Finite Group Databasebeta

← C17×#13398 #16871142

Subgroups — C17×#13398 #16871142

Order 4352.

458 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#469C211yesmaximal, characteristic
2C2×C17×#365C211yesmaximal, characteristic, complemented
3C2×C17×#361C211yesmaximal, characteristic, complemented
4C2×C17×#361C211yesmaximal, characteristic, complemented
5C2×C17×#349C211yesmaximal, characteristic, complemented
6C17×#1811C211yesmaximal, characteristic, complemented
7C17×#1383C211yesmaximal, characteristic, complemented
8C22×D8×C17C2211yescharacteristic
9C22×M16×C17C2211yescharacteristic
10C2×C17×#121—21no—
11C2×C17×M32C2211yescharacteristic
12C2×C17×M32C2211yescharacteristic
13C17×#469—22no—
14C17×#469—22no—
15C2×C17×#108C2211yescharacteristic
16C2×C17×#108C2211yescharacteristic
17C2×C17×#106C2211yescharacteristic
18C2×C17×#102—21no—
19C17×#407—21no—
20C17×#365—22no—
21C17×#361—22no—
22C17×#361—22no—
23C17×#349—22no—
24C17×#341—21no—
25C22×D4×C17—21no—
26C22×D4×C17—41no—
27C23×C4×C17D411yescharacteristic
28C2×D8×C17—21no—
29C2×D8×C17—21no—
30C2×D8×C17—21no—
31C2×D8×C17—21no—
32C2×D8×C17—21no—
33C2×D8×C17D412yes—
34C2×M16×C17—21no—
35C2×M16×C17—21no—
36C2×M16×C17—21no—
37C2×M16×C17—21no—
38C2×M16×C17—21no—
39C2×M16×C17—21no—
40C2×M16×C17—21no—
41C2×M16×C17—21no—
42C22×C8×C17D411yescharacteristic
43C22×C8×C17C2311yescharacteristic
44C17×#121—24no—
45C17×#121—42no—
46C2×C4⋊C4×C17—21no—
47C2×C22⋊C4×C17—41no—
48C17×M32—21no—
49C17×M32—21no—
50C17×M32—21no—
51C17×M32D412yescomplemented
52C2×C16×C17—21no—
53C2×C16×C17—21no—
54C17×#108—21no—
55C17×#108—21no—
56C17×#108—21no—
57C17×#108—21no—
58C17×#106—21no—
59C17×#106D412yes—
60C17×#102—24no—
61C17×C22⋊C8—42no—
62C24×C17—41no—
63C24×C17SD1611yescharacteristic
64C2×D4×C17—22no—
65C2×D4×C17—44no—
66C2×D4×C17—41no—
67C2×D4×C17—41no—
68C2×D4×C17—41no—
69C2×D4×C17—41no—
70C2×D4×C17—41no—
71C2×D4×C17—84no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—41no—
79C22×C4×C17SD1611yescharacteristic
80C22×C4×C17C2×D411yescharacteristic
81D8×C17—22no—
82D8×C17—22no—
83D8×C17—41no—
84D8×C17—41no—
85M16×C17—41no—
86M16×C17—41no—
87M16×C17—41no—
88M16×C17—41no—
89M16×C17—41no—
90M16×C17—41no—
91M16×C17—41no—
92M16×C17—41no—
93C2×C8×C17—21no—
94C2×C8×C17—21no—
95C2×C8×C17—21no—
96C2×C8×C17—41no—
97C2×C8×C17—41no—
98C2×C8×C17C2×D411yescharacteristic
99C2×C8×C17C2×D411yescharacteristic
100C2×C8×C17C2×D411yescharacteristic
101C2×C8×C17#4111yescharacteristic
102C2×C8×C17#4111yescharacteristic
103C2×C8×C17#4111yescharacteristic
104C4⋊C4×C17—22no—
105C4⋊C4×C17—41no—
106C22⋊C4×C17—44no—
107C16×C17—22no—
108C16×C17—41no—
109#13398C1711yesmaximal, characteristic, direct product factor, Sylow
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—21no—
113C23×C17—42no—
114C23×C17—42no—
115C23×C17—82no—
116C23×C17—82no—
117C23×C17—81no—
118C23×C17—81no—
119C23×C17C2×SD1611yescharacteristic
120D4×C17—42no—
121D4×C17—42no—
122D4×C17—88no—
123D4×C17—81no—
124D4×C17—81no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17—41no—
132C2×C4×C17—42no—
133C2×C4×C17—82no—
134C2×C4×C17#12011yescharacteristic
135C2×C4×C17#12111yescharacteristic
136C2×C4×C17#12311yescharacteristic
137C2×C4×C17#13511yescharacteristic
138C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
140C8×C17—41no—
141C8×C17—81no—
142C8×C17—81no—
143C8×C17#12111yescharacteristic
144C8×C17#12111yescharacteristic
145C8×C17#12311yescharacteristic
146C8×C17#12411yescharacteristic
147C2×#469C2×C1711yescharacteristic
148C2×#365C2×C1711yescharacteristic, complemented
149C2×#361C2×C1711yescharacteristic, complemented
150C2×#361C2×C1711yescharacteristic, complemented
151C2×#349C2×C1711yescharacteristic, complemented
152#1811C2×C1711yescharacteristic, complemented
153#1383C2×C1711yescharacteristic, complemented
154C22×C17—22no—
155C22×C17—42no—
156C22×C17—42no—
157C22×C17—41no—
158C22×C17—81no—
159C22×C17—82no—
160C22×C17—82no—
161C22×C17—82no—
162C22×C17—162no—
163C22×C17—162no—
164C22×C17#45011yescharacteristic
165C22×C17#46511yescharacteristic
166C22×C17#48111yescharacteristic
167C4×C17—41no—
