Finite Group Databasebeta

← C17×#34291 #16892035

Subgroups — C17×#34291 #16892035

Order 4352.

2912 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C17C211yesmaximal, characteristic
2C2×C17×#519C211yesmaximal, characteristic, complemented
3C22×C4×Q8×C17C211yesmaximal, characteristic, complemented
4C17×#2365C213yesmaximal, complemented
5C17×#2362C213yesmaximal, complemented
6C17×#2360C213yesmaximal, complemented
7C17×#2352C213yesmaximal
8C17×#2351C211yesmaximal, characteristic, complemented
9Q8×C22⋊C4×C17C211yesmaximal, characteristic, complemented
10Q8×C22⋊C4×C17C211yesmaximal, characteristic, complemented
11C17×#2327C213yesmaximal, complemented
12C17×#2323C213yesmaximal, complemented
13C4×C17×C22⋊Q8C213yesmaximal, complemented
14C17×#2290C213yesmaximal
15C17×#2276C211yesmaximal, characteristic, complemented
16C23×Q8×C17C2211yescharacteristic
17C23×Q8×C17C2211yescharacteristic
18D4×Q8×C17C4116yescomplemented
19C2×C17×C4⋊Q8C2213yes—
20C2×C17×C22⋊Q8C2213yes—
21C2×C17×C22⋊Q8C2213yes—
22C17×#519—28no—
23C2×C4×Q8×C17—28no—
24C2×C4×Q8×C17C2211yescharacteristic
25C2×C4×Q8×C17C2213yes—
26C2×C4×Q8×C17C2213yes—
27C2×C4×Q8×C17C2211yescharacteristic
28C2×C4×Q8×C17C2211yescharacteristic
29C2×C4×Q8×C17C2213yes—
30C2×C4×Q8×C17C2213yes—
31C2×C4×Q8×C17C2211yescharacteristic
32C2×C4×Q8×C17C2211yescharacteristic
33C2×C4×D4×C17C2213yes—
34C2×C17×#117C2213yes—
35C2×C17×#117C2213yes—
36C22×C4⋊C4×C17C2213yes—
37C22×C42×C17C2213yes—
38C17×#391C2213yes—
39C17×#391C2213yes—
40C17×#391C2213yes—
41C17×#391C2213yes—
42C17×#389C2213yes—
43C17×#389C2213yes—
44C17×#389C2216yes—
45C17×#388C2213yes—
46C17×#388C2213yes—
47C17×#388C2216yes—
48C17×#387C2213yes—
49C17×#387C2213yes—
50C17×#387C2216yes—
51C17×#387C2216yes—
52C17×#387C2216yes—
53C17×#386C2211yescharacteristic
54C17×#386C2213yes—
55C17×#385C2213yes—
56C17×#385C2213yes—
57C17×#382C2213yes—
58C17×#380C2213yes—
59C17×#380C2213yes—
60C4×C4⋊C4×C17C2213yes—
61C4×C4⋊C4×C17C2213yes—
62C4×C4⋊C4×C17C2213yes—
63C4×C4⋊C4×C17C2213yes—
64C4×C4⋊C4×C17C2216yes—
65C4×C22⋊C4×C17C2213yes—
66C4×C22⋊C4×C17C2213yes—
67C4×C22⋊C4×C17C2216yes—
68C17×#376C2213yes—
69C22×Q8×C17—24no—
70C22×Q8×C17—24no—
71C22×Q8×C17—24no—
72C22×Q8×C17—24no—
73C22×Q8×C17C2×C418yes—
74C22×Q8×C17C2×C418yescomplemented
75C22×Q8×C17C2313yes—
76C22×Q8×C17C2313yes—
77C22×Q8×C17C2311yescharacteristic
78C22×D4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2313yes—
81C23×C4×C17C2313yes—
82C23×C4×C17C2313yes—
83C17×C4⋊Q8C2×C4124yescomplemented
84C17×C22⋊Q8C2×C4124yes—
85C17×C22⋊Q8C2×C4124yescomplemented
86C4×Q8×C17—24no—
87C4×Q8×C17—24no—
88C4×Q8×C17—24no—
89C4×Q8×C17—212no—
90C4×Q8×C17—212no—
91C4×Q8×C17—212no—
92C4×Q8×C17—212no—
93C4×Q8×C17C2×C418yescomplemented
