Finite Group Databasebeta

← C17×#22588 #16880332

Subgroups — C17×#22588 #16880332

Order 4352.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×#2924C211yesmaximal, characteristic, complemented
2C17×#2896C211yesmaximal, characteristic
3C17×#2880C211yesmaximal, characteristic
4C17×#1938C211yesmaximal, characteristic, complemented
5C17×#1937C211yesmaximal, characteristic, complemented
6C17×#1929C211yesmaximal, characteristic, complemented
7C17×#1929C211yesmaximal, characteristic, complemented
8C17×#1866C211yesmaximal, characteristic, complemented
9C17×#1866C211yesmaximal, characteristic, complemented
10C17×#1826C211yesmaximal, characteristic, complemented
11C17×#1811C211yesmaximal, characteristic, complemented
12C17×#1789C211yesmaximal, characteristic
13C17×#1765C211yesmaximal, characteristic, complemented
14C17×#1764C211yesmaximal, characteristic, complemented
15C17×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C17C2211yescharacteristic
17C2×C17×#131C2211yescharacteristic
18C2×C17×#131C2211yescharacteristic
19C22×M16×C17C2211yescharacteristic
20C2×C17×#117C2211yescharacteristic
21C17×#433—21no—
22C17×#433—21no—
23C17×#432—21no—
24C17×#431—21no—
25C2×C17×#108C2211yescharacteristic, complemented
26C2×C17×#108C2211yescharacteristic, complemented
27C17×#424C2211yescharacteristic, complemented
28C17×#424C2211yescharacteristic, complemented
29C2×C17×#104C2211yescharacteristic
30C2×C17×#104C2211yescharacteristic
31C2×C17×#104C2211yescharacteristic
32C2×C17×#104C2211yescharacteristic
33C17×#419C411yescharacteristic, complemented
34C17×#419C411yescharacteristic, complemented
35C17×#418C411yescharacteristic, complemented
36C17×#418C411yescharacteristic, complemented
37C17×#417C411yescharacteristic, complemented
38C17×#417C411yescharacteristic, complemented
39C17×#417C411yescharacteristic, complemented
40C17×#417C411yescharacteristic, complemented
41C17×#416C2211yescharacteristic
42C17×#416C2211yescharacteristic
43C17×#416C2211yescharacteristic
44C17×#416C2211yescharacteristic
45C17×#408—21no—
46C17×#408—21no—
47C17×#408C2211yescharacteristic
48C17×#408C2211yescharacteristic
49C17×#407—21no—
50C17×#407C2211yescharacteristic
51C17×#407C2211yescharacteristic
52C2×C17×C22⋊C8—21no—
53C2×C17×C22⋊C8C2211yescharacteristic
54C17×#405C2211yescharacteristic, complemented
55C17×#405C2211yescharacteristic, complemented
56C2×C17×#97C2211yescharacteristic, complemented
57C2×C4×C8×C17C2211yescharacteristic, complemented
58C4×C22⋊C4×C17C2211yescharacteristic
59C17×#341C2211yescharacteristic, complemented
60C17×#341C2211yescharacteristic, complemented
61C17×#339C2211yescharacteristic, complemented
62C17×#339C2211yescharacteristic, complemented
63C17×#339C2211yescharacteristic, complemented
64C17×#339C2211yescharacteristic, complemented
65C17×#336C2211yescharacteristic, complemented
66C17×#336C2211yescharacteristic, complemented
