Finite Group Databasebeta

← C17×#7732 #16865476

Subgroups — C17×#7732 #16865476

Order 4352.

420 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2860C211yesmaximal, characteristic
2C17×#1831C211yesmaximal, characteristic, complemented
3C17×#1831C211yesmaximal, characteristic, complemented
4C17×#1271C212yesmaximal, complemented
5C17×#1270C212yesmaximal
6C2×C17×#126—21no—
7C2×C17×C4⋊C8—21no—
8C2×C17×C4⋊C8—21no—
9C17×#390C411yescharacteristic
10C17×#390C411yescharacteristic
11C17×#390C2211yescharacteristic
12C17×#389C411yescharacteristic
13C17×#389C411yescharacteristic
14C17×#389C2211yescharacteristic
15C17×#388—21no—
16C17×#388—21no—
17C17×#388—21no—
18C43×C17C2211yescharacteristic
19C17×#336—21no—
20C17×#336—21no—
21C17×#336C2212yes—
22C17×#336C2212yes—
23C22×D4×C17C2×C411yescharacteristic
24C22×C8×C17—22no—
25C22×C8×C17—22no—
26C17×#126—42no—
27C17×#126—42no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17C2×C411yescharacteristic
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C22⋊C4×C17—21no—
35C2×C22⋊C4×C17—21no—
36C2×C22⋊C4×C17—21no—
37C2×C22⋊C4×C17—21no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—21no—
40C2×C42×C17C2×C411yescharacteristic
41C2×C42×C17C2×C411yescharacteristic
42C2×C42×C17D411yescharacteristic
43C2×C42×C17D411yescharacteristic
44C2×C42×C17D411yescharacteristic
45C2×C42×C17D411yescharacteristic
46C2×C42×C17C2311yescharacteristic
47C17×C4⋊C8—42no—
48C17×C4⋊C8—42no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C24×C17—21no—
53C2×D4×C17—22no—
54C2×D4×C17—41no—
55C2×D4×C17—41no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C22⋊C411yescharacteristic
62C22×C4×C17C22⋊C411yescharacteristic
63C22×C4×C17C22×C411yescharacteristic
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17C2×D411yescharacteristic
66C2×C8×C17—42no—
67C2×C8×C17—42no—
68C2×C8×C17—42no—
69C2×C8×C17—42no—
70C2×C8×C17—42no—
71C2×C8×C17—42no—
72C4⋊C4×C17—22no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—42no—
76C4⋊C4×C17—42no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C22⋊C4×C17—42no—
80C22⋊C4×C17—42no—
81C22⋊C4×C17—42no—
82C22⋊C4×C17—42no—
83C22⋊C4×C17—41no—
84C22⋊C4×C17—41no—
85C22⋊C4×C17—41no—
86C22⋊C4×C17—41no—
87C42×C17—22no—
88C42×C17—21no—
89C42×C17—21no—
90C42×C17—41no—
91C42×C17—41no—
92C42×C17—41no—
93C42×C17—41no—
94C42×C17D812yes—
95C42×C17SD1612yes—
96#7732C1711yesmaximal, characteristic, direct product factor, Sylow
97C23×C17—41no—
98C23×C17—41no—
99C23×C17—41no—
100C23×C17—41no—
101C23×C17—41no—
102C23×C17—41no—
103C23×C17—41no—
104C23×C17C2×C22⋊C411yescharacteristic
105D4×C17—82no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—21no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17—21no—
116C2×C4×C17—21no—
117C2×C4×C17—21no—
118C2×C4×C17—21no—
119C2×C4×C17—21no—
120C2×C4×C17—21no—
121C2×C4×C17—21no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17#10212yes—
132C2×C4×C17#10212yes—
133C2×C4×C17#13112yes—
134C2×C4×C17C2×D811yescharacteristic
135C2×C4×C17C2×SD1611yescharacteristic
136C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C17#13711yescharacteristic
138C8×C17—82no—
139C8×C17—82no—
140#2860C2×C1711yescharacteristic
141#1831C2×C1711yescharacteristic, complemented
142#1831C2×C1711yescharacteristic, complemented
143#1271C2×C1712yescomplemented
144#1270C2×C1712yes—
145C22×C17—81no—
146C22×C17—81no—
147C22×C17—81no—
148C22×C17—81no—
149C22×C17—81no—
150C22×C17—81no—
151C22×C17—81no—
152C22×C17#40811yescharacteristic
153C22×C17#41011yescharacteristic
154C22×C17#41311yescharacteristic
155C22×C17C2×#10211yescharacteristic
156C22×C17#41711yescharacteristic
