Finite Group Databasebeta

← C17×#10410 #16868154

Subgroups — C17×#10410 #16868154

Order 4352.

572 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
1C17×#2548C211yesmaximal, characteristic
2C17×#1957C211yesmaximal, characteristic
3C17×#1948C211yesmaximal, characteristic, complemented
4C17×#1803C211yesmaximal, characteristic, complemented
5C2×C17×#331C211yesmaximal, characteristic
6C2×C17×Q8⋊C8C211yesmaximal, characteristic, complemented
7C17×#1279C211yesmaximal, characteristic, complemented
8C2×C17×#127C2211yescharacteristic
9C2×C17×#124—21no—
10C2×C4×Q8×C17C2211yescharacteristic
11C2×C17×#106—21no—
12C2×C17×C4⋊C8C2211yescharacteristic
13C2×C17×C4⋊C8C2211yescharacteristic
14C2×C17×#103—21no—
15C2×C17×#102—22no—
16C2×C4×C8×C17C2211yescharacteristic
17C17×#394—22no—
18C17×#390—21no—
19C17×#390—21no—
20C17×#390—21no—
21C17×#384C2211yescharacteristic
22C4×C4⋊C4×C17C2211yescharacteristic
23C17×#340—21no—
24C17×#340—21no—
25C17×#331—22no—
26C17×Q8⋊C8—22no—
27C22×Q8×C17D411yescharacteristic
28C22×D4×C17—21no—
29C22×D4×C17—21no—
30C22×D4×C17D412yes—
31C22×C8×C17—21no—
32C22×C8×C17—21no—
33C22×C8×C17—21no—
34C17×#127—21no—
35C17×#127—21no—
36C17×#127—21no—
37C17×#127—21no—
38C17×#124—42no—
39C17×#124—42no—
40C4×Q8×C17—21no—
41C4×Q8×C17—21no—
42C4×Q8×C17—21no—
43C4×Q8×C17—21no—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C4⋊C4×C17—21no—
48C2×C4⋊C4×C17D411yescharacteristic
49C2×C4⋊C4×C17D411yescharacteristic
50C2×C4⋊C4×C17D411yescharacteristic
51C2×C22⋊C4×C17—22no—
52C2×C22⋊C4×C17—22no—
53C2×C22⋊C4×C17—22no—
54C2×C22⋊C4×C17—22no—
55C2×C42×C17—21no—
56C2×C42×C17—21no—
57C2×C42×C17C2311yescharacteristic
58C17×#106—42no—
59C17×C4⋊C8—21no—
60C17×C4⋊C8—21no—
61C17×C4⋊C8—21no—
62C17×C4⋊C8D412yes—
63C17×#103—42no—
64C17×#102—44no—
65C4×C8×C17—21no—
66C4×C8×C17—21no—
67C17×#95—21no—
68C24×C17—22no—
69C2×Q8×C17—21no—
70C2×Q8×C17—21no—
71C2×Q8×C17—21no—
72C2×Q8×C17—21no—
73C2×Q8×C17—21no—
74C2×Q8×C17SD1612yes—
75C2×D4×C17—22no—
76C2×D4×C17—22no—
77C2×D4×C17—42no—
78C2×D4×C17—42no—
79C2×D4×C17—41no—
80C2×D4×C17—41no—
81C2×D4×C17—41no—
82C2×D4×C17—41no—
83C2×D4×C17—41no—
84C2×D4×C17—41no—
85C2×D4×C17—41no—
86C2×D4×C17—41no—
87C2×D4×C17—41no—
88C2×D4×C17—41no—
89C2×D4×C17—41no—
90C2×D4×C17—41no—
91C22×C4×C17—21no—
92C22×C4×C17—21no—
93C22×C4×C17—21no—
94C22×C4×C17—21no—
95C22×C4×C17—41no—
96C22×C4×C17C2×D411yescharacteristic
97C22×C4×C17C2×D411yescharacteristic
98C22×C4×C17C2×D411yescharacteristic
99C2×C8×C17—22no—
100C2×C8×C17—22no—
101C2×C8×C17—41no—
102C2×C8×C17—41no—
103C2×C8×C17—41no—
104C2×C8×C17—41no—
105C2×C8×C17—41no—
106C2×C8×C17—41no—
107C2×C8×C17—41no—
108C4⋊C4×C17—21no—
109C4⋊C4×C17—21no—
110C4⋊C4×C17—21no—
111C4⋊C4×C17—21no—
112C4⋊C4×C17—21no—
113C4⋊C4×C17—21no—
114C4⋊C4×C17—42no—
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—44no—
123C22⋊C4×C17—82no—
124C22⋊C4×C17—82no—
125C42×C17—41no—
126C42×C17—41no—
127C42×C17—41no—
128C42×C17—41no—
129C42×C17C2×D411yescharacteristic
130C42×C17#4111yescharacteristic
131C42×C17#4111yescharacteristic
132C42×C17#4111yescharacteristic
133#10410C1711yesmaximal, characteristic, direct product factor, Sylow
134C23×C17—42no—
135C23×C17—42no—
136C23×C17—42no—
137C23×C17—42no—
138C23×C17—42no—
139C23×C17—42no—
