Finite Group Databasebeta

← #17956529

Subgroups — #17956529

Order 4352.

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

normal subgroups only

This group has 388 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#14544569C211yesmaximal, characteristic
2#14544501C211yesmaximal, characteristic
3#14543660C212yesmaximal
4#14543660C212yesmaximal
5#14537170C211yesmaximal, characteristic
6C2×#10587544—21no—
7C2×#10587542C2212yes—
8C2×#10587542C2212yes—
9#11763675—21no—
10#11763675—21no—
11#11763675—21no—
12#11762708C411yescharacteristic
13#11762707C411yescharacteristic
14#11762705C411yescharacteristic
15#11762695—21no—
16#11762694—21no—
17#11762691—21no—
18#11762690—21no—
19#11762674C2211yescharacteristic
20#11762674C2211yescharacteristic
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
40#10587544—24no—
41#10587542—22no—
42#10587542—24no—
43#10587542Q814yes—
44C17×#95—21no—
45#10587502—21no—
46#10587502—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—24no—
65C2×#3624—42no—
66C2×#3624—42no—
67C2×#3624—42no—
68C2×#3624—42no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—41no—
71C4⋊C4×C17—42no—
72C42×C17—41no—
73C4⋊Dic17—42no—
74C4⋊Dic17—41no—
75C4⋊Dic17—41no—
76#63225—42no—
77#63225—42no—
78C4×Dic17—22no—
79C4×Dic17—41no—
80C4×Dic17—41no—
81C4×Dic17—41no—
82C4×Dic17—41no—
83C4×Dic17C2×Q812yes—
84C4×Dic17#4112yes—
85#9893—171nomaximal, Sylow
86C23×C17C2×C22⋊C411yescharacteristic
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—41no—
96C2×C4×C17—41no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17C4×Q812yes—
102C2×Dic17—21no—
103C2×Dic17—21no—
104C2×Dic17—21no—
105C2×Dic17—21no—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17#10412yes—
118C2×Dic17C22⋊Q812yes—
119C2×Dic17#12411yescharacteristic
120C2×Dic17C4⋊Q811yescharacteristic
121#3624—44no—
122#3624—44no—
123#2864—171no—
124#1767—171no—
125#1745—171no—
126#1295—172no—
127#1295—172no—
128C22×C17#39111yescharacteristic
129C22×C17#41311yescharacteristic
130C22×C17#41311yescharacteristic
131C22×C17C2×#10411yescharacteristic
132C22×C17#42111yescharacteristic
133C22×C17#42111yescharacteristic
134C22×C17#42111yescharacteristic
135C4×C17—22no—
136C4×C17—41no—
137C4×C17—41no—
138C4×C17—81no—
139C4×C17—81no—
140Dic17—21no—
141Dic17—21no—
142Dic17—22no—
143Dic17—22no—
144Dic17—41no—
145Dic17—81no—
146Dic17—81no—
147C2×C4⋊C8—341no—
148C2×#97—172no—
149C2×#97—172no—
150#389—171no—
151#389—171no—
152#389—171no—
153#389#59511yescharacteristic
154#387—341no—
155#387—341no—
156#387—341no—
157#387—341no—
158#382—171no—
159#382—171no—
160C43—171no—
161#336—341no—
162#336—341no—
163#336—341no—
164C2×C17#152911yescharacteristic
165C2×C17#153211yescharacteristic
166C2×C17#153511yescharacteristic
167C2×C17#153511yescharacteristic
168C2×C17#198611yescharacteristic
169C2×C17#199511yescharacteristic
170C2×C17#199811yescharacteristic
171C22×C8—342no—
172C22×C8—342no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—171no—
175C2×C4⋊C4—171no—
176C2×C4⋊C4—341no—
177C2×C4⋊C4—341no—
178C2×C4⋊C4—341no—
179C2×C4⋊C4C2×#59511yescharacteristic
180C2×C4⋊C4C2×#59511yescharacteristic
181C2×C42—171no—
182C2×C42—171no—
183C2×C42—171no—
184C2×C42—171no—
185C2×C42—171no—
186C2×C42—171no—
187C2×C42C2×#59511yescharacteristic
188C4⋊C8—344no—
189#97—174no—
190#97—342no—
191#97—344no—
192#95—21no—
193#95—341no—
194#95—341no—
195#95—341no—
196#95—341no—
197#95—341no—
198#95—341no—
199#95—341no—
200C17#989311yescharacteristic, 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—344no—
213C2×C8—344no—
214C2×C8—682no—
215C2×C8—682no—
216C2×C8—682no—
217C2×C8—682no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—681no—
222C4⋊C4—681no—
223C4⋊C4—682no—
224C4⋊C4—682no—
225C4⋊C4—682no—
226C42—41no—
227C42—172no—
228C42—172no—
229C42—342no—
230C42—681no—
231C42—681no—
232C42—681no—
233C42—681no—
234C23C2×C22⋊#59511yescharacteristic
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—172no—
250C2×C4—171no—
251C2×C4—171no—
252C2×C4—172no—
253C2×C4—341no—
254C2×C4—341no—
255C2×C4—341no—
256C2×C4—341no—
257C2×C4—341no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—341no—
261C2×C4—341no—
262C2×C4—681no—
263C2×C4—681no—
264C2×C4—681no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4—681no—
268C2×C4Q8×#59512yes—
269C8—684no—
270C8—684no—
271C22(C2×#595)⋊Q811yescharacteristic
272C22#1176379511yescharacteristic
273C22#1176379611yescharacteristic
274C22D17⋊#10411yescharacteristic
275C22#1176380611yescharacteristic
276C22#1176380711yescharacteristic
277C22#1176380811yescharacteristic
278C4—22no—
279C4—41no—
280C4—41no—
281C4—81no—
282C4—81no—
283C4—341no—
284C4—341no—
285C4—342no—
286C4—342no—
287C4—681no—
288C4—1361no—
289C4—1361no—
290C2#1454425211yescharacteristic
291C2#1454425911yescharacteristic
292C2#1454426911yescharacteristic
293C2#1454427011yescharacteristic
294C2#1454496111yescharacteristic
295C2#1454497211yescharacteristic
296C2#1454497811yescharacteristic
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#9893
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
200. C17#9893semidirect

Maximal subgroups

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

subgroupindex
#145445692
#145445012
#145436602
#145371702
#989317