Finite Group Databasebeta

← C17×#7599 #16865343

Subgroups — C17×#7599 #16865343

Order 4352.

588 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C17×#121C211yesmaximal, characteristic
2C17×#1817C211yesmaximal, characteristic, complemented
3C17×#1797C211yesmaximal, characteristic, complemented
4C17×#1271C212yesmaximal, complemented
5C17×#1270C212yesmaximal, complemented
6C2×C17×#121C411yescharacteristic
7C2×C4×D4×C17—21no—
8C2×C4×D4×C17C411yescharacteristic
9C22×C42×C17C2211yescharacteristic
10C2×C17×C4⋊C8—21no—
11C2×C17×C22⋊C8—21no—
12C2×C17×C22⋊C8—21no—
13C17×#390C2211yescharacteristic
14C17×#389C2211yescharacteristic
15C17×#388—21no—
16C17×#386—21no—
17C17×#380C411yescharacteristic
18C4×C4⋊C4×C17C411yescharacteristic
19C4×C22⋊C4×C17—21no—
20C17×#336—21no—
21C17×#336C2212yes—
22C17×#336C2212yes—
23C22×D4×C17—21no—
24C22×D4×C17C2×C411yescharacteristic
25C23×C4×C17—21no—
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17D411yescharacteristic
28C23×C4×C17D411yescharacteristic
29C22×C8×C17—22no—
30C22×C8×C17—22no—
31C17×#121—22no—
32C17×#121C814yescomplemented
33C4×D4×C17—42no—
34C4×D4×C17—44no—
35C2×C4⋊C4×C17—21no—
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C4⋊C4×C17C2×C411yescharacteristic
39C2×C22⋊C4×C17—21no—
40C2×C22⋊C4×C17—21no—
41C2×C22⋊C4×C17—21no—
42C2×C22⋊C4×C17—21no—
43C2×C22⋊C4×C17—21no—
44C2×C42×C17—21no—
45C2×C42×C17—42no—
46C2×C42×C17C2×C411yescharacteristic
47C2×C42×C17D411yescharacteristic
48C2×C42×C17D411yescharacteristic
49C2×C42×C17C2311yescharacteristic
50C17×C4⋊C8—42no—
51C17×C22⋊C8—42no—
52C17×C22⋊C8—42no—
53C17×#95—21no—
54C17×#95—21no—
55C17×#95—21no—
56C24×C17—21no—
57C24×C17C22⋊C411yescharacteristic
58C2×D4×C17—24no—
59C2×D4×C17—21no—
60C2×D4×C17—41no—
61C2×D4×C17—41no—
62C2×D4×C17—42no—
63C2×D4×C17—42no—
64C2×D4×C17C2×C812yes—
65C22×C4×C17—21no—
66C22×C4×C17—22no—
67C22×C4×C17—21no—
68C22×C4×C17—22no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—41no—
73C22×C4×C17—41no—
74C22×C4×C17—41no—
75C22×C4×C17—41no—
76C22×C4×C17—41no—
77C22×C4×C17—42no—
78C22×C4×C17—42no—
79C22×C4×C17—42no—
80C22×C4×C17C22⋊C411yescharacteristic
81C22×C4×C17C22⋊C411yescharacteristic
82C22×C4×C17C22⋊C411yescharacteristic
83C22×C4×C17C2×C812yes—
84C22×C4×C17M1612yes—
85C22×C4×C17C22×C411yescharacteristic
86C22×C4×C17C2×D411yescharacteristic
87C22×C4×C17C2×D411yescharacteristic
88C2×C8×C17—42no—
89C2×C8×C17—42no—
90C2×C8×C17—42no—
91C2×C8×C17—42no—
92C2×C8×C17—42no—
93C2×C8×C17—42no—
94C4⋊C4×C17—21no—
95C4⋊C4×C17—41no—
96C4⋊C4×C17—41no—
97C4⋊C4×C17—42no—
98C4⋊C4×C17C2×C812yes—
99C22⋊C4×C17—24no—
100C22⋊C4×C17—42no—
101C22⋊C4×C17—42no—
102C22⋊C4×C17—41no—
103C22⋊C4×C17—42no—
104C22⋊C4×C17—41no—
105C42×C17—22no—
106C42×C17—22no—
107C42×C17—41no—
108C42×C17—41no—
109C42×C17—42no—
110#7599C1711yesmaximal, characteristic, direct product factor, Sylow
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—22no—
118C23×C17—41no—
119C23×C17—41no—
120C23×C17—41no—
