Finite Group Databasebeta

← C17×#17578 #16875322

Subgroups — C17×#17578 #16875322

Order 4352.

1418 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C17×C22⋊Q8C211yesmaximal, characteristic
2C2×C17×#407C211yesmaximal, characteristic
3C17×#2280C211yesmaximal, characteristic
4C17×#1520C214yesmaximal, complemented
5C17×#1511C214yesmaximal, complemented
6C17×#1508C214yesmaximal, complemented
7C23×Q8×C17C411yescharacteristic, complemented
8C24×C4×C17C2211yescharacteristic
9C22×M16×C17—21no—
10C2×C17×C22⋊Q8—21no—
11C2×C17×C22⋊Q8—21no—
12C2×C17×C22⋊Q8—21no—
13C2×C17×C22⋊Q8—21no—
14C2×C17×C22⋊Q8—21no—
15C2×C17×C22⋊Q8—21no—
16C2×C17×C22⋊Q8C412yescomplemented
17C2×C17×C22⋊Q8C412yescomplemented
18C2×C17×C22⋊Q8C412yescomplemented
19C2×C17×C22⋊Q8C2212yes—
20C2×C17×C22⋊Q8C2212yes—
21C2×C17×C22⋊Q8C2212yes—
22C2×C17×#117—21no—
23C22×C4⋊C4×C17—21no—
24C22×C4⋊C4×C17C411yescharacteristic, complemented
25C22×C22⋊C4×C17—21no—
26C17×#407—21no—
27C17×#407—21no—
28C17×#407C2212yes—
29C17×#407C2212yes—
30C2×C17×C22⋊C8—21no—
31C2×C17×C22⋊C8C2212yes—
32C17×#381C2212yes—
33C17×#380—21no—
34C17×#380C2212yes—
35C17×#379—21no—
36C4×C22⋊C4×C17—21no—
37C4×C22⋊C4×C17C2212yes—
38C17×#328C22116yescomplemented
39C25×C17D411yescharacteristic
40C22×Q8×C17—21no—
41C22×Q8×C17—21no—
42C22×Q8×C17—21no—
43C22×Q8×C17—44no—
44C22×Q8×C17C2×C412yes—
45C22×Q8×C17C2×C412yes—
46C22×Q8×C17C2×C412yes—
47C23×C4×C17—21no—
48C23×C4×C17—21no—
49C23×C4×C17—44no—
50C23×C4×C17C2×C411yescharacteristic
51C23×C4×C17C2×C411yescharacteristic
52C23×C4×C17C2×C411yescharacteristic
53C23×C4×C17C2×C411yescharacteristic
54C23×C4×C17D411yescharacteristic
55C23×C4×C17D411yescharacteristic
56C23×C4×C17D411yescharacteristic
57C23×C4×C17D411yescharacteristic
58C23×C4×C17D411yescharacteristic
59C23×C4×C17D411yescharacteristic
60C23×C4×C17D411yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C2×M16×C17—22no—
65C2×M16×C17—22no—
66C2×M16×C17—44no—
67C22×C8×C17—22no—
68C17×C22⋊Q8—22no—
69C17×C22⋊Q8—22no—
70C17×C22⋊Q8—22no—
71C17×C22⋊Q8—22no—
72C17×C22⋊Q8—22no—
73C17×C22⋊Q8—22no—
74C17×C22⋊Q8—22no—
75C17×C22⋊Q8—22no—
76C17×C22⋊Q8—22no—
77C17×C22⋊Q8—22no—
78C17×C22⋊Q8—22no—
79C17×C22⋊Q8—22no—
80C17×C22⋊Q8C2×C414yes—
81C17×C22⋊Q8C2×C414yes—
82C17×C22⋊Q8C2×C414yes—
83C17×C22⋊Q8C2314yes—
84C17×#117—44no—
85C2×C4⋊C4×C17—22no—
86C2×C4⋊C4×C17—22no—
87C2×C4⋊C4×C17—22no—
88C2×C4⋊C4×C17—21no—
89C2×C4⋊C4×C17—21no—
90C2×C4⋊C4×C17—21no—
91C2×C4⋊C4×C17—22no—
92C2×C4⋊C4×C17—22no—
93C2×C4⋊C4×C17—22no—
94C2×C4⋊C4×C17—22no—
95C2×C4⋊C4×C17C2×C412yes—
96C2×C4⋊C4×C17C2×C412yes—
97C2×C4⋊C4×C17C2×C412yes—
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×C42×C17—22no—
108C17×C22⋊C8—22no—
109C17×C22⋊C8—22no—
110C17×C22⋊C8—22no—
111C17×C22⋊C8C2314yes—
112C17×#95—22no—
113C17×#95C2314yes—
114C24×C17—24no—
115C24×C17—42no—
116C24×C17—42no—
117C24×C17C22⋊C411yescharacteristic
118C24×C17C22⋊C411yescharacteristic
119C24×C17C22⋊C411yescharacteristic
