Finite Group Databasebeta

← C17×#10460 #16868204

Subgroups — C17×#10460 #16868204

Order 4352.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3077C211yesmaximal, characteristic
2C17×#1800C211yesmaximal, characteristic
3C17×#1566C211yesmaximal, characteristic, complemented
4C17×#1550C211yesmaximal, characteristic, complemented
5C17×#1493C211yesmaximal, characteristic, complemented
6C2×C17×D4⋊C8C211yesmaximal, characteristic
7C17×#1292C211yesmaximal, characteristic, complemented
8C17×#533C2211yescharacteristic
9C2×C4×D4×C17C2211yescharacteristic
10C17×#478—22no—
11C17×#476—21no—
12C17×#474—21no—
13C17×#428—21no—
14C17×#423C2211yescharacteristic
15C17×#423C2211yescharacteristic
16C17×#423C2211yescharacteristic
17C2×C17×C4⋊C8C2211yescharacteristic
18C17×#418—21no—
19C2×C17×#100—21no—
20C2×C4×C8×C17C2211yescharacteristic
21C17×#343—21no—
22C17×#334—22no—
23C17×#333—21no—
24C17×#332—21no—
25C17×Q8⋊C8—21no—
26C17×Q8⋊C8—21no—
27C17×D4⋊C8—21no—
28C17×D4⋊C8—21no—
29C22×D4×C17D411yescharacteristic
30C23×C4×C17—21no—
31C2×M16×C17—21no—
32C2×M16×C17—21no—
33C2×M16×C17—21no—
34C22×C8×C17—21no—
35C22×C8×C17—21no—
36C17×C4⋊Q8D411yescharacteristic
37C17×C4⋊Q8D411yescharacteristic
38C17×#125—21no—
39C17×C22⋊Q8—21no—
40C17×C22⋊Q8—21no—
41C4×Q8×C17—21no—
42C4×Q8×C17—21no—
43C4×D4×C17—21no—
44C4×D4×C17—21no—
45C4×D4×C17—21no—
46C4×D4×C17—21no—
47C17×#117—21no—
48C2×C4⋊C4×C17D411yescharacteristic
49C2×C22⋊C4×C17—21no—
50C2×C42×C17C2311yescharacteristic
51C17×#107—22no—
52C17×#106—22no—
53C17×C4⋊C8—21no—
54C17×C4⋊C8—21no—
55C17×C4⋊C8—21no—
56C17×C4⋊C8—21no—
57C17×C4⋊C8—21no—
58C17×C4⋊C8—21no—
59C17×C4⋊C8—21no—
60C17×C4⋊C8D412yes—
61C17×#102—22no—
62C17×#102—22no—
63C17×#100—42no—
64C4×C8×C17—21no—
65C4×C8×C17D411yescharacteristic
66C4×C8×C17D411yescharacteristic
67C24×C17—21no—
68C2×Q8×C17—21no—
69C2×Q8×C17—21no—
70C2×D4×C17—21no—
71C2×D4×C17—21no—
72C2×D4×C17—21no—
73C2×D4×C17—21no—
74C2×D4×C17—21no—
75C2×D4×C17SD1612yes—
76C22×C4×C17—21no—
77C22×C4×C17—41no—
78C22×C4×C17—41no—
79C22×C4×C17—81no—
80C22×C4×C17—81no—
81C22×C4×C17C2×D411yescharacteristic
82C22×C4×C17#4111yescharacteristic
83C22×C4×C17#4111yescharacteristic
84M16×C17—41no—
85M16×C17—41no—
86M16×C17—41no—
87M16×C17—41no—
88M16×C17—41no—
89M16×C17—41no—
90C2×C8×C17—21no—
91C2×C8×C17—22no—
92C2×C8×C17—21no—
93C2×C8×C17—42no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C2×C8×C17—41no—
97C2×C8×C17—81no—
98C4⋊C4×C17—21no—
99C4⋊C4×C17—21no—
100C4⋊C4×C17—21no—
101C4⋊C4×C17—21no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C22⋊C4×C17—41no—
107C22⋊C4×C17—41no—
108C22⋊C4×C17—41no—
109C42×C17—41no—
110C42×C17C2×D411yescharacteristic
111C42×C17C2×D411yescharacteristic
112C42×C17C2×D411yescharacteristic
113C42×C17#4111yescharacteristic
114#10460C1711yesmaximal, characteristic, direct product factor, Sylow
115C23×C17—22no—
116C23×C17—41no—
117C23×C17—41no—
118C23×C17—81no—
119C23×C17—81no—
120C23×C17#12311yescharacteristic
121Q8×C17—41no—
122Q8×C17—41no—
123Q8×C17—81no—
124D4×C17—22no—
125D4×C17—22no—
126D4×C17—41no—
127D4×C17—41no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17—82no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17#12011yescharacteristic
139C2×C4×C17#12111yescharacteristic
140C2×C4×C17#12111yescharacteristic
141C2×C4×C17#12111yescharacteristic
142C2×C4×C17#12311yescharacteristic
143C2×C4×C17#12411yescharacteristic
144C2×C4×C17C2×SD1611yescharacteristic
145C2×C4×C17#13511yescharacteristic
146C2×C4×C17#13711yescharacteristic
147C2×C4×C17#13711yescharacteristic
148C8×C17—22no—
149C8×C17—41no—
150C8×C17—42no—
151C8×C17—81no—
152C8×C17—81no—
153C8×C17—81no—
154#3077C2×C1711yescharacteristic
155#1800C2×C1711yescharacteristic
156#1566C2×C1711yescharacteristic, complemented
157#1550C2×C1711yescharacteristic, complemented
158#1493C2×C1711yescharacteristic, complemented
159C2×D4⋊C8C2×C1711yescharacteristic
160#1292C2×C1711yescharacteristic, complemented
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—42no—
164C22×C17—82no—
165C22×C17—82no—
166C22×C17—81no—
167C22×C17—81no—
168C22×C17#39411yescharacteristic
