Finite Group Databasebeta

← C17×#13446 #16871190

Subgroups — C17×#13446 #16871190

Order 4352.

396 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#510C211yesmaximal, characteristic
2C2×C17×#364C211yesmaximal, characteristic, complemented
3C2×C17×#362C211yesmaximal, characteristic, complemented
4C17×#2139C211yesmaximal, characteristic
5C17×#1974C211yesmaximal, characteristic
6C17×#1969C211yesmaximal, characteristic, complemented
7C17×#1387C211yesmaximal, characteristic, complemented
8C2×C17×#135C2211yescharacteristic
9C22×Q16×C17C2211yescharacteristic
10C17×#510—22no—
11C17×#510—22no—
12C2×C17×Q32—21no—
13C2×C17×SD32—21no—
14C2×C17×M32C2211yescharacteristic
15C2×C17×M32C2211yescharacteristic
16C2×C17×#108C2211yescharacteristic
17C2×C17×#107C2211yescharacteristic
18C2×C17×#104—21no—
19C2×C17×#103—21no—
20C17×#408—21no—
21C2×C4×C8×C17C2211yescharacteristic
22C17×#391—21no—
23C17×#364—22no—
24C17×#362—22no—
25C17×#358—21no—
26C17×#357—21no—
27C2×#41×C17—21no—
28C22×Q8×C17—21no—
29C17×#135—21no—
30C17×#135—21no—
31C17×#135—21no—
32C17×#135—21no—
33C2×Q16×C17—21no—
34C2×Q16×C17—21no—
35C2×Q16×C17—21no—
36C2×Q16×C17—21no—
37C2×Q16×C17—21no—
38C2×Q16×C17D411yescharacteristic
39C2×Q16×C17D412yes—
40C2×SD16×C17—21no—
41C2×D8×C17D411yescharacteristic
42C2×M16×C17—21no—
43C22×C8×C17D411yescharacteristic
44C22×C8×C17C2311yescharacteristic
45C2×C4⋊C4×C17—21no—
46C2×C42×C17D411yescharacteristic
47C17×Q32—24no—
48C17×SD32—24no—
49C17×M32—21no—
50C17×M32—21no—
51C17×M32—21no—
52C17×M32D412yes—
53C2×C16×C17—21no—
54C2×C16×C17—21no—
55C17×#108—21no—
56C17×#108—21no—
57C17×#107—21no—
58C17×#107—21no—
59C17×#104—42no—
60C17×#103—42no—
61C17×C22⋊C8—42no—
62C4×C8×C17—21no—
63C4×C8×C17—21no—
64C17×#95—42no—
65#41×C17—41no—
66#41×C17—41no—
67#41×C17—41no—
68#41×C17—41no—
69C2×Q8×C17—21no—
70C2×Q8×C17—22no—
71C2×Q8×C17—41no—
72C2×Q8×C17—41no—
73C2×Q8×C17—41no—
74C2×Q8×C17—41no—
75C2×Q8×C17—41no—
76C2×D4×C17—21no—
77C2×D4×C17—41no—
78C22×C4×C17—21no—
79C22×C4×C17—41no—
80C22×C4×C17—41no—
81C22×C4×C17—41no—
82C22×C4×C17C2×D411yescharacteristic
83Q16×C17—22no—
84Q16×C17—21no—
85Q16×C17—22no—
86Q16×C17—21no—
87Q16×C17—41no—
88Q16×C17—41no—
89SD16×C17—41no—
90SD16×C17—41no—
91D8×C17—21no—
92D8×C17—21no—
93M16×C17—41no—
94M16×C17—41no—
95C2×C8×C17—21no—
96C2×C8×C17—21no—
97C2×C8×C17—41no—
98C2×C8×C17D812yes—
99C2×C8×C17C2×D411yescharacteristic
100C2×C8×C17C2×D411yescharacteristic
101C2×C8×C17C2×D411yescharacteristic
102C2×C8×C17#4111yescharacteristic
103C2×C8×C17#4111yescharacteristic
104C2×C8×C17#4111yescharacteristic
105C4⋊C4×C17—41no—
106C4⋊C4×C17—41no—
107C42×C17—21no—
108C42×C17—21no—
109C16×C17—22no—
110C16×C17—41no—
111#13446C1711yesmaximal, characteristic, direct product factor, Sylow
112C23×C17—41no—
113C23×C17AGL(1,ℤ/8)11yescharacteristic
114Q8×C17—41no—
115Q8×C17—42no—
116Q8×C17—42no—
117Q8×C17—41no—
118Q8×C17—81no—
119Q8×C17—81no—
120D4×C17—41no—
121D4×C17—41no—
122D4×C17—81no—
123D4×C17—81no—
124C2×C4×C17—22no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—42no—
129C2×C4×C17—81no—
130C2×C4×C17—81no—
131C2×C4×C17—81no—
132C2×C4×C17—81no—
133C2×C4×C17—82no—
134C2×C4×C17—81no—
135C2×C4×C17#12111yescharacteristic
136C2×C4×C17#12111yescharacteristic
137C2×C4×C17#12111yescharacteristic
138C2×C4×C17C2×D811yescharacteristic
139C2×C4×C17#13511yescharacteristic
140C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
141C8×C17—22no—
142C8×C17—81no—
143C8×C17#12011yescharacteristic
144C8×C17#12311yescharacteristic
145C8×C17#12311yescharacteristic
146C8×C17#12411yescharacteristic
147C2×#510C2×C1711yescharacteristic
148C2×#364C2×C1711yescharacteristic, complemented
149C2×#362C2×C1711yescharacteristic, complemented
150#2139C2×C1711yescharacteristic
151#1974C2×C1711yescharacteristic
152#1969C2×C1711yescharacteristic, complemented
153#1387C2×C1711yescharacteristic, complemented
154C22×C17—21no—
155C22×C17—21no—
156C22×C17—81no—
157C22×C17—81no—
158C22×C17—81no—
159C22×C17#45911yescharacteristic
