Finite Group Databasebeta

← C17×#10469 #16868213

Subgroups — C17×#10469 #16868213

Order 4352.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3077C211yesmaximal, characteristic
2C17×#1804C211yesmaximal, characteristic
3C17×#1571C211yesmaximal, characteristic, complemented
4C17×#1542C211yesmaximal, characteristic, complemented
5C17×#1518C211yesmaximal, characteristic, complemented
6C17×#1460C211yesmaximal, characteristic
7C17×#1286C211yesmaximal, characteristic, complemented
8C17×#533C2211yescharacteristic
9C2×C4×D4×C17C2211yescharacteristic
10C17×#478—22no—
11C17×#476—21no—
12C17×#474—21no—
13C17×#431C2211yescharacteristic
14C17×#431C2211yescharacteristic
15C17×#428—21no—
16C17×#423C2211yescharacteristic
17C2×C17×C4⋊C8C2211yescharacteristic
18C17×#418—21no—
19C2×C17×#102—21no—
20C17×#382C2211yescharacteristic
21C17×#340—21no—
22C17×#335—22no—
23C17×#333—21no—
24C17×#332—21no—
25C17×#328—22no—
26C17×#323—22no—
27C22×D4×C17D411yescharacteristic
28C23×C4×C17—21no—
29C2×M16×C17—21no—
30C22×C8×C17—21no—
31C17×C4⋊Q8D411yescharacteristic
32C17×C4⋊Q8D411yescharacteristic
33C17×#125—21no—
34C17×C22⋊Q8—21no—
35C17×C22⋊Q8—21no—
36C4×Q8×C17—21no—
37C4×Q8×C17—21no—
38C4×D4×C17—21no—
39C4×D4×C17—21no—
40C4×D4×C17—21no—
41C4×D4×C17—21no—
42C17×#117—21no—
43C2×C4⋊C4×C17—21no—
44C2×C4⋊C4×C17D411yescharacteristic
45C2×C22⋊C4×C17—21no—
46C2×C42×C17C2311yescharacteristic
47C17×#107—22no—
48C17×#106—22no—
49C17×C4⋊C8—21no—
50C17×C4⋊C8—21no—
51C17×C4⋊C8—21no—
52C17×C4⋊C8—21no—
53C17×C4⋊C8—21no—
54C17×C4⋊C8D412yes—
55C17×#102—22no—
56C17×#102—22no—
57C17×#102—42no—
58C17×C22⋊C8—21no—
59C17×C22⋊C8D412yes—
60C4×C8×C17—21no—
61C4×C8×C17—21no—
62C17×#95—21no—
63C17×#95—21no—
64C24×C17—21no—
65C2×Q8×C17—21no—
66C2×Q8×C17—21no—
67C2×D4×C17—21no—
68C2×D4×C17—21no—
69C2×D4×C17—21no—
70C2×D4×C17—21no—
71C2×D4×C17—21no—
72C2×D4×C17Q1612yes—
73C22×C4×C17—21no—
74C22×C4×C17—41no—
75C22×C4×C17—41no—
76C22×C4×C17—41no—
77C22×C4×C17—82no—
78C22×C4×C17C2×D411yescharacteristic
79C22×C4×C17C2×D411yescharacteristic
80C22×C4×C17#4111yescharacteristic
81M16×C17—41no—
82M16×C17—41no—
83C2×C8×C17—22no—
84C2×C8×C17—22no—
85C2×C8×C17—41no—
86C2×C8×C17—41no—
87C2×C8×C17—41no—
88C2×C8×C17—41no—
89C4⋊C4×C17—21no—
90C4⋊C4×C17—21no—
91C4⋊C4×C17—21no—
92C4⋊C4×C17—21no—
93C4⋊C4×C17—21no—
94C4⋊C4×C17—21no—
95C4⋊C4×C17—41no—
96C4⋊C4×C17—41no—
97C4⋊C4×C17—41no—
98C4⋊C4×C17—41no—
99C22⋊C4×C17—41no—
100C22⋊C4×C17—41no—
101C22⋊C4×C17—41no—
102C42×C17—41no—
103C42×C17C2×D411yescharacteristic
104C42×C17C2×D411yescharacteristic
105C42×C17#4111yescharacteristic
106C42×C17#4111yescharacteristic
107#10469C1711yesmaximal, characteristic, direct product factor, Sylow
108C23×C17—22no—
109C23×C17—41no—
110C23×C17—41no—
111C23×C17—81no—
112C23×C17—81no—
113C23×C17#12111yescharacteristic
114Q8×C17—81no—
115Q8×C17—81no—
116D4×C17—22no—
117D4×C17—22no—
118D4×C17—41no—
119D4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—82no—
126C2×C4×C17—82no—
127C2×C4×C17—81no—
128C2×C4×C17—81no—
129C2×C4×C17—81no—
130C2×C4×C17—81no—
131C2×C4×C17#12011yescharacteristic
132C2×C4×C17#12111yescharacteristic
133C2×C4×C17#12111yescharacteristic
134C2×C4×C17#12311yescharacteristic
135C2×C4×C17#12311yescharacteristic
136C2×C4×C17#12411yescharacteristic
137C2×C4×C17C2×Q1611yescharacteristic
138C2×C4×C17#13511yescharacteristic
139C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C17#13711yescharacteristic
141C8×C17—42no—
142C8×C17—42no—
143C8×C17—81no—
144C8×C17—81no—
145#3077C2×C1711yescharacteristic
146#1804C2×C1711yescharacteristic
147#1571C2×C1711yescharacteristic, complemented
148#1542C2×C1711yescharacteristic, complemented
149#1518C2×C1711yescharacteristic, complemented
150#1460C2×C1711yescharacteristic
