Finite Group Databasebeta

← C17×#13400 #16871144

Subgroups — C17×#13400 #16871144

Order 4352.

402 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3060C211yesmaximal, characteristic
2C2×C17×#365C211yesmaximal, characteristic, complemented
3C17×#2148C211yesmaximal, characteristic, complemented
4C17×#2145C211yesmaximal, characteristic, complemented
5C17×#2117C211yesmaximal, characteristic, complemented
6C17×#1814C211yesmaximal, characteristic, complemented
7C17×#1386C211yesmaximal, characteristic, complemented
8C2×C17×#135C2211yescharacteristic
9C2×C17×#131C2211yescharacteristic
10C17×#537—21no—
11C2×C17×M32C2211yescharacteristic
12C2×C17×M32C2211yescharacteristic
13C17×#470—21no—
14C17×#469—21no—
15C17×#465—22no—
16C2×C17×#108C2211yescharacteristic
17C17×#427C2211yescharacteristic
18C2×C17×#106C2211yescharacteristic
19C17×#421—21no—
20C17×#417—21no—
21C17×#365—22no—
22C17×#362—21no—
23C17×#361—21no—
24C17×#360—22no—
25C17×#350—22no—
26C17×#344—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—
50C17×#117—21no—
51C2×C4⋊C4×C17—21no—
52C17×M32—21no—
53C17×M32—21no—
54C17×M32—21no—
55C17×M32D412yescomplemented
56C2×C16×C17—21no—
57C2×C16×C17—21no—
58C17×#108—21no—
59C17×#108—21no—
60C17×#107—21no—
61C17×#106—21no—
62C17×#106—21no—
63C17×#106D412yes—
64C17×#104—42no—
65C17×#103—22no—
66C17×#102—22no—
67#41×C17—21no—
68#41×C17—21no—
69#41×C17—21no—
70#41×C17—21no—
71#41×C17—41no—
72#41×C17—41no—
73#41×C17—41no—
74#41×C17—41no—
75C2×Q8×C17—21no—
76C2×Q8×C17SD1611yescharacteristic
77C2×D4×C17—21no—
78C2×D4×C17—21no—
79C2×D4×C17—41no—
80C2×D4×C17—42no—
81C2×D4×C17SD1611yescharacteristic
82C22×C4×C17—21no—
83C22×C4×C17—41no—
84C22×C4×C17—41no—
85C22×C4×C17C2×D411yescharacteristic
86Q16×C17—21no—
87Q16×C17—21no—
88SD16×C17—41no—
89SD16×C17—41no—
90D8×C17—21no—
91D8×C17—21no—
92M16×C17—21no—
93M16×C17—21no—
94M16×C17—41no—
95M16×C17—41no—
96M16×C17—41no—
97M16×C17—41no—
98C2×C8×C17—21no—
99C2×C8×C17—41no—
100C2×C8×C17—41no—
101C2×C8×C17—41no—
102C2×C8×C17C2×D411yescharacteristic
103C2×C8×C17C2×D411yescharacteristic
104C2×C8×C17C2×D411yescharacteristic
105C2×C8×C17#4111yescharacteristic
106C2×C8×C17#4111yescharacteristic
107C2×C8×C17#4111yescharacteristic
108C4⋊C4×C17—22no—
109C4⋊C4×C17—42no—
110C4⋊C4×C17—41no—
111C4⋊C4×C17—41no—
112C22⋊C4×C17—42no—
113C22⋊C4×C17—42no—
114C22⋊C4×C17—41no—
115C42×C17—41no—
116C16×C17—22no—
117C16×C17—41no—
118#13400C1711yesmaximal, characteristic, direct product factor, Sylow
119C23×C17—21no—
120C23×C17—41no—
121C23×C17AGL(1,ℤ/8)11yescharacteristic
122Q8×C17—21no—
123Q8×C17—21no—
124Q8×C17—41no—
125Q8×C17—41no—
126D4×C17—21no—
127D4×C17—21no—
128D4×C17—41no—
129D4×C17—41no—
130D4×C17—41no—
131D4×C17—41no—
132D4×C17—81no—
133D4×C17—81no—
134D4×C17—162no—
135C2×C4×C17—21no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—42no—
139C2×C4×C17—41no—
140C2×C4×C17—81no—
141C2×C4×C17—81no—
142C2×C4×C17—81no—
143C2×C4×C17—161no—
144C2×C4×C17#12011yescharacteristic
145C2×C4×C17#12111yescharacteristic
146C2×C4×C17#12311yescharacteristic
147C2×C4×C17C2×SD1611yescharacteristic
148C2×C4×C17#13511yescharacteristic
149C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
150C8×C17—41no—
151C8×C17—81no—
152C8×C17#12111yescharacteristic
153C8×C17#12111yescharacteristic
154C8×C17#12311yescharacteristic
155C8×C17#12411yescharacteristic
156#3060C2×C1711yescharacteristic
157C2×#365C2×C1711yescharacteristic, complemented
158#2148C2×C1711yescharacteristic, complemented
159#2145C2×C1711yescharacteristic, complemented
160#2117C2×C1711yescharacteristic, complemented
161#1814C2×C1711yescharacteristic, complemented
162#1386C2×C1711yescharacteristic, complemented
163C22×C17—41no—
164C22×C17—42no—
165C22×C17—41no—
166C22×C17—81no—
167C22×C17—81no—
168C22×C17—81no—
169C22×C17#45011yescharacteristic
170C22×C17#46911yescharacteristic
171C22×C17#48211yescharacteristic
172C4×C17—41no—
173C4×C17—82no—
174C4×C17—81no—
175C4×C17—161no—
176C4×C17#39411yescharacteristic
177C4×C17#44911yescharacteristic
178C4×C17#46511yescharacteristic
