Finite Group Databasebeta

← C17×#16512 #16874256

Subgroups — C17×#16512 #16874256

Order 4352.

2122 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C17×#394C211yesmaximal, characteristic, complemented
2C2×C17×#394C211yesmaximal, characteristic, complemented
3C2×C17×#392C211yesmaximal, characteristic
4C2×C17×#386C211yesmaximal, characteristic, complemented
5C2×C17×#386C211yesmaximal, characteristic, complemented
6C2×C17×#380C211yesmaximal, characteristic, complemented
7C17×#1443C211yesmaximal, characteristic, complemented
8C17×#1441C211yesmaximal, characteristic, complemented
9C17×#1440C211yesmaximal, characteristic, complemented
10C17×#1440C211yesmaximal, characteristic, complemented
11C17×#1439C211yesmaximal, characteristic, complemented
12C17×#1439C211yesmaximal, characteristic, complemented
13C17×#1439C211yesmaximal, characteristic, complemented
14C17×#1438C211yesmaximal, characteristic, complemented
15C17×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C17C2211yescharacteristic
17C23×D4×C17C2211yescharacteristic
18C23×D4×C17C2211yescharacteristic
19C24×C4×C17C2211yescharacteristic
20C22×C4⋊C4×C17C2211yescharacteristic
21C22×C4⋊C4×C17C2211yescharacteristic
22C22×C4⋊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×C22⋊C4×C17C2211yescharacteristic
32C22×C22⋊C4×C17C2211yescharacteristic
33C22×C22⋊C4×C17C2211yescharacteristic
34C22×C22⋊C4×C17C2211yescharacteristic
35C22×C22⋊C4×C17C2211yescharacteristic
36C22×C22⋊C4×C17C2211yescharacteristic
37C17×#394—24no—
38C17×#394—24no—
39C17×#392—24no—
40C17×#386—24no—
41C17×#386—24no—
42C17×#380—24no—
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
56C2×C17×#95C2211yescharacteristic
57C25×C17C2311yescharacteristic
58C25×C17C2311yescharacteristic
59C25×C17C2311yescharacteristic
60C22×D4×C17—22no—
61C22×D4×C17—22no—
62C22×D4×C17—22no—
63C22×D4×C17—22no—
64C22×D4×C17—22no—
65C22×D4×C17—22no—
66C22×D4×C17—22no—
67C22×D4×C17—22no—
68C22×D4×C17—22no—
69C22×D4×C17—22no—
70C22×D4×C17—41no—
71C22×D4×C17—41no—
72C22×D4×C17—41no—
73C22×D4×C17—41no—
74C22×D4×C17—41no—
75C22×D4×C17—41no—
76C22×D4×C17—41no—
77C22×D4×C17—41no—
78C22×D4×C17—41no—
79C22×D4×C17—41no—
80C22×D4×C17D414yes—
81C23×C4×C17—22no—
82C23×C4×C17—22no—
83C23×C4×C17—41no—
84C23×C4×C17—41no—
85C23×C4×C17—41no—
86C23×C4×C17—41no—
87C23×C4×C17D414yescomplemented
88C23×C4×C17C2311yescharacteristic
89C23×C4×C17C2311yescharacteristic
90C23×C4×C17C2311yescharacteristic
91C23×C4×C17C2311yescharacteristic
92C23×C4×C17C2311yescharacteristic
93C23×C4×C17C2311yescharacteristic
94C23×C4×C17C2311yescharacteristic
95C23×C4×C17C2311yescharacteristic
96C23×C4×C17C2311yescharacteristic
97C23×C4×C17C2311yescharacteristic
98C23×C4×C17C2311yescharacteristic
99C23×C4×C17C2311yescharacteristic
100C2×C4⋊C4×C17—22no—
101C2×C4⋊C4×C17—22no—
102C2×C4⋊C4×C17—41no—
103C2×C4⋊C4×C17—41no—
104C2×C4⋊C4×C17—41no—
105C2×C4⋊C4×C17—41no—
106C2×C4⋊C4×C17—41no—
107C2×C4⋊C4×C17—41no—
108C2×C4⋊C4×C17D414yescomplemented
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—22no—
