Finite Group Databasebeta

← #17959912

Subgroups — #17959912

Order 4352.

306 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 76 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#14545142C211yesmaximal, characteristic, complemented
2#14544333C211yesmaximal, characteristic, complemented
3#14543801C212yesmaximal, complemented
4#14543796C212yesmaximal, complemented
5#14539349C211yesmaximal, characteristic
6#11763825—21no—
7#11763730C2212yes—
8C22⋊#63216—21no—
9#11763695—21no—
10#11763673—21no—
11#11763671C2212yes—
12#11763340—21no—
13#11763210C2211yescharacteristic
14#11763192C2211yescharacteristic
15#11763162—21no—
16#11763050C411yescharacteristic
17#11763036—21no—
18#11762903C411yescharacteristic
19#11762900—21no—
20D8×Dic17C411yescharacteristic
21C2×C8×Dic17C2211yescharacteristic
22C17×#466C411yescharacteristic
23C2×D8×C17C2×C411yescharacteristic
24C22×C8×C17C2×C411yescharacteristic
25C17×#121—21no—
26#10587622—21no—
27#10587621—41no—
28D4×Dic17—21no—
29D4×Dic17—41no—
30C2×#63229—21no—
31#10587610—21no—
32C2×C4×Dic17D411yescharacteristic
33C22×#3622D411yescharacteristic
34C2×Dic68C2×C411yescharacteristic
35#10587576—21no—
36#10587573—21no—
37#10587565—41no—
38#10587563—41no—
39C22⋊#3624—41no—
40C4⋊#3624—22no—
41C4×#3624—41no—
42C2×#63216—22no—
43C17×#107C2×C411yescharacteristic
44C17×#102—21no—
45#10587503—21no—
46#10587489C2×C411yescharacteristic
47#10587487—21no—
48C8×Dic17C2×C411yescharacteristic
49C8×Dic17D411yescharacteristic
50C8×Dic17D411yescharacteristic
51C8×Dic17C2311yescharacteristic
52#10587481—21no—
53#10587479—21no—
54C2×D4×C17—21no—
55C2×D4×C17—41no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×Dic17—41no—
58C22×Dic17D811yescharacteristic
59C22×Dic17SD1611yescharacteristic
60C2×Dic34—21no—
61C2×#3624—42no—
62D8×C17—41no—
63C2×C8×C17—41no—
64C2×C8×C17C22⋊C411yescharacteristic
65C2×C8×C17C22×C411yescharacteristic
66C4⋊C4×C17—21no—
67C22⋊C4×C17—41no—
68C22⋊Dic17—41no—
69C22⋊Dic17—41no—
70C22⋊Dic17—41no—
71C22⋊Dic17—41no—
72#63229—42no—
73C4⋊Dic17—21no—
74C4⋊Dic17—41no—
75#63225—41no—
76#63225—41no—
77#63225—41no—
78C4×Dic17—41no—
79C4×Dic17C22⋊C411yescharacteristic
80C4×Dic17D811yescharacteristic
81C4×Dic17SD1611yescharacteristic
82C4×Dic17C2×D411yescharacteristic
83C2×#3622—22no—
84C2×#3622C22⋊C411yescharacteristic
85C2×#3622C2×D411yescharacteristic
86Dic68—41no—
87#63216—42no—
88#11943—171nomaximal, Sylow
89C23×C17—41no—
90C23×C17#10211yescharacteristic
91D4×C17—41no—
92D4×C17—41no—
93D4×C17—82no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—41no—
97C2×C4×C17#10211yescharacteristic
98C2×C4×C17C2×C22⋊C411yescharacteristic
99C2×Dic17—22no—
100C2×Dic17—41no—
101C2×Dic17—41no—
102C2×Dic17—41no—
103C2×Dic17—82no—
104C2×Dic17#10211yescharacteristic
105C2×Dic17#10211yescharacteristic
106C2×Dic17C2×D811yescharacteristic
107C2×Dic17C2×SD1611yescharacteristic
108Dic34—41no—
109Dic34—41no—
110#3624—82no—
111C8×C17—21no—
112C8×C17—21no—
113#3622—21no—
114#3622#13512yes—
115#3168—171no—
116#2162—171no—
117#1564—171no—
118#1363—172no—
119#1360—172no—
120C22×C17—21no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17—81no—
124C22×C17—81no—
125C22×C17—81no—
