Finite Group Databasebeta

← #17034653

Subgroups — #17034653

Order 4352.

738 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#10587558C211yesmaximal, characteristic
2#14528928C212yesmaximal, complemented
3#14528903C212yesmaximal, complemented
4#14528854C212yesmaximal
5#14528765C212yesmaximal
6#14528637C211yesmaximal, characteristic, complemented
7#14528547C212yesmaximal
8#14528532C212yesmaximal, complemented
9C17×#1767C211yesmaximal, characteristic, complemented
10C2×#10587558C2211yescharacteristic
11C2×#10587558C2211yescharacteristic
12C2×C42×D17C2211yescharacteristic
13C2×C4⋊#3622C2212yes—
14C2×#10587491C2214yes—
15C2×#10587474C2212yes—
16C4×#63225C412yes—
17C4×#63225C412yes—
18C4×#63227C412yes—
19C4×#63227C412yes—
20#11762655C2211yescharacteristic
21#11762655C2211yescharacteristic
22C42×Dic17C2211yescharacteristic
23#11762564C2212yes—
24#11762563C2214yes—
25#11762563C2214yes—
26#11762563C2214yes—
27C2×C17×C4⋊C8C2212yes—
28C2×C17×#97C2212yes—
29C43×C17C2211yescharacteristic
30C17×#336C2212yes—
31C22×C4×D17C2×C412yes—
32C22×C4×D17C2311yescharacteristic
33C22×C8×C17C2314yes—
34C2×C42×C17C2×C412yes—
35C2×C42×C17C2×C412yes—
36C2×C42×C17C2311yescharacteristic
37C2×C42×C17C2311yescharacteristic
38C2×C42×C17C2311yescharacteristic
39C2×#63227C2×C412yes—
40C2×#63227C2×C411yescharacteristic
41C2×#63227C2×C411yescharacteristic
42C2×#63225C2×C412yes—
43C2×#63225C2×C411yescharacteristic
44C2×#63225C2×C411yescharacteristic
45C2×C4×Dic17C2×C412yes—
46C2×C4×Dic17C2×C412yes—
47C2×C4×Dic17C2×C412yes—
48C2×C4×Dic17C2311yescharacteristic
49C2×C4×Dic17C2311yescharacteristic
50C2×C4×Dic17C2311yescharacteristic
51C22×#3622C2314yes—
52#10587558—24no—
53#10587558—24no—
54C42×D17—22no—
55C42×D17—22no—
56C17×C4⋊C8—24no—
57C17×#97—24no—
58#10587502C2×C412yes—
59#10587502C2×C412yes—
60#10587502C2×C412yes—
61#10587502C2×C412yes—
62#10587491—28no—
63C4⋊#3622—24no—
64#10587474—24no—
65C23×D17C22×C411yescharacteristic
66C22×C4×C17C22×C412yes—
67C22×C4×C17C22×C412yes—
68C22×C4×C17C22×C411yescharacteristic
69C22×C4×C17C22×C411yescharacteristic
70C22×C4×C17C2411yescharacteristic
71C22×Dic17C22×C412yes—
72C22×Dic17C22×C412yes—
73C22×Dic17C22×C411yescharacteristic
74C22×Dic17C22×C411yescharacteristic
75C22×Dic17C22×C411yescharacteristic
76C2×C4×D17—21no—
77C2×C4×D17—21no—
78C2×C4×D17—22no—
79C2×C4×D17—24no—
80C2×C4×D17—42no—
81C2×C4×D17—42no—
82C2×C4×D17#4114yes—
83C2×C8×C17—24no—
84C2×C8×C17—24no—
85C2×C8×C17—24no—
86C42×C17—22no—
87C42×C17—42no—
88C42×C17—42no—
89C42×C17#4114yes—
90C42×C17#4112yes—
91C42×C17#4112yes—
92#63227—24no—
93#63227—22no—
94#63227—22no—
95#63225—22no—
96#63225—22no—
97#63225—24no—
98C4×Dic17—24no—
