Finite Group Databasebeta

← #16948233

Subgroups — #16948233

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#14541789C211yesmaximal, characteristic
2#14531012C211yesmaximal, characteristic
3#14530936C211yesmaximal, characteristic
4#14528189C211yesmaximal, characteristic
5#14526832C211yesmaximal, characteristic
6#14526764C211yesmaximal, characteristic
7C17×#1332C211yesmaximal, characteristic
8#11763537—21no—
9#11763214C2211yescharacteristic
10#11763189C2211yescharacteristic
11#11763187—21no—
12#11763105—21no—
13#11763019—21no—
14#11763018—22no—
15C8×Dic34C2211yescharacteristic
16#11762903—21no—
17#11762634—21no—
18C4⋊#63214C2211yescharacteristic
19#11762614—22no—
20#11762613—21no—
21#11762557—21no—
22C4×Q16×C17C2211yescharacteristic
23C4×C16×C17C2211yescharacteristic
24C17×#335C2211yescharacteristic
25C2×Q16×C17D411yescharacteristic
26C4×Q8×C17—21no—
27#10587630—22no—
28C2×#63231—22no—
29C2×Dic68—21no—
30C2×Dic68D412yes—
31#10587575—42no—
32#10587573—22no—
33#10587556—41no—
34#10587555—21no—
35#10587555—21no—
36C4×Dic34—41no—
37C4×Dic34D411yescharacteristic
38C2×C16×C17—21no—
39C17×#107D411yescharacteristic
40C17×C4⋊C8—21no—
41C17×#103—21no—
42C4×C8×C17C2311yescharacteristic
43#10587489—21no—
44#10587489—21no—
45#10587489—41no—
46#10587487—41no—
47#10587485—21no—
48C8×Dic17—21no—
49C2×#63214—21no—
50#10587481—22no—
51C4⋊#3622D411yescharacteristic
52C2×Q8×C17—21no—
53C2×Dic34—22no—
54C2×Dic34—41no—
55C2×Dic34D811yescharacteristic
56Q16×C17—21no—
57Q16×C17—21no—
58C2×C8×C17—41no—
59C2×C8×C17C2×D411yescharacteristic
60C2×C8×C17C2×D411yescharacteristic
61C4⋊C4×C17—21no—
62C4⋊C4×C17—41no—
63C42×C17—41no—
64C42×C17C2×D411yescharacteristic
65#63231—82no—
66C4⋊Dic17—41no—
67C4⋊Dic17—41no—
68C4⋊Dic17—41no—
69C4⋊Dic17—41no—
70C4⋊Dic17D811yescharacteristic
71#63225—21no—
72#63225—42no—
73#63225—42no—
74#63225—42no—
75C4×Dic17—21no—
76C4×Dic17—42no—
77C2×#3622—21no—
78Dic68—42no—
79Dic68—41no—
80Dic68—41no—
81C16×C17—41no—
82#63214—41no—
83#12386—171nomaximal, Sylow
84Q8×C17—41no—
85Q8×C17—41no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17#12011yescharacteristic
89C2×C4×C17C2×D811yescharacteristic
90C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
91C2×Dic17—21no—
92C2×Dic17—21no—
93C2×Dic17—42no—
94C2×Dic17—81no—
95Dic34—21no—
96Dic34—42no—
97Dic34—42no—
98Dic34—161no—
99Dic34Q3212yes—
100C8×C17—21no—
101C8×C17—81no—
102C8×C17#13511yescharacteristic
103C8×C17#13711yescharacteristic
104#3622—41no—
105#3395—171no—
106#2241—171no—
107#2227—171no—
108#1676—171no—
109#1362—171no—
110Q8⋊C16—171no—
111#1332D1711yescharacteristic
112C22×C17#44711yescharacteristic
113C4×C17—21no—
114C4×C17—81no—
115C4×C17—81no—
116C4×C17#45211yescharacteristic
117C4×C17#45511yescharacteristic
118C4×C17C2×Q3211yescharacteristic
