Finite Group Databasebeta

← #17948894

Subgroups — #17948894

Order 4352.

336 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 70 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#14544664C211yesmaximal, characteristic
3#14528499C211yesmaximal, characteristic
4C2×#10587529—21no—
5C2×#10587536C412yescomplemented
6#11763780—21no—
7#11763704C412yescomplemented
8C22⋊#63216—21no—
9#11763685—21no—
10C22×C8×D17C2211yescharacteristic
11C2×#10587578—21no—
12#11762572C411yescharacteristic
13#11762571—21no—
14C17×#340C411yescharacteristic
15C22×C4×D17D411yescharacteristic
16C2×#63243—22no—
17C22×C8×C17C2×C411yescharacteristic
18C2×C4⋊C4×C17—21no—
19C2×#63227—41no—
20C2×C4⋊Dic17—21no—
21C2×C4×Dic17—41no—
22C22×#3622D411yescharacteristic
23C2×C8×D17—42no—
24C2×C8×D17C2×C411yescharacteristic
25C2×C8×D17C2×C411yescharacteristic
26C2×C8×D17D411yescharacteristic
27C2×C8×D17Q811yescharacteristic
28#10587578—24no—
29#10587578—42no—
30C22⋊#3624—41no—
31#10587543—41no—
32C2×#63216—22no—
33#10587536—42no—
34#10587529—42no—
35C23×D17SD1611yescharacteristic
36C22×C4×C17—41no—
37C22×C4×C17C22⋊C411yescharacteristic
38C22×Dic17—41no—
39C22×Dic17D811yescharacteristic
40C2×C4×D17—22no—
41C2×C4×D17—22no—
42C2×C4×D17C22⋊C411yescharacteristic
43C2×C4×D17C4⋊C411yescharacteristic
44C2×C4×D17SD1611yescharacteristic
45C2×C4×D17Q1611yescharacteristic
46C2×#3624—42no—
47#63243—42no—
48#63243—42no—
49C2×C8×C17—41no—
50C2×C8×C17C4211yescharacteristic
51C2×C8×C17C4⋊C411yescharacteristic
52C4⋊C4×C17—22no—
53C4⋊C4×C17—41no—
54#63227—44no—
55C4⋊Dic17—22no—
56C4⋊Dic17—41no—
57C4×Dic17—44no—
58C2×#3622—41no—
59C2×#3622C22⋊C411yescharacteristic
60C2×#3622C4⋊C411yescharacteristic
61C8×D17—22no—
62C8×D17—22no—
63C8×D17—41no—
64C8×D17—41no—
65#63216—42no—
66#7260—171nomaximal, Sylow
67C23×C17#10211yescharacteristic
68C22×D17—21no—
69C22×D17—21no—
70C22×D17—22no—
71C22×D17—41no—
72C22×D17#10311yescharacteristic
73C22×D17#10611yescharacteristic
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—42no—
77C2×C4×C17—81no—
78C2×C4×C17—81no—
79C2×C4×C17#9511yescharacteristic
80C2×C4×C17#10311yescharacteristic
81C2×Dic17—22no—
82C2×Dic17—42no—
83C2×Dic17—81no—
84C2×Dic17—81no—
85C2×Dic17#10211yescharacteristic
86C2×Dic17#10711yescharacteristic
87C4×D17—22no—
88C4×D17—21no—
89C4×D17—21no—
90C4×D17—22no—
91C4×D17#9912yes—
92C4×D17#10412yes—
93#3624—82no—
94C8×C17—21no—
95C8×C17—21no—
96#3622—21no—
97#3622—21no—
98C2×C22⋊C16—171no—
99#1810—171no—
100#1735—171no—
101C22×C17—21no—
102C22×C17—21no—
103C22×C17#34011yescharacteristic
104C22×C17#35911yescharacteristic
105C22×C17#35911yescharacteristic
106C2×D17—21no—
107C2×D17—21no—
108C2×D17—21no—
109C2×D17—21no—
110C2×D17—21no—
111C2×D17—42no—
112C2×D17—42no—
113C2×D17#32812yes—
114C4×C17—21no—
115C4×C17—82no—
116C4×C17#33911yescharacteristic
