Finite Group Databasebeta

← C2×#14542463 #17942729

Subgroups — C2×#14542463 #17942729

Order 4352.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587694C211yesmaximal, characteristic, complemented
2C22×#41×D17C211yesmaximal, characteristic, complemented
3#14542463C2132yesmaximal, direct product factor
4C2×Q8×D68C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D17C211yesmaximal, characteristic, complemented
6C2×#11763466C211yesmaximal, characteristic, complemented
7C2×#11763464C213yesmaximal, complemented
8C2×#11763461C213yesmaximal, complemented
9C2×#11763456C213yesmaximal, complemented
10C2×#11763452C213yesmaximal, complemented
11C2×#11763388C213yesmaximal, complemented
12C2×#11763379C213yesmaximal, complemented
13C2×#11763318C213yesmaximal, complemented
14C2×C22⋊Q8×D17C213yesmaximal, complemented
15C2×#11763291C211yesmaximal, characteristic, complemented
16C2×C17×#548C211yesmaximal, characteristic, complemented
17C2×#10587694—216no—
18C2×#10587694C22116yescomplemented
19C22×#63256C2211yescharacteristic
20C22×#63256C2213yescomplemented
21C22×#63252C2213yes—
22C22×#63252C2213yescomplemented
23C22×#63252C2213yescomplemented
24C22×#63254C2213yes—
25C2×#41×D17—216no—
26C2×#41×D17C22116yescomplemented
27C22×Q8×D17C2211yescharacteristic
28C22×Q8×D17C2213yescomplemented
29C22×Q8×D17C2211yescharacteristic, complemented
30C22×D4×D17C2213yes—
31C23×C4×D17C2213yes—
32Q8×D68C22116yescomplemented
33Q8×C22⋊D17C22116yescomplemented
34#11763466C22116yescomplemented
35#11763464C22148yescomplemented
36#11763461C22148yescomplemented
37#11763456C22148yescomplemented
38#11763452C22148yescomplemented
39#11763388C22148yescomplemented
40#11763379C22148yescomplemented
41C2×#10587555C2213yescomplemented
42C2×#10587630C2213yescomplemented
43C2×#10587622C2213yescomplemented
44#11763318C22148yescomplemented
45C2×#10587580C2213yescomplemented
46C2×#10587569C2216yescomplemented
47C2×#10587569C2216yescomplemented
48C2×#10587569C2213yescomplemented
49C2×#10587583C2213yes—
50C2×#10587583C2213yescomplemented
51C2×#10587610C2213yescomplemented
52C2×#10587610C2213yescomplemented
53C2×#10587582C2213yes—
54C2×#10587564C2213yescomplemented
55C2×#10587564C2216yescomplemented
56C2×#10587632C2213yes—
57C22⋊Q8×D17C22148yescomplemented
58C2×#10587570C2211yescharacteristic
59C2×#10587570C2216yescomplemented
60C2×#10587625C2213yescomplemented
61C2×#10587624C2213yescomplemented
62C2×#10587624C2216yescomplemented
63C2×#10587568C2213yes—
64C2×#10587623C2213yes—
65#11763291C22116yescomplemented
66C2×Q8×Dic17C2211yescharacteristic, complemented
67C2×C4×D68C2213yes—
68C2×C4×D68C2213yescomplemented
69C2×#10587579C2213yescomplemented
70C2×C4×C22⋊D17C2213yes—
71C2×C4×C22⋊D17C2213yescomplemented
72C2×#10587558C2213yescomplemented
73C2×C4⋊C4×D17C2213yescomplemented
74C2×C4⋊C4×D17C2216yescomplemented
75C2×C22⋊C4×D17C2216yes—