115C2×C22⋊C4×C17—22no—
116C2×C22⋊C4×C17—22no—
117C2×C22⋊C4×C17—22no—
118C2×C22⋊C4×C17—22no—
119C2×C22⋊C4×C17—22no—
120C2×C22⋊C4×C17—22no—
121C2×C22⋊C4×C17—22no—
122C2×C22⋊C4×C17—22no—
123C2×C22⋊C4×C17—22no—
124C2×C22⋊C4×C17—22no—
125C2×C22⋊C4×C17—22no—
126C2×C22⋊C4×C17—22no—
127C2×C22⋊C4×C17—22no—
128C2×C22⋊C4×C17—22no—
129C2×C22⋊C4×C17—22no—
130C2×C22⋊C4×C17—22no—
131C2×C22⋊C4×C17—22no—
132C2×C22⋊C4×C17—22no—
133C2×C22⋊C4×C17—41no—
134C2×C22⋊C4×C17—41no—
135C2×C22⋊C4×C17—41no—
136C2×C22⋊C4×C17—41no—
137C2×C22⋊C4×C17—41no—
138C2×C22⋊C4×C17—41no—
139C2×C22⋊C4×C17—41no—
140C2×C22⋊C4×C17—41no—
141C2×C22⋊C4×C17—41no—
142C2×C22⋊C4×C17—41no—
143C2×C22⋊C4×C17—41no—
144C2×C22⋊C4×C17—41no—
145C2×C22⋊C4×C17—41no—
146C2×C22⋊C4×C17—41no—
147C2×C22⋊C4×C17—41no—
148C2×C22⋊C4×C17—41no—
149C2×C22⋊C4×C17—41no—
150C2×C22⋊C4×C17—41no—
151C17×#95—22no—
152C17×#95—22no—
153C17×#95—22no—
154C17×#95—22no—
155C17×#95—22no—
156C17×#95—22no—
157C17×#95—22no—
158C17×#95—22no—
159C17×#95—22no—
160C17×#95—22no—
161C17×#95—41no—
162C17×#95—41no—
163C17×#95—41no—
164C17×#95—41no—
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×C17—21no—
179C24×C17—21no—
180C24×C17—21no—
181C24×C17—21no—
182C24×C17—21no—
183C24×C17—21no—
184C24×C17—21no—
185C24×C17—21no—
186C24×C17—21no—
187C24×C17—21no—
188C24×C17—21no—
189C24×C17—21no—
190C24×C17—21no—
191C24×C17—21no—
192C24×C17—21no—
193C24×C17—21no—
194C24×C17—21no—
195C24×C17—21no—
196C24×C17—21no—
197C24×C17—21no—
198C24×C17—21no—
199C24×C17—21no—
200C24×C17—21no—
201C24×C17—21no—
202C24×C17—21no—
203C24×C17—21no—
204C24×C17—21no—
205C24×C17C2×D412yes—
206C24×C17C2×D412yes—
207C24×C17C2×D412yes—
208C24×C17#4112yes—
209C24×C17#4112yes—
210C24×C17C2411yescharacteristic
211C2×D4×C17—28no—
212C2×D4×C17—28no—
213C2×D4×C17—44no—
214C2×D4×C17—44no—
215C2×D4×C17—44no—
216C2×D4×C17—44no—
217C2×D4×C17—44no—
218C2×D4×C17—44no—
219C2×D4×C17—44no—
220C2×D4×C17—44no—
221C2×D4×C17—44no—
222C2×D4×C17—44no—
223C2×D4×C17—44no—
224C2×D4×C17—44no—
225C2×D4×C17—44no—
226C2×D4×C17—44no—
227C2×D4×C17—44no—
228C2×D4×C17—44no—
229C2×D4×C17—44no—
230C2×D4×C17—44no—
231C2×D4×C17—44no—
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—21no—
251C22×C4×C17—21no—
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—28no—
267C22×C4×C17—21no—
268C22×C4×C17—21no—
269C22×C4×C17—21no—
270C22×C4×C17—21no—
271C22×C4×C17—21no—
272C22×C4×C17—21no—
273C22×C4×C17—21no—
274C22×C4×C17—21no—
275C22×C4×C17—21no—
276C22×C4×C17—21no—
277C22×C4×C17—21no—
278C22×C4×C17—21no—
279C22×C4×C17—21no—
280C22×C4×C17—21no—
281C22×C4×C17—21no—
282C22×C4×C17—21no—
283C22×C4×C17—21no—
284C22×C4×C17—21no—
285C22×C4×C17—21no—
286C22×C4×C17—21no—
287C22×C4×C17—21no—
288C22×C4×C17—21no—
289C22×C4×C17—21no—
290C22×C4×C17—21no—
291C22×C4×C17—21no—
292C22×C4×C17—21no—
293C22×C4×C17—21no—
294C22×C4×C17—21no—
295C22×C4×C17—21no—
296C22×C4×C17—21no—
297C22×C4×C17—21no—
298C22×C4×C17—21no—
299C22×C4×C17—21no—
300C22×C4×C17—21no—
301C22×C4×C17—21no—
302C22×C4×C17—21no—
303C22×C4×C17—21no—
304C22×C4×C17—21no—