94C4×Q8×C17D418yescomplemented
95C4×D4×C17C2×C4124yes—
96C17×#117—212no—
97C17×#117—212no—
98C2×C4⋊C4×C17—212no—
99C2×C4⋊C4×C17C2313yes—
100C2×C4⋊C4×C17C2316yes—
101C2×C4⋊C4×C17C2313yes—
102C2×C4⋊C4×C17C2313yes—
103C2×C4⋊C4×C17C2313yes—
104C2×C4⋊C4×C17C2313yes—
105C2×C4⋊C4×C17C2313yes—
106C2×C4⋊C4×C17C2313yes—
107C2×C4⋊C4×C17C2313yes—
108C2×C4⋊C4×C17C2313yes—
109C2×C4⋊C4×C17C2316yes—
110C2×C4⋊C4×C17C2313yes—
111C2×C22⋊C4×C17C2313yes—
112C2×C22⋊C4×C17C2311yescharacteristic
113C2×C22⋊C4×C17C2313yes—
114C2×C22⋊C4×C17C2311yescharacteristic
115C2×C22⋊C4×C17C2311yescharacteristic
116C2×C22⋊C4×C17C2313yes—
117C2×C22⋊C4×C17C2313yes—
118C2×C22⋊C4×C17C2313yes—
119C2×C42×C17—212no—
120C2×C42×C17C2313yes—
121C2×C42×C17C2313yes—
122C2×C42×C17C2313yes—
123C2×C42×C17C2316yes—
124C2×C42×C17C2313yes—
125C2×C42×C17C2313yes—
126C2×C42×C17C2316yes—
127C2×C42×C17C2313yes—
128C2×C42×C17C2313yes—
129C17×#95C2311yescharacteristic
130C17×#95C2313yes—
131C17×#95C2313yes—
132C17×#95C2313yes—
133C17×#95C2313yes—
134C17×#95C2316yes—
135C17×#95C2316yes—
136C17×#95C2313yes—
137C17×#95C2313yes—
138C17×#95C2313yes—
139C17×#95C2311yescharacteristic
140C17×#95C2316yes—
141C17×#95C2313yes—
142C24×C17C2411yescharacteristic
143C24×C17C2411yescharacteristic
144C2×Q8×C17—232no—
145C2×Q8×C17—232no—
146C2×Q8×C17—26no—
147C2×Q8×C17—26no—
148C2×Q8×C17—26no—
149C2×Q8×C17—26no—
150C2×Q8×C17C22×C4112yes—
151C2×Q8×C17C22×C4112yes—
152C2×Q8×C17C22×C414yes—
153C2×Q8×C17C2×D414yes—
154C2×Q8×C17#4114yes—
155C2×D4×C17—22no—
156C2×D4×C17—22no—
157C2×D4×C17C22×C414yes—
158C22×C4×C17—22no—
159C22×C4×C17—26no—
160C22×C4×C17—26no—
161C22×C4×C17—22no—
162C22×C4×C17—26no—
163C22×C4×C17—26no—
164C22×C4×C17—22no—
165C22×C4×C17—26no—
166C22×C4×C17—26no—
167C22×C4×C17—43no—
168C22×C4×C17C22×C4112yes—
169C22×C4×C17C22×C4112yes—
170C22×C4×C17C2413yes—
171C22×C4×C17C2411yescharacteristic
172C22×C4×C17C2413yes—
173C22×C4×C17C2413yes—
174C22×C4×C17C2411yescharacteristic
175C22×C4×C17C2413yes—
176C22×C4×C17C2413yes—
177C22×C4×C17C2411yescharacteristic
178C22×C4×C17C2413yes—
179C22×C4×C17C2411yescharacteristic
180C22×C4×C17C2413yes—
181C22×C4×C17C2411yescharacteristic
182C22×C4×C17C2413yes—
183C4⋊C4×C17—212no—
184C4⋊C4×C17—26no—
185C4⋊C4×C17—26no—
186C4⋊C4×C17—26no—
187C4⋊C4×C17—26no—
188C4⋊C4×C17—26no—
189C4⋊C4×C17—26no—
190C4⋊C4×C17—43no—
191C4⋊C4×C17C22×C4124yes—
192C4⋊C4×C17C22×C4112yes—
193C4⋊C4×C17C22×C4112yes—
194C4⋊C4×C17C2×D4112yes—
195C22⋊C4×C17—26no—
196C22⋊C4×C17—22no—
197C22⋊C4×C17—22no—
198C22⋊C4×C17—26no—
199C22⋊C4×C17—22no—
200C22⋊C4×C17—43no—
201C22⋊C4×C17C22×C4112yes—
202C22⋊C4×C17C22×C4112yes—
203C42×C17—26no—
204C42×C17—26no—
205C42×C17—26no—
206C42×C17—212no—
207C42×C17—26no—
208C42×C17—26no—
209C42×C17—46no—
