Finite Group Databasebeta

← C17×#13385 #16871129

Subgroups — C17×#13385 #16871129

Order 4352.

408 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3061C211yesmaximal, characteristic
2C2×C17×#367C211yesmaximal, characteristic, complemented
3C2×C17×#359C211yesmaximal, characteristic, complemented
4C17×#2139C211yesmaximal, characteristic, complemented
5C2×C17×#350C211yesmaximal, characteristic, complemented
6C17×#1816C211yesmaximal, characteristic, complemented
7C17×#1387C211yesmaximal, characteristic, complemented
8C2×C17×#135C2211yescharacteristic
9C2×C17×#131C2211yescharacteristic
10C17×#537—21no—
11C2×C17×M32C2211yescharacteristic
12C22×C16×C17C2211yescharacteristic
13C17×#468—22no—
14C17×#467—21no—
15C17×#466—21no—
16C2×C17×#108C2211yescharacteristic
17C2×C17×#107C2211yescharacteristic
18C2×C17×#107C2211yescharacteristic
19C17×#417—21no—
20C17×#417—21no—
21C17×#367—22no—
22C17×#359—22no—
23C17×#358—21no—
24C17×#357—21no—
25C17×#350—22no—
26C17×#343—21no—
27C2×#41×C17—21no—
28C2×#41×C17D411yescharacteristic
29C17×#135—21no—
30C17×#135—21no—
31C17×#135—21no—
32C17×#135—21no—
33C2×Q16×C17D411yescharacteristic
34C2×SD16×C17—21no—
35C2×D8×C17D411yescharacteristic
36C17×#131—21no—
37C17×#131—21no—
38C17×#131—21no—
39C17×#131—21no—
40C2×M16×C17—21no—
41C2×M16×C17—21no—
42C2×M16×C17D411yescharacteristic
43C22×C8×C17—21no—
44C22×C8×C17C2311yescharacteristic
45C17×C22⋊Q8—22no—
46C17×C22⋊Q8—41no—
47C17×#121—22no—
48C17×#121—42no—
49C17×#121—41no—
50C2×C4⋊C4×C17—21no—
51C2×C4⋊C4×C17—21no—
52C17×M32—21no—
53C17×M32—21no—
54C2×C16×C17—21no—
55C2×C16×C17—21no—
56C2×C16×C17—21no—
57C2×C16×C17D412yescomplemented
58C17×#108—21no—
59C17×#108—21no—
60C17×#107—21no—
61C17×#107—21no—
62C17×#107—21no—
63C17×#107D412yes—
64C17×#103—22no—
65C17×#103—41no—
66C17×#102—22no—
67C17×#102—41no—
68#41×C17—21no—
69#41×C17—21no—
70#41×C17—21no—
71#41×C17—21no—
72#41×C17—41no—
73#41×C17—41no—
74#41×C17—41no—
75#41×C17—41no—
76C2×Q8×C17—21no—
77C2×Q8×C17D811yescharacteristic
78C2×D4×C17—21no—
79C2×D4×C17—21no—
80C2×D4×C17—41no—
81C2×D4×C17—42no—
82C2×D4×C17D811yescharacteristic
83C22×C4×C17—21no—
84C22×C4×C17—41no—
85C22×C4×C17—41no—
86C22×C4×C17—41no—
87C22×C4×C17C2×D411yescharacteristic
88Q16×C17—21no—
89Q16×C17—21no—
90SD16×C17—41no—
91SD16×C17—41no—
92D8×C17—21no—
93D8×C17—21no—
94M16×C17—21no—
95M16×C17—21no—
96M16×C17—41no—
97M16×C17—41no—
98M16×C17—41no—
99M16×C17—41no—
100C2×C8×C17—21no—
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—
112C4⋊C4×C17—41no—
113C4⋊C4×C17—41no—
114C4⋊C4×C17—41no—
115C22⋊C4×C17—42no—
116C22⋊C4×C17—42no—
117C16×C17—22no—
118C16×C17—41no—
119#13385C1711yesmaximal, characteristic, direct product factor, Sylow
120C23×C17—21no—
121C23×C17—41no—
122C23×C17AGL(1,ℤ/8)11yescharacteristic
123Q8×C17—21no—
124Q8×C17—21no—
125Q8×C17—41no—
126Q8×C17—41no—
127D4×C17—21no—
128D4×C17—21no—
129D4×C17—41no—
130D4×C17—41no—
131D4×C17—41no—
132D4×C17—41no—
133D4×C17—81no—
134D4×C17—81no—
135D4×C17—162no—
136C2×C4×C17—21no—
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—81no—
144C2×C4×C17—161no—
145C2×C4×C17—161no—
146C2×C4×C17#12011yescharacteristic
147C2×C4×C17#12111yescharacteristic
148C2×C4×C17#12311yescharacteristic
149C2×C4×C17C2×D811yescharacteristic
150C2×C4×C17#13511yescharacteristic
151C2×C4×C17#13711yescharacteristic
152C8×C17—41no—
153C8×C17—81no—
154C8×C17#12111yescharacteristic
155C8×C17#12111yescharacteristic
156C8×C17#12311yescharacteristic
157C8×C17#12411yescharacteristic
158#3061C2×C1711yescharacteristic
159C2×#367C2×C1711yescharacteristic, complemented
160C2×#359C2×C1711yescharacteristic, complemented
161#2139C2×C1711yescharacteristic, complemented
162C2×#350C2×C1711yescharacteristic, complemented
163#1816C2×C1711yescharacteristic, complemented
164#1387C2×C1711yescharacteristic, complemented
165C22×C17—21no—
166C22×C17—21no—
167C22×C17—41no—
168C22×C17—41no—
169C22×C17—41no—
170C22×C17—81no—
171C22×C17—81no—
172C22×C17—81no—
173C22×C17#44711yescharacteristic
174C22×C17#46811yescharacteristic
175C22×C17#48211yescharacteristic
176C4×C17—41no—
177C4×C17—82no—
178C4×C17—81no—
179C4×C17—161no—
