Finite Group Databasebeta

← #17959642

Subgroups — #17959642

Order 4352.

334 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 88 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#14545143C211yesmaximal, characteristic
2#14544705C211yesmaximal, characteristic
3#14543773C214yesmaximal
4#14539371C211yesmaximal, characteristic
5#11763755—21no—
6#11763730—21no—
7#11763704C2212yes—
8C4×#63216—21no—
9#11763683—21no—
10#11763683C2212yes—
11#11763364—21no—
12#11763189C411yescharacteristic, complemented
13#11763161—21no—
14#11763051—21no—
15#11763051C2212yes—
16#11762903—21no—
17#11762903C412yescomplemented
18C4×C8×D17C2211yescharacteristic
19C17×#500C411yescharacteristic, complemented
20C2×C4⋊#595—22no—
21C2×C4⋊#595—41no—
22C2×C4⋊#595—41no—
23C17×C4⋊Q8—21no—
24#10587632—41no—
25Q8×Dic17—41no—
26C2×Dic68—21no—
27C2×Dic68C2×C412yes—
28C2×C8×D17D411yescharacteristic
29C2×C8×D17C2311yescharacteristic
30#10587583—22no—
31#10587578—41no—
32#10587576—41no—
33#10587573—22no—
34C42×D17D411yescharacteristic
35#10587555—21no—
36C2×#63216—22no—
37C17×#107—21no—
38C17×#107C2×C412yes—
39C4×C8×C17C2×C411yescharacteristic
40C8×Dic17C2×C411yescharacteristic
41C8×Dic17D411yescharacteristic
42#10587481—22no—
43#10587481—22no—
44C4×#3622D411yescharacteristic
45C22×#595—42no—
46C2×Q8×C17—41no—
47C2×C4×D17D811yescharacteristic
48C2×C4×D17D811yescharacteristic
49C2×C4×D17C2×D411yescharacteristic
50C2×Dic34—22no—
51C4⋊#595—42no—
52C4⋊#595—42no—
53C4⋊#595—82no—
54C4⋊#595—82no—
55C2×C8×C17C22⋊C411yescharacteristic
56C2×C8×C17C22×C411yescharacteristic
57C4⋊C4×C17—22no—
58C4⋊C4×C17—41no—
59C42×C17C22⋊C411yescharacteristic
60#63227—42no—
61C4⋊Dic17—41no—
62C4⋊Dic17—41no—
63C4⋊Dic17—42no—
64#63225—42no—
65C4×Dic17—42no—
66C4×Dic17C22⋊C411yescharacteristic
67C4×Dic17SD1611yescharacteristic
68C4×Dic17SD1611yescharacteristic
69C2×#3622C22⋊C411yescharacteristic
70C2×#3622C2×D411yescharacteristic
71Dic68—42no—
72Dic68—42no—
73C8×D17—41no—
74C8×D17—41no—
75#63216—42no—
76#11857—171nomaximal, Sylow
77C22×D17C2×D811yescharacteristic
78C2×#595—82no—
79C2×#595—82no—
80C2×#595—82no—
81Q8×C17—82no—
82C2×C4×C17—42no—
83C2×C4×C17#10211yescharacteristic
84C2×C4×C17#10211yescharacteristic
85C2×C4×C17C2×C22⋊C411yescharacteristic
86C2×Dic17—42no—
87C2×Dic17#10211yescharacteristic
88C2×Dic17#10211yescharacteristic
89C2×Dic17C2×SD1611yescharacteristic
90C4×D17—22no—
91C4×D17—21no—
92C4×D17—21no—
93C4×D17SD3212yes—
94C4×D17Q3212yes—
95Dic34—42no—
96Dic34—42no—
97C8×C17—21no—
98C8×C17—21no—
99#3622—21no—
100#3622—21no—
101#3170—171no—
102#2162—171no—
103#1834—171no—
104#1348—174no—
105C22×C17C2×#10211yescharacteristic
106C2×D17—21no—
107C2×D17—21no—
108C2×D17C2×SD3211yescharacteristic
109C2×D17C2×Q3211yescharacteristic
110#595—162no—
111C4×C17—82no—
112C4×C17#35812yes—
113C4×C17#36012yes—
114C4×C17#41011yescharacteristic
115C4×C17#42111yescharacteristic
