Finite Group Databasebeta

← C17×#14199 #16871943

Subgroups — C17×#14199 #16871943

Order 4352.

1954 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#394C211yesmaximal, characteristic
2C2×C17×#388C211yesmaximal, characteristic, complemented
3C2×C17×#386C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
6C17×#1440C211yesmaximal, characteristic, complemented
7C17×#1439C211yesmaximal, characteristic, complemented
8C17×#1438C211yesmaximal, characteristic
9C17×#1437C211yesmaximal, characteristic, complemented
10C17×#1437C211yesmaximal, characteristic, complemented
11C17×#1437C211yesmaximal, characteristic, complemented
12C17×#1436C211yesmaximal, characteristic, complemented
13C17×C4⋊#95C211yesmaximal, characteristic, complemented
14C17×#1434C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×D4×C17C2211yescharacteristic
17C24×C4×C17C2211yescharacteristic
18C22×C4⋊C4×C17C2211yescharacteristic
19C22×C4⋊C4×C17C2211yescharacteristic
20C22×C22⋊C4×C17C2211yescharacteristic
21C22×C22⋊C4×C17C2211yescharacteristic
22C22×C22⋊C4×C17C2211yescharacteristic
23C22×C22⋊C4×C17C2211yescharacteristic
24C22×C22⋊C4×C17C2211yescharacteristic
25C22×C22⋊C4×C17C2211yescharacteristic
26C22×C22⋊C4×C17C2211yescharacteristic
27C22×C22⋊C4×C17C2211yescharacteristic
28C22×C22⋊C4×C17C2211yescharacteristic
29C22×C22⋊C4×C17C2211yescharacteristic
30C22×C22⋊C4×C17C2211yescharacteristic
31C22×C42×C17C2211yescharacteristic
32C22×C42×C17C2211yescharacteristic
33C22×C42×C17C2211yescharacteristic
34C22×C42×C17C2211yescharacteristic
35C17×#394C418yescomplemented
36C17×#388—24no—
37C17×#386—24no—
38C4×C22⋊C4×C17—24no—
39C4×C22⋊C4×C17—24no—
40C2×C17×#95C2211yescharacteristic
41C2×C17×#95C2211yescharacteristic
42C2×C17×#95C2211yescharacteristic
43C2×C17×#95C2211yescharacteristic
44C2×C17×#95C2211yescharacteristic
45C2×C17×#95C2211yescharacteristic
46C2×C17×#95C2211yescharacteristic
47C2×C17×#95C2211yescharacteristic
48C2×C17×#95C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C25×C17C2311yescharacteristic
57C25×C17C2311yescharacteristic
58C22×D4×C17—22no—
59C22×D4×C17—22no—
60C22×D4×C17—41no—
61C22×D4×C17—41no—
62C22×D4×C17—41no—
63C22×D4×C17—41no—
64C22×D4×C17C2×C414yes—
65C23×C4×C17—22no—
66C23×C4×C17—22no—
67C23×C4×C17—22no—
68C23×C4×C17—22no—
69C23×C4×C17—41no—
70C23×C4×C17—41no—
71C23×C4×C17D414yes—
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×C4×C17C2311yescharacteristic
76C23×C4×C17C2311yescharacteristic
77C23×C4×C17C2311yescharacteristic
78C23×C4×C17C2311yescharacteristic
79C23×C4×C17C2311yescharacteristic
80C23×C4×C17C2311yescharacteristic
81C23×C4×C17C2311yescharacteristic
82C23×C4×C17C2311yescharacteristic
83C23×C4×C17C2311yescharacteristic
84C23×C4×C17C2311yescharacteristic
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17—41no—
88C2×C4⋊C4×C17—41no—
89C2×C4⋊C4×C17—41no—
90C2×C4⋊C4×C17C2×C414yescomplemented
91C2×C22⋊C4×C17—22no—
92C2×C22⋊C4×C17—22no—
93C2×C22⋊C4×C17—22no—
94C2×C22⋊C4×C17—22no—
95C2×C22⋊C4×C17—22no—
96C2×C22⋊C4×C17—22no—
