Finite Group Databasebeta

← C17×#12751 #16870495

Subgroups — C17×#12751 #16870495

Order 4352.

876 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#578C211yesmaximal, characteristic
2C17×#2148C211yesmaximal, characteristic, complemented
3C2×C17×#362C211yesmaximal, characteristic, complemented
4C17×#2145C211yesmaximal, characteristic, complemented
5C17×#2141C211yesmaximal, characteristic, complemented
6C17×#2117C211yesmaximal, characteristic, complemented
7C17×#1814C211yesmaximal, characteristic, complemented
8C2×C17×2−1+4—21no—
9C17×#578—22no—
10C17×#578—22no—
11C17×#578—22no—
12C17×#578C414yescomplemented
13C2×C17×#137—22no—
14C2×C17×#137—21no—
15C2×C17×#135—21no—
16C2×C17×#135C2211yescharacteristic
17C22×Q16×C17—21no—
18C22×Q16×C17C2211yescharacteristic
19C2×C17×#131C2211yescharacteristic
20C2×C17×M32C2211yescharacteristic
21C2×C17×M32C2211yescharacteristic
22C2×C17×#108C2211yescharacteristic
23C17×#427C2211yescharacteristic
24C17×#421—21no—
25C17×#362—22no—
26C17×#362—21no—
27C17×#361—21no—
28C17×#360—22no—
29C17×#358—22no—
30C17×#350—22no—
31C17×#344—21no—
32C17×2−1+4—24no—
33C17×2−1+4—24no—
34C17×2−1+4—42no—
35C17×2−1+4—42no—
36C2×#41×C17—22no—
37C2×#41×C17—21no—
38C2×#41×C17—42no—
39C2×#41×C17—41no—
40C2×#41×C17D411yescharacteristic
41C22×Q8×C17—22no—
42C22×Q8×C17—21no—
43C22×Q8×C17—41no—
44C17×#137—24no—
45C17×#137—28no—
46C17×#137—28no—
47C17×#137—24no—
48C17×#135—24no—
49C17×#135—24no—
50C17×#135—21no—
51C17×#135—21no—
52C17×#135C2×C412yes—
53C17×#135D412yes—
54C2×Q16×C17—22no—
55C2×Q16×C17—24no—
56C2×Q16×C17—24no—
57C2×Q16×C17—21no—
58C2×Q16×C17—21no—
59C2×Q16×C17—21no—
60C2×Q16×C17C2×C412yes—
61C2×Q16×C17D411yescharacteristic
62C2×Q16×C17D412yes—
63C2×Q16×C17D412yes—
64C2×SD16×C17—22no—
65C2×SD16×C17—21no—
66C2×D8×C17D411yescharacteristic
67C17×#131—21no—
68C17×#131—21no—
69C17×#131C2×C412yes—
70C17×#131D412yes—
71C2×M16×C17—21no—
72C2×M16×C17—21no—
73C2×M16×C17D411yescharacteristic
74C22×C8×C17—21no—
75C22×C8×C17C2311yescharacteristic
76C17×#117—21no—
77C17×M32—21no—
78C17×M32—21no—
79C17×M32—21no—
80C17×M32—21no—
81C2×C16×C17—21no—
82C2×C16×C17—21no—
83C17×#108—21no—
84C17×#108—21no—
85C17×#107—21no—
86C17×#106—21no—
87C17×#104—42no—
88#41×C17—21no—
89#41×C17—21no—
90#41×C17—28no—
91#41×C17—22no—
92#41×C17—22no—
93#41×C17—44no—
94#41×C17—48no—
95#41×C17—48no—
96#41×C17—44no—
97#41×C17—44no—
98#41×C17—41no—
99#41×C17—41no—
100#41×C17C22⋊C412yes—
101#41×C17D812yes—
102C2×Q8×C17—28no—
103C2×Q8×C17—22no—
104C2×Q8×C17—22no—
105C2×Q8×C17—21no—
106C2×Q8×C17—22no—
107C2×Q8×C17—42no—
108C2×Q8×C17—44no—
109C2×Q8×C17—44no—
110C2×Q8×C17—44no—
111C2×Q8×C17—41no—