67C2×#41×C17—21no—
68C2×#41×C17—21no—
69C2×#41×C17—22no—
70C2×#41×C17—22no—
71C2×#41×C17—41no—
72C2×#41×C17—41no—
73C2×#41×C17C2×C411yescharacteristic
74C2×#41×C17C2×C411yescharacteristic
75C2×#41×C17C2311yescharacteristic
76C2×#41×C17C2311yescharacteristic
77C22×Q8×C17C2×C411yescharacteristic
78C22×D4×C17—21no—
79C22×D4×C17C2×C411yescharacteristic
80C23×C4×C17—21no—
81C23×C4×C17C2311yescharacteristic
82C17×#131—22no—
83C17×#131—22no—
84C17×#131—41no—
85C17×#131—41no—
86C2×M16×C17—21no—
87C2×M16×C17—21no—
88C2×M16×C17—41no—
89C2×M16×C17—41no—
90C2×M16×C17C2×C411yescharacteristic
91C2×M16×C17C2×C411yescharacteristic
92C2×M16×C17C2×C411yescharacteristic
93C2×M16×C17C2×C411yescharacteristic
94C2×M16×C17C2311yescharacteristic
95C2×M16×C17C2311yescharacteristic
96C2×M16×C17C2311yescharacteristic
97C2×M16×C17C2311yescharacteristic
98C22×C8×C17—21no—
99C22×C8×C17—21no—
100C22×C8×C17C2311yescharacteristic
101C22×C8×C17C2311yescharacteristic
102C22×C8×C17C2311yescharacteristic
103C22×C8×C17C2311yescharacteristic
104C17×#117—21no—
105C17×#117—21no—
106C17×#117C2×C411yescharacteristic
107C17×#117C2×C411yescharacteristic
108C17×#117C2311yescharacteristic
109C17×#117C2311yescharacteristic
110C2×C4⋊C4×C17C2×C411yescharacteristic
111C2×C4⋊C4×C17C2×C411yescharacteristic
112C2×C22⋊C4×C17—21no—
113C2×C22⋊C4×C17—21no—
114C2×C42×C17—21no—
115C2×C42×C17C2311yescharacteristic
116C2×C42×C17C2311yescharacteristic
117C17×#108—41no—
118C17×#108—41no—
119C17×C4⋊C8—21no—
120C17×C4⋊C8—21no—
121C17×C4⋊C8—21no—
122C17×C4⋊C8—21no—
123C17×#104—22no—
124C17×#104—22no—
125C17×#104—41no—
126C17×#104—41no—
127C17×#103C2×C411yescharacteristic
128C17×#103C2×C411yescharacteristic
129C17×#103C2×C411yescharacteristic
130C17×#103C2×C411yescharacteristic
131C17×#103C2×C411yescharacteristic
132C17×#103C2×C411yescharacteristic
133C17×#103C2×C411yescharacteristic
134C17×#103C2×C411yescharacteristic
135C17×#102C2×C411yescharacteristic
136C17×#102C2×C411yescharacteristic
137C17×#102C2×C411yescharacteristic
138C17×#102C2×C411yescharacteristic
139C17×#102C2×C411yescharacteristic
140C17×#102C2×C411yescharacteristic
141C17×#102C2×C411yescharacteristic
142C17×#102C2×C411yescharacteristic
143C17×C22⋊C8—21no—
144C17×C22⋊C8—21no—
145C17×C22⋊C8—21no—
146C17×C22⋊C8—21no—
147C17×C22⋊C8—21no—
148C17×C22⋊C8—21no—
149C17×C22⋊C8—21no—
150C17×C22⋊C8—21no—
151C17×C22⋊C8D411yescharacteristic
152C17×C22⋊C8D411yescharacteristic
153C17×C22⋊C8D411yescharacteristic
154C17×C22⋊C8D411yescharacteristic
155C17×#97—21no—
156C17×#97—21no—
157C17×#97—41no—
158C4×C8×C17—21no—
159C4×C8×C17—21no—
160C4×C8×C17—41no—
161C17×#95—21no—
162C24×C17—21no—
163C24×C17#4111yescharacteristic
164#41×C17—21no—
165#41×C17—21no—
166#41×C17—22no—
167#41×C17—22no—
168#41×C17—21no—
169#41×C17—21no—
170#41×C17—21no—
171#41×C17—21no—
172#41×C17—42no—
173#41×C17—42no—
174#41×C17—41no—
175#41×C17—41no—