99C4×Dic17—21no—
100C4×Dic17—21no—
101C4×Dic17—22no—
102C4×Dic17—22no—
103C4×Dic17—42no—
104C4×Dic17—42no—
105C2×#3622—24no—
106C2×#3622—24no—
107C2×#3622—24no—
108#20783—171nomaximal, Sylow
109C23×C17C23×C411yescharacteristic
110C22×D17—21no—
111C22×D17—21no—
112C22×D17—22no—
113C22×D17—22no—
114C22×D17#11712yes—
115C2×C4×C17—22no—
116C2×C4×C17—22no—
117C2×C4×C17—22no—
118C2×C4×C17—22no—
119C2×C4×C17—22no—
120C2×C4×C17—22no—
121C2×C4×C17—22no—
122C2×C4×C17#11712yes—
123C2×C4×C17#11712yes—
124C2×C4×C17#11714yes—
125C2×C4×C17C2×#4112yes—
126C2×C4×C17C2×#4111yescharacteristic
127C2×C4×C17C2×#4111yescharacteristic
128C2×C4×C17C2×#4112yes—
129C2×Dic17—21no—
130C2×Dic17—21no—
131C2×Dic17—22no—
132C2×Dic17—22no—
133C2×Dic17—21no—
134C2×Dic17—21no—
135C2×Dic17—22no—
136C2×Dic17—22no—
137C2×Dic17—22no—
138C2×Dic17—22no—
139C2×Dic17—22no—
140C2×Dic17—22no—
141C2×Dic17#11712yes—
142C4×D17—24no—
143C4×D17—24no—
144C4×D17—48no—
145C8×C17—44no—
146#3622—44no—
147C4×#117—171no—
148#1840—172no—
149#1832—172no—
150#1818—172no—
151#1798—172no—
152#1767—171no—
153#1767D1711yescharacteristic, complemented
154#1749—172no—
155#1745—172no—
156C22×C17C2×#11711yescharacteristic
157C22×C17C2×#11711yescharacteristic
158C22×C17C2×#11711yescharacteristic
159C22×C17#56812yes—
160C22×C17#56812yes—
161C2×D17—24no—
162C2×D17—22no—
163C2×D17—42no—
164C2×D17—41no—
165C2×D17—41no—
166C4×C17—24no—
167C4×C17—22no—
168C4×C17—22no—
169C4×C17—42no—
170C4×C17#52912yes—
171C4×C17#52912yes—
172Dic17—22no—
173Dic17—42no—
174Dic17—42no—
175Dic17—41no—
176Dic17—41no—
177C2×#117—171no—
178C2×#117—171no—
179C22×C42—171no—
180C2×C4⋊C8—172no—
181C2×C4⋊C8C2×D1712yes—
182C2×C22⋊C8—174no—
183C2×#97—172no—
184C2×#97C2×D1712yes—
185C4×C4⋊C4—172no—
186C4×C4⋊C4—172no—
187C4×C22⋊C4—172no—
188C4×C22⋊C4—172no—
189#376—171no—
190#376—171no—
191C43—171no—
192C43C2×D1711yescharacteristic
193#336—174no—
194#336—174no—
195#336—174no—
196#336—172no—
197#336C2×D1712yes—
198C2×C17#228311yescharacteristic
199C2×C17#292112yes—
200C2×C17#292312yes—
201C2×C17#292311yescharacteristic
202C2×C17#292311yescharacteristic
203D17—42no—
204C23×C4—171no—
205C23×C4—172no—
206C22×C8—174no—
207C22×C8C22×D1714yes—
208#117—344no—
209#117—344no—
210C2×C4⋊C4—172no—
211C2×C4⋊C4—171no—
212C2×C4⋊C4—171no—
213C2×C22⋊C4—172no—
214C2×C22⋊C4—171no—
215C2×C22⋊C4—171no—
216C2×C42—172no—
217C2×C42—171no—
218C2×C42—171no—
219C2×C42—171no—
220C2×C42—172no—
221C2×C42—172no—
222C2×C42—342no—
223C2×C42—342no—
224C2×C42C4×D1712yes—
225C2×C42C4×D1712yes—
226C2×C42C22×D1711yescharacteristic
227C2×C42C22×D1711yescharacteristic
228C2×C42C22×D1711yescharacteristic
229C4⋊C8—24no—
230C4⋊C8—344no—
231C22⋊C8—348no—
