Finite Group Databasebeta

← C17×#10233 #16867977

Subgroups — C17×#10233 #16867977

Order 4352.

644 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#474C211yesmaximal, characteristic
2C2×C17×#462C211yesmaximal, characteristic, complemented
3C17×#2538C211yesmaximal, characteristic
4C17×#1990C211yesmaximal, characteristic, complemented
5C2×C17×Q8⋊C8C211yesmaximal, characteristic, complemented
6C2×C17×D4⋊C8C211yesmaximal, characteristic
7C17×#1296C211yesmaximal, characteristic, complemented
8C22×Q16×C17—21no—
9C2×C17×C4⋊Q8C2211yescharacteristic
10C2×C17×C22⋊Q8—21no—
11C2×C4×Q8×C17C2211yescharacteristic
12C2×C4×D4×C17C2211yescharacteristic
13C17×#474—22no—
14C17×#474—22no—
15C17×#462—22no—
16C17×#462—22no—
17C2×C17×#107—21no—
18C2×C17×C4⋊C8C2211yescharacteristic
19C2×C17×C4⋊C8C2211yescharacteristic
20C2×C17×#103—21no—
21C2×C17×#102—21no—
22C2×C4×C8×C17C2211yescharacteristic
23C17×#396—22no—
24C17×#390—21no—
25C17×#389—21no—
26C17×#384C2211yescharacteristic
27C17×#380—21no—
28C17×#340—22no—
29C17×Q8⋊C8—22no—
30C17×D4⋊C8—22no—
31C22×Q8×C17—21no—
32C22×Q8×C17D411yescharacteristic
33C22×D4×C17D411yescharacteristic
34C23×C4×C17—21no—
35C2×Q16×C17—24no—
36C2×Q16×C17—42no—
37C2×Q16×C17—42no—
38C22×C8×C17—21no—
39C22×C8×C17—21no—
40C22×C8×C17—21no—
41C17×C4⋊Q8—21no—
42C17×C4⋊Q8—21no—
43C17×C4⋊Q8—21no—
44C17×C4⋊Q8D412yes—
45C17×C22⋊Q8—42no—
46C17×C22⋊Q8—42no—
47C4×Q8×C17—21no—
48C4×Q8×C17—21no—
49C4×Q8×C17—21no—
50C4×Q8×C17—21no—
51C4×D4×C17—21no—
52C4×D4×C17—21no—
53C4×D4×C17—21no—
54C4×D4×C17—21no—
55C2×C4⋊C4×C17—21no—
56C2×C4⋊C4×C17—21no—
57C2×C4⋊C4×C17—22no—
58C2×C4⋊C4×C17—21no—
59C2×C4⋊C4×C17—21no—
60C2×C4⋊C4×C17—21no—
61C2×C4⋊C4×C17D411yescharacteristic
62C2×C4⋊C4×C17D411yescharacteristic
63C2×C4⋊C4×C17D412yes—
64C2×C22⋊C4×C17—22no—
65C2×C22⋊C4×C17—21no—
66C2×C22⋊C4×C17—22no—
67C2×C42×C17—21no—
68C2×C42×C17C2311yescharacteristic
69C17×#107—24no—
70C17×C4⋊C8—21no—
71C17×C4⋊C8—21no—
72C17×C4⋊C8D412yes—
73C17×C4⋊C8D412yes—
74C17×#103—24no—
75C17×#102—24no—
76C4×C8×C17—21no—
77C4×C8×C17—21no—
78C17×#95—22no—
79C24×C17—21no—
80C2×Q8×C17—21no—
81C2×Q8×C17—21no—
82C2×Q8×C17—22no—
83C2×Q8×C17—21no—
84C2×Q8×C17—21no—
85C2×Q8×C17—21no—
86C2×Q8×C17—41no—
87C2×Q8×C17—41no—
88C2×Q8×C17—41no—
89C2×Q8×C17—41no—
90C2×Q8×C17—41no—
91C2×Q8×C17D812yes—
92C2×D4×C17—21no—
93C2×D4×C17—21no—
94C2×D4×C17—21no—
95C2×D4×C17—21no—
96C2×D4×C17—21no—
97C2×D4×C17Q1612yescomplemented
98C22×C4×C17—21no—
99C22×C4×C17—21no—
100C22×C4×C17—21no—
101C22×C4×C17—22no—
102C22×C4×C17—41no—
103C22×C4×C17—41no—
104C22×C4×C17—41no—
105C22×C4×C17—41no—
106C22×C4×C17—41no—
107C22×C4×C17—41no—
108C22×C4×C17—41no—
109C22×C4×C17C2×D411yescharacteristic
110C22×C4×C17C2×D411yescharacteristic
111C22×C4×C17C2×D411yescharacteristic
112Q16×C17—48no—
113C2×C8×C17—22no—
114C2×C8×C17—22no—
115C2×C8×C17—22no—
116C2×C8×C17—41no—
117C2×C8×C17—41no—
118C2×C8×C17—41no—
119C2×C8×C17—41no—
120C2×C8×C17—41no—
121C2×C8×C17—41no—
122C4⋊C4×C17—22no—
123C4⋊C4×C17—21no—
124C4⋊C4×C17—21no—
125C4⋊C4×C17—22no—
126C4⋊C4×C17—21no—
127C4⋊C4×C17—21no—
128C4⋊C4×C17—42no—
129C4⋊C4×C17—44no—
130C4⋊C4×C17—41no—
131C4⋊C4×C17—41no—
132C4⋊C4×C17—41no—
133C4⋊C4×C17—41no—
134C4⋊C4×C17—41no—
135C4⋊C4×C17—41no—
136C4⋊C4×C17—41no—
137C4⋊C4×C17—41no—
138C22⋊C4×C17—44no—
139C22⋊C4×C17—41no—
140C22⋊C4×C17—41no—
141C22⋊C4×C17—82no—
142C42×C17—41no—
143C42×C17—41no—
144C42×C17C2×D411yescharacteristic
145C42×C17C2×D411yescharacteristic
146C42×C17C2×D411yescharacteristic
147C42×C17#4111yescharacteristic
