Finite Group Databasebeta

← C17×#10444 #16868188

Subgroups — C17×#10444 #16868188

Order 4352.

440 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#461C211yesmaximal, characteristic
2C17×#1800C211yesmaximal, characteristic
3C17×#1571C211yesmaximal, characteristic, complemented
4C17×#1546C211yesmaximal, characteristic, complemented
5C17×#1546C211yesmaximal, characteristic, complemented
6C17×#1478C211yesmaximal, characteristic
7C17×#1301C211yesmaximal, characteristic, complemented
8C22×SD16×C17—21no—
9C2×C17×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C17C2211yescharacteristic
11C17×#461—22no—
12C17×#461—22no—
13C17×#431C2211yescharacteristic
14C17×#431C2211yescharacteristic
15C17×#423C2211yescharacteristic
16C17×#423C2211yescharacteristic
17C2×C17×C4⋊C8C2211yescharacteristic
18C2×C17×#103—21no—
19C2×C17×#100—21no—
20C17×#343—21no—
21C17×#335—22no—
22C17×#332—22no—
23C17×#332—22no—
24C17×D4⋊C8—22no—
25C22×Q8×C17—21no—
26C22×D4×C17D411yescharacteristic
27C23×C4×C17—21no—
28C2×SD16×C17—24no—
29C2×SD16×C17—42no—
30C2×SD16×C17—42no—
31C2×M16×C17—21no—
32C2×M16×C17—21no—
33C22×C8×C17—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—21no—
36C17×C4⋊Q8—21no—
37C17×C4⋊Q8D412yes—
38C4×D4×C17—21no—
39C4×D4×C17—21no—
40C4×D4×C17—21no—
41C4×D4×C17—21no—
42C2×C4⋊C4×C17—21no—
43C2×C4⋊C4×C17—21no—
44C2×C4⋊C4×C17D411yescharacteristic
45C2×C22⋊C4×C17—21no—
46C2×C42×C17C2311yescharacteristic
47C17×C4⋊C8—21no—
48C17×C4⋊C8—21no—
49C17×C4⋊C8—21no—
50C17×C4⋊C8—21no—
51C17×C4⋊C8—21no—
52C17×C4⋊C8—21no—
53C17×C4⋊C8D412yes—
54C17×C4⋊C8D412yes—
55C17×#103—24no—
56C17×#100—42no—
57C17×C22⋊C8—21no—
58C17×C22⋊C8—21no—
59C4×C8×C17—21no—
60C4×C8×C17—21no—
61C24×C17—21no—
62C2×Q8×C17—22no—
63C2×Q8×C17—41no—
64C2×Q8×C17—41no—
65C2×Q8×C17—41no—
66C2×Q8×C17—41no—
67C2×Q8×C17—41no—
68C2×D4×C17—21no—
69C2×D4×C17—21no—
70C2×D4×C17—21no—
71C2×D4×C17—21no—
72C2×D4×C17—21no—
73C2×D4×C17D812yes—
74C22×C4×C17—21no—
75C22×C4×C17—41no—
76C22×C4×C17—41no—
77C22×C4×C17—41no—
78C22×C4×C17—82no—
79C22×C4×C17C2×D411yescharacteristic
80C22×C4×C17#4111yescharacteristic
81C22×C4×C17#4111yescharacteristic
82SD16×C17—48no—
83M16×C17—41no—
84M16×C17—41no—
85M16×C17—41no—
86M16×C17—41no—
87C2×C8×C17—22no—
88C2×C8×C17—22no—
89C2×C8×C17—41no—
90C2×C8×C17—41no—
91C2×C8×C17—41no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C4⋊C4×C17—21no—
95C4⋊C4×C17—22no—
96C4⋊C4×C17—21no—
97C4⋊C4×C17—22no—
98C4⋊C4×C17—41no—
99C4⋊C4×C17—41no—
100C22⋊C4×C17—41no—
101C22⋊C4×C17—41no—
102C42×C17C2×D411yescharacteristic
103C42×C17C2×D411yescharacteristic
104C42×C17C2×D411yescharacteristic
105C42×C17#4111yescharacteristic
106#10444C1711yesmaximal, characteristic, direct product factor, Sylow
107C23×C17—22no—
108C23×C17—41no—
109C23×C17—41no—
110C23×C17—81no—
111C23×C17—81no—
112C23×C17#12311yescharacteristic
113Q8×C17—42no—
114Q8×C17—42no—
115Q8×C17—81no—
116Q8×C17—81no—
117D4×C17—22no—
118D4×C17—22no—
119D4×C17—41no—
120D4×C17—41no—
121C2×C4×C17—22no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—42no—
125C2×C4×C17—82no—
126C2×C4×C17—81no—
127C2×C4×C17—81no—
128C2×C4×C17—82no—
129C2×C4×C17—81no—
130C2×C4×C17#12011yescharacteristic
131C2×C4×C17#12111yescharacteristic
132C2×C4×C17#12111yescharacteristic
133C2×C4×C17#12111yescharacteristic
134C2×C4×C17#12311yescharacteristic
135C2×C4×C17#12411yescharacteristic
136C2×C4×C17C2×D811yescharacteristic
137C2×C4×C17#13511yescharacteristic
138C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C17#13711yescharacteristic
140C8×C17—42no—
141C8×C17—42no—
142C8×C17—81no—
143C8×C17—81no—
144C8×C17—81no—
145C2×#461C2×C1711yescharacteristic
146#1800C2×C1711yescharacteristic
147#1571C2×C1711yescharacteristic, complemented
148#1546C2×C1711yescharacteristic, complemented
149#1546C2×C1711yescharacteristic, complemented
150#1478C2×C1711yescharacteristic
151#1301C2×C1711yescharacteristic, complemented
