Finite Group Databasebeta

← #17948814

Subgroups — #17948814

Order 4352.

286 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 62 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#14544661C211yesmaximal, characteristic
3#14528821C211yesmaximal, characteristic
4C2×#10587530C412yescomplemented
5C2×#10587534—21no—
6#11763751—21no—
7#11763704—21no—
8C22⋊#63216—21no—
9#11763683C412yes—
10C22×C8×D17C2211yescharacteristic
11C2×#10587493—21no—
12#11762772—21no—
13#11762574C411yescharacteristic, complemented
14C17×#341C411yescharacteristic, complemented
15C22×C4×D17D411yescharacteristic
16C2×C22⋊#595—41no—
17C2×C4⋊#595—22no—
18C2×M16×C17—21no—
19C22×C8×C17C2×C411yescharacteristic
20C2×#63223—21no—
21C22×#3622D411yescharacteristic
22C2×C8×D17—42no—
23C2×C8×D17C2×C411yescharacteristic
24C2×C8×D17C2×C411yescharacteristic
25C2×C8×D17D411yescharacteristic
26C2×C8×D17Q811yescharacteristic
27(C2×#595)⋊C4—41no—
28C2×#63216—22no—
29#10587534—42no—
30#10587530—42no—
31#10587493—42no—
32#10587491—41no—
33#10587491—41no—
34C23×D17SD1611yescharacteristic
35C22×#595—42no—
36C22×C4×C17C22⋊C411yescharacteristic
37C22×Dic17Q1611yescharacteristic
38C2×C4×D17—41no—
39C2×C4×D17—41no—
40C2×C4×D17C22⋊C411yescharacteristic
41C2×C4×D17C4⋊C411yescharacteristic
42C2×C4×D17D811yescharacteristic
43C2×C4×D17SD1611yescharacteristic
44C22⋊#595—82no—
45C4⋊#595—42no—
46C4⋊#595—42no—
47M16×C17—41no—
48M16×C17—41no—
49C2×C8×C17—41no—
50C2×C8×C17—41no—
51C2×C8×C17C4211yescharacteristic
52C2×C8×C17C4⋊C411yescharacteristic
53#63223—41no—
54#63223—41no—
55C2×#3622—22no—
56C2×#3622—41no—
57C2×#3622C22⋊C411yescharacteristic
58C2×#3622C4⋊C411yescharacteristic
59C8×D17—22no—
60C8×D17—22no—
61C8×D17—41no—
62C8×D17—41no—
63#63216—42no—
64#7235—171nomaximal, Sylow
65C23×C17#10311yescharacteristic
66C22×D17—21no—
67C22×D17—21no—
68C22×D17—41no—
69C22×D17—41no—
70C22×D17#10211yescharacteristic
71C22×D17#10611yescharacteristic
72C2×#595—82no—
73C2×#595—82no—
74C2×#595—82no—
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17#9511yescharacteristic
78C2×C4×C17#10211yescharacteristic
79C2×Dic17—41no—
80C2×Dic17#10311yescharacteristic
81C2×Dic17#10711yescharacteristic
82C4×D17—21no—
83C4×D17—21no—
84C4×D17—21no—
85C4×D17—21no—
86C4×D17—41no—
87C4×D17—41no—
88C8×C17—21no—
89C8×C17—21no—
90C8×C17—81no—
91#3622—21no—
92#3622—81no—
93#3622#9912yes—
94#2112—171no—
95#1810—171no—
96#1808—171no—
97C22×C17—21no—
98C22×C17—21no—
99C22×C17—21no—
100C22×C17#34011yescharacteristic
101C2×D17—21no—
102C2×D17—21no—
103C2×D17—21no—
104C2×D17—21no—
105C2×D17—21no—
106C2×D17—42no—
107C2×D17—42no—
108C2×D17#36111yescharacteristic
109C2×D17#36211yescharacteristic
110#595—162no—
111C4×C17—21no—
112C4×C17H(3,ℤ/4)11yescharacteristic
113C4×C17#34211yescharacteristic
114Dic17—21no—
115Dic17—21no—
116C23×C8—171no—
