Finite Group Databasebeta

← #17948806

Subgroups — #17948806

Order 4352.

292 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 68 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#14544663C211yesmaximal, characteristic
2#14544660C211yesmaximal, characteristic
3C2×#11762588C211yesmaximal, characteristic
4C2×#10587535—21no—
5C2×#10587533—21no—
6#11763780—21no—
7#11763751—21no—
8#11763685C412yescomplemented
9#11763683C412yes—
10C22×C8×D17C2211yescharacteristic
11C22×#63214C411yescharacteristic, complemented
12#11762588—21no—
13#11762588—21no—
14C22×C16×C17C411yescharacteristic, complemented
15C22×C4×D17D411yescharacteristic
16C2×C22⋊#595—41no—
17C2×C4⋊#595—22no—
18C2×#63243—22no—
19C22×C8×C17C2×C411yescharacteristic
20C22×#3622Q811yescharacteristic
21C2×C8×D17—41no—
22C2×C8×D17—41no—
23C2×C8×D17C2×C411yescharacteristic
24C2×C8×D17C2×C411yescharacteristic
25C2×C8×D17D411yescharacteristic
26C2×C8×D17D411yescharacteristic
27C22⋊#3624—41no—
28(C2×#595)⋊C4—41no—
29#10587543—41no—
30#10587535—41no—
31#10587535—41no—
32#10587533—41no—
33#10587533—41no—
34C2×C16×C17—21no—
35C2×C16×C17—41no—
36C2×#63214—21no—
37C2×#63214—41no—
38C23×D17SD1611yescharacteristic
39C22×#595—42no—
40C22×C4×C17C4⋊C411yescharacteristic
41C22×Dic17SD1611yescharacteristic
42C2×C4×D17—41no—
43C2×C4×D17—41no—
44C2×C4×D17C22⋊C411yescharacteristic
45C2×C4×D17C22⋊C411yescharacteristic
46C2×C4×D17D811yescharacteristic
47C2×C4×D17Q1611yescharacteristic
48C22⋊#595—81no—
49C22⋊#595—81no—
50C2×#3624—42no—
51C4⋊#595—42no—
52C4⋊#595—42no—
53#63243—42no—
54#63243—42no—
55C2×C8×C17—21no—
56C2×C8×C17—21no—
57C2×C8×C17C4211yescharacteristic
58C2×C8×C17C22⋊C411yescharacteristic
59C2×#3622—41no—
60C2×#3622C4⋊C411yescharacteristic
61C2×#3622C4⋊C411yescharacteristic
62C8×D17—21no—
63C8×D17—21no—
64C8×D17—21no—
65C8×D17—21no—
66C8×D17—41no—
67C8×D17—41no—
68C16×C17—41no—
69#63214—41no—
70#7232—171nomaximal, Sylow
71C23×C17#10611yescharacteristic
72C22×D17—21no—
73C22×D17—21no—
74C22×D17—22no—
75C22×D17—41no—
76C22×D17#10211yescharacteristic
77C22×D17#10311yescharacteristic
78C2×#595—82no—
79C2×#595—82no—
80C2×#595—82no—
81C2×C4×C17—21no—
82C2×C4×C17—21no—
83C2×C4×C17#9511yescharacteristic
84C2×C4×C17#10711yescharacteristic
85C2×Dic17—41no—
86C2×Dic17#10211yescharacteristic
87C2×Dic17#10311yescharacteristic
88C4×D17—21no—
89C4×D17—21no—
90C4×D17—21no—
91C4×D17—21no—
92C4×D17—41no—
93C4×D17—41no—
94#3624—82no—
95C8×C17—21no—
96C8×C17#9911yescharacteristic
97C8×C17#9911yescharacteristic
98#3622—21no—
99#3622—21no—
100C2×C22⋊C16—171no—
101#1810—171no—
102#1807—171no—
103C22×C17—21no—
104C22×C17—21no—
105C22×C17#34011yescharacteristic
106C22×C17#36511yescharacteristic
107C22×C17#36511yescharacteristic
108C2×D17—21no—
109C2×D17—21no—
110C2×D17—21no—
111C2×D17—21no—
112C2×D17—21no—
113C2×D17—42no—
114C2×D17—42no—
115C2×D17#35912yes—
116#595—162no—
117C4×C17—21no—
118C4×C17H(3,ℤ/4)11yescharacteristic
119C4×C17#34211yescharacteristic
120Dic17—21no—
121Dic17—21no—
122C23×C8—171no—
