Finite Group Databasebeta

← #16948032

Subgroups — #16948032

Order 4352.

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

normal subgroups only

This group has 282 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#14541677C211yesmaximal, characteristic
2#14530831C211yesmaximal, characteristic
3#14528151C211yesmaximal, characteristic
4#14526839C211yesmaximal, characteristic
5#14526764C211yesmaximal, characteristic
6#14526749C211yesmaximal, characteristic
7C17×#2241C211yesmaximal, characteristic
8#11763534—21no—
9C2×#10587500—21no—
10#11763210—21no—
11#11763115—22no—
12#11763091—21no—
13#11763091—21no—
14C8×Dic34C2211yescharacteristic
15C4×Dic68C2211yescharacteristic
16#11762903—21no—
17C4⋊#63214C2211yescharacteristic
18#11762613—21no—
19#11762562C2211yescharacteristic
20#11762555—21no—
21C17×#500C2211yescharacteristic
22C17×#494C2211yescharacteristic
23C17×#358—22no—
24C4×C16×C17C2211yescharacteristic
25C2×Q16×C17—21no—
26C2×Q16×C17—21no—
27C17×C4⋊Q8—21no—
28C17×C4⋊Q8—21no—
29Q8×Dic17—41no—
30#10587630—41no—
31C2×Dic68D411yescharacteristic
32#10587576—22no—
33#10587575—42no—
34#10587573—22no—
35C4×Dic34—21no—
36C4×Dic34D411yescharacteristic
37C2×C16×C17—21no—
38C17×#107—21no—
39C17×#107D412yes—
40C4×C8×C17C2311yescharacteristic
41#10587500—42no—
42#10587489D411yescharacteristic
43#10587487—21no—
44#10587485—21no—
45C8×Dic17—21no—
46C2×#63214—21no—
47#10587481—22no—
48#10587481—41no—
49#10587479—22no—
50#10587479—41no—
51C4⋊#3622—21no—
52C4⋊#3622D411yescharacteristic
53C2×Q8×C17—41no—
54C2×Q8×C17—41no—
55C2×Dic34—21no—
56C2×Dic34D811yescharacteristic
57Q16×C17—42no—
58Q16×C17—41no—
59Q16×C17—41no—
60C2×C8×C17C2×D411yescharacteristic
61C2×C8×C17C2×D411yescharacteristic
62C4⋊C4×C17—22no—
63C4⋊C4×C17—41no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C42×C17C2×D411yescharacteristic
67C4⋊Dic17—21no—
68C4⋊Dic17—42no—
69C4⋊Dic17D811yescharacteristic
70#63225—21no—
71#63225—42no—
72#63225—42no—
73#63225—41no—
74C4×Dic17—21no—
75C4×Dic17—42no—
76C4×Dic17—41no—
77C2×#3622—21no—
78C2×#3622—41no—
79Dic68—21no—
80Dic68SD1612yes—
81C16×C17—41no—
82#63214—41no—
83#12357—171nomaximal, Sylow
84Q8×C17—81no—
85Q8×C17—81no—
86Q8×C17—81no—
87Q8×C17—81no—
88C2×C4×C17—42no—
89C2×C4×C17—81no—
90C2×C4×C17#12011yescharacteristic
91C2×C4×C17C2×D811yescharacteristic
92C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
93C2×Dic17—21no—
94C2×Dic17—21no—
95C2×Dic17—41no—
96C2×Dic17—41no—
97Dic34—22no—
98Dic34—21no—
99Dic34—21no—
100Dic34—41no—
101C8×C17—21no—
102C8×C17C2×SD1611yescharacteristic
103C8×C17#13711yescharacteristic
104#3622—41no—
105#3622—81no—
106#3383—171no—
107#2241D1711yescharacteristic
108#2209—171no—
109#1670—171no—
110#1364—171no—
111Q8⋊C16—171no—
112#1332—171no—
113C22×C17#44711yescharacteristic
114C4×C17—21no—
115C4×C17—82no—
116C4×C17—161no—
