Finite Group Databasebeta

← #17959639

Subgroups — #17959639

Order 4352.

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

normal subgroups only

This group has 378 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, complemented
2#14544705C211yesmaximal, characteristic, complemented
3#14543771C214yesmaximal, complemented
4#14539364C211yesmaximal, characteristic
5#11763755—21no—
6#11763730—21no—
7#11763704C2212yes—
8C4×#63216—21no—
9#11763683—21no—
10#11763683C2212yes—
11#11763360—21no—
12#11763186C411yescharacteristic, complemented
13#11763157—21no—
14#11763046—21no—
15#11763046C2212yes—
16#11762891—21no—
17#11762891C412yescomplemented
18C4×C8×D17C2211yescharacteristic
19C17×#500C411yescharacteristic, complemented
20C2×#63256—41no—
21C2×C4⋊#595—22no—
22C2×C4⋊#595—41no—
23C2×C4⋊#595—41no—
24C17×C4⋊Q8—21no—
25#10587633—41no—
26C2×D136—21no—
27C2×D136C2×C412yes—
28C2×C8×D17D411yescharacteristic
29C2×C8×D17C2311yescharacteristic
30#10587581—22no—
31#10587581—41no—
32#10587579—22no—
33#10587579—41no—
34#10587560—21no—
35C42×D17D411yescharacteristic
36C2×#63216—22no—
37C17×#107—21no—
38C17×#107C2×C412yes—
39C4×C8×C17C2×C411yescharacteristic
40C8×Dic17C2×C411yescharacteristic
41C8×Dic17D411yescharacteristic
42#10587480—22no—
43#10587480—22no—
44C4×#3622D411yescharacteristic
45C22×#595—42no—
46C2×Q8×C17—41no—
47#63256—82no—
48#63256—82no—
49C2×D68—22no—
50C2×D68—42no—
51C2×D68—41no—
52C2×D68—41no—
53C2×C4×D17—42no—
54C2×C4×D17D811yescharacteristic
55C2×C4×D17D811yescharacteristic
56C2×C4×D17C2×D411yescharacteristic
57C4⋊#595—42no—
58C4⋊#595—42no—
59C4⋊#595—82no—
60C4⋊#595—82no—
61C2×C8×C17C22⋊C411yescharacteristic
62C2×C8×C17C22×C411yescharacteristic
63C4⋊C4×C17—22no—
64C4⋊C4×C17—41no—
65C42×C17C22⋊C411yescharacteristic
66#63227—42no—
67#63227—42no—
68C4×Dic17C22⋊C411yescharacteristic
69C4×Dic17SD1611yescharacteristic
70C4×Dic17SD1611yescharacteristic
71C2×#3622C22⋊C411yescharacteristic
72C2×#3622C2×D411yescharacteristic
73D136—42no—
74D136—42no—
75C8×D17—41no—
76C8×D17—41no—
77#63216—42no—
78#11856—171nomaximal, Sylow
79C22×D17—42no—
80C22×D17C2×D811yescharacteristic
81C2×#595—82no—
82C2×#595—82no—
83C2×#595—82no—
84Q8×C17—82no—
85C2×C4×C17—42no—
86C2×C4×C17#10211yescharacteristic
87C2×C4×C17#10211yescharacteristic
88C2×C4×C17C2×C22⋊C411yescharacteristic
89C2×Dic17#10211yescharacteristic
90C2×Dic17#10211yescharacteristic
91C2×Dic17C2×SD1611yescharacteristic
92D68—42no—
93D68—42no—
94D68—82no—
95D68—82no—
96D68—82no—
97D68—82no—
98C4×D17—22no—
99C4×D17—21no—
100C4×D17—21no—
101C4×D17—84no—
102C4×D17D1612yes—
103C4×D17SD3212yes—
104C8×C17—21no—
105C8×C17—21no—
106#3622—21no—
107#3622—21no—
108#3169—171no—
109#2162—171no—
110#1834—171no—
111#1347—174no—
112C22×C17C2×#10211yescharacteristic
113C2×D17—21no—
114C2×D17—21no—
115C2×D17—82no—
116C2×D17—82no—
117C2×D17—82no—
118C2×D17C2×D1611yescharacteristic
119C2×D17C2×SD3211yescharacteristic
120#595—162no—
121C4×C17—82no—
122C4×C17#35712yes—
123C4×C17#36012yes—
124C4×C17#41011yescharacteristic
125C4×C17#42111yescharacteristic
