Finite Group Databasebeta

← C17×#9369 #16867113

Subgroups — C17×#9369 #16867113

Order 4352.

390 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3240C211yesmaximal, characteristic
2C17×#2967C211yesmaximal, characteristic
3C17×#1521C211yesmaximal, characteristic
4C17×#1515C211yesmaximal, characteristic, complemented
5C17×#1485C211yesmaximal, characteristic, complemented
6C17×#1288C211yesmaximal, characteristic, complemented
7C17×#1287C211yesmaximal, characteristic, complemented
8C17×#533C2211yescharacteristic
9C17×#529C2211yescharacteristic
10C17×#501C411yescharacteristic, complemented
11C17×#501C411yescharacteristic, complemented
12C17×#489C411yescharacteristic, complemented
13C17×#489C411yescharacteristic, complemented
14C17×#485—21no—
15C17×#482—21no—
16C17×#479—21no—
17C17×#478—21no—
18C17×#446—21no—
19C17×#436—21no—
20C17×#435—21no—
21C17×#435—21no—
22C17×#433—21no—
23C17×#432C2211yescharacteristic
24C17×#432C2211yescharacteristic
25C17×#431C2211yescharacteristic
26C17×#405—21no—
27C4×M16×C17C2211yescharacteristic
28C17×#383C2211yescharacteristic
29C17×#328—21no—
30C17×#328—21no—
31C17×#328—21no—
32C17×#327—21no—
33C17×Q8⋊C8—21no—
34C17×Q8⋊C8—21no—
35C2×M16×C17—21no—
36C2×M16×C17—21no—
37C22×C8×C17—21no—
38C17×C4⋊Q8C2×C411yescharacteristic
39C17×C4⋊Q8C2×C411yescharacteristic
40C17×#126—21no—
41C17×#125—21no—
42C17×#125C2×C411yescharacteristic
43C17×#124C2×C411yescharacteristic
44C17×#123—21no—
45C17×C22⋊Q8—21no—
46C17×C22⋊Q8—21no—
47C17×C22⋊Q8D411yescharacteristic
48C17×#121D411yescharacteristic
49C4×Q8×C17—21no—
50C4×Q8×C17—21no—
51C4×Q8×C17D411yescharacteristic
52C4×D4×C17—21no—
53C4×D4×C17D411yescharacteristic
54C17×#117—21no—
55C17×#117—21no—
56C2×C42×C17C2311yescharacteristic
57C17×#107—21no—
58C17×#107—21no—
59C17×#106—21no—
60C17×#106—21no—
61C17×C4⋊C8—21no—
62C17×C4⋊C8—21no—
63C17×C4⋊C8—21no—
64C17×C4⋊C8—21no—
65C17×C4⋊C8—21no—
66C17×#103—21no—
67C17×#103—21no—
68C17×#102—21no—
69C17×#102—21no—
70C17×C22⋊C8—21no—
71C17×C22⋊C8—21no—
72C17×C22⋊C8—21no—
73C17×C22⋊C8—21no—
74C17×C22⋊C8D411yescharacteristic
75C17×C22⋊C8D411yescharacteristic
76C17×#97—21no—
77C17×#97—21no—
78C17×#97—21no—
79C17×#97C2×C411yescharacteristic
80C17×#97C2×C411yescharacteristic
81C4×C8×C17—21no—
82C4×C8×C17—21no—
83C4×C8×C17D411yescharacteristic
84C4×C8×C17D411yescharacteristic
85C17×#95—21no—
86C17×#95—21no—
87C17×#95—21no—
88C2×Q8×C17—21no—
89C2×Q8×C17—21no—
90C2×Q8×C17C22⋊C411yescharacteristic
91C2×D4×C17—21no—
92C2×D4×C17C22⋊C411yescharacteristic
93C22×C4×C17—21no—
94C22×C4×C17—41no—
95C22×C4×C17C2×D411yescharacteristic
96C22×C4×C17C2×D411yescharacteristic
97C22×C4×C17#4111yescharacteristic
98M16×C17—42no—
99M16×C17—42no—
100C2×C8×C17—21no—
101C2×C8×C17—21no—
102C2×C8×C17—21no—
103C2×C8×C17—21no—
104C2×C8×C17—21no—
105C2×C8×C17—21no—
106C2×C8×C17—42no—
107C2×C8×C17—41no—
108C4⋊C4×C17—21no—
109C4⋊C4×C17—21no—
110C4⋊C4×C17—21no—
111C4⋊C4×C17—21no—
112C4⋊C4×C17—21no—
113C4⋊C4×C17—21no—
