Finite Group Databasebeta

← C17×#34295 #16892039

Subgroups — C17×#34295 #16892039

Order 4352.

3200 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#550C211yesmaximal, characteristic
2C2×C17×#520C211yesmaximal, characteristic, complemented
3C2×C4×#41×C17C211yesmaximal, characteristic, complemented
4C17×#2366C213yesmaximal, complemented
5C17×#2363C213yesmaximal, complemented
6C17×#2361C213yesmaximal, complemented
7C17×#2352C213yesmaximal, complemented
8C17×#2351C211yesmaximal, characteristic, complemented
9C17×#2341C211yesmaximal, characteristic, complemented
10C17×#2341C211yesmaximal, characteristic, complemented
11C17×#2328C213yesmaximal, complemented
12C17×#2324C213yesmaximal, complemented
13C4×C17×#121C213yesmaximal, complemented
14C17×#2290C213yesmaximal, complemented
15C17×#2276C211yesmaximal, characteristic, complemented
16C22×#41×C17C2211yescharacteristic
17C22×#41×C17C2211yescharacteristic
18C17×#550C4116yescomplemented
19C2×C17×#127C2213yes—
20C2×C17×#121C2213yes—
21C2×C17×#121C2213yes—
22C17×#520—28no—
23C4×#41×C17—28no—
24C2×C4×Q8×C17C2211yescharacteristic
25C2×C4×Q8×C17C2211yescharacteristic
26C2×C4×Q8×C17C2211yescharacteristic
27C2×C4×Q8×C17C2211yescharacteristic
28C2×C4×Q8×C17C2211yescharacteristic
29C2×C4×D4×C17C2213yes—
30C2×C4×D4×C17C2213yes—
31C2×C4×D4×C17C2213yes—
32C2×C4×D4×C17C2213yes—
33C2×C4×D4×C17C2216yes—
34C2×C4×D4×C17C2213yes—
35C2×C17×#117C2213yes—
36C2×C17×#117C2213yes—
37C22×C4⋊C4×C17C2213yes—
38C22×C42×C17C2213yes—
39C17×#390C2213yes—
40C17×#390C2213yes—
41C17×#390C2216yes—
42C17×#390C2213yes—
43C17×#390C2213yes—
44C17×#389C2213yes—
45C17×#389C2213yes—
46C17×#388C2213yes—
47C17×#388C2213yes—
48C17×#388C2216yes—
49C17×#387C2211yescharacteristic
50C17×#387C2213yes—
51C17×#386C2213yes—
52C17×#386C2213yes—
53C17×#386C2216yes—
54C17×#386C2216yes—
55C17×#386C2216yes—
56C17×#385C2213yes—
57C17×#385C2213yes—
58C17×#382C2213yes—
59C17×#380C2213yes—
60C17×#380C2213yes—
61C4×C4⋊C4×C17C2213yes—
62C4×C4⋊C4×C17C2213yes—
63C4×C4⋊C4×C17C2213yes—
64C4×C4⋊C4×C17C2213yes—
65C4×C22⋊C4×C17C2213yes—
66C4×C22⋊C4×C17C2213yes—
67C4×C22⋊C4×C17C2216yes—
68C17×#376C2213yes—
69C2×#41×C17—24no—
70C2×#41×C17—24no—
71C2×#41×C17—24no—
72C2×#41×C17—24no—
73C2×#41×C17C2×C418yescomplemented
74C2×#41×C17C2×C418yescomplemented
75C22×Q8×C17C2311yescharacteristic
76C22×D4×C17C2313yes—
77C22×D4×C17C2313yes—
78C22×D4×C17C2316yes—
79C22×D4×C17C2313yes—
80C23×C4×C17C2313yes—
81C23×C4×C17C2313yes—