305C22×C4×C17—21no—
306C22×C4×C17—21no—
307C22×C4×C17—21no—
308C22×C4×C17—21no—
309C22×C4×C17—44no—
310C22×C4×C17—44no—
311C22×C4×C17—44no—
312C22×C4×C17—44no—
313C22×C4×C17—44no—
314C22×C4×C17—44no—
315C22×C4×C17C2×D412yes—
316C22×C4×C17C2×D412yes—
317C22×C4×C17C2×D412yes—
318C22×C4×C17C2×D412yes—
319C22×C4×C17C2×D412yes—
320C22×C4×C17C2×D412yes—
321C22×C4×C17#4112yes—
322C22×C4×C17#4112yes—
323C4⋊C4×C17—44no—
324C4⋊C4×C17—44no—
325C4⋊C4×C17—44no—
326C22⋊C4×C17—44no—
327C22⋊C4×C17—44no—
328C22⋊C4×C17—44no—
329C22⋊C4×C17—44no—
330C22⋊C4×C17—44no—
331C22⋊C4×C17—44no—
332C22⋊C4×C17—44no—
333C22⋊C4×C17—44no—
334C22⋊C4×C17—44no—
335C22⋊C4×C17—44no—
336C22⋊C4×C17—44no—
337C22⋊C4×C17—44no—
338C22⋊C4×C17—44no—
339C22⋊C4×C17—44no—
340#16512C1711yesmaximal, characteristic, direct product factor, Sylow
341C23×C17—22no—
342C23×C17—22no—
343C23×C17—22no—
344C23×C17—22no—
345C23×C17—22no—
346C23×C17—22no—
347C23×C17—22no—
348C23×C17—22no—
349C23×C17—22no—
350C23×C17—22no—
351C23×C17—22no—
352C23×C17—22no—
353C23×C17—22no—
354C23×C17—22no—
355C23×C17—22no—
356C23×C17—22no—
357C23×C17—22no—
358C23×C17—22no—
359C23×C17—22no—
360C23×C17—22no—
361C23×C17—22no—
362C23×C17—22no—
363C23×C17—22no—
364C23×C17—22no—
365C23×C17—22no—
366C23×C17—22no—
367C23×C17—22no—
368C23×C17—22no—
369C23×C17—22no—
370C23×C17—22no—
371C23×C17—22no—
372C23×C17—22no—
373C23×C17—41no—
374C23×C17—41no—
375C23×C17—41no—
376C23×C17—41no—
377C23×C17—41no—
378C23×C17—41no—
379C23×C17—41no—
380C23×C17—41no—
381C23×C17—41no—
382C23×C17—41no—
383C23×C17—41no—
384C23×C17—41no—
385C23×C17—41no—
386C23×C17—41no—
387C23×C17—41no—
388C23×C17—41no—
389C23×C17—41no—
390C23×C17—41no—
391C23×C17—41no—
392C23×C17—41no—
393C23×C17—41no—
394C23×C17—41no—
395C23×C17—41no—
396C23×C17—41no—
397C23×C17—41no—
398C23×C17—41no—
399C23×C17—41no—
400C23×C17—41no—
401C23×C17—41no—
402C23×C17—41no—
403C23×C17—41no—
404C23×C17—41no—
405C23×C17—41no—
406C23×C17—41no—
407C23×C17—41no—
408C23×C17—41no—
409C23×C17—41no—
410C23×C17—41no—
411C23×C17—41no—
412C23×C17—41no—
413C23×C17—41no—
414C23×C17—41no—
415C23×C17—41no—
416C23×C17—41no—
417C23×C17—41no—
418C23×C17—41no—
419C23×C17—41no—
420C23×C17—41no—
421C23×C17—41no—
422C23×C17—41no—
423C23×C17—41no—
424C23×C17—41no—
425C23×C17—41no—
426C23×C17—41no—
427C23×C17—41no—
428C23×C17—41no—
429C23×C17—41no—
430C23×C17—41no—
431C23×C17—41no—
432C23×C17—41no—
433C23×C17—41no—
434C23×C17—41no—
435C23×C17—41no—
436C23×C17—41no—
437C23×C17—41no—
438C23×C17—41no—
439C23×C17—41no—
440C23×C17—41no—
441C23×C17—41no—
442C23×C17—41no—
443C23×C17—41no—
444C23×C17—41no—
445C23×C17#12114yes—
446C23×C17C22×D411yescharacteristic
447C23×C17C22×D411yescharacteristic
448C23×C17C22×D411yescharacteristic
449C23×C17C2×#4111yescharacteristic
450C23×C17C2×#4111yescharacteristic
451C23×C17C2×#4111yescharacteristic
452C23×C17C2×#4111yescharacteristic
453C23×C17H(5,𝔽2)11yescharacteristic
454C23×C17H(5,𝔽2)11yescharacteristic
455C23×C17H(5,𝔽2)11yescharacteristic
456C23×C17H(5,𝔽2)11yescharacteristic
