Finite Group Databasebeta

← #17959643

Subgroups — #17959643

Order 4352.

358 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 74 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#14545147C211yesmaximal, characteristic, complemented
2#14544706C211yesmaximal, characteristic, complemented
3#14543770C214yesmaximal, complemented
4#14539361C211yesmaximal, characteristic
5#11763753—21no—
6#11763730—21no—
7#11763704C2212yes—
8#11763697—21no—
9#11763683—21no—
10#11763683C2212yes—
11#11763357—21no—
12#11763214C411yescharacteristic, complemented
13#11763155—21no—
14#11763042—21no—
15#11763042C2212yes—
16D8×Dic17—21no—
17D8×Dic17C412yescomplemented
18C4×C8×D17C2211yescharacteristic
19C17×#493C411yescharacteristic, complemented
20C2×#63254—41no—
21C2×C4⋊#595—22no—
22C2×D8×C17—21no—
23C2×D8×C17C2×C412yes—
24C17×#127—21no—
25#10587624—22no—
26#10587624—41no—
27#10587622—41no—
28D4×Dic17—22no—
29D4×Dic17—41no—
30C2×C8×D17D411yescharacteristic
31C2×C8×D17C2311yescharacteristic
32C42×D17D411yescharacteristic
33#10587555—21no—
34(C2×#595)⋊C4—41no—
35(C2×#595)⋊C4—41no—
36C2×#63216—22no—
37C4×C8×C17C2×C411yescharacteristic
38#10587503—22no—
39#10587503—22no—
40#10587489—21no—
41#10587489C2×C412yes—
42C8×Dic17C2×C411yescharacteristic
43C8×Dic17D411yescharacteristic
44C4×#3622D411yescharacteristic
45C22×#595—42no—
46C2×D4×C17—22no—
47C2×D4×C17—41no—
48C2×D4×C17—41no—
49C2×C22⋊D17—42no—
50C22×Dic17—42no—
51#63254—84no—
52C2×C4×D17D811yescharacteristic
53C2×C4×D17D811yescharacteristic
54C2×C4×D17C2×D411yescharacteristic
55C2×Dic34—41no—
56C4⋊#595—42no—
57C4⋊#595—42no—
58D8×C17—42no—
59D8×C17—42no—
60C2×C8×C17C22⋊C411yescharacteristic
61C2×C8×C17C22×C411yescharacteristic
62C42×C17C22⋊C411yescharacteristic
63C22⋊Dic17—42no—
64C22⋊Dic17—42no—
65C4⋊Dic17—22no—
66C4⋊Dic17—41no—
67C4×Dic17C22⋊C411yescharacteristic
68C4×Dic17SD1611yescharacteristic
69C4×Dic17SD1611yescharacteristic
70C2×#3622C22⋊C411yescharacteristic
71C2×#3622C2×D411yescharacteristic
72C8×D17—41no—
73C8×D17—41no—
74#63216—42no—
75#11858—171nomaximal, Sylow
76C23×C17—42no—
77C22×D17C2×D811yescharacteristic
78C2×#595—82no—
79C2×#595—82no—
80C2×#595—82no—
81D4×C17—42no—
82D4×C17—42no—
83D4×C17—82no—
84D4×C17—82no—
85C2×C4×C17#10211yescharacteristic
86C2×C4×C17#10211yescharacteristic
87C2×C4×C17C2×C22⋊C411yescharacteristic
88C22⋊D17—84no—
89C2×Dic17—42no—
90C2×Dic17—84no—
91C2×Dic17#10211yescharacteristic
92C2×Dic17#10211yescharacteristic
93C2×Dic17C2×SD1611yescharacteristic
94C4×D17—22no—
95C4×D17—21no—
96C4×D17—21no—
97C4×D17—41no—
98Dic34—82no—
99C8×C17—21no—
100C8×C17—21no—
101#3622—21no—
102#3622—21no—
103#3169—171no—
104#2163—171no—
105#1835—171no—
106#1347—174no—
107C22×C17—82no—
108C22×C17—82no—
109C22×C17—82no—
110C22×C17C2×#10211yescharacteristic
111C2×D17—21no—
112C2×D17—21no—
113C2×D17#50912yes—
114#595—162no—
115C4×C17—21no—
116C4×C17—21no—
117C4×C17#41011yescharacteristic
