Finite Group Databasebeta

← #16948205

Subgroups — #16948205

Order 4352.

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

normal subgroups only

This group has 288 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#14530926C211yesmaximal, characteristic
4#14528179C211yesmaximal, characteristic
5#14526832C211yesmaximal, characteristic
6#14526764C211yesmaximal, characteristic
7C17×#1332C211yesmaximal, characteristic
8#11763537—21no—
9#11763214C2211yescharacteristic
10#11763189C2211yescharacteristic
11#11763187—21no—
12#11763020—21no—
13#11763019—21no—
14#11763018—22no—
15C8×Dic34C2211yescharacteristic
16#11762903—21no—
17#11762636—21no—
18C4⋊#63214C2211yescharacteristic
19#11762614—22no—
20#11762613—21no—
21#11762556—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×Dic68—41no—
31C2×Dic68D412yes—
32#10587575—42no—
33#10587573—22no—
34#10587556—41no—
35#10587555—21no—
36#10587555—21no—
37C4×Dic34—41no—
38C4×Dic34D411yescharacteristic
39C2×C16×C17—21no—
40C17×#107D411yescharacteristic
41C17×C4⋊C8—21no—
42C17×#103—21no—
43C4×C8×C17C2311yescharacteristic
44#10587489—21no—
45#10587489—21no—
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—
81Dic68—82no—
82C16×C17—41no—
83#63214—41no—
84#12382—171nomaximal, Sylow
85Q8×C17—41no—
86Q8×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17#12011yescharacteristic
90C2×C4×C17C2×D811yescharacteristic
91C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
92C2×Dic17—21no—
93C2×Dic17—21no—
94C2×Dic17—42no—
95C2×Dic17—81no—
96Dic34—21no—
97Dic34—42no—
98Dic34—42no—
99Dic34—81no—
100Dic34—81no—
101Dic34SD3212yes—
102C8×C17—21no—
103C8×C17—81no—
104C8×C17#13511yescharacteristic
105C8×C17#13711yescharacteristic
106#3622—41no—
107#3395—171no—
108#2241—171no—
109#2225—171no—
110#1674—171no—
111#1362—171no—
112Q8⋊C16—171no—
113#1332D1711yescharacteristic
114C22×C17#44711yescharacteristic
115C4×C17—21no—
116C4×C17—81no—
117C4×C17—81no—
118C4×C17#45211yescharacteristic
119C4×C17#45511yescharacteristic
120C4×C17C2×SD3211yescharacteristic
121C4×C17#51011yescharacteristic
122Dic17—22no—
123Dic17—41no—
124Dic17—82no—
125Dic17—161no—
126#557—341no—
127#500—171no—
128#494—171no—
129#494—341no—
130#462—342no—
131#462—341no—
132#462—341no—
133C8×Q8—171no—
134C4×Q16—341no—
135C4×Q16C2×D1711yescharacteristic
136#367—341no—
137C4⋊C16—171no—
138#358—342no—
139#358—341no—
140C4×C16C2×D1711yescharacteristic
141#335C2×D1711yescharacteristic
142#332—341no—
143C2×C17#164111yescharacteristic
144C2×C17#218511yescharacteristic
145C2×C17#219511yescharacteristic
146C2×Q16—172no—
147C2×Q16—342no—
148C2×Q16—341no—
149C2×Q16—681no—
150C2×Q16D6811yescharacteristic
151C4⋊Q8—342no—
152C4⋊Q8—341no—
153C4⋊Q8—341no—
154#125—681no—
155#125—682no—
156C4×Q8—21no—
157C4×Q8—171no—
158C4×Q8—342no—
159C4×Q8—681no—
160C2×C16—21no—
161C2×C16—341no—
162#107—341no—
163#107—341no—
164#107D6811yescharacteristic
165C4⋊C8—21no—
166C4⋊C8—171no—
167C4⋊C8—341no—
168#103—21no—
169#103—342no—
170#103—681no—
171C4×C8—341no—
172C4×C8C22×D1711yescharacteristic
173C17#1238211yescharacteristic, complemented, Sylow
174C2×Q8—21no—
175C2×Q8—171no—
176C2×Q8—342no—
177C2×Q8—681no—
178Q16—21no—
179Q16—21no—
180Q16—682no—
181Q16—681no—
182Q16—681no—
183Q16—1362no—
184Q16—1362no—
185C2×C8—41no—
186C2×C8—341no—
187C2×C8C2×D6811yescharacteristic
188C2×C8D4×D1711yescharacteristic
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—171no—
192C4⋊C4—341no—
193C4⋊C4—682no—
194C4⋊C4—682no—
195C4⋊C4—682no—
196C4⋊C4—681no—
197C4⋊C4—681no—
198C4⋊C4—681no—
199C4⋊C4—681no—
200C42—41no—
201C42—341no—
202C42—682no—
203C42D4×D1711yescharacteristic
204C16—41no—
205C16—681no—
206Q8—41no—
207Q8—41no—
208Q8—172no—
209Q8—341no—
210Q8—682no—
211Q8—682no—
212Q8—1361no—
213Q8—1361no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—341no—
217C2×C4—341no—
218C2×C4—682no—
219C2×C4—1361no—
220C2×C4#1058756811yescharacteristic
221C2×C4D8×D1711yescharacteristic
222C2×C4#1058760011yescharacteristic
223C8—21no—
224C8—81no—
225C8—681no—
226C8#1058759011yescharacteristic
227C8#1058759511yescharacteristic
228C22#1176294411yescharacteristic
229C4—21no—
230C4—81no—
231C4—81no—
232C4—2721no—
233C4—342no—
234C4—681no—
235C4—1362no—
236C4#1176297311yescharacteristic
237C4#1176298811yescharacteristic
238C4SD32×D1711yescharacteristic
239C4#1176325111yescharacteristic
240C2#1452798011yescharacteristic
241C2#1453070211yescharacteristic
242C2#1453076311yescharacteristic
subgroupG/H
centerC22#11762944
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1332C2
socle, prime radicalC22×C17#447
hypercenter#1332D17
hypocenterC17#12382
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
173. C17#12382semidirect

Maximal subgroups

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

subgroupindex
#145417892
#145310122
#145309262
#145281792
#145268322
#145267642
C17×#13322
#1238217