176#41×C17—42no—
177#41×C17—42no—
178#41×C17#4112yes—
179#41×C17#4112yes—
180C2×Q8×C17—21no—
181C2×Q8×C17—22no—
182C2×Q8×C17—41no—
183C2×Q8×C17C22×C411yescharacteristic
184C2×Q8×C17C22×C411yescharacteristic
185C2×D4×C17—21no—
186C2×D4×C17—22no—
187C2×D4×C17—21no—
188C2×D4×C17—21no—
189C2×D4×C17—21no—
190C2×D4×C17—21no—
191C2×D4×C17—41no—
192C2×D4×C17—42no—
193C2×D4×C17—42no—
194C2×D4×C17C22×C411yescharacteristic
195C2×D4×C17C22×C411yescharacteristic
196C22×C4×C17—21no—
197C22×C4×C17—21no—
198C22×C4×C17—21no—
199C22×C4×C17—21no—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—42no—
210C22×C4×C17—42no—
211C22×C4×C17C22×C411yescharacteristic
212C22×C4×C17C22×C411yescharacteristic
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D411yescharacteristic
215C22×C4×C17#4111yescharacteristic
216C22×C4×C17C2411yescharacteristic
217M16×C17—21no—
218M16×C17—21no—
219M16×C17—21no—
220M16×C17—21no—
221M16×C17—21no—
222M16×C17—21no—
223M16×C17—21no—
224M16×C17—21no—
225M16×C17—41no—
226M16×C17—41no—
227M16×C17—41no—
228M16×C17—41no—
229M16×C17—42no—
230M16×C17—42no—
231C2×C8×C17—21no—
232C2×C8×C17—21no—
233C2×C8×C17—21no—
234C2×C8×C17—21no—
235C2×C8×C17—21no—
236C2×C8×C17—21no—
237C2×C8×C17—21no—
238C2×C8×C17—21no—
239C2×C8×C17—21no—
240C2×C8×C17—21no—
241C2×C8×C17—21no—
242C2×C8×C17—21no—
243C2×C8×C17—42no—
244C2×C8×C17—42no—
245C2×C8×C17C22×C411yescharacteristic
246C2×C8×C17C22×C411yescharacteristic
247C2×C8×C17C22×C411yescharacteristic
248C2×C8×C17C22×C411yescharacteristic
249C2×C8×C17C2×D411yescharacteristic
250C2×C8×C17C2×D411yescharacteristic
251C2×C8×C17C2×D411yescharacteristic
252C2×C8×C17C2×D411yescharacteristic
253C4⋊C4×C17—21no—
254C4⋊C4×C17—21no—
255C4⋊C4×C17C22×C411yescharacteristic
256C4⋊C4×C17C22×C411yescharacteristic
257C4⋊C4×C17C22×C411yescharacteristic
258C4⋊C4×C17C22×C411yescharacteristic
259C22⋊C4×C17—21no—
260C22⋊C4×C17—21no—
261C22⋊C4×C17—21no—
262C22⋊C4×C17—21no—
263C22⋊C4×C17—42no—
264C42×C17—21no—
265C42×C17—21no—
266C42×C17—21no—
267C42×C17—21no—
268C42×C17—21no—
269C42×C17—21no—
270C42×C17—21no—
271C42×C17—21no—
272#22588C1711yesmaximal, characteristic, direct product factor, Sylow
273C23×C17—21no—
274C23×C17—21no—
275C23×C17—21no—
276C23×C17—21no—
277C23×C17—41no—
278C23×C17—41no—
279C23×C17—42no—
280C23×C17—42no—
281C23×C17—81no—
282C23×C17C4×D411yescharacteristic
283C23×C17C4×D411yescharacteristic
284C23×C17C2×#4111yescharacteristic
285Q8×C17—21no—
286Q8×C17—21no—
287Q8×C17—21no—
288Q8×C17—42no—
289Q8×C17#11712yes—
290D4×C17—22no—
291D4×C17—22no—
292D4×C17—21no—
293D4×C17—21no—
294D4×C17—21no—
295D4×C17—42no—
296D4×C17—42no—
297D4×C17—42no—
298D4×C17—41no—
299D4×C17—41no—
300D4×C17#11712yes—
301C2×C4×C17—21no—
302C2×C4×C17—21no—
303C2×C4×C17—21no—
304C2×C4×C17—21no—
305C2×C4×C17—21no—
306C2×C4×C17—21no—
307C2×C4×C17—21no—
308C2×C4×C17—22no—
309C2×C4×C17—22no—
310C2×C4×C17—21no—
