Finite Group Databasebeta

← C2×#14542575 #17942792

Subgroups — C2×#14542575 #17942792

Order 4352.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587694C211yesmaximal, characteristic, complemented
2C22×#10587696C211yesmaximal, characteristic, complemented
3#14542575C2132yesmaximal, direct product factor
4C2×#11763471C211yesmaximal, characteristic, complemented
5C2×#11763470C211yesmaximal, characteristic, complemented
6C2×#11763466C211yesmaximal, characteristic, complemented
7C2×#11763456C213yesmaximal, complemented
8C2×#11763455C213yesmaximal, complemented
9C2×#11763452C213yesmaximal, complemented
10C2×#11763450C213yesmaximal, complemented
11C2×#11763382C213yesmaximal, complemented
12C2×#11763375C213yesmaximal, complemented
13C2×#11763356C213yesmaximal, complemented
14C2×#124×D17C213yesmaximal, complemented
15C2×C4×#63256C211yesmaximal, characteristic, complemented
16C2×C17×#548C211yesmaximal, characteristic, complemented
17C2×#10587694—216no—
18C2×#10587694C22116yescomplemented
19C2×#10587696—216no—
20C2×#10587696C22116yescomplemented
21C22×#63256C2211yescharacteristic
22C22×#63256C2211yescharacteristic
23C22×#63256C2213yescomplemented
24C22×#63252C2213yes—
25C22×#63252C2213yescomplemented
26C22×#63252C2213yescomplemented
27C22×Q8×D17C2213yescomplemented
28C22×Q8×D17C2211yescharacteristic, complemented
29C23×D68C2213yes—
30C22×D4×D17C2213yes—
31C22×D4×D17C2213yes—
32#11763471C22116yescomplemented
33#11763470C22116yescomplemented
34#11763466C22116yescomplemented
35#11763456C22148yescomplemented
36#11763455C22148yescomplemented
37#11763452C22148yescomplemented
38#11763450C22148yescomplemented
39#11763382C22148yescomplemented
40#11763375C22148yescomplemented
41#11763356C22148yescomplemented
42C2×#10587574C2213yescomplemented
43C2×#10587626C2213yescomplemented
44C2×#10587633C2213yescomplemented
45C2×#10587561C2213yescomplemented
46C2×#10587622C2213yescomplemented
47C2×#10587571C2216yescomplemented
48C2×#10587571C2213yescomplemented
49C2×#10587571C2211yescharacteristic, complemented
50#124×D17C22148yescomplemented
51C2×#10587580C2216yescomplemented
52C2×#10587569C2216yescomplemented
53C2×#10587583C2213yescomplemented
54C2×#10587610C2213yescomplemented
55C2×#10587632C2213yescomplemented
56C2×#10587581C2213yescomplemented
57C2×#10587581C2213yescomplemented
58C2×#10587616C2213yescomplemented
59C2×#10587570C2213yescomplemented
60C2×#10587570C2213yescomplemented
61C2×#10587624C2213yescomplemented
62C2×#10587624C2213yescomplemented
63C2×#10587568C2216yescomplemented
64C2×#10587623C2216yescomplemented
65C4×#63256C22116yescomplemented
66C2×Q8×Dic17C2211yescharacteristic, complemented
67C2×C4×D68C2213yescomplemented
68C2×C4×D68C2213yescomplemented
69C2×#10587579C2213yescomplemented
70C2×C4×C22⋊D17C2213yescomplemented
71C2×C4×C22⋊D17C2213yescomplemented
72C2×#10587578C2213yescomplemented
73C2×C22⋊C4×D17C2216yescomplemented