120C24×C17C22⋊C411yescharacteristic
121C24×C17C2×D411yescharacteristic
122C24×C17C2×D411yescharacteristic
123C24×C17C2×D411yescharacteristic
124C2×Q8×C17—22no—
125C2×Q8×C17—22no—
126C2×Q8×C17—22no—
127C2×Q8×C17—44no—
128C2×Q8×C17—44no—
129C2×Q8×C17—44no—
130C2×Q8×C17—44no—
131C2×Q8×C17—44no—
132C2×Q8×C17—44no—
133C2×Q8×C17C22×C414yes—
134C22×C4×C17—24no—
135C22×C4×C17—24no—
136C22×C4×C17—24no—
137C22×C4×C17—22no—
138C22×C4×C17—22no—
139C22×C4×C17—22no—
140C22×C4×C17—22no—
141C22×C4×C17—22no—
142C22×C4×C17—22no—
143C22×C4×C17—24no—
144C22×C4×C17—42no—
145C22×C4×C17—42no—
146C22×C4×C17—42no—
147C22×C4×C17—42no—
148C22×C4×C17—42no—
149C22×C4×C17—42no—
150C22×C4×C17—42no—
151C22×C4×C17—42no—
152C22×C4×C17—42no—
153C22×C4×C17—42no—
154C22×C4×C17—42no—
155C22×C4×C17—44no—
156C22×C4×C17—44no—
157C22×C4×C17C22⋊C411yescharacteristic
158C22×C4×C17C22⋊C411yescharacteristic
159C22×C4×C17C22⋊C411yescharacteristic
160C22×C4×C17C22⋊C411yescharacteristic
161C22×C4×C17C22⋊C411yescharacteristic
162C22×C4×C17C22⋊C411yescharacteristic
163C22×C4×C17C22⋊C411yescharacteristic
164C22×C4×C17C22⋊C411yescharacteristic
165C22×C4×C17C22⋊C411yescharacteristic
166C22×C4×C17C22⋊C411yescharacteristic
167C22×C4×C17C22⋊C411yescharacteristic
168C22×C4×C17C22⋊C411yescharacteristic
169C22×C4×C17C22×C411yescharacteristic
170C22×C4×C17C22×C411yescharacteristic
171C22×C4×C17C22×C411yescharacteristic
172C22×C4×C17C22×C411yescharacteristic
173C22×C4×C17C22×C411yescharacteristic
174C22×C4×C17C22×C411yescharacteristic
175C22×C4×C17C2×D411yescharacteristic
176C22×C4×C17C2×D411yescharacteristic
177C22×C4×C17C2×D411yescharacteristic
178C22×C4×C17C2×D411yescharacteristic
179C22×C4×C17C2×D411yescharacteristic
180C22×C4×C17C2×D411yescharacteristic
181C22×C4×C17C2×D411yescharacteristic
182C22×C4×C17C2×D411yescharacteristic
183C22×C4×C17C2×D411yescharacteristic
184C22×C4×C17C2411yescharacteristic
185M16×C17—44no—
186M16×C17—44no—
187C2×C8×C17—24no—
188C2×C8×C17—44no—
189C4⋊C4×C17—22no—
190C4⋊C4×C17—22no—
191C4⋊C4×C17—22no—
192C4⋊C4×C17—24no—
193C4⋊C4×C17—24no—
194C4⋊C4×C17—24no—
195C4⋊C4×C17—24no—
196C4⋊C4×C17—44no—
197C4⋊C4×C17C22×C414yes—
198C22⋊C4×C17—24no—
199C22⋊C4×C17—24no—
200C22⋊C4×C17—24no—
201C22⋊C4×C17—24no—
202C22⋊C4×C17—44no—
203C22⋊C4×C17—44no—
204C22⋊C4×C17—44no—
205C42×C17—44no—
206#17578C1711yesmaximal, characteristic, direct product factor, Sylow
207C23×C17—22no—
208C23×C17—22no—
209C23×C17—22no—
210C23×C17—22no—
211C23×C17—22no—
212C23×C17—22no—
213C23×C17—22no—
214C23×C17—22no—
215C23×C17—22no—
216C23×C17—22no—
217C23×C17—22no—
218C23×C17—22no—
219C23×C17—41no—
220C23×C17—41no—
221C23×C17—41no—
222C23×C17—41no—
223C23×C17—41no—
224C23×C17—41no—
225C23×C17—41no—
226C23×C17—41no—
227C23×C17—416no—
228C23×C17C2×C22⋊C411yescharacteristic
229C23×C17C2×C22⋊C411yescharacteristic
230C23×C17C2×C22⋊C411yescharacteristic
231C23×C17C2×C22⋊C411yescharacteristic
232C23×C17C2×C22⋊C411yescharacteristic
