Finite Group Databasebeta

← #16947283

Subgroups — #16947283

Order 4352.

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

normal subgroups only

This group has 324 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#14527825C211yesmaximal, characteristic
3#14527791C211yesmaximal, characteristic
4#14526811C211yesmaximal, characteristic
5#14526790C211yesmaximal, characteristic
6#14526728C211yesmaximal, characteristic
7C17×#2769C211yesmaximal, characteristic
8#11763440C2211yescharacteristic
9#11763144—21no—
10#11763139—21no—
11#11762849—21no—
12#11762578C2211yescharacteristic
13#11762569—21no—
14#11762545—21no—
15#11762545—21no—
16#11762535C2211yescharacteristic
17#11762535C2211yescharacteristic
18C17×#400—21no—
19C17×#400C2211yescharacteristic
20C17×#398—21no—
21C17×#398C2211yescharacteristic
22C17×#389—21no—
23C17×#387—21no—
24C17×#387—21no—
25C17×#383—21no—
26C17×#382C2211yescharacteristic
27C2×C4⋊C4×C17—21no—
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×C17D411yescharacteristic
34C2×C4⋊C4×C17C2311yescharacteristic
35C2×C42×C17—21no—
36C2×C42×C17D411yescharacteristic
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×#95D411yescharacteristic
53C17×#95D411yescharacteristic
54C22⋊#3622—21no—
55C22⋊#3622—21no—
56#10587481—41no—
57#10587481—41no—
58#10587479—41no—
59#10587479—41no—
60#10587478—41no—
61#10587478—41no—
62C22×C4×C17—21no—
63C22×C4×C17—21no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17C2×D411yescharacteristic
70C22×C4×C17C2×D411yescharacteristic
71C2×Dic34—21no—
72C2×Dic34—21no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—42no—
78C4⋊C4×C17—42no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—81no—
82C42×C17—21no—
83C42×C17—21no—
84C42×C17—42no—
85C22⋊Dic17—41no—
86C4⋊Dic17—21no—
87C4⋊Dic17—21no—
88C4⋊Dic17—21no—
89C4⋊Dic17—21no—
90#63225—41no—
91#63225—41no—
92C4×Dic17—41no—
93#63223—22no—
94#63223—41no—
95C2×#3622—41no—
96C2×#3622—41no—
97C2×#3622—41no—
98#12241—171nomaximal, Sylow
99C23×C17#12011yescharacteristic
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—22no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
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—41no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17#13511yescharacteristic
125C2×C4×C17#13711yescharacteristic
126C2×Dic17—41no—
127C2×Dic17—41no—
128Dic34—81no—
129Dic34—81no—
130#3622—42no—
131#3622—81no—
132#3622—81no—
133#2769D1711yescharacteristic
134#2061—171no—
135#1617—171no—
136#1611—171no—
137#1353—171no—
138#1346—171no—
139#1324—171no—
140C22×C17—21no—
141C22×C17—21no—
142C22×C17#45211yescharacteristic
143C22×C17#45611yescharacteristic
144C22×C17B(4,𝔽2)11yescharacteristic
145C4×C17—21no—
146C4×C17—21no—
147C4×C17—42no—
148C4×C17—41no—
149C4×C17—41no—
150C4×C17—81no—
151C4×C17—81no—
152C4×C17—81no—
153C4×C17—81no—
154C4×C17—81no—
155Dic17—81no—
156Dic17—81no—
157#544—171no—
158#484—341no—
159#483—341no—
160#428—341no—
161#400—21no—
162#400C2×D1711yescharacteristic
163#398—21no—
164#398C2×D1711yescharacteristic
165#389—21no—
166#387—21no—
167#387—21no—
168#383—21no—
169#382C2×D1711yescharacteristic
170#343—171no—
171#339—341no—
172#328—341no—
173#328—341no—
174#324—171no—
175#324—171no—
176C2×C17—21no—
177C2×C17—21no—
178C2×C17#160311yescharacteristic
179C2×C17#220111yescharacteristic
180C2×C17#220411yescharacteristic
181C2×M16—341no—
182C4⋊Q8—681no—
183#125—681no—
184C22⋊Q8—341no—
185C22⋊Q8—341no—
186#117—341no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C22⋊D1711yescharacteristic
192C2×C4⋊C4C22⋊D1711yescharacteristic
193C2×C4⋊C4C22⋊D1711yescharacteristic
194C2×C4⋊C4C22×D1711yescharacteristic
195C2×C42—21no—
196C2×C42C22⋊D1711yescharacteristic
197#107—681no—
198#107—681no—
199#106—681no—
200#106—681no—
201#103—681no—
202#103—681no—
203C22⋊C8—341no—
204C22⋊C8—341no—
205#95—21no—
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#95C22⋊D1711yescharacteristic
215#95C22⋊D1711yescharacteristic
216C17#1224111yescharacteristic, complemented, Sylow
217C2×Q8—341no—
218C2×Q8—341no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C2×C22⋊D1711yescharacteristic
226C22×C4C2×C22⋊D1711yescharacteristic
227C22×C4C2×C22⋊D1711yescharacteristic
228M16—342no—
229M16—681no—
230C2×C8—681no—
231C2×C8—681no—
232C2×C8—681no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—81no—
242C4⋊C4—341no—
243C4⋊C4—341no—
244C4⋊C4—341no—
245C4⋊C4—341no—
246C4⋊C4—681no—
247C4⋊C4—681no—
248C22⋊C4—681no—
249C42—21no—
250C42—21no—
251C42—42no—
252C42—681no—
253C23#1058763911yescharacteristic
254Q8—1361no—
255Q8—1361no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
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—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—681no—
281C2×C4—681no—
282C2×C4#1058763611yescharacteristic
283C2×C4#1058763711yescharacteristic
284C8—682no—
285C8—1361no—
286C8—1361no—
287C22—21no—
288C22—21no—
289C22#1176297111yescharacteristic
290C22#1176299211yescharacteristic
291C22#1176299611yescharacteristic
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—1361no—
303C4—1361no—
304C2—21no—
305C2—21no—
306C2#1452774711yescharacteristic
307C2#1453079711yescharacteristic
308C2#1453081011yescharacteristic
subgroupG/H
centerC22#11762996
commutator, cosocleC2×C4⋊C4×C17C23
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2769C2
socleC22×C17B(4,𝔽2)
prime radicalC23×C17#120
hypercenter#2769D17
hypocenterC17#12241
LCSG ▷ C2×C4⋊C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2769

Complements

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

NH ≅ G/Ntype
216. C17#12241semidirect

Maximal subgroups

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

subgroupindex
#145301342
#145278252
#145277912
#145268112
#145267902
#145267282
C17×#27692
#1224117