112C2×Q8×C17—41no—
113C2×Q8×C17—41no—
114C2×Q8×C17SD1611yescharacteristic
115C2×D4×C17—21no—
116C2×D4×C17—21no—
117C2×D4×C17—42no—
118C2×D4×C17—41no—
119C2×D4×C17SD1611yescharacteristic
120C22×C4×C17—21no—
121C22×C4×C17—42no—
122C22×C4×C17—42no—
123C22×C4×C17—41no—
124C22×C4×C17—41no—
125C22×C4×C17C2×D411yescharacteristic
126Q16×C17—28no—
127Q16×C17—22no—
128Q16×C17—21no—
129Q16×C17—22no—
130Q16×C17—22no—
131Q16×C17C22⋊C412yes—
132Q16×C17C22⋊C414yes—
133SD16×C17—28no—
134SD16×C17—22no—
135SD16×C17—22no—
136D8×C17—21no—
137D8×C17C22⋊C412yes—
138M16×C17—21no—
139M16×C17—22no—
140M16×C17—22no—
141M16×C17—41no—
142M16×C17—41no—
143M16×C17C22⋊C412yes—
144C2×C8×C17—21no—
145C2×C8×C17—22no—
146C2×C8×C17—22no—
147C2×C8×C17—41no—
148C2×C8×C17C22×C411yescharacteristic
149C2×C8×C17C2×D411yescharacteristic
150C2×C8×C17C2×D411yescharacteristic
151C2×C8×C17C2×D411yescharacteristic
152C2×C8×C17C2×D411yescharacteristic
153C2×C8×C17C2×D411yescharacteristic
154C4⋊C4×C17—41no—
155C22⋊C4×C17—41no—
156C42×C17—41no—
157C16×C17—41no—
158C16×C17—41no—
159#12751C1711yesmaximal, characteristic, direct product factor, Sylow
160C23×C17—21no—
161C23×C17—41no—
162C23×C17AGL(1,ℤ/8)11yescharacteristic
163Q8×C17—21no—
164Q8×C17—24no—
165Q8×C17—22no—
166Q8×C17—48no—
167Q8×C17—42no—
168Q8×C17—41no—
169Q8×C17—42no—
170Q8×C17—42no—
171Q8×C17#10212yes—
172D4×C17—22no—
173D4×C17—22no—
174D4×C17—22no—
175D4×C17—21no—
176D4×C17—48no—
177D4×C17—42no—
178D4×C17—42no—
179D4×C17—41no—
180D4×C17#10212yes—
181C2×C4×C17—21no—
182C2×C4×C17—22no—
183C2×C4×C17—22no—
184C2×C4×C17—48no—
185C2×C4×C17—48no—
186C2×C4×C17—42no—
187C2×C4×C17—42no—
188C2×C4×C17—42no—
189C2×C4×C17—41no—
190C2×C4×C17—42no—
191C2×C4×C17—42no—
192C2×C4×C17—81no—
193C2×C4×C17C2×C22⋊C411yescharacteristic
194C2×C4×C17#12011yescharacteristic
195C2×C4×C17#12011yescharacteristic
196C2×C4×C17C2×D811yescharacteristic
197C2×C4×C17C2×SD1611yescharacteristic
198C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
199C8×C17—22no—
200C8×C17—81no—
201C8×C17C2×C22⋊C411yescharacteristic
202C8×C17C2×C22⋊C411yescharacteristic
203C8×C17#12011yescharacteristic
204C8×C17#12011yescharacteristic
205C2×#578C2×C1711yescharacteristic
206#2148C2×C1711yescharacteristic, complemented
207C2×#362C2×C1711yescharacteristic, complemented
208#2145C2×C1711yescharacteristic, complemented
209#2141C2×C1711yescharacteristic, complemented
210#2117C2×C1711yescharacteristic, complemented
211#1814C2×C1711yescharacteristic, complemented
212C22×C17—22no—
213C22×C17—41no—
214C22×C17—42no—
215C22×C17—42no—
216C22×C17—82no—
217C22×C17#41811yescharacteristic
218C22×C17#44711yescharacteristic
