Finite Group Databasebeta

← C17×#10195 #16867939

Subgroups — C17×#10195 #16867939

Order 4352.

554 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#3249C211yesmaximal, characteristic, complemented
2C17×#3208C211yesmaximal, characteristic
3C17×#3138C211yesmaximal, characteristic
4C17×#1986C211yesmaximal, characteristic, complemented
5C17×#1982C211yesmaximal, characteristic
6C17×#1503C211yesmaximal, characteristic, complemented
7C17×#1283C211yesmaximal, characteristic, complemented
8C17×#533C2211yescharacteristic
9C17×#533C2211yescharacteristic
10C2×C17×#127C2211yescharacteristic
11C17×#492—21no—
12C17×#490—22no—
13C17×#486—21no—
14C17×#486—21no—
15C17×#486—21no—
16C17×#477—21no—
17C17×#477—21no—
18C17×#467—22no—
19C17×#462—21no—
20C17×#462—21no—
21C17×#460—22no—
22C17×#450—22no—
23C17×#431C2211yescharacteristic
24C2×C17×C4⋊C8C2211yescharacteristic
25C17×#418—22no—
26C2×C17×#102—22no—
27C4×M16×C17C2211yescharacteristic
28C4×C4⋊C4×C17C2211yescharacteristic
29C17×#339—22no—
30C17×#328—22no—
31C22×D4×C17—21no—
32C22×D4×C17—21no—
33C22×D4×C17—21no—
34C2×Q16×C17—22no—
35C2×SD16×C17—24no—
36C2×M16×C17D412yes—
37C22×C8×C17D412yes—
38C17×C4⋊Q8D411yescharacteristic
39C17×C4⋊Q8D411yescharacteristic
40C17×C4⋊Q8D411yescharacteristic
41C17×C4⋊Q8D411yescharacteristic
42C17×#127—21no—
43C17×#127—21no—
44C17×#127—21no—
45C17×#127D412yes—
46C17×#125—21no—
47C17×#125—21no—
48C17×C22⋊Q8—21no—
49C17×C22⋊Q8—21no—
50C17×C22⋊Q8—21no—
51C17×C22⋊Q8—21no—
52C4×Q8×C17—21no—
53C4×Q8×C17—21no—
54C4×Q8×C17—21no—
55C4×Q8×C17—21no—
56C17×#117—21no—
57C17×#117—21no—
58C2×C4⋊C4×C17—21no—
59C2×C42×C17—21no—
60C2×C42×C17C2311yescharacteristic
61C17×#107—22no—
62C17×C4⋊C8—21no—
63C17×C4⋊C8—21no—
64C17×C4⋊C8—21no—
65C17×#103—22no—
66C17×#103—22no—
67C17×#102—24no—
68C17×#102—24no—
69C17×#102—24no—
70C17×#102—44no—
71C17×C22⋊C8D412yes—
72C17×#97—21no—
73C4×C8×C17—21no—
74C4×C8×C17—21no—
75C17×#95—21no—
76C24×C17—41no—
77C2×Q8×C17—21no—
78C2×Q8×C17—21no—
79C2×Q8×C17—21no—
80C2×Q8×C17—21no—
81C2×D4×C17—22no—
82C2×D4×C17—22no—
83C2×D4×C17—22no—
84C2×D4×C17—42no—
85C2×D4×C17—42no—
86C2×D4×C17—41no—
87C2×D4×C17—41no—
88C2×D4×C17—41no—
89C2×D4×C17—42no—
90C2×D4×C17—42no—
91C2×D4×C17—82no—
92C22×C4×C17—41no—
93C22×C4×C17C2×D411yescharacteristic
94C22×C4×C17C2×D411yescharacteristic
95C22×C4×C17C2×D411yescharacteristic
96Q16×C17—82no—
97SD16×C17—84no—
98M16×C17—22no—
99M16×C17—22no—
100C2×C8×C17—22no—
101C2×C8×C17—22no—
102C2×C8×C17—22no—
103C2×C8×C17—42no—
104C4⋊C4×C17—22no—
105C4⋊C4×C17—21no—
106C4⋊C4×C17—21no—
107C4⋊C4×C17—21no—
108C4⋊C4×C17—21no—
109C4⋊C4×C17—21no—
110C4⋊C4×C17—21no—
111C4⋊C4×C17—21no—
112C4⋊C4×C17—21no—
113C4⋊C4×C17—41no—
114C4⋊C4×C17—41no—
115C4⋊C4×C17—41no—
116C4⋊C4×C17—41no—
117C4⋊C4×C17—41no—
118C22⋊C4×C17—41no—
119C22⋊C4×C17—41no—
120C42×C17—41no—
