Finite Group Databasebeta

← #17197044

Subgroups — #17197044

Order 4352.

1800 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17⋊#564C211yesmaximal, characteristic
2#14531969C212yesmaximal
3#14531968C214yesmaximal
4#14531967C214yesmaximal
5#14531966C214yesmaximal
6#125×Dic17C211yesmaximal, characteristic
7#14531343C214yesmaximal
8#14531341C214yesmaximal
9#14531341C214yesmaximal
10#14531339C212yesmaximal
11C17×#2382C211yesmaximal, characteristic
12C17⋊#564C4116yescomplemented
13C2×#10587556C2212yes—
14C2×#10587576C2214yes—
15C2×#10587575C2214yes—
16C2×#10587575C2214yes—
17#11762708C2212yes—
18#11762707C2214yes—
19#11762706C2214yes—
20#11762706C2214yes—
21#11762705C2212yes—
22#11762705C2212yes—
23#11762704C2214yes—
24#11762704C2214yes—
25#11762696C2214yes—
26#11762696C2214yes—
27#11762695C2214yes—
28#11762694C2214yes—
29#11762694C2214yes—
30#11762693C2214yes—
31#11762693C2214yes—
32#11762692C2214yes—
33#11762692C2214yes—
34#11762691C2214yes—
35#11762691C2214yes—
36#11762690C2214yes—
37#11762690C2214yes—
38#11762675C2211yescharacteristic
39#11762674C2214yes—
40#11762673C2214yes—
41#11762673C2214yes—
42C4⋊C4×Dic17C2212yes—
43C4⋊C4×Dic17C2212yes—
44C4⋊C4×Dic17C2212yes—
45C4⋊C4×Dic17C2214yes—
46C4⋊C4×Dic17C2214yes—
47#11762660C2214yes—
48#11762660C2214yes—
49#11762660C2214yes—
50#11762660C2214yes—
51C42×Dic17C2211yescharacteristic
52C42×Dic17C2214yes—
53C2×C17×#125C2211yescharacteristic
54C17×#389C2214yes—
55C17×#387C2214yes—
56C17×#387C2214yes—
57C17×#382C2212yes—
58C17×#125C2×C418yes—
59C2×C4⋊C4×C17C2312yes—
60C2×C4⋊C4×C17C2314yes—
61C2×C4⋊C4×C17C2312yes—
62C2×C4⋊C4×C17C2314yes—
63C2×C4⋊C4×C17C2312yes—
64C2×C42×C17C2314yes—
65C2×C42×C17C2311yescharacteristic
66C2×C4⋊Dic17C2314yes—
67C2×C4⋊Dic17C2312yes—
68C2×C4⋊Dic17C2312yes—
69C2×C4⋊Dic17C2314yes—
70C2×C4⋊Dic17C2312yes—
71C2×#63225C2314yes—
72C2×#63225C2314yes—
73C2×#63225C2314yes—
74C2×#63225C2314yes—
75C2×#63225C2314yes—
76C2×#63225C2314yes—
77C2×#63225C2314yes—
78C2×#63225C2314yes—
79C2×C4×Dic17C2314yes—
80C2×C4×Dic17C2311yescharacteristic
81C2×C4×Dic17C2314yes—
82C2×C4×Dic17C2312yes—
83C2×C4×Dic17C2314yes—
84C2×C4×Dic17C2314yes—
85C2×C4×Dic17C2311yescharacteristic
86C2×C4×Dic17C2312yes—
87C2×C4×Dic17C2314yes—
88C2×C4×Dic17C2314yes—
89#10587576C2×C4132yes—
90#10587575C2×C4132yes—
91#10587575C2×C4132yes—
92#10587556C2×C4116yes—
93C17×#95C2314yes—
94C17×#95C2314yes—
95C17×#95C2314yes—
96C17×#95C2314yes—
97#10587502C2314yes—
98#10587502C2314yes—
99#10587502C2314yes—
100#10587502C2314yes—
101#10587502C2314yes—
102#10587502C2314yes—
103#10587502C2314yes—
104#10587502C2314yes—
105#10587502C2314yes—
106#10587502C2314yes—
107#10587502C2314yes—
108C22×C4×C17C2414yes—
109C22×C4×C17C2414yes—
110C22×C4×C17C2414yes—
111C22×C4×C17C2412yes—
112C22×C4×C17C2411yescharacteristic
113C22×Dic17C2411yescharacteristic
114C22×Dic17C2412yes—
115C22×Dic17C2414yes—
116C22×Dic17C2414yes—
117C22×Dic17C2414yes—