97C2×C22⋊C4×C17—22no—
98C2×C22⋊C4×C17—22no—
99C2×C22⋊C4×C17—22no—
100C2×C22⋊C4×C17—22no—
101C2×C22⋊C4×C17—22no—
102C2×C22⋊C4×C17—22no—
103C2×C22⋊C4×C17—22no—
104C2×C22⋊C4×C17—22no—
105C2×C22⋊C4×C17—22no—
106C2×C22⋊C4×C17—22no—
107C2×C22⋊C4×C17—22no—
108C2×C22⋊C4×C17—22no—
109C2×C22⋊C4×C17—22no—
110C2×C22⋊C4×C17—22no—
111C2×C22⋊C4×C17—22no—
112C2×C22⋊C4×C17—22no—
113C2×C22⋊C4×C17—22no—
114C2×C22⋊C4×C17—41no—
115C2×C22⋊C4×C17—41no—
116C2×C22⋊C4×C17—41no—
117C2×C22⋊C4×C17—41no—
118C2×C22⋊C4×C17—41no—
119C2×C22⋊C4×C17—41no—
120C2×C22⋊C4×C17C2×C414yes—
121C2×C22⋊C4×C17C2×C414yes—
122C2×C22⋊C4×C17C2×C414yescomplemented
123C2×C22⋊C4×C17C2×C414yescomplemented
124C2×C42×C17—22no—
125C2×C42×C17—22no—
126C2×C42×C17—22no—
127C2×C42×C17—22no—
128C2×C42×C17—22no—
129C2×C42×C17—22no—
130C2×C42×C17—22no—
131C2×C42×C17—22no—
132C2×C42×C17—41no—
133C2×C42×C17—41no—
134C2×C42×C17—41no—
135C2×C42×C17—41no—
136C17×#95—22no—
137C17×#95—22no—
138C17×#95—22no—
139C17×#95—22no—
140C17×#95—22no—
141C17×#95—22no—
142C17×#95—22no—
143C17×#95—22no—
144C17×#95—22no—
145C17×#95—41no—
146C17×#95—41no—
147C17×#95—41no—
148C17×#95—41no—
149C17×#95—41no—
150C17×#95C2×C414yescomplemented
151C17×#95D414yescomplemented
152C24×C17—21no—
153C24×C17—21no—
154C24×C17—21no—
155C24×C17—21no—
156C24×C17—21no—
157C24×C17—21no—
158C24×C17—21no—
159C24×C17—21no—
160C24×C17—21no—
161C24×C17—21no—
162C24×C17—21no—
163C24×C17—21no—
164C24×C17—21no—
165C24×C17—21no—
166C24×C17—21no—
167C24×C17—21no—
168C24×C17—21no—
169C24×C17—21no—
170C24×C17—21no—
171C24×C17—21no—
172C24×C17—21no—
173C24×C17—21no—
174C24×C17—21no—
175C24×C17—21no—
176C24×C17—21no—
177C24×C17—21no—
178C24×C17C22×C412yes—
179C24×C17C22×C412yes—
180C24×C17C2×D412yes—
181C24×C17#4112yes—
182C24×C17C2411yescharacteristic
183C2×D4×C17—28no—
184C2×D4×C17—44no—
185C2×D4×C17—44no—
186C2×D4×C17—44no—
187C2×D4×C17—44no—
188C2×D4×C17—44no—
189C2×D4×C17—44no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17—21no—
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—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—21no—
235C22×C4×C17—21no—
236C22×C4×C17—21no—
237C22×C4×C17—21no—
238C22×C4×C17—21no—
239C22×C4×C17—21no—
240C22×C4×C17—21no—
241C22×C4×C17—21no—
242C22×C4×C17—21no—
243C22×C4×C17—21no—
244C22×C4×C17—21no—
245C22×C4×C17—21no—
246C22×C4×C17—21no—
247C22×C4×C17—21no—
248C22×C4×C17—21no—
249C22×C4×C17—21no—
250C22×C4×C17—28no—
251C22×C4×C17—28no—
252C22×C4×C17—21no—
253C22×C4×C17—21no—
254C22×C4×C17—21no—
255C22×C4×C17—21no—
256C22×C4×C17—21no—
257C22×C4×C17—21no—
258C22×C4×C17—21no—
259C22×C4×C17—21no—
260C22×C4×C17—21no—
261C22×C4×C17—21no—
262C22×C4×C17—21no—
263C22×C4×C17—21no—
264C22×C4×C17—21no—
265C22×C4×C17—21no—
266C22×C4×C17—44no—
267C22×C4×C17—44no—
268C22×C4×C17—44no—
269C22×C4×C17—44no—
270C22×C4×C17—44no—
271C22×C4×C17C22×C412yes—
272C22×C4×C17C22×C412yes—
273C22×C4×C17C22×C412yes—
274C22×C4×C17C22×C412yes—
275C22×C4×C17C22×C412yes—
276C22×C4×C17C2×D412yes—
277C22×C4×C17C2×D412yes—
278C22×C4×C17C2×D412yes—
