Finite Group Databasebeta

← #17949734

Subgroups — #17949734

Order 4352.

426 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 110 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
2C4×#10587544C211yesmaximal, characteristic
3#14543603C212yesmaximal
4#14543602C212yesmaximal
5C4×#10587576C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×C4×#3624—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#10587576C814yescomplemented
44#10587544—24no—
45C4×#3624—42no—
46C17×#95—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C22×Dic17—21no—
58C22×Dic17—21no—
59C22×Dic17C22⋊C411yescharacteristic
60C22×Dic17C22⋊C411yescharacteristic
61C22×Dic17C2×D411yescharacteristic
62C22×Dic17C2×D411yescharacteristic
63C2×#3624—24no—
64C2×#3624—42no—
65C2×#3624—42no—
66C2×#3624—42no—
67C2×#3624—42no—
68C2×#3624—42no—
69C4⋊C4×C17—21no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17C2×C812yes—
72C42×C17—22no—
73C42×C17—42no—
74C4⋊Dic17—21no—
75C4⋊Dic17—24no—
76C4⋊Dic17—41no—
77C4⋊Dic17—41no—
78C4⋊Dic17—41no—
79C4⋊Dic17C2×C812yes—
80#63225—24no—
81#63225—42no—
82C4×Dic17—22no—
83C4×Dic17—22no—
84C4×Dic17—21no—
85C4×Dic17—21no—
86C4×Dic17—41no—
87C4×Dic17—41no—
88C4×Dic17—42no—
89C4×Dic17C2×C812yes—
90C4×Dic17M1612yes—
91#7585—171nomaximal, Sylow
92C23×C17C2×C22⋊C411yescharacteristic
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—22no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17#10112yes—
106C2×C4×C17#10412yes—
107C2×C4×C17C22×C811yescharacteristic
108C2×C4×C17C2×M1611yescharacteristic
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—22no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17C22⋊C812yes—
124C2×Dic17C22⋊C812yes—
125C2×Dic17#13512yes—
126C2×Dic17AGL(1,ℤ/8)11yescharacteristic
127C2×Dic17#13711yescharacteristic
128#3624—44no—
129#3624—82no—
130C4×#125—171no—
131#1839—171no—
132C4×C4⋊C8—171no—
133#1271—172no—
134#1271—172no—
135C22×C17C2×C22⋊C811yescharacteristic
136C22×C17#41011yescharacteristic
137C22×C17C2×#10111yescharacteristic
138C22×C17#41611yescharacteristic
139C22×C17#41711yescharacteristic
140C22×C17C2×#10411yescharacteristic
141C22×C17#42111yescharacteristic
142C4×C17—22no—
143C4×C17—21no—
144C4×C17—21no—
145C4×C17—22no—
146C4×C17—42no—
147C4×C17—81no—
148Dic17—22no—
149Dic17—22no—
150Dic17—21no—
151Dic17—21no—
152Dic17—22no—
153Dic17—42no—
154Dic17—81no—
155C2×#125—171no—
156C2×C4⋊C8—341no—
157C2×C4×C8—341no—
158#389—171no—
159#389—171no—
160#387—341no—
161#387—341no—
162#382—171no—
163C4×C4⋊C4—171no—
164C4×C4⋊C4—341no—
165C4×C4⋊C4—341no—
166C4×C4⋊C4#59511yescharacteristic
167C43—171no—
168#336—172no—
169#336—172no—
170#336—341no—
171#336—341no—
172C2×C17#146111yescharacteristic
173C2×C17#147611yescharacteristic
174C2×C17#147711yescharacteristic
175C2×C17#150911yescharacteristic
176C2×C17#152111yescharacteristic
177C2×C17#152811yescharacteristic
178C2×C17#155211yescharacteristic
179C22×C8—342no—
180C22×C8—342no—
181#125—174no—
182#125—342no—
183C2×C4⋊C4—171no—
184C2×C4⋊C4—171no—
185C2×C4⋊C4—341no—
186C2×C4⋊C4—341no—
187C2×C4⋊C4—341no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4C2×#59511yescharacteristic
190C2×C4⋊C4C2×#59511yescharacteristic
191C2×C42—21no—
192C2×C42—171no—
193C2×C42—171no—
194C2×C42—171no—
195C2×C42—171no—
196C2×C42—171no—
197C2×C42—171no—
198C2×C42—341no—
199C2×C42C2×#59511yescharacteristic
200C4⋊C8—344no—
201C4×C8—682no—
202#95—21no—
203#95—341no—
204#95—341no—
205#95—341no—
206#95—341no—
207#95—341no—
208C17#758511yescharacteristic, complemented, Sylow
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—171no—
212C22×C4—171no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—341no—
216C22×C4—341no—
217C22×C4C22⋊#59511yescharacteristic
218C22×C4C22⋊#59511yescharacteristic
219C22×C4C22×#59511yescharacteristic
220C2×C8—344no—
221C2×C8—682no—
222C2×C8—682no—
223C2×C8—682no—
224C2×C8—682no—
225C2×C8—682no—
226C4⋊C4—21no—
227C4⋊C4—41no—
228C4⋊C4—172no—
229C4⋊C4—344no—
230C4⋊C4—344no—
231C4⋊C4—341no—
232C4⋊C4—681no—
233C4⋊C4—682no—
234C4⋊C4—681no—
235C4⋊C4—681no—
236C4⋊C4#6324212yes—
237C42—22no—
238C42—42no—
239C42—172no—
240C42—172no—
241C42—341no—
242C42—342no—
243C42—341no—
244C42—342no—
245C42—681no—
246C42—681no—
247C42—682no—
248C23C2×C22⋊#59511yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—172no—
262C2×C4—172no—
263C2×C4—172no—
264C2×C4—171no—
265C2×C4—171no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—341no—
271C2×C4—341no—
272C2×C4—341no—
273C2×C4—341no—
274C2×C4—342no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4#1058754512yes—
281C2×C4#1058755012yes—
282C2×C4C2×#6324211yescharacteristic
283C2×C4D17⋊M1611yescharacteristic
284C8—684no—
285C8—1362no—
286C22#1176377711yescharacteristic
287C22#1176378811yescharacteristic
288C22C2×#1058754511yescharacteristic
289C22#1176379911yescharacteristic
290C22#1176380011yescharacteristic
291C22C2×#1058755011yescharacteristic
292C22#1176380711yescharacteristic
293C4—22no—
294C4—21no—
295C4—21no—
296C4—22no—
297C4—42no—
298C4—81no—
299C4—341no—
300C4—341no—
301C4—342no—
302C4—342no—
303C4—342no—
304C4—682no—
305C4—1361no—
306C2#1454402611yescharacteristic
307C2#1454407811yescharacteristic
308C2#1454408011yescharacteristic
309C2#1454418811yescharacteristic
310C2#1454422611yescharacteristic
311C2#1454424811yescharacteristic
312C2#1454430511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#7585
LCSG ▷ C2×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
43. #10587576C8semidirect
208. C17#7585semidirect

Maximal subgroups

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

subgroupindex
#145447122
C4×#105875442
#145436032
#145436022
C4×#105875762
#758517