74C2×C22⋊C4×D17C2216yescomplemented
75C2×C42×D17C2213yescomplemented
76C22×#41×C17C2211yescharacteristic
77C23×Q8×C17C2211yescharacteristic, complemented
78C17×#548C22116yescomplemented
79C2×C17×#124C2213yescomplemented
80C2×C17×C22⋊Q8C2213yescomplemented
81C2×C17×#121C2213yescomplemented
82C2×C4×Q8×C17C2211yescharacteristic, complemented
83C2×C4×D4×C17C2213yescomplemented
84C24×D17C2316yes—
85C2×#41×C17—28no—
86C2×#41×C17C2318yes—
87C22×Q8×C17—28no—
88C22×Q8×C17C2313yes—
89C22×Q8×C17C2311yescharacteristic
90C22×Q8×C17C2318yescomplemented
91C22×D4×C17C2313yes—
92C22×D4×C17C2313yes—
93C23×C4×C17C2313yes—
94C23×C4×C17C2313yes—
95C22×C22⋊D17C2313yes—
96C22×C22⋊D17C2313yes—
97C22×C22⋊D17C2313yes—
98C22×C22⋊D17C2311yescharacteristic
99C22×C22⋊D17C2313yes—
100C22×C22⋊D17C2313yes—
101#10587696—2128no—
102#10587694—2128no—
103C2×#63256—28no—
104C2×#63256—224no—
105C2×#63256D4116yescomplemented
106C2×#63256C2318yes—
107C2×#63256C2318yes—
108C2×#63256C23124yescomplemented
109C2×Q8×D17—28no—
110C2×Q8×D17—224no—
111C2×Q8×D17C2318yescomplemented
112C2×Q8×D17C23124yescomplemented
113C2×D4×D17—224no—
114C2×D4×D17—224no—
115C2×D4×D17C23124yes—
116C2×D4×D17C23124yes—
117C2×#63252—224no—
118C2×#63252—224no—
119C2×#63252—224no—
120C2×#63252C23124yes—
121C2×#63252C23124yescomplemented
122C2×#63252C23124yescomplemented
123C22×D68—224no—
124C22×D68C2313yes—
125C22×D68C2313yes—
126C22×D68C2313yes—
127C22×D68C23124yes—
128C22×D68C2313yes—
129C22×D68C2313yes—
130C22×C4×D17C2316yes—
131C22×C4×D17C2313yes—
132C22×C4×D17C2313yes—
133C22×C4×D17C2313yes—
134C22×C4×D17C2313yes—
135C22×C4×D17C2313yes—
136C22×Dic34C2313yes—
137C22×Dic34C2313yes—
138C22×Dic34C2311yescharacteristic
139C17×#124C23124yescomplemented
140C17×C22⋊Q8C23124yescomplemented
141C17×#121C23124yescomplemented
142C4×Q8×C17C2318yescomplemented
143C4×D4×C17C23124yescomplemented
144C2×C4⋊C4×C17C2313yes—
145C2×C4⋊C4×C17C2313yes—
146C2×C22⋊C4×C17C2311yescharacteristic
147C2×C22⋊C4×C17C2313yes—
148C2×C22⋊C4×C17C2316yes—
149C2×C42×C17C2313yes—
150C2×C22⋊Dic17C2313yes—
151C2×C22⋊Dic17C2316yes—
152C2×C22⋊Dic17C2311yescharacteristic
153#10587633C23124yescomplemented
154#10587632C23124yescomplemented
155Q8×Dic17C2318yescomplemented
156#10587626C23124yescomplemented
157#10587624C23124yescomplemented
158#10587624C23124yescomplemented
159#10587623C23148yescomplemented
160#10587622C23124yescomplemented
161#10587616C23124yescomplemented
162C4×C22⋊D17C23124yescomplemented
163C4×C22⋊D17C23124yescomplemented
164C2×#63227C2313yes—
165C2×#63227C2313yes—
166C2×#63227C2316yes—
167C2×#63227C2316yes—
168C2×#63227C2316yes—
169C2×#63227C2311yescharacteristic
170C2×#63227C2311yescharacteristic
171C2×C4⋊Dic17C2313yes—
172C2×C4⋊Dic17C2313yes—
173#10587610C23124yescomplemented
174C2×#63225C2313yes—
175C2×#63225C2313yes—
176C2×C4×Dic17C2311yescharacteristic
177C2×C4×Dic17C2313yes—
