Finite Group Databasebeta

← C17×#13449 #16871193

Subgroups — C17×#13449 #16871193

Order 4352.

446 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C17×SD32C211yesmaximal, characteristic
2C2×C17×C4⋊C16C211yesmaximal, characteristic, complemented
3C2×C17×#358C211yesmaximal, characteristic, complemented
4C2×C17×#357C211yesmaximal, characteristic
5C17×#1970C211yesmaximal, characteristic
6C17×#1969C211yesmaximal, characteristic, complemented
7C17×#1380C211yesmaximal, characteristic, complemented
8C22×Q16×C17C2211yescharacteristic
9C22×D8×C17C2211yescharacteristic
10C2×C17×SD32—22no—
11C2×C17×SD32—22no—
12C2×C17×SD32—22no—
13C22×C16×C17C2211yescharacteristic
14C22×C16×C17C2211yescharacteristic
15C2×C17×#107C2211yescharacteristic
16C2×C17×#107C2211yescharacteristic
17C2×C17×#103—21no—
18C2×C17×#102—21no—
19C2×C4×C8×C17C2211yescharacteristic
20C17×#391—21no—
21C17×#390—21no—
22C17×C4⋊C16—22no—
23C17×#358—22no—
24C17×#357—22no—
25C22×Q8×C17—21no—
26C22×D4×C17—21no—
27C2×Q16×C17—21no—
28C2×Q16×C17—21no—
29C2×Q16×C17—21no—
30C2×Q16×C17—21no—
31C2×Q16×C17—21no—
32C2×Q16×C17D412yes—
33C2×D8×C17—21no—
34C2×D8×C17—21no—
35C2×D8×C17—21no—
36C2×D8×C17—21no—
37C2×D8×C17—21no—
38C2×D8×C17D412yes—
39C22×C8×C17D411yescharacteristic
40C22×C8×C17C2311yescharacteristic
41C2×C4⋊C4×C17—21no—
42C2×C4⋊C4×C17—21no—
43C2×C22⋊C4×C17—41no—
44C2×C22⋊C4×C17—41no—
45C2×C42×C17D411yescharacteristic
46C17×SD32—28no—
47C2×C16×C17—21no—
48C2×C16×C17—21no—
49C2×C16×C17—21no—
50C2×C16×C17—21no—
51C2×C16×C17—21no—
52C2×C16×C17D412yes—
53C17×#107—21no—
54C17×#107—21no—
55C17×#107—21no—
56C17×#107—21no—
57C17×#103—42no—
58C17×#102—42no—
59C4×C8×C17—21no—
60C4×C8×C17—21no—
61C17×#95—41no—
62C17×#95—41no—
63C24×C17—41no—
64C2×Q8×C17—22no—
65C2×Q8×C17—41no—
66C2×Q8×C17—41no—
67C2×Q8×C17—41no—
68C2×Q8×C17—41no—
69C2×Q8×C17—41no—
70C2×D4×C17—22no—
71C2×D4×C17—41no—
72C2×D4×C17—41no—
73C2×D4×C17—41no—
74C2×D4×C17—41no—
75C2×D4×C17—41no—
76C22×C4×C17—41no—
77C22×C4×C17—41no—
78C22×C4×C17—41no—
79C22×C4×C17D811yescharacteristic
80C22×C4×C17D811yescharacteristic
81C22×C4×C17C2×D411yescharacteristic
82Q16×C17—22no—
83Q16×C17—22no—
84Q16×C17—41no—
85Q16×C17—41no—
86D8×C17—22no—
87D8×C17—22no—
88D8×C17—41no—
89D8×C17—41no—
90C2×C8×C17—21no—
91C2×C8×C17—21no—
92C2×C8×C17—21no—
93C2×C8×C17C2×D411yescharacteristic
94C2×C8×C17C2×D411yescharacteristic
95C2×C8×C17C2×D411yescharacteristic
96C2×C8×C17#4111yescharacteristic
97C2×C8×C17#4111yescharacteristic
98C2×C8×C17#4111yescharacteristic
99C4⋊C4×C17—41no—
100C4⋊C4×C17—41no—
101C4⋊C4×C17—41no—
102C4⋊C4×C17—41no—
103C22⋊C4×C17—82no—
104C22⋊C4×C17—82no—
105C42×C17—21no—
106C42×C17—21no—
107C16×C17—22no—
108C16×C17—41no—
109#13449C1711yesmaximal, characteristic, direct product factor, Sylow
110C23×C17—42no—
111C23×C17—81no—
112C23×C17—81no—
113C23×C17—81no—
114C23×C17—81no—
115C23×C17—81no—
116C23×C17—81no—