121C23×C17—41no—
122C23×C17—41no—
123C23×C17—41no—
124C23×C17C22⋊C812yes—
125C23×C17C2×C22⋊C411yescharacteristic
126D4×C17—42no—
127D4×C17—42no—
128D4×C17—48no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17—21no—
139C2×C4×C17—22no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—42no—
144C2×C4×C17—42no—
145C2×C4×C17—44no—
146C2×C4×C17—42no—
147C2×C4×C17—42no—
148C2×C4×C17—41no—
149C2×C4×C17—41no—
150C2×C4×C17—41no—
151C2×C4×C17—41no—
152C2×C4×C17—41no—
153C2×C4×C17—41no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17—84no—
157C2×C4×C17C22⋊C812yes—
158C2×C4×C17#9912yes—
159C2×C4×C17C22×C811yescharacteristic
160C2×C4×C17C2×M1611yescharacteristic
161C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C17AGL(1,ℤ/8)12yes—
163C2×C4×C17#13711yescharacteristic
164C8×C17—82no—
165C8×C17—82no—
166C4×#121C2×C1711yescharacteristic
167#1817C2×C1711yescharacteristic, complemented
168#1797C2×C1711yescharacteristic, complemented
169#1271C2×C1712yescomplemented
170#1270C2×C1712yescomplemented
171C22×C17—22no—
172C22×C17—22no—
173C22×C17—22no—
174C22×C17—41no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17—41no—
178C22×C17—42no—
179C22×C17—42no—
180C22×C17—42no—
181C22×C17—81no—
182C22×C17—81no—
183C22×C17—81no—
184C22×C17—81no—
185C22×C17C2×C22⋊C811yescharacteristic
186C22×C17C2×#9911yescharacteristic
187C22×C17#41311yescharacteristic
188C22×C17#41711yescharacteristic
189C22×C17#41811yescharacteristic
190C22×C17#42111yescharacteristic
191C22×C17#42111yescharacteristic
192C4×C17—22no—
193C4×C17—21no—
194C4×C17—21no—
195C4×C17—22no—
196C4×C17—22no—
197C4×C17—21no—
198C4×C17—21no—
199C4×C17—42no—
200C4×C17—41no—
201C4×C17—81no—
202C4×C17—81no—
203C2×#121C4×C1711yescharacteristic
204C2×C4×D4—21no—
205C2×C4×D4C4×C1711yescharacteristic
206C22×C42C22×C1711yescharacteristic
207C2×C4⋊C8—21no—
208C2×C22⋊C8—21no—
209C2×C22⋊C8—21no—
210#390C22×C1711yescharacteristic
211#389C22×C1711yescharacteristic
212#388—21no—
213#386—21no—
214#380C4×C1711yescharacteristic
215C4×C4⋊C4C4×C1711yescharacteristic
216C4×C22⋊C4—21no—
217#336—21no—
218#336C22×C1712yes—
219#336C22×C1712yes—
220C2×C17—42no—
221C2×C17—82no—
222C2×C17#145911yescharacteristic
223C2×C17#147711yescharacteristic
224C2×C17#147811yescharacteristic
225C2×C17#151011yescharacteristic
226C2×C17#151311yescharacteristic
227C2×C17#153511yescharacteristic
228C2×C17#155711yescharacteristic
229C22×D4—21no—
230C22×D4C2×C4×C1711yescharacteristic
231C23×C4—21no—
232C23×C4C2×C4×C1711yescharacteristic
233C23×C4D4×C1711yescharacteristic
234C23×C4D4×C1711yescharacteristic
235C22×C8—22no—
236C22×C8—22no—
237#121—22no—
238#121C8×C1714yescomplemented
239C4×D4—42no—
240C4×D4—44no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4C2×C4×C1711yescharacteristic
243C2×C4⋊C4C2×C4×C1711yescharacteristic
244C2×C4⋊C4C2×C4×C1711yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C42—21no—
251C2×C42—42no—
252C2×C42C2×C4×C1711yescharacteristic