178C2×C4×Dic17C2313yes—
179#10587583C23124yescomplemented
180#10587581C23124yescomplemented
181#10587581C23124yescomplemented
182#10587580C23148yescomplemented
183#10587579C23124yescomplemented
184#10587578C23124yescomplemented
185#10587574C23124yescomplemented
186#10587571C23124yescomplemented
187#10587571C23148yescomplemented
188#10587571C2318yescomplemented
189#10587570C23124yescomplemented
190#10587570C23124yescomplemented
191#10587569C23148yescomplemented
192#10587568C23148yescomplemented
193C22⋊C4×D17C23148yescomplemented
194C22⋊C4×D17C23148yescomplemented
195#10587561C23124yescomplemented
196C4×D68C23124yescomplemented
197C4×D68C23124yescomplemented
198C42×D17C23124yescomplemented
199C24×C17C2411yescharacteristic
200C24×C17C2413yes—
201C23×D17—224no—
202C23×D17—412no—
203C23×D17—412no—
204C23×D17C2411yescharacteristic
205C23×D17C2413yes—
206C23×D17C2413yes—
207C23×D17C24124yes—
208#41×C17—232no—
209C2×Q8×C17—232no—
210C2×Q8×C17—212no—
211C2×Q8×C17C2×D418yes—
212C2×Q8×C17C24112yes—
213C2×Q8×C17C2414yes—
214C2×D4×C17—212no—
215C2×D4×C17—46no—
216C2×D4×C17C24112yes—
217C2×D4×C17C24112yes—
218C22×C4×C17—212no—
219C22×C4×C17—212no—
220C22×C4×C17C24112yes—
221C22×C4×C17C2413yes—
222C22×C4×C17C2411yescharacteristic
223C22×C4×C17C2411yescharacteristic
224C22×C4×C17C2413yes—
225C22×C4×C17C24112yes—
226C22×C4×C17C2413yes—
227C2×C22⋊D17—212no—
228C2×C22⋊D17—212no—
229C2×C22⋊D17—24no—
230C2×C22⋊D17—212no—
231C2×C22⋊D17—46no—
232C2×C22⋊D17—46no—
233C2×C22⋊D17C24112yes—
234C2×C22⋊D17C24112yes—
235C2×C22⋊D17C24112yes—
236C2×C22⋊D17C2414yes—
237C2×C22⋊D17C24112yes—
238C2×C22⋊D17C24112yes—
239C22×Dic17C2413yes—
240C22×Dic17C2411yescharacteristic
241C22×Dic17C2411yescharacteristic
242C22×Dic17C2413yes—
243C22×Dic17C2411yescharacteristic
244#63256—232no—
245#63256—296no—
246#63256C2×D4164yescomplemented
247Q8×D17—232no—
248Q8×D17—296no—
249D4×D17—296no—
250D4×D17—296no—
251#63252—296no—
252#63252—296no—
253#63252—296no—
254C2×D68—212no—
255C2×D68—212no—
256C2×D68—212no—
257C2×D68—296no—
258C2×D68—46no—
259C2×D68C2×D4124yes—
260C2×D68C24112yes—
261C2×D68C24112yes—
262C2×D68C24112yes—
263C2×D68C24112yes—
264C2×D68C24112yes—
265C2×C4×D17—224no—
266C2×C4×D17—212no—
267C2×C4×D17—212no—
268C2×C4×D17—46no—
269C2×C4×D17—46no—
270C2×C4×D17C2×D4124yes—
271C2×C4×D17C24112yes—
272C2×C4×D17C24112yes—
273C2×C4×D17C24124yes—
274C2×C4×D17C24112yes—
275C2×C4×D17C24112yes—
276C2×C4×D17C24112yes—
277C2×Dic34—212no—
278C2×Dic34—24no—
279C2×Dic34—212no—
280C2×Dic34C2414yes—
281C2×Dic34C24112yes—
282C2×Dic34C24112yes—
283C4⋊C4×C17C24112yes—
284C4⋊C4×C17C24112yes—
285C22⋊C4×C17C24124yes—
286C22⋊C4×C17C24112yes—
287C22⋊C4×C17C2414yes—
288C42×C17C24112yes—
289C22⋊Dic17C24112yes—
290C22⋊Dic17C24124yes—
291C22⋊Dic17C2414yes—
292#63227C2414yes—
293#63227C24112yes—
294#63227C24124yes—
295#63227C24124yes—
296#63227C24112yes—
297#63227C24124yes—