117C23×C17C2×D811yescharacteristic
118Q8×C17—42no—
119Q8×C17—42no—
120Q8×C17—81no—
121Q8×C17—81no—
122D4×C17—42no—
123D4×C17—42no—
124D4×C17—81no—
125D4×C17—81no—
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—81no—
133C2×C4×C17—81no—
134C2×C4×C17—81no—
135C2×C4×C17—81no—
136C2×C4×C17—81no—
137C2×C4×C17—81no—
138C2×C4×C17—81no—
139C2×C4×C17—81no—
140C2×C4×C17SD3212yescomplemented
141C2×C4×C17#12111yescharacteristic
142C2×C4×C17#12111yescharacteristic
143C2×C4×C17#12111yescharacteristic
144C2×C4×C17#13511yescharacteristic
145C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
147C8×C17—41no—
148C8×C17#12011yescharacteristic
149C8×C17#12311yescharacteristic
150C8×C17#12311yescharacteristic
151C8×C17#12411yescharacteristic
152C22×SD32C2×C1711yescharacteristic
153C2×C4⋊C16C2×C1711yescharacteristic, complemented
154C2×#358C2×C1711yescharacteristic, complemented
155C2×#357C2×C1711yescharacteristic
156#1970C2×C1711yescharacteristic
157#1969C2×C1711yescharacteristic, complemented
158#1380C2×C1711yescharacteristic, complemented
159C22×C17—82no—
160C22×C17—82no—
161C22×C17—82no—
162C22×C17—161no—
163C22×C17—161no—
164C22×C17—161no—
165C22×C17—161no—
166C22×C17#45911yescharacteristic
167C22×C17#45911yescharacteristic
168C22×C17#46611yescharacteristic
169C22×C17C2×SD3211yescharacteristic
170C22×C17#50811yescharacteristic
171C22×C17#50911yescharacteristic
172C22×C17#51011yescharacteristic
173C4×C17—22no—
174C4×C17—41no—
175C4×C17—82no—
176C4×C17—161no—
177C4×C17—161no—
178C4×C17#39411yescharacteristic
179C4×C17#46311yescharacteristic
180C4×C17#46311yescharacteristic
181C4×C17#46911yescharacteristic
182C22×Q16C22×C1711yescharacteristic
183C22×D8C22×C1711yescharacteristic
184C2×SD32—22no—
185C2×SD32—22no—
186C2×SD32—22no—
187C22×C16C22×C1711yescharacteristic
188C22×C16C22×C1711yescharacteristic
189C2×#107C22×C1711yescharacteristic
190C2×#107C22×C1711yescharacteristic
191C2×#103—21no—
192C2×#102—21no—
193C2×C4×C8C22×C1711yescharacteristic
194#391—21no—
195#390—21no—
196C4⋊C16—22no—
197#358—22no—
198#357—22no—
199C2×C17—162no—
200C2×C17#205411yescharacteristic
201C2×C17#220711yescharacteristic
202C2×C17#220811yescharacteristic
203C2×C17#221011yescharacteristic
204C2×C17#221111yescharacteristic
205C2×C17#221711yescharacteristic
206C2×C17#222011yescharacteristic
207C22×Q8—21no—
208C22×D4—21no—
209C2×Q16—21no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—21no—
214C2×Q16D4×C1712yes—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8D4×C1712yes—
221C22×C8D4×C1711yescharacteristic
222C22×C8C23×C1711yescharacteristic
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C22⋊C4—41no—
226C2×C22⋊C4—41no—
227C2×C42D4×C1711yescharacteristic
228SD32—28no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16D4×C1712yes—
235#107—21no—
236#107—21no—
237#107—21no—
238#107—21no—
239#103—42no—
240#102—42no—
241C4×C8—21no—
242C4×C8—21no—