116Dic17—21no—
117Dic17—21no—
118Dic17—82no—
119Dic17#35812yes—
120#533—341no—
121#500#59511yescharacteristic, complemented
122#494—171no—
123#487—341no—
124#467—172no—
125#467—341no—
126C4×Q16—172no—
127C4×Q16—341no—
128C2×C4×C8—171no—
129#384—341no—
130C4⋊C16—341no—
131C22⋊C16—172no—
132C4×C16—341no—
133#340—172no—
134#340—341no—
135C2×C17#151711yescharacteristic
136C2×C17C2×#35811yescharacteristic
137C2×C17C2×#36011yescharacteristic
138D17—21no—
139D17—21no—
140C2×Q16—172no—
141C2×Q16—341no—
142C22×C8—171no—
143C22×C8—171no—
144C4⋊Q8—21no—
145C4⋊Q8—341no—
146#125—681no—
147C22⋊Q8—342no—
148C22⋊Q8—681no—
149C4×Q8—342no—
150C4×Q8—681no—
151#117—681no—
152C2×C4⋊C4—342no—
153C2×C4⋊C4—681no—
154C2×C4⋊C4—681no—
155C2×C42—171no—
156C2×C16—342no—
157#107—21no—
158#107C2×#59512yes—
159#103—342no—
160#103—342no—
161C4×C8—171no—
162C4×C8—171no—
163C4×C8—171no—
164C4×C8C2×#59511yescharacteristic
165C17#1185711yescharacteristic, complemented, Sylow
166C2×Q8—41no—
167C2×Q8—342no—
168C22×C4—171no—
169C22×C4—171no—
170C22×C4—171no—
171C22×C4—682no—
172Q16—682no—
173Q16—682no—
174C2×C8—171no—
175C2×C8—171no—
176C2×C8—681no—
177C2×C8—681no—
178C2×C8C22⋊#59511yescharacteristic
179C2×C8C22×#59511yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—41no—
182C4⋊C4—682no—
183C4⋊C4—682no—
184C4⋊C4—682no—
185C4⋊C4—682no—
186C4⋊C4—681no—
187C4⋊C4—681no—
188C4⋊C4—1362no—
189C4⋊C4—1362no—
190C22⋊C4—682no—
191C42—171no—
192C42—171no—
193C42—171no—
194C42—682no—
195C42C22⋊#59511yescharacteristic
196C16—682no—
197C23—171no—
198Q8—82no—
199Q8—682no—
200Q8—682no—
201C2×C4—42no—
202C2×C4—171no—
203C2×C4—172no—
204C2×C4—172no—
205C2×C4—171no—
206C2×C4—171no—
207C2×C4—342no—
208C2×C4—341no—
209C2×C4—341no—
210C2×C4—682no—
211C2×C4—1362no—
212C2×C4—1362no—
213C2×C4—1362no—
214C2×C4#1058754711yescharacteristic
215C2×C4#1058754711yescharacteristic
216C2×C4C2×C22⋊#59511yescharacteristic
217C8—21no—
218C8—21no—
219C8—341no—
220C8—341no—
221C22—171no—
222C22—171no—
223C22—341no—
224C22—341no—
225C22C2×#1058754711yescharacteristic
226C4—82no—
227C4—2722no—
228C4—172no—
229C4—341no—
230C4—341no—
231C4—1362no—
232C4#1176372212yes—
233C4#1176372512yes—
234C4#1176379011yescharacteristic
235C4#1176380811yescharacteristic
236C2—341no—
237C2—341no—
238C2#1454421511yescharacteristic
239C2C2×#1176372211yescharacteristic
240C2C2×#1176372511yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC17×#500C4
socleC22×C17C2×#102
prime radicalC22×D17C2×D8
cosocleC2×C8×D17C23
hypercenter#500#595
hypocenterC17#11857
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
12. #11763189C4semidirect
17. #11762903C4semidirect
19. C17×#500C4semidirect
121. #500#595semidirect
165. C17#11857semidirect

Maximal subgroups

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

subgroupindex
#145451432
#145447052
#145437732
#145393712
#1185717