114C4⋊C4×C17—21no—
115C4⋊C4×C17—21no—
116C4⋊C4×C17—41no—
117C4⋊C4×C17—41no—
118C4⋊C4×C17C22⋊C411yescharacteristic
119C4⋊C4×C17C22⋊C411yescharacteristic
120C22⋊C4×C17—21no—
121C22⋊C4×C17—21no—
122C22⋊C4×C17—21no—
123C22⋊C4×C17—21no—
124C22⋊C4×C17—21no—
125C22⋊C4×C17—41no—
126C42×C17—21no—
127C42×C17—41no—
128C42×C17C22×C411yescharacteristic
129C42×C17C2×D411yescharacteristic
130C42×C17C2×D411yescharacteristic
131C42×C17#4111yescharacteristic
132#9369C1711yesmaximal, characteristic, direct product factor, Sylow
133C23×C17—21no—
134C23×C17#12111yescharacteristic
135Q8×C17—41no—
136Q8×C17—42no—
137Q8×C17—81no—
138D4×C17—41no—
139D4×C17—81no—
140C2×C4×C17—21no—
141C2×C4×C17—21no—
142C2×C4×C17—21no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—41no—
150C2×C4×C17—81no—
151C2×C4×C17—81no—
152C2×C4×C17—81no—
153C2×C4×C17C2×C22⋊C411yescharacteristic
154C2×C4×C17C4×D411yescharacteristic
155C2×C4×C17C4×D411yescharacteristic
156C2×C4×C17#12011yescharacteristic
157C2×C4×C17#12111yescharacteristic
158C2×C4×C17#12311yescharacteristic
159C8×C17—22no—
160C8×C17—41no—
161C8×C17—41no—
162C8×C17—41no—
163C8×C17—41no—
164C8×C17—41no—
165C8×C17—81no—
166#3240C2×C1711yescharacteristic
167#2967C2×C1711yescharacteristic
168#1521C2×C1711yescharacteristic
169#1515C2×C1711yescharacteristic, complemented
170#1485C2×C1711yescharacteristic, complemented
171#1288C2×C1711yescharacteristic, complemented
172#1287C2×C1711yescharacteristic, complemented
173C22×C17—21no—
174C22×C17—21no—
175C22×C17—21no—
176C22×C17—41no—
177C22×C17—41no—
178C22×C17—41no—
179C22×C17#38611yescharacteristic
180C4×C17—21no—
181C4×C17—21no—
182C4×C17—21no—
183C4×C17—21no—
184C4×C17—21no—
185C4×C17—21no—
186C4×C17—41no—
187C4×C17—41no—
188C4×C17—41no—
189C4×C17—81no—
190C4×C17—81no—
191C4×C17—161no—
192#533C22×C1711yescharacteristic
193#529C22×C1711yescharacteristic
194#501C4×C1711yescharacteristic, complemented
195#501C4×C1711yescharacteristic, complemented
196#489C4×C1711yescharacteristic, complemented
197#489C4×C1711yescharacteristic, complemented
198#485—21no—
199#482—21no—
200#479—21no—
201#478—21no—
202#446—21no—
203#436—21no—
204#435—21no—
205#435—21no—
206#433—21no—
207#432C22×C1711yescharacteristic
208#432C22×C1711yescharacteristic
209#431C22×C1711yescharacteristic
210#405—21no—
211C4×M16C22×C1711yescharacteristic
212#383C22×C1711yescharacteristic
213#328—21no—
214#328—21no—
215#328—21no—
216#327—21no—
217Q8⋊C8—21no—
218Q8⋊C8—21no—
219C2×C17—41no—
220C2×C17—81no—
221C2×C17#188111yescharacteristic
222C2×C17#190611yescharacteristic
223C2×C17#190911yescharacteristic
224C2×M16—21no—
225C2×M16—21no—
226C22×C8—21no—
227C4⋊Q8C2×C4×C1711yescharacteristic
228C4⋊Q8C2×C4×C1711yescharacteristic
229#126—21no—
230#125—21no—
231#125C2×C4×C1711yescharacteristic
232#124C2×C4×C1711yescharacteristic
233#123—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8D4×C1711yescharacteristic
237#121D4×C1711yescharacteristic