311C2×C4×C17—21no—
312C2×C4×C17—21no—
313C2×C4×C17—21no—
314C2×C4×C17—22no—
315C2×C4×C17—21no—
316C2×C4×C17—21no—
317C2×C4×C17—21no—
318C2×C4×C17—21no—
319C2×C4×C17—21no—
320C2×C4×C17—42no—
321C2×C4×C17—42no—
322C2×C4×C17—42no—
323C2×C4×C17—41no—
324C2×C4×C17—42no—
325C2×C4×C17—41no—
326C2×C4×C17—41no—
327C2×C4×C17—41no—
328C2×C4×C17—41no—
329C2×C4×C17—41no—
330C2×C4×C17—41no—
331C2×C4×C17—81no—
332C2×C4×C17C4×D411yescharacteristic
333C2×C4×C17C4×D411yescharacteristic
334C2×C4×C17C23×C411yescharacteristic
335C2×C4×C17C22×D411yescharacteristic
336C2×C4×C17C2×#4111yescharacteristic
337C2×C4×C17C2×#4111yescharacteristic
338C2×C4×C17H(5,𝔽2)11yescharacteristic
339C2×C4×C17H(5,𝔽2)11yescharacteristic
340C8×C17—21no—
341C8×C17—21no—
342C8×C17—21no—
343C8×C17—21no—
344C8×C17—21no—
345C8×C17—21no—
346C8×C17—21no—
347C8×C17—21no—
348C8×C17—41no—
349C8×C17—41no—
350C8×C17—41no—
351C8×C17—41no—
352#2924C2×C1711yescharacteristic, complemented
353#2896C2×C1711yescharacteristic
354#2880C2×C1711yescharacteristic
355#1938C2×C1711yescharacteristic, complemented
356#1937C2×C1711yescharacteristic, complemented
357#1929C2×C1711yescharacteristic, complemented
358#1929C2×C1711yescharacteristic, complemented
359#1866C2×C1711yescharacteristic, complemented
360#1866C2×C1711yescharacteristic, complemented
361#1826C2×C1711yescharacteristic, complemented
362#1811C2×C1711yescharacteristic, complemented
363#1789C2×C1711yescharacteristic
364#1765C2×C1711yescharacteristic, complemented
365#1764C2×C1711yescharacteristic, complemented
366#1753C2×C1711yescharacteristic, complemented
367C22×C17—21no—
368C22×C17—21no—
369C22×C17—21no—
370C22×C17—21no—
371C22×C17—22no—
372C22×C17—21no—
373C22×C17—21no—
374C22×C17—21no—
375C22×C17—21no—
376C22×C17—41no—
377C22×C17—41no—
378C22×C17—41no—
379C22×C17—41no—
380C22×C17—41no—
381C22×C17—81no—
382C22×C17—81no—
383C22×C17—84no—
384C22×C17C2×C4×D411yescharacteristic
385C22×C17#55111yescharacteristic
386C22×C17#55111yescharacteristic
387C4×C17—21no—
388C4×C17—21no—
389C4×C17—22no—
390C4×C17—42no—
391C4×C17—41no—
392C4×C17—41no—
393C4×C17—41no—
394C4×C17—41no—
395C4×C17—41no—
396C4×C17—81no—
397C4×C17C2×#11711yescharacteristic
398C4×C17#51811yescharacteristic
399C4×C17#54611yescharacteristic
400C4×C17#54611yescharacteristic
401C22×#41C22×C1711yescharacteristic
402C2×#131C22×C1711yescharacteristic
403C2×#131C22×C1711yescharacteristic
404C22×M16C22×C1711yescharacteristic
405C2×#117C22×C1711yescharacteristic
406#433—21no—
407#433—21no—
408#432—21no—
409#431—21no—
410C2×#108C22×C1711yescharacteristic, complemented
411C2×#108C22×C1711yescharacteristic, complemented
412#424C22×C1711yescharacteristic, complemented
413#424C22×C1711yescharacteristic, complemented
414C2×#104C22×C1711yescharacteristic
415C2×#104C22×C1711yescharacteristic
416C2×#104C22×C1711yescharacteristic
417C2×#104C22×C1711yescharacteristic
