Finite Group Databasebeta

← C17×#60253 #16917997

Subgroups — C17×#60253 #16917997

Order 4352.

1702 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#41×C17C211yesmaximal, characteristic
2C17×#2986C216yesmaximal, complemented
3C17×#2985C216yesmaximal, complemented
4C17×#2984C212yesmaximal, complemented
5C17×#2982C212yesmaximal, complemented
6Q8×M16×C17C211yesmaximal, characteristic, complemented
7C17×#2962C213yesmaximal, complemented
8C17×#2960C213yesmaximal, complemented
9C2×C8×Q8×C17C211yesmaximal, characteristic, complemented
10C17×#2925C213yesmaximal
11C17×#2922C213yesmaximal
12Q82×C17C411yescharacteristic
13C17×#557C413yes—
14C17×#554C416yes—
15C17×#554C413yes—
16D4×Q8×C17C412yes—
17D4×Q8×C17C411yescharacteristic
18C17×#533C2213yes—
19C17×#533C2216yes—
20C4×#41×C17C2213yes—
21C2×C4×Q8×C17C2211yescharacteristic
22C2×C4×Q8×C17C2212yes—
23C17×#446C2216yes—
24C17×#446C2216yes—
25C17×#446C2216yes—
26C17×#446C22112yes—
27C17×#446C2216yes—
28C8×Q8×C17C2211yescharacteristic
29C8×Q8×C17C2211yescharacteristic
30C8×Q8×C17C2213yes—
31C8×Q8×C17C2213yes—
32C8×Q8×C17C2216yes—
33C8×Q8×C17C2216yes—
34C8×Q8×C17C2216yes—
35C8×Q8×C17C2212yes—
36C17×#433C2216yes—
37C17×#433C22112yes—
38C17×#433C2216yes—
39C17×#432C2216yes—
40C17×#431C2216yes—
41C17×#431C2216yes—
42C17×#431C2216yes—
43C17×#424C2213yes—
44C17×#424C2213yes—
45C17×#423C2213yes—
46C2×C17×C4⋊C8C2213yes—
47C17×#408C2211yescharacteristic
48C17×#408C2213yes—
49C17×#405C2216yes—
50C4×M16×C17C2213yes—
51C2×C4×C8×C17C2213yes—
52C2×#41×C17C2311yescharacteristic
53C22×Q8×C17C2×C411yescharacteristic
54C22×Q8×C17C2×C412yes—
55C2×M16×C17C2311yescharacteristic
56C2×M16×C17C2313yes—
57C22×C8×C17C2311yescharacteristic
58C22×C8×C17C2313yes—
59C17×C4⋊Q8C2×C413yes—
60C17×C4⋊Q8C2×C416yes—
61C17×C4⋊Q8C2×C413yes—
62C17×C4⋊Q8C2×C416yes—
63C17×#125C2×C416yes—
64C17×#125C2×C4112yes—
65C17×C22⋊Q8C2×C416yes—
66C17×C22⋊Q8C2×C416yes—
67C17×C22⋊Q8C2×C416yes—
68C17×C22⋊Q8C2×C416yes—
69C17×C22⋊Q8C2×C4112yes—
70C4×Q8×C17C2×C411yescharacteristic
71C4×Q8×C17C2×C412yes—
72C4×Q8×C17C2×C413yes—
73C4×Q8×C17C2×C416yes—
74C4×Q8×C17C2×C413yes—
75C4×Q8×C17C2×C413yes—
76C4×Q8×C17C2311yescharacteristic
77C4×Q8×C17C2313yes—
78C4×Q8×C17C2316yes—
79C4×Q8×C17C2316yes—
80C4×D4×C17C2×C416yes—
81C4×D4×C17C2×C413yes—
82C4×D4×C17C2×C416yes—
83C4×D4×C17C2×C413yes—
84C17×#117C2313yes—
85C17×#117C2316yes—
86C2×C4⋊C4×C17C2×C413yes—
87C2×C4⋊C4×C17C2×C416yes—
88C2×C42×C17C2313yes—
89C2×C42×C17C2316yes—
90C17×C4⋊C8C2313yes—
91C17×C4⋊C8C2313yes—
92C17×C4⋊C8C2316yes—
93C17×C4⋊C8C2316yes—
94C17×C4⋊C8C2316yes—
95C17×C4⋊C8C2316yes—
96C17×C4⋊C8C2316yes—
97C17×C4⋊C8C2316yes—
98C17×C4⋊C8C2316yes—
99C17×C22⋊C8C2312yes—
100C17×C22⋊C8C2312yes—
101C17×C22⋊C8C2316yes—
102C17×C22⋊C8C2316yes—
103C17×#97C2316yes—
104C17×#97C23112yes—
105C4×C8×C17C2313yes—
106C4×C8×C17C2313yes—
