Finite Group Databasebeta

← C17×#21794 #16879538

Subgroups — C17×#21794 #16879538

Order 4352.

1394 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#532C211yesmaximal, characteristic
2C17×#2283C212yesmaximal, complemented
3C17×#1964C218yesmaximal, complemented
4C17×#1782C214yesmaximal, complemented
5C22×#41×C17C2212yes—
6C17×#532—22no—
7C17×#532—22no—
8C17×#532—22no—
9C17×#532—22no—
10C2×C17×C4⋊Q8C411yescharacteristic, complemented
11C2×C17×#127C411yescharacteristic, complemented
12C2×C17×#124C412yescomplemented
13C2×C17×#121C2214yes—
14C2×C4×D4×C17C414yescomplemented
15C22×C42×C17C2211yescharacteristic
16C2×C17×#99C22116yes—
17C17×#383—22no—
18C17×#382—22no—
19C17×#381C2214yes—
20C17×#380C2214yes—
21C4×C4⋊C4×C17—22no—
22C4×C22⋊C4×C17C2214yes—
23C17×#376—22no—
24C2×#41×C17—24no—
25C2×#41×C17—24no—
26C2×#41×C17—48no—
27C22×Q8×C17C2×C412yes—
28C22×D4×C17C2×C414yes—
29C22×D4×C17C2×C412yes—
30C22×D4×C17C2314yes—
31C23×C4×C17C2×C414yes—
32C23×C4×C17C2311yescharacteristic
33C23×C4×C17C2312yes—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—22no—
36C17×C4⋊Q8—21no—
37C17×#127—21no—
38C17×#127—22no—
39C17×#127—21no—
40C17×#124—22no—
41C17×#124—24no—
42C17×#124—22no—
43C17×#121—24no—
44C17×#121—24no—
45C17×#121—24no—
46C17×#121—24no—
47C4×D4×C17—24no—
48C4×D4×C17—24no—
49C4×D4×C17—24no—
50C4×D4×C17—24no—
51C2×C4⋊C4×C17—24no—
52C2×C4⋊C4×C17C2×C414yes—
53C2×C22⋊C4×C17C2×C418yes—
54C2×C22⋊C4×C17C2318yes—
55C2×C42×C17—24no—
56C2×C42×C17C2×C412yes—
57C2×C42×C17C2×C411yescharacteristic
58C2×C42×C17C2×C411yescharacteristic
59C2×C42×C17D412yes—
60C2×C42×C17D412yes—
61C2×C42×C17D412yes—
62C2×C42×C17D412yes—
63C17×#99—416no—
64C17×#95—24no—
65C17×#95—24no—
66C17×#95—24no—
67C17×#95—24no—
68C24×C17C22×C414yes—
69C24×C17C2411yescharacteristic
70#41×C17—416no—
71#41×C17—416no—
72C2×Q8×C17—22no—
73C2×Q8×C17—22no—
74C2×Q8×C17—44no—
75C2×D4×C17—28no—
76C2×D4×C17—216no—
77C2×D4×C17—22no—
78C2×D4×C17—22no—
79C2×D4×C17—24no—
80C2×D4×C17—24no—
81C2×D4×C17—44no—
82C2×D4×C17—48no—
83C22×C4×C17—24no—
84C22×C4×C17—28no—
85C22×C4×C17—28no—
86C22×C4×C17—44no—
87C22×C4×C17—48no—
88C22×C4×C17C22×C414yes—
89C22×C4×C17C22×C411yescharacteristic
90C22×C4×C17C22×C411yescharacteristic
91C22×C4×C17C22×C412yes—
92C22×C4×C17C22×C412yes—
93C22×C4×C17C2×D412yes—
94C22×C4×C17C2×D412yes—
95C22×C4×C17C2×D412yes—
96C22×C4×C17C2×D412yes—
97C22×C4×C17C2×D412yes—
98C22×C4×C17C2×D412yes—
99C4⋊C4×C17—24no—
100C4⋊C4×C17—24no—
101C4⋊C4×C17—48no—
102C22⋊C4×C17—28no—
103C22⋊C4×C17—28no—
104C22⋊C4×C17—216no—
105C42×C17—48no—
106C42×C17C22⋊C411yescharacteristic
107C42×C17C22⋊C412yes—
108C42×C17C22⋊C411yescharacteristic
109C42×C17C22⋊C411yescharacteristic
110C42×C17C22⋊C412yes—
111C42×C17C22⋊C411yescharacteristic
112C42×C17C22⋊C412yes—
113C42×C17C22⋊C412yes—
114C42×C17C22⋊C412yes—
115C42×C17C22⋊C412yes—