126C22×C17C2×#10211yescharacteristic
127C4×C17—21no—
128C4×C17—81no—
129C4×C17#41311yescharacteristic
130C4×C17#41611yescharacteristic
131Dic17—21no—
132Dic17—21no—
133Dic17—21no—
134Dic17—81no—
135Dic17—81no—
136Dic17#35912yes—
137#529—341no—
138#499—171no—
139#495—171no—
140#488—341no—
141#467—171no—
142#466#59511yescharacteristic
143#465—341no—
144C4×Q16—171no—
145C4×SD16—341no—
146C4×D8—171no—
147#431—341no—
148C2×C4×C8—171no—
149C4⋊C16—172no—
150C22⋊C16—341no—
151C4×C16—341no—
152#335—341no—
153#334—172no—
154C2×C17—41no—
155C2×C17—161no—
156C2×C17#154011yescharacteristic
157C2×C17C2×#35911yescharacteristic
158C2×C17#214511yescharacteristic
159C2×Q16—171no—
160C2×SD16—341no—
161C2×D8C2×#59511yescharacteristic
162C22×C8—171no—
163C22×C8C2×#59511yescharacteristic
164#126—681no—
165#125—341no—
166#124—341no—
167#123—681no—
168C22⋊Q8—341no—
169#121—21no—
170C4×Q8—341no—
171C4×D4—341no—
172C4×D4—681no—
173#117—681no—
174C2×C42—171no—
175C2×C16—342no—
176#107—171no—
177#107C2×#59511yescharacteristic
178#106—341no—
179C4⋊C8—342no—
180#103—341no—
181#103—341no—
182#102—21no—
183#102—341no—
184C22⋊C8—681no—
185C4×C8—171no—
186C4×C8—171no—
187C4×C8—171no—
188C4×C8—171no—
189C4×C8—681no—
190C17#1194311yescharacteristic, complemented, Sylow
191C2×Q8—341no—
192C2×D4—21no—
193C2×D4—41no—
194C22×C4—171no—
195C22×C4—171no—
196C22×C4—681no—
197C22×C4C22⋊#59511yescharacteristic
198Q16—681no—
199SD16—682no—
200D8—41no—
201C2×C8—41no—
202C2×C8—171no—
203C2×C8—171no—
204C2×C8—342no—
205C2×C8—682no—
206C2×C8C22⋊#59511yescharacteristic
207C2×C8C22×#59511yescharacteristic
208C4⋊C4—21no—
209C4⋊C4—341no—
210C4⋊C4—681no—
211C4⋊C4—681no—
212C4⋊C4—681no—
213C4⋊C4—681no—
214C22⋊C4—41no—
215C22⋊C4—681no—
216C22⋊C4—681no—
217C22⋊C4—681no—
218C22⋊C4—681no—
219C42—171no—
220C42—171no—
221C42—171no—
222C42—171no—
223C42—681no—
224C16—682no—
225C23—41no—
226C23#1058754711yescharacteristic
227Q8—681no—
228Q8—681no—
229D4—41no—
230D4—41no—
231D4—82no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—171no—
236C2×C4—171no—
237C2×C4—171no—
238C2×C4—171no—
239C2×C4—342no—
240C2×C4—681no—
241C2×C4—681no—
242C2×C4—681no—
243C2×C4—1362no—
244C2×C4#1058754711yescharacteristic
245C2×C4C2×C22⋊#59511yescharacteristic
246C8—21no—
247C8—21no—
248C8—172no—
249C8—341no—
250C8—1362no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—81no—
255C22—81no—
256C22—81no—
257C22C2×#1058754711yescharacteristic
258C4—21no—
259C4—81no—
260C4—172no—
261C4—341no—
262C4—341no—
263C4—341no—
264C4—1361no—
265C4—1361no—
266C4#1176379611yescharacteristic
267C4#1176379911yescharacteristic
268C2—41no—
269C2—161no—
270C2#1454428211yescharacteristic
271C2D17⋊#35911yescharacteristic
272C2#1454510511yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
Fitting, prime radicalC17×#466C4
socleC22×C17C2×#102
cosocleC8×Dic17C23
hypercenter#466#595
hypocenterC17#11943
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #14545142C2semidirect
2. #14544333C2semidirect
3. #14543801C2semidirect
4. #14543796C2semidirect
190. C17#11943semidirect

Maximal subgroups

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

subgroupindex
#145451422
#145443332
#145438012
#145437962
#145393492
#1194317