Finite Group Databasebeta

← #17958326

Subgroups — #17958326

Order 4352.

460 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544020C212yesmaximal
2#14543727C212yesmaximal, complemented
3#14543715C212yesmaximal, complemented
4#14531494C211yesmaximal, characteristic
5C2×C22⋊#3624—22no—
6#11763654C2214yes—
7#11763652—22no—
8C2×#10587622C411yescharacteristic
9C2×#10587573C411yescharacteristic
10C2×D4×Dic17C2211yescharacteristic
11#11762715C2211yescharacteristic
12#11762703—22no—
13#11762681—22no—
14#11762678C2211yescharacteristic
15#11762655C411yescharacteristic
16C17×#390C411yescharacteristic
17C22×D4×C17C2×C411yescharacteristic
18C23×Dic17D412yes—
19C22×Dic34C2×C411yescharacteristic
20C22×#3624—42no—
21C2×C4⋊C4×C17C2×C411yescharacteristic
22C2×C22⋊C4×C17—22no—
23C2×C42×C17C2×C411yescharacteristic
24C2×C22⋊Dic17—22no—
25C2×C22⋊Dic17D412yes—
26#10587622—22no—
27#10587622C814yescomplemented
28D4×Dic17—42no—
29C2×C4⋊Dic17C2311yescharacteristic
30C2×#63225—21no—
31C2×#63225—22no—
32C2×C4×Dic17—21no—
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17C2×C411yescharacteristic
35#10587573—42no—
36C22⋊#3624—24no—
37C22⋊#3624—42no—
38#10587502—21no—
39#10587502—21no—
40#10587502—22no—
41C24×C17C22⋊C412yes—
42C2×D4×C17—41no—
43C2×D4×C17—41no—
44C2×D4×C17C2×C812yes—
45C2×D4×C17M1612yes—
46C22×C4×C17—21no—
47C22×C4×C17—21no—
48C22×C4×C17C22×C411yescharacteristic
49C22×Dic17—21no—
50C22×Dic17—21no—
51C22×Dic17—22no—
52C22×Dic17—22no—
53C22×Dic17—82no—
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C2×D412yes—
57C2×Dic34—21no—
58C2×Dic34—41no—
59C2×Dic34—41no—
60C2×Dic34C2×C812yescomplemented
61C2×#3624—44no—
62C2×#3624—84no—
63C4⋊C4×C17—41no—
64C22⋊C4×C17—82no—
65C42×C17—41no—
66C22⋊Dic17—28no—
67C22⋊Dic17—42no—
68C4⋊Dic17—41no—
69#63225—42no—
70#63225—82no—
71C4×Dic17—21no—
72C4×Dic17—22no—
73C4×Dic17—42no—
74C4×Dic17C2×C812yescomplemented
75#11481—171nomaximal, Sylow
76C23×C17—22no—
77C23×C17—22no—
78C23×C17—42no—
79C23×C17—42no—
80C23×C17C22⋊C814yes—
81C23×C17C2×C22⋊C411yescharacteristic
82D4×C17—42no—
83D4×C17—42no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—41no—
87C2×C4×C17—42no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—41no—
91C2×C4×C17C22×C811yescharacteristic
92C2×C4×C17C2×M1611yescharacteristic
93C2×Dic17—22no—
94C2×Dic17—22no—
95C2×Dic17—21no—
96C2×Dic17—22no—
97C2×Dic17—41no—
98C2×Dic17—44no—
99C2×Dic17—41no—
100C2×Dic17—41no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17—42no—
104C2×Dic17—41no—
105C2×Dic17—82no—
106C2×Dic17#9912yes—
107Dic34—42no—
108Dic34—42no—
109#3624—84no—
110#2326—171no—
111#1459—172no—
112#1325—172no—
113#1319—172no—
114C22×C17—21no—
115C22×C17—21no—
116C22×C17—24no—
117C22×C17—44no—
118C22×C17—42no—
119C22×C17—42no—
120C22×C17—82no—
121C22×C17C2×C22⋊C811yescharacteristic
122C22×C17C2×#9911yescharacteristic
123C22×C17#41311yescharacteristic
124C4×C17—21no—
125C4×C17—21no—
126C4×C17—81no—
127C4×C17—81no—
128Dic17—22no—
129Dic17—42no—
130Dic17—42no—
131Dic17—41no—
132Dic17—42no—
