Finite Group Databasebeta

← #17948748

Subgroups — #17948748

Order 4352.

290 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 50 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#14544682C211yesmaximal, characteristic
2#14544513C211yesmaximal, characteristic
3#14527117C211yesmaximal, characteristic
4C2×#10587543—21no—
5C2×#10587542C411yescharacteristic, complemented
6C2×C4×#3624C411yescharacteristic, complemented
7#11763752—21no—
8#11763687—21no—
9#11763687C412yes—
10#11763675—21no—
11C2×#10587578C2211yescharacteristic
12#11762863—21no—
13#11762535C411yescharacteristic, complemented
14#11762532—21no—
15C17×#324C411yescharacteristic, complemented
16C22×C4×D17D411yescharacteristic
17C2×C22⋊#595—22no—
18C22×#3624—21no—
19C22×#3624—21no—
20C2×C4⋊C4×C17C2×C411yescharacteristic
21C2×#63227C2×C411yescharacteristic
22C2×#63227D411yescharacteristic
23C2×C4⋊Dic17Q811yescharacteristic
24C2×C4×Dic17C2×C411yescharacteristic
25C2×C4×Dic17D411yescharacteristic
26#10587578—41no—
27#10587578—41no—
28(C2×#595)⋊C4—41no—
29(C2×#595)⋊C4—41no—
30#10587543—24no—
31#10587542—41no—
32C4×#3624—41no—
33C17×C22⋊C8—21no—
34C22⋊#3622—21no—
35#10587486—41no—
36#10587485—41no—
37C23×D17C22⋊C411yescharacteristic
38C22×#595—42no—
39C22×C4×C17C4211yescharacteristic
40C22×C4×C17C22⋊C411yescharacteristic
41C22×C4×C17C4⋊C411yescharacteristic
42C22×Dic17C22⋊C411yescharacteristic
43C22×Dic17C4⋊C411yescharacteristic
44C22×Dic17C4⋊C411yescharacteristic
45C2×C4×D17—22no—
46C2×C4×D17—21no—
47C2×C4×D17—21no—
48C2×C4×D17—41no—
49C22⋊#595—42no—
50C22⋊#595—42no—
51C2×#3624—22no—
52C2×#3624—22no—
53C2×#3624—41no—
54C2×#3624—41no—
55C2×#3624—41no—
56C2×#3624—41no—
57C2×C8×C17—41no—
58C4⋊C4×C17—41no—
59#63227—41no—
60#63227—41no—
61C4⋊Dic17—41no—
62C4×Dic17—21no—
63C4×Dic17—21no—
64C4×Dic17—21no—
65C4×Dic17—21no—
66C2×#3622—41no—
67#7214—171nomaximal, Sylow
68C23×C17#9511yescharacteristic
69C22×D17—21no—
70C22×D17—21no—
71C22×D17—41no—
72C22×D17—41no—
73C22×D17#10412yes—
74C2×#595—82no—
75C2×#595—82no—
76C2×#595—82no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—21no—
82C2×C4×C17—41no—
83C2×C4×C17—41no—
84C2×Dic17—21no—
85C2×Dic17—21no—
86C2×Dic17—21no—
87C2×Dic17—21no—
88C2×Dic17—41no—
89C2×Dic17—41no—
90C2×Dic17#9911yescharacteristic
91C2×Dic17#9911yescharacteristic
92C4×D17—42no—
93C4×D17—42no—
94#3624—42no—
95#3624—42no—
96C8×C17—81no—
97#3622—81no—
98#1820—171no—
99#1750—171no—
100#1464—171no—
101C22×C17—21no—
102C22×C17—21no—
103C22×C17H(3,ℤ/4)11yescharacteristic
104C22×C17#33911yescharacteristic
105C22×C17#34211yescharacteristic
106C2×D17—22no—
107C2×D17—41no—
108C2×D17—41no—
109C2×D17—42no—
110C2×D17—81no—
111#595—162no—
112C4×C17—41no—
113C4×C17—41no—
114C4×C17—41no—
115Dic17—21no—
116Dic17—21no—
117Dic17—41no—