180C4×C17#39411yescharacteristic
181C4×C17#45211yescharacteristic
182C4×C17#46611yescharacteristic
183C4×C17#48011yescharacteristic
184C2×#135C22×C1711yescharacteristic
185C2×#131C22×C1711yescharacteristic
186#537—21no—
187C2×M32C22×C1711yescharacteristic
188C22×C16C22×C1711yescharacteristic
189#468—22no—
190#467—21no—
191#466—21no—
192C2×#108C22×C1711yescharacteristic
193C2×#107C22×C1711yescharacteristic
194C2×#107C22×C1711yescharacteristic
195#417—21no—
196#417—21no—
197#367—22no—
198#359—22no—
199#358—21no—
200#357—21no—
201#350—22no—
202#343—21no—
203C2×C17—21no—
204C2×C17—21no—
205C2×C17—81no—
206C2×C17—161no—
207C2×C17#203311yescharacteristic
208C2×C17#219311yescharacteristic
209C2×C17#219411yescharacteristic
210C2×#41—21no—
211C2×#41D4×C1711yescharacteristic
212#135—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216C2×Q16D4×C1711yescharacteristic
217C2×SD16—21no—
218C2×D8D4×C1711yescharacteristic
219#131—21no—
220#131—21no—
221#131—21no—
222#131—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16D4×C1711yescharacteristic
226C22×C8—21no—
227C22×C8C23×C1711yescharacteristic
228C22⋊Q8—22no—
229C22⋊Q8—41no—
230#121—22no—
231#121—42no—
232#121—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235M32—21no—
236M32—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16D4×C1712yescomplemented
241#108—21no—
242#108—21no—
243#107—21no—
244#107—21no—
245#107—21no—
246#107D4×C1712yes—
247#103—22no—
248#103—41no—
249#102—22no—
250#102—41no—
251C17#1338511yescharacteristic, direct product factor, Sylow
252#41—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×Q8D8×C1711yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—42no—
266C2×D4D8×C1711yescharacteristic
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C2×D4×C1711yescharacteristic
272Q16—21no—
273Q16—21no—
274SD16—41no—
275SD16—41no—
276D8—21no—
277D8—21no—
278M16—21no—
279M16—21no—
280M16—41no—
281M16—41no—
282M16—41no—
283M16—41no—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8C2×D4×C1711yescharacteristic
289C2×C8C2×D4×C1711yescharacteristic
290C2×C8C2×D4×C1711yescharacteristic
291C2×C8#41×C1711yescharacteristic
292C2×C8#41×C1711yescharacteristic
293C2×C8#41×C1711yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C16—22no—
302C16—41no—
303C23—21no—
304C23—41no—
305C23C17×AGL(1,ℤ/8)11yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—41no—
309Q8—41no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—81no—
317D4—81no—
318D4—162no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—161no—
328C2×C4—161no—
329C2×C4C17×#12011yescharacteristic
330C2×C4C17×#12111yescharacteristic
331C2×C4C17×#12311yescharacteristic
332C2×C4C2×D8×C1711yescharacteristic
333C2×C4C17×#13511yescharacteristic
334C2×C4C17×#13711yescharacteristic
335C8—41no—
336C8—81no—
337C8C17×#12111yescharacteristic
338C8C17×#12111yescharacteristic
339C8C17×#12311yescharacteristic
340C8C17×#12411yescharacteristic
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22C17×#44711yescharacteristic
350C22C17×#46811yescharacteristic
351C22C17×#48211yescharacteristic
352C4—41no—
353C4—82no—
354C4—81no—
355C4—161no—
356C4C17×#39411yescharacteristic
357C4C17×#45211yescharacteristic
358C4C17×#46611yescharacteristic
359C4C17×#48011yescharacteristic
360C2—21no—
361C2—21no—
362C2—81no—
363C2—161no—
364C2C17×#203311yescharacteristic
365C2C17×#219311yescharacteristic
366C2C17×#219411yescharacteristic
subgroupG/H
center, socleC22×C17#447
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC17×#3061C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#367C2semidirect
3. C2×C17×#359C2semidirect
4. C17×#2139C2semidirect
5. C2×C17×#350C2semidirect
6. C17×#1816C2semidirect
7. C17×#1387C2semidirect
57. C2×C16×C17D4semidirect
119. #13385C17direct (N × H)
159. C2×#367C2×C17semidirect
160. C2×#359C2×C17semidirect
161. #2139C2×C17semidirect
162. C2×#350C2×C17semidirect
163. #1816C2×C17semidirect
164. #1387C2×C17semidirect
240. C2×C16D4×C17semidirect
251. C17#13385direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30612
C2×C17×#3672
C2×C17×#3592
C17×#21392
C2×C17×#3502
C17×#18162
C17×#13872
#1338517