107C4×C8×C17C2313yes—
108C4×C8×C17C2313yes—
109C4×C8×C17C2316yes—
110C4×C8×C17C23112yes—
111#41×C17—22no—
112#41×C17—22no—
113C2×Q8×C17—24no—
114C2×Q8×C17—28no—
115C2×Q8×C17C22×C416yes—
116C2×Q8×C17C22×C413yes—
117C2×Q8×C17C22×C411yescharacteristic
118C2×Q8×C17C22×C416yes—
119C2×Q8×C17C22×C411yescharacteristic
120C2×D4×C17C22×C412yes—
121C2×D4×C17C22×C411yescharacteristic
122C22×C4×C17C22×C416yes—
123C22×C4×C17C22×C413yes—
124C22×C4×C17C22×C416yes—
125C22×C4×C17C22×C413yes—
126C22×C4×C17C2412yes—
127C22×C4×C17C2411yescharacteristic
128M16×C17—22no—
129M16×C17—26no—
130C2×C8×C17—26no—
131C2×C8×C17—22no—
132C2×C8×C17C2411yescharacteristic
133C2×C8×C17C2411yescharacteristic
134C2×C8×C17C2413yes—
135C2×C8×C17C2413yes—
136C2×C8×C17C2412yes—
137C2×C8×C17C2416yes—
138C4⋊C4×C17C22×C4112yes—
139C4⋊C4×C17C22×C416yes—
140C4⋊C4×C17C22×C4112yes—
141C4⋊C4×C17C22×C416yes—
142C4⋊C4×C17C22×C416yes—
143C4⋊C4×C17C22×C413yes—
144C4⋊C4×C17C22×C416yes—
145C4⋊C4×C17C22×C416yes—
146C4⋊C4×C17C22×C413yes—
147C4⋊C4×C17C22×C413yes—
148C4⋊C4×C17C22×C413yes—
149C22⋊C4×C17C22×C416yes—
150C22⋊C4×C17C22×C416yes—
151C22⋊C4×C17C22×C416yes—
152C42×C17C22×C416yes—
153C42×C17C22×C413yes—
154C42×C17C22×C416yes—
155C42×C17C22×C413yes—
156C42×C17C2413yes—
157C42×C17C2413yes—
158C42×C17C2416yes—
159#60253C1711yesmaximal, characteristic, direct product factor, Sylow
160C23×C17C23×C412yes—
161C23×C17C23×C411yescharacteristic
162Q8×C17—22no—
163Q8×C17—26no—
164Q8×C17—212no—
165Q8×C17—46no—
166Q8×C17#13114yes—
167D4×C17—24no—
168D4×C17—22no—
169C2×C4×C17—26no—
170C2×C4×C17—212no—
171C2×C4×C17—22no—
172C2×C4×C17—22no—
173C2×C4×C17—43no—
174C2×C4×C17—46no—
175C2×C4×C17C23×C412yes—
176C2×C4×C17C23×C413yes—
177C2×C4×C17C23×C416yes—
178C2×C4×C17C23×C413yes—
179C2×C4×C17C23×C416yes—
180C2×C4×C17C23×C413yes—
181C2×C4×C17C23×C411yescharacteristic
182C2×C4×C17C23×C413yes—
183C2×C4×C172−1+412yes—
184C2×C4×C172−1+412yes—
185C2×C4×C17C2511yescharacteristic
186C8×C17—23no—
187C8×C17—21no—
188C8×C17—21no—
189C8×C17—23no—
190C8×C17—22no—
191C8×C17—26no—
192Q8×#41C2×C1711yescharacteristic
193#2986C2×C1716yescomplemented
194#2985C2×C1716yescomplemented
195#2984C2×C1712yescomplemented
196#2982C2×C1712yescomplemented
197Q8×M16C2×C1711yescharacteristic, complemented
198#2962C2×C1713yescomplemented
199#2960C2×C1713yescomplemented
200C2×C8×Q8C2×C1711yescharacteristic, complemented
201#2925C2×C1713yes—
202#2922C2×C1713yes—
203C22×C17—21no—
204C22×C17—21no—
205C22×C17—22no—
206C22×C17—22no—
207C22×C17—22no—
208C22×C17#51912yes—
209C22×C17C24×C411yescharacteristic
210C4×C17—22no—
211C4×C17—23no—
212C4×C17—26no—
213C4×C17—23no—
214C4×C17—23no—
215C4×C17—26no—
216C4×C17#51912yes—
217C4×C17C2×#13116yes—
218C4×C17C2×2−1+411yescharacteristic
219C4×C17C2×2−1+411yescharacteristic
220Q82C4×C1711yescharacteristic