160C22×C17#46311yescharacteristic
161C22×C17#46911yescharacteristic
162C4×C17—42no—
163C4×C17—81no—
164C4×C17—82no—
165C4×C17—161no—
166C4×C17#39411yescharacteristic
167C4×C17#45911yescharacteristic
168C4×C17#46311yescharacteristic
169C4×C17#46611yescharacteristic
170C2×#135C22×C1711yescharacteristic
171C22×Q16C22×C1711yescharacteristic
172#510—22no—
173#510—22no—
174C2×Q32—21no—
175C2×SD32—21no—
176C2×M32C22×C1711yescharacteristic
177C2×M32C22×C1711yescharacteristic
178C2×#108C22×C1711yescharacteristic
179C2×#107C22×C1711yescharacteristic
180C2×#104—21no—
181C2×#103—21no—
182#408—21no—
183C2×C4×C8C22×C1711yescharacteristic
184#391—21no—
185#364—22no—
186#362—22no—
187#358—21no—
188#357—21no—
189C2×C17—21no—
190C2×C17—21no—
191C2×C17—161no—
192C2×C17#205411yescharacteristic
193C2×C17#221211yescharacteristic
194C2×C17#221411yescharacteristic
195C2×#41—21no—
196C22×Q8—21no—
197#135—21no—
198#135—21no—
199#135—21no—
200#135—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16D4×C1712yes—
207C2×Q16D4×C1711yescharacteristic
208C2×SD16—21no—
209C2×D8D4×C1711yescharacteristic
210C2×M16—21no—
211C22×C8D4×C1711yescharacteristic
212C22×C8C23×C1711yescharacteristic
213C2×C4⋊C4—21no—
214C2×C42D4×C1711yescharacteristic
215Q32—24no—
216SD32—24no—
217M32—21no—
218M32—21no—
219M32—21no—
220M32D4×C1712yes—
221C2×C16—21no—
222C2×C16—21no—
223#108—21no—
224#108—21no—
225#107—21no—
226#107—21no—
227#104—42no—
228#103—42no—
229C22⋊C8—42no—
230C4×C8—21no—
231C4×C8—21no—
232#95—42no—
233C17#1344611yescharacteristic, direct product factor, Sylow
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×D4—21no—
246C2×D4—41no—
247C22×C4—21no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×D4×C1711yescharacteristic
252Q16—22no—
253Q16—21no—
254Q16—22no—
255Q16—21no—
256Q16—41no—
257Q16—41no—
258SD16—41no—
259SD16—41no—
260D8—21no—
261D8—21no—
262M16—41no—
263M16—41no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—41no—
267C2×C8D8×C1712yes—
268C2×C8C2×D4×C1711yescharacteristic
269C2×C8C2×D4×C1711yescharacteristic
270C2×C8C2×D4×C1711yescharacteristic
271C2×C8#41×C1711yescharacteristic
272C2×C8#41×C1711yescharacteristic
273C2×C8#41×C1711yescharacteristic
274C4⋊C4—41no—
275C4⋊C4—41no—
276C42—21no—
277C42—21no—
278C16—22no—
279C16—41no—
280C23—41no—
281C23C17×AGL(1,ℤ/8)11yescharacteristic
282Q8—41no—
283Q8—42no—
284Q8—42no—
285Q8—41no—
286Q8—81no—
287Q8—81no—
288D4—41no—
289D4—41no—
290D4—81no—
291D4—81no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—82no—
302C2×C4—81no—
303C2×C4C17×#12111yescharacteristic
304C2×C4C17×#12111yescharacteristic
305C2×C4C17×#12111yescharacteristic
306C2×C4C2×D8×C1711yescharacteristic
307C2×C4C17×#13511yescharacteristic
308C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
309C8—22no—
310C8—81no—
311C8C17×#12011yescharacteristic
312C8C17×#12311yescharacteristic
313C8C17×#12311yescharacteristic
314C8C17×#12411yescharacteristic
315C22—21no—
316C22—21no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22C17×#45911yescharacteristic
321C22C17×#46311yescharacteristic
322C22C17×#46911yescharacteristic
323C4—42no—
324C4—81no—
325C4—82no—
326C4—161no—
327C4C17×#39411yescharacteristic
328C4C17×#45911yescharacteristic
329C4C17×#46311yescharacteristic
330C4C17×#46611yescharacteristic
331C2—21no—
332C2—21no—
333C2—161no—
334C2C17×#205411yescharacteristic
335C2C17×#221211yescharacteristic
336C2C17×#221411yescharacteristic
subgroupG/H
center, socleC22×C17#459
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC2×C17×#135C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#364C2semidirect
3. C2×C17×#362C2semidirect
6. C17×#1969C2semidirect
7. C17×#1387C2semidirect
111. #13446C17direct (N × H)
148. C2×#364C2×C17semidirect
149. C2×#362C2×C17semidirect
152. #1969C2×C17semidirect
153. #1387C2×C17semidirect
233. C17#13446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#5102
C2×C17×#3642
C2×C17×#3622
C17×#21392
C17×#19742
C17×#19692
C17×#13872
#1344617