117C4×C17#34211yescharacteristic
118Dic17—21no—
119Dic17—82no—
120Dic17#32712yes—
121C23×C8—171no—
122C2×#117—341no—
123C22×C16—341no—
124C2×#108—172no—
125#407—341no—
126C22⋊C16—172no—
127C22⋊C16—341no—
128#341—341no—
129#340—171no—
130#340—341no—
131#340#59511yescharacteristic
132C2×C17—21no—
133C2×C17—21no—
134C2×C17#129411yescharacteristic
135C2×C17#138211yescharacteristic
136C2×C17#138911yescharacteristic
137D17—22no—
138D17—41no—
139C23×C4—171no—
140C2×M16—342no—
141C22×C8—171no—
142C22×C8—171no—
143C22×C8—171no—
144C22×C8—171no—
145C22×C8—171no—
146C22×C8—682no—
147C22×C8C2×#59511yescharacteristic
148#117—344no—
149#117—682no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—341no—
152C2×C22⋊C4—681no—
153C2×C42—681no—
154C2×C16—342no—
155C2×C16—682no—
156#108—682no—
157C22⋊C8—681no—
158C22⋊C8—681no—
159C17#726011yescharacteristic, complemented, Sylow
160C24—171no—
161C22×C4—41no—
162C22×C4—171no—
163C22×C4—171no—
164C22×C4—171no—
165C22×C4—171no—
166C22×C4—171no—
167C22×C4—342no—
168C22×C4—342no—
169C22×C4—681no—
170C22×C4C22⋊#59511yescharacteristic
171M16—682no—
172M16—682no—
173C2×C8—41no—
174C2×C8—171no—
175C2×C8—171no—
176C2×C8—342no—
177C2×C8—342no—
178C2×C8—681no—
179C2×C8—681no—
180C2×C8—681no—
181C2×C8—682no—
182C2×C8C4×#59511yescharacteristic
183C2×C8C4⋊#59511yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—41no—
186C4⋊C4—342no—
187C4⋊C4—681no—
188C22⋊C4—684no—
189C42—684no—
190C16—682no—
191C23—171no—
192C23—171no—
193C23—342no—
194C23—341no—
195C23—341no—
196C23—681no—
197C23#1058754711yescharacteristic
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—171no—
204C2×C4—172no—
205C2×C4—172no—
206C2×C4—171no—
207C2×C4—342no—
208C2×C4—342no—
209C2×C4—342no—
210C2×C4—341no—
211C2×C4—341no—
212C2×C4—682no—
213C2×C4—1361no—
214C2×C4—1361no—
215C2×C4(C2×#595)⋊C411yescharacteristic
216C2×C4#1058754911yescharacteristic
217C8—21no—
218C8—21no—
219C8—341no—
220C8—341no—
221C8—1362no—
222C22—21no—
223C22—21no—
224C22—172no—
225C22—341no—
226C22—341no—
227C22—341no—
228C22—341no—
229C22—341no—
230C22—682no—
231C22—682no—
232C22#1176368211yescharacteristic
233C22#1176372311yescharacteristic
234C22#1176372411yescharacteristic
235C4—21no—
236C4—82no—
237C4—172no—
238C4—341no—
239C4—1362no—
240C4#1176368011yescharacteristic
241C4#1176368611yescharacteristic
242C2—21no—
243C2—21no—
244C2—342no—
245C2—681no—
246C2#1454365811yescharacteristic
247C2#1454384511yescharacteristic
248C2#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#7260
LCSG ▷ C2×C8×C17 ▷ C2×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
5. C2×#10587536C4semidirect
7. #11763704C4semidirect
159. C17#7260semidirect

Maximal subgroups

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

subgroupindex
#145450092
#145446642
#145284992
#726017