210C42×C17C22×C4112yes—
211C42×C17C2×D4112yes—
212#34291C1711yesmaximal, characteristic, direct product factor, Sylow
213C23×C17—21no—
214C23×C17—21no—
215C23×C17—21no—
216C23×C17—21no—
217C23×C17—21no—
218C23×C17—21no—
219C23×C17—21no—
220C23×C17—21no—
221C23×C17—21no—
222C23×C17—21no—
223C23×C17C23×C412yes—
224C23×C17C23×C412yes—
225C23×C172−1+412yes—
226C23×C172−1+412yes—
227C23×C17C2511yescharacteristic
228Q8×C17—224no—
229Q8×C17—224no—
230Q8×C17C4×D4116yes—
231D4×C17—28no—
232C2×C4×C17—28no—
233C2×C4×C17—21no—
234C2×C4×C17—23no—
235C2×C4×C17—23no—
236C2×C4×C17—23no—
237C2×C4×C17—23no—
238C2×C4×C17—23no—
239C2×C4×C17—21no—
240C2×C4×C17—21no—
241C2×C4×C17—21no—
242C2×C4×C17—23no—
243C2×C4×C17—21no—
244C2×C4×C17—21no—
245C2×C4×C17—23no—
246C2×C4×C17—23no—
247C2×C4×C17—224no—
248C2×C4×C17—224no—
249C2×C4×C17—23no—
250C2×C4×C17—21no—
251C2×C4×C17—23no—
252C2×C4×C17—21no—
253C2×C4×C17—23no—
254C2×C4×C17—23no—
255C2×C4×C17—21no—
256C2×C4×C17—23no—
257C2×C4×C17—21no—
258C2×C4×C17—21no—
259C2×C4×C17—23no—
260C2×C4×C17—23no—
261C2×C4×C17—23no—
262C2×C4×C17—23no—
263C2×C4×C17—21no—
264C2×C4×C17—412no—
265C2×C4×C17C23×C412yes—
266C2×C4×C17C23×C416yes—
267C2×C4×C17C23×C416yes—
268C2×C4×C17C23×C416yes—
269C2×C4×C17C23×C416yes—
270C2×C4×C17C22×D412yes—
271C2×C4×C17C22×D416yes—
272C2×C4×C17C22×D416yes—
273C2×C4×C17C2×#4116yes—
274C2×C4×C172−1+412yes—
275C2×D4×Q8C2×C1711yescharacteristic
276C2×#519C2×C1711yescharacteristic, complemented
277C22×C4×Q8C2×C1711yescharacteristic, complemented
278#2365C2×C1713yescomplemented
279#2362C2×C1713yescomplemented
280#2360C2×C1713yescomplemented
281#2352C2×C1713yes—
282#2351C2×C1711yescharacteristic, complemented
283Q8×C22⋊C4C2×C1711yescharacteristic, complemented
284Q8×C22⋊C4C2×C1711yescharacteristic, complemented
285#2327C2×C1713yescomplemented
286#2323C2×C1713yescomplemented
287C4×C22⋊Q8C2×C1713yescomplemented
288#2290C2×C1713yes—
289#2276C2×C1711yescharacteristic, complemented
290C22×C17—22no—
291C22×C17—22no—
292C22×C17—22no—
293C22×C17—22no—
294C22×C17—22no—
295C22×C17—22no—
296C22×C17—22no—
297C22×C17—22no—
298C22×C17—22no—
299C22×C17—41no—
300C22×C17—41no—
301C22×C17—41no—
302C22×C17—41no—
303C22×C17#51914yescomplemented
304C22×C17C24×C411yescharacteristic
305C22×C17C23×D411yescharacteristic
306C22×C17C22×#4111yescharacteristic
307C22×C17C2×2−1+411yescharacteristic
308C22×C17C2×2−1+411yescharacteristic
309C22×C17C2×2−1+411yescharacteristic
310C22×C17#58511yescharacteristic
311C4×C17—26no—
312C4×C17—26no—
313C4×C17—22no—
314C4×C17—26no—
315C4×C17—22no—
316C4×C17—22no—
317C4×C17—26no—
318C4×C17—43no—
319C4×C17—41no—
320C4×C17—43no—
321C4×C17—43no—
322C4×C17—41no—
323C4×C17C2×C4×D4112yes—
324C23×Q8C22×C1711yescharacteristic
