Finite Group Databasebeta

← C17×#25489 #16883233

Subgroups — C17×#25489 #16883233

Order 4352.

664 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3165C211yesmaximal, characteristic, complemented
2C17×#3077C211yesmaximal, characteristic
3C2×C17×#474C211yesmaximal, characteristic
4C17×#2962C211yesmaximal, characteristic, complemented
5C17×#2089C212yesmaximal, complemented
6C17×#2063C212yesmaximal
7C17×#1997C211yesmaximal, characteristic, complemented
8C17×#1952C212yesmaximal, complemented
9C17×#1950C211yesmaximal, characteristic, complemented
10C17×#1931C212yesmaximal
11C4×C17×#100C211yesmaximal, characteristic
12C17×#533C2211yescharacteristic
13C2×C17×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C17C2211yescharacteristic
15C17×#501—22no—
16C17×#500—21no—
17C17×#498—21no—
18C17×#478—22no—
19C17×#476—21no—
20C17×#474—21no—
21C17×#474—21no—
22C17×#474—22no—
23C17×#474—21no—
24C17×#446—22no—
25C17×#446—21no—
26C8×Q8×C17—21no—
27C2×C17×#108C2212yes—
28C17×#428C2212yes—
29C17×#428C2212yes—
30C17×#428C2212yes—
31C2×C17×#107C2212yes—
32C17×#424C2212yes—
33C17×#423C2211yescharacteristic
34C2×C17×C4⋊C8C2211yescharacteristic
35C17×#418C2212yes—
36C2×C17×#102C2212yes—
37C2×C17×#100C2211yescharacteristic
38C2×C17×#100C2211yescharacteristic
39C17×#405C2212yes—
40C4×M16×C17C2211yescharacteristic
41C4×M16×C17C2211yescharacteristic
42C17×#343C2212yes—
43C17×#343C2211yescharacteristic
44C17×#343C2212yes—
45C17×#343C2211yescharacteristic
46C17×#341C2212yes—
47C22×Q8×C17—21no—
48C22×D4×C17C2311yescharacteristic
49C23×C4×C17—21no—
50C2×M16×C17C2312yes—
51C2×M16×C17C2311yescharacteristic
52C2×M16×C17C2311yescharacteristic
53C2×M16×C17C2311yescharacteristic
54C2×M16×C17C2311yescharacteristic
55C22×C8×C17C2312yes—
56C17×C4⋊Q8—21no—
57C17×C4⋊Q8—21no—
58C17×C4⋊Q8—21no—
59C17×C4⋊Q8—21no—
60C17×C4⋊Q8D411yescharacteristic
61C17×C4⋊Q8D411yescharacteristic
62C17×#125D412yes—
63C17×C22⋊Q8—21no—
64C17×C22⋊Q8—21no—
65C4×Q8×C17—21no—
66C4×Q8×C17—21no—
67C4×D4×C17—21no—
68C4×D4×C17—21no—
69C4×D4×C17—21no—
70C4×D4×C17—21no—
71C17×#117C2312yes—
72C2×C4⋊C4×C17—21no—
73C2×C4⋊C4×C17C2311yescharacteristic
74C2×C4⋊C4×C17C2312yes—
75C2×C22⋊C4×C17—21no—
76C2×C42×C17C2311yescharacteristic
77C17×#108—24no—
78C17×#107—22no—
79C17×#107—22no—
80C17×#107—22no—
81C17×#107—22no—
82C17×#107—22no—
83C17×#106—22no—
84C17×#106—22no—
85C17×#106—22no—
86C17×C4⋊C8—22no—
87C17×C4⋊C8—22no—
88C17×C4⋊C8—21no—
89C17×C4⋊C8—21no—
90C17×C4⋊C8D411yescharacteristic
91C17×C4⋊C8D411yescharacteristic
92C17×C4⋊C8D412yes—
93C17×#102—22no—
94C17×#102—22no—
95C17×#102—22no—
96C17×#102—22no—
97C17×#100—22no—
98C17×#100Q814yescomplemented
99C17×#97—22no—
100C17×#97—21no—
101C17×#97—21no—
102C4×C8×C17—22no—
103C4×C8×C17—21no—