82C23×C4×C17C2313yes—
83C23×C4×C17C2313yes—
84C23×C4×C17C2316yes—
85C17×#127C2×C4124yescomplemented
86C17×#121C2×C4124yescomplemented
87C17×#121C2×C4124yescomplemented
88C4×Q8×C17—24no—
89C4×Q8×C17—24no—
90C4×Q8×C17—24no—
91C4×Q8×C17C2×C418yescomplemented
92C4×Q8×C17D418yescomplemented
93C4×D4×C17—212no—
94C4×D4×C17—212no—
95C4×D4×C17—212no—
96C4×D4×C17—212no—
97C4×D4×C17—412no—
98C4×D4×C17C2×C4124yescomplemented
99C17×#117—212no—
100C17×#117—212no—
101C2×C4⋊C4×C17—212no—
102C2×C4⋊C4×C17C2313yes—
103C2×C4⋊C4×C17C2313yes—
104C2×C4⋊C4×C17C2311yescharacteristic
105C2×C4⋊C4×C17C2313yes—
106C2×C4⋊C4×C17C2313yes—
107C2×C4⋊C4×C17C2313yes—
108C2×C4⋊C4×C17C2313yes—
109C2×C4⋊C4×C17C2311yescharacteristic
110C2×C4⋊C4×C17C2313yes—
111C2×C4⋊C4×C17C2313yes—
112C2×C22⋊C4×C17C2313yes—
113C2×C22⋊C4×C17C2316yes—
114C2×C22⋊C4×C17C2313yes—
115C2×C22⋊C4×C17C2313yes—
116C2×C22⋊C4×C17C2316yes—
117C2×C22⋊C4×C17C2316yes—
118C2×C22⋊C4×C17C2313yes—
119C2×C22⋊C4×C17C2313yes—
120C2×C22⋊C4×C17C2313yes—
121C2×C22⋊C4×C17C2313yes—
122C2×C22⋊C4×C17C2313yes—
123C2×C42×C17—212no—
124C2×C42×C17C2311yescharacteristic
125C2×C42×C17C2313yes—
126C2×C42×C17C2313yes—
127C2×C42×C17C2313yes—
128C2×C42×C17C2313yes—
129C2×C42×C17C2316yes—
130C2×C42×C17C2313yes—
131C2×C42×C17C2313yes—
132C17×#95C2311yescharacteristic
133C17×#95C2313yes—
134C17×#95C2313yes—
135C17×#95C2313yes—
136C17×#95C2313yes—
137C17×#95C2311yescharacteristic
138C17×#95C2311yescharacteristic
139C17×#95C2313yes—
140C17×#95C2316yes—
141C17×#95C2311yescharacteristic
142C17×#95C2313yes—
143C24×C17C2413yes—
144C24×C17C2413yes—
145#41×C17—232no—
146#41×C17—232no—
147C2×Q8×C17C22×C414yes—
148C2×Q8×C17C2×D414yes—
149C2×Q8×C17#4114yes—
150C2×D4×C17—26no—
151C2×D4×C17—26no—
152C2×D4×C17—26no—
153C2×D4×C17—26no—
154C2×D4×C17—46no—
155C2×D4×C17—43no—
156C2×D4×C17—43no—
157C2×D4×C17—46no—
158C2×D4×C17C22×C4112yes—
159C2×D4×C17C22×C4112yes—
160C2×D4×C17C22×C4112yes—
161C2×D4×C17C22×C4124yes—
162C22×C4×C17—26no—
163C22×C4×C17—26no—
164C22×C4×C17—26no—
165C22×C4×C17—26no—
166C22×C4×C17—26no—
167C22×C4×C17—26no—
168C22×C4×C17—26no—
169C22×C4×C17—212no—
170C22×C4×C17—43no—
171C22×C4×C17—43no—
172C22×C4×C17—43no—
173C22×C4×C17—46no—
174C22×C4×C17—46no—
175C22×C4×C17C22×C4112yes—
176C22×C4×C17C22×C4112yes—
177C22×C4×C17C2413yes—
178C22×C4×C17C2413yes—
179C22×C4×C17C2411yescharacteristic
180C22×C4×C17C2413yes—
181C22×C4×C17C2411yescharacteristic
182C22×C4×C17C2411yescharacteristic
