Finite Group Databasebeta

← C17×#8152 #16865896

Subgroups — C17×#8152 #16865896

Order 4352.

914 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊C4×C17C211yesmaximal, characteristic
2C17×#1749C212yesmaximal, complemented
3C2×C17×#323C212yesmaximal
4C17×#1280C212yesmaximal, complemented
5C24×C4×C17C411yescharacteristic
6C22×C22⋊C4×C17C411yescharacteristic
7C22×C22⋊C4×C17C2211yescharacteristic
8C22×C42×C17C411yescharacteristic
9C22×C42×C17C2211yescharacteristic
10C2×C17×C22⋊C8C2214yes—
11C2×C17×#97—22no—
12C4×C22⋊C4×C17—22no—
13C4×C22⋊C4×C17—22no—
14C2×C17×#95C411yescharacteristic
15C2×C17×#95C2211yescharacteristic
16C17×#336—22no—
17C17×#323C418yescomplemented
18C25×C17C2×C411yescharacteristic
19C23×C4×C17—22no—
20C23×C4×C17—21no—
21C23×C4×C17—21no—
22C23×C4×C17—22no—
23C23×C4×C17—42no—
24C23×C4×C17—42no—
25C23×C4×C17C2×C411yescharacteristic
26C23×C4×C17C2×C411yescharacteristic
27C23×C4×C17C2×C411yescharacteristic
28C23×C4×C17C2×C411yescharacteristic
29C23×C4×C17C2×C411yescharacteristic
30C23×C4×C17C2311yescharacteristic
31C22×C8×C17—24no—
32C2×C22⋊C4×C17—22no—
33C2×C22⋊C4×C17—22no—
34C2×C22⋊C4×C17—22no—
35C2×C22⋊C4×C17—22no—
36C2×C22⋊C4×C17—22no—
37C2×C22⋊C4×C17C2×C414yes—
38C2×C42×C17—21no—
39C2×C42×C17—21no—
40C2×C42×C17—42no—
41C2×C42×C17—42no—
42C2×C42×C17D412yes—
43C2×C42×C17D412yes—
44C17×C22⋊C8—24no—
45C17×C22⋊C8C2×C418yescomplemented
46C17×#97—44no—
47C17×#95—22no—
48C17×#95—22no—
49C24×C17—21no—
50C24×C17—21no—
51C24×C17—21no—
52C24×C17—21no—
53C24×C17—41no—
54C24×C17—41no—
55C24×C17—41no—
56C24×C17—41no—
57C24×C17C4212yes—
58C24×C17M1612yes—
59C24×C17M1612yes—
60C24×C17C22×C411yescharacteristic
61C22×C4×C17—21no—
62C22×C4×C17—21no—
63C22×C4×C17—22no—
64C22×C4×C17—22no—
65C22×C4×C17—24no—
66C22×C4×C17—24no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—41no—
76C22×C4×C17—41no—
77C22×C4×C17—41no—
78C22×C4×C17—41no—
79C22×C4×C17—48no—
80C22×C4×C17—48no—
81C22×C4×C17—42no—
82C22×C4×C17—42no—
83C22×C4×C17—42no—
84C22×C4×C17—42no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17—41no—
88C22×C4×C17—41no—
89C22×C4×C17—41no—
90C22×C4×C17—41no—
91C22×C4×C17C4212yes—
92C22×C4×C17C22⋊C412yes—
93C22×C4×C17C22⋊C411yescharacteristic
94C22×C4×C17C22⋊C411yescharacteristic
95C22×C4×C17M1612yes—
96C22×C4×C17M1612yes—
97C22×C4×C17C22×C412yes—
98C22×C4×C17C2×D412yes—
99C22×C4×C17#4112yes—
100C2×C8×C17—28no—
101C2×C8×C17—44no—
102C2×C8×C17—44no—
103C22⋊C4×C17—28no—
104C22⋊C4×C17—28no—
105C42×C17—24no—
106C42×C17—42no—
107C42×C17—42no—
108C42×C17—42no—
109#8152C1711yesmaximal, characteristic, direct product factor, Sylow
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—21no—
114C23×C17—22no—
115C23×C17—22no—
116C23×C17—22no—
117C23×C17—22no—
118C23×C17—22no—
119C23×C17—22no—
120C23×C17—42no—
121C23×C17—42no—
122C23×C17—42no—
123C23×C17—42no—
124C23×C17—42no—
125C23×C17—42no—
126C23×C17—42no—
127C23×C17—42no—
128C23×C17—42no—
129C23×C17—42no—
130C23×C17—42no—
131C23×C17—42no—
132C23×C17—41no—
133C23×C17—41no—
134C23×C17—41no—
135C23×C17—41no—
136C23×C17#9714yescomplemented