116#21794C1711yesmaximal, characteristic, direct product factor, Sylow
117C23×C17—24no—
118C23×C17—28no—
119C23×C17—42no—
120C23×C17—48no—
121C23×C17C23×C411yescharacteristic
122C23×C17C22×D412yes—
123C23×C17H(5,𝔽2)14yes—
124Q8×C17—44no—
125Q8×C17—44no—
126D4×C17—48no—
127D4×C17—44no—
128D4×C17—44no—
129D4×C17—416no—
130D4×C17—48no—
131C2×C4×C17—22no—
132C2×C4×C17—22no—
133C2×C4×C17—24no—
134C2×C4×C17—24no—
135C2×C4×C17—24no—
136C2×C4×C17—24no—
137C2×C4×C17—24no—
138C2×C4×C17—24no—
139C2×C4×C17—28no—
140C2×C4×C17—42no—
141C2×C4×C17—42no—
142C2×C4×C17—42no—
143C2×C4×C17—416no—
144C2×C4×C17—48no—
145C2×C4×C17—48no—
146C2×C4×C17—48no—
147C2×C4×C17C2×C22⋊C412yes—
148C2×C4×C17C2×C22⋊C412yes—
149C2×C4×C17C2×C22⋊C412yes—
150C2×C4×C17C2×C22⋊C412yes—
151C2×C4×C17C2×C22⋊C411yescharacteristic
152C2×C4×C17C2×C22⋊C411yescharacteristic
153C2×C4×C17C2×C22⋊C412yes—
154C2×#532C2×C1711yescharacteristic
155#2283C2×C1712yescomplemented
156#1964C2×C1718yescomplemented
157#1782C2×C1714yescomplemented
158C22×C17—22no—
159C22×C17—22no—
160C22×C17—22no—
161C22×C17—44no—
162C22×C17—44no—
163C22×C17—48no—
164C22×C17—88no—
165C22×C17C22×C22⋊C411yescharacteristic
166C22×C17#51812yes—
167C22×C17#53514yes—
168C4×C17—22no—
169C4×C17—21no—
170C4×C17—21no—
171C4×C17—22no—
172C4×C17—22no—
173C4×C17—22no—
174C4×C17—44no—
175C4×C17—88no—
176C4×C17#41014yes—
177C22×#41C22×C1712yes—
178#532—22no—
179#532—22no—
180#532—22no—
181#532—22no—
182C2×C4⋊Q8C4×C1711yescharacteristic, complemented
183C2×#127C4×C1711yescharacteristic, complemented
184C2×#124C4×C1712yescomplemented
185C2×#121C22×C1714yes—
186C2×C4×D4C4×C1714yescomplemented
187C22×C42C22×C1711yescharacteristic
188C2×#99C22×C17116yes—
189#383—22no—
190#382—22no—
191#381C22×C1714yes—
192#380C22×C1714yes—
193C4×C4⋊C4—22no—
194C4×C22⋊C4C22×C1714yes—
195#376—22no—
196C2×C17—24no—
197C2×C17—22no—
198C2×C17—84no—
199C2×C17#230911yescharacteristic
200C2×C17C2×#41012yes—
201C2×#41—24no—
202C2×#41—24no—
203C2×#41—48no—
204C22×Q8C2×C4×C1712yes—
205C22×D4C2×C4×C1714yes—
206C22×D4C2×C4×C1712yes—
207C22×D4C23×C1714yes—
208C23×C4C2×C4×C1714yes—
209C23×C4C23×C1711yescharacteristic
210C23×C4C23×C1712yes—
211C4⋊Q8—21no—
212C4⋊Q8—22no—
213C4⋊Q8—21no—
214#127—21no—
215#127—22no—
216#127—21no—
217#124—22no—
218#124—24no—
219#124—22no—
220#121—24no—
221#121—24no—
222#121—24no—
223#121—24no—
224C4×D4—24no—
225C4×D4—24no—
226C4×D4—24no—
227C4×D4—24no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4C2×C4×C1714yes—
230C2×C22⋊C4C2×C4×C1718yes—
231C2×C22⋊C4C23×C1718yes—
232C2×C42—24no—
233C2×C42C2×C4×C1712yes—
234C2×C42C2×C4×C1711yescharacteristic
235C2×C42C2×C4×C1711yescharacteristic
236C2×C42D4×C1712yes—
237C2×C42D4×C1712yes—
238C2×C42D4×C1712yes—
239C2×C42D4×C1712yes—
240#99—416no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—24no—
