Finite Group Databasebeta

← C17×#13380 #16871124

Subgroups — C17×#13380 #16871124

Order 4352.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#466C211yesmaximal, characteristic
2C2×C17×#366C211yesmaximal, characteristic, complemented
3C2×C17×#357C211yesmaximal, characteristic, complemented
4C2×C17×#357C211yesmaximal, characteristic, complemented
5C2×C17×C22⋊C16C211yesmaximal, characteristic, complemented
6C17×#1808C211yesmaximal, characteristic, complemented
7C17×#1380C211yesmaximal, characteristic, complemented
8C22×D8×C17C2211yescharacteristic
9C23×C8×C17C2211yescharacteristic
10C2×C17×#121—21no—
11C22×C16×C17C2211yescharacteristic
12C22×C16×C17C2211yescharacteristic
13C17×#466—22no—
14C17×#466—22no—
15C2×C17×#107C2211yescharacteristic
16C2×C17×#107C2211yescharacteristic
17C2×C17×#107C2211yescharacteristic
18C2×C17×#102—21no—
19C17×#380—21no—
20C17×#366—22no—
21C17×#357—22no—
22C17×#357—22no—
23C17×C22⋊C16—22no—
24C17×#340—21no—
25C22×D4×C17—21no—
26C22×D4×C17—41no—
27C23×C4×C17D411yescharacteristic
28C2×D8×C17—21no—
29C2×D8×C17—21no—
30C2×D8×C17—21no—
31C2×D8×C17—21no—
32C2×D8×C17—21no—
33C2×D8×C17D412yes—
34C22×C8×C17—21no—
35C22×C8×C17—21no—
36C22×C8×C17—21no—
37C22×C8×C17—21no—
38C22×C8×C17—21no—
39C22×C8×C17—21no—
40C22×C8×C17D411yescharacteristic
41C22×C8×C17C2311yescharacteristic
42C17×#121—24no—
43C17×#121—42no—
44C2×C4⋊C4×C17—21no—
45C2×C4⋊C4×C17—21no—
46C2×C4⋊C4×C17—21no—
47C2×C22⋊C4×C17—41no—
48C2×C22⋊C4×C17—41no—
49C2×C16×C17—21no—
50C2×C16×C17—21no—
51C2×C16×C17—21no—
52C2×C16×C17—21no—
53C2×C16×C17—21no—
54C2×C16×C17D412yescomplemented
55C17×#107—21no—
56C17×#107—21no—
57C17×#107—21no—
58C17×#107—21no—
59C17×#107—21no—
60C17×#107D412yes—
61C17×#102—24no—
62C17×#95—41no—
63C24×C17—41no—
64C24×C17D811yescharacteristic
65C2×D4×C17—22no—
66C2×D4×C17—44no—
67C2×D4×C17—41no—
68C2×D4×C17—41no—
69C2×D4×C17—41no—
70C2×D4×C17—41no—
71C2×D4×C17—41no—
72C2×D4×C17—82no—
73C2×D4×C17—82no—
74C22×C4×C17—21no—
75C22×C4×C17—21no—
76C22×C4×C17—21no—
77C22×C4×C17—21no—
78C22×C4×C17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—41no—
81C22×C4×C17—41no—
82C22×C4×C17—41no—
83C22×C4×C17D811yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85D8×C17—22no—
86D8×C17—22no—
87D8×C17—41no—
88D8×C17—41no—
89C2×C8×C17—21no—
90C2×C8×C17—21no—
91C2×C8×C17—21no—
92C2×C8×C17—41no—
93C2×C8×C17—41no—
94C2×C8×C17—41no—
95C2×C8×C17—41no—
96C2×C8×C17C2×D411yescharacteristic
97C2×C8×C17C2×D411yescharacteristic
98C2×C8×C17C2×D411yescharacteristic
99C2×C8×C17#4111yescharacteristic
100C2×C8×C17#4111yescharacteristic
101C2×C8×C17#4111yescharacteristic
102C4⋊C4×C17—22no—
103C4⋊C4×C17—41no—
104C4⋊C4×C17—41no—
105C4⋊C4×C17—41no—
106C4⋊C4×C17—41no—
107C4⋊C4×C17—41no—
108C22⋊C4×C17—44no—
109C22⋊C4×C17—82no—
110C16×C17—22no—
111C16×C17—41no—
112#13380C1711yesmaximal, characteristic, direct product factor, Sylow
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—42no—
120C23×C17—81no—
121C23×C17—81no—
122C23×C17—81no—
123C23×C17—81no—
124C23×C17—81no—
125C23×C17—81no—
126C23×C17D1612yes—
127C23×C17C2×D811yescharacteristic
128D4×C17—42no—
129D4×C17—42no—
130D4×C17—88no—
131D4×C17—81no—
132D4×C17—81no—
133C2×C4×C17—21no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—42no—
141C2×C4×C17—81no—
142C2×C4×C17—81no—
143C2×C4×C17—81no—
144C2×C4×C17—81no—
145C2×C4×C17—81no—
146C2×C4×C17—81no—
147C2×C4×C17—81no—
148C2×C4×C17—81no—
149C2×C4×C17#12011yescharacteristic
150C2×C4×C17#12111yescharacteristic
151C2×C4×C17#12311yescharacteristic
152C2×C4×C17#13511yescharacteristic
153C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C17#13711yescharacteristic
155C8×C17—41no—
156C8×C17#12111yescharacteristic
157C8×C17#12111yescharacteristic
158C8×C17#12311yescharacteristic
159C8×C17#12411yescharacteristic
160C2×#466C2×C1711yescharacteristic
161C2×#366C2×C1711yescharacteristic, complemented
162C2×#357C2×C1711yescharacteristic, complemented
163C2×#357C2×C1711yescharacteristic, complemented
164C2×C22⋊C16C2×C1711yescharacteristic, complemented
165#1808C2×C1711yescharacteristic, complemented
166#1380C2×C1711yescharacteristic, complemented
167C22×C17—22no—
168C22×C17—22no—
169C22×C17—22no—
170C22×C17—41no—
171C22×C17—41no—
172C22×C17—41no—
173C22×C17—41no—
174C22×C17—82no—
175C22×C17—82no—
176C22×C17—82no—
177C22×C17—161no—
178C22×C17—161no—
179C22×C17—161no—
180C22×C17—161no—
181C22×C17#44711yescharacteristic
182C22×C17#46611yescharacteristic