137C23×C17C2×C4211yescharacteristic
138C23×C17C2×C22⋊C411yescharacteristic
139C23×C17#11711yescharacteristic
140C23×C17C2×M1611yescharacteristic
141C23×C17C2×M1611yescharacteristic
142C23×C17C2×M1611yescharacteristic
143C23×C17C2×M1611yescharacteristic
144C2×C4×C17—24no—
145C2×C4×C17—24no—
146C2×C4×C17—21no—
147C2×C4×C17—21no—
148C2×C4×C17—22no—
149C2×C4×C17—21no—
150C2×C4×C17—22no—
151C2×C4×C17—21no—
152C2×C4×C17—22no—
153C2×C4×C17—22no—
154C2×C4×C17—22no—
155C2×C4×C17—22no—
156C2×C4×C17—22no—
157C2×C4×C17—22no—
158C2×C4×C17—42no—
159C2×C4×C17—42no—
160C2×C4×C17—48no—
161C2×C4×C17—48no—
162C2×C4×C17—42no—
163C2×C4×C17—42no—
164C2×C4×C17—42no—
165C2×C4×C17—42no—
166C2×C4×C17—42no—
167C2×C4×C17—41no—
168C2×C4×C17—41no—
169C2×C4×C17—41no—
170C2×C4×C17—41no—
171C2×C4×C17—41no—
172C2×C4×C17—41no—
173C2×C4×C17—42no—
174C2×C4×C17—42no—
175C2×C4×C17—42no—
176C2×C4×C17#9912yes—
177C2×C4×C17#10012yes—
178C2×C4×C17C4×D414yes—
179C8×C17—48no—
180C2×C4×C22⋊C4C2×C1711yescharacteristic
181#1749C2×C1712yescomplemented
182C2×#323C2×C1712yes—
183#1280C2×C1712yescomplemented
184C22×C17—21no—
185C22×C17—21no—
186C22×C17—21no—
187C22×C17—21no—
188C22×C17—21no—
189C22×C17—21no—
190C22×C17—21no—
191C22×C17—21no—
192C22×C17—21no—
193C22×C17—21no—
194C22×C17—21no—
195C22×C17—21no—
196C22×C17—24no—
197C22×C17—44no—
198C22×C17—44no—
199C22×C17—44no—
200C22×C17—44no—
201C22×C17—42no—
202C22×C17—42no—
203C22×C17—42no—
204C22×C17—42no—
205C22×C17—42no—
206C22×C17—42no—
207C22×C17C4×C22⋊C411yescharacteristic
208C22×C17C2×#9711yescharacteristic
209C22×C17C4×M1611yescharacteristic
210C22×C17#40711yescharacteristic
211C22×C17#40711yescharacteristic
212C22×C17C2×#9911yescharacteristic
213C22×C17#41011yescharacteristic
214C22×C17C2×#10011yescharacteristic
215C22×C17#41311yescharacteristic
216C22×C17#43211yescharacteristic
217C22×C17#43211yescharacteristic
218C4×C17—22no—
219C4×C17—22no—
220C4×C17—24no—
221C4×C17—42no—
222C4×C17—42no—
223C4×C17—42no—
224C4×C17—42no—
225C24×C4C4×C1711yescharacteristic
226C22×C22⋊C4C4×C1711yescharacteristic
227C22×C22⋊C4C22×C1711yescharacteristic
228C22×C42C4×C1711yescharacteristic
229C22×C42C22×C1711yescharacteristic
230C2×C22⋊C8C22×C1714yes—
231C2×#97—22no—
232C4×C22⋊C4—22no—
233C4×C22⋊C4—22no—
234C2×#95C4×C1711yescharacteristic
235C2×#95C22×C1711yescharacteristic
236#336—22no—
237#323C4×C1718yescomplemented
238C2×C17—21no—
239C2×C17—21no—
240C2×C17—21no—
241C2×C17—21no—
242C2×C17—44no—
243C2×C17#146211yescharacteristic
244C2×C17#146411yescharacteristic
245C2×C17#146511yescharacteristic
246C2×C17#146611yescharacteristic
247C2×C17#174911yescharacteristic
248C2×C17C4×#9911yescharacteristic
249C2×C17C4×#10011yescharacteristic
250C25C2×C4×C1711yescharacteristic
251C23×C4—22no—
252C23×C4—21no—
253C23×C4—21no—
254C23×C4—22no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4C2×C4×C1711yescharacteristic
258C23×C4C2×C4×C1711yescharacteristic
259C23×C4C2×C4×C1711yescharacteristic
260C23×C4C2×C4×C1711yescharacteristic
261C23×C4C2×C4×C1711yescharacteristic
262C23×C4C23×C1711yescharacteristic
263C22×C8—24no—
