Finite Group Databasebeta

← C17×#9169 #16866913

Subgroups — C17×#9169 #16866913

Order 4352.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3079C211yesmaximal, characteristic
2C17×#2906C211yesmaximal, characteristic
3C17×#1549C211yesmaximal, characteristic, complemented
4C2×C17×#333C211yesmaximal, characteristic, complemented
5C17×#1477C211yesmaximal, characteristic
6C17×#1301C211yesmaximal, characteristic, complemented
7C17×#1292C211yesmaximal, characteristic, complemented
8C2×C17×#131—21no—
9C2×C17×C4⋊Q8C2211yescharacteristic
10C4×#41×C17C2211yescharacteristic
11C17×#477—21no—
12C17×#476—21no—
13C17×#475C412yes—
14C17×#474C412yes—
15C17×#431C2211yescharacteristic
16C17×#428—21no—
17C17×#424—21no—
18C17×#424—22no—
19C17×#423—21no—
20C17×#423C2211yescharacteristic
21C17×#423C2211yescharacteristic
22C2×C17×C4⋊C8—21no—
23C2×C17×C4⋊C8C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C17×#417—21no—
26C17×#333—21no—
27C17×#333—21no—
28C17×#332—22no—
29C17×Q8⋊C8—21no—
30C17×D4⋊C8—21no—
31C2×#41×C17D411yescharacteristic
32C22×Q8×C17—21no—
33C17×#131—42no—
34C17×#131—42no—
35C2×M16×C17—22no—
36C2×M16×C17—21no—
37C2×M16×C17—21no—
38C22×C8×C17—22no—
39C22×C8×C17—21no—
40C22×C8×C17—21no—
41C17×C4⋊Q8—21no—
42C17×C4⋊Q8—21no—
43C17×C4⋊Q8—21no—
44C17×C4⋊Q8C2×C412yes—
45C4×Q8×C17C2×C411yescharacteristic
46C4×Q8×C17D411yescharacteristic
47C4×D4×C17—21no—
48C4×D4×C17—21no—
49C4×D4×C17C2×C411yescharacteristic
50C4×D4×C17D411yescharacteristic
51C17×#117—21no—
52C17×#117D411yescharacteristic
53C2×C4⋊C4×C17—21no—
54C2×C4⋊C4×C17—21no—
55C2×C42×C17—21no—
56C2×C42×C17C2311yescharacteristic
57C17×#107—22no—
58C17×#106—22no—
59C17×C4⋊C8—22no—
60C17×C4⋊C8—22no—
61C17×C4⋊C8—21no—
62C17×C4⋊C8—21no—
63C17×C4⋊C8—21no—
64C17×C4⋊C8—21no—
65C17×C4⋊C8—21no—
66C17×C4⋊C8—21no—
67C17×C4⋊C8C2×C412yes—
68C17×C4⋊C8D412yes—
69C17×C4⋊C8D411yescharacteristic
70C17×C4⋊C8D411yescharacteristic
71C17×#103—22no—
72C17×#102—22no—
73C17×C22⋊C8—21no—
74C4×C8×C17—21no—
75#41×C17—21no—
76#41×C17—21no—
77#41×C17SD1612yes—
78#41×C17Q1612yes—
79C2×Q8×C17—22no—
80C2×Q8×C17—41no—
81C2×Q8×C17—82no—
82C2×Q8×C17C22⋊C411yescharacteristic
83C2×D4×C17—21no—
84C2×D4×C17C22⋊C411yescharacteristic
85C22×C4×C17—21no—
86C22×C4×C17—21no—
87C22×C4×C17—21no—
88C22×C4×C17—41no—
89C22×C4×C17C2×D411yescharacteristic
90C22×C4×C17#4111yescharacteristic
91C22×C4×C17#4111yescharacteristic
92M16×C17—44no—
93M16×C17—41no—
94M16×C17—41no—
95M16×C17—41no—
96M16×C17—41no—
97C2×C8×C17—22no—
98C2×C8×C17—21no—
99C2×C8×C17—22no—
100C2×C8×C17—21no—
101C2×C8×C17—44no—
102C2×C8×C17—41no—
103C2×C8×C17—41no—
104C2×C8×C17—41no—
105C2×C8×C17—41no—
106C2×C8×C17—81no—
107C4⋊C4×C17—21no—
108C4⋊C4×C17—21no—
109C4⋊C4×C17—22no—
110C4⋊C4×C17—22no—
111C4⋊C4×C17—41no—
112C4⋊C4×C17—41no—
113C4⋊C4×C17C22⋊C411yescharacteristic
114C4⋊C4×C17C22⋊C411yescharacteristic
115C22⋊C4×C17—21no—
116C22⋊C4×C17—21no—
117C22⋊C4×C17—21no—
118C42×C17—21no—
119C42×C17—21no—
120C42×C17—21no—
121C42×C17C22×C411yescharacteristic
122C42×C17C2×D411yescharacteristic