104C4×C8×C17—21no—
105C24×C17—21no—
106C2×Q8×C17—21no—
107C2×Q8×C17—21no—
108C2×Q8×C17—41no—
109C2×Q8×C17—41no—
110C2×Q8×C17—82no—
111C2×D4×C17—21no—
112C2×D4×C17—21no—
113C2×D4×C17—21no—
114C2×D4×C17—21no—
115C2×D4×C17—21no—
116C2×D4×C17C2×Q812yes—
117C22×C4×C17—21no—
118C22×C4×C17—22no—
119C22×C4×C17—41no—
120C22×C4×C17—41no—
121C22×C4×C17—82no—
122C22×C4×C17#4111yescharacteristic
123C22×C4×C17#4111yescharacteristic
124C22×C4×C17C2411yescharacteristic
125M16×C17—21no—
126M16×C17—21no—
127M16×C17—21no—
128M16×C17—21no—
129M16×C17—22no—
130M16×C17—21no—
131M16×C17—22no—
132M16×C17C2×Q812yes—
133M16×C17C2×Q812yes—
134M16×C17#4112yes—
135C2×C8×C17—21no—
136C2×C8×C17—21no—
137C2×C8×C17—21no—
138C2×C8×C17—22no—
139C2×C8×C17—22no—
140C2×C8×C17—21no—
141C2×C8×C17—22no—
142C2×C8×C17C2×D412yes—
143C2×C8×C17C2×D412yes—
144C4⋊C4×C17—22no—
145C4⋊C4×C17—22no—
146C4⋊C4×C17—21no—
147C4⋊C4×C17—21no—
148C4⋊C4×C17—22no—
149C4⋊C4×C17—22no—
150C4⋊C4×C17—21no—
151C4⋊C4×C17—21no—
152C4⋊C4×C17—41no—
153C4⋊C4×C17—41no—
154C4⋊C4×C17C2×D412yes—
155C4⋊C4×C17C2×D412yes—
156C22⋊C4×C17—22no—
157C22⋊C4×C17—41no—
158C22⋊C4×C17—41no—
159C42×C17—22no—
160C42×C17C2×D411yescharacteristic
161C42×C17C2×D411yescharacteristic
162C42×C17C2×D411yescharacteristic
163C42×C17C2×D411yescharacteristic
164#25489C1711yesmaximal, characteristic, direct product factor, Sylow
165C23×C17—22no—
166C23×C17—41no—
167C23×C17—41no—
168C23×C17—81no—
169C23×C17—81no—
170C23×C17C2×#4111yescharacteristic
171Q8×C17—42no—
172Q8×C17—81no—
173Q8×C17—82no—
174Q8×C17—82no—
175D4×C17—22no—
176D4×C17—22no—
177D4×C17—41no—
178D4×C17—41no—
179C2×C4×C17—22no—
180C2×C4×C17—22no—
181C2×C4×C17—22no—
182C2×C4×C17—41no—
183C2×C4×C17—41no—
184C2×C4×C17—42no—
185C2×C4×C17—82no—
186C2×C4×C17—82no—
187C2×C4×C17—81no—
188C2×C4×C17—82no—
189C2×C4×C17#12111yescharacteristic
190C2×C4×C17#12111yescharacteristic
191C2×C4×C17#12111yescharacteristic
192C2×C4×C17#12111yescharacteristic
193C2×C4×C17C22×D411yescharacteristic
194C2×C4×C17C22×D411yescharacteristic
195C2×C4×C17C22×Q811yescharacteristic
196C2×C4×C17C2×#4111yescharacteristic
197C2×C4×C172−1+411yescharacteristic
198C2×C4×C172−1+411yescharacteristic
199C8×C17—22no—
200C8×C17—22no—
201C8×C17—22no—
202C8×C17—22no—
203C8×C17—22no—
204C8×C17—41no—
205C8×C17—42no—
206#3165C2×C1711yescharacteristic, complemented
207#3077C2×C1711yescharacteristic
208C2×#474C2×C1711yescharacteristic
209#2962C2×C1711yescharacteristic, complemented
210#2089C2×C1712yescomplemented
211#2063C2×C1712yes—
212#1997C2×C1711yescharacteristic, complemented
213#1952C2×C1712yescomplemented
214#1950C2×C1711yescharacteristic, complemented
215#1931C2×C1712yes—
216C4×#100C2×C1711yescharacteristic
217C22×C17—21no—
218C22×C17—21no—
