17×#387—21no—
25C17×#387—21no—
26C17×#382C2211yescharacteristic
27C22×Q8×C17D411yescharacteristic
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C4⋊C4×C17C2311yescharacteristic
34C2×C42×C17—21no—
35C2×C42×C17D411yescharacteristic
36C2×#63231—41no—
37#10587612—21no—
38#10587610—21no—
39#10587610—21no—
40C2×#63223—21no—
41#10587576—41no—
42#10587574—41no—
43C17×#95—21no—
44C17×#95—21no—
45C17×#95—21no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C17×#95D411yescharacteristic
54C17×#95D411yescharacteristic
55#10587506—41no—
56C22⋊#3622—21no—
57C22⋊#3622—21no—
58#10587481—41no—
59#10587479—41no—
60#10587479—41no—
61#10587478—41no—
62C2×Q8×C17—42no—
63C2×Q8×C17—41no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17C2×D411yescharacteristic
71C22×C4×C17C2×D411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C2×Dic34—21no—
74C2×Dic34—21no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—42no—
79C4⋊C4×C17—42no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C42×C17—21no—
83C42×C17—21no—
84C42×C17—81no—
85C22⋊Dic17—41no—
86#63231—82no—
87C4⋊Dic17—21no—
88C4⋊Dic17—21no—
89C4⋊Dic17—21no—
90C4⋊Dic17—21no—
91#63225—41no—
92#63225—41no—
93C4×Dic17—41no—
94#63223—22no—
95#63223—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98C2×#3622—41no—
99#12237—171nomaximal, Sylow
100C23×C17#12011yescharacteristic
101Q8×C17—42no—
102Q8×C17—81no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—22no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—42no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17#13511yescharacteristic
127C2×C4×C17#13711yescharacteristic
128C2×Dic17—41no—
129C2×Dic17—41no—
130Dic34—81no—
131Dic34—81no—
132#3622—42no—
133#3622—81no—
134#3622—81no—
135#2789D1711yescharacteristic
136#2061—171no—
137#1611—171no—
138#1605—171no—
139#1354—171no—
140#1346—171no—
141#1324—171no—
142C22×C17—21no—
143C22×C17—21no—
144C22×C17#45211yescharacteristic
145C22×C17#45611yescharacteristic
146C22×C17B(4,𝔽2)11yescharacteristic
147C4×C17—21no—
148C4×C17—21no—
149C4×C17—41no—
150C4×C17—41no—
151C4×C17—42no—
152C4×C17—81no—
153C4×C17—81no—
154C4×C17—81no—
155C4×C17—81no—
156C4×C17—81no—
157Dic17—81no—
158Dic17—81no—
159#544—171no—
160#483—341no—
161#451—341no—
162#428—341no—
163#401—21no—
164#400—21no—
165#398C2×D1711yescharacteristic
166#395C2×D1711yescharacteristic
167#391—21no—
168#387—21no—
169#387—21no—
170#387—21no—
171#382C2×D1711yescharacteristic
172#343—171no—
173#339—341no—
174#328—341no—
175#328—341no—
176#324—171no—
177#324—171no—
178C2×C17—21no—
179C2×C17—21no—
180C2×C17#160311yescharacteristic
181C2×C17#219711yescharacteristic
182C2×C17#220311yescharacteristic
183C22×Q8C22⋊D1711yescharacteristic
184C2×Q16—681no—
185C2×M16—341no—
186C4⋊Q8—681no—
187#125—681no—
188C22⋊Q8—341no—
189C22⋊Q8—341no—
190#117—341no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C22⋊D1711yescharacteristic
195C2×C4⋊C4C22⋊D1711yescharacteristic
196C2×C4⋊C4C22×D1711yescharacteristic
197C2×C42—21no—
198C2×C42C22⋊D1711yescharacteristic
199#107—681no—
200#106—681no—
201#106—681no—
202#103—681no—
203#103—681no—
204C22⋊C8—341no—
205C22⋊C8—341no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95C22⋊D1711yescharacteristic
217#95C22⋊D1711yescharacteristic
218C17#1223711yescharacteristic, complemented, Sylow
219C2×Q8—42no—
220C2×Q8—41no—
221C2×Q8—341no—
222C2×Q8—341no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4C2×C22⋊D1711yescharacteristic
230C22×C4C2×C22⋊D1711yescharacteristic
231C22×C4C2×C22⋊D1711yescharacteristic
232Q16—1362no—
233M16—342no—
234M16—681no—
235C2×C8—681no—
236C2×C8—681no—
237C2×C8—681no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—341no—
246C4⋊C4—341no—
247C4⋊C4—341no—
248C4⋊C4—341no—
249C4⋊C4—681no—
250C4⋊C4—681no—
251C22⋊C4—681no—
252C42—21no—
253C42—21no—
254C42—81no—
255C42—681no—
256C23#1058763911yescharacteristic
257Q8—42no—
258Q8—81no—
259Q8—1361no—
260Q8—1361no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4#1058763611yescharacteristic
287C2×C4#1058763711yescharacteristic
288C8—682no—
289C8—1361no—
290C8—1361no—
291C22—21no—
292C22—21no—
293C22#1176297111yescharacteristic
294C22#1176299211yescharacteristic
295C22#1176299611yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—42no—
301C4—81no—
302C4—81no—
303C4—81no—
304C4—81no—
305C4—81no—
306C4—1361no—
307C4—1361no—
308C2—21no—
309C2—21no—
310C2#1452774711yescharacteristic
311C2#1453077411yescharacteristic
312C2#1453080511yescharacteristic
subgroupG/H
centerC22#11762996
commutator, cosocleC2×C4⋊C4×C17C23
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2789C2
socleC22×C17B(4,𝔽2)
prime radicalC23×C17#120
hypercenter#2789D17
hypocenterC17#12237
LCSG ▷ C2×C4⋊C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2789

Complements

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

NH ≅ G/Ntype
218. C17#12237semidirect

Maximal subgroups

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

subgroupindex
#145301342
#145277912
#145277572
#145268142
#145267902
#145267282
C17×#27892
#1223717