Finite Group Databasebeta

← C17×#13395 #16871139

Subgroups — C17×#13395 #16871139

Order 4352.

422 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×#3050C211yesmaximal, characteristic
2C17×#2155C211yesmaximal, characteristic, complemented
3C17×#2148C211yesmaximal, characteristic, complemented
4C17×#2143C211yesmaximal, characteristic, complemented
5C17×#2112C211yesmaximal, characteristic, complemented
6C17×#1810C211yesmaximal, characteristic, complemented
7C17×#1389C211yesmaximal, characteristic, complemented
8C2×C17×#135C2211yescharacteristic
9C23×C8×C17C2211yescharacteristic
10C17×#525—21no—
11C2×C17×M32C2211yescharacteristic
12C2×C17×M32C2211yescharacteristic
13C17×#467—21no—
14C17×#466—21no—
15C17×#465—22no—
16C2×C17×#108C2211yescharacteristic
17C2×C17×#108C2211yescharacteristic
18C17×#427C2211yescharacteristic
19C17×#416—21no—
20C17×#407—21no—
21C17×#365—22no—
22C17×#362—21no—
23C17×#361—21no—
24C17×#359—22no—
25C17×C22⋊C16—22no—
26C17×#341—21no—
27C2×#41×C17—21no—
28C23×C4×C17D411yescharacteristic
29C17×#135—21no—
30C17×#135—21no—
31C17×#135—21no—
32C17×#135—21no—
33C2×Q16×C17D411yescharacteristic
34C2×SD16×C17—21no—
35C2×D8×C17D411yescharacteristic
36C2×M16×C17—21no—
37C2×M16×C17—21no—
38C22×C8×C17—21no—
39C22×C8×C17—21no—
40C22×C8×C17—21no—
41C22×C8×C17—21no—
42C22×C8×C17—21no—
43C22×C8×C17—21no—
44C22×C8×C17D411yescharacteristic
45C22×C8×C17C2311yescharacteristic
46C17×#123—41no—
47C17×C22⋊Q8—22no—
48C17×#121—22no—
49C17×#120—41no—
50C4×D4×C17—42no—
51C17×#117—21no—
52C17×M32—21no—
53C17×M32—21no—
54C17×M32—21no—
55C17×M32—21no—
56C2×C16×C17—21no—
57C2×C16×C17D412yescomplemented
58C17×#108—21no—
59C17×#108—21no—
60C17×#108—21no—
61C17×#108—21no—
62C17×#107—21no—
63C17×#106D412yes—
64C17×#103—22no—
65C17×#102—22no—
66C17×C22⋊C8—42no—
67C24×C17SD1611yescharacteristic
68#41×C17—41no—
69#41×C17—41no—
70#41×C17—41no—
71#41×C17—41no—
72C2×Q8×C17—21no—
73C2×D4×C17—21no—
74C2×D4×C17—42no—
75C2×D4×C17—41no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—21no—
81C22×C4×C17—21no—
82C22×C4×C17—41no—
83C22×C4×C17SD1611yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85Q16×C17—21no—
86Q16×C17—21no—
87SD16×C17—41no—
88SD16×C17—41no—
89D8×C17—21no—
90D8×C17—21no—
91M16×C17—41no—
92M16×C17—41no—
93M16×C17—41no—
94M16×C17—41no—
95C2×C8×C17—21no—
96C2×C8×C17—21no—
97C2×C8×C17—21no—
98C2×C8×C17—41no—
99C2×C8×C17—41no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C2×C8×C17—41no—
103C2×C8×C17—41no—
104C2×C8×C17C2×D411yescharacteristic
105C2×C8×C17C2×D411yescharacteristic
106C2×C8×C17C2×D411yescharacteristic
107C2×C8×C17#4111yescharacteristic
108C2×C8×C17#4111yescharacteristic
109C2×C8×C17#4111yescharacteristic
110C4⋊C4×C17—22no—
111C4⋊C4×C17—42no—
112C22⋊C4×C17—42no—
113C22⋊C4×C17—42no—
114C22⋊C4×C17—41no—
115C42×C17—41no—
116C16×C17—22no—
117C16×C17—41no—
118#13395C1711yesmaximal, characteristic, direct product factor, Sylow
119C23×C17—21no—
120C23×C17—21no—
121C23×C17—21no—
122C23×C17—42no—
123C23×C17—41no—
124C23×C17C2×SD1611yescharacteristic
125Q8×C17—41no—
126Q8×C17—41no—
127D4×C17—41no—
128D4×C17—41no—
129D4×C17—84no—
130D4×C17—81no—
131D4×C17—81no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—42no—
140C2×C4×C17—41no—
141C2×C4×C17—81no—
142C2×C4×C17—81no—
143C2×C4×C17#12011yescharacteristic
144C2×C4×C17#12111yescharacteristic
145C2×C4×C17#12311yescharacteristic
146C2×C4×C17#13511yescharacteristic
147C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
149C8×C17—41no—
150C8×C17—81no—
151C8×C17—81no—
152C8×C17#12111yescharacteristic
153C8×C17#12111yescharacteristic
154C8×C17#12311yescharacteristic
155C8×C17#12411yescharacteristic
156#3050C2×C1711yescharacteristic
157#2155C2×C1711yescharacteristic, complemented
158#2148C2×C1711yescharacteristic, complemented
159#2143C2×C1711yescharacteristic, complemented
160#2112C2×C1711yescharacteristic, complemented
161#1810C2×C1711yescharacteristic, complemented
162#1389C2×C1711yescharacteristic, complemented
163C22×C17—22no—
164C22×C17—22no—
165C22×C17—22no—
166C22×C17—41no—
167C22×C17—41no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17—41no—
171C22×C17—82no—