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×D17C2313yes—
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⋊D17C2311yescharacteristic
96C22×C22⋊D17C2313yes—
97C22×C22⋊D17C2316yes—
98C22×C22⋊D17C2311yescharacteristic
99C22×C22⋊D17C2313yes—
100C23×Dic17C2313yes—
101#41×D17—2128no—
102#10587694—2128no—
103C2×#63256—224no—
104C2×#63256D4116yescomplemented
105C2×#63256C2318yes—
106C2×#63256C23124yescomplemented
107C2×Q8×D17—28no—
108C2×Q8×D17—28no—
109C2×Q8×D17—224no—
110C2×Q8×D17C2318yes—
111C2×Q8×D17C2318yescomplemented
112C2×Q8×D17C23124yescomplemented
113C2×#63254—224no—
114C2×#63254C23124yes—
115C2×D4×D17—224no—
116C2×D4×D17C23124yes—
117C2×#63252—224no—
118C2×#63252—224no—
119C2×#63252—224no—
120C2×#63252C23124yes—
121C2×#63252C23124yescomplemented
122C2×#63252C23124yescomplemented
123C22×D68C2311yescharacteristic
124C22×D68C2313yes—
125C22×D68C2313yes—
126C22×C4×D17—224no—
127C22×C4×D17C2316yes—
128C22×C4×D17C2313yes—
129C22×C4×D17C2313yes—
130C22×C4×D17C2313yes—
131C22×C4×D17C2311yescharacteristic
132C22×C4×D17C23124yes—
133C22×C4×D17C2316yes—
134C22×C4×D17C2313yes—
135C22×Dic34C2313yes—
136C22×Dic34C2313yes—
137C22×Dic34C2313yes—
138C17×#124C23124yescomplemented
139C17×C22⋊Q8C23124yescomplemented
140C17×#121C23124yescomplemented
141C4×Q8×C17C2318yescomplemented
142C4×D4×C17C23124yescomplemented
143C2×C4⋊C4×C17C2313yes—
144C2×C4⋊C4×C17C2313yes—
145C2×C22⋊C4×C17C2311yescharacteristic
146C2×C22⋊C4×C17C2313yes—
147C2×C22⋊C4×C17C2316yes—
148C2×C42×C17C2313yes—
149C2×C22⋊Dic17C2316yes—
150C2×C22⋊Dic17C2313yes—
151C2×C22⋊Dic17C2313yes—
152#10587632C23124yes—
153Q8×Dic17C2318yescomplemented
154#10587630C23124yescomplemented
155#10587625C23124yescomplemented
156#10587624C23148yescomplemented
157#10587624C23124yescomplemented
158#10587623C23124yes—
159#10587622C23124yescomplemented
160C4×C22⋊D17C23124yes—
161C4×C22⋊D17C23124yescomplemented
162C2×#63227C2313yes—
163C2×#63227C2313yes—
164C2×#63227C2313yes—
165C2×#63227C2313yes—
166C2×#63227C2311yescharacteristic
167C2×#63227C2313yes—
168C2×C4⋊Dic17C2313yes—
169C2×C4⋊Dic17C2316yes—
170C2×C4⋊Dic17C2313yes—
171#10587610C23124yescomplemented
172#10587610C23124yescomplemented
173C2×#63225C2313yes—
174C2×#63225C2313yes—
175C2×#63225C2316yes—
176C2×#63225C2311yescharacteristic
177C2×#63225C2313yes—
178C2×C4×Dic17C2313yes—
179#10587583C23124yes—
180#10587583C23124yescomplemented
181#10587582C23124yes—
182#10587580C23124yescomplemented
183#10587579C23124yescomplemented
184C4⋊C4×D17C23148yescomplemented
185C4⋊C4×D17C23124yescomplemented
186#10587570C2318yes—
187#10587570C23148yescomplemented
188#10587569C23148yescomplemented
189#10587569C23124yescomplemented
190#10587569C23148yescomplemented
191#10587568C23124yes—
192C22⋊C4×D17C23148yes—
193#10587564C23148yescomplemented
194#10587564C23124yescomplemented
195C4×D68C23124yes—
196C4×D68C23124yescomplemented