118C22×Dic17C2411yescharacteristic
119C4⋊C4×C17—44no—
120C4⋊C4×C17—42no—
121C4⋊C4×C17—42no—
122C4⋊C4×C17C22×C418yes—
123C4⋊C4×C17C22×C4116yes—
124C42×C17—44no—
125C42×C17C22×C414yes—
126C4⋊Dic17—42no—
127C4⋊Dic17—44no—
128C4⋊Dic17C22×C418yes—
129C4⋊Dic17C22×C418yes—
130C4⋊Dic17C22×C4116yes—
131#63225—44no—
132#63225—44no—
133#63225—44no—
134#63225—44no—
135#63225C22×C4116yes—
136#63225C22×C4116yes—
137#63225C22×C4116yes—
138#63225C22×C4116yes—
139C4×Dic17—28no—
140C4×Dic17—28no—
141C4×Dic17—22no—
142C4×Dic17—24no—
143C4×Dic17—28no—
144C4×Dic17—44no—
145C4×Dic17—44no—
146C4×Dic17—41no—
147C4×Dic17—42no—
148C4×Dic17C22×C4116yes—
149C4×#564—171nomaximal, Sylow
150C23×C17C2511yescharacteristic
151C2×C4×C17—24no—
152C2×C4×C17—22no—
153C2×C4×C17—21no—
154C2×C4×C17—24no—
155C2×C4×C17—22no—
156C2×C4×C17—21no—
157C2×C4×C17—24no—
158C2×C4×C17—24no—
159C2×C4×C17—24no—
160C2×C4×C17—24no—
161C2×C4×C17—24no—
162C2×C4×C17—24no—
163C2×C4×C17C23×C412yes—
164C2×C4×C17C23×C414yes—
165C2×C4×C17C23×C418yes—
166C2×Dic17—24no—
167C2×Dic17—24no—
168C2×Dic17—24no—
169C2×Dic17—24no—
170C2×Dic17—21no—
171C2×Dic17—22no—
172C2×Dic17—24no—
173C2×Dic17—22no—
174C2×Dic17—22no—
175C2×Dic17—24no—
176C2×Dic17—24no—
177C2×Dic17—22no—
178C2×Dic17C23×C418yes—
179C2×Dic17C23×C418yes—
180C2×Dic172−1+412yes—
181C2×Dic172−1+414yes—
182C2×#564—171no—
183#2382—174no—
184#2382—174no—
185#2382—174no—
186#2382—172no—
187#2382D1711yescharacteristic
188C4×#125—174no—
189C4×#125—174no—
190C4×#125—174no—
191C4×#125—172no—
192C4×#125—171no—
193C22×C17C24×C411yescharacteristic
194C22×C17C2×2−1+411yescharacteristic
195C22×C17C2×2−1+412yes—
196C22×C17#58512yes—
197C22×C17#58511yescharacteristic
198C4×C17—22no—
199C4×C17—28no—
200C4×C17—24no—
201C4×C17—44no—
202C4×C17—44no—
203Dic17—28no—
204Dic17—28no—
205Dic17—41no—
206Dic17—42no—
207Dic17—44no—
208Dic17#56414yescomplemented
209#564—1716no—
210C2×#125—174no—
211C2×#125—174no—
212C2×#125—174no—
213C2×#125—172no—
214C2×#125C2×D1711yescharacteristic
215#389—174no—
216#389—174no—
217#389—172no—
218#389—172no—
219#389—172no—
220#389—174no—
221#389—174no—
222#389—174no—
223#389C2×D1714yes—
224#387—174no—
225#387—174no—
226#387—174no—
227#387—174no—
228#387—174no—
229#387—174no—
230#387—174no—
231#387—174no—
232#387—174no—
233#387—174no—
234#387—174no—
235#387—174no—
236#387—174no—
237#387C2×D1714yes—
238#387C2×D1714yes—
239#382—174no—
240#382—171no—
241#382—174no—
242#382—174no—
243#382C2×D1712yes—
244C4×C4⋊C4—174no—
245C4×C4⋊C4—172no—
246C4×C4⋊C4—172no—
247C4×C4⋊C4—174no—
248C4×C4⋊C4—172no—
249C4×C4⋊C4—174no—
250C4×C4⋊C4—174no—
251C4×C4⋊C4—174no—
252C4×C4⋊C4—174no—
253C43—174no—
254C43—171no—
255C2×C17C4×2−1+411yescharacteristic
256C2×C17C4×2−1+412yes—
257C2×C17C2×#56411yescharacteristic
258C2×C17#353111yescharacteristic
259C2×C17#353112yes—
260#125—1732no—
261#125—1732no—
262#125—1732no—
263#125—1716no—
264#125C4×D1718yes—
265C2×C4⋊C4—174no—
266C2×C4⋊C4—174no—