245C17#2179411yescharacteristic, direct product factor, Sylow
246C24C22×C4×C1714yes—
247C24C24×C1711yescharacteristic
248#41—416no—
249#41—416no—
250C2×Q8—22no—
251C2×Q8—22no—
252C2×Q8—44no—
253C2×D4—28no—
254C2×D4—216no—
255C2×D4—24no—
256C2×D4—24no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—44no—
260C2×D4—48no—
261C22×C4—24no—
262C22×C4—28no—
263C22×C4—28no—
264C22×C4—44no—
265C22×C4—48no—
266C22×C4C22×C4×C1714yes—
267C22×C4C22×C4×C1712yes—
268C22×C4C22×C4×C1711yescharacteristic
269C22×C4C22×C4×C1711yescharacteristic
270C22×C4C22×C4×C1712yes—
271C22×C4C2×D4×C1712yes—
272C22×C4C2×D4×C1712yes—
273C22×C4C2×D4×C1712yes—
274C22×C4C2×D4×C1712yes—
275C22×C4C2×D4×C1712yes—
276C22×C4C2×D4×C1712yes—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—48no—
280C22⋊C4—28no—
281C22⋊C4—28no—
282C22⋊C4—216no—
283C42—48no—
284C42C22⋊C4×C1712yes—
285C42C22⋊C4×C1712yes—
286C42C22⋊C4×C1712yes—
287C42C22⋊C4×C1712yes—
288C42C22⋊C4×C1711yescharacteristic
289C42C22⋊C4×C1712yes—
290C42C22⋊C4×C1711yescharacteristic
291C42C22⋊C4×C1711yescharacteristic
292C42C22⋊C4×C1712yes—
293C42C22⋊C4×C1711yescharacteristic
294C23—24no—
295C23—28no—
296C23—42no—
297C23—48no—
298C23C23×C4×C1711yescharacteristic
299C23C22×D4×C1712yes—
300C23C17×H(5,𝔽2)14yes—
301Q8—44no—
302Q8—44no—
303D4—44no—
304D4—44no—
305D4—48no—
306D4—416no—
307D4—48no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—28no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—416no—
321C2×C4—48no—
322C2×C4—48no—
323C2×C4—48no—
324C2×C4C2×C22⋊C4×C1712yes—
325C2×C4C2×C22⋊C4×C1712yes—
326C2×C4C2×C22⋊C4×C1712yes—
327C2×C4C2×C22⋊C4×C1712yes—
328C2×C4C2×C22⋊C4×C1711yescharacteristic
329C2×C4C2×C22⋊C4×C1711yescharacteristic
330C2×C4C2×C22⋊C4×C1712yes—
331C22—22no—
332C22—22no—
333C22—22no—
334C22—44no—
335C22—44no—
336C22—48no—
337C22—88no—
338C22C22×C22⋊C4×C1711yescharacteristic
339C22C17×#51812yes—
340C22C17×#53514yes—
341C4—22no—
342C4—21no—
343C4—21no—
344C4—22no—
345C4—22no—
346C4—22no—
347C4—44no—
348C4—88no—
349C4C17×#41014yes—
350C2—24no—
351C2—22no—
352C2—84no—
353C2C17×#230911yescharacteristic
354C2C2×C17×#41012yes—
subgroupG/H
center, socleC22×C17C22×C22⋊C4
commutatorC23C23×C4×C17
Frattini, cosocleC24C24×C17
prime radicalC2×C17×#532C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2283C2semidirect
3. C17×#1964C2semidirect
4. C17×#1782C2semidirect
10. C2×C17×C4⋊Q8C4semidirect
11. C2×C17×#127C4semidirect
12. C2×C17×#124C4semidirect
14. C2×C4×D4×C17C4semidirect
116. #21794C17direct (N × H)
155. #2283C2×C17semidirect
156. #1964C2×C17semidirect
157. #1782C2×C17semidirect
182. C2×C4⋊Q8C4×C17semidirect
183. C2×#127C4×C17semidirect
184. C2×#124C4×C17semidirect
186. C2×C4×D4C4×C17semidirect
245. C17#21794direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#5322
C17×#22832
C17×#19642
C17×#17822
#2179417