Finite Group Databasebeta

← #17949960

Subgroups — #17949960

Order 4352.

384 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 94 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#14543603C212yesmaximal
4#14543602C212yesmaximal
5C4×#10587576C211yesmaximal, characteristic
6#11763675—21no—
7#11763675—21no—
8#11763675—21no—
9#11763675—21no—
10#11763675C2212yes—
11#11763675C2212yes—
12C2×#10587576C411yescharacteristic
13#11762708C2211yescharacteristic
14#11762705C2211yescharacteristic
15#11762696—21no—
16#11762692—21no—
17#11762674C411yescharacteristic
18C4×#63225—21no—
19C4×C4⋊Dic17—21no—
20C4×C4⋊Dic17C411yescharacteristic
21C42×Dic17C2211yescharacteristic
22C4×C4⋊C4×C17C411yescharacteristic
23C22×#3624—22no—
24C22×#3624—22no—
25C2×C4⋊C4×C17C2×C411yescharacteristic
26C2×C4⋊C4×C17C2×C411yescharacteristic
27C2×C42×C17—21no—
28C2×C42×C17C2×C411yescharacteristic
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17C2×C411yescharacteristic
32C2×C4⋊Dic17C2×C411yescharacteristic
33C2×#63225—21no—
34C2×#63225—21no—
35C2×C4×Dic17—21no—
36C2×C4×Dic17C2×C411yescharacteristic
37C2×C4×Dic17D411yescharacteristic
38C2×C4×Dic17D411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17C2311yescharacteristic
42#10587576—22no—
43#10587576—22no—
44C17×#95—21no—
45#10587502—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—21no—
56C22×Dic17—21no—
57C22×Dic17C22⋊C411yescharacteristic
58C22×Dic17C22⋊C411yescharacteristic
59C22×Dic17C2×D411yescharacteristic
60C22×Dic17C2×D411yescharacteristic
61C2×#3624—42no—
62C2×#3624—42no—
63C2×#3624—42no—
64C2×#3624—42no—
65C2×#3624—42no—
66C2×#3624—42no—
67C4⋊C4×C17—21no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17M1612yes—
70C42×C17—22no—
71C42×C17—42no—
72C4⋊Dic17—24no—
73C4⋊Dic17—21no—
74C4⋊Dic17—42no—
75C4⋊Dic17—41no—
76C4⋊Dic17M1612yes—
77#63225—24no—
78#63225—42no—
79C4×Dic17—21no—
80C4×Dic17—21no—
81C4×Dic17—22no—
82C4×Dic17—22no—
83C4×Dic17—41no—
84C4×Dic17—41no—
85C4×Dic17—41no—
86C4×Dic17—42no—
87#7650—171nomaximal, Sylow
88C23×C17C2×C22⋊C411yescharacteristic
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—22no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17#10112yes—
103C2×C4×C17C2×M1611yescharacteristic
104C2×C4×C17C2×M1611yescharacteristic
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—22no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17#13512yes—
122C2×Dic17#13512yes—
123#3624—82no—
124#3624—82no—
125C4×#125—171no—
126#1839—171no—
127#1839—171no—
128#1271—172no—
129#1271—172no—
130C22×C17#40711yescharacteristic
131C22×C17#41011yescharacteristic
132C22×C17C2×#10111yescharacteristic
133C22×C17#41611yescharacteristic
134C22×C17#41611yescharacteristic
135C22×C17#42111yescharacteristic
136C22×C17#42111yescharacteristic
137C4×C17—21no—
138C4×C17—21no—
139C4×C17—22no—
140C4×C17—41no—
141C4×C17—42no—
142C4×C17—81no—
143Dic17—22no—
144Dic17—22no—
145Dic17—41no—
146Dic17—41no—
147Dic17—42no—
148Dic17—81no—
149C2×#125—171no—
150#389—171no—
151#389—171no—
152#387—341no—
153#387—341no—
154#382—171no—
155C4×C4⋊C4—171no—
156C4×C4⋊C4—341no—
157C4×C4⋊C4—341no—
158C4×C4⋊C4#59511yescharacteristic
159C43—171no—
160#336—172no—
161#336—172no—
162#336—341no—
163#336—341no—
164#336—341no—
165#336—341no—
166C2×C17#146711yescharacteristic
167C2×C17#148811yescharacteristic
168C2×C17#148811yescharacteristic
169C2×C17#152111yescharacteristic
170C2×C17#152111yescharacteristic
171C2×C17#153411yescharacteristic
172C2×C17#154411yescharacteristic
173C22×C8—342no—
174C22×C8—342no—
175#125—342no—
176#125—342no—
177C2×C4⋊C4—171no—
178C2×C4⋊C4—171no—
179C2×C4⋊C4—341no—
180C2×C4⋊C4—341no—
181C2×C4⋊C4—341no—
182C2×C4⋊C4—341no—
183C2×C4⋊C4C2×#59511yescharacteristic
184C2×C4⋊C4C2×#59511yescharacteristic
185C2×C42—21no—
186C2×C42—171no—
187C2×C42—171no—
188C2×C42—171no—
189C2×C42—171no—
190C2×C42—171no—
191C2×C42—171no—
192C2×C42—341no—
193C2×C42C2×#59511yescharacteristic
194#95—21no—
195#95—341no—
196#95—341no—
197#95—341no—
198#95—341no—
199#95—341no—
200C17#765011yescharacteristic, complemented, Sylow
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—171no—
204C22×C4—171no—
205C22×C4—171no—
206C22×C4—171no—
207C22×C4—341no—
208C22×C4—341no—
209C22×C4C22⋊#59511yescharacteristic
210C22×C4C22⋊#59511yescharacteristic
211C22×C4C22×#59511yescharacteristic
212C2×C8—682no—
213C2×C8—682no—
214C2×C8—682no—
215C2×C8—682no—
216C2×C8—682no—
217C2×C8—682no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—172no—
221C4⋊C4—344no—
222C4⋊C4—344no—
223C4⋊C4—341no—
224C4⋊C4—681no—
225C4⋊C4—682no—
226C4⋊C4—682no—
227C4⋊C4#6324312yes—
228C42—22no—
229C42—42no—
230C42—342no—
231C42—342no—
232C42—341no—
233C42—341no—
234C42—681no—
235C42—681no—
236C42—681no—
237C42—682no—
238C23C2×C22⋊#59511yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—172no—
253C2×C4—172no—
254C2×C4—341no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—341no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—342no—
261C2×C4—341no—
262C2×C4—341no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4—681no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4#1058754512yes—
271C2×C4C2×#6324311yescharacteristic
272C2×C4D17⋊M1611yescharacteristic
273C8—1362no—
274C8—1362no—
275C22#1176378011yescharacteristic
276C22#1176378811yescharacteristic
277C22C2×#1058754511yescharacteristic
278C22#1176379911yescharacteristic
279C22#1176379911yescharacteristic
280C22#1176380711yescharacteristic
281C22#1176380811yescharacteristic
282C4—22no—
283C4—21no—
284C4—21no—
285C4—41no—
286C4—42no—
287C4—81no—
288C4—342no—
289C4—342no—
290C4—681no—
291C4—681no—
292C4—682no—
293C4—1361no—
294C2#1454404611yescharacteristic
295C2#1454411611yescharacteristic
296C2#1454411811yescharacteristic
297C2#1454422611yescharacteristic
298C2#1454422811yescharacteristic
299C2#1454426611yescharacteristic
300C2#1454428911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#7650
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
200. C17#7650semidirect

Maximal subgroups

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

subgroupindex
#145447122
#145436032
#145436022
C4×#105875762
#765017