123C42×C17C2×D411yescharacteristic
124C42×C17C2×D411yescharacteristic
125#9169C1711yesmaximal, characteristic, direct product factor, Sylow
126C23×C17—21no—
127C23×C17#12311yescharacteristic
128Q8×C17—21no—
129Q8×C17—82no—
130Q8×C17—82no—
131Q8×C17#10312yes—
132D4×C17—22no—
133D4×C17—22no—
134D4×C17—21no—
135D4×C17#10312yes—
136C2×C4×C17—21no—
137C2×C4×C17—22no—
138C2×C4×C17—22no—
139C2×C4×C17—21no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—42no—
147C2×C4×C17—81no—
148C2×C4×C17—82no—
149C2×C4×C17C2×C22⋊C411yescharacteristic
150C2×C4×C17C4×D411yescharacteristic
151C2×C4×C17C4×D411yescharacteristic
152C2×C4×C17#12011yescharacteristic
153C2×C4×C17#12111yescharacteristic
154C2×C4×C17#12111yescharacteristic
155C2×C4×C17C2×SD1611yescharacteristic
156C2×C4×C17C2×Q1611yescharacteristic
157C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C17#13711yescharacteristic
159C8×C17—42no—
160C8×C17—41no—
161C8×C17—42no—
162C8×C17—41no—
163C8×C17—81no—
164C8×C17—81no—
165#3079C2×C1711yescharacteristic
166#2906C2×C1711yescharacteristic
167#1549C2×C1711yescharacteristic, complemented
168C2×#333C2×C1711yescharacteristic, complemented
169#1477C2×C1711yescharacteristic
170#1301C2×C1711yescharacteristic, complemented
171#1292C2×C1711yescharacteristic, complemented
172C22×C17—21no—
173C22×C17—21no—
174C22×C17—22no—
175C22×C17—41no—
176C22×C17—41no—
177C22×C17#38611yescharacteristic
178C22×C17#48311yescharacteristic
179C22×C17#48411yescharacteristic
180C4×C17—22no—
181C4×C17—21no—
182C4×C17—21no—
183C4×C17—21no—
184C4×C17—41no—
185C4×C17—41no—
186C4×C17—82no—
187C4×C17C2×#10311yescharacteristic
188C4×C17#41711yescharacteristic
189C4×C17#45011yescharacteristic
190C4×C17#45111yescharacteristic
191C4×C17#47111yescharacteristic
192C4×C17#47311yescharacteristic
193C2×#131—21no—
194C2×C4⋊Q8C22×C1711yescharacteristic
195C4×#41C22×C1711yescharacteristic
196#477—21no—
197#476—21no—
198#475C4×C1712yes—
199#474C4×C1712yes—
200#431C22×C1711yescharacteristic
201#428—21no—
202#424—21no—
203#424—22no—
204#423—21no—
205#423C22×C1711yescharacteristic
206#423C22×C1711yescharacteristic
207C2×C4⋊C8—21no—
208C2×C4⋊C8C22×C1711yescharacteristic
209C2×C4⋊C8C22×C1711yescharacteristic
210#417—21no—
211#333—21no—
212#333—21no—
213#332—22no—
214Q8⋊C8—21no—
215D4⋊C8—21no—
216C2×C17—21no—
217C2×C17—21no—
218C2×C17—42no—
219C2×C17#187211yescharacteristic
220C2×C17#190311yescharacteristic
221C2×C17#190811yescharacteristic
222C2×#41D4×C1711yescharacteristic
223C22×Q8—21no—
224#131—42no—
225#131—42no—
226C2×M16—22no—
227C2×M16—21no—
228C2×M16—21no—
229C22×C8—22no—
230C22×C8—21no—
231C22×C8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8C2×C4×C1712yes—
236C4×Q8C2×C4×C1711yescharacteristic
237C4×Q8D4×C1711yescharacteristic
238C4×D4—21no—
239C4×D4—21no—
240C4×D4C2×C4×C1711yescharacteristic
241C4×D4D4×C1711yescharacteristic
242#117—21no—
243#117D4×C1711yescharacteristic
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C42—21no—
247C2×C42C23×C1711yescharacteristic
248#107—22no—
249#106—22no—
250C4⋊C8—22no—