279C22×C4×C17C2×D412yes—
280C22×C4×C17C2×D412yes—
281C22×C4×C17#4112yes—
282C22×C4×C17#4112yes—
283C22×C4×C17#4112yes—
284C22×C4×C17#4112yes—
285C22×C4×C17#4112yes—
286C22×C4×C17#4112yes—
287C22×C4×C17#4112yes—
288C4⋊C4×C17—44no—
289C4⋊C4×C17—44no—
290C22⋊C4×C17—28no—
291C22⋊C4×C17—28no—
292C22⋊C4×C17—28no—
293C22⋊C4×C17—28no—
294C22⋊C4×C17—28no—
295C22⋊C4×C17—44no—
296C22⋊C4×C17—44no—
297C22⋊C4×C17—44no—
298C22⋊C4×C17—44no—
299C22⋊C4×C17—44no—
300C22⋊C4×C17—44no—
301C42×C17—44no—
302C42×C17—44no—
303C42×C17—44no—
304C42×C17—44no—
305#14199C1711yesmaximal, characteristic, direct product factor, Sylow
306C23×C17—22no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—22no—
310C23×C17—22no—
311C23×C17—22no—
312C23×C17—22no—
313C23×C17—22no—
314C23×C17—22no—
315C23×C17—22no—
316C23×C17—22no—
317C23×C17—22no—
318C23×C17—22no—
319C23×C17—22no—
320C23×C17—22no—
321C23×C17—22no—
322C23×C17—22no—
323C23×C17—22no—
324C23×C17—22no—
325C23×C17—22no—
326C23×C17—22no—
327C23×C17—22no—
328C23×C17—22no—
329C23×C17—22no—
330C23×C17—22no—
331C23×C17—41no—
332C23×C17—41no—
333C23×C17—41no—
334C23×C17—41no—
335C23×C17—41no—
336C23×C17—41no—
337C23×C17—41no—
338C23×C17—41no—
339C23×C17—41no—
340C23×C17—41no—
341C23×C17—41no—
342C23×C17—41no—
343C23×C17—41no—
344C23×C17—41no—
345C23×C17—41no—
346C23×C17—41no—
347C23×C17—41no—
348C23×C17—41no—
349C23×C17—41no—
350C23×C17—41no—
351C23×C17—41no—
352C23×C17—41no—
353C23×C17—41no—
354C23×C17—41no—
355C23×C17—41no—
356C23×C17—41no—
357C23×C17—41no—
358C23×C17—41no—
359C23×C17—41no—
360C23×C17—41no—
361C23×C17—41no—
362C23×C17—41no—
363C23×C17—41no—
364C23×C17—41no—
365C23×C17—41no—
366C23×C17—41no—
367C23×C17—41no—
368C23×C17—41no—
369C23×C17—41no—
370C23×C17—41no—
371C23×C17—41no—
372C23×C17—41no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17C4×D414yes—
376C23×C17C23×C411yescharacteristic
377C23×C17C22×D411yescharacteristic
378C23×C17C22×D411yescharacteristic
379C23×C17C2×#4111yescharacteristic
380C23×C17C2×#4111yescharacteristic
381C23×C17C2×#4111yescharacteristic
382C23×C17C2×#4111yescharacteristic
383C23×C17C2×#4111yescharacteristic
384C23×C17C2×#4111yescharacteristic
385C23×C17C2×#4111yescharacteristic
386C23×C17C2×#4111yescharacteristic
387C23×C17H(5,𝔽2)11yescharacteristic
388C23×C17H(5,𝔽2)11yescharacteristic
389C23×C17H(5,𝔽2)11yescharacteristic
390C23×C17H(5,𝔽2)11yescharacteristic
391D4×C17—416no—
392C2×C4×C17—22no—
393C2×C4×C17—22no—
394C2×C4×C17—22no—
395C2×C4×C17—22no—
396C2×C4×C17—22no—
397C2×C4×C17—22no—
398C2×C4×C17—22no—
399C2×C4×C17—22no—
400C2×C4×C17—22no—
401C2×C4×C17—22no—
402C2×C4×C17—22no—
403C2×C4×C17—22no—
404C2×C4×C17—22no—
405C2×C4×C17—22no—
406C2×C4×C17—22no—
407C2×C4×C17—22no—
408C2×C4×C17—22no—
409C2×C4×C17—22no—
410C2×C4×C17—22no—
411C2×C4×C17—22no—
412C2×C4×C17—22no—
413C2×C4×C17—22no—
414C2×C4×C17—22no—
415C2×C4×C17—22no—
416C2×C4×C17—22no—
417C2×C4×C17—22no—
418C2×C4×C17—22no—
419C2×C4×C17—22no—
420C2×C4×C17—22no—
421C2×C4×C17—22no—
422C2×C4×C17—22no—