183C22×C4×C17C2411yescharacteristic
184C22×C4×C17C2411yescharacteristic
185C22×C4×C17C2413yes—
186C22×C4×C17C2411yescharacteristic
187C22×C4×C17C2413yes—
188C22×C4×C17C2411yescharacteristic
189C22×C4×C17C2413yes—
190C4⋊C4×C17—26no—
191C4⋊C4×C17—26no—
192C4⋊C4×C17—22no—
193C4⋊C4×C17—26no—
194C4⋊C4×C17—26no—
195C4⋊C4×C17—26no—
196C4⋊C4×C17—43no—
197C4⋊C4×C17C22×C414yes—
198C4⋊C4×C17C22×C4112yes—
199C4⋊C4×C17C2×D4112yes—
200C22⋊C4×C17—26no—
201C22⋊C4×C17—212no—
202C22⋊C4×C17—26no—
203C22⋊C4×C17—26no—
204C22⋊C4×C17—43no—
205C22⋊C4×C17—46no—
206C22⋊C4×C17—43no—
207C22⋊C4×C17—43no—
208C22⋊C4×C17—46no—
209C22⋊C4×C17C22×C4112yes—
210C22⋊C4×C17C22×C4112yes—
211C42×C17—22no—
212C42×C17—26no—
213C42×C17—26no—
214C42×C17—26no—
215C42×C17—26no—
216C42×C17—46no—
217C42×C17C22×C4112yes—
218C42×C17C2×D4112yes—
219#34295C1711yesmaximal, characteristic, direct product factor, Sylow
220C23×C17—23no—
221C23×C17—23no—
222C23×C17—23no—
223C23×C17—23no—
224C23×C17—23no—
225C23×C17—23no—
226C23×C17—23no—
227C23×C17—23no—
228C23×C17—23no—
229C23×C17—23no—
230C23×C17—23no—
231C23×C17—23no—
232C23×C17C23×C416yes—
233C23×C17C23×C416yes—
234C23×C17C2511yescharacteristic
235Q8×C17C4×D4116yescomplemented
236D4×C17—224no—
237D4×C17—224no—
238D4×C17—412no—
239D4×C17—424no—
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—21no—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17—23no—
246C2×C4×C17—23no—
247C2×C4×C17—23no—
248C2×C4×C17—21no—
249C2×C4×C17—21no—
250C2×C4×C17—21no—
251C2×C4×C17—23no—
252C2×C4×C17—21no—
253C2×C4×C17—21no—
254C2×C4×C17—224no—
255C2×C4×C17—224no—
256C2×C4×C17—21no—
257C2×C4×C17—23no—
258C2×C4×C17—23no—
259C2×C4×C17—21no—
260C2×C4×C17—23no—
261C2×C4×C17—23no—
262C2×C4×C17—23no—
263C2×C4×C17—21no—
264C2×C4×C17—23no—
265C2×C4×C17—21no—
266C2×C4×C17—21no—
267C2×C4×C17—23no—
268C2×C4×C17—23no—
269C2×C4×C17—23no—
270C2×C4×C17—21no—
271C2×C4×C17—412no—
272C2×C4×C17—412no—
273C2×C4×C17—812no—
274C2×C4×C17C23×C412yes—
275C2×C4×C17C23×C416yes—
276C2×C4×C17C23×C412yes—
277C2×C4×C17C23×C412yes—
278C2×C4×C17C23×C416yes—
279C2×C4×C17C22×D412yes—
280C2×C4×C17C22×D416yes—
281C2×C4×C17C22×D416yes—
282C2×C4×C17C2×#4116yes—
283C2×C4×C17H(5,𝔽2)12yes—
284C2×#550C2×C1711yescharacteristic
285C2×#520C2×C1711yescharacteristic, complemented
286C2×C4×#41C2×C1711yescharacteristic, complemented
287#2366C2×C1713yescomplemented
288#2363C2×C1713yescomplemented
289#2361C2×C1713yescomplemented
290#2352C2×C1713yescomplemented