197#10587558C23124yescomplemented
198#10587555C23124yescomplemented
199C24×C17C2413yes—
200C24×C17C2411yescharacteristic
201C23×D17—212no—
202C23×D17—212no—
203C23×D17—46no—
204C23×D17C2411yescharacteristic
205C23×D17C24112yes—
206C23×D17C2413yes—
207C23×D17C2411yescharacteristic
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×C17C2413yes—
224C22×C4×C17C2411yescharacteristic
225C22×C4×C17C24112yes—
226C22×C4×C17C2413yes—
227C2×C22⋊D17—212no—
228C2×C22⋊D17—224no—
229C2×C22⋊D17—24no—
230C2×C22⋊D17—24no—
231C2×C22⋊D17—46no—
232C2×C22⋊D17C24124yes—
233C2×C22⋊D17C24112yes—
234C2×C22⋊D17C2414yes—
235C2×C22⋊D17C2414yes—
236C2×C22⋊D17C24112yes—
237C22×Dic17—212no—
238C22×Dic17C2413yes—
239C22×Dic17C2413yes—
240C22×Dic17C24112yes—
241C22×Dic17C2413yes—
242C22×Dic17C2411yescharacteristic
243C22×Dic17C2411yescharacteristic
244#63256—296no—
245#63256C2×D4164yescomplemented
246Q8×D17—232no—
247Q8×D17—232no—
248Q8×D17—296no—
249#63254—296no—
250D4×D17—296no—
251#63252—296no—
252#63252—296no—
253#63252—296no—
254C2×D68—212no—
255C2×D68—24no—
256C2×D68C2×D4124yes—
257C2×D68C24112yes—
258C2×D68C2414yes—
259C2×D68C24112yes—
260C2×C4×D17—212no—
261C2×C4×D17—224no—
262C2×C4×D17—212no—
263C2×C4×D17—212no—
264C2×C4×D17—24no—
265C2×C4×D17—296no—
266C2×C4×D17—412no—
267C2×C4×D17C2×D4124yes—
268C2×C4×D17C2414yes—
269C2×C4×D17C24112yes—
270C2×C4×D17C24112yes—
271C2×C4×D17C24112yes—
272C2×C4×D17C24124yes—
273C2×C4×D17C24124yes—
274C2×C4×D17C24112yes—
275C2×Dic34—212no—
276C2×Dic34—212no—
277C2×Dic34—212no—
278C2×Dic34C24112yes—
279C2×Dic34C24112yes—
280C2×Dic34C24112yes—
281C4⋊C4×C17C24112yes—
282C4⋊C4×C17C24112yes—
283C22⋊C4×C17C24124yes—
284C22⋊C4×C17C24112yes—
285C22⋊C4×C17C2414yes—
286C42×C17C24112yes—
287C22⋊Dic17C24124yes—
288C22⋊Dic17C24112yes—
289C22⋊Dic17C24112yes—
290#63227C24112yes—
291#63227C24112yes—
292#63227C24112yes—
293#63227C24112yes—
294#63227C24112yes—
295#63227C2414yes—
296C4⋊Dic17C24112yes—
297C4⋊Dic17C24124yes—
298C4⋊Dic17C24112yes—
299#63225C2414yes—
300#63225C24112yes—
301#63225C24112yes—
302#63225C24124yes—
303#63225C24112yes—
304C4×Dic17C24112yes—
305C2×#3489—171nomaximal, Sylow
306C23×C17—26no—
307C23×C17—22no—
308C23×C17—22no—
309C23×C17—26no—
310C23×C17—26no—
311C23×C17—22no—
312C23×C17C2516yes—
313C23×C17C2512yes—
314C23×C17C2511yescharacteristic
315C22×D17—22no—
316C22×D17—26no—
317C22×D17—26no—
318C22×D17—22no—
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—224no—
323C22×D17—224no—
324C22×D17—412no—
325C22×D17—448no—
326C22×D17C22×D4112yes—
327C22×D172−1+414yescomplemented
328C22×D17C2512yes—
329C22×D17C2516yes—
330C22×D17C2512yes—
331Q8×C17—224no—
332Q8×C17C22×D4116yes—
333D4×C17—224no—
334D4×C17—412no—
335C2×C4×C17—26no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—26no—
339C2×C4×C17—224no—
340C2×C4×C17—224no—
341C2×C4×C17C22×D4112yes—
342C2×C4×C17C2512yes—
343C2×C4×C17C2516yes—