183C22×C17#48011yescharacteristic
184C22×C17C2×D1611yescharacteristic
185C22×C17#50811yescharacteristic
186C22×C17#50911yescharacteristic
187C22×C17#51011yescharacteristic
188C4×C17—41no—
189C4×C17—82no—
190C4×C17—161no—
191C4×C17—161no—
192C4×C17#39411yescharacteristic
193C4×C17#45211yescharacteristic
194C4×C17#46811yescharacteristic
195C4×C17#48211yescharacteristic
196C22×D8C22×C1711yescharacteristic
197C23×C8C22×C1711yescharacteristic
198C2×#121—21no—
199C22×C16C22×C1711yescharacteristic
200C22×C16C22×C1711yescharacteristic
201#466—22no—
202#466—22no—
203C2×#107C22×C1711yescharacteristic
204C2×#107C22×C1711yescharacteristic
205C2×#107C22×C1711yescharacteristic
206C2×#102—21no—
207#380—21no—
208#366—22no—
209#357—22no—
210#357—22no—
211C22⋊C16—22no—
212#340—21no—
213C2×C17—42no—
214C2×C17—162no—
215C2×C17#203311yescharacteristic
216C2×C17#218411yescharacteristic
217C2×C17#218911yescharacteristic
218C2×C17#221511yescharacteristic
219C2×C17#222011yescharacteristic
220C2×C17#223211yescharacteristic
221C2×C17#223411yescharacteristic
222C22×D4—21no—
223C22×D4—41no—
224C23×C4D4×C1711yescharacteristic
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8D4×C1712yes—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8D4×C1711yescharacteristic
238C22×C8C23×C1711yescharacteristic
239#121—24no—
240#121—42no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C22⋊C4—41no—
245C2×C22⋊C4—41no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16D4×C1712yescomplemented
252#107—21no—
253#107—21no—
254#107—21no—
255#107—21no—
256#107—21no—
257#107D4×C1712yes—
258#102—24no—
259#95—41no—
260C17#1338011yescharacteristic, direct product factor, Sylow
261C24—41no—
262C24D8×C1711yescharacteristic
263C2×D4—22no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—82no—
271C2×D4—82no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4D8×C1711yescharacteristic
282C22×C4C2×D4×C1711yescharacteristic
283D8—22no—
284D8—22no—
285D8—41no—
286D8—41no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8C2×D4×C1711yescharacteristic
295C2×C8C2×D4×C1711yescharacteristic
296C2×C8C2×D4×C1711yescharacteristic
297C2×C8#41×C1711yescharacteristic
298C2×C8#41×C1711yescharacteristic
299C2×C8#41×C1711yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—44no—
307C22⋊C4—82no—
308C16—22no—
309C16—41no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23C17×D1612yes—
324C23C2×D8×C1711yescharacteristic
325D4—42no—
326D4—42no—
327D4—88no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C17×#12011yescharacteristic
347C2×C4C17×#12111yescharacteristic
348C2×C4C17×#12311yescharacteristic
349C2×C4C17×#13511yescharacteristic
350C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
351C2×C4C17×#13711yescharacteristic
352C8—41no—
353C8C17×#12111yescharacteristic
354C8C17×#12111yescharacteristic
355C8C17×#12311yescharacteristic
356C8C17×#12411yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—161no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22C17×#44711yescharacteristic
372C22C17×#46611yescharacteristic
373C22C17×#48011yescharacteristic
374C22C2×C17×D1611yescharacteristic
375C22C17×#50811yescharacteristic
376C22C17×#50911yescharacteristic
377C22C17×#51011yescharacteristic
378C4—41no—
379C4—82no—
380C4—161no—
381C4—161no—
382C4C17×#39411yescharacteristic
383C4C17×#45211yescharacteristic
384C4C17×#46811yescharacteristic
385C4C17×#48211yescharacteristic
386C2—42no—
387C2—162no—
388C2C17×#203311yescharacteristic
389C2C17×#218411yescharacteristic
390C2C17×#218911yescharacteristic
391C2C17×#221511yescharacteristic
392C2C17×#222011yescharacteristic
393C2C17×#223211yescharacteristic
394C2C17×#223411yescharacteristic
subgroupG/H
center, socleC23×C17C2×D8
commutator, Frattini, cosocleC22×C8C23×C17
prime radicalC2×C17×#466C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#366C2semidirect
3. C2×C17×#357C2semidirect
4. C2×C17×#357C2semidirect
5. C2×C17×C22⋊C16C2semidirect
6. C17×#1808C2semidirect
7. C17×#1380C2semidirect
54. C2×C16×C17D4semidirect
112. #13380C17direct (N × H)
161. C2×#366C2×C17semidirect
162. C2×#357C2×C17semidirect
163. C2×#357C2×C17semidirect
164. C2×C22⋊C16C2×C17semidirect
165. #1808C2×C17semidirect
166. #1380C2×C17semidirect
251. C2×C16D4×C17semidirect
260. C17#13380direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#4662
C2×C17×#3662
C2×C17×#3572
C2×C17×C22⋊C162
C17×#18082
C17×#13802
#1338017