Finite Group Databasebeta

← C17×#10434 #16868178

Subgroups — C17×#10434 #16868178

Order 4352.

546 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2538C211yesmaximal, characteristic
2C17×#1845C211yesmaximal, characteristic, complemented
3C17×#1803C211yesmaximal, characteristic, complemented
4C17×#1802C211yesmaximal, characteristic
5C2×C17×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C17×D4⋊C8C211yesmaximal, characteristic
7C17×#1296C211yesmaximal, characteristic, complemented
8C2×C17×C22⋊Q8—21no—
9C2×C4×Q8×C17C2211yescharacteristic
10C2×C4×D4×C17C2211yescharacteristic
11C2×C17×#107—22no—
12C2×C17×C4⋊C8C2211yescharacteristic
13C2×C17×C4⋊C8C2211yescharacteristic
14C2×C17×#103—21no—
15C2×C17×#102—21no—
16C2×C4×C8×C17C2211yescharacteristic
17C17×#396—22no—
18C17×#390—21no—
19C17×#389—21no—
20C17×#384C2211yescharacteristic
21C17×#384C2211yescharacteristic
22C17×#380—21no—
23C17×#340—21no—
24C17×#340—21no—
25C17×Q8⋊C8—22no—
26C17×D4⋊C8—22no—
27C22×Q8×C17D411yescharacteristic
28C22×D4×C17D411yescharacteristic
29C23×C4×C17—21no—
30C22×C8×C17—21no—
31C22×C8×C17—21no—
32C22×C8×C17—21no—
33C17×C22⋊Q8—42no—
34C17×C22⋊Q8—42no—
35C4×Q8×C17—21no—
36C4×Q8×C17—21no—
37C4×Q8×C17—21no—
38C4×Q8×C17—21no—
39C4×D4×C17—21no—
40C4×D4×C17—21no—
41C4×D4×C17—21no—
42C4×D4×C17—21no—
43C2×C4⋊C4×C17—22no—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17—21no—
48C2×C4⋊C4×C17—21no—
49C2×C4⋊C4×C17—21no—
50C2×C4⋊C4×C17D411yescharacteristic
51C2×C4⋊C4×C17D411yescharacteristic
52C2×C4⋊C4×C17D412yes—
53C2×C22⋊C4×C17—22no—
54C2×C22⋊C4×C17—21no—
55C2×C22⋊C4×C17—22no—
56C2×C42×C17—21no—
57C2×C42×C17C2311yescharacteristic
58C17×#107—44no—
59C17×C4⋊C8—21no—
60C17×C4⋊C8—21no—
61C17×C4⋊C8—21no—
62C17×C4⋊C8—21no—
63C17×#103—42no—
64C17×#102—42no—
65C4×C8×C17—21no—
66C4×C8×C17D412yes—
67C17×#95—22no—
68C24×C17—21no—
69C2×Q8×C17—21no—
70C2×Q8×C17—21no—
71C2×Q8×C17—21no—
72C2×Q8×C17—21no—
73C2×Q8×C17—21no—
74C2×Q8×C17D812yes—
75C2×D4×C17—21no—
76C2×D4×C17—21no—
77C2×D4×C17—21no—
78C2×D4×C17—21no—
79C2×D4×C17—21no—
80C2×D4×C17Q1612yes—
81C22×C4×C17—21no—
82C22×C4×C17—21no—
83C22×C4×C17—21no—
84C22×C4×C17—22no—
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×C17—41no—
92C22×C4×C17C2×D411yescharacteristic
93C22×C4×C17C2×D411yescharacteristic
94C22×C4×C17C2×D411yescharacteristic
95C2×C8×C17—22no—
96C2×C8×C17—22no—
97C2×C8×C17—22no—
98C2×C8×C17—41no—
99C2×C8×C17—41no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C2×C8×C17—41no—
103C2×C8×C17—41no—
104C4⋊C4×C17—21no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—21no—
108C4⋊C4×C17—42no—
109C4⋊C4×C17—44no—
110C4⋊C4×C17—42no—
111C4⋊C4×C17—41no—
112C4⋊C4×C17—41no—
113C4⋊C4×C17—41no—
114C4⋊C4×C17—41no—
115C4⋊C4×C17—41no—
116C4⋊C4×C17—41no—
117C4⋊C4×C17—41no—
118C4⋊C4×C17—41no—
119C4⋊C4×C17—41no—
120C4⋊C4×C17—41no—
121C22⋊C4×C17—44no—
122C22⋊C4×C17—41no—
123C22⋊C4×C17—41no—
124C22⋊C4×C17—82no—
125C42×C17—41no—
126C42×C17—41no—
127C42×C17C2×D411yescharacteristic
128C42×C17#4111yescharacteristic
129C42×C17#4111yescharacteristic
130C42×C17#4111yescharacteristic
131#10434C1711yesmaximal, characteristic, direct product factor, Sylow
132C23×C17—22no—
133C23×C17—41no—
134C23×C17—41no—
135C23×C17—41no—
136C23×C17—41no—
137C23×C17—41no—
