Finite Group Databasebeta

← C2×C17×#1341 #16869430

Subgroups — C2×C17×#1341 #16869430

Order 4352.

480 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#469C211yesmaximal, characteristic
2C2×C17×#349C211yesmaximal, characteristic, complemented
3C2×C17×#338C211yesmaximal, characteristic, complemented
4C17×#1341C214yesmaximal, direct product factor
5C22×D8×C17C411yescharacteristic
6C22×M16×C17—21no—
7C22×M16×C17C2211yescharacteristic
8C2×C17×#121—21no—
9C2×C17×M32—21no—
10C17×#469—21no—
11C17×#469—21no—
12C17×#469C412yes—
13C17×#469C2212yes—
14C2×C17×#106C411yescharacteristic
15C2×C17×#102—21no—
16C17×#349—21no—
17C17×#349C2212yescomplemented
18C17×#338—21no—
19C17×#338C2212yescomplemented
20C22×D4×C17—21no—
21C22×D4×C17—41no—
22C23×C4×C17D411yescharacteristic
23C2×D8×C17—21no—
24C2×D8×C17—41no—
25C2×D8×C17—41no—
26C2×D8×C17C2×C412yes—
27C2×M16×C17—22no—
28C2×M16×C17—22no—
29C2×M16×C17—41no—
30C2×M16×C17—41no—
31C2×M16×C17—41no—
32C2×M16×C17—41no—
33C2×M16×C17—41no—
34C2×M16×C17—41no—
35C2×M16×C17C2×C411yescharacteristic
36C2×M16×C17D411yescharacteristic
37C2×M16×C17D411yescharacteristic
38C2×M16×C17C2311yescharacteristic
39C22×C8×C17—22no—
40C22×C8×C17C2×C411yescharacteristic
41C22×C8×C17D411yescharacteristic
42C17×#121—22no—
43C17×#121—22no—
44C17×#121—41no—
45C17×#121—41no—
46C2×C4⋊C4×C17—21no—
47C2×C22⋊C4×C17—41no—
48C17×M32—22no—
49C17×M32—41no—
50C2×C16×C17—41no—
51C17×#106—21no—
52C17×#106C2×C412yes—
53C17×#102—22no—
54C17×#102—22no—
55C24×C17—41no—
56C24×C17SD1611yescharacteristic
57C2×D4×C17—22no—
58C2×D4×C17—42no—
59C2×D4×C17—42no—
60C2×D4×C17—41no—
61C2×D4×C17—41no—
62C2×D4×C17—41no—
63C2×D4×C17—41no—
64C2×D4×C17—41no—
65C2×D4×C17—84no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17—41no—
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17D811yescharacteristic
74C22×C4×C17D811yescharacteristic
75C22×C4×C17SD1611yescharacteristic
76C22×C4×C17C2×D411yescharacteristic
77D8×C17—42no—
78D8×C17—42no—
79M16×C17—41no—
80M16×C17—41no—
81M16×C17—41no—
82M16×C17—41no—
83M16×C17—42no—
84M16×C17—42no—
85M16×C17—42no—
86M16×C17—42no—
87C2×C8×C17—21no—
88C2×C8×C17—21no—
89C2×C8×C17—21no—
90C2×C8×C17—21no—
91C2×C8×C17—24no—
92C2×C8×C17—42no—
93C2×C8×C17—42no—
94C2×C8×C17C22⋊C411yescharacteristic
95C2×C8×C17C22⋊C411yescharacteristic
96C2×C8×C17C22×C411yescharacteristic
97C2×C8×C17C2×D411yescharacteristic
98C4⋊C4×C17—22no—
99C4⋊C4×C17—41no—
100C22⋊C4×C17—42no—
101C22⋊C4×C17—42no—
102C16×C17—42no—
103C2×#1341C1711yesmaximal, characteristic, direct product factor, Sylow
104C23×C17—21no—
105C23×C17—21no—
106C23×C17—42no—
107C23×C17—42no—
108C23×C17—82no—
109C23×C17—82no—
110C23×C17—81no—
111C23×C17—81no—
112C23×C17#10211yescharacteristic
113C23×C17#10211yescharacteristic
114C23×C17C2×SD1611yescharacteristic
115D4×C17—42no—
116D4×C17—42no—
117D4×C17—84no—
118D4×C17—84no—
119D4×C17—81no—
120D4×C17—81no—
121C2×C4×C17—21no—
122C2×C4×C17—21no—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—21no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—42no—
132C2×C4×C17—82no—
133C2×C4×C17#9911yescharacteristic
134C2×C4×C17#9911yescharacteristic
135C2×C4×C17#10211yescharacteristic
136C2×C4×C17#10211yescharacteristic
137C2×C4×C17#10411yescharacteristic
138C2×C4×C17#10411yescharacteristic
139C2×C4×C17C2×C22⋊C411yescharacteristic
140C2×C4×C17C2×D811yescharacteristic
141C8×C17—21no—
142C8×C17—21no—
143C8×C17—21no—
144C8×C17—21no—
145C8×C17—44no—
146C2×#469C2×C1711yescharacteristic
147C2×#349C2×C1711yescharacteristic, complemented
148C2×#338C2×C1711yescharacteristic, complemented
149#1341C2×C1714yesdirect product factor
150C22×C17—22no—
151C22×C17—21no—
152C22×C17—21no—
153C22×C17—41no—
154C22×C17—41no—
155C22×C17—42no—
156C22×C17—81no—
157C22×C17—82no—
158C22×C17—82no—
159C22×C17—82no—
160C22×C17—162no—
161C22×C17—162no—
162C22×C17#32711yescharacteristic
163C22×C17#32711yescharacteristic
164C22×C17C2×#10211yescharacteristic
165C4×C17—21no—
166C4×C17—21no—
167C4×C17—82no—
168C4×C17#32711yescharacteristic
169C4×C17#32711yescharacteristic
170C4×C17C2×#9911yescharacteristic
171C4×C17C2×#10411yescharacteristic
