Finite Group Databasebeta

← C17×#13399 #16871143

Subgroups — C17×#13399 #16871143

Order 4352.

406 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#470C211yesmaximal, characteristic
2C2×C17×#365C211yesmaximal, characteristic, complemented
3C2×C17×#362C211yesmaximal, characteristic, complemented
4C2×C17×#362C211yesmaximal, characteristic, complemented
5C2×C17×#349C211yesmaximal, characteristic
6C17×#1811C211yesmaximal, characteristic
7C17×#1383C211yesmaximal, characteristic, complemented
8C22×Q16×C17C2211yescharacteristic
9C22×M16×C17C2211yescharacteristic
10C2×C17×C22⋊Q8—21no—
11C2×C17×M32C2211yescharacteristic
12C2×C17×M32C2211yescharacteristic
13C17×#470—22no—
14C17×#470—22no—
15C2×C17×#108C2211yescharacteristic
16C2×C17×#108C2211yescharacteristic
17C2×C17×#106C2211yescharacteristic
18C2×C17×#103—21no—
19C17×#407—21no—
20C17×#365—22no—
21C17×#362—22no—
22C17×#362—22no—
23C17×#349—22no—
24C17×#341—21no—
25C22×Q8×C17—21no—
26C23×C4×C17D411yescharacteristic
27C2×Q16×C17—21no—
28C2×Q16×C17—21no—
29C2×Q16×C17—21no—
30C2×Q16×C17—21no—
31C2×Q16×C17—21no—
32C2×Q16×C17D412yes—
33C2×M16×C17—21no—
34C2×M16×C17—21no—
35C2×M16×C17—21no—
36C2×M16×C17—21no—
37C2×M16×C17—21no—
38C2×M16×C17—21no—
39C2×M16×C17—21no—
40C2×M16×C17—21no—
41C22×C8×C17D411yescharacteristic
42C22×C8×C17C2311yescharacteristic
43C17×C22⋊Q8—24no—
44C17×C22⋊Q8—42no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—41no—
47C2×C22⋊C4×C17—41no—
48C17×M32—21no—
49C17×M32—21no—
50C17×M32—21no—
51C17×M32D412yes—
52C2×C16×C17—21no—
53C2×C16×C17—21no—
54C17×#108—21no—
55C17×#108—21no—
56C17×#108—21no—
57C17×#108—21no—
58C17×#106—21no—
59C17×#106D412yes—
60C17×#103—24no—
61C17×C22⋊C8—42no—
62C24×C17SD1611yescharacteristic
63C2×Q8×C17—22no—
64C2×Q8×C17—41no—
65C2×Q8×C17—41no—
66C2×Q8×C17—41no—
67C2×Q8×C17—41no—
68C2×Q8×C17—41no—
69C22×C4×C17—21no—
70C22×C4×C17—21no—
71C22×C4×C17—21no—
72C22×C4×C17—21no—
73C22×C4×C17—21no—
74C22×C4×C17—21no—
75C22×C4×C17—41no—
76C22×C4×C17—41no—
77C22×C4×C17SD1611yescharacteristic
78C22×C4×C17C2×D411yescharacteristic
79Q16×C17—22no—
80Q16×C17—22no—
81Q16×C17—41no—
82Q16×C17—41no—
83M16×C17—41no—
84M16×C17—41no—
85M16×C17—41no—
86M16×C17—41no—
87M16×C17—41no—
88M16×C17—41no—
89M16×C17—41no—
90M16×C17—41no—
91C2×C8×C17—21no—
92C2×C8×C17—21no—
93C2×C8×C17—21no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C2×C8×C17C2×D411yescharacteristic
97C2×C8×C17C2×D411yescharacteristic
98C2×C8×C17C2×D411yescharacteristic
99C2×C8×C17#4111yescharacteristic
100C2×C8×C17#4111yescharacteristic
101C2×C8×C17#4111yescharacteristic
102C4⋊C4×C17—22no—
103C4⋊C4×C17—44no—
104C4⋊C4×C17—41no—
105C22⋊C4×C17—44no—
106C16×C17—22no—
107C16×C17—41no—
108#13399C1711yesmaximal, characteristic, direct product factor, Sylow
109C23×C17—21no—
110C23×C17—21no—
111C23×C17—21no—
112C23×C17—42no—
113C23×C17C2×SD1611yescharacteristic
114Q8×C17—42no—
115Q8×C17—42no—
116Q8×C17—81no—
117Q8×C17—81no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—42no—
126C2×C4×C17—42no—
127C2×C4×C17—82no—
128C2×C4×C17—81no—
129C2×C4×C17—81no—
130C2×C4×C17#12011yescharacteristic
131C2×C4×C17#12111yescharacteristic
132C2×C4×C17#12311yescharacteristic
133C2×C4×C17#13511yescharacteristic
134C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
136C8×C17—41no—
137C8×C17—81no—
138C8×C17—81no—
139C8×C17#12111yescharacteristic
140C8×C17#12111yescharacteristic
141C8×C17#12311yescharacteristic
142C8×C17#12411yescharacteristic
143C2×#470C2×C1711yescharacteristic
144C2×#365C2×C1711yescharacteristic, complemented
145C2×#362C2×C1711yescharacteristic, complemented
146C2×#362C2×C1711yescharacteristic, complemented
147C2×#349C2×C1711yescharacteristic
148#1811C2×C1711yescharacteristic
149#1383C2×C1711yescharacteristic, complemented
150C22×C17—22no—
151C22×C17—42no—