140C23×C17—42no—
141C23×C17#12011yescharacteristic
142Q8×C17—22no—
143Q8×C17—22no—
144Q8×C17—41no—
145Q8×C17—41no—
146D4×C17—44no—
147D4×C17—82no—
148D4×C17—81no—
149D4×C17—81no—
150D4×C17—81no—
151D4×C17—81no—
152D4×C17—81no—
153D4×C17—81no—
154D4×C17—81no—
155D4×C17—81no—
156C2×C4×C17—21no—
157C2×C4×C17—21no—
158C2×C4×C17—22no—
159C2×C4×C17—41no—
160C2×C4×C17—41no—
161C2×C4×C17—41no—
162C2×C4×C17—41no—
163C2×C4×C17—41no—
164C2×C4×C17—41no—
165C2×C4×C17—41no—
166C2×C4×C17—41no—
167C2×C4×C17—41no—
168C2×C4×C17—41no—
169C2×C4×C17—41no—
170C2×C4×C17—81no—
171C2×C4×C17—81no—
172C2×C4×C17—81no—
173C2×C4×C17#12111yescharacteristic
174C2×C4×C17#12111yescharacteristic
175C2×C4×C17#12111yescharacteristic
176C2×C4×C17#12311yescharacteristic
177C2×C4×C17#12311yescharacteristic
178C2×C4×C17#12411yescharacteristic
179C2×C4×C17C2×SD1611yescharacteristic
180C2×C4×C17#13511yescharacteristic
181C2×C4×C17#13511yescharacteristic
182C2×C4×C17#13511yescharacteristic
183C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C17#13711yescharacteristic
187C8×C17—42no—
188C8×C17—42no—
189C8×C17—81no—
190#2548C2×C1711yescharacteristic
191#1957C2×C1711yescharacteristic
192#1948C2×C1711yescharacteristic, complemented
193#1803C2×C1711yescharacteristic, complemented
194C2×#331C2×C1711yescharacteristic
195C2×Q8⋊C8C2×C1711yescharacteristic, complemented
196#1279C2×C1711yescharacteristic, complemented
197C22×C17—82no—
198C22×C17—82no—
199C22×C17—82no—
200C22×C17—82no—
201C22×C17—82no—
202C22×C17—82no—
203C22×C17—82no—
204C22×C17#39411yescharacteristic
205C22×C17#44911yescharacteristic
206C22×C17#44911yescharacteristic
207C22×C17#45011yescharacteristic
208C22×C17#45211yescharacteristic
209C22×C17#45311yescharacteristic
210C22×C17#45511yescharacteristic
211C4×C17—21no—
212C4×C17—21no—
213C4×C17—42no—
214C4×C17—81no—
215C4×C17—81no—
216C4×C17—81no—
217C4×C17—161no—
218C4×C17#46311yescharacteristic
219C4×C17#46411yescharacteristic
220C4×C17#46511yescharacteristic
221C4×C17#46911yescharacteristic
222C4×C17#48111yescharacteristic
223C4×C17#48211yescharacteristic
224C4×C17#48811yescharacteristic
225C4×C17#48911yescharacteristic
226C2×#127C22×C1711yescharacteristic
227C2×#124—21no—
228C2×C4×Q8C22×C1711yescharacteristic
229C2×#106—21no—
230C2×C4⋊C8C22×C1711yescharacteristic
231C2×C4⋊C8C22×C1711yescharacteristic
232C2×#103—21no—
233C2×#102—22no—
234C2×C4×C8C22×C1711yescharacteristic
235#394—22no—
236#390—21no—
237#390—21no—
238#390—21no—
239#384C22×C1711yescharacteristic
240C4×C4⋊C4C22×C1711yescharacteristic
241#340—21no—
242#340—21no—
243#331—22no—
244Q8⋊C8—22no—
245C2×C17—162no—
246C2×C17#162011yescharacteristic
247C2×C17#163111yescharacteristic
248C2×C17#164011yescharacteristic
249C2×C17#164211yescharacteristic
250C2×C17#203411yescharacteristic
251C2×C17#203711yescharacteristic
252C2×C17#204211yescharacteristic
253C22×Q8D4×C1711yescharacteristic
254C22×D4—21no—
255C22×D4—21no—
256C22×D4D4×C1712yes—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260#127—21no—
261#127—21no—
262#127—21no—
263#127—21no—
264#124—42no—
265#124—42no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4D4×C1711yescharacteristic
275C2×C4⋊C4D4×C1711yescharacteristic
276C2×C4⋊C4D4×C1711yescharacteristic
