Finite Group Databasebeta

← #16938822

Subgroups — #16938822

Order 4352.

406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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#14537056C211yesmaximal, characteristic
2#14528953C211yesmaximal, characteristic
3#14528952C212yesmaximal
4#14526666C212yesmaximal
5C17×#1295C211yesmaximal, characteristic
6C2×#10587489—22no—
7C2×#10587478—21no—
8C2×#10587488—22no—
9C2×#10587479—21no—
10C2×#10587474C2211yescharacteristic
11#11762751—22no—
12#11762748—21no—
13#11762730—22no—
14#11762729—21no—
15#11762679C2211yescharacteristic
16#11762675C2212yes—
17C2×C17×#97C2212yes—
18C17×#382C2211yescharacteristic
19C22×Dic34—21no—
20C22×C8×C17—22no—
21C2×C4⋊C4×C17D411yescharacteristic
22C2×C4⋊C4×C17D411yescharacteristic
23C2×C42×C17C2311yescharacteristic
24C2×C4⋊Dic17—21no—
25C2×C4⋊Dic17—21no—
26C2×C4⋊Dic17—22no—
27C2×C4⋊Dic17D412yes—
28C2×C4⋊Dic17D412yes—
29C2×#63225—22no—
30C22×#3622—21no—
31C17×#97—22no—
32C17×#97Q814yescomplemented
33C17×#95—22no—
34#10587502—21no—
35#10587502—22no—
36#10587502—21no—
37#10587502—22no—
38#10587502—22no—
39#10587489—44no—
40#10587488—44no—
41#10587479—42no—
42#10587478—42no—
43#10587474—21no—
44#10587474Q812yescomplemented
45C22×C4×C17—21no—
46C22×C4×C17—21no—
47C22×C4×C17C2×D411yescharacteristic
48C22×C4×C17C2×D412yes—
49C22×Dic17—22no—
50C22×Dic17—22no—
51C22×Dic17—41no—
52C2×Dic34—82no—
53C2×Dic34—81no—
54C2×C8×C17—24no—
55C2×C8×C17—24no—
56C2×C8×C17—24no—
57C4⋊C4×C17—41no—
58C4⋊C4×C17—41no—
59C42×C17C2×Q812yes—
60C42×C17C2×Q811yescharacteristic
61C42×C17#4111yescharacteristic
62C4⋊Dic17—42no—
63C4⋊Dic17—42no—
64C4⋊Dic17—41no—
65C4⋊Dic17—41no—
66C4⋊Dic17—42no—
67C4⋊Dic17—42no—
68C4⋊Dic17—81no—
69#63225—82no—
70C2×#3622—22no—
71C2×#3622—22no—
72C2×#3622—22no—
73#10583—171nomaximal, Sylow
74C23×C17#12011yescharacteristic
75C2×C4×C17—21no—
76C2×C4×C17—22no—
77C2×C4×C17—22no—
78C2×C4×C17—21no—
79C2×C4×C17—41no—
80C2×C4×C17—41no—
81C2×C4×C17—42no—
82C2×C4×C17—42no—
83C2×C4×C17C22⋊Q812yes—
84C2×C4×C17C22⋊Q811yescharacteristic
85C2×C4×C17C4⋊Q811yescharacteristic
86C2×C4×C17C4⋊Q812yes—
87C2×Dic17—42no—
88C2×Dic17—42no—
89C2×Dic17—42no—
90C2×Dic17—42no—
91C2×Dic17—42no—
92C2×Dic17—42no—
93C2×Dic17—82no—
94C2×Dic17—81no—
95Dic34—84no—
96C8×C17—28no—
97#3622—24no—
98#2844—171no—
99#1847—172no—
100#1847—171no—
101#1295—172no—
102#1295D1711yescharacteristic
103C22×C17#39511yescharacteristic
104C22×C17#45312yes—
105C22×C17#45311yescharacteristic
106C22×C17#45612yes—
107C22×C17#45611yescharacteristic
108C4×C17—21no—
109C4×C17—22no—
110C4×C17—22no—
111C4×C17—21no—
112C4×C17—81no—
113C4×C17—81no—
114Dic17—82no—
115Dic17—82no—
116Dic17—161no—
117C2×#107—342no—
118C2×#107—341no—
119C2×#106—342no—
120C2×#106—341no—
121C2×#97—171no—
122C2×#97C2×D1712yes—
123#400—342no—
124#400—341no—
125#395—342no—
126#395—341no—
127#384—171no—
128#382—172no—
129#382C2×D1711yescharacteristic
130C2×C17#165511yescharacteristic
131C2×C17#166011yescharacteristic
132C2×C17#166012yes—
133C2×C17#206012yes—
134C2×C17#206011yescharacteristic
135C22×Q8—341no—
136C22×C8—22no—
137C22×C8—341no—
138C2×C4⋊C4—172no—
139C2×C4⋊C4—172no—
140C2×C4⋊C4—341no—
141C2×C4⋊C4—342no—
142C2×C4⋊C4—342no—
143C2×C4⋊C4—341no—
144C2×C4⋊C4D6811yescharacteristic
145C2×C4⋊C4D6811yescharacteristic
146C2×C42C22×D1711yescharacteristic
147#107—682no—
148#107—684no—
149#106—682no—
150#106—684no—
151#97—22no—
152#97—172no—
153#97—341no—
154#97Dic3414yescomplemented
155#95—22no—
156#95—342no—
157#95—341no—
158#95—341no—
159#95—342no—
160#95—342no—
161C17#1058311yescharacteristic, complemented, Sylow
162C2×Q8—1362no—
163C2×Q8—1361no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—342no—
167C22×C4—342no—
168C22×C4—681no—
169C22×C4C2×D6811yescharacteristic
170C22×C4D4×D1712yes—
171C2×C8—24no—
172C2×C8—24no—
173C2×C8—24no—
174C2×C8—342no—
175C2×C8—342no—
176C2×C8—342no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—682no—
180C4⋊C4—682no—
181C4⋊C4—682no—
182C4⋊C4—681no—
183C4⋊C4—682no—
184C4⋊C4—681no—
185C4⋊C4—1362no—
186C4⋊C4—1361no—
187C42C2×Dic3412yes—
188C42#6325411yescharacteristic
189C42Q8×D1711yescharacteristic
190C23#1058756811yescharacteristic
191Q8—1364no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—682no—
201C2×C4—682no—
202C2×C4—682no—
203C2×C4—682no—
204C2×C4—682no—
205C2×C4—682no—
206C2×C4—1362no—
207C2×C4—1361no—
208C2×C4#1058755511yescharacteristic
209C2×C4#1058756412yes—
210C2×C4#1058757412yes—
211C2×C4#1058758311yescharacteristic
212C8—28no—
213C8—344no—
214C22#1176273011yescharacteristic
215C22#1176297812yes—
216C22#1176297911yescharacteristic
217C22#1176299312yes—
218C22#1176299411yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—81no—
224C4—81no—
225C4—2721no—
226C4—1362no—
227C4—1362no—
228C2#1452807411yescharacteristic
229C2#1452809611yescharacteristic
230C2#1452809712yes—
231C2#1453012812yes—
232C2#1453013011yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1295C2
socle, prime radicalC23×C17#120
hypercenter#1295D17
hypocenterC17#10583
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
32. C17×#97Q8semidirect
44. #10587474Q8semidirect
154. #97Dic34semidirect
161. C17#10583semidirect

Maximal subgroups

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

subgroupindex
#145370562
#145289532
#145289522
#145266662
C17×#12952
#1058317