121C42×C17—41no—
122C42×C17—42no—
123C42×C17C2×D411yescharacteristic
124C42×C17C2×D411yescharacteristic
125C42×C17C2×D411yescharacteristic
126C42×C17#4111yescharacteristic
127#10195C1711yesmaximal, characteristic, direct product factor, Sylow
128C23×C17—42no—
129C23×C17—82no—
130C23×C17—82no—
131C23×C17—81no—
132C23×C17—81no—
133C23×C17#12711yescharacteristic
134Q8×C17—42no—
135Q8×C17—41no—
136Q8×C17—41no—
137Q8×C17—41no—
138Q8×C17—41no—
139Q8×C17—81no—
140D4×C17—44no—
141D4×C17—44no—
142D4×C17—44no—
143D4×C17—82no—
144D4×C17—81no—
145D4×C17—81no—
146D4×C17—82no—
147C2×C4×C17—21no—
148C2×C4×C17—21no—
149C2×C4×C17—41no—
150C2×C4×C17—42no—
151C2×C4×C17—41no—
152C2×C4×C17—41no—
153C2×C4×C17—41no—
154C2×C4×C17—41no—
155C2×C4×C17—81no—
156C2×C4×C17—81no—
157C2×C4×C17#12011yescharacteristic
158C2×C4×C17#12011yescharacteristic
159C2×C4×C17#12011yescharacteristic
160C2×C4×C17#12111yescharacteristic
161C2×C4×C17#12111yescharacteristic
162C2×C4×C17#12111yescharacteristic
163C2×C4×C17#13512yes—
164C2×C4×C17#13712yes—
165C8×C17—42no—
166C8×C17—42no—
167C8×C17—42no—
168#3249C2×C1711yescharacteristic, complemented
169#3208C2×C1711yescharacteristic
170#3138C2×C1711yescharacteristic
171#1986C2×C1711yescharacteristic, complemented
172#1982C2×C1711yescharacteristic
173#1503C2×C1711yescharacteristic, complemented
174#1283C2×C1711yescharacteristic, complemented
175C22×C17—21no—
176C22×C17—21no—
177C22×C17—82no—
178C22×C17—82no—
179C22×C17—82no—
180C22×C17—162no—
181C22×C17—162no—
182C22×C17#39211yescharacteristic
183C22×C17#49511yescharacteristic
184C22×C17#49711yescharacteristic
185C4×C17—21no—
186C4×C17—21no—
187C4×C17—21no—
188C4×C17—82no—
189C4×C17—81no—
190C4×C17—81no—
191C4×C17—81no—
192C4×C17—81no—
193C4×C17#45212yes—
194C4×C17#45311yescharacteristic
195C4×C17#45411yescharacteristic
196C4×C17#46412yes—
197#533C22×C1711yescharacteristic
198#533C22×C1711yescharacteristic
199C2×#127C22×C1711yescharacteristic
200#492—21no—
201#490—22no—
202#486—21no—
203#486—21no—
204#486—21no—
205#477—21no—
206#477—21no—
207#467—22no—
208#462—21no—
209#462—21no—
210#460—22no—
211#450—22no—
212#431C22×C1711yescharacteristic
213C2×C4⋊C8C22×C1711yescharacteristic
214#418—22no—
215C2×#102—22no—
216C4×M16C22×C1711yescharacteristic
217C4×C4⋊C4C22×C1711yescharacteristic
218#339—22no—
219#328—22no—
220C2×C17—21no—
221C2×C17—21no—
222C2×C17—162no—
223C2×C17#200611yescharacteristic
224C2×C17#200811yescharacteristic
225C2×C17#201511yescharacteristic
226C22×D4—21no—
227C22×D4—21no—
228C22×D4—21no—
229C2×Q16—22no—
230C2×SD16—24no—
231C2×M16D4×C1712yes—
232C22×C8D4×C1712yes—
233C4⋊Q8D4×C1711yescharacteristic
234C4⋊Q8D4×C1711yescharacteristic
235C4⋊Q8D4×C1711yescharacteristic
236C4⋊Q8D4×C1711yescharacteristic
237#127—21no—
238#127—21no—
239#127—21no—
240#127D4×C1712yes—