221#557C4×C1713yes—
222#554C4×C1716yes—
223#554C4×C1713yes—
224D4×Q8C4×C1711yescharacteristic
225D4×Q8C4×C1712yes—
226#533C22×C1713yes—
227#533C22×C1716yes—
228C4×#41C22×C1713yes—
229C2×C4×Q8C22×C1711yescharacteristic
230C2×C4×Q8C22×C1712yes—
231#446C22×C1716yes—
232#446C22×C1716yes—
233#446C22×C1716yes—
234#446C22×C17112yes—
235#446C22×C1716yes—
236C8×Q8C22×C1711yescharacteristic
237C8×Q8C22×C1711yescharacteristic
238C8×Q8C22×C1713yes—
239C8×Q8C22×C1713yes—
240C8×Q8C22×C1716yes—
241C8×Q8C22×C1716yes—
242C8×Q8C22×C1716yes—
243C8×Q8C22×C1712yes—
244#433C22×C1716yes—
245#433C22×C1716yes—
246#433C22×C17112yes—
247#432C22×C1716yes—
248#431C22×C1716yes—
249#431C22×C1716yes—
250#431C22×C1716yes—
251#424C22×C1713yes—
252#424C22×C1713yes—
253#423C22×C1713yes—
254C2×C4⋊C8C22×C1713yes—
255#408C22×C1711yescharacteristic
256#408C22×C1713yes—
257#405C22×C1716yes—
258C4×M16C22×C1713yes—
259C2×C4×C8C22×C1713yes—
260C2×C17—22no—
261C2×C17—42no—
262C2×C17C2×#51911yescharacteristic
263C2×C17C22×#13111yescharacteristic
264C2×C17#357311yescharacteristic
265C2×#41C23×C1711yescharacteristic
266C22×Q8C2×C4×C1711yescharacteristic
267C22×Q8C2×C4×C1712yes—
268C2×M16C23×C1711yescharacteristic
269C2×M16C23×C1713yes—
270C22×C8C23×C1711yescharacteristic
271C22×C8C23×C1713yes—
272C4⋊Q8C2×C4×C1713yes—
273C4⋊Q8C2×C4×C1716yes—
274C4⋊Q8C2×C4×C1713yes—
275C4⋊Q8C2×C4×C1716yes—
276#125C2×C4×C1716yes—
277#125C2×C4×C17112yes—
278C22⋊Q8C2×C4×C1716yes—
279C22⋊Q8C2×C4×C1716yes—
280C22⋊Q8C2×C4×C1716yes—
281C22⋊Q8C2×C4×C1716yes—
282C22⋊Q8C2×C4×C17112yes—
283C4×Q8C2×C4×C1711yescharacteristic
284C4×Q8C2×C4×C1712yes—
285C4×Q8C2×C4×C1713yes—
286C4×Q8C2×C4×C1716yes—
287C4×Q8C2×C4×C1713yes—
288C4×Q8C2×C4×C1713yes—
289C4×Q8C23×C1711yescharacteristic
290C4×Q8C23×C1713yes—
291C4×Q8C23×C1716yes—
292C4×Q8C23×C1716yes—
293C4×D4C2×C4×C1716yes—
294C4×D4C2×C4×C1713yes—
295C4×D4C2×C4×C1716yes—
296C4×D4C2×C4×C1713yes—
297#117C23×C1713yes—
298#117C23×C1716yes—
299C2×C4⋊C4C2×C4×C1713yes—
300C2×C4⋊C4C2×C4×C1716yes—
301C2×C42C23×C1713yes—
302C2×C42C23×C1716yes—
303C4⋊C8C23×C1713yes—
304C4⋊C8C23×C1713yes—
305C4⋊C8C23×C1716yes—
306C4⋊C8C23×C1716yes—
307C4⋊C8C23×C1716yes—
308C4⋊C8C23×C1716yes—
309C4⋊C8C23×C1716yes—
310C4⋊C8C23×C1716yes—
311C4⋊C8C23×C1716yes—
312C22⋊C8C23×C1712yes—
313C22⋊C8C23×C1712yes—
314C22⋊C8C23×C1716yes—
315C22⋊C8C23×C1716yes—
316#97C23×C1716yes—
317#97C23×C17112yes—
318C4×C8C23×C1713yes—
319C4×C8C23×C1713yes—
320C4×C8C23×C1713yes—
321C4×C8C23×C1713yes—
322C4×C8C23×C1716yes—
323C4×C8C23×C17112yes—
324C17#6025311yescharacteristic, direct product factor, Sylow
325#41—22no—
326#41—22no—
327C2×Q8—24no—
328C2×Q8—28no—
329C2×Q8C22×C4×C1711yescharacteristic
330C2×Q8C22×C4×C1713yes—
331C2×Q8C22×C4×C1716yes—
332C2×Q8C22×C4×C1716yes—
333C2×Q8C22×C4×C1711yescharacteristic
334C2×D4C22×C4×C1712yes—