418#419C4×C1711yescharacteristic, complemented
419#419C4×C1711yescharacteristic, complemented
420#418C4×C1711yescharacteristic, complemented
421#418C4×C1711yescharacteristic, complemented
422#417C4×C1711yescharacteristic, complemented
423#417C4×C1711yescharacteristic, complemented
424#417C4×C1711yescharacteristic, complemented
425#417C4×C1711yescharacteristic, complemented
426#416C22×C1711yescharacteristic
427#416C22×C1711yescharacteristic
428#416C22×C1711yescharacteristic
429#416C22×C1711yescharacteristic
430#408—21no—
431#408—21no—
432#408C22×C1711yescharacteristic
433#408C22×C1711yescharacteristic
434#407—21no—
435#407C22×C1711yescharacteristic
436#407C22×C1711yescharacteristic
437C2×C22⋊C8—21no—
438C2×C22⋊C8C22×C1711yescharacteristic
439#405C22×C1711yescharacteristic, complemented
440#405C22×C1711yescharacteristic, complemented
441C2×#97C22×C1711yescharacteristic, complemented
442C2×C4×C8C22×C1711yescharacteristic, complemented
443C4×C22⋊C4C22×C1711yescharacteristic
444#341C22×C1711yescharacteristic, complemented
445#341C22×C1711yescharacteristic, complemented
446#339C22×C1711yescharacteristic, complemented
447#339C22×C1711yescharacteristic, complemented
448#339C22×C1711yescharacteristic, complemented
449#339C22×C1711yescharacteristic, complemented
450#336C22×C1711yescharacteristic, complemented
451#336C22×C1711yescharacteristic, complemented
452C2×C17—21no—
453C2×C17—21no—
454C2×C17—41no—
455C2×C17—41no—
456C2×C17—42no—
457C2×C17—81no—
458C2×C17#234211yescharacteristic
459C2×C17#295511yescharacteristic
460C2×C17#295611yescharacteristic
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C2×#41C2×C4×C1711yescharacteristic
468C2×#41C2×C4×C1711yescharacteristic
469C2×#41C23×C1711yescharacteristic
470C2×#41C23×C1711yescharacteristic
471C22×Q8C2×C4×C1711yescharacteristic
472C22×D4—21no—
473C22×D4C2×C4×C1711yescharacteristic
474C23×C4—21no—
475C23×C4C23×C1711yescharacteristic
476#131—22no—
477#131—22no—
478#131—41no—
479#131—41no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—41no—
483C2×M16—41no—
484C2×M16C2×C4×C1711yescharacteristic
485C2×M16C2×C4×C1711yescharacteristic
486C2×M16C2×C4×C1711yescharacteristic
487C2×M16C2×C4×C1711yescharacteristic
488C2×M16C23×C1711yescharacteristic
489C2×M16C23×C1711yescharacteristic
490C2×M16C23×C1711yescharacteristic
491C2×M16C23×C1711yescharacteristic
492C22×C8—21no—
493C22×C8—21no—
494C22×C8C23×C1711yescharacteristic
495C22×C8C23×C1711yescharacteristic
496C22×C8C23×C1711yescharacteristic
497C22×C8C23×C1711yescharacteristic
498#117—21no—
499#117—21no—
500#117C2×C4×C1711yescharacteristic
501#117C2×C4×C1711yescharacteristic
502#117C23×C1711yescharacteristic
503#117C23×C1711yescharacteristic
504C2×C4⋊C4C2×C4×C1711yescharacteristic
505C2×C4⋊C4C2×C4×C1711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C42—21no—
509C2×C42C23×C1711yescharacteristic
510C2×C42C23×C1711yescharacteristic