133C2×#124—171no—
134C2×C4×Q8—171no—
135C2×C4×D4—171no—
136C2×C22⋊C8—342no—
137#391—171no—
138#390#59511yescharacteristic
139#388—342no—
140#385—342no—
141#384—171no—
142#376—171no—
143#324—174no—
144#323—342no—
145C2×C17—21no—
146C2×C17—21no—
147C2×C17—44no—
148C2×C17#145911yescharacteristic
149C2×C17#212711yescharacteristic
150C2×C17#213511yescharacteristic
151C22×Q8—171no—
152C22×D4C2×#59511yescharacteristic
153C23×C4—172no—
154C22×C8—682no—
155#124—174no—
156#124—342no—
157C4×Q8—682no—
158C4×D4—682no—
159C2×C4⋊C4—171no—
160C2×C4⋊C4—341no—
161C2×C4⋊C4—342no—
162C2×C4⋊C4C2×#59511yescharacteristic
163C2×C22⋊C4—22no—
164C2×C22⋊C4—172no—
165C2×C22⋊C4—342no—
166C2×C42—171no—
167C2×C42—171no—
168C2×C42—341no—
169C2×C42C2×#59511yescharacteristic
170C22⋊C8—344no—
171C22⋊C8—682no—
172#95—341no—
173#95—341no—
174#95—342no—
175C17#1148111yescharacteristic, complemented, Sylow
176C24C22⋊#59512yes—
177C2×Q8—172no—
178C2×Q8—341no—
179C2×Q8—681no—
180C2×Q8—681no—
181C2×D4—41no—
182C2×D4—41no—
183C2×D4#6324212yes—
184C2×D4#6324312yes—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—171no—
188C22×C4—171no—
189C22×C4—172no—
190C22×C4—342no—
191C22×C4—342no—
192C22×C4—341no—
193C22×C4—341no—
194C22×C4—1362no—
195C22×C4C22×#59511yescharacteristic
196C2×C8—684no—
197C2×C8—1364no—
198C4⋊C4—41no—
199C4⋊C4—681no—
200C4⋊C4—682no—
201C4⋊C4—1362no—
202C22⋊C4—82no—
203C22⋊C4—348no—
204C22⋊C4—682no—
205C42—41no—
206C42—172no—
207C42—342no—
208C42—341no—
209C42—682no—
210C23—22no—
211C23—22no—
212C23—42no—
213C23—42no—
214C23#1058754314yes—
215C23C2×C22⋊#59511yescharacteristic
216Q8—682no—
217Q8—682no—
218D4—42no—
219D4—42no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—172no—
228C2×C4—342no—
229C2×C4—342no—
230C2×C4—341no—
231C2×C4—342no—
232C2×C4—681no—
233C2×C4—684no—
234C2×C4—681no—
235C2×C4—681no—
236C2×C4—681no—
237C2×C4—681no—
238C2×C4—682no—
239C2×C4—681no—
240C2×C4—1362no—
241C2×C4C2×#6324211yescharacteristic
242C2×C4C2×#6324311yescharacteristic
243C8—1364no—
244C22—21no—
245C22—21no—
246C22—24no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—82no—
251C22C2×#1058754311yescharacteristic
252C22D17⋊#9911yescharacteristic
253C22#1176379611yescharacteristic
254C4—21no—
255C4—21no—
256C4—81no—
257C4—81no—
258C4—342no—
259C4—682no—
260C4—682no—
261C4—682no—
262C4—681no—
263C2—21no—
264C2—21no—
265C2—44no—
266C2#1454402211yescharacteristic
267C2#1454506011yescharacteristic
268C2#1454508711yescharacteristic
subgroupG/H
centerC22D17⋊#99
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC17×#390C4
socleC22×C17C2×#99
prime radicalC22×D4×C17C2×C4
cosocleC2×C4⋊Dic17C23
hypercenter#390#595
hypocenterC17#11481
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #14543727C2semidirect
3. #14543715C2semidirect
27. #10587622C8semidirect
60. C2×Dic34C2×C8semidirect
74. C4×Dic17C2×C8semidirect
175. C17#11481semidirect

Maximal subgroups

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

subgroupindex
#145440202
#145437272
#145437152
#145314942
#1148117