291#2351C2×C1711yescharacteristic, complemented
292#2341C2×C1711yescharacteristic, complemented
293#2341C2×C1711yescharacteristic, complemented
294#2328C2×C1713yescomplemented
295#2324C2×C1713yescomplemented
296C4×#121C2×C1713yescomplemented
297#2290C2×C1713yescomplemented
298#2276C2×C1711yescharacteristic, complemented
299C22×C17—26no—
300C22×C17—26no—
301C22×C17—26no—
302C22×C17—26no—
303C22×C17—26no—
304C22×C17—26no—
305C22×C17—43no—
306C22×C17—43no—
307C22×C17—43no—
308C22×C17—43no—
309C22×C17—43no—
310C22×C17—43no—
311C22×C17—43no—
312C22×C17—43no—
313C22×C17C24×C411yescharacteristic
314C22×C17C23×D411yescharacteristic
315C22×C17C22×#4111yescharacteristic
316C22×C17C2×H(5,𝔽2)11yescharacteristic
317C22×C17#58511yescharacteristic
318C22×C17#58511yescharacteristic
319C22×C17#58511yescharacteristic
320C4×C17—22no—
321C4×C17—22no—
322C4×C17—22no—
323C4×C17—26no—
324C4×C17—22no—
325C4×C17—22no—
326C4×C17—26no—
327C4×C17—41no—
328C4×C17—43no—
329C4×C17—43no—
330C4×C17—43no—
331C4×C17—41no—
332C4×C17C2×C4×D4112yes—
333C22×#41C22×C1711yescharacteristic
334C22×#41C22×C1711yescharacteristic
335#550C4×C17116yescomplemented
336C2×#127C22×C1713yes—
337C2×#121C22×C1713yes—
338C2×#121C22×C1713yes—
339#520—28no—
340C4×#41—28no—
341C2×C4×Q8C22×C1711yescharacteristic
342C2×C4×Q8C22×C1711yescharacteristic
343C2×C4×Q8C22×C1711yescharacteristic
344C2×C4×Q8C22×C1711yescharacteristic
345C2×C4×Q8C22×C1711yescharacteristic
346C2×C4×D4C22×C1713yes—
347C2×C4×D4C22×C1713yes—
348C2×C4×D4C22×C1713yes—
349C2×C4×D4C22×C1713yes—
350C2×C4×D4C22×C1716yes—
351C2×C4×D4C22×C1713yes—
352C2×#117C22×C1713yes—
353C2×#117C22×C1713yes—
354C22×C4⋊C4C22×C1713yes—
355C22×C42C22×C1713yes—
356#390C22×C1713yes—
357#390C22×C1716yes—
358#390C22×C1713yes—
359#390C22×C1713yes—
360#390C22×C1713yes—
361#389C22×C1713yes—
362#389C22×C1713yes—
363#388C22×C1716yes—
364#388C22×C1713yes—
365#388C22×C1713yes—
366#387C22×C1713yes—
367#387C22×C1711yescharacteristic
368#386C22×C1716yes—
369#386C22×C1713yes—
370#386C22×C1716yes—
371#386C22×C1716yes—
372#386C22×C1713yes—
373#385C22×C1713yes—
374#385C22×C1713yes—
375#382C22×C1713yes—
376#380C22×C1713yes—
377#380C22×C1713yes—
378C4×C4⋊C4C22×C1713yes—
379C4×C4⋊C4C22×C1713yes—
380C4×C4⋊C4C22×C1713yes—
381C4×C4⋊C4C22×C1713yes—
382C4×C22⋊C4C22×C1713yes—
383C4×C22⋊C4C22×C1713yes—
384C4×C22⋊C4C22×C1716yes—
385#376C22×C1713yes—
386C2×C17—46no—
387C2×C17—46no—
388C2×C17C22×C4×D411yescharacteristic