157C22×C17#42111yescharacteristic
158C22×C17#42111yescharacteristic
159C4×C17—22no—
160C4×C17—22no—
161C4×C17—22no—
162C4×C17—21no—
163C4×C17—21no—
164C4×C17—21no—
165C4×C17—21no—
166C4×C17—41no—
167C4×C17—41no—
168C4×C17—81no—
169C4×C17—81no—
170C4×C17—81no—
171C2×#126—21no—
172C2×C4⋊C8—21no—
173C2×C4⋊C8—21no—
174#390C4×C1711yescharacteristic
175#390C4×C1711yescharacteristic
176#390C22×C1711yescharacteristic
177#389C4×C1711yescharacteristic
178#389C4×C1711yescharacteristic
179#389C22×C1711yescharacteristic
180#388—21no—
181#388—21no—
182#388—21no—
183C43C22×C1711yescharacteristic
184#336—21no—
185#336—21no—
186#336C22×C1712yes—
187#336C22×C1712yes—
188C2×C17—161no—
189C2×C17#147311yescharacteristic
190C2×C17#148011yescharacteristic
191C2×C17#149511yescharacteristic
192C2×C17#151211yescharacteristic
193C2×C17#151711yescharacteristic
194C2×C17#153511yescharacteristic
195C2×C17#154711yescharacteristic
196C22×D4C2×C4×C1711yescharacteristic
197C22×C8—22no—
198C22×C8—22no—
199#126—42no—
200#126—42no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×C4×C1711yescharacteristic
205C2×C4⋊C4C2×C4×C1711yescharacteristic
206C2×C4⋊C4C2×C4×C1711yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42C2×C4×C1711yescharacteristic
214C2×C42C2×C4×C1711yescharacteristic
215C2×C42D4×C1711yescharacteristic
216C2×C42D4×C1711yescharacteristic
217C2×C42D4×C1711yescharacteristic
218C2×C42D4×C1711yescharacteristic
219C2×C42C23×C1711yescharacteristic
220C4⋊C8—42no—
221C4⋊C8—42no—
222#95—21no—
223#95—21no—
224#95—21no—
225C17#773211yescharacteristic, direct product factor, Sylow
226C24—21no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4C22⋊C4×C1711yescharacteristic
234C22×C4C22⋊C4×C1711yescharacteristic
235C22×C4C22⋊C4×C1711yescharacteristic
236C22×C4C22⋊C4×C1711yescharacteristic
237C22×C4C22×C4×C1711yescharacteristic
238C22×C4C2×D4×C1711yescharacteristic
239C22×C4C2×D4×C1711yescharacteristic
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C42—22no—
262C42—21no—
263C42—21no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42D8×C1712yes—
269C42SD16×C1712yes—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊C4×C1711yescharacteristic
278D4—82no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4C17×#10212yes—
305C2×C4C17×#10212yes—
306C2×C4C17×#13112yes—
307C2×C4C2×D8×C1711yescharacteristic
308C2×C4C2×SD16×C1711yescharacteristic
309C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
310C2×C4C17×#13711yescharacteristic
311C8—82no—
312C8—82no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22C17×#40811yescharacteristic
321C22C17×#41011yescharacteristic
322C22C17×#41311yescharacteristic
323C22C2×C17×#10211yescharacteristic
324C22C17×#41711yescharacteristic
325C22C17×#42111yescharacteristic
326C22C17×#42111yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—161no—
340C2C17×#147311yescharacteristic
341C2C17×#148011yescharacteristic
342C2C17×#149511yescharacteristic
343C2C17×#151211yescharacteristic
344C2C17×#151711yescharacteristic
345C2C17×#153511yescharacteristic
346C2C17×#154711yescharacteristic
subgroupG/H
center, socleC23×C17C2×C22⋊C4
commutatorC22×C4C22×C4×C17
Frattini, cosocleC2×C42C23×C17
prime radicalC22×D4×C17C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C43×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#1831C2semidirect
3. C17×#1831C2semidirect
4. C17×#1271C2semidirect
96. #7732C17direct (N × H)
141. #1831C2×C17semidirect
142. #1831C2×C17semidirect
143. #1271C2×C17semidirect
225. C17#7732direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#28602
C17×#18312
C17×#12712
C17×#12702
#773217