344C2×C4×C17C2516yes—
345C2×C4×C17C2512yes—
346C2×C4×C17C2516yes—
347C22⋊D17—224no—
348C22⋊D17—248no—
349C22⋊D17—28no—
350C22⋊D17—28no—
351C22⋊D17—412no—
352C2×Dic17—26no—
353C2×Dic17—26no—
354C2×Dic17—22no—
355C2×Dic17—26no—
356C2×Dic17—224no—
357C2×Dic17C22×D414yes—
358C2×Dic17C2516yes—
359C2×Dic17C2516yes—
360C2×Dic17C2512yes—
361C2×Dic17C2516yes—
362C2×Dic17C2512yes—
363D68—224no—
364D68—28no—
365D68C22×D4148yes—
366C4×D17—224no—
367C4×D17—248no—
368C4×D17—224no—
369C4×D17—224no—
370C4×D17—28no—
371C4×D17—424no—
372C4×D17C22×D4148yes—
373Dic34—224no—
374Dic34—224no—
375Dic34—224no—
376C22×2−1+4—171no—
377C23×#41—171no—
378#3489—1732no—
379C2×D4×Q8—171no—
380C2×D4×Q8—171no—
381C2×#548—171no—
382C2×#548D1711yescharacteristic, complemented
383C2×#547—173no—
384C2×#547—173no—
385C2×#546—173no—
386C2×#546—173no—
387C2×#537—173no—
388C2×#536—173no—
389C2×#525—173no—
390C22×C22⋊Q8—173no—
391C2×#520—171no—
392C22×C17—26no—
393C22×C17—22no—
394C22×C17—22no—
395C22×C17—26no—
396C22×C17—26no—
397C22×C17—22no—
398C22×C17—412no—
399C22×C17—44no—
400C22×C17C23×D412yes—
401C22×C17C2×2−1+412yes—
402C22×C17#58512yes—
403C22×C17C2611yescharacteristic
404C2×D17—22no—
405C2×D17—26no—
406C2×D17—26no—
407C2×D17—22no—
408C2×D17—28no—
409C2×D17—224no—
410C2×D17—22no—
411C2×D17—22no—
412C2×D17—22no—
413C2×D17—448no—
414C2×D17—44no—
415C2×D17C23×D4112yes—
416C2×D17C2×2−1+414yescomplemented
417C4×C17—26no—
418C4×C17—22no—
419C4×C17—22no—
420C4×C17—26no—
421C4×C17C23×D4112yes—
422Dic17—26no—
423Dic17—26no—
424Dic17—22no—
425Dic17—26no—
426Dic17C23×D414yes—
427C2×2−1+4—1716no—
428C2×2−1+4—3416no—
429C22×#41—1716no—
430C22×#41—171no—
431C22×#41—173no—
432C22×#41—173no—
433C22×#41—173no—
434C22×#41—173no—
435C22×#41—173no—
436C22×#41—3416no—
437C22×#41C2×D1711yescharacteristic
438C23×Q8—171no—
439C23×Q8—173no—
440C23×Q8—171no—
441C23×Q8C2×D1711yescharacteristic, complemented
442C23×D4—173no—
443C24×C4—173no—
444D4×Q8—1716no—
445D4×Q8—1716no—
446#548—1716no—
447#548C2×D17116yescomplemented
448#547—1748no—
449#547—1748no—
450#546—1748no—
451#546—1748no—
452#537—1748no—
453#536—1748no—
454C2×C4⋊Q8—173no—
455C2×C4⋊Q8—173no—
456C2×#124—173no—
457C2×#124C2×D1713yescomplemented
458#525—1748no—
459C2×#123—173no—
460C2×#123—173no—
461C2×#123—176no—
462C2×#123—176no—
463C2×C22⋊Q8—173no—
464C2×C22⋊Q8—173no—
465C2×C22⋊Q8—173no—
466C2×C22⋊Q8—1748no—
467C2×C22⋊Q8—173no—
468C2×C22⋊Q8—173no—
469C2×C22⋊Q8—173no—
470C2×C22⋊Q8—176no—
471C2×C22⋊Q8—173no—
472C2×C22⋊Q8C2×D1713yescomplemented
473C2×#121—176no—
474C2×#121—173no—
475C2×#121—173no—
476C2×#121—171no—
477C2×#121—176no—
478C2×#121C2×D1713yescomplemented
479C2×#120—173no—
480C2×#120—173no—
481#520—1716no—
482C2×C4×Q8—171no—
483C2×C4×Q8C2×D1711yescharacteristic, complemented
484C2×C4×D4—173no—
485C2×C4×D4—173no—
486C2×C4×D4—173no—
487C2×C4×D4—173no—
488C2×C4×D4—173no—