243#95—41no—
244#95—41no—
245C17#1344911yescharacteristic, direct product factor, Sylow
246C24—41no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4D8×C1711yescharacteristic
263C22×C4D8×C1711yescharacteristic
264C22×C4C2×D4×C1711yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269D8—22no—
270D8—22no—
271D8—41no—
272D8—41no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8C2×D4×C1711yescharacteristic
277C2×C8C2×D4×C1711yescharacteristic
278C2×C8C2×D4×C1711yescharacteristic
279C2×C8#41×C1711yescharacteristic
280C2×C8#41×C1711yescharacteristic
281C2×C8#41×C1711yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C22⋊C4—82no—
287C22⋊C4—82no—
288C42—21no—
289C42—21no—
290C16—22no—
291C16—41no—
292C23—42no—
293C23—81no—
294C23—81no—
295C23—81no—
296C23—81no—
297C23—81no—
298C23—81no—
299C23C2×D8×C1711yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—81no—
303Q8—81no—
304D4—42no—
305D4—42no—
306D4—81no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4C17×SD3212yescomplemented
323C2×C4C17×#12111yescharacteristic
324C2×C4C17×#12111yescharacteristic
325C2×C4C17×#12111yescharacteristic
326C2×C4C17×#13511yescharacteristic
327C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
328C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
329C8—41no—
330C8C17×#12011yescharacteristic
331C8C17×#12311yescharacteristic
332C8C17×#12311yescharacteristic
333C8C17×#12411yescharacteristic
334C22—82no—
335C22—82no—
336C22—82no—
337C22—161no—
338C22—161no—
339C22—161no—
340C22—161no—
341C22C17×#45911yescharacteristic
342C22C17×#45911yescharacteristic
343C22C17×#46611yescharacteristic
344C22C2×C17×SD3211yescharacteristic
345C22C17×#50811yescharacteristic
346C22C17×#50911yescharacteristic
347C22C17×#51011yescharacteristic
348C4—22no—
349C4—41no—
350C4—82no—
351C4—161no—
352C4—161no—
353C4C17×#39411yescharacteristic
354C4C17×#46311yescharacteristic
355C4C17×#46311yescharacteristic
356C4C17×#46911yescharacteristic
357C2—162no—
358C2C17×#205411yescharacteristic
359C2C17×#220711yescharacteristic
360C2C17×#220811yescharacteristic
361C2C17×#221011yescharacteristic
362C2C17×#221111yescharacteristic
363C2C17×#221711yescharacteristic
364C2C17×#222011yescharacteristic
subgroupG/H
center, socleC23×C17C2×D8
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC22×D8×C17C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×C4⋊C16C2semidirect
3. C2×C17×#358C2semidirect
6. C17×#1969C2semidirect
7. C17×#1380C2semidirect
109. #13449C17direct (N × H)
140. C2×C4×C17SD32semidirect
153. C2×C4⋊C16C2×C17semidirect
154. C2×#358C2×C17semidirect
157. #1969C2×C17semidirect
158. #1380C2×C17semidirect
245. C17#13449direct (N × H)
322. C2×C4C17×SD32semidirect

Maximal subgroups

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

subgroupindex
C22×C17×SD322
C2×C17×C4⋊C162
C2×C17×#3582
C2×C17×#3572
C17×#19702
C17×#19692
C17×#13802
#1344917