Finite Group Databasebeta

← #17958983

Subgroups — #17958983

Order 4352.

332 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C2×#11763695C211yesmaximal, characteristic, complemented
2#14544346C211yesmaximal, characteristic, complemented
3#14543741C212yesmaximal, complemented
4#14543738C212yesmaximal, complemented
5#14539349C211yesmaximal, characteristic
6C22×#63216—21no—
7#11763830—21no—
8#11763695—21no—
9#11763695C2212yes—
10#11763672C2212yes—
11#11763671—21no—
12#11763340—21no—
13#11763210C411yescharacteristic
14#11763192C411yescharacteristic
15#11763162—21no—
16#11763050C411yescharacteristic
17#11763036—21no—
18#11762903C2211yescharacteristic
19#11762900—21no—
20D8×Dic17C2211yescharacteristic
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—
40#10587542—41no—
41C4⋊#3624—22no—
42C2×#63216—24no—
43C2×#63216—22no—
44C17×#107C2×C411yescharacteristic
45C17×#102—21no—
46#10587503—21no—
47#10587489C2×C411yescharacteristic
48#10587487—21no—
49C8×Dic17C2×C411yescharacteristic
50C8×Dic17D411yescharacteristic
51C8×Dic17D411yescharacteristic
52C8×Dic17C2311yescharacteristic
53#10587481—21no—
54#10587479—21no—
55C2×D4×C17—21no—
56C2×D4×C17—41no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×Dic17—41no—
59C22×Dic17D811yescharacteristic
60C22×Dic17SD1611yescharacteristic
61C2×Dic34—21no—
62C2×#3624—42no—
63D8×C17—22no—
64C2×C8×C17—22no—
65C2×C8×C17C22⋊C411yescharacteristic
66C2×C8×C17C22×C411yescharacteristic
67C4⋊C4×C17—21no—
68C22⋊C4×C17—41no—
69C22⋊Dic17—41no—
70C22⋊Dic17—41no—
71C22⋊Dic17—41no—
72C22⋊Dic17—41no—
73#63229—42no—
74C4⋊Dic17—21no—
75C4⋊Dic17—41no—
76#63225—41no—
77#63225—41no—
78#63225—41no—
79C4×Dic17—41no—
80C4×Dic17C22⋊C411yescharacteristic
81C4×Dic17D811yescharacteristic
82C4×Dic17SD1611yescharacteristic
83C4×Dic17C2×D411yescharacteristic
84C2×#3622—22no—
85C2×#3622C22⋊C411yescharacteristic
86C2×#3622C2×D411yescharacteristic
87Dic68—22no—
88#63216—24no—
89#11673—171nomaximal, Sylow
90C23×C17—41no—
91C23×C17#10211yescharacteristic
92D4×C17—41no—
93D4×C17—41no—
94D4×C17—82no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—41no—
98C2×C4×C17#10211yescharacteristic
99C2×C4×C17C2×C22⋊C411yescharacteristic
100C2×Dic17—22no—
101C2×Dic17—22no—
102C2×Dic17—41no—
103C2×Dic17—41no—
104C2×Dic17—82no—
105C2×Dic17#10211yescharacteristic
106C2×Dic17#10211yescharacteristic
107C2×Dic17C2×D811yescharacteristic
108C2×Dic17C2×SD1611yescharacteristic
109Dic34—41no—
110Dic34—41no—
111#3624—82no—
112C8×C17—21no—
113C8×C17#13112yes—
114#3622—21no—
115#3622#10412yes—
116#3168—171no—
117C2×C4×C16—171no—
118#1568—171no—
119#1332—172no—
120#1331—172no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17—81no—
124C22×C17—81no—
125C22×C17—81no—
126C22×C17#35912yes—
127C22×C17C2×#10211yescharacteristic
128C4×C17—21no—
129C4×C17—81no—
130C4×C17#40811yescharacteristic
131C4×C17C2×#10411yescharacteristic
132Dic17—21no—
133Dic17—21no—
134Dic17—21no—
135Dic17—81no—
136Dic17—81no—
137Dic17#50812yes—
138#529—341no—
139C22×C16—341no—
140#499—171no—
141#495—171no—