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8D4×C1711yescharacteristic
241C4×D4—21no—
242C4×D4D4×C1711yescharacteristic
243#117—21no—
244#117—21no—
245C2×C42C23×C1711yescharacteristic
246#107—21no—
247#107—21no—
248#106—21no—
249#106—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255#103—21no—
256#103—21no—
257#102—21no—
258#102—21no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8D4×C1711yescharacteristic
264C22⋊C8D4×C1711yescharacteristic
265#97—21no—
266#97—21no—
267#97—21no—
268#97C2×C4×C1711yescharacteristic
269#97C2×C4×C1711yescharacteristic
270C4×C8—21no—
271C4×C8—21no—
272C4×C8D4×C1711yescharacteristic
273C4×C8D4×C1711yescharacteristic
274#95—21no—
275#95—21no—
276#95—21no—
277C17#936911yescharacteristic, direct product factor, Sylow
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8C22⋊C4×C1711yescharacteristic
281C2×D4—21no—
282C2×D4C22⋊C4×C1711yescharacteristic
283C22×C4—21no—
284C22×C4—41no—
285C22×C4C2×D4×C1711yescharacteristic
286C22×C4C2×D4×C1711yescharacteristic
287C22×C4#41×C1711yescharacteristic
288M16—42no—
289M16—42no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—42no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4C22⋊C4×C1711yescharacteristic
309C4⋊C4C22⋊C4×C1711yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—41no—
316C42—21no—
317C42—41no—
318C42C22×C4×C1711yescharacteristic
319C42C2×D4×C1711yescharacteristic
320C42C2×D4×C1711yescharacteristic
321C42#41×C1711yescharacteristic
322C23—21no—
323C23C17×#12111yescharacteristic
324Q8—41no—
325Q8—42no—
326Q8—81no—
327D4—41no—
328D4—81no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4C2×C22⋊C4×C1711yescharacteristic
343C2×C4C4×D4×C1711yescharacteristic
344C2×C4C4×D4×C1711yescharacteristic
345C2×C4C17×#12011yescharacteristic
346C2×C4C17×#12111yescharacteristic
347C2×C4C17×#12311yescharacteristic
348C8—22no—
349C8—41no—
350C8—41no—
351C8—41no—
352C8—41no—
353C8—41no—
354C8—81no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C17×#38611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—81no—
372C4—81no—
373C4—161no—
374C2—41no—
375C2—81no—
376C2C17×#188111yescharacteristic
377C2C17×#190611yescharacteristic
378C2C17×#190911yescharacteristic
subgroupG/H
center, socleC22×C17#386
commutatorC42C22×C4×C17
Frattini, cosocleC2×C42C23×C17
prime radicalC17×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
4. C17×#1515C2semidirect
5. C17×#1485C2semidirect
6. C17×#1288C2semidirect
7. C17×#1287C2semidirect
10. C17×#501C4semidirect
11. C17×#501C4semidirect
12. C17×#489C4semidirect
13. C17×#489C4semidirect
132. #9369C17direct (N × H)
169. #1515C2×C17semidirect
170. #1485C2×C17semidirect
171. #1288C2×C17semidirect
172. #1287C2×C17semidirect
194. #501C4×C17semidirect
195. #501C4×C17semidirect
196. #489C4×C17semidirect
197. #489C4×C17semidirect
277. C17#9369direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#32402
C17×#29672
C17×#15212
C17×#15152
C17×#14852
C17×#12882
C17×#12872
#936917