151#1286C2×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#46711yescharacteristic
161C22×C17#46811yescharacteristic
162C4×C17—21no—
163C4×C17—21no—
164C4×C17—21no—
165C4×C17—21no—
166C4×C17—81no—
167C4×C17—81no—
168C4×C17—81no—
169C4×C17—161no—
170C4×C17#44911yescharacteristic
171C4×C17#45111yescharacteristic
172C4×C17#48411yescharacteristic
173C4×C17#48511yescharacteristic
174#533C22×C1711yescharacteristic
175C2×C4×D4C22×C1711yescharacteristic
176#478—22no—
177#476—21no—
178#474—21no—
179#431C22×C1711yescharacteristic
180#431C22×C1711yescharacteristic
181#428—21no—
182#423C22×C1711yescharacteristic
183C2×C4⋊C8C22×C1711yescharacteristic
184#418—21no—
185C2×#102—21no—
186#382C22×C1711yescharacteristic
187#340—21no—
188#335—22no—
189#333—21no—
190#332—21no—
191#328—22no—
192#323—22no—
193C2×C17—21no—
194C2×C17—21no—
195C2×C17—82no—
196C2×C17#203611yescharacteristic
197C2×C17#204811yescharacteristic
198C2×C17#205311yescharacteristic
199C22×D4D4×C1711yescharacteristic
200C23×C4—21no—
201C2×M16—21no—
202C22×C8—21no—
203C4⋊Q8D4×C1711yescharacteristic
204C4⋊Q8D4×C1711yescharacteristic
205#125—21no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208C4×Q8—21no—
209C4×Q8—21no—
210C4×D4—21no—
211C4×D4—21no—
212C4×D4—21no—
213C4×D4—21no—
214#117—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4D4×C1711yescharacteristic
217C2×C22⋊C4—21no—
218C2×C42C23×C1711yescharacteristic
219#107—22no—
220#106—22no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8D4×C1712yes—
227#102—22no—
228#102—22no—
229#102—42no—
230C22⋊C8—21no—
231C22⋊C8D4×C1712yes—
232C4×C8—21no—
233C4×C8—21no—
234#95—21no—
235#95—21no—
236C17#1046911yescharacteristic, direct product factor, Sylow
237C24—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4Q16×C1712yes—
246C22×C4—21no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—82no—
251C22×C4C2×D4×C1711yescharacteristic
252C22×C4C2×D4×C1711yescharacteristic
253C22×C4#41×C1711yescharacteristic
254M16—41no—
255M16—41no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C42—41no—
276C42C2×D4×C1711yescharacteristic
277C42C2×D4×C1711yescharacteristic
278C42#41×C1711yescharacteristic
279C42#41×C1711yescharacteristic
280C23—22no—
281C23—41no—
282C23—41no—
283C23—81no—
284C23—81no—
285C23C17×#12111yescharacteristic
286Q8—81no—
287Q8—81no—
288D4—22no—
289D4—22no—
290D4—41no—
291D4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4C17×#12011yescharacteristic
304C2×C4C17×#12111yescharacteristic
305C2×C4C17×#12111yescharacteristic
306C2×C4C17×#12311yescharacteristic
307C2×C4C17×#12311yescharacteristic
308C2×C4C17×#12411yescharacteristic
309C2×C4C2×Q16×C1711yescharacteristic
310C2×C4C17×#13511yescharacteristic
311C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
312C2×C4C17×#13711yescharacteristic
313C8—42no—
314C8—42no—
315C8—81no—
316C8—81no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—82no—
321C22—82no—
322C22—81no—
323C22—81no—
324C22C17×#39411yescharacteristic
325C22C17×#46711yescharacteristic
326C22C17×#46811yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—161no—
335C4C17×#44911yescharacteristic
336C4C17×#45111yescharacteristic
337C4C17×#48411yescharacteristic
338C4C17×#48511yescharacteristic
339C2—21no—
340C2—21no—
341C2—82no—
342C2C17×#203611yescharacteristic
343C2C17×#204811yescharacteristic
344C2C17×#205311yescharacteristic
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×#1542C2semidirect
5. C17×#1518C2semidirect
7. C17×#1286C2semidirect
107. #10469C17direct (N × H)
147. #1571C2×C17semidirect
148. #1542C2×C17semidirect
149. #1518C2×C17semidirect
151. #1286C2×C17semidirect
236. C17#10469direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#30772
C17×#18042
C17×#15712
C17×#15422
C17×#15182
C17×#14602
C17×#12862
#1046917