148#10233C1711yesmaximal, characteristic, direct product factor, Sylow
149C23×C17—22no—
150C23×C17—41no—
151C23×C17—41no—
152C23×C17—41no—
153C23×C17—41no—
154C23×C17—41no—
155C23×C17—41no—
156C23×C17#12011yescharacteristic
157Q8×C17—22no—
158Q8×C17—22no—
159Q8×C17—41no—
160Q8×C17—41no—
161Q8×C17—42no—
162Q8×C17—42no—
163Q8×C17—81no—
164Q8×C17—81no—
165D4×C17—22no—
166D4×C17—22no—
167D4×C17—41no—
168D4×C17—41no—
169C2×C4×C17—21no—
170C2×C4×C17—21no—
171C2×C4×C17—22no—
172C2×C4×C17—41no—
173C2×C4×C17—41no—
174C2×C4×C17—41no—
175C2×C4×C17—41no—
176C2×C4×C17—42no—
177C2×C4×C17—42no—
178C2×C4×C17—41no—
179C2×C4×C17—41no—
180C2×C4×C17—42no—
181C2×C4×C17—41no—
182C2×C4×C17—42no—
183C2×C4×C17—41no—
184C2×C4×C17—81no—
185C2×C4×C17—81no—
186C2×C4×C17—81no—
187C2×C4×C17—81no—
188C2×C4×C17—81no—
189C2×C4×C17—81no—
190C2×C4×C17#12011yescharacteristic
191C2×C4×C17#12011yescharacteristic
192C2×C4×C17#12111yescharacteristic
193C2×C4×C17#12111yescharacteristic
194C2×C4×C17#12111yescharacteristic
195C2×C4×C17#12711yescharacteristic
196C2×C4×C17C2×D811yescharacteristic
197C2×C4×C17C2×Q1611yescharacteristic
198C2×C4×C17#13511yescharacteristic
199C2×C4×C17#13511yescharacteristic
200C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
202C2×C4×C17#13711yescharacteristic
203C2×C4×C17#13711yescharacteristic
204C8×C17—42no—
205C8×C17—42no—
206C8×C17—42no—
207C2×#474C2×C1711yescharacteristic
208C2×#462C2×C1711yescharacteristic, complemented
209#2538C2×C1711yescharacteristic
210#1990C2×C1711yescharacteristic, complemented
211C2×Q8⋊C8C2×C1711yescharacteristic, complemented
212C2×D4⋊C8C2×C1711yescharacteristic
213#1296C2×C1711yescharacteristic, complemented
214C22×C17—42no—
215C22×C17—42no—
216C22×C17—42no—
217C22×C17—81no—
218C22×C17—81no—
219C22×C17—81no—
220C22×C17—81no—
221C22×C17#39211yescharacteristic
222C22×C17#44711yescharacteristic
223C22×C17#44911yescharacteristic
224C22×C17#45111yescharacteristic
225C22×C17#45211yescharacteristic
226C22×C17#45511yescharacteristic
227C22×C17#45611yescharacteristic
228C4×C17—21no—
229C4×C17—21no—
230C4×C17—42no—
231C4×C17—82no—
232C4×C17—81no—
233C4×C17—82no—
234C4×C17—81no—
235C4×C17#44711yescharacteristic
236C4×C17#44911yescharacteristic
237C4×C17#45111yescharacteristic
238C4×C17#45211yescharacteristic
239C4×C17#46611yescharacteristic
240C4×C17#46711yescharacteristic
241C4×C17#46911yescharacteristic
242C4×C17#47011yescharacteristic
243C22×Q16—21no—
244C2×C4⋊Q8C22×C1711yescharacteristic
245C2×C22⋊Q8—21no—
246C2×C4×Q8C22×C1711yescharacteristic
247C2×C4×D4C22×C1711yescharacteristic
248#474—22no—
249#474—22no—
250#462—22no—
251#462—22no—
252C2×#107—21no—
253C2×C4⋊C8C22×C1711yescharacteristic
254C2×C4⋊C8C22×C1711yescharacteristic
255C2×#103—21no—
256C2×#102—21no—
257C2×C4×C8C22×C1711yescharacteristic
258#396—22no—
259#390—21no—
260#389—21no—
261#384C22×C1711yescharacteristic
262#380—21no—
263#340—22no—
264Q8⋊C8—22no—
265D4⋊C8—22no—
266C2×C17—82no—
267C2×C17#164111yescharacteristic
268C2×C17#164411yescharacteristic
269C2×C17#164911yescharacteristic
270C2×C17#165211yescharacteristic
271C2×C17#199911yescharacteristic
272C2×C17#200111yescharacteristic
273C2×C17#200711yescharacteristic
274C22×Q8—21no—
275C22×Q8D4×C1711yescharacteristic
276C22×D4D4×C1711yescharacteristic
277C23×C4—21no—
278C2×Q16—24no—
279C2×Q16—42no—
280C2×Q16—42no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8D4×C1712yes—
288C22⋊Q8—42no—
289C22⋊Q8—42no—
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C1711yescharacteristic
305C2×C4⋊C4D4×C1711yescharacteristic