142#488—341no—
143#467—171no—
144#466#59511yescharacteristic
145#465—341no—
146C4×Q16—171no—
147C4×SD16—341no—
148C4×D8—171no—
149#432—341no—
150C2×C4×C8—171no—
151C4×C16—172no—
152C4×C16—341no—
153#335—172no—
154#334—341no—
155C2×C17—22no—
156C2×C17—161no—
157C2×C17#149211yescharacteristic
158C2×C17#213811yescharacteristic
159C2×C17C2×#35911yescharacteristic
160C2×Q16—171no—
161C2×SD16—341no—
162C2×D8C2×#59511yescharacteristic
163C22×C8—171no—
164C22×C8C2×#59511yescharacteristic
165#126—681no—
166#125—341no—
167#124—341no—
168#123—681no—
169C22⋊Q8—341no—
170#121—21no—
171C4×Q8—341no—
172C4×D4—341no—
173C4×D4—681no—
174#117—681no—
175C2×C42—171no—
176C2×C16—342no—
177C2×C16—344no—
178#107—171no—
179#107C2×#59511yescharacteristic
180#106—341no—
181C4⋊C8—342no—
182#103—341no—
183#103—341no—
184#102—21no—
185#102—341no—
186C22⋊C8—681no—
187#97—681no—
188C4×C8—171no—
189C4×C8—171no—
190C4×C8—171no—
191C4×C8—171no—
192C17#1167311yescharacteristic, complemented, Sylow
193C2×Q8—341no—
194C2×D4—21no—
195C2×D4—41no—
196C22×C4—171no—
197C22×C4—171no—
198C22×C4—681no—
199C22×C4C22⋊#59511yescharacteristic
200Q16—342no—
201SD16—682no—
202D8—22no—
203C2×C8—22no—
204C2×C8—171no—
205C2×C8—171no—
206C2×C8—342no—
207C2×C8—682no—
208C2×C8C22⋊#59511yescharacteristic
209C2×C8C22×#59511yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—341no—
212C4⋊C4—681no—
213C4⋊C4—681no—
214C4⋊C4—681no—
215C4⋊C4—681no—
216C22⋊C4—41no—
217C22⋊C4—681no—
218C22⋊C4—681no—
219C22⋊C4—681no—
220C22⋊C4—681no—
221C42—171no—
222C42—171no—
223C42—171no—
224C42—171no—
225C42—681no—
226C16—344no—
227C23—41no—
228C23#1058754711yescharacteristic
229Q8—681no—
230Q8—681no—
231D4—41no—
232D4—41no—
233D4—82no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—171no—
238C2×C4—171no—
239C2×C4—171no—
240C2×C4—171no—
241C2×C4—342no—
242C2×C4—342no—
243C2×C4—681no—
244C2×C4—681no—
245C2×C4—1362no—
246C2×C4#1058754711yescharacteristic
247C2×C4C2×C22⋊#59511yescharacteristic
248C8—21no—
249C8—172no—
250C8—341no—
251C8—1362no—
252C8#1058767812yes—
253C22—21no—
254C22—21no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22#1176372312yes—
259C22C2×#1058754711yescharacteristic
260C4—21no—
261C4—81no—
262C4—172no—
263C4—341no—
264C4—341no—
265C4—341no—
266C4—1361no—
267C4—1361no—
268C4#1176378211yescharacteristic
269C4D17⋊#10411yescharacteristic
270C2—22no—
271C2—161no—
272C2#1454412911yescharacteristic
273C2#1454509111yescharacteristic
274C2C2×#1176372311yescharacteristic
subgroupG/H
centerC22C2×#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
Fitting, prime radicalC17×#466C4
socleC22×C17C2×#102
cosocleC8×Dic17C23
hypercenter#466#595
hypocenterC17#11673
LCSG ▷ C2×C8×C17 ▷ 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. C2×#11763695C2semidirect
2. #14544346C2semidirect
3. #14543741C2semidirect
4. #14543738C2semidirect
192. C17#11673semidirect

Maximal subgroups

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

subgroupindex
C2×#117636952
#145443462
#145437412
#145437382
#145393492
#1167317