Finite Group Databasebeta

← #17950242

Subgroups — #17950242

Order 4352.

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

normal subgroups only

This group has 346 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
1#14544712C211yesmaximal, characteristic
2#14544712C211yesmaximal, characteristic
3#14543605C212yesmaximal
4#14543603C212yesmaximal
5#14537167C211yesmaximal, characteristic
6#11763675—21no—
7#11763675—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12#11762715C411yescharacteristic
13#11762714C411yescharacteristic
14#11762714C2211yescharacteristic
15#11762708C411yescharacteristic
16#11762705C2211yescharacteristic
17#11762695—21no—
18#11762692—21no—
19#11762690—21no—
20#11762676—21no—
21C42×Dic17C2211yescharacteristic
22C17×#389C411yescharacteristic
23C22×Dic34C2×C411yescharacteristic
24C22×#3624—22no—
25C22×#3624—22no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C4⋊C4×C17C2×C411yescharacteristic
29C2×C42×C17C2×C411yescharacteristic
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×#63225—21no—
33C2×C4×Dic17C2×C411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36C2×C4×Dic17D411yescharacteristic
37C2×C4×Dic17D411yescharacteristic
38C2×C4×Dic17C2311yescharacteristic
39C17×#95—21no—
40#10587502—21no—
41#10587502—21no—
42#10587502—21no—
43#10587502—21no—
44#10587502—21no—
45#10587502—21no—
46#10587502—21no—
47#10587502—21no—
48C22×C4×C17—21no—
49C22×C4×C17—21no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17—21no—
54C22×Dic17—21no—
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C22⋊C411yescharacteristic
57C22×Dic17C2×D411yescharacteristic
58C22×Dic17C2×D411yescharacteristic
59C2×Dic34—22no—
60C2×Dic34—41no—
61C2×Dic34—41no—
62C2×#3624—42no—
63C2×#3624—42no—
64C2×#3624—42no—
65C2×#3624—42no—
66C2×#3624—42no—
67C2×#3624—42no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—42no—
71C42×C17—41no—
72C4⋊Dic17—22no—
73C4⋊Dic17—42no—
74#63225—42no—
75C4×Dic17—22no—
76C4×Dic17—22no—
77C4×Dic17—22no—
78C4×Dic17—41no—
79C4×Dic17—41no—
80C4×Dic17—41no—
81#7729—171nomaximal, Sylow
82C23×C17C2×C22⋊C411yescharacteristic
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—21no—
86C2×C4×C17—21no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—41no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17#13112yes—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—21no—
101C2×Dic17—21no—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—41no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17#13512yes—
115C2×Dic17#13712yes—
116Dic34—82no—
117#3624—82no—
118#3624—82no—
119#2863—171no—
120#1839—171no—
121#1839—171no—
122#1272—172no—
123#1271—172no—
124C22×C17#40811yescharacteristic
125C22×C17#41011yescharacteristic
126C22×C17#41311yescharacteristic
127C22×C17#41611yescharacteristic
128C22×C17#41911yescharacteristic
129C22×C17#42111yescharacteristic
130C22×C17#42111yescharacteristic
131C4×C17—22no—
132C4×C17—41no—
133C4×C17—41no—
134C4×C17—81no—
135C4×C17—81no—
136Dic17—22no—
137Dic17—22no—
138Dic17—41no—
139Dic17—41no—
140Dic17—81no—
141Dic17—81no—
142#391—171no—
143#391—171no—
144#391—171no—
145#389—171no—
146#389—171no—
147#389#59511yescharacteristic
148#387—341no—
149#387—341no—
150#387—341no—
151#383—341no—
152C43—171no—
153#336—172no—
154#336—172no—
155#336—341no—
156#336—341no—
157#336—341no—
158#336—341no—
159C2×C17#147311yescharacteristic
160C2×C17#148211yescharacteristic
161C2×C17#149711yescharacteristic
162C2×C17#151511yescharacteristic
163C2×C17#152111yescharacteristic
164C2×C17#153511yescharacteristic
165C2×C17#155411yescharacteristic
166C22×Q8—171no—
167C22×C8—342no—
168C22×C8—342no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—171no—
171C2×C4⋊C4—341no—
172C2×C4⋊C4—341no—
173C2×C4⋊C4C2×#59511yescharacteristic
174C2×C4⋊C4C2×#59511yescharacteristic
175C2×C42—171no—
176C2×C42—171no—
177C2×C42—171no—
178C2×C42—171no—
179C2×C42—171no—
180C2×C42—171no—
181C2×C42C2×#59511yescharacteristic
182#95—21no—
183#95—341no—
184#95—341no—
185#95—341no—
186#95—341no—
187#95—341no—
188#95—341no—
189#95—341no—
190#95—341no—
191C17#772911yescharacteristic, complemented, Sylow
192C2×Q8—342no—
193C2×Q8—681no—
194C2×Q8—681no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—171no—
198C22×C4—171no—
199C22×C4—171no—
200C22×C4—171no—
201C22×C4—341no—
202C22×C4—341no—
203C22×C4C22⋊#59511yescharacteristic
204C22×C4C22⋊#59511yescharacteristic
205C22×C4C22×#59511yescharacteristic
206C2×C8—682no—
207C2×C8—682no—
208C2×C8—682no—
209C2×C8—682no—
210C2×C8—682no—
211C2×C8—682no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—342no—
216C4⋊C4—682no—
217C4⋊C4—682no—
218C42—41no—
219C42—342no—
220C42—342no—
221C42—342no—
222C42—681no—
223C42—681no—
224C42—681no—
225C23C2×C22⋊#59511yescharacteristic
226Q8—1362no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—172no—
242C2×C4—172no—
243C2×C4—341no—
244C2×C4—341no—
245C2×C4—341no—
246C2×C4—341no—
247C2×C4—341no—
248C2×C4—341no—
249C2×C4—341no—
250C2×C4—341no—
251C2×C4—341no—
252C2×C4—341no—
253C2×C4—681no—
254C2×C4—681no—
255C2×C4—681no—
256C2×C4—681no—
257C2×C4—681no—
258C2×C4—681no—
259C2×C4#1058768012yes—
260C8—1362no—
261C8—1362no—
262C22#1176378411yescharacteristic
263C22#1176378811yescharacteristic
264C22#1176379611yescharacteristic
265C22#1176379911yescharacteristic
266C22#1176380211yescharacteristic
267C22#1176380611yescharacteristic
268C22#1176380711yescharacteristic
269C4—22no—
270C4—41no—
271C4—41no—
272C4—81no—
273C4—81no—
274C4—342no—
275C4—342no—
276C4—681no—
277C4—681no—
278C4—1361no—
279C4—1361no—
280C2#1454406711yescharacteristic
281C2#1454409811yescharacteristic
282C2#1454414811yescharacteristic
283C2#1454420611yescharacteristic
284C2#1454422611yescharacteristic
285C2#1454426911yescharacteristic
286C2#1454431011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#389C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#389#595
hypocenterC17#7729
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
191. C17#7729semidirect

Maximal subgroups

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

subgroupindex
#145447122
#145436052
#145436032
#145371672
#772917