123C22×C16—171no—
124C22×C16#59511yescharacteristic, complemented
125C2×#108—341no—
126C2×#106—341no—
127#407—341no—
128#380—341no—
129C22⋊C16—341no—
130C22⋊C16—341no—
131#341—172no—
132#340—172no—
133C2×C17—21no—
134C2×C17—21no—
135C2×C17#128911yescharacteristic
136C2×C17#138211yescharacteristic
137C2×C17#138311yescharacteristic
138D17—22no—
139D17—41no—
140C23×C4—171no—
141C2×M16—342no—
142C22×C8—171no—
143C22×C8—171no—
144C22×C8—171no—
145C22×C8—171no—
146C22×C8—171no—
147C22×C8—681no—
148C22×C8—681no—
149C22×C8C2×#59511yescharacteristic
150C2×C4⋊C4—342no—
151C2×C22⋊C4—681no—
152C2×C16—21no—
153C2×C16—41no—
154C2×C16—341no—
155C2×C16—681no—
156#108—681no—
157#108—681no—
158#106—681no—
159#106—681no—
160C22⋊C8—681no—
161C22⋊C8—681no—
162#95—681no—
163C17#723211yescharacteristic, complemented, Sylow
164C24—171no—
165C22×C4—171no—
166C22×C4—171no—
167C22×C4—171no—
168C22×C4—171no—
169C22×C4—171no—
170C22×C4—681no—
171C22×C4—681no—
172C22×C4—682no—
173C22×C4C4⋊#59511yescharacteristic
174M16—682no—
175M16—682no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—171no—
179C2×C8—171no—
180C2×C8—341no—
181C2×C8—341no—
182C2×C8—341no—
183C2×C8—341no—
184C2×C8—681no—
185C2×C8—681no—
186C2×C8—681no—
187C2×C8—682no—
188C2×C8C4×#59511yescharacteristic
189C2×C8C22⋊#59511yescharacteristic
190C4⋊C4—682no—
191C4⋊C4—682no—
192C22⋊C4—1361no—
193C22⋊C4—1361no—
194C16—41no—
195C16—681no—
196C23—171no—
197C23—171no—
198C23—342no—
199C23—341no—
200C23—341no—
201C23—681no—
202C23#1058753311yescharacteristic
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—171no—
206C2×C4—171no—
207C2×C4—341no—
208C2×C4—341no—
209C2×C4—341no—
210C2×C4—341no—
211C2×C4—681no—
212C2×C4—681no—
213C2×C4—681no—
214C2×C4—1362no—
215C2×C4—1362no—
216C2×C4—1362no—
217C2×C4#1058753411yescharacteristic
218C2×C4(C2×#595)⋊C411yescharacteristic
219C8—21no—
220C8—341no—
221C8—341no—
222C8—1362no—
223C8#1058753911yescharacteristic
224C8#1058755111yescharacteristic
225C22—21no—
226C22—21no—
227C22—172no—
228C22—341no—
229C22—341no—
230C22—341no—
231C22—341no—
232C22—341no—
233C22—682no—
234C22—682no—
235C22#1176368311yescharacteristic
236C22#1176373311yescharacteristic
237C22#1176373411yescharacteristic
238C4—21no—
239C4—2722no—
240C4—341no—
241C4—341no—
242C4#1176367711yescharacteristic
243C4#1176368711yescharacteristic
244C2—21no—
245C2—21no—
246C2—342no—
247C2—681no—
248C2#1454364711yescharacteristic
249C2#1454384611yescharacteristic
250C2#1454384911yescharacteristic
subgroupG/H
centerC22#11763683
commutatorC2×C8×C17C42
FrattiniC22×C8C2×#595
FittingC22×C16×C17C4
socleC22×C17#340
prime radicalC23×D17SD16
cosocleC22×C8×D17C22
hypercenterC22×C16#595
hypocenterC17#7232
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
8. #11763685C4semidirect
11. C22×#63214C4semidirect
14. C22×C16×C17C4semidirect
124. C22×C16#595semidirect
163. C17#7232semidirect

Maximal subgroups

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

subgroupindex
#145446632
#145446602
C2×#117625882
#723217