179C4×C17#48111yescharacteristic
180C2×#135C22×C1711yescharacteristic
181C2×#131C22×C1711yescharacteristic
182#537—21no—
183C2×M32C22×C1711yescharacteristic
184C2×M32C22×C1711yescharacteristic
185#470—21no—
186#469—21no—
187#465—22no—
188C2×#108C22×C1711yescharacteristic
189#427C22×C1711yescharacteristic
190C2×#106C22×C1711yescharacteristic
191#421—21no—
192#417—21no—
193#365—22no—
194#362—21no—
195#361—21no—
196#360—22no—
197#350—22no—
198#344—21no—
199C2×C17—21no—
200C2×C17—21no—
201C2×C17—21no—
202C2×C17—81no—
203C2×C17—161no—
204C2×C17#203411yescharacteristic
205C2×#41—21no—
206C2×#41D4×C1711yescharacteristic
207#135—21no—
208#135—21no—
209#135—21no—
210#135—21no—
211C2×Q16D4×C1711yescharacteristic
212C2×SD16—21no—
213C2×D8D4×C1711yescharacteristic
214#131—21no—
215#131—21no—
216#131—21no—
217#131—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16D4×C1711yescharacteristic
221C22×C8—21no—
222C22×C8C23×C1711yescharacteristic
223C22⋊Q8—22no—
224C22⋊Q8—41no—
225#121—22no—
226#121—42no—
227#121—41no—
228#117—21no—
229C2×C4⋊C4—21no—
230M32—21no—
231M32—21no—
232M32—21no—
233M32D4×C1712yescomplemented
234C2×C16—21no—
235C2×C16—21no—
236#108—21no—
237#108—21no—
238#107—21no—
239#106—21no—
240#106—21no—
241#106D4×C1712yes—
242#104—42no—
243#103—22no—
244#102—22no—
245C17#1340011yescharacteristic, direct product factor, Sylow
246#41—21no—
247#41—21no—
248#41—21no—
249#41—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8SD16×C1711yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—42no—
260C2×D4SD16×C1711yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C1711yescharacteristic
265Q16—21no—
266Q16—21no—
267SD16—41no—
268SD16—41no—
269D8—21no—
270D8—21no—
271M16—21no—
272M16—21no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16—41no—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8C2×D4×C1711yescharacteristic
282C2×C8C2×D4×C1711yescharacteristic
283C2×C8C2×D4×C1711yescharacteristic
284C2×C8#41×C1711yescharacteristic
285C2×C8#41×C1711yescharacteristic
286C2×C8#41×C1711yescharacteristic
287C4⋊C4—22no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C42—41no—
295C16—22no—
296C16—41no—
297C23—21no—
298C23—41no—
299C23C17×AGL(1,ℤ/8)11yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—41no—
303Q8—41no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—41no—
308D4—41no—
309D4—41no—
310D4—81no—
311D4—81no—
312D4—162no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—161no—
322C2×C4C17×#12011yescharacteristic
323C2×C4C17×#12111yescharacteristic
324C2×C4C17×#12311yescharacteristic
325C2×C4C2×SD16×C1711yescharacteristic
326C2×C4C17×#13511yescharacteristic
327C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
328C8—41no—
329C8—81no—
330C8C17×#12111yescharacteristic
331C8C17×#12111yescharacteristic
332C8C17×#12311yescharacteristic
333C8C17×#12411yescharacteristic
334C22—41no—
335C22—42no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C17×#45011yescharacteristic
341C22C17×#46911yescharacteristic
342C22C17×#48211yescharacteristic
343C4—41no—
344C4—82no—
345C4—81no—
346C4—161no—
347C4C17×#39411yescharacteristic
348C4C17×#44911yescharacteristic
349C4C17×#46511yescharacteristic
350C4C17×#48111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—81no—
355C2—161no—
356C2C17×#203411yescharacteristic
subgroupG/H
center, socleC2×C17#2034
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC17×#3060C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×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×#365C2semidirect
3. C17×#2148C2semidirect
4. C17×#2145C2semidirect
5. C17×#2117C2semidirect
6. C17×#1814C2semidirect
7. C17×#1386C2semidirect
55. C17×M32D4semidirect
118. #13400C17direct (N × H)
157. C2×#365C2×C17semidirect
158. #2148C2×C17semidirect
159. #2145C2×C17semidirect
160. #2117C2×C17semidirect
161. #1814C2×C17semidirect
162. #1386C2×C17semidirect
233. M32D4×C17semidirect
245. C17#13400direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30602
C2×C17×#3652
C17×#21482
C17×#21452
C17×#21172
C17×#18142
C17×#13862
#1340017