325C23×Q8C22×C1711yescharacteristic
326D4×Q8C4×C17116yescomplemented
327C2×C4⋊Q8C22×C1713yes—
328C2×C22⋊Q8C22×C1713yes—
329C2×C22⋊Q8C22×C1713yes—
330#519—28no—
331C2×C4×Q8—28no—
332C2×C4×Q8C22×C1713yes—
333C2×C4×Q8C22×C1713yes—
334C2×C4×Q8C22×C1711yescharacteristic
335C2×C4×Q8C22×C1711yescharacteristic
336C2×C4×Q8C22×C1711yescharacteristic
337C2×C4×Q8C22×C1713yes—
338C2×C4×Q8C22×C1713yes—
339C2×C4×Q8C22×C1711yescharacteristic
340C2×C4×Q8C22×C1711yescharacteristic
341C2×C4×D4C22×C1713yes—
342C2×#117C22×C1713yes—
343C2×#117C22×C1713yes—
344C22×C4⋊C4C22×C1713yes—
345C22×C42C22×C1713yes—
346#391C22×C1713yes—
347#391C22×C1713yes—
348#391C22×C1713yes—
349#391C22×C1713yes—
350#389C22×C1713yes—
351#389C22×C1716yes—
352#389C22×C1713yes—
353#388C22×C1713yes—
354#388C22×C1716yes—
355#388C22×C1713yes—
356#387C22×C1716yes—
357#387C22×C1713yes—
358#387C22×C1716yes—
359#387C22×C1716yes—
360#387C22×C1713yes—
361#386C22×C1713yes—
362#386C22×C1711yescharacteristic
363#385C22×C1713yes—
364#385C22×C1713yes—
365#382C22×C1713yes—
366#380C22×C1713yes—
367#380C22×C1713yes—
368C4×C4⋊C4C22×C1713yes—
369C4×C4⋊C4C22×C1713yes—
370C4×C4⋊C4C22×C1713yes—
371C4×C4⋊C4C22×C1713yes—
372C4×C4⋊C4C22×C1716yes—
373C4×C22⋊C4C22×C1713yes—
374C4×C22⋊C4C22×C1713yes—
375C4×C22⋊C4C22×C1716yes—
376#376C22×C1713yes—
377C2×C17—24no—
378C2×C17—42no—
379C2×C17C22×C4×D411yescharacteristic
380C2×C17C2×#51911yescharacteristic
381C2×C17C4×2−1+411yescharacteristic
382C2×C17#348611yescharacteristic
383C2×C17#348911yescharacteristic
384C2×C17#351611yescharacteristic
385C2×C17#352311yescharacteristic
386C22×Q8—24no—
387C22×Q8—24no—
388C22×Q8—24no—
389C22×Q8—24no—
390C22×Q8C2×C4×C1718yes—
391C22×Q8C2×C4×C1718yescomplemented
392C22×Q8C23×C1713yes—
393C22×Q8C23×C1713yes—
394C22×Q8C23×C1711yescharacteristic
395C22×D4C23×C1711yescharacteristic
396C23×C4C23×C1711yescharacteristic
397C23×C4C23×C1713yes—
398C23×C4C23×C1713yes—
399C23×C4C23×C1713yes—
400C4⋊Q8C2×C4×C17124yescomplemented
401C22⋊Q8C2×C4×C17124yes—
402C22⋊Q8C2×C4×C17124yescomplemented
403C4×Q8—24no—
404C4×Q8—24no—
405C4×Q8—24no—
406C4×Q8—212no—
407C4×Q8—212no—
408C4×Q8—212no—
409C4×Q8—212no—
410C4×Q8C2×C4×C1718yescomplemented
411C4×Q8D4×C1718yescomplemented
412C4×D4C2×C4×C17124yes—
413#117—212no—
414#117—212no—
415C2×C4⋊C4—212no—
416C2×C4⋊C4C23×C1713yes—
417C2×C4⋊C4C23×C1716yes—
418C2×C4⋊C4C23×C1713yes—
419C2×C4⋊C4C23×C1713yes—
420C2×C4⋊C4C23×C1713yes—
421C2×C4⋊C4C23×C1713yes—
422C2×C4⋊C4C23×C1713yes—
423C2×C4⋊C4C23×C1713yes—
424C2×C4⋊C4C23×C1713yes—
425C2×C4⋊C4C23×C1713yes—
426C2×C4⋊C4C23×C1716yes—
427C2×C4⋊C4C23×C1713yes—
428C2×C22⋊C4C23×C1713yes—
429C2×C22⋊C4C23×C1711yescharacteristic
430C2×C22⋊C4C23×C1713yes—
431C2×C22⋊C4C23×C1711yescharacteristic
432C2×C22⋊C4C23×C1711yescharacteristic