172C22×D8C4×C1711yescharacteristic
173C22×M16—21no—
174C22×M16C22×C1711yescharacteristic
175C2×#121—21no—
176C2×M32—21no—
177#469—21no—
178#469—21no—
179#469C4×C1712yes—
180#469C22×C1712yes—
181C2×#106C4×C1711yescharacteristic
182C2×#102—21no—
183#349—21no—
184#349C22×C1712yescomplemented
185#338—21no—
186#338C22×C1712yescomplemented
187C2×C17—21no—
188C2×C17—21no—
189C2×C17—41no—
190C2×C17—41no—
191C2×C17—162no—
192C2×C17#134112yesdirect product factor
193C2×C17C2×#32711yescharacteristic
194C22×D4—21no—
195C22×D4—41no—
196C23×C4D4×C1711yescharacteristic
197C2×D8—21no—
198C2×D8—41no—
199C2×D8—41no—
200C2×D8C2×C4×C1712yes—
201C2×M16—22no—
202C2×M16—22no—
203C2×M16—41no—
204C2×M16—41no—
205C2×M16—41no—
206C2×M16—41no—
207C2×M16—41no—
208C2×M16—41no—
209C2×M16C2×C4×C1711yescharacteristic
210C2×M16D4×C1711yescharacteristic
211C2×M16D4×C1711yescharacteristic
212C2×M16C23×C1711yescharacteristic
213C22×C8—22no—
214C22×C8C2×C4×C1711yescharacteristic
215C22×C8D4×C1711yescharacteristic
216#121—22no—
217#121—22no—
218#121—41no—
219#121—41no—
220C2×C4⋊C4—21no—
221C2×C22⋊C4—41no—
222M32—22no—
223M32—41no—
224C2×C16—41no—
225#106—21no—
226#106C2×C4×C1712yes—
227#102—22no—
228#102—22no—
229C17C2×#134111yescharacteristic, direct product factor, Sylow
230C24—41no—
231C24SD16×C1711yescharacteristic
232C2×D4—22no—
233C2×D4—42no—
234C2×D4—42no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—84no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4C22⋊C4×C1711yescharacteristic
247C22×C4C22⋊C4×C1711yescharacteristic
248C22×C4D8×C1711yescharacteristic
249C22×C4D8×C1711yescharacteristic
250C22×C4SD16×C1711yescharacteristic
251C22×C4C2×D4×C1711yescharacteristic
252D8—42no—
253D8—42no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258M16—42no—
259M16—42no—
260M16—42no—
261M16—42no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—24no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8C22⋊C4×C1711yescharacteristic
270C2×C8C22⋊C4×C1711yescharacteristic
271C2×C8C22×C4×C1711yescharacteristic
272C2×C8C2×D4×C1711yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C16—42no—
278C23—21no—
279C23—21no—
280C23—42no—
281C23—42no—
282C23—82no—
283C23—82no—
284C23—81no—
285C23—81no—
286C23C17×#10211yescharacteristic
287C23C17×#10211yescharacteristic
288C23C2×SD16×C1711yescharacteristic
289D4—42no—
290D4—42no—
291D4—84no—
292D4—84no—
293D4—81no—
294D4—81no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—82no—
307C2×C4C17×#9911yescharacteristic
308C2×C4C17×#9911yescharacteristic
309C2×C4C17×#10211yescharacteristic
310C2×C4C17×#10211yescharacteristic
311C2×C4C17×#10411yescharacteristic
312C2×C4C17×#10411yescharacteristic
313C2×C4C2×C22⋊C4×C1711yescharacteristic
314C2×C4C2×D8×C1711yescharacteristic
315C8—21no—
316C8—21no—
317C8—21no—
318C8—21no—
319C8—44no—
320C22—22no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—42no—
326C22—81no—
327C22—82no—
328C22—82no—
329C22—82no—
330C22—162no—
331C22—162no—
332C22C17×#32711yescharacteristic
333C22C17×#32711yescharacteristic
334C22C2×C17×#10211yescharacteristic
335C4—21no—
336C4—21no—
337C4—82no—
338C4C17×#32711yescharacteristic
339C4C17×#32711yescharacteristic
340C4C2×C17×#9911yescharacteristic
341C4C2×C17×#10411yescharacteristic
342C2—21no—
343C2—21no—
344C2—41no—
345C2—41no—
346C2—162no—
347C2C17×#134112yesdirect product factor
348C2C2×C17×#32711yescharacteristic
subgroupG/H
center, socleC22×C17#327
commutatorC2×C8C22×C4×C17
Frattini, cosocleC2×M16C23×C17
prime radicalC2×C17×#469C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C22×M16×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#349C2semidirect
3. C2×C17×#338C2semidirect
4. C17×#1341C2direct (N × H)
17. C17×#349C22semidirect
19. C17×#338C22semidirect
103. C2×#1341C17direct (N × H)
147. C2×#349C2×C17semidirect
148. C2×#338C2×C17semidirect
149. #1341C2×C17direct (N × H)
184. #349C22×C17semidirect
186. #338C22×C17semidirect
192. C2×C17#1341direct (N × H)
229. C17C2×#1341direct (N × H)
347. C2C17×#1341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#4692
C2×C17×#3492
C2×C17×#3382
C17×#13412
C2×#134117