233C23×C17C2×C22⋊C411yescharacteristic
234C23×C17#13714yes—
235C23×C17C22×D411yescharacteristic
236Q8×C17—44no—
237Q8×C17—44no—
238Q8×C17—44no—
239Q8×C17—44no—
240C2×C4×C17—22no—
241C2×C4×C17—22no—
242C2×C4×C17—22no—
243C2×C4×C17—22no—
244C2×C4×C17—22no—
245C2×C4×C17—22no—
246C2×C4×C17—22no—
247C2×C4×C17—22no—
248C2×C4×C17—22no—
249C2×C4×C17—22no—
250C2×C4×C17—22no—
251C2×C4×C17—22no—
252C2×C4×C17—22no—
253C2×C4×C17—22no—
254C2×C4×C17—22no—
255C2×C4×C17—24no—
256C2×C4×C17—24no—
257C2×C4×C17—41no—
258C2×C4×C17—41no—
259C2×C4×C17—41no—
260C2×C4×C17—41no—
261C2×C4×C17—41no—
262C2×C4×C17—41no—
263C2×C4×C17—41no—
264C2×C4×C17—41no—
265C2×C4×C17—41no—
266C2×C4×C17—41no—
267C2×C4×C17—41no—
268C2×C4×C17—41no—
269C2×C4×C17—44no—
270C2×C4×C17—44no—
271C2×C4×C17—44no—
272C2×C4×C17—44no—
273C2×C4×C17—44no—
274C2×C4×C17—44no—
275C2×C4×C17—44no—
276C2×C4×C17—44no—
277C2×C4×C17—44no—
278C2×C4×C17#9914yes—
279C2×C4×C17C2×C22⋊C411yescharacteristic
280C2×C4×C17C2×C22⋊C411yescharacteristic
281C2×C4×C17C2×C22⋊C411yescharacteristic
282C2×C4×C17C2×C22⋊C411yescharacteristic
283C2×C4×C17C2×C22⋊C411yescharacteristic
284C2×C4×C17C2×C22⋊C411yescharacteristic
285C2×C4×C17C23×C411yescharacteristic
286C2×C4×C17C22×D411yescharacteristic
287C8×C17—44no—
288C22×C22⋊Q8C2×C1711yescharacteristic
289C2×#407C2×C1711yescharacteristic
290#2280C2×C1711yescharacteristic
291#1520C2×C1714yescomplemented
292#1511C2×C1714yescomplemented
293#1508C2×C1714yescomplemented
294C22×C17—28no—
295C22×C17—21no—
296C22×C17—21no—
297C22×C17—21no—
298C22×C17—21no—
299C22×C17—21no—
300C22×C17—21no—
301C22×C17—21no—
302C22×C17—21no—
303C22×C17—21no—
304C22×C17—21no—
305C22×C17—21no—
306C22×C17—21no—
307C22×C17—21no—
308C22×C17—21no—
309C22×C17—21no—
310C22×C17—21no—
311C22×C17—44no—
312C22×C17—44no—
313C22×C17—44no—
314C22×C17—44no—
315C22×C17—44no—
316C22×C17—44no—
317C22×C17C2×#9912yes—
318C22×C17#41912yes—
319C22×C17#41912yes—
320C22×C17#42112yes—
321C22×C17C22×C22⋊C411yescharacteristic
322C22×C17C2×#13712yes—
323C4×C17—21no—
324C4×C17—21no—
325C4×C17—21no—
326C4×C17—21no—
327C4×C17—21no—
328C4×C17—21no—
329C4×C17—44no—
330C4×C17—44no—
331C4×C17—84no—
332C4×C17C2×#9912yes—
333C4×C17C2×#9912yes—
334C23×Q8C4×C1711yescharacteristic, complemented
335C24×C4C22×C1711yescharacteristic
336C22×M16—21no—
337C2×C22⋊Q8—21no—
338C2×C22⋊Q8—21no—
339C2×C22⋊Q8—21no—
340C2×C22⋊Q8—21no—
341C2×C22⋊Q8—21no—
342C2×C22⋊Q8—21no—
343C2×C22⋊Q8C4×C1712yescomplemented
344C2×C22⋊Q8C4×C1712yescomplemented
345C2×C22⋊Q8C4×C1712yescomplemented
346C2×C22⋊Q8C22×C1712yes—
347C2×C22⋊Q8C22×C1712yes—
348C2×C22⋊Q8C22×C1712yes—
349C2×#117—21no—
350C22×C4⋊C4—21no—
351C22×C4⋊C4C4×C1711yescharacteristic, complemented
352C22×C22⋊C4—21no—
353#407—21no—
354#407—21no—
355#407C22×C1712yes—
356#407C22×C1712yes—
357C2×C22⋊C8—21no—
358C2×C22⋊C8C22×C1712yes—
359#381C22×C1712yes—
360#380—21no—
361#380C22×C1712yes—
362#379—21no—
363C4×C22⋊C4—21no—
364C4×C22⋊C4C22×C1712yes—
365#328C22×C17116yescomplemented
