Finite Group Databasebeta

← #17948807

Subgroups — #17948807

Order 4352.

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

normal subgroups only

This group has 292 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#14545009C211yesmaximal, characteristic
2#14544660C211yesmaximal, characteristic
3#14528821C211yesmaximal, characteristic
4C2×#10587529C412yescomplemented
5C2×#10587533—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#10587533—42no—
30#10587529—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#7232—171nomaximal, Sylow
65C23×C17#10311yescharacteristic
66C22×D17—22no—
67C22×D17—22no—
68C22×D17—41no—
69C22×D17#10211yescharacteristic
70C22×D17#10611yescharacteristic
71C2×#595—82no—
72C2×#595—82no—
73C2×#595—82no—
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17#9511yescharacteristic
77C2×C4×C17#10211yescharacteristic
78C2×Dic17—41no—
79C2×Dic17#10311yescharacteristic
80C2×Dic17#10711yescharacteristic
81C4×D17—21no—
82C4×D17—21no—
83C4×D17—21no—
84C4×D17—21no—
85C4×D17—41no—
86C4×D17—41no—
87C8×C17—21no—
88C8×C17—21no—
89C8×C17—81no—
90#3622—21no—
91#3622—81no—
92#3622#9912yes—
93C2×C22⋊C16—171no—
94#1810—171no—
95#1807—171no—
96C22×C17—21no—
97C22×C17—21no—
98C22×C17—21no—
99C22×C17#34011yescharacteristic
100C2×D17—21no—
101C2×D17—21no—
102C2×D17—21no—
103C2×D17—21no—
104C2×D17—44no—
105C2×D17#35912yes—
106C2×D17#36512yes—
107#595—162no—
108C4×C17—21no—
109C4×C17H(3,ℤ/4)11yescharacteristic
110C4×C17#34211yescharacteristic
111Dic17—21no—
112Dic17—21no—
113C23×C8—171no—
114C22×C16—172no—
115C2×#108—341no—
116C2×#106—341no—
117#407—341no—
118#380—341no—
119C22⋊C16—341no—
120C22⋊C16—341no—
121#341—171no—
122#341#59511yescharacteristic, complemented
123#340—172no—
124C2×C17—41no—
125C2×C17#128911yescharacteristic
126C2×C17#138211yescharacteristic
127C2×C17#138311yescharacteristic
128D17—22no—
129D17—22no—
130C23×C4—171no—
131C2×M16—21no—
132C2×M16—341no—
133C22×C8—171no—
134C22×C8—171no—
135C22×C8—171no—
136C22×C8—171no—
137C22×C8—171no—
138C22×C8—682no—
139C22×C8C2×#59511yescharacteristic
140C2×C4⋊C4—342no—
141C2×C22⋊C4—681no—
142C2×C16—342no—
143C2×C16—682no—
144#108—682no—
145#106—682no—
146C22⋊C8—681no—
147C22⋊C8—681no—
148#95—681no—
149C17#723211yescharacteristic, complemented, Sylow
150C24—171no—
151C22×C4—171no—
152C22×C4—171no—
153C22×C4—171no—
154C22×C4—171no—
155C22×C4—171no—
156C22×C4—681no—
157C22×C4—681no—
158C22×C4—682no—
159C22×C4C22⋊#59511yescharacteristic
160M16—41no—
161M16—41no—
162M16—681no—
163M16—681no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—171no—
167C2×C8—171no—
168C2×C8—342no—
169C2×C8—342no—
170C2×C8—342no—
171C2×C8—681no—
172C2×C8—681no—
173C2×C8—681no—
174C2×C8C4×#59511yescharacteristic
175C2×C8C4⋊#59511yescharacteristic
176C4⋊C4—682no—
177C4⋊C4—682no—
178C22⋊C4—1362no—
179C16—682no—
180C23—171no—
181C23—171no—
182C23—342no—
183C23—342no—
184C23—681no—
185C23#1058754911yescharacteristic
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—171no—
189C2×C4—171no—
190C2×C4—341no—
191C2×C4—341no—
192C2×C4—341no—
193C2×C4—341no—
194C2×C4—681no—
195C2×C4—681no—
196C2×C4—681no—
197C2×C4—1362no—
198C2×C4—1362no—
199C2×C4—1362no—
200C2×C4(C2×#595)⋊C411yescharacteristic
201C2×C4#1058754711yescharacteristic
202C8—21no—
203C8—21no—
204C8—81no—
205C8—172no—
206C8—341no—
207C8—1361no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—172no—
212C22—172no—
213C22—341no—
214C22—341no—
215C22—341no—
216C22—341no—
217C22—684no—
218C22#1176368211yescharacteristic
219C4—21no—
220C4—2722no—
221C4—341no—
222C4—341no—
223C4#1176367611yescharacteristic
224C4#1176368611yescharacteristic
225C2—41no—
226C2—342no—
227C2—342no—
228C2#1454364611yescharacteristic
229C2#1454384711yescharacteristic
230C2#1454385011yescharacteristic
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#7232
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×#10587529C4semidirect
13. #11762574C4semidirect
14. C17×#341C4semidirect
122. #341#595semidirect
149. C17#7232semidirect

Maximal subgroups

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

subgroupindex
#145450092
#145446602
#145288212
#723217