Finite Group Databasebeta

← #17948812

Subgroups — #17948812

Order 4352.

286 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 64 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#14544663C211yesmaximal, characteristic
3#14528812C211yesmaximal, characteristic
4C2×#10587530C412yescomplemented
5C2×#10587535—21no—
6#11763780—21no—
7#11763704—21no—
8C22⋊#63216—21no—
9#11763685C412yescomplemented
10C22×C8×D17C2211yescharacteristic
11C2×#10587478—21no—
12#11762666—21no—
13#11762572C411yescharacteristic
14C17×#340C411yescharacteristic
15C22×C4×D17D411yescharacteristic
16C2×#63243—22no—
17C22×C8×C17C2×C411yescharacteristic
18C2×C4⋊C4×C17—21no—
19C2×#63227—41no—
20C2×C4⋊Dic17—21no—
21C22×#3622D411yescharacteristic
22C2×C8×D17—42no—
23C2×C8×D17C2×C411yescharacteristic
24C2×C8×D17C2×C411yescharacteristic
25C2×C8×D17D411yescharacteristic
26C2×C8×D17Q811yescharacteristic
27C22⋊#3624—41no—
28#10587543—41no—
29C2×#63216—22no—
30#10587535—42no—
31#10587530—42no—
32#10587502—41no—
33#10587478—42no—
34C23×D17SD1611yescharacteristic
35C22×C4×C17—41no—
36C22×C4×C17C22⋊C411yescharacteristic
37C22×Dic17—41no—
38C22×Dic17D811yescharacteristic
39C2×C4×D17—41no—
40C2×C4×D17—41no—
41C2×C4×D17C22⋊C411yescharacteristic
42C2×C4×D17C4⋊C411yescharacteristic
43C2×C4×D17SD1611yescharacteristic
44C2×C4×D17Q1611yescharacteristic
45C2×#3624—42no—
46#63243—42no—
47#63243—42no—
48C2×C8×C17—41no—
49C2×C8×C17C4211yescharacteristic
50C2×C8×C17C4⋊C411yescharacteristic
51C4⋊C4×C17—41no—
52C4⋊C4×C17—41no—
53#63227—82no—
54C4⋊Dic17—41no—
55C4⋊Dic17—41no—
56C2×#3622—22no—
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#10211yescharacteristic
66C22×D17—21no—
67C22×D17—21no—
68C22×D17—41no—
69C22×D17—41no—
70C22×D17#10311yescharacteristic
71C22×D17#10611yescharacteristic
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—81no—
75C2×C4×C17—81no—
76C2×C4×C17—81no—
77C2×C4×C17#9511yescharacteristic
78C2×C4×C17#10311yescharacteristic
79C2×Dic17—41no—
80C2×Dic17—81no—
81C2×Dic17—81no—
82C2×Dic17—81no—
83C2×Dic17#10211yescharacteristic
84C2×Dic17#10711yescharacteristic
85C4×D17—21no—
86C4×D17—21no—
87C4×D17—21no—
88C4×D17—21no—
89C4×D17—41no—
90C4×D17—41no—
91#3624—82no—
92C8×C17—21no—
93C8×C17—21no—
94#3622—21no—
95#3622#9912yes—
96#2112—171no—
97#1810—171no—
98#1808—171no—
99C22×C17—21no—
100C22×C17—21no—
101C22×C17#34011yescharacteristic
102C22×C17#36111yescharacteristic
103C22×C17#36211yescharacteristic
104C2×D17—21no—
105C2×D17—21no—
106C2×D17—21no—
107C2×D17—21no—
108C2×D17—21no—
109C2×D17—21no—
110C2×D17—42no—
111C2×D17—42no—
112C4×C17—21no—
113C4×C17—161no—
114C4×C17H(3,ℤ/4)11yescharacteristic
115C4×C17#34211yescharacteristic
116Dic17—21no—
117Dic17—21no—
118Dic17—161no—
119C23×C8—171no—
120C2×M32—172no—
121C2×#108—341no—
122C2×#107—341no—
123#407—341no—
124#380—341no—
125C22⋊C16—341no—
126C22⋊C16—341no—
127#341—172no—
128#340—171no—
129#340#59511yescharacteristic
130C2×C17—21no—
131C2×C17—21no—
132C2×C17#128911yescharacteristic
133C2×C17#138711yescharacteristic
134C2×C17#138911yescharacteristic
135D17—41no—
136D17—41no—
137C23×C4—171no—
138C2×M16—342no—
139C22×C8—171no—
140C22×C8—171no—
141C22×C8—171no—
142C22×C8—171no—
143C22×C8—171no—
144C22×C8—682no—
145C22×C8C2×#59511yescharacteristic
146C2×C4⋊C4—21no—
147C2×C4⋊C4—341no—
148C2×C22⋊C4—681no—
149M32—682no—
150C2×C16—342no—
151#108—682no—
152#107—682no—
153C22⋊C8—681no—
154C22⋊C8—681no—
155#95—681no—
156C17#723511yescharacteristic, complemented, Sylow
157C24—171no—
158C22×C4—41no—
159C22×C4—171no—
160C22×C4—171no—
161C22×C4—171no—
162C22×C4—171no—
163C22×C4—171no—
164C22×C4—681no—
165C22×C4—681no—
166C22×C4—681no—
167C22×C4C22⋊#59511yescharacteristic
168M16—682no—
169M16—682no—
170C2×C8—41no—
171C2×C8—171no—
172C2×C8—171no—
173C2×C8—342no—
174C2×C8—342no—
175C2×C8—342no—
176C2×C8—681no—
177C2×C8—681no—
178C2×C8—682no—
179C2×C8C4×#59511yescharacteristic
180C2×C8C4⋊#59511yescharacteristic
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—681no—
184C4⋊C4—681no—
185C22⋊C4—1362no—
186C16—682no—
187C23—171no—
188C23—171no—
189C23—341no—
190C23—341no—
191C23—681no—
192C23—681no—
193C23#1058754711yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—171no—
200C2×C4—171no—
201C2×C4—341no—
202C2×C4—341no—
203C2×C4—341no—
204C2×C4—341no—
205C2×C4—681no—
206C2×C4—681no—
207C2×C4—681no—
208C2×C4—1361no—
209C2×C4—1361no—
210C2×C4—1361no—
211C2×C4(C2×#595)⋊C411yescharacteristic
212C2×C4#1058754911yescharacteristic
213C8—21no—
214C8—21no—
215C8—172no—
216C8—341no—
217C8—1362no—
218C22—21no—
219C22—21no—
220C22—341no—
221C22—341no—
222C22—341no—
223C22—341no—
224C22—341no—
225C22—341no—
226C22—682no—
227C22—682no—
228C22#1176368211yescharacteristic
229C22#1176372711yescharacteristic
230C22#1176372811yescharacteristic
231C4—21no—
232C4—161no—
233C4—2721no—
234C4—341no—
235C4—341no—
236C4#1176367611yescharacteristic
237C4#1176368611yescharacteristic
238C2—21no—
239C2—21no—
240C2—681no—
241C2—681no—
242C2#1454364611yescharacteristic
243C2#1454385811yescharacteristic
244C2#1454386611yescharacteristic
subgroupG/H
centerC22#11763682
commutatorC2×C8×C17C42
FrattiniC22×C8C2×#595
FittingC17×#340C4
socleC22×C17#340
prime radicalC23×D17SD16
cosocleC22×C8×D17C22
hypercenter#340#595
hypocenterC17#7235
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. #11763685C4semidirect
156. C17#7235semidirect

Maximal subgroups

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

subgroupindex
#145450122
#145446632
#145288122
#723517