232#97—24no—
233#97—344no—
234#95—172no—
235#95—172no—
236#95—172no—
237#95—172no—
238C17#2078311yescharacteristic, complemented, Sylow
239C24—171no—
240C22×C4—171no—
241C22×C4—174no—
242C22×C4—172no—
243C22×C4—172no—
244C22×C4—171no—
245C22×C4—171no—
246C22×C4—342no—
247C22×C4—341no—
248C22×C4—341no—
249C22×C4—344no—
250C22×C4—682no—
251C22×C4—682no—
252C22×C4C2×C4×D1712yes—
253C22×C4C2×C4×D1711yescharacteristic
254C22×C4C2×C4×D1711yescharacteristic
255C22×C4C2×C4×D1712yes—
256C22×C4C23×D1711yescharacteristic
257C2×C8—24no—
258C2×C8—24no—
259C2×C8—24no—
260C2×C8—344no—
261C2×C8—344no—
262C2×C8—344no—
263C4⋊C4—344no—
264C4⋊C4—342no—
265C4⋊C4—342no—
266C22⋊C4—344no—
267C22⋊C4—342no—
268C22⋊C4—342no—
269C42—22no—
270C42—42no—
271C42—42no—
272C42—342no—
273C42—341no—
274C42—341no—
275C42—342no—
276C42—344no—
277C42—682no—
278C42—682no—
279C42#6325214yes—
280C42#6325412yes—
281C42#6325612yes—
282C23—172no—
283C23—341no—
284C23—341no—
285C23—342no—
286C23—342no—
287C23C22×C4×D1711yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—172no—
296C2×C4—341no—
297C2×C4—341no—
298C2×C4—344no—
299C2×C4—344no—
300C2×C4—342no—
301C2×C4—341no—
302C2×C4—341no—
303C2×C4—342no—
304C2×C4—342no—
305C2×C4—342no—
306C2×C4—342no—
307C2×C4—342no—
308C2×C4—342no—
309C2×C4—342no—
310C2×C4—688no—
311C2×C4#1058755812yes—
312C2×C4#1058755812yes—
313C2×C4#1058757814yes—
314C2×C4C2×#6325212yes—
315C2×C4C2×#6325411yescharacteristic
316C2×C4C2×#6325611yescharacteristic
317C2×C4#41×D1712yes—
318C8—44no—
319C8—684no—
320C22—342no—
321C22—344no—
322C22—682no—
323C22—681no—
324C22—681no—
325C22#117×D1711yescharacteristic
326C22C2×#1058755811yescharacteristic
327C22C2×#1058757811yescharacteristic
328C22#1176357512yes—
329C22#1176357512yes—
330C4—24no—
331C4—22no—
332C4—22no—
333C4—42no—
334C4—342no—
335C4—682no—
336C4—682no—
337C4—681no—
338C4—681no—
339C4#1176334112yes—
340C4#1176334612yes—
341C2—682no—
342C2#1453118011yescharacteristic
343C2#1453742112yes—
344C2#1453743012yes—
345C2#1453743311yescharacteristic
346C2#1453743611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D17
commutator, socleC23×C17C23×C4
FittingC17×#1767C2
prime radicalC23×D17C22×C4
cosocleC22×C4×C17C24
hypercenter#1767D17
hypocenterC17#20783
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. #14528928C2semidirect
3. #14528903C2semidirect
6. #14528637C2semidirect
8. #14528532C2semidirect
9. C17×#1767C2semidirect
153. #1767D17semidirect
238. C17#20783semidirect

Maximal subgroups

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

subgroupindex
C4×#105875582
#145289282
#145289032
#145288542
#145287652
#145286372
#145285472
#145285322
C17×#17672
#2078317