169C22×C17#48311yescharacteristic
170C22×C17#48511yescharacteristic
171C4×C17—21no—
172C4×C17—21no—
173C4×C17—21no—
174C4×C17—81no—
175C4×C17—81no—
176C4×C17—81no—
177C4×C17#44811yescharacteristic
178C4×C17#45211yescharacteristic
179C4×C17#46511yescharacteristic
180C4×C17#47011yescharacteristic
181C4×C17#47111yescharacteristic
182C4×C17#47211yescharacteristic
183#533C22×C1711yescharacteristic
184C2×C4×D4C22×C1711yescharacteristic
185#478—22no—
186#476—21no—
187#474—21no—
188#428—21no—
189#423C22×C1711yescharacteristic
190#423C22×C1711yescharacteristic
191#423C22×C1711yescharacteristic
192C2×C4⋊C8C22×C1711yescharacteristic
193#418—21no—
194C2×#100—21no—
195C2×C4×C8C22×C1711yescharacteristic
196#343—21no—
197#334—22no—
198#333—21no—
199#332—21no—
200Q8⋊C8—21no—
201Q8⋊C8—21no—
202D4⋊C8—21no—
203D4⋊C8—21no—
204C2×C17—21no—
205C2×C17—21no—
206C2×C17—82no—
207C2×C17#203511yescharacteristic
208C2×C17#205011yescharacteristic
209C2×C17#205111yescharacteristic
210C22×D4D4×C1711yescharacteristic
211C23×C4—21no—
212C2×M16—21no—
213C2×M16—21no—
214C2×M16—21no—
215C22×C8—21no—
216C22×C8—21no—
217C4⋊Q8D4×C1711yescharacteristic
218C4⋊Q8D4×C1711yescharacteristic
219#125—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×D4—21no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—21no—
228#117—21no—
229C2×C4⋊C4D4×C1711yescharacteristic
230C2×C22⋊C4—21no—
231C2×C42C23×C1711yescharacteristic
232#107—22no—
233#106—22no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8D4×C1712yes—
242#102—22no—
243#102—22no—
244#100—42no—
245C4×C8—21no—
246C4×C8D4×C1711yescharacteristic
247C4×C8D4×C1711yescharacteristic
248C17#1046011yescharacteristic, direct product factor, Sylow
249C24—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4SD16×C1712yes—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4C2×D4×C1711yescharacteristic
264C22×C4#41×C1711yescharacteristic
265C22×C4#41×C1711yescharacteristic
266M16—41no—
267M16—41no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—41no—
272C2×C8—21no—
273C2×C8—22no—
274C2×C8—21no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—81no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42—41no—
292C42C2×D4×C1711yescharacteristic
293C42C2×D4×C1711yescharacteristic
294C42C2×D4×C1711yescharacteristic
295C42#41×C1711yescharacteristic
296C23—22no—
297C23—41no—
298C23—41no—
299C23—81no—
300C23—81no—
301C23C17×#12311yescharacteristic
302Q8—41no—
303Q8—41no—
304Q8—81no—
305D4—22no—
306D4—22no—
307D4—41no—
308D4—41no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4C17×#12011yescharacteristic
320C2×C4C17×#12111yescharacteristic
321C2×C4C17×#12111yescharacteristic
322C2×C4C17×#12111yescharacteristic
323C2×C4C17×#12311yescharacteristic
324C2×C4C17×#12411yescharacteristic
325C2×C4C2×SD16×C1711yescharacteristic
326C2×C4C17×#13511yescharacteristic
327C2×C4C17×#13711yescharacteristic
328C2×C4C17×#13711yescharacteristic
329C8—22no—
330C8—41no—
331C8—42no—
332C8—81no—
333C8—81no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—82no—
339C22—82no—
340C22—81no—
341C22—81no—
342C22C17×#39411yescharacteristic
343C22C17×#48311yescharacteristic
344C22C17×#48511yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4C17×#44811yescharacteristic
352C4C17×#45211yescharacteristic
353C4C17×#46511yescharacteristic
354C4C17×#47011yescharacteristic
355C4C17×#47111yescharacteristic
356C4C17×#47211yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C17×#203511yescharacteristic
361C2C17×#205011yescharacteristic
362C2C17×#205111yescharacteristic
subgroupG/H
center, socleC22×C17#394
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC22×D4×C17D4
LCSG ▷ C2×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×#1566C2semidirect
4. C17×#1550C2semidirect
5. C17×#1493C2semidirect
7. C17×#1292C2semidirect
114. #10460C17direct (N × H)
156. #1566C2×C17semidirect
157. #1550C2×C17semidirect
158. #1493C2×C17semidirect
160. #1292C2×C17semidirect
248. C17#10460direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30772
C17×#18002
C17×#15662
C17×#15502
C17×#14932
C2×C17×D4⋊C82
C17×#12922
#1046017