117C2×M32—172no—
118C2×#108—341no—
119C2×#107—341no—
120#407—341no—
121#380—341no—
122C22⋊C16—341no—
123C22⋊C16—341no—
124#341—171no—
125#341#59511yescharacteristic, complemented
126#340—172no—
127C2×C17—41no—
128C2×C17#128911yescharacteristic
129C2×C17#138711yescharacteristic
130C2×C17#138911yescharacteristic
131D17—21no—
132D17—21no—
133D17—41no—
134C23×C4—171no—
135C2×M16—21no—
136C2×M16—341no—
137C22×C8—171no—
138C22×C8—171no—
139C22×C8—171no—
140C22×C8—171no—
141C22×C8—171no—
142C22×C8—682no—
143C22×C8C2×#59511yescharacteristic
144C2×C4⋊C4—342no—
145C2×C22⋊C4—681no—
146M32—682no—
147C2×C16—342no—
148#108—682no—
149#107—682no—
150C22⋊C8—681no—
151C22⋊C8—681no—
152#95—681no—
153C17#723511yescharacteristic, complemented, Sylow
154C24—171no—
155C22×C4—171no—
156C22×C4—171no—
157C22×C4—171no—
158C22×C4—171no—
159C22×C4—171no—
160C22×C4—681no—
161C22×C4—681no—
162C22×C4—682no—
163C22×C4C22⋊#59511yescharacteristic
164M16—41no—
165M16—41no—
166M16—681no—
167M16—681no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—171no—
171C2×C8—171no—
172C2×C8—342no—
173C2×C8—342no—
174C2×C8—342no—
175C2×C8—681no—
176C2×C8—681no—
177C2×C8—681no—
178C2×C8C4×#59511yescharacteristic
179C2×C8C4⋊#59511yescharacteristic
180C4⋊C4—682no—
181C4⋊C4—682no—
182C22⋊C4—1362no—
183C16—682no—
184C23—171no—
185C23—171no—
186C23—341no—
187C23—341no—
188C23—681no—
189C23—681no—
190C23#1058754911yescharacteristic
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—171no—
194C2×C4—171no—
195C2×C4—341no—
196C2×C4—341no—
197C2×C4—341no—
198C2×C4—341no—
199C2×C4—681no—
200C2×C4—681no—
201C2×C4—681no—
202C2×C4—1362no—
203C2×C4—1362no—
204C2×C4—1362no—
205C2×C4(C2×#595)⋊C411yescharacteristic
206C2×C4#1058754711yescharacteristic
207C8—21no—
208C8—21no—
209C8—81no—
210C8—172no—
211C8—341no—
212C8—1361no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—171no—
217C22—171no—
218C22—341no—
219C22—341no—
220C22—341no—
221C22—341no—
222C22—341no—
223C22—682no—
224C22—682no—
225C22#1176368211yescharacteristic
226C4—21no—
227C4—2722no—
228C4—341no—
229C4—341no—
230C4#1176367611yescharacteristic
231C4#1176368611yescharacteristic
232C2—41no—
233C2—341no—
234C2—341no—
235C2—681no—
236C2#1454364611yescharacteristic
237C2#1454386011yescharacteristic
238C2#1454386411yescharacteristic
subgroupG/H
centerC22#11763682
commutatorC2×C8×C17C42
FrattiniC22×C8C2×#595
FittingC17×#341C4
socleC22×C17#340
prime radicalC23×D17SD16
cosocleC22×C8×D17C22
hypercenter#341#595
hypocenterC17#7235
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
4. C2×#10587530C4semidirect
13. #11762574C4semidirect
14. C17×#341C4semidirect
125. #341#595semidirect
153. C17#7235semidirect

Maximal subgroups

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

subgroupindex
#145450122
#145446612
#145288212
#723517