Finite Group Databasebeta

← C17×#13418 #16871162

Subgroups — C17×#13418 #16871162

Order 4352.

422 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3156C211yesmaximal, characteristic
2C17×#2148C211yesmaximal, characteristic
3C2×C17×#362C211yesmaximal, characteristic, complemented
4C2×C17×#362C211yesmaximal, characteristic, complemented
5C17×#2143C211yesmaximal, characteristic
6C17×#1953C211yesmaximal, characteristic, complemented
7C17×#1378C211yesmaximal, characteristic, complemented
8C2×C17×#137—21no—
9C2×C17×#135C2211yescharacteristic
10C22×Q16×C17C2211yescharacteristic
11C17×#536—21no—
12C2×C17×M32C2211yescharacteristic
13C2×C17×M32C2211yescharacteristic
14C17×#497—22no—
15C17×#495—21no—
16C17×#494—21no—
17C17×#430—21no—
18C2×C17×#108C2211yescharacteristic
19C2×C17×#108C2211yescharacteristic
20C17×#405C2211yescharacteristic
21C17×#362—22no—
22C17×#362—22no—
23C17×#362—21no—
24C17×#361—21no—
25C17×#359—22no—
26C17×#344—21no—
27C2×#41×C17—21no—
28C22×Q8×C17—21no—
29C17×#137—42no—
30C17×#137—42no—
31C17×#135—21no—
32C17×#135—21no—
33C17×#135—21no—
34C17×#135—21no—
35C2×Q16×C17—22no—
36C2×Q16×C17—21no—
37C2×Q16×C17—21no—
38C2×Q16×C17—21no—
39C2×Q16×C17—21no—
40C2×Q16×C17—21no—
41C2×Q16×C17D411yescharacteristic
42C2×Q16×C17D412yes—
43C2×SD16×C17—22no—
44C2×SD16×C17—21no—
45C2×D8×C17D411yescharacteristic
46C2×M16×C17—21no—
47C2×M16×C17—21no—
48C2×M16×C17D411yescharacteristic
49C22×C8×C17C2311yescharacteristic
50C17×C4⋊Q8—22no—
51C17×#124—22no—
52C17×#123—42no—
53C17×C22⋊Q8—42no—
54C17×#117D411yescharacteristic
55C17×M32—21no—
56C17×M32—21no—
57C17×M32—21no—
58C17×M32—21no—
59C2×C16×C17—21no—
60C2×C16×C17—21no—
61C17×#108—21no—
62C17×#108—21no—
63C17×#108—21no—
64C17×#108—42no—
65C17×#108D412yes—
66C17×#97—21no—
67C4×C8×C17—21no—
68#41×C17—41no—
69#41×C17—41no—
70#41×C17—41no—
71#41×C17—41no—
72C2×Q8×C17—22no—
73C2×Q8×C17—21no—
74C2×Q8×C17—41no—
75C2×Q8×C17—41no—
76C2×Q8×C17—41no—
77C2×Q8×C17—41no—
78C2×Q8×C17—41no—
79C2×D4×C17—21no—
80C2×D4×C17—41no—
81C22×C4×C17—41no—
82C22×C4×C17—41no—
83C22×C4×C17C2×D411yescharacteristic
84Q16×C17—22no—
85Q16×C17—21no—
86Q16×C17—22no—
87Q16×C17—21no—
88Q16×C17—44no—
89Q16×C17—41no—
90Q16×C17—41no—
91SD16×C17—44no—
92SD16×C17—41no—
93SD16×C17—41no—
94D8×C17—21no—
95D8×C17—21no—
96M16×C17—21no—
97M16×C17—22no—
98M16×C17—41no—
99M16×C17—41no—
100M16×C17—41no—
101M16×C17D812yes—
102C2×C8×C17—21no—
103C2×C8×C17—41no—
104C2×C8×C17—41no—
105C2×C8×C17C2×D411yescharacteristic
106C2×C8×C17C2×D411yescharacteristic
107C2×C8×C17C2×D411yescharacteristic
108C2×C8×C17#4111yescharacteristic
109C2×C8×C17#4111yescharacteristic
110C2×C8×C17#4111yescharacteristic
111C4⋊C4×C17—21no—
112C4⋊C4×C17—44no—
113C22⋊C4×C17—44no—
114C22⋊C4×C17SD1612yes—
115C42×C17—21no—
116C16×C17—41no—
117C16×C17—41no—
118#13418C1711yesmaximal, characteristic, direct product factor, Sylow
119C23×C17—41no—
120C23×C17C2×SD1611yescharacteristic
121Q8×C17—41no—
122Q8×C17—42no—
123Q8×C17—42no—
124Q8×C17—41no—
125Q8×C17—81no—
126Q8×C17—81no—
127D4×C17—41no—
128D4×C17—41no—
129D4×C17—81no—
130D4×C17—81no—
131C2×C4×C17—22no—
132C2×C4×C17—42no—
133C2×C4×C17—41no—
134C2×C4×C17—81no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17#12011yescharacteristic
139C2×C4×C17#12111yescharacteristic
140C2×C4×C17#12411yescharacteristic
141C2×C4×C17C2×D811yescharacteristic
142C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
144C8×C17—22no—
145C8×C17—42no—
146C8×C17—81no—
147C8×C17#12111yescharacteristic
148C8×C17#12111yescharacteristic
149C8×C17#12311yescharacteristic
150C8×C17#12311yescharacteristic
151#3156C2×C1711yescharacteristic
152#2148C2×C1711yescharacteristic
153C2×#362C2×C1711yescharacteristic, complemented
154C2×#362C2×C1711yescharacteristic, complemented
155#2143C2×C1711yescharacteristic
156#1953C2×C1711yescharacteristic, complemented
157#1378C2×C1711yescharacteristic, complemented
158C22×C17—41no—
159C22×C17—82no—
160C22×C17—81no—
161C22×C17#45011yescharacteristic