433C2×C22⋊C4C23×C1713yes—
434C2×C22⋊C4C23×C1713yes—
435C2×C22⋊C4C23×C1713yes—
436C2×C42—212no—
437C2×C42C23×C1716yes—
438C2×C42C23×C1713yes—
439C2×C42C23×C1713yes—
440C2×C42C23×C1713yes—
441C2×C42C23×C1713yes—
442C2×C42C23×C1713yes—
443C2×C42C23×C1716yes—
444C2×C42C23×C1713yes—
445C2×C42C23×C1713yes—
446#95C23×C1711yescharacteristic
447#95C23×C1713yes—
448#95C23×C1713yes—
449#95C23×C1713yes—
450#95C23×C1713yes—
451#95C23×C1716yes—
452#95C23×C1716yes—
453#95C23×C1713yes—
454#95C23×C1713yes—
455#95C23×C1713yes—
456#95C23×C1711yescharacteristic
457#95C23×C1716yes—
458#95C23×C1713yes—
459C17#3429111yescharacteristic, direct product factor, Sylow
460C24C24×C1711yescharacteristic
461C24C24×C1711yescharacteristic
462C2×Q8—232no—
463C2×Q8—232no—
464C2×Q8—26no—
465C2×Q8—26no—
466C2×Q8—26no—
467C2×Q8—26no—
468C2×Q8C22×C4×C17112yes—
469C2×Q8C22×C4×C17112yes—
470C2×Q8C22×C4×C1714yes—
471C2×Q8C2×D4×C1714yes—
472C2×Q8#41×C1714yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4C22×C4×C1714yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—26no—
479C22×C4—26no—
480C22×C4—26no—
481C22×C4—26no—
482C22×C4—22no—
483C22×C4—26no—
484C22×C4—26no—
485C22×C4—43no—
486C22×C4C22×C4×C17112yes—
487C22×C4C22×C4×C17112yes—
488C22×C4C24×C1711yescharacteristic
489C22×C4C24×C1713yes—
490C22×C4C24×C1713yes—
491C22×C4C24×C1713yes—
492C22×C4C24×C1711yescharacteristic
493C22×C4C24×C1711yescharacteristic
494C22×C4C24×C1713yes—
495C22×C4C24×C1713yes—
496C22×C4C24×C1713yes—
497C22×C4C24×C1711yescharacteristic
498C22×C4C24×C1713yes—
499C22×C4C24×C1711yescharacteristic
500C22×C4C24×C1713yes—
501C4⋊C4—212no—
502C4⋊C4—26no—
503C4⋊C4—26no—
504C4⋊C4—26no—
505C4⋊C4—26no—
506C4⋊C4—26no—
507C4⋊C4—26no—
508C4⋊C4—43no—
509C4⋊C4C22×C4×C17112yes—
510C4⋊C4C22×C4×C17112yes—
511C4⋊C4C22×C4×C17124yes—
512C4⋊C4C2×D4×C17112yes—
513C22⋊C4—26no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—26no—
517C22⋊C4—22no—
518C22⋊C4—43no—
519C22⋊C4C22×C4×C17112yes—
520C22⋊C4C22×C4×C17112yes—
521C42—26no—
522C42—26no—
523C42—26no—
524C42—212no—
525C42—26no—
526C42—26no—
527C42—46no—
528C42C22×C4×C17112yes—
529C42C2×D4×C17112yes—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23C23×C4×C1712yes—
541C23C23×C4×C1712yes—
542C23C17×2−1+412yes—
543C23C17×2−1+412yes—
544C23C25×C1711yescharacteristic
545Q8—224no—
546Q8—224no—
547Q8C4×D4×C17116yes—
548D4—28no—
549C2×C4—28no—
550C2×C4—21no—
551C2×C4—23no—
552C2×C4—23no—
553C2×C4—23no—
554C2×C4—23no—
555C2×C4—23no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—23no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—23no—
563C2×C4—23no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—23no—
567C2×C4—21no—
568C2×C4—23no—
569C2×C4—21no—
570C2×C4—23no—