511#108—41no—
512#108—41no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517#104—22no—
518#104—22no—
519#104—41no—
520#104—41no—
521#103C2×C4×C1711yescharacteristic
522#103C2×C4×C1711yescharacteristic
523#103C2×C4×C1711yescharacteristic
524#103C2×C4×C1711yescharacteristic
525#103C2×C4×C1711yescharacteristic
526#103C2×C4×C1711yescharacteristic
527#103C2×C4×C1711yescharacteristic
528#103C2×C4×C1711yescharacteristic
529#102C2×C4×C1711yescharacteristic
530#102C2×C4×C1711yescharacteristic
531#102C2×C4×C1711yescharacteristic
532#102C2×C4×C1711yescharacteristic
533#102C2×C4×C1711yescharacteristic
534#102C2×C4×C1711yescharacteristic
535#102C2×C4×C1711yescharacteristic
536#102C2×C4×C1711yescharacteristic
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8D4×C1711yescharacteristic
546C22⋊C8D4×C1711yescharacteristic
547C22⋊C8D4×C1711yescharacteristic
548C22⋊C8D4×C1711yescharacteristic
549#97—21no—
550#97—21no—
551#97—41no—
552C4×C8—21no—
553C4×C8—21no—
554C4×C8—41no—
555#95—21no—
556C17#2258811yescharacteristic, direct product factor, Sylow
557C24—21no—
558C24#41×C1711yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#41×C1712yes—
574#41#41×C1712yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×C4×C1711yescharacteristic
579C2×Q8C22×C4×C1711yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×C4×C1711yescharacteristic
590C2×D4C22×C4×C1711yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C22×C4×C1711yescharacteristic
607C22×C4C22×C4×C1711yescharacteristic
608C22×C4C2×D4×C1711yescharacteristic
609C22×C4C2×D4×C1711yescharacteristic
610C22×C4#41×C1711yescharacteristic
611C22×C4C24×C1711yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—42no—
625M16—42no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8C22×C4×C1711yescharacteristic
641C2×C8C22×C4×C1711yescharacteristic
642C2×C8C22×C4×C1711yescharacteristic
643C2×C8C22×C4×C1711yescharacteristic
644C2×C8C2×D4×C1711yescharacteristic
645C2×C8C2×D4×C1711yescharacteristic
646C2×C8C2×D4×C1711yescharacteristic
647C2×C8C2×D4×C1711yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×C4×C1711yescharacteristic
651C4⋊C4C22×C4×C1711yescharacteristic
652C4⋊C4C22×C4×C1711yescharacteristic
653C4⋊C4C22×C4×C1711yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×D4×C1711yescharacteristic
677C23C4×D4×C1711yescharacteristic
678C23C2×#41×C1711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8C17×#11712yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4C17×#11712yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4C4×D4×C1711yescharacteristic
727C2×C4C4×D4×C1711yescharacteristic
728C2×C4C23×C4×C1711yescharacteristic
729C2×C4C22×D4×C1711yescharacteristic
730C2×C4C2×#41×C1711yescharacteristic
731C2×C4C2×#41×C1711yescharacteristic
732C2×C4C17×H(5,𝔽2)11yescharacteristic
733C2×C4C17×H(5,𝔽2)11yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×D4×C1711yescharacteristic