298#63227C2414yes—
299C4⋊Dic17C24112yes—
300C4⋊Dic17C24112yes—
301#63225C24112yes—
302#63225C24112yes—
303C4×Dic17C2414yes—
304C4×Dic17C24112yes—
305C4×Dic17C24112yes—
306C2×#3500—171nomaximal, Sylow
307C23×C17—22no—
308C23×C17—26no—
309C23×C17—22no—
310C23×C17—26no—
311C23×C17—22no—
312C23×C17—26no—
313C23×C17C2516yes—
314C23×C17C2512yes—
315C23×C17C2511yescharacteristic
316C22×D17—26no—
317C22×D17—26no—
318C22×D17—22no—
319C22×D17—26no—
320C22×D17—22no—
321C22×D17—26no—
322C22×D17—22no—
323C22×D17—26no—
324C22×D17—248no—
325C22×D17—424no—
326C22×D17—424no—
327C22×D17—848no—
328C22×D17C22×D4112yes—
329C22×D17C2512yes—
330C22×D17C2516yes—
331C22×D17C2516yes—
332Q8×C17—224no—
333Q8×C17C22×D4116yes—
334D4×C17—224no—
335D4×C17—412no—
336C2×C4×C17—26no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—26no—
340C2×C4×C17—224no—
341C2×C4×C17—224no—
342C2×C4×C17C22×D4112yes—
343C2×C4×C17C2512yes—
344C2×C4×C17C2516yes—
345C2×C4×C17C2516yes—
346C2×C4×C17C2512yes—
347C2×C4×C17C2516yes—
348C22⋊D17—224no—
349C22⋊D17—224no—
350C22⋊D17—28no—
351C22⋊D17—224no—
352C22⋊D17—412no—
353C22⋊D17—412no—
354C2×Dic17—26no—
355C2×Dic17—22no—
356C2×Dic17—22no—
357C2×Dic17—26no—
358C2×Dic17C22×D414yes—
359C2×Dic17C2512yes—
360C2×Dic17C2516yes—
361C2×Dic17C2516yes—
362C2×Dic17C2512yes—
363C2×Dic17C2512yes—
364D68—224no—
365D68—224no—
366D68—224no—
367D68—412no—
368D68C22×D4148yes—
369C4×D17—248no—
370C4×D17—224no—
371C4×D17—224no—
372C4×D17—412no—
373C4×D17—412no—
374C4×D17C22×D4148yes—
375Dic34—224no—
376Dic34—28no—
377Dic34—224no—
378C22×2−1+4—171no—
379C22×H(5,𝔽2)—171no—
380#3500—1732no—
381C2×#548—171no—
382C2×#548—171no—
383C2×#548—171no—
384C2×#548D1711yescharacteristic, complemented
385C2×#546—173no—
386C2×#546—173no—
387C2×#546—173no—
388C2×#546—173no—
389C2×#536—173no—
390C2×#535—173no—
391C2×#532—173no—
392C22×#124—173no—
393C2×C4×#41—171no—
394C22×C17—22no—
395C22×C17—26no—
396C22×C17—22no—
397C22×C17—26no—
398C22×C17—22no—
399C22×C17—26no—
400C22×C17—412no—
401C22×C17—44no—
402C22×C17C23×D412yes—
403C22×C17#58512yes—
404C22×C17#58512yes—
405C22×C17C2611yescharacteristic
406C2×D17—26no—
407C2×D17—26no—
408C2×D17—224no—
409C2×D17—22no—
410C2×D17—26no—
411C2×D17—22no—
412C2×D17—26no—
413C2×D17—22no—
414C2×D17—26no—
415C2×D17—44no—
416C2×D17—412no—
417C2×D17—848no—
418C2×D17C23×D4112yes—
419C4×C17—26no—
420C4×C17—22no—
421C4×C17—22no—
422C4×C17—26no—
423C4×C17C23×D4112yes—
424Dic17—26no—
425Dic17—22no—
426Dic17—22no—
427Dic17—26no—
428Dic17C23×D414yes—
429C2×2−1+4—1716no—
430C2×2−1+4—3416no—
431C2×H(5,𝔽2)—1716no—
432C2×H(5,𝔽2)—3416no—
433C22×#41—171no—
434C22×#41—171no—
435C22×#41—173no—
436C22×#41—173no—
437C22×#41—173no—
438C22×#41—173no—
439C22×#41C2×D1711yescharacteristic
440C23×Q8—173no—
441C23×Q8—171no—
442C23×Q8C2×D1711yescharacteristic, complemented
443C23×D4—173no—
444C23×D4—173no—
445C23×D4—173no—
446#548—1716no—
447#548—1716no—