457C23×C17H(5,𝔽2)11yescharacteristic
458C23×C17H(5,𝔽2)11yescharacteristic
459C23×C17H(5,𝔽2)11yescharacteristic
460C23×C172−1+411yescharacteristic
461D4×C17—416no—
462D4×C17—416no—
463D4×C17—416no—
464C2×C4×C17—22no—
465C2×C4×C17—22no—
466C2×C4×C17—22no—
467C2×C4×C17—22no—
468C2×C4×C17—22no—
469C2×C4×C17—22no—
470C2×C4×C17—22no—
471C2×C4×C17—22no—
472C2×C4×C17—22no—
473C2×C4×C17—22no—
474C2×C4×C17—22no—
475C2×C4×C17—22no—
476C2×C4×C17—22no—
477C2×C4×C17—22no—
478C2×C4×C17—22no—
479C2×C4×C17—22no—
480C2×C4×C17—22no—
481C2×C4×C17—22no—
482C2×C4×C17—22no—
483C2×C4×C17—22no—
484C2×C4×C17—22no—
485C2×C4×C17—416no—
486C2×C4×C17—41no—
487C2×C4×C17—41no—
488C2×C4×C17—41no—
489C2×C4×C17—41no—
490C2×C4×C17—41no—
491C2×C4×C17—41no—
492C2×C4×C17—41no—
493C2×C4×C17—41no—
494C2×C4×C17—41no—
495C2×C4×C17—41no—
496C2×C4×C17—41no—
497C2×C4×C17—41no—
498C2×C4×C17—41no—
499C2×C4×C17—41no—
500C2×C4×C17—41no—
501C2×C4×C17—41no—
502C2×C4×C17—41no—
503C2×C4×C17—41no—
504C2×C4×C17—41no—
505C2×C4×C17—41no—
506C2×C4×C17—41no—
507C2×C4×C17—41no—
508C2×C4×C17—41no—
509C2×C4×C17—41no—
510C2×C4×C17—41no—
511C2×C4×C17—41no—
512C2×C4×C17—41no—
513C2×C4×C17—41no—
514C2×C4×C17—41no—
515C2×C4×C17—41no—
516C2×C4×C17—41no—
517C2×C4×C17—41no—
518C2×C4×C17—41no—
519C2×C4×C17—41no—
520C2×C4×C17—41no—
521C2×C4×C17—41no—
522C2×C4×C17—41no—
523C2×C4×C17—41no—
524C2×C4×C17—41no—
525C2×C4×C17—41no—
526C2×C4×C17—41no—
527C2×C4×C17—41no—
528C2×C4×C17—41no—
529C2×C4×C17—41no—
530C2×C4×C17—41no—
531C2×C4×C17—41no—
532C2×C4×C17—41no—
533C2×C4×C17—41no—
534C2×C4×C17—41no—
535C2×C4×C17—41no—
536C2×C4×C17—41no—
537C2×C4×C17—41no—
538C2×C4×C17—41no—
539C2×C4×C17—41no—
540C2×C4×C17—41no—
541C2×C4×C17—41no—
542C2×C4×C17—41no—
543C2×C4×C17—41no—
544C2×C4×C17—41no—
545C2×C4×C17—41no—
546C2×C4×C17—41no—
547C2×C4×C17—41no—
548C2×C4×C17#12114yes—
549C2×#394C2×C1711yescharacteristic, complemented
550C2×#394C2×C1711yescharacteristic, complemented
551C2×#392C2×C1711yescharacteristic
552C2×#386C2×C1711yescharacteristic, complemented
553C2×#386C2×C1711yescharacteristic, complemented
554C2×#380C2×C1711yescharacteristic, complemented
555#1443C2×C1711yescharacteristic, complemented
556#1441C2×C1711yescharacteristic, complemented
557#1440C2×C1711yescharacteristic, complemented
558#1440C2×C1711yescharacteristic, complemented
559#1439C2×C1711yescharacteristic, complemented
560#1439C2×C1711yescharacteristic, complemented
561#1439C2×C1711yescharacteristic, complemented
562#1438C2×C1711yescharacteristic, complemented
563#1438C2×C1711yescharacteristic, complemented
564C22×C17—24no—
565C22×C17—24no—
566C22×C17—24no—
567C22×C17—42no—
568C22×C17—42no—
569C22×C17—42no—
570C22×C17—42no—
571C22×C17—42no—
572C22×C17—42no—
573C22×C17—42no—
574C22×C17—42no—
575C22×C17—42no—
576C22×C17—42no—
577C22×C17—42no—
578C22×C17—42no—
579C22×C17—42no—
580C22×C17—42no—
581C22×C17—42no—
582C22×C17—42no—
583C22×C17—42no—
584C22×C17—42no—
585C22×C17—42no—
586C22×C17—42no—
587C22×C17—42no—
588C22×C17—42no—
589C22×C17—42no—
590C22×C17—42no—
591C22×C17—42no—