423C2×C4×C17—22no—
424C2×C4×C17—22no—
425C2×C4×C17—22no—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—22no—
434C2×C4×C17—416no—
435C2×C4×C17—41no—
436C2×C4×C17—41no—
437C2×C4×C17—41no—
438C2×C4×C17—41no—
439C2×C4×C17—41no—
440C2×C4×C17—41no—
441C2×C4×C17—41no—
442C2×C4×C17—41no—
443C2×C4×C17—41no—
444C2×C4×C17—41no—
445C2×C4×C17—41no—
446C2×C4×C17—41no—
447C2×C4×C17—41no—
448C2×C4×C17—41no—
449C2×C4×C17—41no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17—41no—
457C2×C4×C17—41no—
458C2×C4×C17—41no—
459C2×C4×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17—41no—
464C2×C4×C17—41no—
465C2×C4×C17—41no—
466C2×C4×C17—41no—
467C2×C4×C17—41no—
468C2×C4×C17—41no—
469C2×C4×C17—41no—
470C2×C4×C17—41no—
471C2×C4×C17—41no—
472C2×C4×C17—41no—
473C2×C4×C17—41no—
474C2×C4×C17—41no—
475C2×C4×C17—41no—
476C2×C4×C17—41no—
477C2×C4×C17—41no—
478C2×C4×C17—41no—
479C2×C4×C17—41no—
480C2×C4×C17—41no—
481C2×C4×C17C4×D414yes—
482C2×C4×C17#12114yes—
483C2×C4×C17#12314yes—
484C2×#394C2×C1711yescharacteristic
485C2×#388C2×C1711yescharacteristic, complemented
486C2×#386C2×C1711yescharacteristic
487C2×C4×C22⋊C4C2×C1711yescharacteristic, complemented
488C2×C4×C22⋊C4C2×C1711yescharacteristic, complemented
489#1440C2×C1711yescharacteristic, complemented
490#1439C2×C1711yescharacteristic, complemented
491#1438C2×C1711yescharacteristic
492#1437C2×C1711yescharacteristic, complemented
493#1437C2×C1711yescharacteristic, complemented
494#1437C2×C1711yescharacteristic, complemented
495#1436C2×C1711yescharacteristic, complemented
496C4⋊#95C2×C1711yescharacteristic, complemented
497#1434C2×C1711yescharacteristic, complemented
498#1434C2×C1711yescharacteristic, complemented
499C22×C17—24no—
500C22×C17—24no—
501C22×C17—24no—
502C22×C17—42no—
503C22×C17—42no—
504C22×C17—42no—
505C22×C17—42no—
506C22×C17—42no—
507C22×C17—42no—
508C22×C17—42no—
509C22×C17—42no—
510C22×C17—42no—
511C22×C17—42no—
512C22×C17—42no—
513C22×C17—42no—
514C22×C17—42no—
515C22×C17—42no—
516C22×C17—42no—
517C22×C17—42no—
518C22×C17—42no—
519C22×C17—42no—
520C22×C17—42no—
521C22×C17—81no—
522C22×C17—81no—
523C22×C17—81no—
524C22×C17—81no—
525C22×C17—81no—
526C22×C17—81no—
527C22×C17—81no—
528C22×C17—81no—
529C22×C17C2×C4×D411yescharacteristic
530C22×C17C2×C4×D411yescharacteristic
531C22×C17C4×#4111yescharacteristic
532C22×C17C4×#4111yescharacteristic
533C22×C17C4×#4111yescharacteristic
534C22×C17#51811yescharacteristic
535C22×C17#51811yescharacteristic
536C22×C17C2×#12111yescharacteristic
537C22×C17C2×#12311yescharacteristic
538C22×C17#52511yescharacteristic
539C22×C17#52511yescharacteristic
540C22×C17#52911yescharacteristic
541C22×C17#52911yescharacteristic
542C22×C17#52911yescharacteristic
543C22×C17#53211yescharacteristic
544C22×C17#53411yescharacteristic
545C22×C17#53511yescharacteristic
546C22×C17#53811yescharacteristic
547C22×C17#53811yescharacteristic
548C22×C17#54611yescharacteristic
549C22×C17#54611yescharacteristic
550C22×C17#54611yescharacteristic
551C22×C17#55011yescharacteristic