448#548—1716no—
449#548C2×D17116yescomplemented
450#546—1748no—
451#546—1748no—
452#546—1748no—
453#546—1748no—
454#536—1748no—
455#535—1748no—
456#532—1748no—
457C2×C4⋊Q8—173no—
458C2×#127—173no—
459C2×#124—173no—
460C2×#124—173no—
461C2×#124—1748no—
462C2×#124—173no—
463C2×#124—176no—
464C2×#124—171no—
465C2×#124—173no—
466C2×#124C2×D1713yescomplemented
467C2×#123—176no—
468C2×#123—176no—
469C2×C22⋊Q8—173no—
470C2×C22⋊Q8—173no—
471C2×C22⋊Q8—173no—
472C2×C22⋊Q8C2×D1713yescomplemented
473C2×#121—173no—
474C2×#121—173no—
475C2×#121—173no—
476C2×#121—173no—
477C2×#121—173no—
478C2×#121—173no—
479C2×#121—173no—
480C2×#121C2×D1713yescomplemented
481C2×#120—176no—
482C2×#120—176no—
483C4×#41—1716no—
484C2×C4×Q8—171no—
485C2×C4×Q8C2×D1711yescharacteristic, complemented
486C2×C4×D4—173no—
487C2×C4×D4—173no—
488C2×C4×D4—173no—
489C2×C4×D4—173no—
490C2×C4×D4—173no—
491C2×C4×D4C2×D1713yescomplemented
492C2×#117—173no—
493C22×C22⋊C4—176no—
494C22×C22⋊C4—176no—
495C22×C42—173no—
496C2×C17—46no—
497C2×C17—42no—
498C2×C17#350014yescomplemented
499C2×C17C24×D411yescharacteristic
500C2×C17C2×#58511yescharacteristic
501C2×C17C2×#58511yescharacteristic
502D17—212no—
503D17—42no—
504D17—46no—
505C25—176no—
5062−1+4—34128no—
507H(5,𝔽2)—34128no—
508C2×#41—28no—
509C2×#41—1716no—
510C2×#41—178no—
511C2×#41—1724no—
512C2×#41—178no—
513C2×#41—1724no—
514C2×#41—1724no—
515C2×#41—1724no—
516C2×#41—3424no—
517C2×#41—3424no—
518C2×#41—3424no—
519C2×#41—3424no—
520C2×#41—348no—
521C2×#41C22×D1718yes—
522C22×Q8—28no—
523C22×Q8—1724no—
524C22×Q8—178no—
525C22×Q8—173no—
526C22×Q8—173no—
527C22×Q8—171no—
528C22×Q8—3424no—
529C22×Q8—348no—
530C22×Q8C22×D1713yes—
531C22×Q8C22×D1711yescharacteristic
532C22×Q8C22×D1718yescomplemented
533C22×D4—173no—
534C22×D4—173no—
535C22×D4—173no—
536C22×D4—171no—
537C22×D4—173no—
538C22×D4—173no—
539C22×D4—1724no—
540C22×D4—1724no—
541C22×D4—173no—
542C22×D4—173no—
543C22×D4—173no—
544C22×D4—173no—
545C22×D4—1724no—
546C22×D4—173no—
547C22×D4—3424no—
548C22×D4—3424no—
549C22×D4—3424no—
550C22×D4C22×D1713yes—
551C22×D4C22×D1713yes—
552C23×C4—173no—
553C23×C4—176no—
554C23×C4—173no—
555C23×C4—173no—
556C23×C4—173no—
557C23×C4—173no—
558C23×C4C22×D1713yes—
559C23×C4C22×D1713yes—
560C4⋊Q8—1724no—
561#127—1724no—
562#124—1724no—
563#124—1724no—
564#124—1724no—
565#124—1748no—
566#124—178no—
567#124—1724no—
568#124C22×D17124yescomplemented
569#123—1748no—
570#123—1748no—
571C22⋊Q8—1724no—
572C22⋊Q8—1724no—
573C22⋊Q8—1724no—
574C22⋊Q8C22×D17124yescomplemented
575#121—1724no—
576#121—1724no—
577#121—1724no—
578#121—1724no—
579#121—1724no—
580#121—1724no—
581#121—1724no—
582#121C22×D17124yescomplemented
583#120—1748no—
584#120—1748no—
585C4×Q8—178no—
586C4×Q8C22×D1718yescomplemented
587C4×D4—1724no—
588C4×D4—1724no—
589C4×D4—1724no—
590C4×D4—1724no—
591C4×D4—1724no—
592C4×D4C22×D17124yescomplemented