592C22×C17—42no—
593C22×C17—81no—
594C22×C17—81no—
595C22×C17—81no—
596C22×C17—81no—
597C22×C17—81no—
598C22×C17—81no—
599C22×C17—81no—
600C22×C17—81no—
601C22×C17—81no—
602C22×C17—81no—
603C22×C17—81no—
604C22×C17—81no—
605C22×C17—81no—
606C22×C17—81no—
607C22×C17—81no—
608C22×C17—81no—
609C22×C17C2×#12111yescharacteristic
610C22×C17C2×#12111yescharacteristic
611C22×C17#52511yescharacteristic
612C22×C17#53411yescharacteristic
613C22×C17#53411yescharacteristic
614C22×C17#53411yescharacteristic
615C22×C17#53411yescharacteristic
616C22×C17#53411yescharacteristic
617C22×C17#53511yescharacteristic
618C22×C17#53511yescharacteristic
619C22×C17#53711yescharacteristic
620C22×C17#53811yescharacteristic
621C22×C17#53811yescharacteristic
622C22×C17#53811yescharacteristic
623C22×C17#53811yescharacteristic
624C22×C17#53811yescharacteristic
625C22×C17#53911yescharacteristic
626C22×C17#54011yescharacteristic
627C22×C17#54211yescharacteristic
628C22×C17D4211yescharacteristic
629C22×C17#54611yescharacteristic
630C22×C17#54611yescharacteristic
631C22×C17#54611yescharacteristic
632C22×C17#54711yescharacteristic
633C22×C17#54811yescharacteristic
634C22×C17#55011yescharacteristic
635C22×C17#55111yescharacteristic
636C22×C17#55111yescharacteristic
637C22×C17#55311yescharacteristic
638C22×C17#55311yescharacteristic
639C22×C17#55511yescharacteristic
640C22×C17#56011yescharacteristic
641C22×C17#56011yescharacteristic
642C22×C17#56211yescharacteristic
643C22×C17#56211yescharacteristic
644C4×C17—24no—
645C4×C17—42no—
646C4×C17—42no—
647C4×C17—42no—
648C4×C17—42no—
649C4×C17—42no—
650C4×C17—81no—
651C4×C17—81no—
652C4×C17—81no—
653C4×C17—81no—
654C4×C17—81no—
655C4×C17—81no—
656C23×D4C22×C1711yescharacteristic
657C23×D4C22×C1711yescharacteristic
658C23×D4C22×C1711yescharacteristic
659C24×C4C22×C1711yescharacteristic
660C22×C4⋊C4C22×C1711yescharacteristic
661C22×C4⋊C4C22×C1711yescharacteristic
662C22×C4⋊C4C22×C1711yescharacteristic
663C22×C22⋊C4C22×C1711yescharacteristic
664C22×C22⋊C4C22×C1711yescharacteristic
665C22×C22⋊C4C22×C1711yescharacteristic
666C22×C22⋊C4C22×C1711yescharacteristic
667C22×C22⋊C4C22×C1711yescharacteristic
668C22×C22⋊C4C22×C1711yescharacteristic
669C22×C22⋊C4C22×C1711yescharacteristic
670C22×C22⋊C4C22×C1711yescharacteristic
671C22×C22⋊C4C22×C1711yescharacteristic
672C22×C22⋊C4C22×C1711yescharacteristic
673C22×C22⋊C4C22×C1711yescharacteristic
674C22×C22⋊C4C22×C1711yescharacteristic
675C22×C22⋊C4C22×C1711yescharacteristic
676C22×C22⋊C4C22×C1711yescharacteristic
677#394—24no—
678#394—24no—
679#392—24no—
680#386—24no—
681#386—24no—
682#380—24no—
683C2×#95C22×C1711yescharacteristic
684C2×#95C22×C1711yescharacteristic
685C2×#95C22×C1711yescharacteristic
686C2×#95C22×C1711yescharacteristic
687C2×#95C22×C1711yescharacteristic
688C2×#95C22×C1711yescharacteristic
689C2×#95C22×C1711yescharacteristic
690C2×#95C22×C1711yescharacteristic
691C2×#95C22×C1711yescharacteristic
692C2×#95C22×C1711yescharacteristic
693C2×#95C22×C1711yescharacteristic
694C2×#95C22×C1711yescharacteristic