119C4×C17#51011yescharacteristic
120Dic17—22no—
121Dic17—41no—
122Dic17—82no—
123Dic17—161no—
124#557—341no—
125#500—171no—
126#494—171no—
127#494—341no—
128#477—341no—
129#462—342no—
130#462—341no—
131C8×Q8—171no—
132C4×Q16—341no—
133C4×Q16C2×D1711yescharacteristic
134#366—341no—
135C4⋊C16—171no—
136#358—342no—
137#358—341no—
138C4×C16C2×D1711yescharacteristic
139#335C2×D1711yescharacteristic
140#333—341no—
141C2×C17#164111yescharacteristic
142C2×C17#218811yescharacteristic
143C2×C17#219311yescharacteristic
144C2×Q16—172no—
145C2×Q16—342no—
146C2×Q16—341no—
147C2×Q16D6811yescharacteristic
148C4⋊Q8—342no—
149C4⋊Q8—341no—
150C4⋊Q8—341no—
151#125—681no—
152#125—682no—
153C4×Q8—21no—
154C4×Q8—171no—
155C4×Q8—342no—
156C4×Q8—681no—
157C2×C16—21no—
158C2×C16—341no—
159#107—341no—
160#107—341no—
161#107—681no—
162#107D6811yescharacteristic
163C4⋊C8—21no—
164C4⋊C8—171no—
165C4⋊C8—341no—
166#103—21no—
167#103—342no—
168#103—681no—
169C4×C8—341no—
170C4×C8C22×D1711yescharacteristic
171C17#1238611yescharacteristic, complemented, Sylow
172C2×Q8—21no—
173C2×Q8—171no—
174C2×Q8—342no—
175C2×Q8—681no—
176Q16—21no—
177Q16—21no—
178Q16—682no—
179Q16—681no—
180Q16—681no—
181Q16—1362no—
182C2×C8—41no—
183C2×C8—341no—
184C2×C8C2×D6811yescharacteristic
185C2×C8D4×D1711yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—41no—
188C4⋊C4—171no—
189C4⋊C4—341no—
190C4⋊C4—682no—
191C4⋊C4—682no—
192C4⋊C4—682no—
193C4⋊C4—681no—
194C4⋊C4—681no—
195C4⋊C4—681no—
196C4⋊C4—681no—
197C42—41no—
198C42—341no—
199C42—682no—
200C42D4×D1711yescharacteristic
201C16—41no—
202C16—681no—
203Q8—41no—
204Q8—41no—
205Q8—2721no—
206Q8—172no—
207Q8—341no—
208Q8—682no—
209Q8—682no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—341no—
213C2×C4—341no—
214C2×C4—682no—
215C2×C4—1361no—
216C2×C4#1058756811yescharacteristic
217C2×C4D8×D1711yescharacteristic
218C2×C4#1058760011yescharacteristic
219C8—21no—
220C8—81no—
221C8—681no—
222C8#1058759011yescharacteristic
223C8#1058759511yescharacteristic
224C22#1176294411yescharacteristic
225C4—21no—
226C4—81no—
227C4—81no—
228C4—2721no—
229C4—342no—
230C4—681no—
231C4—1362no—
232C4#1176297311yescharacteristic
233C4#1176298811yescharacteristic
234C4Q32×D1711yescharacteristic
235C4#1176324811yescharacteristic
236C2#1452798011yescharacteristic
237C2#1453071911yescharacteristic
238C2#1453074911yescharacteristic
subgroupG/H
centerC22#11762944
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1332C2
socle, prime radicalC22×C17#447
hypercenter#1332D17
hypocenterC17#12386
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
171. C17#12386semidirect

Maximal subgroups

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

subgroupindex
#145417892
#145310122
#145309362
#145281892
#145268322
#145267642
C17×#13322
#1238617