118Dic17—41no—
119C2×#117—171no—
120#432—341no—
121C2×C22⋊C8—341no—
122C2×#97—171no—
123C2×C4×C8—171no—
124#381—341no—
125#342—172no—
126#342—341no—
127#336—341no—
128#324—171no—
129#324#59511yescharacteristic, complemented
130#323—341no—
131C2×C17—21no—
132C2×C17—21no—
133C2×C17#128411yescharacteristic
134C2×C17#139111yescharacteristic
135C2×C17#139511yescharacteristic
136D17—42no—
137C23×C4—171no—
138C22×C8—341no—
139C22×C8—341no—
140#117—681no—
141#117—681no—
142C2×C4⋊C4—171no—
143C2×C4⋊C4C2×#59511yescharacteristic
144C2×C22⋊C4—171no—
145C2×C22⋊C4—171no—
146C2×C22⋊C4—342no—
147C2×C42—171no—
148C2×C42—171no—
149C4⋊C8—681no—
150C22⋊C8—21no—
151C22⋊C8—344no—
152C22⋊C8—341no—
153#97—681no—
154#97—681no—
155C4×C8—681no—
156#95—681no—
157#95—681no—
158C17#721411yescharacteristic, complemented, Sylow
159C24—171no—
160C22×C4—171no—
161C22×C4—171no—
162C22×C4—171no—
163C22×C4—341no—
164C22×C4—341no—
165C22×C4—342no—
166C22×C4—681no—
167C22×C4—682no—
168C22×C4C4×#59511yescharacteristic
169C22×C4C4⋊#59511yescharacteristic
170C22×C4C22⋊#59511yescharacteristic
171C2×C8—41no—
172C2×C8—342no—
173C2×C8—342no—
174C2×C8—681no—
175C2×C8—681no—
176C2×C8—681no—
177C2×C8—681no—
178C2×C8—681no—
179C4⋊C4—41no—
180C4⋊C4—681no—
181C22⋊C4—681no—
182C22⋊C4—681no—
183C22⋊C4—682no—
184C22⋊C4—682no—
185C42—341no—
186C42—341no—
187C42—341no—
188C42—341no—
189C23—172no—
190C23—341no—
191C23—341no—
192C23—681no—
193C23—681no—
194C23(C2×#595)⋊C411yescharacteristic
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—171no—
203C2×C4—171no—
204C2×C4—341no—
205C2×C4—341no—
206C2×C4—341no—
207C2×C4—341no—
208C2×C4—682no—
209C2×C4—682no—
210C2×C4—681no—
211C2×C4—681no—
212C2×C4—1362no—
213C2×C4—1362no—
214C2×C4—1362no—
215C8—81no—
216C8—682no—
217C8—682no—
218C8—1361no—
219C22—21no—
220C22—21no—
221C22—342no—
222C22—682no—
223C22—681no—
224C22—681no—
225C22—1361no—
226C22#1176367711yescharacteristic
227C22#1176368111yescharacteristic
228C22#1176368611yescharacteristic
229C4—41no—
230C4—41no—
231C4—41no—
232C4—2722no—
233C4—341no—
234C4—341no—
235C4—681no—
236C4—681no—
237C2—21no—
238C2—21no—
239C2—682no—
240C2#1454363311yescharacteristic
241C2#1454387111yescharacteristic
242C2#1454388611yescharacteristic
subgroupG/H
centerC22#11763686
commutatorC22×C4×C17C42
FrattiniC2×C4⋊C4C2×#595
FittingC17×#324C4
socleC22×C17#342
prime radicalC23×D17C22⋊C4
cosocleC2×#10587578C22
hypercenter#324#595
hypocenterC17#7214
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
5. C2×#10587542C4semidirect
6. C2×C4×#3624C4semidirect
13. #11762535C4semidirect
15. C17×#324C4semidirect
129. #324#595semidirect
158. C17#7214semidirect

Maximal subgroups

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

subgroupindex
#145446822
#145445132
#145271172
#721417