172C22×C17—81no—
173C22×C17#45011yescharacteristic
174C22×C17#46511yescharacteristic
175C22×C17#48111yescharacteristic
176C4×C17—41no—
177C4×C17—82no—
178C4×C17—81no—
179C4×C17#39411yescharacteristic
180C4×C17#44911yescharacteristic
181C4×C17#46911yescharacteristic
182C4×C17#48211yescharacteristic
183C2×#135C22×C1711yescharacteristic
184C23×C8C22×C1711yescharacteristic
185#525—21no—
186C2×M32C22×C1711yescharacteristic
187C2×M32C22×C1711yescharacteristic
188#467—21no—
189#466—21no—
190#465—22no—
191C2×#108C22×C1711yescharacteristic
192C2×#108C22×C1711yescharacteristic
193#427C22×C1711yescharacteristic
194#416—21no—
195#407—21no—
196#365—22no—
197#362—21no—
198#361—21no—
199#359—22no—
200C22⋊C16—22no—
201#341—21no—
202C2×C17—21no—
203C2×C17—21no—
204C2×C17—21no—
205C2×C17—42no—
206C2×C17—161no—
207C2×C17#203411yescharacteristic
208C2×#41—21no—
209C23×C4D4×C1711yescharacteristic
210#135—21no—
211#135—21no—
212#135—21no—
213#135—21no—
214C2×Q16D4×C1711yescharacteristic
215C2×SD16—21no—
216C2×D8D4×C1711yescharacteristic
217C2×M16—21no—
218C2×M16—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8D4×C1711yescharacteristic
226C22×C8C23×C1711yescharacteristic
227#123—41no—
228C22⋊Q8—22no—
229#121—22no—
230#120—41no—
231C4×D4—42no—
232#117—21no—
233M32—21no—
234M32—21no—
235M32—21no—
236M32—21no—
237C2×C16—21no—
238C2×C16D4×C1712yescomplemented
239#108—21no—
240#108—21no—
241#108—21no—
242#108—21no—
243#107—21no—
244#106D4×C1712yes—
245#103—22no—
246#102—22no—
247C22⋊C8—42no—
248C17#1339511yescharacteristic, direct product factor, Sylow
249C24SD16×C1711yescharacteristic
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×D4—21no—
256C2×D4—42no—
257C2×D4—41no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4SD16×C1711yescharacteristic
266C22×C4C2×D4×C1711yescharacteristic
267Q16—21no—
268Q16—21no—
269SD16—41no—
270SD16—41no—
271D8—21no—
272D8—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8C2×D4×C1711yescharacteristic
287C2×C8C2×D4×C1711yescharacteristic
288C2×C8C2×D4×C1711yescharacteristic
289C2×C8#41×C1711yescharacteristic
290C2×C8#41×C1711yescharacteristic
291C2×C8#41×C1711yescharacteristic
292C4⋊C4—22no—
293C4⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C42—41no—
298C16—22no—
299C16—41no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—42no—
304C23—41no—
305C23C2×SD16×C1711yescharacteristic
306Q8—41no—
307Q8—41no—
308D4—41no—
309D4—41no—
310D4—84no—
311D4—81no—
312D4—81no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C17×#12011yescharacteristic
325C2×C4C17×#12111yescharacteristic
326C2×C4C17×#12311yescharacteristic
327C2×C4C17×#13511yescharacteristic
328C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
329C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
330C8—41no—
331C8—81no—
332C8—81no—
333C8C17×#12111yescharacteristic
334C8C17×#12111yescharacteristic
335C8C17×#12311yescharacteristic
336C8C17×#12411yescharacteristic
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—82no—
346C22—81no—
347C22C17×#45011yescharacteristic
348C22C17×#46511yescharacteristic
349C22C17×#48111yescharacteristic
350C4—41no—
351C4—82no—
352C4—81no—
353C4C17×#39411yescharacteristic
354C4C17×#44911yescharacteristic
355C4C17×#46911yescharacteristic
356C4C17×#48211yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—161no—
362C2C17×#203411yescharacteristic
subgroupG/H
centerC4×C17#469
commutator, Frattini, cosocleC22×C8C23×C17
socleC2×C17#2034
prime radicalC17×#3050C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C23×C8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2155C2semidirect
3. C17×#2148C2semidirect
4. C17×#2143C2semidirect
5. C17×#2112C2semidirect
6. C17×#1810C2semidirect
7. C17×#1389C2semidirect
57. C2×C16×C17D4semidirect
118. #13395C17direct (N × H)
157. #2155C2×C17semidirect
158. #2148C2×C17semidirect
159. #2143C2×C17semidirect
160. #2112C2×C17semidirect
161. #1810C2×C17semidirect
162. #1389C2×C17semidirect
238. C2×C16D4×C17semidirect
248. C17#13395direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30502
C17×#21552
C17×#21482
C17×#21432
C17×#21122
C17×#18102
C17×#13892
#1339517