593#117—1724no—
594C2×C4⋊C4—173no—
595C2×C4⋊C4—173no—
596C2×C4⋊C4—173no—
597C2×C4⋊C4—173no—
598C2×C4⋊C4C22×D1713yes—
599C2×C4⋊C4C22×D1713yes—
600C2×C22⋊C4—173no—
601C2×C22⋊C4—176no—
602C2×C22⋊C4—171no—
603C2×C22⋊C4—173no—
604C2×C22⋊C4—173no—
605C2×C22⋊C4—176no—
606C2×C22⋊C4—176no—
607C2×C22⋊C4—176no—
608C2×C22⋊C4—171no—
609C2×C22⋊C4—171no—
610C2×C22⋊C4—1748no—
611C2×C22⋊C4—1748no—
612C2×C22⋊C4C22×D1713yes—
613C2×C22⋊C4C22×D1716yes—
614C2×C22⋊C4C22×D1711yescharacteristic
615C2×C42—173no—
616C2×C42—173no—
617C2×C42—171no—
618C2×C42—1724no—
619C2×C42C22×D1713yes—
620C17C2×#350011yescharacteristic, complemented, Sylow
621C24—173no—
622C24—173no—
623C24—171no—
624C24—1724no—
625C24—3424no—
626C24—6812no—
627C24—6812no—
628C24C23×D1713yes—
629C24C23×D1711yescharacteristic
630#41—232no—
631#41—1764no—
632#41—3496no—
633#41—3496no—
634#41—3496no—
635#41—3496no—
636#41—3432no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—1712no—
640C2×Q8—1712no—
641C2×Q8—174no—
642C2×Q8—3412no—
643C2×Q8—344no—
644C2×Q8—3496no—
645C2×Q8—3432no—
646C2×Q8—3412no—
647C2×Q8D4×D1718yes—
648C2×Q8C23×D17112yes—
649C2×Q8C23×D1714yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—1712no—
653C2×D4—1712no—
654C2×D4—1712no—
655C2×D4—174no—
656C2×D4—1712no—
657C2×D4—1712no—
658C2×D4—1724no—
659C2×D4—1712no—
660C2×D4—1712no—
661C2×D4—1712no—
662C2×D4—1712no—
663C2×D4—1712no—
664C2×D4—3496no—
665C2×D4—3412no—
666C2×D4—3412no—
667C2×D4—3496no—
668C2×D4—3412no—
669C2×D4—344no—
670C2×D4—3496no—
671C2×D4—3412no—
672C2×D4—3412no—
673C2×D4—3412no—
674C2×D4—686no—
675C2×D4—686no—
676C2×D4—686no—
677C2×D4C23×D17112yes—
678C2×D4C23×D17112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—171no—
682C22×C4—1724no—
683C22×C4—1712no—
684C22×C4—171no—
685C22×C4—173no—
686C22×C4—173no—
687C22×C4—171no—
688C22×C4—1724no—
689C22×C4—1712no—
690C22×C4—1712no—
691C22×C4—1712no—
692C22×C4—1712no—
693C22×C4—3424no—
694C22×C4—3412no—
695C22×C4—3412no—
696C22×C4—686no—
697C22×C4—686no—
698C22×C4C23×D17112yes—
699C22×C4C23×D17112yes—
700C22×C4C23×D1711yescharacteristic
701C22×C4C23×D1713yes—
702C22×C4C23×D1713yes—
703C22×C4C23×D1711yescharacteristic
704C22×C4C23×D1713yes—
705C4⋊C4—1712no—
706C4⋊C4—1712no—
707C4⋊C4—1712no—
708C4⋊C4—1712no—
709C4⋊C4C23×D17112yes—
710C4⋊C4C23×D17112yes—
711C22⋊C4—1712no—
712C22⋊C4—1724no—
713C22⋊C4—174no—
714C22⋊C4—1712no—
715C22⋊C4—1712no—
716C22⋊C4—1724no—
717C22⋊C4—1724no—
718C22⋊C4—1724no—
719C22⋊C4—174no—
720C22⋊C4—174no—
721C22⋊C4C23×D17112yes—
722C22⋊C4C23×D17124yes—
723C22⋊C4C23×D1714yes—
724C42—174no—
725C42—1712no—
726C42—1712no—
727C42C23×D17112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—1712no—
735C23—176no—
736C23—176no—
737C23—172no—
738C23—3448no—
739C23—346no—
740C23—346no—
741C23—342no—
742C23—346no—
743C23—342no—
744C23—346no—
745C23—342no—
746C23—346no—
747C23—6824no—
748C23—6824no—
749C23—13648no—