253C2×C42D4×C1711yescharacteristic
254C2×C42D4×C1711yescharacteristic
255C2×C42C23×C1711yescharacteristic
256C4⋊C8—42no—
257C22⋊C8—42no—
258C22⋊C8—42no—
259#95—21no—
260#95—21no—
261#95—21no—
262C17#759911yescharacteristic, direct product factor, Sylow
263C24—21no—
264C24C22⋊C4×C1711yescharacteristic
265C2×D4—24no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4C2×C8×C1712yes—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4C22⋊C4×C1711yescharacteristic
288C22×C4C22⋊C4×C1711yescharacteristic
289C22×C4C22⋊C4×C1711yescharacteristic
290C22×C4C2×C8×C1712yes—
291C22×C4M16×C1712yes—
292C22×C4C22×C4×C1711yescharacteristic
293C22×C4C2×D4×C1711yescharacteristic
294C22×C4C2×D4×C1711yescharacteristic
295C2×C8—42no—
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—42no—
300C2×C8—42no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—42no—
305C4⋊C4C2×C8×C1712yes—
306C22⋊C4—24no—
307C22⋊C4—42no—
308C22⋊C4—42no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C42—22no—
313C42—22no—
314C42—41no—
315C42—41no—
316C42—42no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—22no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23C17×C22⋊C812yes—
331C23C2×C22⋊C4×C1711yescharacteristic
332D4—42no—
333D4—42no—
334D4—48no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—84no—
363C2×C4C17×C22⋊C812yes—
364C2×C4C17×#9912yes—
365C2×C4C22×C8×C1711yescharacteristic
366C2×C4C2×M16×C1711yescharacteristic
367C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
368C2×C4C17×AGL(1,ℤ/8)12yes—
369C2×C4C17×#13711yescharacteristic
370C8—82no—
371C8—82no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—42no—
380C22—42no—
381C22—42no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C2×C17×C22⋊C811yescharacteristic
387C22C2×C17×#9911yescharacteristic
388C22C17×#41311yescharacteristic
389C22C17×#41711yescharacteristic
390C22C17×#41811yescharacteristic
391C22C17×#42111yescharacteristic
392C22C17×#42111yescharacteristic
393C4—21no—
394C4—21no—
395C4—22no—
396C4—22no—
397C4—22no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—41no—
402C4—81no—
403C4—81no—
404C2—42no—
405C2—82no—
406C2C17×#145911yescharacteristic
407C2C17×#147711yescharacteristic
408C2C17×#147811yescharacteristic
409C2C17×#151011yescharacteristic
410C2C17×#151311yescharacteristic
411C2C17×#153511yescharacteristic
412C2C17×#155711yescharacteristic
subgroupG/H
center, socleC23×C17C2×C22⋊C4
commutatorC2×C4C22×C8×C17
Frattini, cosocleC2×C42C23×C17
prime radicalC2×C17×#121C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1817C2semidirect
3. C17×#1797C2semidirect
4. C17×#1271C2semidirect
5. C17×#1270C2semidirect
32. C17×#121C8semidirect
110. #7599C17direct (N × H)
167. #1817C2×C17semidirect
168. #1797C2×C17semidirect
169. #1271C2×C17semidirect
170. #1270C2×C17semidirect
238. #121C8×C17semidirect
262. C17#7599direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C17×#1212
C17×#18172
C17×#17972
C17×#12712
C17×#12702
#759917