219C22×C17#45011yescharacteristic
220C4×C17—22no—
221C4×C17—44no—
222C4×C17—42no—
223C4×C17—161no—
224C4×C17#37911yescharacteristic
225C4×C17C2×#10211yescharacteristic
226C4×C17#44711yescharacteristic
227C4×C17#45011yescharacteristic
228C2×2−1+4—21no—
229#578—22no—
230#578—22no—
231#578—22no—
232#578C4×C1714yescomplemented
233C2×#137—22no—
234C2×#137—21no—
235C2×#135—21no—
236C2×#135C22×C1711yescharacteristic
237C22×Q16—21no—
238C22×Q16C22×C1711yescharacteristic
239C2×#131C22×C1711yescharacteristic
240C2×M32C22×C1711yescharacteristic
241C2×M32C22×C1711yescharacteristic
242C2×#108C22×C1711yescharacteristic
243#427C22×C1711yescharacteristic
244#421—21no—
245#362—22no—
246#362—21no—
247#361—21no—
248#360—22no—
249#358—22no—
250#350—22no—
251#344—21no—
252C2×C17—21no—
253C2×C17—21no—
254C2×C17—21no—
255C2×C17—42no—
256C2×C17—82no—
257C2×C17#178611yescharacteristic
2582−1+4—24no—
2592−1+4—24no—
2602−1+4—42no—
2612−1+4—42no—
262C2×#41—22no—
263C2×#41—21no—
264C2×#41—42no—
265C2×#41—41no—
266C2×#41D4×C1711yescharacteristic
267C22×Q8—22no—
268C22×Q8—21no—
269C22×Q8—41no—
270#137—24no—
271#137—28no—
272#137—28no—
273#137—24no—
274#135—24no—
275#135—24no—
276#135—21no—
277#135—21no—
278#135C2×C4×C1712yes—
279#135D4×C1712yes—
280C2×Q16—22no—
281C2×Q16—24no—
282C2×Q16—24no—
283C2×Q16—21no—
284C2×Q16—21no—
285C2×Q16—21no—
286C2×Q16C2×C4×C1712yes—
287C2×Q16D4×C1711yescharacteristic
288C2×Q16D4×C1712yes—
289C2×Q16D4×C1712yes—
290C2×SD16—22no—
291C2×SD16—21no—
292C2×D8D4×C1711yescharacteristic
293#131—21no—
294#131—21no—
295#131C2×C4×C1712yes—
296#131D4×C1712yes—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16D4×C1711yescharacteristic
300C22×C8—21no—
301C22×C8C23×C1711yescharacteristic
302#117—21no—
303M32—21no—
304M32—21no—
305M32—21no—
306M32—21no—
307C2×C16—21no—
308C2×C16—21no—
309#108—21no—
310#108—21no—
311#107—21no—
312#106—21no—
313#104—42no—
314C17#1275111yescharacteristic, direct product factor, Sylow
315#41—21no—
316#41—21no—
317#41—28no—
318#41—22no—
319#41—22no—
320#41—44no—
321#41—48no—
322#41—48no—
323#41—44no—
324#41—44no—
325#41—41no—
326#41—41no—
327#41C22⋊C4×C1712yes—
328#41D8×C1712yes—
329C2×Q8—28no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—21no—
333C2×Q8—22no—
334C2×Q8—42no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8—44no—
338C2×Q8—41no—
339C2×Q8—41no—
340C2×Q8—41no—
341C2×Q8SD16×C1711yescharacteristic
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—42no—
345C2×D4—41no—
346C2×D4SD16×C1711yescharacteristic
347C22×C4—21no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4C2×D4×C1711yescharacteristic
353Q16—28no—