695C2×#95C22×C1711yescharacteristic
696C2×#95C22×C1711yescharacteristic
697C2×C17—44no—
698C2×C17—82no—
699C2×C17—82no—
700C2×C17#241411yescharacteristic
701C2×C17#241611yescharacteristic
702C2×C17#253411yescharacteristic
703C2×C17#261711yescharacteristic
704C2×C17#261711yescharacteristic
705C2×C17#263011yescharacteristic
706C2×C17#266811yescharacteristic
707C2×C17#267311yescharacteristic
708C2×C17#268611yescharacteristic
709C2×C17#269611yescharacteristic
710C2×C17#270811yescharacteristic
711C2×C17#273011yescharacteristic
712C2×C17#275611yescharacteristic
713C2×C17#277811yescharacteristic
714C2×C17#281311yescharacteristic
715C25C23×C1711yescharacteristic
716C25C23×C1711yescharacteristic
717C25C23×C1711yescharacteristic
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4D4×C1714yes—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4D4×C1714yescomplemented
746C23×C4C23×C1711yescharacteristic
747C23×C4C23×C1711yescharacteristic
748C23×C4C23×C1711yescharacteristic
749C23×C4C23×C1711yescharacteristic
750C23×C4C23×C1711yescharacteristic
751C23×C4C23×C1711yescharacteristic
752C23×C4C23×C1711yescharacteristic
753C23×C4C23×C1711yescharacteristic
754C23×C4C23×C1711yescharacteristic
755C23×C4C23×C1711yescharacteristic
756C23×C4C23×C1711yescharacteristic
757C23×C4C23×C1711yescharacteristic
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—41no—
761C2×C4⋊C4—41no—
762C2×C4⋊C4—41no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C4⋊C4—41no—
766C2×C4⋊C4D4×C1714yescomplemented
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823C17#1651211yescharacteristic, direct product factor, Sylow
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24C2×D4×C1712yes—
865C24C2×D4×C1712yes—
866C24C2×D4×C1712yes—
867C24#41×C1712yes—
868C24#41×C1712yes—
869C24C24×C1711yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—28no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4C2×D4×C1712yes—
975C22×C4C2×D4×C1712yes—
976C22×C4C2×D4×C1712yes—
977C22×C4C2×D4×C1712yes—
978C22×C4C2×D4×C1712yes—
979C22×C4C2×D4×C1712yes—
980C22×C4#41×C1712yes—
981C22×C4#41×C1712yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C4⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23C17×#12114yes—
1104C23C22×D4×C1711yescharacteristic
1105C23C22×D4×C1711yescharacteristic
1106C23C22×D4×C1711yescharacteristic
1107C23C2×#41×C1711yescharacteristic
1108C23C2×#41×C1711yescharacteristic
1109C23C2×#41×C1711yescharacteristic
1110C23C2×#41×C1711yescharacteristic
1111C23C17×H(5,𝔽2)11yescharacteristic
1112C23C17×H(5,𝔽2)11yescharacteristic
1113C23C17×H(5,𝔽2)11yescharacteristic
1114C23C17×H(5,𝔽2)11yescharacteristic
1115C23C17×H(5,𝔽2)11yescharacteristic
1116C23C17×H(5,𝔽2)11yescharacteristic
1117C23C17×H(5,𝔽2)11yescharacteristic
1118C23C17×2−1+411yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—416no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4C17×#12114yes—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22C2×C17×#12111yescharacteristic
1253C22C2×C17×#12111yescharacteristic