117C4×C17#44811yescharacteristic
118C4×C17#45411yescharacteristic
119C4×C17#50811yescharacteristic
120C4×C17#51011yescharacteristic
121Dic17—42no—
122Dic17—41no—
123Dic17—41no—
124Dic17—81no—
125#557—341no—
126C2×Q32—341no—
127#500C2×D1711yescharacteristic
128#499—341no—
129#494C2×D1711yescharacteristic
130#479—342no—
131#475—341no—
132#475—341no—
133C8×Q8—171no—
134C4×Q16—171no—
135C4×Q16—341no—
136C4⋊C16—171no—
137#358—22no—
138#358—341no—
139C4×C16C2×D1711yescharacteristic
140#335—171no—
141#332—341no—
142C2×C17#162711yescharacteristic
143C2×C17#218911yescharacteristic
144C2×C17#219511yescharacteristic
145C2×Q16—21no—
146C2×Q16—21no—
147C2×Q16—171no—
148C4⋊Q8—21no—
149C4⋊Q8—21no—
150C4⋊Q8—681no—
151#125—342no—
152#125—682no—
153C4×Q8—171no—
154C4×Q8—342no—
155C4×Q8—341no—
156C4×Q8—681no—
157Q32—682no—
158C2×C16—21no—
159C2×C16—341no—
160#107—21no—
161#107—171no—
162#107C22⋊D1712yes—
163#106—342no—
164#106—681no—
165C4⋊C8—171no—
166C4⋊C8—341no—
167C4⋊C8—341no—
168#103—342no—
169#103—341no—
170#103—681no—
171C4×C8—341no—
172C4×C8C22×D1711yescharacteristic
173C17#1235711yescharacteristic, complemented, Sylow
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—171no—
177C2×Q8—341no—
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16—172no—
182Q16—341no—
183C2×C8—341no—
184C2×C8—681no—
185C2×C8D4×D1711yescharacteristic
186C2×C8C2×C22⋊D1711yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—171no—
192C4⋊C4—341no—
193C4⋊C4—341no—
194C4⋊C4—682no—
195C4⋊C4—682no—
196C4⋊C4—682no—
197C4⋊C4—681no—
198C42—341no—
199C42—682no—
200C42—681no—
201C42D4×D1711yescharacteristic
202C16—41no—
203C16—681no—
204Q8—81no—
205Q8—81no—
206Q8—81no—
207Q8—81no—
208Q8—342no—
209Q8—341no—
210Q8—341no—
211Q8—681no—
212C2×C4—42no—
213C2×C4—81no—
214C2×C4—341no—
215C2×C4—341no—
216C2×C4—681no—
217C2×C4—681no—
218C2×C4D8×D1711yescharacteristic
219C2×C4#1058759711yescharacteristic
220C2×C4#1058762311yescharacteristic
221C8—21no—
222C8—681no—
223C8—1361no—
224C8SD16×D1711yescharacteristic
225C8#1058760111yescharacteristic
226C22#1176294111yescharacteristic
227C4—21no—
228C4—82no—
229C4—161no—
230C4—682no—
231C4—681no—
232C4—681no—
233C4—1361no—
234C4#1176294611yescharacteristic
235C4#1176298111yescharacteristic
236C4#1176324011yescharacteristic
237C4#1176324811yescharacteristic
238C2#1452788411yescharacteristic
239C2#1453072111yescharacteristic
240C2#1453076111yescharacteristic
subgroupG/H
centerC22#11762941
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#2241C2
socle, prime radicalC22×C17#447
hypercenter#2241D17
hypocenterC17#12357
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
173. C17#12357semidirect

Maximal subgroups

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

subgroupindex
#145416772
#145308312
#145281512
#145268392
#145267642
#145267492
C17×#22412
#1235717