241#125—21no—
242#125—21no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251#117—21no—
252#117—21no—
253C2×C4⋊C4—21no—
254C2×C42—21no—
255C2×C42C23×C1711yescharacteristic
256#107—22no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260#103—22no—
261#103—22no—
262#102—24no—
263#102—24no—
264#102—24no—
265#102—44no—
266C22⋊C8D4×C1712yes—
267#97—21no—
268C4×C8—21no—
269C4×C8—21no—
270#95—21no—
271C17#1019511yescharacteristic, direct product factor, Sylow
272C24—41no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—42no—
281C2×D4—42no—
282C2×D4—42no—
283C2×D4—42no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—82no—
288C22×C4—41no—
289C22×C4C2×D4×C1711yescharacteristic
290C22×C4C2×D4×C1711yescharacteristic
291C22×C4C2×D4×C1711yescharacteristic
292Q16—82no—
293SD16—84no—
294M16—22no—
295M16—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—42no—
300C4⋊C4—22no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C42—41no—
317C42—41no—
318C42—42no—
319C42C2×D4×C1711yescharacteristic
320C42C2×D4×C1711yescharacteristic
321C42C2×D4×C1711yescharacteristic
322C42#41×C1711yescharacteristic
323C23—42no—
324C23—82no—
325C23—82no—
326C23—81no—
327C23—81no—
328C23C17×#12711yescharacteristic
329Q8—42no—
330Q8—41no—
331Q8—41no—
332Q8—41no—
333Q8—41no—
334Q8—81no—
335D4—44no—
336D4—44no—
337D4—44no—
338D4—82no—
339D4—81no—
340D4—81no—
341D4—82no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4C17×#12011yescharacteristic
353C2×C4C17×#12011yescharacteristic
354C2×C4C17×#12011yescharacteristic
355C2×C4C17×#12111yescharacteristic
356C2×C4C17×#12111yescharacteristic
357C2×C4C17×#12111yescharacteristic
358C2×C4C17×#13512yes—
359C2×C4C17×#13712yes—
360C8—42no—
361C8—42no—
362C8—42no—
363C22—21no—
364C22—21no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22—162no—
369C22—162no—
370C22C17×#39211yescharacteristic
371C22C17×#49511yescharacteristic
372C22C17×#49711yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—82no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4C17×#45212yes—
382C4C17×#45311yescharacteristic
383C4C17×#45411yescharacteristic
384C4C17×#46412yes—
385C2—21no—
386C2—21no—
387C2—162no—
388C2C17×#200611yescharacteristic
389C2C17×#200811yescharacteristic
390C2C17×#201511yescharacteristic
subgroupG/H
center, socleC22×C17#392
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC2×C17×#127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#3249C2semidirect
4. C17×#1986C2semidirect
6. C17×#1503C2semidirect
7. C17×#1283C2semidirect
127. #10195C17direct (N × H)
168. #3249C2×C17semidirect
171. #1986C2×C17semidirect
173. #1503C2×C17semidirect
174. #1283C2×C17semidirect
271. C17#10195direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#32492
C17×#32082
C17×#31382
C17×#19862
C17×#19822
C17×#15032
C17×#12832
#1019517