1254C22C17×#52511yescharacteristic
1255C22C17×#53411yescharacteristic
1256C22C17×#53411yescharacteristic
1257C22C17×#53411yescharacteristic
1258C22C17×#53411yescharacteristic
1259C22C17×#53411yescharacteristic
1260C22C17×#53511yescharacteristic
1261C22C17×#53511yescharacteristic
1262C22C17×#53711yescharacteristic
1263C22C17×#53811yescharacteristic
1264C22C17×#53811yescharacteristic
1265C22C17×#53811yescharacteristic
1266C22C17×#53811yescharacteristic
1267C22C17×#53811yescharacteristic
1268C22C17×#53911yescharacteristic
1269C22C17×#54011yescharacteristic
1270C22C17×#54211yescharacteristic
1271C22D42×C1711yescharacteristic
1272C22C17×#54611yescharacteristic
1273C22C17×#54611yescharacteristic
1274C22C17×#54611yescharacteristic
1275C22C17×#54711yescharacteristic
1276C22C17×#54811yescharacteristic
1277C22C17×#55011yescharacteristic
1278C22C17×#55111yescharacteristic
1279C22C17×#55111yescharacteristic
1280C22C17×#55311yescharacteristic
1281C22C17×#55311yescharacteristic
1282C22C17×#55511yescharacteristic
1283C22C17×#56011yescharacteristic
1284C22C17×#56011yescharacteristic
1285C22C17×#56211yescharacteristic
1286C22C17×#56211yescharacteristic
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C17×#241411yescharacteristic
1303C2C17×#241611yescharacteristic
1304C2C17×#253411yescharacteristic
1305C2C17×#261711yescharacteristic
1306C2C17×#261711yescharacteristic
1307C2C17×#263011yescharacteristic
1308C2C17×#266811yescharacteristic
1309C2C17×#267311yescharacteristic
1310C2C17×#268611yescharacteristic
1311C2C17×#269611yescharacteristic
1312C2C17×#270811yescharacteristic
1313C2C17×#273011yescharacteristic
1314C2C17×#275611yescharacteristic
1315C2C17×#277811yescharacteristic
1316C2C17×#281311yescharacteristic
subgroupG/H
center, socleC24×C17C24
commutator, Frattini, cosocleC24C24×C17
prime radicalC2×C17×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C17 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C17×#394C2semidirect
2. C2×C17×#394C2semidirect
4. C2×C17×#386C2semidirect
5. C2×C17×#386C2semidirect
6. C2×C17×#380C2semidirect
7. C17×#1443C2semidirect
8. C17×#1441C2semidirect
9. C17×#1440C2semidirect
10. C17×#1440C2semidirect
11. C17×#1439C2semidirect
12. C17×#1439C2semidirect
13. C17×#1439C2semidirect
14. C17×#1438C2semidirect
15. C17×#1438C2semidirect
87. C23×C4×C17D4semidirect
108. C2×C4⋊C4×C17D4semidirect
340. #16512C17direct (N × H)
549. C2×#394C2×C17semidirect
550. C2×#394C2×C17semidirect
552. C2×#386C2×C17semidirect
553. C2×#386C2×C17semidirect
554. C2×#380C2×C17semidirect
555. #1443C2×C17semidirect
556. #1441C2×C17semidirect
557. #1440C2×C17semidirect
558. #1440C2×C17semidirect
559. #1439C2×C17semidirect
560. #1439C2×C17semidirect
561. #1439C2×C17semidirect
562. #1438C2×C17semidirect
563. #1438C2×C17semidirect
745. C23×C4D4×C17semidirect
766. C2×C4⋊C4D4×C17semidirect
823. C17#16512direct (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×#3922
C2×C17×#3862
C2×C17×#3802
C17×#14432
C17×#14412
C17×#14402
C17×#14392
C17×#14382
#1651217