552C22×C17#55111yescharacteristic
553C22×C17#55111yescharacteristic
554C22×C17#55111yescharacteristic
555C22×C17#55311yescharacteristic
556C22×C17#55311yescharacteristic
557C22×C17#55311yescharacteristic
558C22×C17#55311yescharacteristic
559C22×C17#55311yescharacteristic
560C22×C17#55511yescharacteristic
561C22×C17#55511yescharacteristic
562C22×C17#55511yescharacteristic
563C22×C17#55911yescharacteristic
564C4×C17—24no—
565C4×C17—24no—
566C4×C17—24no—
567C4×C17—42no—
568C4×C17—42no—
569C4×C17—42no—
570C4×C17—42no—
571C4×C17—42no—
572C4×C17—42no—
573C4×C17—42no—
574C4×C17—42no—
575C4×C17—81no—
576C4×C17—81no—
577C23×D4C22×C1711yescharacteristic
578C24×C4C22×C1711yescharacteristic
579C22×C4⋊C4C22×C1711yescharacteristic
580C22×C4⋊C4C22×C1711yescharacteristic
581C22×C22⋊C4C22×C1711yescharacteristic
582C22×C22⋊C4C22×C1711yescharacteristic
583C22×C22⋊C4C22×C1711yescharacteristic
584C22×C22⋊C4C22×C1711yescharacteristic
585C22×C22⋊C4C22×C1711yescharacteristic
586C22×C22⋊C4C22×C1711yescharacteristic
587C22×C22⋊C4C22×C1711yescharacteristic
588C22×C22⋊C4C22×C1711yescharacteristic
589C22×C22⋊C4C22×C1711yescharacteristic
590C22×C22⋊C4C22×C1711yescharacteristic
591C22×C22⋊C4C22×C1711yescharacteristic
592C22×C42C22×C1711yescharacteristic
593C22×C42C22×C1711yescharacteristic
594C22×C42C22×C1711yescharacteristic
595C22×C42C22×C1711yescharacteristic
596#394C4×C1718yescomplemented
597#388—24no—
598#386—24no—
599C4×C22⋊C4—24no—
600C4×C22⋊C4—24no—
601C2×#95C22×C1711yescharacteristic
602C2×#95C22×C1711yescharacteristic
603C2×#95C22×C1711yescharacteristic
604C2×#95C22×C1711yescharacteristic
605C2×#95C22×C1711yescharacteristic
606C2×#95C22×C1711yescharacteristic
607C2×#95C22×C1711yescharacteristic
608C2×#95C22×C1711yescharacteristic
609C2×#95C22×C1711yescharacteristic
610C2×#95C22×C1711yescharacteristic
611C2×#95C22×C1711yescharacteristic
612C2×#95C22×C1711yescharacteristic
613C2×#95C22×C1711yescharacteristic
614C2×#95C22×C1711yescharacteristic
615C2×#95C22×C1711yescharacteristic
616C2×#95C22×C1711yescharacteristic
617C2×C17—44no—
618C2×C17—82no—
619C2×C17C4×#12111yescharacteristic
620C2×C17C4×#12311yescharacteristic
621C2×C17#232111yescharacteristic
622C2×C17#236311yescharacteristic
623C2×C17#236411yescharacteristic
624C2×C17#237211yescharacteristic
625C2×C17#237411yescharacteristic
626C2×C17#241211yescharacteristic
627C2×C17#241411yescharacteristic
628C2×C17#245911yescharacteristic
629C2×C17#246711yescharacteristic
630C2×C17#250011yescharacteristic
631C2×C17#251811yescharacteristic
632C2×C17#251811yescharacteristic
633C2×C17#260211yescharacteristic
634C25C23×C1711yescharacteristic
635C25C23×C1711yescharacteristic
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4—41no—
641C22×D4—41no—
642C22×D4C2×C4×C1714yes—
643C23×C4—22no—
644C23×C4—22no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—41no—
648C23×C4—41no—
649C23×C4D4×C1714yes—
650C23×C4C23×C1711yescharacteristic
651C23×C4C23×C1711yescharacteristic
652C23×C4C23×C1711yescharacteristic