389C2×C17#342811yescharacteristic
390C2×C17C4×H(5,𝔽2)11yescharacteristic
391C2×C17#348711yescharacteristic
392C2×C17#348811yescharacteristic
393C2×C17#351711yescharacteristic
394C2×C17#352411yescharacteristic
395C2×#41—24no—
396C2×#41—24no—
397C2×#41—24no—
398C2×#41—24no—
399C2×#41C2×C4×C1718yescomplemented
400C2×#41C2×C4×C1718yescomplemented
401C22×Q8C23×C1711yescharacteristic
402C22×D4C23×C1713yes—
403C22×D4C23×C1713yes—
404C22×D4C23×C1716yes—
405C22×D4C23×C1713yes—
406C23×C4C23×C1713yes—
407C23×C4C23×C1713yes—
408C23×C4C23×C1713yes—
409C23×C4C23×C1716yes—
410C23×C4C23×C1713yes—
411#127C2×C4×C17124yescomplemented
412#121C2×C4×C17124yescomplemented
413#121C2×C4×C17124yescomplemented
414C4×Q8—24no—
415C4×Q8—24no—
416C4×Q8—24no—
417C4×Q8C2×C4×C1718yescomplemented
418C4×Q8D4×C1718yescomplemented
419C4×D4—212no—
420C4×D4—212no—
421C4×D4—212no—
422C4×D4—212no—
423C4×D4—412no—
424C4×D4C2×C4×C17124yescomplemented
425#117—212no—
426#117—212no—
427C2×C4⋊C4—212no—
428C2×C4⋊C4C23×C1713yes—
429C2×C4⋊C4C23×C1713yes—
430C2×C4⋊C4C23×C1711yescharacteristic
431C2×C4⋊C4C23×C1713yes—
432C2×C4⋊C4C23×C1713yes—
433C2×C4⋊C4C23×C1713yes—
434C2×C4⋊C4C23×C1713yes—
435C2×C4⋊C4C23×C1711yescharacteristic
436C2×C4⋊C4C23×C1713yes—
437C2×C4⋊C4C23×C1713yes—
438C2×C22⋊C4C23×C1713yes—
439C2×C22⋊C4C23×C1716yes—
440C2×C22⋊C4C23×C1713yes—
441C2×C22⋊C4C23×C1713yes—
442C2×C22⋊C4C23×C1716yes—
443C2×C22⋊C4C23×C1716yes—
444C2×C22⋊C4C23×C1713yes—
445C2×C22⋊C4C23×C1713yes—
446C2×C22⋊C4C23×C1713yes—
447C2×C22⋊C4C23×C1713yes—
448C2×C22⋊C4C23×C1713yes—
449C2×C42—212no—
450C2×C42C23×C1713yes—
451C2×C42C23×C1713yes—
452C2×C42C23×C1713yes—
453C2×C42C23×C1713yes—
454C2×C42C23×C1711yescharacteristic
455C2×C42C23×C1716yes—
456C2×C42C23×C1713yes—
457C2×C42C23×C1713yes—
458#95C23×C1711yescharacteristic
459#95C23×C1713yes—
460#95C23×C1713yes—
461#95C23×C1713yes—
462#95C23×C1713yes—
463#95C23×C1711yescharacteristic
464#95C23×C1711yescharacteristic
465#95C23×C1713yes—
466#95C23×C1716yes—
467#95C23×C1711yescharacteristic
468#95C23×C1713yes—
469C17#3429511yescharacteristic, direct product factor, Sylow
470C24C24×C1713yes—
471C24C24×C1713yes—
472#41—232no—
473#41—232no—
474C2×Q8C22×C4×C1714yes—
475C2×Q8C2×D4×C1714yes—
476C2×Q8#41×C1714yes—
477C2×D4—26no—
478C2×D4—26no—
479C2×D4—26no—
480C2×D4—26no—
481C2×D4—46no—
482C2×D4—46no—
483C2×D4—43no—
484C2×D4—43no—
485C2×D4C22×C4×C17112yes—
486C2×D4C22×C4×C17112yes—
487C2×D4C22×C4×C17112yes—
488C2×D4C22×C4×C17124yes—