118C4×C17#42111yescharacteristic
119Dic17—21no—
120Dic17—21no—
121Dic17—21no—
122Dic17—82no—
123#532—341no—
124#500—171no—
125#493#59511yescharacteristic, complemented
126#486—341no—
127#466—172no—
128#466—341no—
129C4×D8—172no—
130C4×D8—341no—
131C2×C4×C8—171no—
132#382—341no—
133C4⋊C16—341no—
134C22⋊C16—172no—
135#346—341no—
136#340—172no—
137#340—341no—
138C2×C17—162no—
139C2×C17#151711yescharacteristic
140C2×C17#214011yescharacteristic
141C2×C17#214511yescharacteristic
142D17—22no—
143C2×#41—681no—
144C2×D8—21no—
145C2×D8C2×#59512yes—
146C22×C8—171no—
147C22×C8—171no—
148C4⋊Q8—341no—
149#127—21no—
150#124—681no—
151#121—342no—
152#121—681no—
153C4×D4—342no—
154C4×D4—681no—
155C2×C4⋊C4—342no—
156C2×C42—171no—
157C2×C16—342no—
158#107—172no—
159#107—341no—
160#102—342no—
161#102—342no—
162C4×C8—171no—
163C4×C8—171no—
164C4×C8—171no—
165C4×C8C2×#59511yescharacteristic
166#95—681no—
167#95—681no—
168C17#1185811yescharacteristic, complemented, Sylow
169#41—1364no—
170C2×Q8—681no—
171C2×D4—22no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4—682no—
175C22×C4—171no—
176C22×C4—171no—
177C22×C4—171no—
178C22×C4—682no—
179C22×C4—682no—
180D8—42no—
181D8—42no—
182C2×C8—171no—
183C2×C8—171no—
184C2×C8—681no—
185C2×C8—681no—
186C2×C8C22⋊#59511yescharacteristic
187C2×C8C22×#59511yescharacteristic
188C4⋊C4—342no—
189C4⋊C4—682no—
190C4⋊C4—682no—
191C4⋊C4—681no—
192C22⋊C4—682no—
193C22⋊C4—682no—
194C42—171no—
195C42—171no—
196C42—171no—
197C42C22⋊#59511yescharacteristic
198C16—682no—
199C23—42no—
200C23—171no—
201Q8—1362no—
202D4—42no—
203D4—42no—
204D4—82no—
205D4—82no—
206D4—1364no—
207C2×C4—171no—
208C2×C4—171no—
209C2×C4—171no—
210C2×C4—342no—
211C2×C4—341no—
212C2×C4—341no—
213C2×C4—681no—
214C2×C4—682no—
215C2×C4—1362no—
216C2×C4—1362no—
217C2×C4—1362no—
218C2×C4—1364no—
219C2×C4#1058754711yescharacteristic
220C2×C4#1058754711yescharacteristic
221C2×C4C2×C22⋊#59511yescharacteristic
222C8—21no—
223C8—21no—
224C8—341no—
225C8—341no—
226C22—82no—
227C22—82no—
228C22—82no—
229C22—172no—
230C22—341no—
231C22—341no—
232C22C2×#1058754711yescharacteristic
233C4—21no—
234C4—21no—
235C4—2722no—
236C4—341no—
237C4—341no—
238C4—341no—
239C4—1362no—
240C4#1176378911yescharacteristic
241C4#1176380711yescharacteristic
242C2—162no—
243C2—342no—
244C2#1454421311yescharacteristic
245C2#1454509311yescharacteristic
246C2#1454510511yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC17×#493C4
socleC22×C17C2×#102
prime radical#14539361C2
cosocleC2×C8×D17C23
hypercenter#493#595
hypocenterC17#11858
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #14545147C2semidirect
2. #14544706C2semidirect
3. #14543770C2semidirect
12. #11763214C4semidirect
17. D8×Dic17C4semidirect
19. C17×#493C4semidirect
125. #493#595semidirect
168. C17#11858semidirect

Maximal subgroups

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

subgroupindex
#145451472
#145447062
#145437702
#145393612
#1185817