138C23×C17—41no—
139C23×C17#12011yescharacteristic
140Q8×C17—22no—
141Q8×C17—22no—
142Q8×C17—41no—
143Q8×C17—41no—
144D4×C17—22no—
145D4×C17—22no—
146D4×C17—41no—
147D4×C17—41no—
148C2×C4×C17—21no—
149C2×C4×C17—21no—
150C2×C4×C17—22no—
151C2×C4×C17—41no—
152C2×C4×C17—41no—
153C2×C4×C17—41no—
154C2×C4×C17—41no—
155C2×C4×C17—42no—
156C2×C4×C17—41no—
157C2×C4×C17—42no—
158C2×C4×C17—41no—
159C2×C4×C17—41no—
160C2×C4×C17—42no—
161C2×C4×C17—41no—
162C2×C4×C17—81no—
163C2×C4×C17—81no—
164C2×C4×C17—81no—
165C2×C4×C17—81no—
166C2×C4×C17—81no—
167C2×C4×C17—81no—
168C2×C4×C17—81no—
169C2×C4×C17#12111yescharacteristic
170C2×C4×C17#12111yescharacteristic
171C2×C4×C17#12111yescharacteristic
172C2×C4×C17#12311yescharacteristic
173C2×C4×C17#12311yescharacteristic
174C2×C4×C17#12411yescharacteristic
175C2×C4×C17C2×D811yescharacteristic
176C2×C4×C17C2×Q1611yescharacteristic
177C2×C4×C17#13511yescharacteristic
178C2×C4×C17#13511yescharacteristic
179C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C17#13711yescharacteristic
182C2×C4×C17#13711yescharacteristic
183C8×C17—24no—
184C8×C17—81no—
185C8×C17—81no—
186#2538C2×C1711yescharacteristic
187#1845C2×C1711yescharacteristic, complemented
188#1803C2×C1711yescharacteristic, complemented
189#1802C2×C1711yescharacteristic
190C2×Q8⋊C8C2×C1711yescharacteristic, complemented
191C2×D4⋊C8C2×C1711yescharacteristic
192#1296C2×C1711yescharacteristic, complemented
193C22×C17—42no—
194C22×C17—42no—
195C22×C17—42no—
196C22×C17—81no—
197C22×C17—81no—
198C22×C17—81no—
199C22×C17—81no—
200C22×C17#39411yescharacteristic
201C22×C17#44711yescharacteristic
202C22×C17#44911yescharacteristic
203C22×C17#45111yescharacteristic
204C22×C17#45211yescharacteristic
205C22×C17#45311yescharacteristic
206C22×C17#45611yescharacteristic
207C4×C17—21no—
208C4×C17—21no—
209C4×C17—42no—
210C4×C17—82no—
211C4×C17—81no—
212C4×C17—81no—
213C4×C17—161no—
214C4×C17#46611yescharacteristic
215C4×C17#46711yescharacteristic
216C4×C17#46811yescharacteristic
217C4×C17#46811yescharacteristic
218C4×C17#48011yescharacteristic
219C4×C17#48211yescharacteristic
220C4×C17#48411yescharacteristic
221C4×C17#48511yescharacteristic
222C2×C22⋊Q8—21no—
223C2×C4×Q8C22×C1711yescharacteristic
224C2×C4×D4C22×C1711yescharacteristic
225C2×#107—22no—
226C2×C4⋊C8C22×C1711yescharacteristic
227C2×C4⋊C8C22×C1711yescharacteristic
228C2×#103—21no—
229C2×#102—21no—
230C2×C4×C8C22×C1711yescharacteristic
231#396—22no—
232#390—21no—
233#389—21no—
234#384C22×C1711yescharacteristic
235#384C22×C1711yescharacteristic
236#380—21no—
237#340—21no—
238#340—21no—
239Q8⋊C8—22no—
240D4⋊C8—22no—
241C2×C17—82no—
242C2×C17#162111yescharacteristic
243C2×C17#163211yescharacteristic
244C2×C17#164911yescharacteristic
245C2×C17#165011yescharacteristic
246C2×C17#203311yescharacteristic
247C2×C17#203611yescharacteristic
248C2×C17#203911yescharacteristic
249C22×Q8D4×C1711yescharacteristic
250C22×D4D4×C1711yescharacteristic
251C23×C4—21no—
252C22×C8—21no—
253C22×C8—21no—
254C22×C8—21no—
255C22⋊Q8—42no—
256C22⋊Q8—42no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4D4×C1711yescharacteristic
273C2×C4⋊C4D4×C1711yescharacteristic
274C2×C4⋊C4D4×C1712yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—22no—
