Finite Group Databasebeta

← #17949986

Subgroups — #17949986

Order 4352.

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

normal subgroups only

This group has 370 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#14544712C211yesmaximal, characteristic
2#14544498C211yesmaximal, characteristic
3#14543603C212yesmaximal
4#14543602C212yesmaximal
5#14537170C211yesmaximal, characteristic
6C2×C4×#3624—21no—
7#11763675—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12#11762708C2211yescharacteristic
13#11762707C411yescharacteristic
14#11762705C2211yescharacteristic
15#11762695—21no—
16#11762694—21no—
17#11762691—21no—
18#11762690—21no—
19#11762674C411yescharacteristic
20#11762674C411yescharacteristic
21C42×Dic17C2211yescharacteristic
22C17×#389C411yescharacteristic
23C22×#3624—22no—
24C22×#3624—22no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C4⋊C4×C17C2×C411yescharacteristic
28C2×C42×C17C2×C411yescharacteristic
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×#63225—21no—
33C2×#63225—21no—
34C2×C4×Dic17C2×C411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36C2×C4×Dic17D411yescharacteristic
37C2×C4×Dic17D411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17C2311yescharacteristic
40C4×#3624—24no—
41C17×#95—21no—
42#10587502—21no—
43#10587502—21no—
44#10587502—21no—
45#10587502—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49C22×C4×C17—21no—
50C22×C4×C17—21no—
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22×C411yescharacteristic
54C22×Dic17—21no—
55C22×Dic17—21no—
56C22×Dic17C22⋊C411yescharacteristic
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C2×D411yescharacteristic
59C22×Dic17C2×D411yescharacteristic
60C2×#3624—24no—
61C2×#3624—42no—
62C2×#3624—42no—
63C2×#3624—42no—
64C2×#3624—42no—
65C2×#3624—42no—
66C4⋊C4×C17—22no—
67C4⋊C4×C17—41no—
68C4⋊C4×C17—42no—
69C42×C17—22no—
70C4⋊Dic17—22no—
71C4⋊Dic17—42no—
72C4⋊Dic17—41no—
73#63225—42no—
74#63225—42no—
75C4×Dic17—22no—
76C4×Dic17—22no—
77C4×Dic17—22no—
78C4×Dic17—22no—
79C4×Dic17—41no—
80C4×Dic17—41no—
81#7657—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—41no—
91C2×C4×C17—41no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17—41no—
96C2×C4×C17#10412yes—
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—41no—
108C2×Dic17—41no—
109C2×Dic17—41no—
110C2×Dic17—41no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17#10112yes—
114C2×Dic17#13512yes—
115C2×Dic17#13512yes—
116#3624—44no—
117#3624—82no—
118#2864—171no—
119#1839—171no—
120#1744—171no—
121#1271—172no—
122#1271—172no—
123C22×C17#40811yescharacteristic
124C22×C17#41011yescharacteristic
125C22×C17C2×#10111yescharacteristic
126C22×C17#41611yescharacteristic
127C22×C17#41611yescharacteristic
128C22×C17C2×#10411yescharacteristic
129C22×C17#42111yescharacteristic
130C4×C17—22no—
131C4×C17—22no—
132C4×C17—41no—
133C4×C17—81no—
134C4×C17—81no—
135Dic17—22no—
136Dic17—22no—
137Dic17—22no—
138Dic17—41no—
139Dic17—81no—
140Dic17—81no—
141C2×C4×C8—341no—
142#389—171no—
143#389—171no—
144#389—171no—
145#389#59511yescharacteristic
146#387—341no—
147#387—341no—
148#387—341no—
149#387—341no—
150#382—171no—
151#382—171no—
152C43—171no—
153#336—172no—
154#336—172no—
155#336—341no—
156#336—341no—
157#336—341no—
158C2×C17#147011yescharacteristic
159C2×C17#148211yescharacteristic
160C2×C17#149411yescharacteristic
161C2×C17#150011yescharacteristic
162C2×C17#152111yescharacteristic
163C2×C17#153111yescharacteristic
164C2×C17#154411yescharacteristic
165C22×C8—342no—
166C22×C8—342no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—171no—
169C2×C4⋊C4—171no—
170C2×C4⋊C4—341no—
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
182C4×C8—344no—
183#95—21no—
184#95—341no—
185#95—341no—
186#95—341no—
187#95—341no—
188#95—341no—
189#95—341no—
190#95—341no—
191C17#765711yescharacteristic, complemented, Sylow
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—171no—
195C22×C4—171no—
196C22×C4—171no—
197C22×C4—171no—
198C22×C4—341no—
199C22×C4—341no—
200C22×C4C22⋊#59511yescharacteristic
201C22×C4C22⋊#59511yescharacteristic
202C22×C4C22×#59511yescharacteristic
203C2×C8—344no—
204C2×C8—682no—
205C2×C8—682no—
206C2×C8—682no—
207C2×C8—682no—
208C2×C8—682no—
209C4⋊C4—22no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—342no—
213C4⋊C4—681no—
214C4⋊C4—682no—
215C4⋊C4—682no—
216C4⋊C4—682no—
217C42—22no—
218C42—342no—
219C42—342no—
220C42—342no—
221C42—342no—
222C42—681no—
223C42—681no—
224C23C2×C22⋊#59511yescharacteristic
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—172no—
239C2×C4—172no—
240C2×C4—172no—
241C2×C4—341no—
242C2×C4—341no—
243C2×C4—341no—
244C2×C4—341no—
245C2×C4—341no—
246C2×C4—341no—
247C2×C4—341no—
248C2×C4—341no—
249C2×C4—341no—
250C2×C4—681no—
251C2×C4—681no—
252C2×C4—681no—
253C2×C4—681no—
254C2×C4—681no—
255C2×C4—681no—
256C2×C4#1058755012yes—
257C2×C4#1058767812yes—
258C8—684no—
259C8—1362no—
260C22#1176378211yescharacteristic
261C22#1176378811yescharacteristic
262C22D17⋊#10111yescharacteristic
263C22#1176379911yescharacteristic
264C22#1176379911yescharacteristic
265C22C2×#1058755011yescharacteristic
266C22#1176380711yescharacteristic
267C4—22no—
268C4—22no—
269C4—41no—
270C4—81no—
271C4—81no—
272C4—342no—
273C4—342no—
274C4—342no—
275C4—681no—
276C4—1361no—
277C4—1361no—
278C2#1454405611yescharacteristic
279C2#1454409511yescharacteristic
280C2#1454413711yescharacteristic
281C2#1454415711yescharacteristic
282C2#1454422611yescharacteristic
283C2#1454425811yescharacteristic
284C2#1454429011yescharacteristic
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#7657
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#7657semidirect

Maximal subgroups

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

subgroupindex
#145447122
#145444982
#145436032
#145436022
#145371702
#765717