Finite Group Databasebeta

← C17×#13411 #16871155

Subgroups — C17×#13411 #16871155

Order 4352.

462 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3155C211yesmaximal, characteristic
2C2×C17×#361C211yesmaximal, characteristic, complemented
3C2×C17×#359C211yesmaximal, characteristic, complemented
4C17×#2139C211yesmaximal, characteristic, complemented
5C2×C17×#357C211yesmaximal, characteristic, complemented
6C17×#1952C211yesmaximal, characteristic, complemented
7C17×#1379C211yesmaximal, characteristic, complemented
8C2×C17×AGL(1,ℤ/8)—21no—
9C2×C17×#135C2211yescharacteristic
10C22×D8×C17C2211yescharacteristic
11C17×#535—21no—
12C2×C17×M32C2211yescharacteristic
13C22×C16×C17C2211yescharacteristic
14C17×#496—22no—
15C17×#495—21no—
16C17×#493—21no—
17C2×C17×#108C2211yescharacteristic
18C17×#428—21no—
19C2×C17×#107C2211yescharacteristic
20C17×#405C2211yescharacteristic
21C17×#361—22no—
22C17×#359—22no—
23C17×#358—21no—
24C17×#357—22no—
25C17×#357—21no—
26C17×#343—21no—
27C2×#41×C17—21no—
28C22×D4×C17—21no—
29C17×AGL(1,ℤ/8)—42no—
30C17×AGL(1,ℤ/8)—42no—
31C17×#135—21no—
32C17×#135—21no—
33C17×#135—21no—
34C17×#135—21no—
35C2×Q16×C17D411yescharacteristic
36C2×SD16×C17—22no—
37C2×SD16×C17—21no—
38C2×D8×C17—22no—
39C2×D8×C17—21no—
40C2×D8×C17—21no—
41C2×D8×C17—21no—
42C2×D8×C17—21no—
43C2×D8×C17—21no—
44C2×D8×C17D411yescharacteristic
45C2×D8×C17D412yes—
46C2×M16×C17—21no—
47C2×M16×C17D411yescharacteristic
48C22×C8×C17C2311yescharacteristic
49C17×#127—22no—
50C17×#124—22no—
51C17×#121—41no—
52C17×#121—41no—
53C17×#120—42no—
54C17×#117D411yescharacteristic
55C2×C4⋊C4×C17—21no—
56C17×M32—21no—
57C17×M32—21no—
58C2×C16×C17—21no—
59C2×C16×C17—21no—
60C2×C16×C17—21no—
61C2×C16×C17—21no—
62C17×#108—21no—
63C17×#108D412yescomplemented
64C17×#107—21no—
65C17×#107—21no—
66C17×#107—41no—
67C17×#106—41no—
68C17×#97—21no—
69C4×C8×C17—21no—
70C24×C17—41no—
71#41×C17—41no—
72#41×C17—41no—
73#41×C17—41no—
74#41×C17—41no—
75C2×Q8×C17—21no—
76C2×D4×C17—22no—
77C2×D4×C17—21no—
78C2×D4×C17—42no—
79C2×D4×C17—42no—
80C2×D4×C17—41no—
81C2×D4×C17—41no—
82C2×D4×C17—41no—
83C2×D4×C17—41no—
84C2×D4×C17—41no—
85C2×D4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17—41no—
88C22×C4×C17C2×D411yescharacteristic
89Q16×C17—21no—
90Q16×C17—21no—
91SD16×C17—44no—
92SD16×C17—41no—
93SD16×C17—41no—
94D8×C17—22no—
95D8×C17—21no—
96D8×C17—22no—
97D8×C17—21no—
98D8×C17—44no—
99D8×C17—41no—
100D8×C17—41no—
101M16×C17—21no—
102M16×C17—22no—
103M16×C17—41no—
104M16×C17SD1612yes—
105C2×C8×C17—21no—
106C2×C8×C17—41no—
107C2×C8×C17C2×D411yescharacteristic
108C2×C8×C17C2×D411yescharacteristic
109C2×C8×C17C2×D411yescharacteristic
110C2×C8×C17#4111yescharacteristic
111C2×C8×C17#4111yescharacteristic
112C2×C8×C17#4111yescharacteristic
113C4⋊C4×C17—41no—
114C4⋊C4×C17—41no—
115C4⋊C4×C17D811yescharacteristic
116C4⋊C4×C17D811yescharacteristic
117C22⋊C4×C17—21no—
118C22⋊C4×C17—42no—
119C22⋊C4×C17—42no—
120C42×C17—21no—
121C16×C17—41no—
122C16×C17—41no—
123#13411C1711yesmaximal, characteristic, direct product factor, Sylow