306C2×C4⋊C4D4×C1712yes—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—22no—
310C2×C42—21no—
311C2×C42C23×C1711yescharacteristic
312#107—24no—
313C4⋊C8—21no—
314C4⋊C8—21no—
315C4⋊C8D4×C1712yes—
316C4⋊C8D4×C1712yes—
317#103—24no—
318#102—24no—
319C4×C8—21no—
320C4×C8—21no—
321#95—22no—
322C17#1023311yescharacteristic, direct product factor, Sylow
323C24—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—21no—
330C2×Q8—41no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8D8×C1712yes—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4Q16×C1712yescomplemented
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4C2×D4×C1711yescharacteristic
354C22×C4C2×D4×C1711yescharacteristic
355C22×C4C2×D4×C1711yescharacteristic
356Q16—48no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—42no—
373C4⋊C4—44no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C22⋊C4—44no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—82no—
386C42—41no—
387C42—41no—
388C42C2×D4×C1711yescharacteristic
389C42C2×D4×C1711yescharacteristic
390C42C2×D4×C1711yescharacteristic
391C42#41×C1711yescharacteristic
392C23—22no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23C17×#12011yescharacteristic
400Q8—22no—
401Q8—22no—
402Q8—41no—
403Q8—41no—
404Q8—42no—
405Q8—42no—
406Q8—81no—
407Q8—81no—
408D4—22no—
409D4—22no—
410D4—41no—
411D4—41no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4C17×#12011yescharacteristic
434C2×C4C17×#12011yescharacteristic
435C2×C4C17×#12111yescharacteristic
436C2×C4C17×#12111yescharacteristic
437C2×C4C17×#12111yescharacteristic
438C2×C4C17×#12711yescharacteristic
439C2×C4C2×D8×C1711yescharacteristic
440C2×C4C2×Q16×C1711yescharacteristic
441C2×C4C17×#13511yescharacteristic
442C2×C4C17×#13511yescharacteristic
443C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
444C2×C4C17×AGL(1,ℤ/8)11yescharacteristic
445C2×C4C17×#13711yescharacteristic
446C2×C4C17×#13711yescharacteristic
447C8—42no—
448C8—42no—
449C8—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22C17×#39211yescharacteristic
458C22C17×#44711yescharacteristic
459C22C17×#44911yescharacteristic
460C22C17×#45111yescharacteristic
461C22C17×#45211yescharacteristic
462C22C17×#45511yescharacteristic
463C22C17×#45611yescharacteristic
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—82no—
469C4—81no—
470C4—82no—
471C4C17×#44711yescharacteristic
472C4C17×#44911yescharacteristic
473C4C17×#45111yescharacteristic
474C4C17×#45211yescharacteristic
475C4C17×#46611yescharacteristic
476C4C17×#46711yescharacteristic
477C4C17×#46911yescharacteristic
478C4C17×#47011yescharacteristic
479C2—82no—
480C2C17×#164111yescharacteristic
481C2C17×#164411yescharacteristic
482C2C17×#164911yescharacteristic
483C2C17×#165211yescharacteristic
484C2C17×#199911yescharacteristic
485C2C17×#200111yescharacteristic
486C2C17×#200711yescharacteristic
subgroupG/H
center, socleC23×C17#120
commutator, Frattini, cosocleC2×C42C23×C17
prime radicalC22×D4×C17D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#462C2semidirect
4. C17×#1990C2semidirect
5. C2×C17×Q8⋊C8C2semidirect
7. C17×#1296C2semidirect
97. C2×D4×C17Q16semidirect
148. #10233C17direct (N × H)
208. C2×#462C2×C17semidirect
210. #1990C2×C17semidirect
211. C2×Q8⋊C8C2×C17semidirect
213. #1296C2×C17semidirect
322. C17#10233direct (N × H)
341. C2×D4Q16×C17semidirect

Maximal subgroups

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

subgroupindex
C2×C17×#4742
C2×C17×#4622
C17×#25382
C17×#19902
C2×C17×Q8⋊C82
C2×C17×D4⋊C82
C17×#12962
#1023317