571C2×C4—23no—
572C2×C4—21no—
573C2×C4—23no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—23no—
577C2×C4—23no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—21no—
581C2×C4—412no—
582C2×C4C23×C4×C1712yes—
583C2×C4C23×C4×C1716yes—
584C2×C4C23×C4×C1716yes—
585C2×C4C23×C4×C1716yes—
586C2×C4C23×C4×C1716yes—
587C2×C4C22×D4×C1712yes—
588C2×C4C22×D4×C1716yes—
589C2×C4C22×D4×C1716yes—
590C2×C4C2×#41×C1716yes—
591C2×C4C17×2−1+412yes—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22C17×#51914yescomplemented
606C22C24×C4×C1711yescharacteristic
607C22C23×D4×C1711yescharacteristic
608C22C22×#41×C1711yescharacteristic
609C22C2×C17×2−1+411yescharacteristic
610C22C2×C17×2−1+411yescharacteristic
611C22C2×C17×2−1+411yescharacteristic
612C22C17×#58511yescharacteristic
613C4—22no—
614C4—22no—
615C4—26no—
616C4—26no—
617C4—26no—
618C4—22no—
619C4—26no—
620C4—43no—
621C4—43no—
622C4—41no—
623C4—43no—
624C4—41no—
625C4C2×C4×D4×C17112yes—
626C2—24no—
627C2—42no—
628C2C22×C4×D4×C1711yescharacteristic
629C2C2×C17×#51911yescharacteristic
630C2C4×C17×2−1+411yescharacteristic
631C2C17×#348611yescharacteristic
632C2C17×#348911yescharacteristic
633C2C17×#351611yescharacteristic
634C2C17×#352311yescharacteristic
subgroupG/H
center, socleC23×C17C25
commutatorC22C24×C4×C17
Frattini, cosocleC23C25×C17
prime radicalC22×D4×C17C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#519C2semidirect
3. C22×C4×Q8×C17C2semidirect
4. C17×#2365C2semidirect
5. C17×#2362C2semidirect
6. C17×#2360C2semidirect
8. C17×#2351C2semidirect
9. Q8×C22⋊C4×C17C2semidirect
10. Q8×C22⋊C4×C17C2semidirect
11. C17×#2327C2semidirect
12. C17×#2323C2semidirect
13. C4×C17×C22⋊Q8C2semidirect
15. C17×#2276C2semidirect
18. D4×Q8×C17C4semidirect
74. C22×Q8×C17C2×C4semidirect
83. C17×C4⋊Q8C2×C4semidirect
85. C17×C22⋊Q8C2×C4semidirect
93. C4×Q8×C17C2×C4semidirect
94. C4×Q8×C17D4semidirect
212. #34291C17direct (N × H)
276. C2×#519C2×C17semidirect
277. C22×C4×Q8C2×C17semidirect
278. #2365C2×C17semidirect
279. #2362C2×C17semidirect
280. #2360C2×C17semidirect
282. #2351C2×C17semidirect
283. Q8×C22⋊C4C2×C17semidirect
284. Q8×C22⋊C4C2×C17semidirect
285. #2327C2×C17semidirect
286. #2323C2×C17semidirect
287. C4×C22⋊Q8C2×C17semidirect
289. #2276C2×C17semidirect
303. C22×C17#519semidirect
326. D4×Q8C4×C17semidirect
391. C22×Q8C2×C4×C17semidirect
400. C4⋊Q8C2×C4×C17semidirect
402. C22⋊Q8C2×C4×C17semidirect
410. C4×Q8C2×C4×C17semidirect
411. C4×Q8D4×C17semidirect
459. C17#34291direct (N × H)
605. C22C17×#519semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C172
C2×C17×#5192
C22×C4×Q8×C172
C17×#23652
C17×#23622
C17×#23602
C17×#23522
C17×#23512
Q8×C22⋊C4×C172
C17×#23272
C17×#23232
C4×C17×C22⋊Q82
C17×#22902
C17×#22762
#3429117