152C22×C17—42no—
153C22×C17—41no—
154C22×C17—81no—
155C22×C17#45011yescharacteristic
156C22×C17#46511yescharacteristic
157C22×C17#48111yescharacteristic
158C4×C17—41no—
159C4×C17—82no—
160C4×C17—82no—
161C4×C17#39411yescharacteristic
162C4×C17#44911yescharacteristic
163C4×C17#46911yescharacteristic
164C4×C17#48211yescharacteristic
165C22×Q16C22×C1711yescharacteristic
166C22×M16C22×C1711yescharacteristic
167C2×C22⋊Q8—21no—
168C2×M32C22×C1711yescharacteristic
169C2×M32C22×C1711yescharacteristic
170#470—22no—
171#470—22no—
172C2×#108C22×C1711yescharacteristic
173C2×#108C22×C1711yescharacteristic
174C2×#106C22×C1711yescharacteristic
175C2×#103—21no—
176#407—21no—
177#365—22no—
178#362—22no—
179#362—22no—
180#349—22no—
181#341—21no—
182C2×C17—21no—
183C2×C17—21no—
184C2×C17—81no—
185C2×C17#203411yescharacteristic
186C2×C17#223912yes—
187C22×Q8—21no—
188C23×C4D4×C1711yescharacteristic
189C2×Q16—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16D4×C1712yes—
195C2×M16—21no—
196C2×M16—21no—
197C2×M16—21no—
198C2×M16—21no—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—21no—
203C22×C8D4×C1711yescharacteristic
204C22×C8C23×C1711yescharacteristic
205C22⋊Q8—24no—
206C22⋊Q8—42no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—41no—
209C2×C22⋊C4—41no—
210M32—21no—
211M32—21no—
212M32—21no—
213M32D4×C1712yes—
214C2×C16—21no—
215C2×C16—21no—
216#108—21no—
217#108—21no—
218#108—21no—
219#108—21no—
220#106—21no—
221#106D4×C1712yes—
222#103—24no—
223C22⋊C8—42no—
224C17#1339911yescharacteristic, direct product factor, Sylow
225C24SD16×C1711yescharacteristic
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4SD16×C1711yescharacteristic
241C22×C4C2×D4×C1711yescharacteristic
242Q16—22no—
243Q16—22no—
244Q16—41no—
245Q16—41no—
246M16—41no—
247M16—41no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8C2×D4×C1711yescharacteristic
260C2×C8C2×D4×C1711yescharacteristic
261C2×C8C2×D4×C1711yescharacteristic
262C2×C8#41×C1711yescharacteristic
263C2×C8#41×C1711yescharacteristic
264C2×C8#41×C1711yescharacteristic
265C4⋊C4—22no—
266C4⋊C4—44no—
267C4⋊C4—41no—
268C22⋊C4—44no—
269C16—22no—
270C16—41no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—42no—
275C23C2×SD16×C1711yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—82no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C17×#12011yescharacteristic
293C2×C4C17×#12111yescharacteristic
294C2×C4C17×#12311yescharacteristic
295C2×C4C17×#13511yescharacteristic
296C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
297C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
298C8—41no—
299C8—81no—
300C8—81no—
301C8C17×#12111yescharacteristic
302C8C17×#12111yescharacteristic
303C8C17×#12311yescharacteristic
304C8C17×#12411yescharacteristic
305C22—22no—
306C22—42no—
307C22—42no—
308C22—41no—
309C22—81no—
310C22C17×#45011yescharacteristic
311C22C17×#46511yescharacteristic
312C22C17×#48111yescharacteristic
313C4—41no—
314C4—82no—
315C4—82no—
316C4C17×#39411yescharacteristic
317C4C17×#44911yescharacteristic
318C4C17×#46911yescharacteristic
319C4C17×#48211yescharacteristic
320C2—21no—
321C2—21no—
322C2—81no—
323C2C17×#203411yescharacteristic
324C2C17×#223912yes—
subgroupG/H
center, socleC22×C17#481
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC24×C17SD16
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C22×M16×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#365C2semidirect
3. C2×C17×#362C2semidirect
4. C2×C17×#362C2semidirect
7. C17×#1383C2semidirect
108. #13399C17direct (N × H)
144. C2×#365C2×C17semidirect
145. C2×#362C2×C17semidirect
146. C2×#362C2×C17semidirect
149. #1383C2×C17semidirect
224. C17#13399direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#4702
C2×C17×#3652
C2×C17×#3622
C2×C17×#3492
C17×#18112
C17×#13832
#1339917