489C2×C4×D4C2×D1713yescomplemented
490C2×#117—173no—
491C22×C4⋊C4—173no—
492C22×C4⋊C4—176no—
493C22×C22⋊C4—176no—
494C2×C17—46no—
495C2×C17—42no—
496C2×C17#348914yescomplemented
497C2×C17C24×D411yescharacteristic
498C2×C17C22×2−1+411yescharacteristic
499C2×C17C2×#58511yescharacteristic
500D17—24no—
501D17—212no—
502D17—42no—
503C25—173no—
5042−1+4—34128no—
505C2×#41—28no—
506C2×#41—1716no—
507C2×#41—178no—
508C2×#41—1724no—
509C2×#41—1724no—
510C2×#41—1724no—
511C2×#41—1724no—
512C2×#41—1724no—
513C2×#41—3424no—
514C2×#41—3424no—
515C2×#41—3424no—
516C2×#41—3424no—
517C2×#41—3424no—
518C2×#41—34128no—
519C2×#41C22×D1718yes—
520C22×Q8—28no—
521C22×Q8—1724no—
522C22×Q8—178no—
523C22×Q8—178no—
524C22×Q8—173no—
525C22×Q8—173no—
526C22×Q8—173no—
527C22×Q8—3424no—
528C22×Q8—348no—
529C22×Q8—348no—
530C22×Q8C22×D1713yes—
531C22×Q8C22×D1711yescharacteristic
532C22×Q8C22×D1718yescomplemented
533C22×D4—171no—
534C22×D4—173no—
535C22×D4—171no—
536C22×D4—176no—
537C22×D4—173no—
538C22×D4—1724no—
539C22×D4—173no—
540C22×D4—171no—
541C22×D4—173no—
542C22×D4—3424no—
543C22×D4C22×D1713yes—
544C22×D4C22×D1713yes—
545C23×C4—173no—
546C23×C4—173no—
547C23×C4—176no—
548C23×C4—173no—
549C23×C4—173no—
550C23×C4—173no—
551C23×C4—171no—
552C23×C4—1724no—
553C23×C4—176no—
554C23×C4—3424no—
555C23×C4C22×D1713yes—
556C23×C4C22×D1713yes—
557C4⋊Q8—1724no—
558C4⋊Q8—1724no—
559#124—1724no—
560#124C22×D17124yescomplemented
561#123—1724no—
562#123—1724no—
563#123—1748no—
564#123—1748no—
565C22⋊Q8—1724no—
566C22⋊Q8—1724no—
567C22⋊Q8—1724no—
568C22⋊Q8—1724no—
569C22⋊Q8—1724no—
570C22⋊Q8—1724no—
571C22⋊Q8—1748no—
572C22⋊Q8—1724no—
573C22⋊Q8C22×D17124yescomplemented
574#121—1724no—
575#121—1748no—
576#121—1724no—
577#121—178no—
578#121—1748no—
579#121C22×D17124yescomplemented
580#120—1724no—
581#120—1724no—
582C4×Q8—178no—
583C4×Q8C22×D1718yescomplemented
584C4×D4—1724no—
585C4×D4—1724no—
586C4×D4—1724no—
587C4×D4—1724no—
588C4×D4—1724no—
589C4×D4C22×D17124yescomplemented
590#117—1724no—
591C2×C4⋊C4—173no—
592C2×C4⋊C4—173no—
593C2×C4⋊C4—173no—
594C2×C4⋊C4—176no—
595C2×C4⋊C4—176no—
596C2×C4⋊C4—171no—
597C2×C4⋊C4—173no—
598C2×C4⋊C4—173no—
599C2×C4⋊C4—1724no—
600C2×C4⋊C4—1748no—
601C2×C4⋊C4C22×D1713yes—
602C2×C4⋊C4C22×D1713yes—
603C2×C22⋊C4—176no—
604C2×C22⋊C4—173no—
605C2×C22⋊C4—173no—
606C2×C22⋊C4—173no—
607C2×C22⋊C4—173no—
608C2×C22⋊C4—173no—
609C2×C22⋊C4—173no—
610C2×C22⋊C4—171no—
611C2×C22⋊C4—173no—
612C2×C22⋊C4—1748no—
613C2×C22⋊C4C22×D1716yes—
614C2×C22⋊C4C22×D1711yescharacteristic
615C2×C22⋊C4C22×D1713yes—
616C2×C42—173no—
617C2×C42C22×D1713yes—
618C17C2×#348911yescharacteristic, complemented, Sylow
619C24—171no—
620C24—173no—
621C24—171no—
622C24—1712no—
623C24—3412no—
624C24—3412no—
625C24—686no—
626C24C23×D1713yes—
627C24C23×D1711yescharacteristic
628#41—232no—
629#41—1764no—
630#41—3496no—
631#41—3496no—
632#41—3496no—