278C2×C42—21no—
279C2×C42C23×C1711yescharacteristic
280#107—44no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285#103—42no—
286#102—42no—
287C4×C8—21no—
288C4×C8D4×C1712yes—
289#95—22no—
290C17#1043411yescharacteristic, direct product factor, Sylow
291C24—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8D8×C1712yes—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4Q16×C1712yes—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4C2×D4×C1711yescharacteristic
316C22×C4C2×D4×C1711yescharacteristic
317C22×C4C2×D4×C1711yescharacteristic
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—42no—
332C4⋊C4—44no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C22⋊C4—44no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—82no—
348C42—41no—
349C42—41no—
350C42C2×D4×C1711yescharacteristic
351C42#41×C1711yescharacteristic
352C42#41×C1711yescharacteristic
353C42#41×C1711yescharacteristic
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23C17×#12011yescharacteristic
362Q8—22no—
363Q8—22no—
364Q8—41no—
365Q8—41no—
366D4—22no—
367D4—22no—
368D4—41no—
369D4—41no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4C17×#12111yescharacteristic
392C2×C4C17×#12111yescharacteristic
393C2×C4C17×#12111yescharacteristic
394C2×C4C17×#12311yescharacteristic
395C2×C4C17×#12311yescharacteristic
396C2×C4C17×#12411yescharacteristic
397C2×C4C2×D8×C1711yescharacteristic
398C2×C4C2×Q16×C1711yescharacteristic
399C2×C4C17×#13511yescharacteristic
400C2×C4C17×#13511yescharacteristic
401C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
402C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
403C2×C4C17×#13711yescharacteristic
404C2×C4C17×#13711yescharacteristic
405C8—24no—
406C8—81no—
407C8—81no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—81no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22C17×#39411yescharacteristic
416C22C17×#44711yescharacteristic
417C22C17×#44911yescharacteristic
418C22C17×#45111yescharacteristic
419C22C17×#45211yescharacteristic
420C22C17×#45311yescharacteristic
421C22C17×#45611yescharacteristic
422C4—21no—
423C4—21no—
424C4—42no—
425C4—81no—
426C4—81no—
427C4—82no—
428C4—161no—
429C4C17×#46611yescharacteristic
430C4C17×#46711yescharacteristic
431C4C17×#46811yescharacteristic
432C4C17×#46811yescharacteristic
433C4C17×#48011yescharacteristic
434C4C17×#48211yescharacteristic
435C4C17×#48411yescharacteristic
436C4C17×#48511yescharacteristic
437C2—82no—
438C2C17×#162111yescharacteristic
439C2C17×#163211yescharacteristic
440C2C17×#164911yescharacteristic
441C2C17×#165011yescharacteristic
442C2C17×#203311yescharacteristic
443C2C17×#203611yescharacteristic
444C2C17×#203911yescharacteristic
subgroupG/H
center, socleC23×C17#120
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC22×D4×C17D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1845C2semidirect
3. C17×#1803C2semidirect
5. C2×C17×Q8⋊C8C2semidirect
7. C17×#1296C2semidirect
131. #10434C17direct (N × H)
187. #1845C2×C17semidirect
188. #1803C2×C17semidirect
190. C2×Q8⋊C8C2×C17semidirect
192. #1296C2×C17semidirect
290. C17#10434direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#25382
C17×#18452
C17×#18032
C17×#18022
C2×C17×Q8⋊C82
C2×C17×D4⋊C82
C17×#12962
#1043417