750C23C24×D1716yes—
751C23C24×D1712yes—
752C23C24×D1711yescharacteristic
753Q8—224no—
754Q8—3424no—
755Q8—348no—
756Q8—3424no—
757Q8C2×D4×D17116yes—
758D4—224no—
759D4—412no—
760D4—1748no—
761D4—3424no—
762D4—3424no—
763D4—3424no—
764D4—348no—
765D4—3424no—
766D4—3424no—
767D4—3424no—
768D4—6812no—
769D4—6812no—
770D4—6812no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—174no—
778C2×C4—172no—
779C2×C4—1748no—
780C2×C4—172no—
781C2×C4—176no—
782C2×C4—176no—
783C2×C4—172no—
784C2×C4—3448no—
785C2×C4—342no—
786C2×C4—346no—
787C2×C4—342no—
788C2×C4—346no—
789C2×C4—3424no—
790C2×C4—3424no—
791C2×C4—6812no—
792C2×C4—6812no—
793C2×C4C2×D4×D17112yes—
794C2×C4C24×D1712yes—
795C2×C4C24×D1716yes—
796C2×C4C24×D1716yes—
797C2×C4C24×D1712yes—
798C2×C4C24×D1716yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—1712no—
808C22—346no—
809C22—346no—
810C22—3424no—
811C22—342no—
812C22—346no—
813C22—342no—
814C22—346no—
815C22—342no—
816C22—346no—
817C22—6812no—
818C22—684no—
819C22—13648no—
820C22C22×D4×D1712yes—
821C22#1176364512yes—
822C22#1176364612yes—
823C22C25×D1711yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—174no—
829C4—342no—
830C4—346no—
831C4—342no—
832C4—346no—
833C4C22×D4×D17112yes—
834C2—46no—
835C2—42no—
836C2—3412no—
837C2—686no—
838C2—682no—
839C2#1454257514yesdirect product factor
840C2C23×D4×D1711yescharacteristic
841C2C2×#1176364511yescharacteristic
842C2C2×#1176364611yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#548C2
socleC23×C17C25
hypercenterC2×#548D17
hypocenterC17C2×#3500
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#10587694C2semidirect
2. C22×#10587696C2semidirect
3. #14542575C2direct (N × H)
4. C2×#11763471C2semidirect
5. C2×#11763470C2semidirect
6. C2×#11763466C2semidirect
7. C2×#11763456C2semidirect
8. C2×#11763455C2semidirect
9. C2×#11763452C2semidirect
10. C2×#11763450C2semidirect
11. C2×#11763382C2semidirect
12. C2×#11763375C2semidirect
13. C2×#11763356C2semidirect
14. C2×#124×D17C2semidirect
15. C2×C4×#63256C2semidirect
16. C2×C17×#548C2semidirect
18. C2×#10587694C22semidirect
20. C2×#10587696C22semidirect
23. C22×#63256C22semidirect
25. C22×#63252C22semidirect
26. C22×#63252C22semidirect
27. C22×Q8×D17C22semidirect
28. C22×Q8×D17C22semidirect
32. #11763471C22semidirect
33. #11763470C22semidirect
34. #11763466C22semidirect
35. #11763456C22semidirect
36. #11763455C22semidirect
37. #11763452C22semidirect
38. #11763450C22semidirect
39. #11763382C22semidirect
40. #11763375C22semidirect
41. #11763356C22semidirect
42. C2×#10587574C22semidirect
43. C2×#10587626C22semidirect
44. C2×#10587633C22semidirect
45. C2×#10587561C22semidirect
46. C2×#10587622C22semidirect
47. C2×#10587571C22semidirect
48. C2×#10587571C22semidirect
49. C2×#10587571C22semidirect
50. #124×D17C22semidirect
51. C2×#10587580C22semidirect
52. C2×#10587569C22semidirect
53. C2×#10587583C22semidirect