124C23×C17—42no—
125C23×C17—41no—
126C23×C17—81no—
127C23×C17—81no—
128C23×C17—161no—
129C23×C17—161no—
130C23×C17AGL(1,ℤ/8)11yescharacteristic
131Q8×C17—41no—
132Q8×C17—41no—
133D4×C17—42no—
134D4×C17—41no—
135D4×C17—41no—
136D4×C17—42no—
137D4×C17—81no—
138D4×C17—81no—
139D4×C17—81no—
140D4×C17—81no—
141D4×C17—162no—
142D4×C17—162no—
143C2×C4×C17—21no—
144C2×C4×C17—21no—
145C2×C4×C17—41no—
146C2×C4×C17—81no—
147C2×C4×C17—81no—
148C2×C4×C17—81no—
149C2×C4×C17—161no—
150C2×C4×C17#12011yescharacteristic
151C2×C4×C17#12111yescharacteristic
152C2×C4×C17#12411yescharacteristic
153C2×C4×C17C2×D811yescharacteristic
154C2×C4×C17C2×SD1611yescharacteristic
155C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
156C8×C17—22no—
157C8×C17—42no—
158C8×C17#12111yescharacteristic
159C8×C17#12111yescharacteristic
160C8×C17#12311yescharacteristic
161C8×C17#12311yescharacteristic
162#3155C2×C1711yescharacteristic
163C2×#361C2×C1711yescharacteristic, complemented
164C2×#359C2×C1711yescharacteristic, complemented
165#2139C2×C1711yescharacteristic, complemented
166C2×#357C2×C1711yescharacteristic, complemented
167#1952C2×C1711yescharacteristic, complemented
168#1379C2×C1711yescharacteristic, complemented
169C22×C17—21no—
170C22×C17—21no—
171C22×C17—81no—
172C22×C17—82no—
173C22×C17—81no—
174C22×C17—82no—
175C22×C17—81no—
176C22×C17—82no—
177C22×C17—162no—
178C22×C17—162no—
179C22×C17#44711yescharacteristic
180C22×C17#46011yescharacteristic
181C22×C17#49011yescharacteristic
182C4×C17—41no—
183C4×C17—41no—
184C4×C17—81no—
185C4×C17—161no—
186C4×C17#39411yescharacteristic
187C4×C17#45011yescharacteristic
188C4×C17#45911yescharacteristic
189C4×C17#48611yescharacteristic
190C2×AGL(1,ℤ/8)—21no—
191C2×#135C22×C1711yescharacteristic
192C22×D8C22×C1711yescharacteristic
193#535—21no—
194C2×M32C22×C1711yescharacteristic
195C22×C16C22×C1711yescharacteristic
196#496—22no—
197#495—21no—
198#493—21no—
199C2×#108C22×C1711yescharacteristic
200#428—21no—
201C2×#107C22×C1711yescharacteristic
202#405C22×C1711yescharacteristic
203#361—22no—
204#359—22no—
205#358—21no—
206#357—22no—
207#357—21no—
208#343—21no—
209C2×C17—21no—
210C2×C17—21no—
211C2×C17—161no—
212C2×C17—162no—
213C2×C17#204111yescharacteristic
214C2×C17#219211yescharacteristic
215C2×C17#219411yescharacteristic
216C2×#41—21no—
217C22×D4—21no—
218AGL(1,ℤ/8)—42no—
219AGL(1,ℤ/8)—42no—
220#135—21no—
221#135—21no—
222#135—21no—
223#135—21no—
224C2×Q16D4×C1711yescharacteristic
225C2×SD16—22no—
226C2×SD16—21no—
227C2×D8—22no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8—21no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8D4×C1712yes—
234C2×D8D4×C1711yescharacteristic
235C2×M16—21no—
236C2×M16D4×C1711yescharacteristic
237C22×C8C23×C1711yescharacteristic
238#127—22no—
239#124—22no—
240#121—41no—
241#121—41no—
242#120—42no—
243#117D4×C1711yescharacteristic
244C2×C4⋊C4—21no—
245M32—21no—
246M32—21no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251#108—21no—
252#108D4×C1712yescomplemented
