Finite Group Databasebeta

← #17948808

Subgroups — #17948808

Order 4352.

308 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 66 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#14545012C211yesmaximal, characteristic
2#14544660C211yesmaximal, characteristic
3#14528808C211yesmaximal, characteristic
4C2×#10587530C412yescomplemented
5C2×#10587533—21no—
6#11763751—21no—
7#11763704—21no—
8C22⋊#63216—21no—
9#11763683C412yescomplemented
10C22×C8×D17C2211yescharacteristic
11C2×#10587479—21no—
12#11762666—21no—
13#11762572C411yescharacteristic, complemented
14C17×#340C411yescharacteristic, complemented
15C22×C4×D17D411yescharacteristic
16C2×C22⋊#595—41no—
17C2×C4⋊#595—22no—
18C22×C8×C17C2×C411yescharacteristic
19C2×C4⋊C4×C17—21no—
20C2×#63227—41no—
21C2×C4⋊Dic17—21no—
22C22×#3622D411yescharacteristic
23C2×C8×D17—42no—
24C2×C8×D17C2×C411yescharacteristic
25C2×C8×D17C2×C411yescharacteristic
26C2×C8×D17D411yescharacteristic
27C2×C8×D17Q811yescharacteristic
28(C2×#595)⋊C4—41no—
29C2×#63216—22no—
30#10587533—42no—
31#10587530—42no—
32#10587502—41no—
33#10587479—42no—
34C23×D17D811yescharacteristic
35C22×#595—42no—
36C22×C4×C17—41no—
37C22×C4×C17C22⋊C411yescharacteristic
38C22×Dic17—41no—
39C22×Dic17SD1611yescharacteristic
40C2×C4×D17—41no—
41C2×C4×D17—41no—
42C2×C4×D17C22⋊C411yescharacteristic
43C2×C4×D17C4⋊C411yescharacteristic
44C2×C4×D17SD1611yescharacteristic
45C2×C4×D17Q1611yescharacteristic
46C22⋊#595—81no—
47C22⋊#595—81no—
48C4⋊#595—42no—
49C4⋊#595—42no—
50C2×C8×C17—41no—
51C2×C8×C17C4211yescharacteristic
52C2×C8×C17C4⋊C411yescharacteristic
53C4⋊C4×C17—41no—
54C4⋊C4×C17—41no—
55#63227—82no—
56C4⋊Dic17—41no—
57C4⋊Dic17—41no—
58C2×#3622—22no—
59C2×#3622C22⋊C411yescharacteristic
60C2×#3622C4⋊C411yescharacteristic
61C8×D17—22no—
62C8×D17—22no—
63C8×D17—41no—
64C8×D17—41no—
65#63216—42no—
66#7233—171nomaximal, Sylow
67C23×C17#10211yescharacteristic
68C22×D17—21no—
69C22×D17—21no—
70C22×D17—22no—
71C22×D17—41no—
72C22×D17#10211yescharacteristic
73C22×D17#10711yescharacteristic
74C2×#595—82no—
75C2×#595—82no—
76C2×#595—82no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—81no—
80C2×C4×C17—81no—
81C2×C4×C17—81no—
82C2×C4×C17#9511yescharacteristic
83C2×C4×C17#10311yescharacteristic
84C2×Dic17—41no—
85C2×Dic17—81no—
86C2×Dic17—81no—
87C2×Dic17—81no—
88C2×Dic17#10311yescharacteristic
89C2×Dic17#10611yescharacteristic
90C4×D17—21no—
91C4×D17—21no—
92C4×D17—21no—
93C4×D17—21no—
94C4×D17—41no—
95C4×D17—41no—
96C8×C17—21no—
97C8×C17—21no—
98#3622—21no—
99#3622#9912yes—
100#2112—171no—
101#1807—171no—
102#1807—171no—
103C22×C17—21no—
104C22×C17—21no—
105C22×C17#34011yescharacteristic
106C22×C17#36011yescharacteristic
107C22×C17#36011yescharacteristic
108C2×D17—21no—
109C2×D17—21no—
110C2×D17—21no—
111C2×D17—21no—
112C2×D17—21no—
113C2×D17—42no—
114C2×D17—42no—
115C2×D17#36012yes—
116#595—162no—
117C4×C17—21no—
118C4×C17—161no—
119C4×C17H(3,ℤ/4)11yescharacteristic
120C4×C17#34211yescharacteristic
121Dic17—21no—
122Dic17—21no—