366C2×C17—22no—
367C2×C17—22no—
368C2×C17—22no—
369C2×C17—22no—
370C2×C17—22no—
371C2×C17—41no—
372C2×C17—41no—
373C2×C17C22×#9911yescharacteristic
374C2×C17C2×#41911yescharacteristic
375C2×C17C2×#42111yescharacteristic
376C25D4×C1711yescharacteristic
377C22×Q8—21no—
378C22×Q8—21no—
379C22×Q8—21no—
380C22×Q8—44no—
381C22×Q8C2×C4×C1712yes—
382C22×Q8C2×C4×C1712yes—
383C22×Q8C2×C4×C1712yes—
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—44no—
387C23×C4C2×C4×C1711yescharacteristic
388C23×C4C2×C4×C1711yescharacteristic
389C23×C4C2×C4×C1711yescharacteristic
390C23×C4C2×C4×C1711yescharacteristic
391C23×C4D4×C1711yescharacteristic
392C23×C4D4×C1711yescharacteristic
393C23×C4D4×C1711yescharacteristic
394C23×C4D4×C1711yescharacteristic
395C23×C4D4×C1711yescharacteristic
396C23×C4D4×C1711yescharacteristic
397C23×C4D4×C1711yescharacteristic
398C23×C4C23×C1711yescharacteristic
399C23×C4C23×C1711yescharacteristic
400C23×C4C23×C1711yescharacteristic
401C2×M16—22no—
402C2×M16—22no—
403C2×M16—44no—
404C22×C8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8C2×C4×C1714yes—
418C22⋊Q8C2×C4×C1714yes—
419C22⋊Q8C2×C4×C1714yes—
420C22⋊Q8C23×C1714yes—
421#117—44no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4C2×C4×C1712yes—
433C2×C4⋊C4C2×C4×C1712yes—
434C2×C4⋊C4C2×C4×C1712yes—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C42—22no—
445C22⋊C8—22no—
446C22⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8C23×C1714yes—
449#95—22no—
450#95C23×C1714yes—
451C17#1757811yescharacteristic, direct product factor, Sylow
452C24—24no—
453C24—42no—
454C24—42no—
455C24C22⋊C4×C1711yescharacteristic
456C24C22⋊C4×C1711yescharacteristic
457C24C22⋊C4×C1711yescharacteristic
458C24C22⋊C4×C1711yescharacteristic
459C24C2×D4×C1711yescharacteristic
460C24C2×D4×C1711yescharacteristic
461C24C2×D4×C1711yescharacteristic
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—22no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8C22×C4×C1714yes—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4C22⋊C4×C1711yescharacteristic
496C22×C4C22⋊C4×C1711yescharacteristic
497C22×C4C22⋊C4×C1711yescharacteristic
498C22×C4C22⋊C4×C1711yescharacteristic
499C22×C4C22⋊C4×C1711yescharacteristic
500C22×C4C22⋊C4×C1711yescharacteristic
501C22×C4C22⋊C4×C1711yescharacteristic
502C22×C4C22⋊C4×C1711yescharacteristic
503C22×C4C22⋊C4×C1711yescharacteristic
504C22×C4C22⋊C4×C1711yescharacteristic
505C22×C4C22⋊C4×C1711yescharacteristic
506C22×C4C22⋊C4×C1711yescharacteristic
507C22×C4C22×C4×C1711yescharacteristic
508C22×C4C22×C4×C1711yescharacteristic
509C22×C4C22×C4×C1711yescharacteristic
510C22×C4C22×C4×C1711yescharacteristic
511C22×C4C22×C4×C1711yescharacteristic
512C22×C4C22×C4×C1711yescharacteristic
513C22×C4C2×D4×C1711yescharacteristic
514C22×C4C2×D4×C1711yescharacteristic
515C22×C4C2×D4×C1711yescharacteristic
516C22×C4C2×D4×C1711yescharacteristic
517C22×C4C2×D4×C1711yescharacteristic