253#107—21no—
254#107—21no—
255#107—41no—
256#106—41no—
257#97—21no—
258C4×C8—21no—
259C17#1341111yescharacteristic, direct product factor, Sylow
260C24—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264#41—41no—
265C2×Q8—21no—
266C2×D4—22no—
267C2×D4—21no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×D4×C1711yescharacteristic
279Q16—21no—
280Q16—21no—
281SD16—44no—
282SD16—41no—
283SD16—41no—
284D8—22no—
285D8—21no—
286D8—22no—
287D8—21no—
288D8—44no—
289D8—41no—
290D8—41no—
291M16—21no—
292M16—22no—
293M16—41no—
294M16SD16×C1712yes—
295C2×C8—21no—
296C2×C8—41no—
297C2×C8C2×D4×C1711yescharacteristic
298C2×C8C2×D4×C1711yescharacteristic
299C2×C8C2×D4×C1711yescharacteristic
300C2×C8#41×C1711yescharacteristic
301C2×C8#41×C1711yescharacteristic
302C2×C8#41×C1711yescharacteristic
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4D8×C1711yescharacteristic
306C4⋊C4D8×C1711yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C42—21no—
311C16—41no—
312C16—41no—
313C23—42no—
314C23—41no—
315C23—81no—
316C23—81no—
317C23—161no—
318C23—161no—
319C23C17×AGL(1,ℤ/8)11yescharacteristic
320Q8—41no—
321Q8—41no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—42no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—162no—
331D4—162no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—161no—
339C2×C4C17×#12011yescharacteristic
340C2×C4C17×#12111yescharacteristic
341C2×C4C17×#12411yescharacteristic
342C2×C4C2×D8×C1711yescharacteristic
343C2×C4C2×SD16×C1711yescharacteristic
344C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
345C8—22no—
346C8—42no—
347C8C17×#12111yescharacteristic
348C8C17×#12111yescharacteristic
349C8C17×#12311yescharacteristic
350C8C17×#12311yescharacteristic
351C22—21no—
352C22—21no—
353C22—81no—
354C22—82no—
355C22—81no—
356C22—82no—
357C22—81no—
358C22—82no—
359C22—162no—
360C22—162no—
361C22C17×#44711yescharacteristic
362C22C17×#46011yescharacteristic
363C22C17×#49011yescharacteristic
364C4—41no—
365C4—41no—
366C4—81no—
367C4—161no—
368C4C17×#39411yescharacteristic
369C4C17×#45011yescharacteristic
370C4C17×#45911yescharacteristic
371C4C17×#48611yescharacteristic
372C2—21no—
373C2—21no—
374C2—162no—
375C2—161no—
376C2C17×#204111yescharacteristic
377C2C17×#219211yescharacteristic
378C2C17×#219411yescharacteristic
subgroupG/H
center, socleC22×C17#447
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC17×#3155C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#361C2semidirect
3. C2×C17×#359C2semidirect
4. C17×#2139C2semidirect
5. C2×C17×#357C2semidirect
6. C17×#1952C2semidirect
7. C17×#1379C2semidirect
63. C17×#108D4semidirect
123. #13411C17direct (N × H)
163. C2×#361C2×C17semidirect
164. C2×#359C2×C17semidirect
165. #2139C2×C17semidirect
166. C2×#357C2×C17semidirect
167. #1952C2×C17semidirect
168. #1379C2×C17semidirect
252. #108D4×C17semidirect
259. C17#13411direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#31552
C2×C17×#3612
C2×C17×#3592
C17×#21392
C2×C17×#3572
C17×#19522
C17×#13792
#1341117