633#41—3496no—
634#41—3496no—
635C2×Q8—232no—
636C2×Q8—212no—
637C2×Q8—1712no—
638C2×Q8—1712no—
639C2×Q8—1712no—
640C2×Q8—3412no—
641C2×Q8—3496no—
642C2×Q8—3432no—
643C2×Q8—3432no—
644C2×Q8—3412no—
645C2×Q8—3412no—
646C2×Q8D4×D1718yes—
647C2×Q8C23×D17112yes—
648C2×Q8C23×D1714yes—
649C2×D4—212no—
650C2×D4—46no—
651C2×D4—174no—
652C2×D4—1712no—
653C2×D4—174no—
654C2×D4—1724no—
655C2×D4—1712no—
656C2×D4—1724no—
657C2×D4—1712no—
658C2×D4—174no—
659C2×D4—1712no—
660C2×D4—344no—
661C2×D4—3412no—
662C2×D4—344no—
663C2×D4—3496no—
664C2×D4—344no—
665C2×D4—3424no—
666C2×D4—3412no—
667C2×D4—686no—
668C2×D4C23×D17112yes—
669C2×D4C23×D17112yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—171no—
673C22×C4—1724no—
674C22×C4—1712no—
675C22×C4—1712no—
676C22×C4—171no—
677C22×C4—173no—
678C22×C4—173no—
679C22×C4—173no—
680C22×C4—1724no—
681C22×C4—1712no—
682C22×C4—1712no—
683C22×C4—1712no—
684C22×C4—174no—
685C22×C4—1724no—
686C22×C4—344no—
687C22×C4—3496no—
688C22×C4—3412no—
689C22×C4—3424no—
690C22×C4—3412no—
691C22×C4—3412no—
692C22×C4—3412no—
693C22×C4—6812no—
694C22×C4C23×D17112yes—
695C22×C4C23×D17112yes—
696C22×C4C23×D1711yescharacteristic
697C22×C4C23×D1713yes—
698C22×C4C23×D1713yes—
699C22×C4C23×D1711yescharacteristic
700C22×C4C23×D1713yes—
701C4⋊C4—1712no—
702C4⋊C4—1712no—
703C4⋊C4—1712no—
704C4⋊C4—1724no—
705C4⋊C4—1724no—
706C4⋊C4—174no—
707C4⋊C4—1712no—
708C4⋊C4—1712no—
709C4⋊C4C23×D17112yes—
710C4⋊C4C23×D17112yes—
711C22⋊C4—1724no—
712C22⋊C4—1712no—
713C22⋊C4—1712no—
714C22⋊C4—1712no—
715C22⋊C4—1712no—
716C22⋊C4—1712no—
717C22⋊C4—1712no—
718C22⋊C4—174no—
719C22⋊C4—1712no—
720C22⋊C4C23×D17124yes—
721C22⋊C4C23×D1714yes—
722C22⋊C4C23×D17112yes—
723C42—1712no—
724C42C23×D17112yes—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—22no—
730C23—26no—
731C23—1712no—
732C23—174no—
733C23—172no—
734C23—176no—
735C23—172no—
736C23—3424no—
737C23—3424no—
738C23—342no—
739C23—346no—
740C23—346no—
741C23—342no—
742C23—342no—
743C23—342no—
744C23—342no—
745C23—6812no—
746C23—6848no—
747C23C24×D1716yes—
748C23C24×D1712yes—
749C23C24×D1711yescharacteristic
750Q8—224no—
751Q8—3424no—
752Q8—3424no—
753Q8—3424no—
754Q8C2×D4×D17116yes—
755D4—224no—
756D4—412no—
757D4—1748no—
758D4—3424no—
759D4—348no—
760D4—348no—
761D4—3448no—
762D4—3424no—
763D4—348no—
764D4—6812no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—174no—
772C2×C4—172no—
773C2×C4—1748no—
774C2×C4—172no—
775C2×C4—176no—
776C2×C4—176no—
777C2×C4—176no—
778C2×C4—348no—
779C2×C4—3424no—
780C2×C4—3448no—
781C2×C4—3424no—
782C2×C4—346no—
783C2×C4—346no—
784C2×C4—342no—
785C2×C4—346no—
786C2×C4—3424no—
787C2×C4—3424no—
788C2×C4—6824no—
789C2×C4C2×D4×D17112yes—
790C2×C4C24×D1712yes—
791C2×C4C24×D1716yes—
792C2×C4C24×D1716yes—
793C2×C4C24×D1712yes—
794C2×C4C24×D1716yes—
795C22—22no—
796C22—26no—
797C22—22no—
798C22—26no—
799C22—22no—
800C22—26no—