354Q16—22no—
355Q16—21no—
356Q16—22no—
357Q16—22no—
358Q16C22⋊C4×C1712yes—
359Q16C22⋊C4×C1714yes—
360SD16—28no—
361SD16—22no—
362SD16—22no—
363D8—21no—
364D8C22⋊C4×C1712yes—
365M16—21no—
366M16—22no—
367M16—22no—
368M16—41no—
369M16—41no—
370M16C22⋊C4×C1712yes—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—41no—
375C2×C8C22×C4×C1711yescharacteristic
376C2×C8C2×D4×C1711yescharacteristic
377C2×C8C2×D4×C1711yescharacteristic
378C2×C8C2×D4×C1711yescharacteristic
379C2×C8C2×D4×C1711yescharacteristic
380C2×C8C2×D4×C1711yescharacteristic
381C4⋊C4—41no—
382C22⋊C4—41no—
383C42—41no—
384C16—41no—
385C16—41no—
386C23—21no—
387C23—41no—
388C23C17×AGL(1,ℤ/8)11yescharacteristic
389Q8—21no—
390Q8—24no—
391Q8—22no—
392Q8—48no—
393Q8—42no—
394Q8—41no—
395Q8—42no—
396Q8—42no—
397Q8C17×#10212yes—
398D4—22no—
399D4—22no—
400D4—22no—
401D4—21no—
402D4—48no—
403D4—42no—
404D4—42no—
405D4—41no—
406D4C17×#10212yes—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—48no—
411C2×C4—48no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—81no—
419C2×C4C2×C22⋊C4×C1711yescharacteristic
420C2×C4C17×#12011yescharacteristic
421C2×C4C17×#12011yescharacteristic
422C2×C4C2×D8×C1711yescharacteristic
423C2×C4C2×SD16×C1711yescharacteristic
424C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
425C8—22no—
426C8—81no—
427C8C2×C22⋊C4×C1711yescharacteristic
428C8C2×C22⋊C4×C1711yescharacteristic
429C8C17×#12011yescharacteristic
430C8C17×#12011yescharacteristic
431C22—22no—
432C22—41no—
433C22—42no—
434C22—42no—
435C22—82no—
436C22C17×#41811yescharacteristic
437C22C17×#44711yescharacteristic
438C22C17×#45011yescharacteristic
439C4—22no—
440C4—44no—
441C4—42no—
442C4—161no—
443C4C17×#37911yescharacteristic
444C4C2×C17×#10211yescharacteristic
445C4C17×#44711yescharacteristic
446C4C17×#45011yescharacteristic
447C2—21no—
448C2—21no—
449C2—21no—
450C2—42no—
451C2—82no—
452C2C17×#178611yescharacteristic
subgroupG/H
center, socleC2×C17#1786
commutatorC2×C8C22×C4×C17
Frattini, cosocleC22×C8C23×C17
prime radicalC2×C17×#578C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2148C2semidirect
3. C2×C17×#362C2semidirect
4. C17×#2145C2semidirect
5. C17×#2141C2semidirect
6. C17×#2117C2semidirect
7. C17×#1814C2semidirect
12. C17×#578C4semidirect
159. #12751C17direct (N × H)
206. #2148C2×C17semidirect
207. C2×#362C2×C17semidirect
208. #2145C2×C17semidirect
209. #2141C2×C17semidirect
210. #2117C2×C17semidirect
211. #1814C2×C17semidirect
232. #578C4×C17semidirect
314. C17#12751direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#5782
C17×#21482
C2×C17×#3622
C17×#21452
C17×#21412
C17×#21172
C17×#18142
#1275117