264C2×C22⋊C4—22no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4C2×C4×C1714yes—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42—42no—
273C2×C42—42no—
274C2×C42D4×C1712yes—
275C2×C42D4×C1712yes—
276C22⋊C8—24no—
277C22⋊C8C2×C4×C1718yescomplemented
278#97—44no—
279#95—22no—
280#95—22no—
281C17#815211yescharacteristic, direct product factor, Sylow
282C24—21no—
283C24—21no—
284C24—21no—
285C24—21no—
286C24—41no—
287C24—41no—
288C24—41no—
289C24—41no—
290C24C42×C1712yes—
291C24M16×C1712yes—
292C24M16×C1712yes—
293C24C22×C4×C1711yescharacteristic
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—48no—
313C22×C4—48no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4C42×C1712yes—
325C22×C4C22⋊C4×C1712yes—
326C22×C4C22⋊C4×C1711yescharacteristic
327C22×C4C22⋊C4×C1711yescharacteristic
328C22×C4M16×C1712yes—
329C22×C4M16×C1712yes—
330C22×C4C22×C4×C1712yes—
331C22×C4C2×D4×C1712yes—
332C22×C4#41×C1712yes—
333C2×C8—28no—
334C2×C8—44no—
335C2×C8—44no—
336C22⋊C4—28no—
337C22⋊C4—28no—
338C42—24no—
339C42—42no—
340C42—42no—
341C42—42no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23C17×#9714yescomplemented
369C23C2×C42×C1711yescharacteristic
370C23C2×C22⋊C4×C1711yescharacteristic
371C23C17×#11711yescharacteristic
372C23C2×M16×C1711yescharacteristic
373C23C2×M16×C1711yescharacteristic
374C23C2×M16×C1711yescharacteristic
375C23C2×M16×C1711yescharacteristic
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—48no—
393C2×C4—48no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4C17×#9912yes—
409C2×C4C17×#10012yes—
410C2×C4C4×D4×C1714yes—
411C8—48no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—24no—
425C22—44no—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22C4×C22⋊C4×C1711yescharacteristic
436C22C2×C17×#9711yescharacteristic
437C22C4×M16×C1711yescharacteristic
438C22C17×#40711yescharacteristic
439C22C17×#40711yescharacteristic
440C22C2×C17×#9911yescharacteristic
441C22C17×#41011yescharacteristic
442C22C2×C17×#10011yescharacteristic
443C22C17×#41311yescharacteristic
444C22C17×#43211yescharacteristic
445C22C17×#43211yescharacteristic
446C4—22no—
447C4—22no—
448C4—24no—
449C4—42no—
450C4—42no—
451C4—42no—
452C4—42no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—44no—
458C2C17×#146211yescharacteristic
459C2C17×#146411yescharacteristic
460C2C17×#146511yescharacteristic
461C2C17×#146611yescharacteristic
462C2C17×#174911yescharacteristic
463C2C4×C17×#9911yescharacteristic
464C2C4×C17×#10011yescharacteristic
subgroupG/H
center, socleC23×C17C2×C22⋊C4
commutatorC23C2×C42×C17
Frattini, cosocleC23×C4C23×C17
prime radicalC25×C17C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1749C2semidirect
4. C17×#1280C2semidirect
17. C17×#323C4semidirect
45. C17×C22⋊C8C2×C4semidirect
109. #8152C17direct (N × H)
136. C23×C17#97semidirect
181. #1749C2×C17semidirect
183. #1280C2×C17semidirect
237. #323C4×C17semidirect
277. C22⋊C8C2×C4×C17semidirect
281. C17#8152direct (N × H)
368. C23C17×#97semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊C4×C172
C17×#17492
C2×C17×#3232
C17×#12802
#815217