219C22×C17—42no—
220C22×C17—82no—
221C22×C17—82no—
222C22×C17—81no—
223C22×C17—81no—
224C22×C17C2×#12111yescharacteristic
225C22×C17#53311yescharacteristic
226C22×C17#54111yescharacteristic
227C4×C17—21no—
228C4×C17—21no—
229C4×C17—21no—
230C4×C17—42no—
231C4×C17—42no—
232C4×C17—81no—
233C4×C17—82no—
234C4×C17#47212yes—
235C4×C17#54711yescharacteristic
236C4×C17#54811yescharacteristic
237C4×C17D4×Q811yescharacteristic
238C4×C17D4×Q811yescharacteristic
239#533C22×C1711yescharacteristic
240C2×C4⋊Q8C22×C1711yescharacteristic
241C2×C4×D4C22×C1711yescharacteristic
242#501—22no—
243#500—21no—
244#498—21no—
245#478—22no—
246#476—21no—
247#474—21no—
248#474—21no—
249#474—22no—
250#474—21no—
251#446—22no—
252#446—21no—
253C8×Q8—21no—
254C2×#108C22×C1712yes—
255#428C22×C1712yes—
256#428C22×C1712yes—
257#428C22×C1712yes—
258C2×#107C22×C1712yes—
259#424C22×C1712yes—
260#423C22×C1711yescharacteristic
261C2×C4⋊C8C22×C1711yescharacteristic
262#418C22×C1712yes—
263C2×#102C22×C1712yes—
264C2×#100C22×C1711yescharacteristic
265C2×#100C22×C1711yescharacteristic
266#405C22×C1712yes—
267C4×M16C22×C1711yescharacteristic
268C4×M16C22×C1711yescharacteristic
269#343C22×C1712yes—
270#343C22×C1711yescharacteristic
271#343C22×C1712yes—
272#343C22×C1711yescharacteristic
273#341C22×C1712yes—
274C2×C17—21no—
275C2×C17—21no—
276C2×C17—82no—
277C2×C17#242911yescharacteristic
278C2×C17C2×#47211yescharacteristic
279C2×C17#306911yescharacteristic
280C22×Q8—21no—
281C22×D4C23×C1711yescharacteristic
282C23×C4—21no—
283C2×M16C23×C1712yes—
284C2×M16C23×C1711yescharacteristic
285C2×M16C23×C1711yescharacteristic
286C2×M16C23×C1711yescharacteristic
287C2×M16C23×C1711yescharacteristic
288C22×C8C23×C1712yes—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8D4×C1711yescharacteristic
294C4⋊Q8D4×C1711yescharacteristic
295#125D4×C1712yes—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304#117C23×C1712yes—
305C2×C4⋊C4—21no—
306C2×C4⋊C4C23×C1711yescharacteristic
307C2×C4⋊C4C23×C1712yes—
308C2×C22⋊C4—21no—
309C2×C42C23×C1711yescharacteristic
310#108—24no—
311#107—22no—
312#107—22no—
313#107—22no—
314#107—22no—
315#107—22no—
316#106—22no—
317#106—22no—
318#106—22no—
319C4⋊C8—22no—
320C4⋊C8—22no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8D4×C1711yescharacteristic
324C4⋊C8D4×C1711yescharacteristic
325C4⋊C8D4×C1712yes—
326#102—22no—
327#102—22no—
328#102—22no—
329#102—22no—
330#100—22no—
331#100Q8×C1714yescomplemented
332#97—22no—
333#97—21no—
334#97—21no—
335C4×C8—22no—
336C4×C8—21no—
337C4×C8—21no—
338C17#2548911yescharacteristic, direct product factor, Sylow
339C24—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—82no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4C2×Q8×C1712yes—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—82no—