489C22×C4—26no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—26no—
494C22×C4—26no—
495C22×C4—26no—
496C22×C4—212no—
497C22×C4—43no—
498C22×C4—43no—
499C22×C4—43no—
500C22×C4—46no—
501C22×C4—46no—
502C22×C4C22×C4×C17112yes—
503C22×C4C22×C4×C17112yes—
504C22×C4C24×C1711yescharacteristic
505C22×C4C24×C1713yes—
506C22×C4C24×C1713yes—
507C22×C4C24×C1713yes—
508C22×C4C24×C1711yescharacteristic
509C22×C4C24×C1711yescharacteristic
510C22×C4C24×C1711yescharacteristic
511C22×C4C24×C1713yes—
512C22×C4C24×C1711yescharacteristic
513C22×C4C24×C1711yescharacteristic
514C22×C4C24×C1713yes—
515C22×C4C24×C1711yescharacteristic
516C22×C4C24×C1713yes—
517C4⋊C4—26no—
518C4⋊C4—26no—
519C4⋊C4—22no—
520C4⋊C4—26no—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—43no—
524C4⋊C4C22×C4×C1714yes—
525C4⋊C4C22×C4×C17112yes—
526C4⋊C4C2×D4×C17112yes—
527C22⋊C4—26no—
528C22⋊C4—212no—
529C22⋊C4—26no—
530C22⋊C4—26no—
531C22⋊C4—43no—
532C22⋊C4—46no—
533C22⋊C4—43no—
534C22⋊C4—43no—
535C22⋊C4—46no—
536C22⋊C4C22×C4×C17112yes—
537C22⋊C4C22×C4×C17112yes—
538C42—22no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—26no—
543C42—46no—
544C42C22×C4×C17112yes—
545C42C2×D4×C17112yes—
546C23—23no—
547C23—23no—
548C23—23no—
549C23—23no—
550C23—23no—
551C23—23no—
552C23—23no—
553C23—23no—
554C23—23no—
555C23—23no—
556C23—23no—
557C23—23no—
558C23C23×C4×C1716yes—
559C23C23×C4×C1716yes—
560C23C25×C1711yescharacteristic
561Q8C4×D4×C17116yescomplemented
562D4—224no—
563D4—224no—
564D4—412no—
565D4—424no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—23no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—23no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—21no—
583C2×C4—23no—
584C2×C4—23no—
585C2×C4—21no—
586C2×C4—23no—
587C2×C4—23no—
588C2×C4—23no—
589C2×C4—21no—
590C2×C4—23no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—23no—
594C2×C4—23no—
595C2×C4—23no—
596C2×C4—21no—
597C2×C4—412no—
598C2×C4—412no—
599C2×C4—812no—
600C2×C4C23×C4×C1712yes—
601C2×C4C23×C4×C1716yes—
602C2×C4C23×C4×C1712yes—
603C2×C4C23×C4×C1712yes—
604C2×C4C23×C4×C1716yes—
605C2×C4C22×D4×C1712yes—
606C2×C4C22×D4×C1716yes—
607C2×C4C22×D4×C1716yes—
608C2×C4C2×#41×C1716yes—
609C2×C4C17×H(5,𝔽2)12yes—
610C22—26no—
611C22—26no—
612C22—26no—
613C22—26no—
614C22—26no—
615C22—26no—
616C22—43no—
617C22—43no—
618C22—43no—
619C22—43no—
620C22—43no—
621C22—43no—
622C22—43no—
623C22—43no—
624C22C24×C4×C1711yescharacteristic
625C22C23×D4×C1711yescharacteristic