126Dic17—21no—
127Dic17—21no—
128Dic17#35712yes—
129#532—341no—
130#500#59511yescharacteristic, complemented
131#493—171no—
132#486—341no—
133#466—172no—
134#466—341no—
135C4×D8—172no—
136C4×D8—341no—
137C2×C4×C8—171no—
138#384—341no—
139C4⋊C16—341no—
140C22⋊C16—172no—
141C4×C16—341no—
142#340—172no—
143#340—341no—
144C2×C17#151711yescharacteristic
145C2×C17C2×#35711yescharacteristic
146C2×C17C2×#36011yescharacteristic
147D17—21no—
148D17—21no—
149D17—162no—
150C2×#41—681no—
151C2×D8—172no—
152C2×D8—341no—
153C22×C8—171no—
154C22×C8—171no—
155C4⋊Q8—21no—
156#127—341no—
157#124—681no—
158#121—342no—
159#121—681no—
160C4×D4—342no—
161C4×D4—681no—
162C2×C4⋊C4—342no—
163C2×C4⋊C4—681no—
164C2×C4⋊C4—681no—
165C2×C42—171no—
166C2×C16—342no—
167#107—21no—
168#107C2×#59512yes—
169#102—342no—
170#102—342no—
171C4×C8—171no—
172C4×C8—171no—
173C4×C8—171no—
174C4×C8C2×#59511yescharacteristic
175C17#1185611yescharacteristic, complemented, Sylow
176#41—1362no—
177#41—1362no—
178C2×Q8—41no—
179C2×D4—342no—
180C2×D4—682no—
181C2×D4—681no—
182C2×D4—681no—
183C22×C4—171no—
184C22×C4—171no—
185C22×C4—171no—
186C22×C4—682no—
187C22×C4—682no—
188D8—682no—
189D8—682no—
190C2×C8—171no—
191C2×C8—171no—
192C2×C8—681no—
193C2×C8—681no—
194C2×C8C22⋊#59511yescharacteristic
195C2×C8C22×#59511yescharacteristic
196C4⋊C4—22no—
197C4⋊C4—41no—
198C4⋊C4—682no—
199C4⋊C4—682no—
200C4⋊C4—1362no—
201C4⋊C4—1362no—
202C22⋊C4—682no—
203C22⋊C4—682no—
204C42—171no—
205C42—171no—
206C42—171no—
207C42C22⋊#59511yescharacteristic
208C16—682no—
209C23—171no—
210C23—682no—
211Q8—82no—
212D4—682no—
213D4—682no—
214D4—1362no—
215D4—1362no—
216D4—1362no—
217D4—1362no—
218C2×C4—42no—
219C2×C4—171no—
220C2×C4—172no—
221C2×C4—172no—
222C2×C4—171no—
223C2×C4—171no—
224C2×C4—342no—
225C2×C4—341no—
226C2×C4—341no—
227C2×C4—1364no—
228C2×C4—1362no—
229C2×C4—1362no—
230C2×C4—1362no—
231C2×C4#1058754711yescharacteristic
232C2×C4#1058754711yescharacteristic
233C2×C4C2×C22⋊#59511yescharacteristic
234C8—21no—
235C8—21no—
236C8—341no—
237C8—341no—
238C22—171no—
239C22—171no—
240C22—341no—
241C22—341no—
242C22—1362no—
243C22—1362no—
244C22—1362no—
245C22C2×#1058754711yescharacteristic
246C4—82no—
247C4—2722no—
248C4—172no—
249C4—341no—
250C4—341no—
251C4#1176372112yes—
252C4#1176372612yes—
253C4#1176379011yescharacteristic
254C4#1176380811yescharacteristic
255C2—2722no—
256C2—341no—
257C2—341no—
258C2#1454421511yescharacteristic
259C2C2×#1176372111yescharacteristic
260C2C2×#1176372611yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC17×#500C4
socleC22×C17C2×#102
prime radical#14539364C2
cosocleC2×C8×D17C23
hypercenter#500#595
hypocenterC17#11856
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
1. #14545143C2semidirect
2. #14544705C2semidirect
3. #14543771C2semidirect
12. #11763186C4semidirect
17. #11762891C4semidirect
19. C17×#500C4semidirect
130. #500#595semidirect
175. C17#11856semidirect

Maximal subgroups

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

subgroupindex
#145451432
#145447052
#145437712
#145393642
#1185617