277C2×C22⋊C4—22no—
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—22no—
281C2×C42—21no—
282C2×C42—21no—
283C2×C42C23×C1711yescharacteristic
284#106—42no—
285C4⋊C8—21no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8D4×C1712yes—
289#103—42no—
290#102—44no—
291C4×C8—21no—
292C4×C8—21no—
293#95—21no—
294C17#1041011yescharacteristic, direct product factor, Sylow
295C24—22no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8SD16×C1712yes—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4C2×D4×C1711yescharacteristic
324C22×C4C2×D4×C1711yescharacteristic
325C22×C4C2×D4×C1711yescharacteristic
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C22⋊C4—44no—
349C22⋊C4—44no—
350C22⋊C4—82no—
351C22⋊C4—82no—
352C42—41no—
353C42—41no—
354C42—41no—
355C42—41no—
356C42C2×D4×C1711yescharacteristic
357C42#41×C1711yescharacteristic
358C42#41×C1711yescharacteristic
359C42#41×C1711yescharacteristic
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23C17×#12011yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372D4—44no—
373D4—82no—
374D4—81no—
375D4—81no—
376D4—81no—
377D4—81no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C17×#12111yescharacteristic
400C2×C4C17×#12111yescharacteristic
401C2×C4C17×#12111yescharacteristic
402C2×C4C17×#12311yescharacteristic
403C2×C4C17×#12311yescharacteristic
404C2×C4C17×#12411yescharacteristic
405C2×C4C2×SD16×C1711yescharacteristic
406C2×C4C17×#13511yescharacteristic
407C2×C4C17×#13511yescharacteristic
408C2×C4C17×#13511yescharacteristic
409C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
410C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
411C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
412C2×C4C17×#13711yescharacteristic
413C8—42no—
414C8—42no—
415C8—81no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—82no—
422C22—82no—
423C22C17×#39411yescharacteristic
424C22C17×#44911yescharacteristic
425C22C17×#44911yescharacteristic
426C22C17×#45011yescharacteristic
427C22C17×#45211yescharacteristic
428C22C17×#45311yescharacteristic
429C22C17×#45511yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—81no—
435C4—81no—
436C4—161no—
437C4C17×#46311yescharacteristic
438C4C17×#46411yescharacteristic
439C4C17×#46511yescharacteristic
440C4C17×#46911yescharacteristic
441C4C17×#48111yescharacteristic
442C4C17×#48211yescharacteristic
443C4C17×#48811yescharacteristic
444C4C17×#48911yescharacteristic
445C2—162no—
446C2C17×#162011yescharacteristic
447C2C17×#163111yescharacteristic
448C2C17×#164011yescharacteristic
449C2C17×#164211yescharacteristic
450C2C17×#203411yescharacteristic
451C2C17×#203711yescharacteristic
452C2C17×#204211yescharacteristic
subgroupG/H
center, socleC23×C17#120
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC2×C17×#127C22
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
3. C17×#1948C2semidirect
4. C17×#1803C2semidirect
6. C2×C17×Q8⋊C8C2semidirect
7. C17×#1279C2semidirect
133. #10410C17direct (N × H)
192. #1948C2×C17semidirect
193. #1803C2×C17semidirect
195. C2×Q8⋊C8C2×C17semidirect
196. #1279C2×C17semidirect
294. C17#10410direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#25482
C17×#19572
C17×#19482
C17×#18032
C2×C17×#3312
C2×C17×Q8⋊C82
C17×#12792
#1041017