152C22×C17—21no—
153C22×C17—21no—
154C22×C17—42no—
155C22×C17—82no—
156C22×C17—82no—
157C22×C17—81no—
158C22×C17—81no—
159C22×C17#39411yescharacteristic
160C22×C17#48011yescharacteristic
161C22×C17#48211yescharacteristic
162C4×C17—21no—
163C4×C17—21no—
164C4×C17—21no—
165C4×C17—82no—
166C4×C17—81no—
167C4×C17#44711yescharacteristic
168C4×C17#45211yescharacteristic
169C4×C17#46611yescharacteristic
170C4×C17#46811yescharacteristic
171C4×C17#47112yes—
172C22×SD16—21no—
173C2×C4⋊Q8C22×C1711yescharacteristic
174C2×C4×D4C22×C1711yescharacteristic
175#461—22no—
176#461—22no—
177#431C22×C1711yescharacteristic
178#431C22×C1711yescharacteristic
179#423C22×C1711yescharacteristic
180#423C22×C1711yescharacteristic
181C2×C4⋊C8C22×C1711yescharacteristic
182C2×#103—21no—
183C2×#100—21no—
184#343—21no—
185#335—22no—
186#332—22no—
187#332—22no—
188D4⋊C8—22no—
189C2×C17—21no—
190C2×C17—21no—
191C2×C17—82no—
192C2×C17#203311yescharacteristic
193C2×C17#204611yescharacteristic
194C2×C17#204911yescharacteristic
195C22×Q8—21no—
196C22×D4D4×C1711yescharacteristic
197C23×C4—21no—
198C2×SD16—24no—
199C2×SD16—42no—
200C2×SD16—42no—
201C2×M16—21no—
202C2×M16—21no—
203C22×C8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8D4×C1712yes—
208C4×D4—21no—
209C4×D4—21no—
210C4×D4—21no—
211C4×D4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4D4×C1711yescharacteristic
215C2×C22⋊C4—21no—
216C2×C42C23×C1711yescharacteristic
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8D4×C1712yes—
224C4⋊C8D4×C1712yes—
225#103—24no—
226#100—42no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C4×C8—21no—
230C4×C8—21no—
231C17#1044411yescharacteristic, direct product factor, Sylow
232C24—21no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4D8×C1712yes—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—82no—
250C22×C4C2×D4×C1711yescharacteristic
251C22×C4#41×C1711yescharacteristic
252C22×C4#41×C1711yescharacteristic
253SD16—48no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C42C2×D4×C1711yescharacteristic
274C42C2×D4×C1711yescharacteristic
275C42C2×D4×C1711yescharacteristic
276C42#41×C1711yescharacteristic
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23C17×#12311yescharacteristic
283Q8—42no—
284Q8—42no—
285Q8—81no—
286Q8—81no—
287D4—22no—
288D4—22no—
289D4—41no—
290D4—41no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4C17×#12011yescharacteristic
301C2×C4C17×#12111yescharacteristic
302C2×C4C17×#12111yescharacteristic
303C2×C4C17×#12111yescharacteristic
304C2×C4C17×#12311yescharacteristic
305C2×C4C17×#12411yescharacteristic
306C2×C4C2×D8×C1711yescharacteristic
307C2×C4C17×#13511yescharacteristic
308C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
309C2×C4C17×#13711yescharacteristic
310C8—42no—
311C8—42no—
312C8—81no—
313C8—81no—
314C8—81no—
315C22—21no—
316C22—21no—
317C22—42no—
318C22—82no—
319C22—82no—
320C22—81no—
321C22—81no—
322C22C17×#39411yescharacteristic
323C22C17×#48011yescharacteristic
324C22C17×#48211yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—82no—
329C4—81no—
330C4C17×#44711yescharacteristic
331C4C17×#45211yescharacteristic
332C4C17×#46611yescharacteristic
333C4C17×#46811yescharacteristic
334C4C17×#47112yes—
335C2—21no—
336C2—21no—
337C2—82no—
338C2C17×#203311yescharacteristic
339C2C17×#204611yescharacteristic
340C2C17×#204911yescharacteristic
subgroupG/H
center, socleC22×C17#394
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC22×D4×C17D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
3. C17×#1571C2semidirect
4. C17×#1546C2semidirect
5. C17×#1546C2semidirect
7. C17×#1301C2semidirect
106. #10444C17direct (N × H)
147. #1571C2×C17semidirect
148. #1546C2×C17semidirect
149. #1546C2×C17semidirect
151. #1301C2×C17semidirect
231. C17#10444direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#4612
C17×#18002
C17×#15712
C17×#15462
C17×#14782
C17×#13012
#1044417