162C22×C17#46011yescharacteristic
163C22×C17#48611yescharacteristic
164C4×C17—42no—
165C4×C17—81no—
166C4×C17—82no—
167C4×C17#39411yescharacteristic
168C4×C17#44711yescharacteristic
169C4×C17#45911yescharacteristic
170C4×C17#49011yescharacteristic
171C2×#137—21no—
172C2×#135C22×C1711yescharacteristic
173C22×Q16C22×C1711yescharacteristic
174#536—21no—
175C2×M32C22×C1711yescharacteristic
176C2×M32C22×C1711yescharacteristic
177#497—22no—
178#495—21no—
179#494—21no—
180#430—21no—
181C2×#108C22×C1711yescharacteristic
182C2×#108C22×C1711yescharacteristic
183#405C22×C1711yescharacteristic
184#362—22no—
185#362—21no—
186#362—22no—
187#361—21no—
188#359—22no—
189#344—21no—
190C2×C17—21no—
191C2×C17—21no—
192C2×C17—21no—
193C2×C17—161no—
194C2×C17#204111yescharacteristic
195C2×#41—21no—
196C22×Q8—21no—
197#137—42no—
198#137—42no—
199#135—21no—
200#135—21no—
201#135—21no—
202#135—21no—
203C2×Q16—22no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16D4×C1712yes—
210C2×Q16D4×C1711yescharacteristic
211C2×SD16—22no—
212C2×SD16—21no—
213C2×D8D4×C1711yescharacteristic
214C2×M16—21no—
215C2×M16—21no—
216C2×M16D4×C1711yescharacteristic
217C22×C8C23×C1711yescharacteristic
218C4⋊Q8—22no—
219#124—22no—
220#123—42no—
221C22⋊Q8—42no—
222#117D4×C1711yescharacteristic
223M32—21no—
224M32—21no—
225M32—21no—
226M32—21no—
227C2×C16—21no—
228C2×C16—21no—
229#108—21no—
230#108—21no—
231#108—21no—
232#108—42no—
233#108D4×C1712yes—
234#97—21no—
235C4×C8—21no—
236C17#1341811yescharacteristic, direct product factor, Sylow
237#41—41no—
238#41—41no—
239#41—41no—
240#41—41no—
241C2×Q8—22no—
242C2×Q8—21no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×D4—21no—
249C2×D4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4C2×D4×C1711yescharacteristic
253Q16—22no—
254Q16—21no—
255Q16—22no—
256Q16—21no—
257Q16—44no—
258Q16—41no—
259Q16—41no—
260SD16—44no—
261SD16—41no—
262SD16—41no—
263D8—21no—
264D8—21no—
265M16—21no—
266M16—22no—
267M16—41no—
268M16—41no—
269M16—41no—
270M16D8×C1712yes—
271C2×C8—21no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8C2×D4×C1711yescharacteristic
275C2×C8C2×D4×C1711yescharacteristic
276C2×C8C2×D4×C1711yescharacteristic
277C2×C8#41×C1711yescharacteristic
278C2×C8#41×C1711yescharacteristic
279C2×C8#41×C1711yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—44no—
282C22⋊C4—44no—
283C22⋊C4SD16×C1712yes—
284C42—21no—
285C16—41no—
286C16—41no—
287C23—41no—
288C23C2×SD16×C1711yescharacteristic
289Q8—41no—
290Q8—42no—
291Q8—42no—
292Q8—41no—
293Q8—81no—
294Q8—81no—
295D4—41no—
296D4—41no—
297D4—81no—
298D4—81no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4C17×#12011yescharacteristic
307C2×C4C17×#12111yescharacteristic
308C2×C4C17×#12411yescharacteristic
309C2×C4C2×D8×C1711yescharacteristic
310C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
311C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
312C8—22no—
313C8—42no—
314C8—81no—
315C8C17×#12111yescharacteristic
316C8C17×#12111yescharacteristic
317C8C17×#12311yescharacteristic
318C8C17×#12311yescharacteristic
319C22—41no—
320C22—82no—
321C22—81no—
322C22C17×#45011yescharacteristic
323C22C17×#46011yescharacteristic
324C22C17×#48611yescharacteristic
325C4—42no—
326C4—81no—
327C4—82no—
328C4C17×#39411yescharacteristic
329C4C17×#44711yescharacteristic
330C4C17×#45911yescharacteristic
331C4C17×#49011yescharacteristic
332C2—21no—
333C2—21no—
334C2—21no—
335C2—161no—
336C2C17×#204111yescharacteristic
subgroupG/H
center, socleC2×C17#2041
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC2×C17×#135C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C17×#362C2semidirect
4. C2×C17×#362C2semidirect
6. C17×#1953C2semidirect
7. C17×#1378C2semidirect
118. #13418C17direct (N × H)
153. C2×#362C2×C17semidirect
154. C2×#362C2×C17semidirect
156. #1953C2×C17semidirect
157. #1378C2×C17semidirect
236. C17#13418direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#31562
C17×#21482
C2×C17×#3622
C17×#21432
C17×#19532
C17×#13782
#1341817