518C22×C4C2×D4×C1711yescharacteristic
519C22×C4C2×D4×C1711yescharacteristic
520C22×C4C2×D4×C1711yescharacteristic
521C22×C4C2×D4×C1711yescharacteristic
522C22×C4C24×C1711yescharacteristic
523M16—44no—
524M16—44no—
525C2×C8—24no—
526C2×C8—44no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—44no—
535C4⋊C4C22×C4×C1714yes—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—24no—
540C22⋊C4—44no—
541C22⋊C4—44no—
542C22⋊C4—44no—
543C42—44no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—416no—
565C23C2×C22⋊C4×C1711yescharacteristic
566C23C2×C22⋊C4×C1711yescharacteristic
567C23C2×C22⋊C4×C1711yescharacteristic
568C23C2×C22⋊C4×C1711yescharacteristic
569C23C2×C22⋊C4×C1711yescharacteristic
570C23C2×C22⋊C4×C1711yescharacteristic
571C23C17×#13714yes—
572C23C22×D4×C1711yescharacteristic
573Q8—44no—
574Q8—44no—
575Q8—44no—
576Q8—44no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—44no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—44no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4C17×#9914yes—
616C2×C4C2×C22⋊C4×C1711yescharacteristic
617C2×C4C2×C22⋊C4×C1711yescharacteristic
618C2×C4C2×C22⋊C4×C1711yescharacteristic
619C2×C4C2×C22⋊C4×C1711yescharacteristic
620C2×C4C2×C22⋊C4×C1711yescharacteristic
621C2×C4C2×C22⋊C4×C1711yescharacteristic
622C2×C4C23×C4×C1711yescharacteristic
623C2×C4C22×D4×C1711yescharacteristic
624C8—44no—
625C22—28no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—44no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22—44no—
648C22C2×C17×#9912yes—
649C22C17×#41912yes—
650C22C17×#41912yes—
651C22C17×#42112yes—
652C22C22×C22⋊C4×C1711yescharacteristic
653C22C2×C17×#13712yes—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—44no—
661C4—44no—
662C4—84no—
663C4C2×C17×#9912yes—
664C4C2×C17×#9912yes—
665C2—22no—
666C2—22no—
667C2—22no—
668C2—22no—
669C2—22no—
670C2—41no—
671C2—41no—
672C2C22×C17×#9911yescharacteristic
673C2C2×C17×#41911yescharacteristic
674C2C2×C17×#42111yescharacteristic
subgroupG/H
center, socleC22×C17C22×C22⋊C4
commutatorC2×C4C23×C4×C17
Frattini, cosocleC22×C4C24×C17
prime radicalC25×C17D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C17 ◁ C24×C4×C17 ◁ G

Complements

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

NH ≅ G/Ntype
4. C17×#1520C2semidirect
5. C17×#1511C2semidirect
6. C17×#1508C2semidirect
7. C23×Q8×C17C4semidirect
16. C2×C17×C22⋊Q8C4semidirect
17. C2×C17×C22⋊Q8C4semidirect
18. C2×C17×C22⋊Q8C4semidirect
24. C22×C4⋊C4×C17C4semidirect
38. C17×#328C22semidirect
206. #17578C17direct (N × H)
291. #1520C2×C17semidirect
292. #1511C2×C17semidirect
293. #1508C2×C17semidirect
334. C23×Q8C4×C17semidirect
343. C2×C22⋊Q8C4×C17semidirect
344. C2×C22⋊Q8C4×C17semidirect
345. C2×C22⋊Q8C4×C17semidirect
351. C22×C4⋊C4C4×C17semidirect
365. #328C22×C17semidirect
451. C17#17578direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C17×C22⋊Q82
C2×C17×#4072
C17×#22802
C17×#15202
C17×#15112
C17×#15082
#1757817