626C22C22×#41×C1711yescharacteristic
627C22C2×C17×H(5,𝔽2)11yescharacteristic
628C22C17×#58511yescharacteristic
629C22C17×#58511yescharacteristic
630C22C17×#58511yescharacteristic
631C4—22no—
632C4—22no—
633C4—26no—
634C4—22no—
635C4—22no—
636C4—22no—
637C4—26no—
638C4—43no—
639C4—41no—
640C4—43no—
641C4—43no—
642C4—41no—
643C4C2×C4×D4×C17112yes—
644C2—46no—
645C2—46no—
646C2C22×C4×D4×C1711yescharacteristic
647C2C17×#342811yescharacteristic
648C2C4×C17×H(5,𝔽2)11yescharacteristic
649C2C17×#348711yescharacteristic
650C2C17×#348811yescharacteristic
651C2C17×#351711yescharacteristic
652C2C17×#352411yescharacteristic
subgroupG/H
center, socleC23×C17C25
commutatorC22C24×C4×C17
Frattini, cosocleC23C25×C17
prime radicalC2×C17×#550C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#520C2semidirect
3. C2×C4×#41×C17C2semidirect
4. C17×#2366C2semidirect
5. C17×#2363C2semidirect
6. C17×#2361C2semidirect
7. C17×#2352C2semidirect
8. C17×#2351C2semidirect
9. C17×#2341C2semidirect
10. C17×#2341C2semidirect
11. C17×#2328C2semidirect
12. C17×#2324C2semidirect
13. C4×C17×#121C2semidirect
14. C17×#2290C2semidirect
15. C17×#2276C2semidirect
18. C17×#550C4semidirect
73. C2×#41×C17C2×C4semidirect
74. C2×#41×C17C2×C4semidirect
85. C17×#127C2×C4semidirect
86. C17×#121C2×C4semidirect
87. C17×#121C2×C4semidirect
91. C4×Q8×C17C2×C4semidirect
92. C4×Q8×C17D4semidirect
98. C4×D4×C17C2×C4semidirect
219. #34295C17direct (N × H)
235. Q8×C17C4×D4semidirect
285. C2×#520C2×C17semidirect
286. C2×C4×#41C2×C17semidirect
287. #2366C2×C17semidirect
288. #2363C2×C17semidirect
289. #2361C2×C17semidirect
290. #2352C2×C17semidirect
291. #2351C2×C17semidirect
292. #2341C2×C17semidirect
293. #2341C2×C17semidirect
294. #2328C2×C17semidirect
295. #2324C2×C17semidirect
296. C4×#121C2×C17semidirect
297. #2290C2×C17semidirect
298. #2276C2×C17semidirect
335. #550C4×C17semidirect
399. C2×#41C2×C4×C17semidirect
400. C2×#41C2×C4×C17semidirect
411. #127C2×C4×C17semidirect
412. #121C2×C4×C17semidirect
413. #121C2×C4×C17semidirect
417. C4×Q8C2×C4×C17semidirect
418. C4×Q8D4×C17semidirect
424. C4×D4C2×C4×C17semidirect
469. C17#34295direct (N × H)
561. Q8C4×D4×C17semidirect

Maximal subgroups

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

subgroupindex
C2×C17×#5502
C2×C17×#5202
C2×C4×#41×C172
C17×#23662
C17×#23632
C17×#23612
C17×#23522
C17×#23512
C17×#23412
C17×#23282
C17×#23242
C4×C17×#1212
C17×#22902
C17×#22762
#3429517