653C23×C4C23×C1711yescharacteristic
654C23×C4C23×C1711yescharacteristic
655C23×C4C23×C1711yescharacteristic
656C23×C4C23×C1711yescharacteristic
657C23×C4C23×C1711yescharacteristic
658C23×C4C23×C1711yescharacteristic
659C23×C4C23×C1711yescharacteristic
660C23×C4C23×C1711yescharacteristic
661C23×C4C23×C1711yescharacteristic
662C23×C4C23×C1711yescharacteristic
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4C2×C4×C1714yescomplemented
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4C2×C4×C1714yes—
699C2×C22⋊C4C2×C4×C1714yes—
700C2×C22⋊C4C2×C4×C1714yescomplemented
701C2×C22⋊C4C2×C4×C1714yescomplemented
702C2×C42—22no—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42—41no—
713C2×C42—41no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—41no—
724#95—41no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95C2×C4×C1714yescomplemented
729#95D4×C1714yescomplemented
730C17#1419911yescharacteristic, direct product factor, Sylow
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24C22×C4×C1712yes—
758C24C22×C4×C1712yes—
759C24C2×D4×C1712yes—
760C24#41×C1712yes—
761C24C24×C1711yescharacteristic
762C2×D4—28no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4C22×C4×C1712yes—
851C22×C4C22×C4×C1712yes—
852C22×C4C22×C4×C1712yes—
853C22×C4C22×C4×C1712yes—
854C22×C4C22×C4×C1712yes—
855C22×C4C2×D4×C1712yes—
856C22×C4C2×D4×C1712yes—
857C22×C4C2×D4×C1712yes—
858C22×C4C2×D4×C1712yes—
859C22×C4C2×D4×C1712yes—
860C22×C4#41×C1712yes—
861C22×C4#41×C1712yes—
862C22×C4#41×C1712yes—
863C22×C4#41×C1712yes—
864C22×C4#41×C1712yes—
865C22×C4#41×C1712yes—
866C22×C4#41×C1712yes—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C42—44no—
881C42—44no—
882C42—44no—
883C42—44no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23C4×D4×C1714yes—
954C23C23×C4×C1711yescharacteristic
955C23C22×D4×C1711yescharacteristic
956C23C22×D4×C1711yescharacteristic
957C23C2×#41×C1711yescharacteristic
958C23C2×#41×C1711yescharacteristic
959C23C2×#41×C1711yescharacteristic
960C23C2×#41×C1711yescharacteristic
961C23C2×#41×C1711yescharacteristic
962C23C2×#41×C1711yescharacteristic
963C23C2×#41×C1711yescharacteristic
964C23C2×#41×C1711yescharacteristic
965C23C17×H(5,𝔽2)11yescharacteristic
966C23C17×H(5,𝔽2)11yescharacteristic
967C23C17×H(5,𝔽2)11yescharacteristic
968C23C17×H(5,𝔽2)11yescharacteristic
969D4—416no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4C4×D4×C1714yes—
1060C2×C4C17×#12114yes—
1061C2×C4C17×#12314yes—
1062C22—24no—
1063C22—24no—
1064C22—24no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—81no—
1085C22—81no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22C2×C4×D4×C1711yescharacteristic
1093C22C2×C4×D4×C1711yescharacteristic
1094C22C4×#41×C1711yescharacteristic
1095C22C4×#41×C1711yescharacteristic
1096C22C4×#41×C1711yescharacteristic
1097C22C17×#51811yescharacteristic
1098C22C17×#51811yescharacteristic
1099C22C2×C17×#12111yescharacteristic
1100C22C2×C17×#12311yescharacteristic
1101C22C17×#52511yescharacteristic
1102C22C17×#52511yescharacteristic
