Finite Group Databasebeta

← C17×#7672 #16865416

Subgroups — C17×#7672 #16865416

Order 4352.

438 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2860C211yesmaximal, characteristic
2C17×#1839C211yesmaximal, characteristic, complemented
3C4×C17×C4⋊C8C211yesmaximal, characteristic, complemented
4C17×#1271C212yesmaximal, complemented
5C17×#1270C212yesmaximal
6C2×C17×#126—21no—
7C2×C17×C4⋊C8—21no—
8C2×C4×C8×C17—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—24no—
48C4×C8×C17—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—24no—
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—42no—
86C42×C17—22no—
87C42×C17—22no—
88C42×C17—22no—
89C42×C17—41no—
90C42×C17—41no—
91C42×C17—41no—
92C42×C17D812yes—
93C42×C17SD1612yes—
94#7672C1711yesmaximal, characteristic, direct product factor, Sylow
95C23×C17—41no—
96C23×C17—41no—
97C23×C17—41no—
98C23×C17—41no—
99C23×C17—41no—
100C23×C17—41no—
101C23×C17—41no—
102C23×C17C2×C22⋊C411yescharacteristic
103D4×C17—82no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
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—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
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#10212yes—
129C2×C4×C17#10212yes—
130C2×C4×C17#10412yes—
131C2×C4×C17#13112yes—
132C2×C4×C17C2×D811yescharacteristic
133C2×C4×C17C2×SD1611yescharacteristic
134C2×C4×C17#13512yes—
135C8×C17—44no—
136C8×C17—82no—
137#2860C2×C1711yescharacteristic
138#1839C2×C1711yescharacteristic, complemented
139C4×C4⋊C8C2×C1711yescharacteristic, complemented
140#1271C2×C1712yescomplemented
141#1270C2×C1712yes—
142C22×C17—81no—
143C22×C17—81no—
144C22×C17—81no—
145C22×C17—81no—
146C22×C17—81no—
147C22×C17—81no—
148C22×C17—81no—
149C22×C17#40811yescharacteristic
150C22×C17#41011yescharacteristic
151C22×C17#41311yescharacteristic
152C22×C17C2×#10211yescharacteristic
153C22×C17#41611yescharacteristic
154C22×C17C2×#10411yescharacteristic
155C22×C17#42111yescharacteristic
156C4×C17—22no—
157C4×C17—22no—
158C4×C17—22no—
159C4×C17—22no—
160C4×C17—21no—
161C4×C17—21no—
162C4×C17—22no—
163C4×C17—41no—
164C4×C17—81no—
165C4×C17—81no—
166C4×C17—81no—
167C2×#126—21no—
168C2×C4⋊C8—21no—
169C2×C4×C8—21no—
170#390C4×C1711yescharacteristic
171#390C4×C1711yescharacteristic
172#390C22×C1711yescharacteristic
173#389C4×C1711yescharacteristic
174#389C4×C1711yescharacteristic
175#389C22×C1711yescharacteristic
176#388—21no—
177#388—21no—
178#388—21no—
179C43C22×C1711yescharacteristic
180#336—21no—
181#336—21no—
182#336C22×C1712yes—
183#336C22×C1712yes—
184C2×C17—161no—
185C2×C17#147311yescharacteristic
186C2×C17#148011yescharacteristic
187C2×C17#149411yescharacteristic
188C2×C17#150211yescharacteristic
189C2×C17#152111yescharacteristic
190C2×C17#152911yescharacteristic
191C2×C17#154011yescharacteristic
192C22×D4C2×C4×C1711yescharacteristic
193C22×C8—22no—
194C22×C8—22no—
195#126—42no—
196#126—42no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4C2×C4×C1711yescharacteristic
201C2×C4⋊C4C2×C4×C1711yescharacteristic
202C2×C4⋊C4C2×C4×C1711yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C42C2×C4×C1711yescharacteristic
210C2×C42C2×C4×C1711yescharacteristic
211C2×C42D4×C1711yescharacteristic
212C2×C42D4×C1711yescharacteristic
213C2×C42D4×C1711yescharacteristic
214C2×C42D4×C1711yescharacteristic
215C2×C42C23×C1711yescharacteristic
216C4⋊C8—24no—
217C4×C8—42no—
218#95—21no—
219#95—21no—
220#95—21no—
221C17#767211yescharacteristic, direct product factor, Sylow
222C24—21no—
223C2×D4—22no—
224C2×D4—41no—
225C2×D4—41no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4C22⋊C4×C1711yescharacteristic
230C22×C4C22⋊C4×C1711yescharacteristic
231C22×C4C22⋊C4×C1711yescharacteristic
232C22×C4C22⋊C4×C1711yescharacteristic
233C22×C4C22×C4×C1711yescharacteristic
234C22×C4C2×D4×C1711yescharacteristic
235C22×C4C2×D4×C1711yescharacteristic
236C2×C8—24no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C4⋊C4—22no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42D8×C1712yes—
263C42SD16×C1712yes—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23C2×C22⋊C4×C1711yescharacteristic
272D4—82no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
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—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4C17×#10212yes—
298C2×C4C17×#10212yes—
299C2×C4C17×#10412yes—
300C2×C4C17×#13112yes—
301C2×C4C2×D8×C1711yescharacteristic
302C2×C4C2×SD16×C1711yescharacteristic
303C2×C4C17×#13512yes—
304C8—44no—
305C8—82no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C17×#40811yescharacteristic
314C22C17×#41011yescharacteristic
315C22C17×#41311yescharacteristic
316C22C2×C17×#10211yescharacteristic
317C22C17×#41611yescharacteristic
318C22C2×C17×#10411yescharacteristic
319C22C17×#42111yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—21no—
324C4—21no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2C17×#147311yescharacteristic
333C2C17×#148011yescharacteristic
334C2C17×#149411yescharacteristic
335C2C17×#150211yescharacteristic
336C2C17×#152111yescharacteristic
337C2C17×#152911yescharacteristic
338C2C17×#154011yescharacteristic
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×#1839C2semidirect
3. C4×C17×C4⋊C8C2semidirect
4. C17×#1271C2semidirect
94. #7672C17direct (N × H)
138. #1839C2×C17semidirect
139. C4×C4⋊C8C2×C17semidirect
140. #1271C2×C17semidirect
221. C17#7672direct (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×#18392
C4×C17×C4⋊C82
C17×#12712
C17×#12702
#767217