267C2×C4⋊C4—174no—
268C2×C4⋊C4—174no—
269C2×C4⋊C4—172no—
270C2×C4⋊C4—174no—
271C2×C4⋊C4—172no—
272C2×C4⋊C4—174no—
273C2×C4⋊C4—174no—
274C2×C4⋊C4—174no—
275C2×C4⋊C4—174no—
276C2×C4⋊C4—174no—
277C2×C4⋊C4—172no—
278C2×C4⋊C4C22×D1714yes—
279C2×C4⋊C4C22×D1712yes—
280C2×C4⋊C4C22×D1712yes—
281C2×C4⋊C4C22×D1714yes—
282C2×C4⋊C4C22×D1712yes—
283C2×C42—174no—
284C2×C42—174no—
285C2×C42—174no—
286C2×C42—174no—
287C2×C42—172no—
288C2×C42—171no—
289C2×C42—174no—
290C2×C42—174no—
291C2×C42—172no—
292C2×C42—171no—
293C2×C42C22×D1714yes—
294C2×C42C22×D1711yescharacteristic
295#95—174no—
296#95—174no—
297#95—174no—
298#95—174no—
299#95—174no—
300#95—174no—
301#95—174no—
302#95—174no—
303#95—174no—
304#95—174no—
305#95—174no—
306#95C22×D1714yes—
307#95C22×D1714yes—
308#95C22×D1714yes—
309#95C22×D1714yes—
310C17C4×#56411yescharacteristic, complemented, Sylow
311C22×C4—171no—
312C22×C4—174no—
313C22×C4—174no—
314C22×C4—171no—
315C22×C4—174no—
316C22×C4—172no—
317C22×C4C23×D1714yes—
318C22×C4C23×D1714yes—
319C22×C4C23×D1714yes—
320C22×C4C23×D1712yes—
321C22×C4C23×D1711yescharacteristic
322C4⋊C4—44no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—1716no—
326C4⋊C4—1716no—
327C4⋊C4—1716no—
328C4⋊C4—1716no—
329C4⋊C4—1716no—
330C4⋊C4—178no—
331C4⋊C4—178no—
332C4⋊C4—684no—
333C4⋊C4—684no—
334C4⋊C4—684no—
335C4⋊C4—684no—
336C4⋊C4—684no—
337C4⋊C4—682no—
338C4⋊C4C2×C4×D1718yes—
339C4⋊C4C2×C4×D17116yes—
340C42—44no—
341C42—1716no—
342C42—342no—
343C42—348no—
344C42—344no—
345C42—348no—
346C42—348no—
347C42—682no—
348C42—681no—
349C42—684no—
350C42—684no—
351C42C2×C4×D1714yes—
352C23C24×D1711yescharacteristic
353C2×C4—21no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—172no—
366C2×C4—174no—
367C2×C4—178no—
368C2×C4—178no—
369C2×C4—344no—
370C2×C4—344no—
371C2×C4—344no—
372C2×C4—344no—
373C2×C4—341no—
374C2×C4—344no—
375C2×C4—342no—
376C2×C4—342no—
377C2×C4—344no—
378C2×C4—342no—
379C2×C4—342no—
380C2×C4—344no—
381C2×C4C22×C4×D1718yes—
382C2×C4C22×C4×D1712yes—
383C2×C4C22×C4×D1714yes—
384C22C23×C4×D1711yescharacteristic
385C222−1+4×D1711yescharacteristic
386C222−1+4×D1712yes—
387C22#1176364412yes—
388C22#1176364611yescharacteristic
389C4—22no—
390C4—28no—
391C4—24no—
392C4—44no—
393C4—44no—
394C4—174no—
395C4—348no—
396C4—348no—
397C4—681no—
398C4—684no—
399C4—682no—
400C2#1454199311yescharacteristic
401C2#1454199512yes—
402C2D17×#56411yescharacteristic
403C2#1454292811yescharacteristic
404C2#1454293012yes—
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2382C2
socle, prime radical, cosocleC23×C17C25
hypercenter#2382D17
hypocenterC17C4×#564
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
12. C17⋊#564C4semidirect
208. Dic17#564semidirect
310. C17C4×#564semidirect

Maximal subgroups

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

subgroupindex
C2×C17⋊#5642
#145319692
#145319682
#145319672
#145319662
#125×Dic172
#145313432
#145313412
#145313392
C17×#23822
C4×#56417