251C4⋊C8—22no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8C2×C4×C1712yes—
259C4⋊C8D4×C1712yes—
260C4⋊C8D4×C1711yescharacteristic
261C4⋊C8D4×C1711yescharacteristic
262#103—22no—
263#102—22no—
264C22⋊C8—21no—
265C4×C8—21no—
266C17#916911yescharacteristic, direct product factor, Sylow
267#41—21no—
268#41—21no—
269#41SD16×C1712yes—
270#41Q16×C1712yes—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—82no—
274C2×Q8C22⋊C4×C1711yescharacteristic
275C2×D4—21no—
276C2×D4C22⋊C4×C1711yescharacteristic
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4C2×D4×C1711yescharacteristic
282C22×C4#41×C1711yescharacteristic
283C22×C4#41×C1711yescharacteristic
284M16—44no—
285M16—41no—
286M16—41no—
287M16—41no—
288M16—41no—
289C2×C8—22no—
290C2×C8—21no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—44no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—81no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4C22⋊C4×C1711yescharacteristic
306C4⋊C4C22⋊C4×C1711yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—21no—
310C42—21no—
311C42—21no—
312C42—21no—
313C42C22×C4×C1711yescharacteristic
314C42C2×D4×C1711yescharacteristic
315C42C2×D4×C1711yescharacteristic
316C42C2×D4×C1711yescharacteristic
317C23—21no—
318C23C17×#12311yescharacteristic
319Q8—21no—
320Q8—82no—
321Q8—82no—
322Q8C17×#10312yes—
323D4—22no—
324D4—22no—
325D4—21no—
326D4C17×#10312yes—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4C2×C22⋊C4×C1711yescharacteristic
341C2×C4C4×D4×C1711yescharacteristic
342C2×C4C4×D4×C1711yescharacteristic
343C2×C4C17×#12011yescharacteristic
344C2×C4C17×#12111yescharacteristic
345C2×C4C17×#12111yescharacteristic
346C2×C4C2×SD16×C1711yescharacteristic
347C2×C4C2×Q16×C1711yescharacteristic
348C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
349C2×C4C17×#13711yescharacteristic
350C8—42no—
351C8—41no—
352C8—42no—
353C8—41no—
354C8—81no—
355C8—81no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22C17×#38611yescharacteristic
362C22C17×#48311yescharacteristic
363C22C17×#48411yescharacteristic
364C4—22no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—82no—
371C4C2×C17×#10311yescharacteristic
372C4C17×#41711yescharacteristic
373C4C17×#45011yescharacteristic
374C4C17×#45111yescharacteristic
375C4C17×#47111yescharacteristic
376C4C17×#47311yescharacteristic
377C2—21no—
378C2—21no—
379C2—42no—
380C2C17×#187211yescharacteristic
381C2C17×#190311yescharacteristic
382C2C17×#190811yescharacteristic
subgroupG/H
center, socleC22×C17#386
commutatorC42C22×C4×C17
Frattini, cosocleC2×C42C23×C17
prime radicalC2×#41×C17D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
3. C17×#1549C2semidirect
4. C2×C17×#333C2semidirect
6. C17×#1301C2semidirect
7. C17×#1292C2semidirect
125. #9169C17direct (N × H)
167. #1549C2×C17semidirect
168. C2×#333C2×C17semidirect
170. #1301C2×C17semidirect
171. #1292C2×C17semidirect
266. C17#9169direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30792
C17×#29062
C17×#15492
C2×C17×#3332
C17×#14772
C17×#13012
C17×#12922
#916917