54. C2×#10587610C22semidirect
55. C2×#10587632C22semidirect
56. C2×#10587581C22semidirect
57. C2×#10587581C22semidirect
58. C2×#10587616C22semidirect
59. C2×#10587570C22semidirect
60. C2×#10587570C22semidirect
61. C2×#10587624C22semidirect
62. C2×#10587624C22semidirect
63. C2×#10587568C22semidirect
64. C2×#10587623C22semidirect
65. C4×#63256C22semidirect
66. C2×Q8×Dic17C22semidirect
67. C2×C4×D68C22semidirect
68. C2×C4×D68C22semidirect
69. C2×#10587579C22semidirect
70. C2×C4×C22⋊D17C22semidirect
71. C2×C4×C22⋊D17C22semidirect
72. C2×#10587578C22semidirect
73. C2×C22⋊C4×D17C22semidirect
74. C2×C22⋊C4×D17C22semidirect
75. C2×C42×D17C22semidirect
77. C23×Q8×C17C22semidirect
78. C17×#548C22semidirect
79. C2×C17×#124C22semidirect
80. C2×C17×C22⋊Q8C22semidirect
81. C2×C17×#121C22semidirect
82. C2×C4×Q8×C17C22semidirect
83. C2×C4×D4×C17C22semidirect
90. C22×Q8×C17C23semidirect
105. C2×#63256D4semidirect
108. C2×#63256C23semidirect
111. C2×Q8×D17C23semidirect
112. C2×Q8×D17C23semidirect
121. C2×#63252C23semidirect
122. C2×#63252C23semidirect
139. C17×#124C23semidirect
140. C17×C22⋊Q8C23semidirect
141. C17×#121C23semidirect
142. C4×Q8×C17C23semidirect
143. C4×D4×C17C23semidirect
153. #10587633C23semidirect
154. #10587632C23semidirect
155. Q8×Dic17C23semidirect
156. #10587626C23semidirect
157. #10587624C23semidirect
158. #10587624C23semidirect
159. #10587623C23semidirect
160. #10587622C23semidirect
161. #10587616C23semidirect
162. C4×C22⋊D17C23semidirect
163. C4×C22⋊D17C23semidirect
173. #10587610C23semidirect
179. #10587583C23semidirect
180. #10587581C23semidirect
181. #10587581C23semidirect
182. #10587580C23semidirect
183. #10587579C23semidirect
184. #10587578C23semidirect
185. #10587574C23semidirect
186. #10587571C23semidirect
187. #10587571C23semidirect
188. #10587571C23semidirect
189. #10587570C23semidirect
190. #10587570C23semidirect
191. #10587569C23semidirect
192. #10587568C23semidirect
193. C22⋊C4×D17C23semidirect
194. C22⋊C4×D17C23semidirect
195. #10587561C23semidirect
196. C4×D68C23semidirect
197. C4×D68C23semidirect
198. C42×D17C23semidirect
246. #63256C2×D4semidirect
384. C2×#548D17semidirect
442. C23×Q8C2×D17semidirect
449. #548C2×D17semidirect
466. C2×#124C2×D17semidirect
472. C2×C22⋊Q8C2×D17semidirect
480. C2×#121C2×D17semidirect
485. C2×C4×Q8C2×D17semidirect
491. C2×C4×D4C2×D17semidirect
498. C2×C17#3500semidirect
532. C22×Q8C22×D17semidirect
568. #124C22×D17semidirect
574. C22⋊Q8C22×D17semidirect
582. #121C22×D17semidirect
586. C4×Q8C22×D17semidirect
592. C4×D4C22×D17semidirect
620. C17C2×#3500semidirect
839. C2#14542575direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105876942
C22×#105876962
#145425752
C2×#117634712
C2×#117634702
C2×#117634662
C2×#117634562
C2×#117634552
C2×#117634522
C2×#117634502
C2×#117633822
C2×#117633752
C2×#117633562
C2×#124×D172
C2×C4×#632562
C2×C17×#5482
C2×#350017