123Dic17—161no—
124C23×C8—171no—
125C2×M32—172no—
126C2×#106—341no—
127C2×#106—341no—
128#380—341no—
129#380—341no—
130C22⋊C16—341no—
131C22⋊C16—341no—
132#340—172no—
133#340—171no—
134#340#59511yescharacteristic, complemented
135C2×C17—21no—
136C2×C17—21no—
137C2×C17#128911yescharacteristic
138C2×C17#138611yescharacteristic
139C2×C17#138611yescharacteristic
140D17—22no—
141D17—41no—
142C23×C4—171no—
143C22×C8—171no—
144C22×C8—171no—
145C22×C8—171no—
146C22×C8—171no—
147C22×C8—171no—
148C22×C8—682no—
149C22×C8C2×#59511yescharacteristic
150C2×C4⋊C4—21no—
151C2×C4⋊C4—342no—
152C2×C4⋊C4—341no—
153C2×C22⋊C4—681no—
154C2×C22⋊C4—681no—
155M32—682no—
156C2×C16—342no—
157#106—682no—
158#106—682no—
159#95—681no—
160#95—681no—
161C17#723311yescharacteristic, complemented, Sylow
162C24—171no—
163C22×C4—41no—
164C22×C4—171no—
165C22×C4—171no—
166C22×C4—171no—
167C22×C4—171no—
168C22×C4—171no—
169C22×C4—681no—
170C22×C4—681no—
171C22×C4—682no—
172C22×C4—681no—
173C22×C4C22⋊#59511yescharacteristic
174C2×C8—41no—
175C2×C8—171no—
176C2×C8—171no—
177C2×C8—342no—
178C2×C8—342no—
179C2×C8—342no—
180C2×C8—681no—
181C2×C8—681no—
182C2×C8C4×#59511yescharacteristic
183C2×C8C4⋊#59511yescharacteristic
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—681no—
187C4⋊C4—681no—
188C4⋊C4—682no—
189C4⋊C4—682no—
190C22⋊C4—1362no—
191C22⋊C4—1361no—
192C22⋊C4—1361no—
193C16—682no—
194C23—171no—
195C23—171no—
196C23—342no—
197C23—341no—
198C23—341no—
199C23—681no—
200C23#1058754711yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4—81no—
206C2×C4—171no—
207C2×C4—171no—
208C2×C4—341no—
209C2×C4—341no—
210C2×C4—341no—
211C2×C4—341no—
212C2×C4—681no—
213C2×C4—681no—
214C2×C4—681no—
215C2×C4—1361no—
216C2×C4—1361no—
217C2×C4—1362no—
218C2×C4—1362no—
219C2×C4—1362no—
220C2×C4—1361no—
221C2×C4(C2×#595)⋊C411yescharacteristic
222C2×C4#1058754911yescharacteristic
223C8—21no—
224C8—21no—
225C8—172no—
226C8—341no—
227C22—21no—
228C22—21no—
229C22—172no—
230C22—341no—
231C22—341no—
232C22—341no—
233C22—341no—
234C22—341no—
235C22—682no—
236C22—682no—
237C22#1176368211yescharacteristic
238C22#1176372511yescharacteristic
239C22#1176372611yescharacteristic
240C4—21no—
241C4—161no—
242C4—2721no—
243C4—2722no—
244C4—341no—
245C4—341no—
246C4#1176367611yescharacteristic
247C4#1176368611yescharacteristic
248C2—21no—
249C2—21no—
250C2—342no—
251C2—681no—
252C2#1454364611yescharacteristic
253C2#1454385511yescharacteristic
254C2#1454385711yescharacteristic
subgroupG/H
centerC22#11763682
commutatorC2×C8×C17C42
FrattiniC22×C8C2×#595
FittingC17×#340C4
socleC22×C17#340
prime radicalC23×D17D8
cosocleC22×C8×D17C22
hypercenter#340#595
hypocenterC17#7233
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
4. C2×#10587530C4semidirect
9. #11763683C4semidirect
13. #11762572C4semidirect
14. C17×#340C4semidirect
134. #340#595semidirect
161. C17#7233semidirect

Maximal subgroups

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

subgroupindex
#145450122
#145446602
#145288082
#723317