764C22C17×#55111yescharacteristic
765C22C17×#55111yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4C2×C17×#11711yescharacteristic
777C4C17×#51811yescharacteristic
778C4C17×#54611yescharacteristic
779C4C17×#54611yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2C17×#234211yescharacteristic
787C2C17×#295511yescharacteristic
788C2C17×#295611yescharacteristic
subgroupG/H
centerC2×C4×C17C22×D4
commutatorC2×C4C23×C4×C17
Frattini, cosocleC22×C4C24×C17
socleC22×C17C2×C4×D4
prime radicalC22×#41×C17C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C17 ◁ C2×C17×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C17×#2924C2semidirect
4. C17×#1938C2semidirect
5. C17×#1937C2semidirect
6. C17×#1929C2semidirect
7. C17×#1929C2semidirect
8. C17×#1866C2semidirect
9. C17×#1866C2semidirect
10. C17×#1826C2semidirect
11. C17×#1811C2semidirect
13. C17×#1765C2semidirect
14. C17×#1764C2semidirect
15. C17×#1753C2semidirect
25. C2×C17×#108C22semidirect
26. C2×C17×#108C22semidirect
27. C17×#424C22semidirect
28. C17×#424C22semidirect
33. C17×#419C4semidirect
34. C17×#419C4semidirect
35. C17×#418C4semidirect
36. C17×#418C4semidirect
37. C17×#417C4semidirect
38. C17×#417C4semidirect
39. C17×#417C4semidirect
40. C17×#417C4semidirect
54. C17×#405C22semidirect
55. C17×#405C22semidirect
56. C2×C17×#97C22semidirect
57. C2×C4×C8×C17C22semidirect
59. C17×#341C22semidirect
60. C17×#341C22semidirect
61. C17×#339C22semidirect
62. C17×#339C22semidirect
63. C17×#339C22semidirect
64. C17×#339C22semidirect
65. C17×#336C22semidirect
66. C17×#336C22semidirect
272. #22588C17direct (N × H)
352. #2924C2×C17semidirect
355. #1938C2×C17semidirect
356. #1937C2×C17semidirect
357. #1929C2×C17semidirect
358. #1929C2×C17semidirect
359. #1866C2×C17semidirect
360. #1866C2×C17semidirect
361. #1826C2×C17semidirect
362. #1811C2×C17semidirect
364. #1765C2×C17semidirect
365. #1764C2×C17semidirect
366. #1753C2×C17semidirect
410. C2×#108C22×C17semidirect
411. C2×#108C22×C17semidirect
412. #424C22×C17semidirect
413. #424C22×C17semidirect
418. #419C4×C17semidirect
419. #419C4×C17semidirect
420. #418C4×C17semidirect
421. #418C4×C17semidirect
422. #417C4×C17semidirect
423. #417C4×C17semidirect
424. #417C4×C17semidirect
425. #417C4×C17semidirect
439. #405C22×C17semidirect
440. #405C22×C17semidirect
441. C2×#97C22×C17semidirect
442. C2×C4×C8C22×C17semidirect
444. #341C22×C17semidirect
445. #341C22×C17semidirect
446. #339C22×C17semidirect
447. #339C22×C17semidirect
448. #339C22×C17semidirect
449. #339C22×C17semidirect
450. #336C22×C17semidirect
451. #336C22×C17semidirect
556. C17#22588direct (N × H)

Maximal subgroups

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

subgroupindex
C17×#29242
C17×#28962
C17×#28802
C17×#19382
C17×#19372
C17×#19292
C17×#18662
C17×#18262
C17×#18112
C17×#17892
C17×#17652
C17×#17642
C17×#17532
#2258817