168C4×C17—82no—
169C4×C17#39411yescharacteristic
170C4×C17#44911yescharacteristic
171C4×C17#46911yescharacteristic
172C4×C17#48211yescharacteristic
173C22×D8C22×C1711yescharacteristic
174C22×M16C22×C1711yescharacteristic
175C2×#121—21no—
176C2×M32C22×C1711yescharacteristic
177C2×M32C22×C1711yescharacteristic
178#469—22no—
179#469—22no—
180C2×#108C22×C1711yescharacteristic
181C2×#108C22×C1711yescharacteristic
182C2×#106C22×C1711yescharacteristic
183C2×#102—21no—
184#407—21no—
185#365—22no—
186#361—22no—
187#361—22no—
188#349—22no—
189#341—21no—
190C2×C17—21no—
191C2×C17—21no—
192C2×C17—81no—
193C2×C17—162no—
194C2×C17#203411yescharacteristic
195C2×C17#223812yes—
196C22×D4—21no—
197C22×D4—41no—
198C23×C4D4×C1711yescharacteristic
199C2×D8—21no—
200C2×D8—21no—
201C2×D8—21no—
202C2×D8—21no—
203C2×D8—21no—
204C2×D8D4×C1712yes—
205C2×M16—21no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—21no—
211C2×M16—21no—
212C2×M16—21no—
213C22×C8D4×C1711yescharacteristic
214C22×C8C23×C1711yescharacteristic
215#121—24no—
216#121—42no—
217C2×C4⋊C4—21no—
218C2×C22⋊C4—41no—
219M32—21no—
220M32—21no—
221M32—21no—
222M32D4×C1712yescomplemented
223C2×C16—21no—
224C2×C16—21no—
225#108—21no—
226#108—21no—
227#108—21no—
228#108—21no—
229#106—21no—
230#106D4×C1712yes—
231#102—24no—
232C22⋊C8—42no—
233C17#1339811yescharacteristic, direct product factor, Sylow
234C24—41no—
235C24SD16×C1711yescharacteristic
236C2×D4—22no—
237C2×D4—44no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—84no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4SD16×C1711yescharacteristic
252C22×C4C2×D4×C1711yescharacteristic
253D8—22no—
254D8—22no—
255D8—41no—
256D8—41no—
257M16—41no—
258M16—41no—
259M16—41no—
260M16—41no—
261M16—41no—
262M16—41no—
263M16—41no—
264M16—41no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8C2×D4×C1711yescharacteristic
271C2×C8C2×D4×C1711yescharacteristic
272C2×C8C2×D4×C1711yescharacteristic
273C2×C8#41×C1711yescharacteristic
274C2×C8#41×C1711yescharacteristic
275C2×C8#41×C1711yescharacteristic
276C4⋊C4—22no—
277C4⋊C4—41no—
278C22⋊C4—44no—
279C16—22no—
280C16—41no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—42no—
285C23—42no—
286C23—82no—
287C23—82no—
288C23—81no—
289C23—81no—
290C23C2×SD16×C1711yescharacteristic
291D4—42no—
292D4—42no—
293D4—88no—
294D4—81no—
295D4—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—82no—
305C2×C4C17×#12011yescharacteristic
306C2×C4C17×#12111yescharacteristic
307C2×C4C17×#12311yescharacteristic
308C2×C4C17×#13511yescharacteristic
309C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
310C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
311C8—41no—
312C8—81no—
313C8—81no—
314C8C17×#12111yescharacteristic
315C8C17×#12111yescharacteristic
316C8C17×#12311yescharacteristic
317C8C17×#12411yescharacteristic
318C22—22no—
319C22—42no—
320C22—42no—
321C22—41no—
322C22—81no—
323C22—82no—
324C22—82no—
325C22—82no—
326C22—162no—
327C22—162no—
328C22C17×#45011yescharacteristic
329C22C17×#46511yescharacteristic
330C22C17×#48111yescharacteristic
331C4—41no—
332C4—82no—
333C4C17×#39411yescharacteristic
334C4C17×#44911yescharacteristic
335C4C17×#46911yescharacteristic
336C4C17×#48211yescharacteristic
337C2—21no—
338C2—21no—
339C2—81no—
340C2—162no—
341C2C17×#203411yescharacteristic
342C2C17×#223812yes—
subgroupG/H
center, socleC22×C17#481
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC2×C17×#469C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C22×M16×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#365C2semidirect
3. C2×C17×#361C2semidirect
4. C2×C17×#361C2semidirect
5. C2×C17×#349C2semidirect
6. C17×#1811C2semidirect
7. C17×#1383C2semidirect
51. C17×M32D4semidirect
109. #13398C17direct (N × H)
148. C2×#365C2×C17semidirect
149. C2×#361C2×C17semidirect
150. C2×#361C2×C17semidirect
151. C2×#349C2×C17semidirect
152. #1811C2×C17semidirect
153. #1383C2×C17semidirect
222. M32D4×C17semidirect
233. C17#13398direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#4692
C2×C17×#3652
C2×C17×#3612
C2×C17×#3492
C17×#18112
C17×#13832
#1339817