335C2×D4C22×C4×C1711yescharacteristic
336C22×C4C22×C4×C1716yes—
337C22×C4C22×C4×C1713yes—
338C22×C4C22×C4×C1716yes—
339C22×C4C22×C4×C1713yes—
340C22×C4C24×C1712yes—
341C22×C4C24×C1711yescharacteristic
342M16—22no—
343M16—26no—
344C2×C8—26no—
345C2×C8—22no—
346C2×C8C24×C1711yescharacteristic
347C2×C8C24×C1713yes—
348C2×C8C24×C1711yescharacteristic
349C2×C8C24×C1712yes—
350C2×C8C24×C1716yes—
351C2×C8C24×C1713yes—
352C4⋊C4C22×C4×C1713yes—
353C4⋊C4C22×C4×C1716yes—
354C4⋊C4C22×C4×C17112yes—
355C4⋊C4C22×C4×C1713yes—
356C4⋊C4C22×C4×C1716yes—
357C4⋊C4C22×C4×C1716yes—
358C4⋊C4C22×C4×C1716yes—
359C4⋊C4C22×C4×C1713yes—
360C4⋊C4C22×C4×C1713yes—
361C4⋊C4C22×C4×C17112yes—
362C4⋊C4C22×C4×C1716yes—
363C22⋊C4C22×C4×C1716yes—
364C22⋊C4C22×C4×C1716yes—
365C22⋊C4C22×C4×C1716yes—
366C42C22×C4×C1716yes—
367C42C22×C4×C1713yes—
368C42C22×C4×C1716yes—
369C42C22×C4×C1713yes—
370C42C24×C1713yes—
371C42C24×C1713yes—
372C42C24×C1716yes—
373C23C23×C4×C1712yes—
374C23C23×C4×C1711yescharacteristic
375Q8—22no—
376Q8—26no—
377Q8—212no—
378Q8—46no—
379Q8C17×#13114yes—
380D4—24no—
381D4—22no—
382C2×C4—26no—
383C2×C4—212no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—43no—
387C2×C4—46no—
388C2×C4C23×C4×C1712yes—
389C2×C4C23×C4×C1713yes—
390C2×C4C23×C4×C1716yes—
391C2×C4C23×C4×C1713yes—
392C2×C4C23×C4×C1716yes—
393C2×C4C23×C4×C1713yes—
394C2×C4C23×C4×C1711yescharacteristic
395C2×C4C23×C4×C1713yes—
396C2×C4C17×2−1+412yes—
397C2×C4C17×2−1+412yes—
398C2×C4C25×C1711yescharacteristic
399C8—23no—
400C8—21no—
401C8—21no—
402C8—23no—
403C8—22no—
404C8—26no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22C17×#51912yes—
411C22C24×C4×C1711yescharacteristic
412C4—23no—
413C4—26no—
414C4—23no—
415C4—23no—
416C4—26no—
417C4—22no—
418C4C17×#51912yes—
419C4C2×C17×#13116yes—
420C4C2×C17×2−1+411yescharacteristic
421C4C2×C17×2−1+411yescharacteristic
422C2—22no—
423C2—42no—
424C2C2×C17×#51911yescharacteristic
425C2C22×C17×#13111yescharacteristic
426C2C17×#357311yescharacteristic
subgroupG/H
centerC2×C4×C17C25
commutatorC22C24×C4×C17
Frattini, cosocleC2×C4C25×C17
socleC22×C17C24×C4
prime radicalC2×#41×C17C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C17×#2986C2semidirect
3. C17×#2985C2semidirect
4. C17×#2984C2semidirect
5. C17×#2982C2semidirect
6. Q8×M16×C17C2semidirect
7. C17×#2962C2semidirect
8. C17×#2960C2semidirect
9. C2×C8×Q8×C17C2semidirect
159. #60253C17direct (N × H)
193. #2986C2×C17semidirect
194. #2985C2×C17semidirect
195. #2984C2×C17semidirect
196. #2982C2×C17semidirect
197. Q8×M16C2×C17semidirect
198. #2962C2×C17semidirect
199. #2960C2×C17semidirect
200. C2×C8×Q8C2×C17semidirect
324. C17#60253direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×#41×C172
C17×#29862
C17×#29852
C17×#29842
C17×#29822
Q8×M16×C172
C17×#29622
C17×#29602
C2×C8×Q8×C172
C17×#29252
C17×#29222
#6025317