356C22×C4#41×C1711yescharacteristic
357C22×C4#41×C1711yescharacteristic
358C22×C4C24×C1711yescharacteristic
359M16—21no—
360M16—21no—
361M16—21no—
362M16—21no—
363M16—22no—
364M16—21no—
365M16—22no—
366M16C2×Q8×C1712yes—
367M16C2×Q8×C1712yes—
368M16#41×C1712yes—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8C2×D4×C1712yes—
377C2×C8C2×D4×C1712yes—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4C2×D4×C1712yes—
389C4⋊C4C2×D4×C1712yes—
390C22⋊C4—22no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C42—22no—
394C42C2×D4×C1711yescharacteristic
395C42C2×D4×C1711yescharacteristic
396C42C2×D4×C1711yescharacteristic
397C42C2×D4×C1711yescharacteristic
398C23—22no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23C2×#41×C1711yescharacteristic
404Q8—42no—
405Q8—81no—
406Q8—82no—
407Q8—82no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—81no—
421C2×C4—82no—
422C2×C4C17×#12111yescharacteristic
423C2×C4C17×#12111yescharacteristic
424C2×C4C17×#12111yescharacteristic
425C2×C4C17×#12111yescharacteristic
426C2×C4C22×D4×C1711yescharacteristic
427C2×C4C22×D4×C1711yescharacteristic
428C2×C4C22×Q8×C1711yescharacteristic
429C2×C4C2×#41×C1711yescharacteristic
430C2×C4C17×2−1+411yescharacteristic
431C2×C4C17×2−1+411yescharacteristic
432C8—22no—
433C8—22no—
434C8—22no—
435C8—22no—
436C8—22no—
437C8—41no—
438C8—42no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—82no—
443C22—82no—
444C22—81no—
445C22—81no—
446C22C2×C17×#12111yescharacteristic
447C22C17×#53311yescharacteristic
448C22C17×#54111yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—42no—
453C4—42no—
454C4—81no—
455C4—82no—
456C4C17×#47212yes—
457C4C17×#54711yescharacteristic
458C4C17×#54811yescharacteristic
459C4D4×Q8×C1711yescharacteristic
460C4D4×Q8×C1711yescharacteristic
461C2—21no—
462C2—21no—
463C2—82no—
464C2C17×#242911yescharacteristic
465C2C2×C17×#47211yescharacteristic
466C2C17×#306911yescharacteristic
subgroupG/H
center, socleC22×C17C2×#121
commutator, Frattini, cosocleC22×C4C24×C17
prime radicalC22×D4×C17C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3165C2semidirect
4. C17×#2962C2semidirect
5. C17×#2089C2semidirect
7. C17×#1997C2semidirect
8. C17×#1952C2semidirect
9. C17×#1950C2semidirect
98. C17×#100Q8semidirect
164. #25489C17direct (N × H)
206. #3165C2×C17semidirect
209. #2962C2×C17semidirect
210. #2089C2×C17semidirect
212. #1997C2×C17semidirect
213. #1952C2×C17semidirect
214. #1950C2×C17semidirect
331. #100Q8×C17semidirect
338. C17#25489direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#31652
C17×#30772
C2×C17×#4742
C17×#29622
C17×#20892
C17×#20632
C17×#19972
C17×#19522
C17×#19502
C17×#19312
C4×C17×#1002
#2548917