1103C22C17×#52911yescharacteristic
1104C22C17×#52911yescharacteristic
1105C22C17×#52911yescharacteristic
1106C22C17×#53211yescharacteristic
1107C22C17×#53411yescharacteristic
1108C22C17×#53511yescharacteristic
1109C22C17×#53811yescharacteristic
1110C22C17×#53811yescharacteristic
1111C22C17×#54611yescharacteristic
1112C22C17×#54611yescharacteristic
1113C22C17×#54611yescharacteristic
1114C22C17×#55011yescharacteristic
1115C22C17×#55111yescharacteristic
1116C22C17×#55111yescharacteristic
1117C22C17×#55111yescharacteristic
1118C22C17×#55311yescharacteristic
1119C22C17×#55311yescharacteristic
1120C22C17×#55311yescharacteristic
1121C22C17×#55311yescharacteristic
1122C22C17×#55311yescharacteristic
1123C22C17×#55511yescharacteristic
1124C22C17×#55511yescharacteristic
1125C22C17×#55511yescharacteristic
1126C22C17×#55911yescharacteristic
1127C4—24no—
1128C4—24no—
1129C4—24no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—81no—
1140C2—44no—
1141C2—82no—
1142C2C4×C17×#12111yescharacteristic
1143C2C4×C17×#12311yescharacteristic
1144C2C17×#232111yescharacteristic
1145C2C17×#236311yescharacteristic
1146C2C17×#236411yescharacteristic
1147C2C17×#237211yescharacteristic
1148C2C17×#237411yescharacteristic
1149C2C17×#241211yescharacteristic
1150C2C17×#241411yescharacteristic
1151C2C17×#245911yescharacteristic
1152C2C17×#246711yescharacteristic
1153C2C17×#250011yescharacteristic
1154C2C17×#251811yescharacteristic
1155C2C17×#251811yescharacteristic
1156C2C17×#260211yescharacteristic
subgroupG/H
center, socleC24×C17C24
commutatorC23C23×C4×C17
Frattini, cosocleC24C24×C17
prime radicalC23×D4×C17C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C17 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C17×#388C2semidirect
4. C2×C4×C22⋊C4×C17C2semidirect
5. C2×C4×C22⋊C4×C17C2semidirect
6. C17×#1440C2semidirect
7. C17×#1439C2semidirect
9. C17×#1437C2semidirect
10. C17×#1437C2semidirect
11. C17×#1437C2semidirect
12. C17×#1436C2semidirect
13. C17×C4⋊#95C2semidirect
14. C17×#1434C2semidirect
15. C17×#1434C2semidirect
35. C17×#394C4semidirect
90. C2×C4⋊C4×C17C2×C4semidirect
122. C2×C22⋊C4×C17C2×C4semidirect
123. C2×C22⋊C4×C17C2×C4semidirect
150. C17×#95C2×C4semidirect
151. C17×#95D4semidirect
305. #14199C17direct (N × H)
485. C2×#388C2×C17semidirect
487. C2×C4×C22⋊C4C2×C17semidirect
488. C2×C4×C22⋊C4C2×C17semidirect
489. #1440C2×C17semidirect
490. #1439C2×C17semidirect
492. #1437C2×C17semidirect
493. #1437C2×C17semidirect
494. #1437C2×C17semidirect
495. #1436C2×C17semidirect
496. C4⋊#95C2×C17semidirect
497. #1434C2×C17semidirect
498. #1434C2×C17semidirect
596. #394C4×C17semidirect
668. C2×C4⋊C4C2×C4×C17semidirect
700. C2×C22⋊C4C2×C4×C17semidirect
701. C2×C22⋊C4C2×C4×C17semidirect
728. #95C2×C4×C17semidirect
729. #95D4×C17semidirect
730. C17#14199direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C17×#3942
C2×C17×#3882
C2×C17×#3862
C2×C4×C22⋊C4×C172
C17×#14402
C17×#14392
C17×#14382
C17×#14372
C17×#14362
C17×C4⋊#952
C17×#14342
#1419917