801C22—412no—
802C22—44no—
803C22—1712no—
804C22—174no—
805C22—348no—
806C22—3424no—
807C22—342no—
808C22—346no—
809C22—346no—
810C22—342no—
811C22—342no—
812C22—342no—
813C22—342no—
814C22—6848no—
815C22—684no—
816C22C22×D4×D1712yes—
817C222−1+4×D1712yes—
818C22#1176364512yes—
819C22C25×D1711yescharacteristic
820C4—22no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—174no—
825C4—346no—
826C4—346no—
827C4—342no—
828C4—346no—
829C4C22×D4×D17112yes—
830C2—46no—
831C2—42no—
832C2—344no—
833C2—3412no—
834C2—682no—
835C2#1454246314yesdirect product factor
836C2C23×D4×D1711yescharacteristic
837C2C2×2−1+4×D1711yescharacteristic
838C2C2×#1176364511yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#548C2
socleC23×C17C25
hypercenterC2×#548D17
hypocenterC17C2×#3489
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×#41×D17C2semidirect
3. #14542463C2direct (N × H)
4. C2×Q8×D68C2semidirect
5. C2×Q8×C22⋊D17C2semidirect
6. C2×#11763466C2semidirect
7. C2×#11763464C2semidirect
8. C2×#11763461C2semidirect
9. C2×#11763456C2semidirect
10. C2×#11763452C2semidirect
11. C2×#11763388C2semidirect
12. C2×#11763379C2semidirect
13. C2×#11763318C2semidirect
14. C2×C22⋊Q8×D17C2semidirect
15. C2×#11763291C2semidirect
16. C2×C17×#548C2semidirect
18. C2×#10587694C22semidirect
20. C22×#63256C22semidirect
22. C22×#63252C22semidirect
23. C22×#63252C22semidirect
26. C2×#41×D17C22semidirect
28. C22×Q8×D17C22semidirect
29. C22×Q8×D17C22semidirect
32. Q8×D68C22semidirect
33. Q8×C22⋊D17C22semidirect
34. #11763466C22semidirect
35. #11763464C22semidirect
36. #11763461C22semidirect
37. #11763456C22semidirect
38. #11763452C22semidirect
39. #11763388C22semidirect
40. #11763379C22semidirect
41. C2×#10587555C22semidirect
42. C2×#10587630C22semidirect
43. C2×#10587622C22semidirect
44. #11763318C22semidirect
45. C2×#10587580C22semidirect
46. C2×#10587569C22semidirect
47. C2×#10587569C22semidirect
48. C2×#10587569C22semidirect
50. C2×#10587583C22semidirect
51. C2×#10587610C22semidirect
52. C2×#10587610C22semidirect
54. C2×#10587564C22semidirect
55. C2×#10587564C22semidirect
57. C22⋊Q8×D17C22semidirect
59. C2×#10587570C22semidirect
60. C2×#10587625C22semidirect
61. C2×#10587624C22semidirect
62. C2×#10587624C22semidirect
65. #11763291C22semidirect
66. C2×Q8×Dic17C22semidirect
68. C2×C4×D68C22semidirect
69. C2×#10587579C22semidirect
71. C2×C4×C22⋊D17C22semidirect
72. C2×#10587558C22semidirect
73. C2×C4⋊C4×D17C22semidirect
74. C2×C4⋊C4×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
104. C2×#63256D4semidirect
106. C2×#63256C23semidirect
111. C2×Q8×D17C23semidirect
112. C2×Q8×D17C23semidirect
121. C2×#63252C23semidirect
122. C2×#63252C23semidirect
138. C17×#124C23semidirect
139. C17×C22⋊Q8C23semidirect
140. C17×#121C23semidirect
141. C4×Q8×C17C23semidirect
142. C4×D4×C17C23semidirect
153. Q8×Dic17C23semidirect
154. #10587630C23semidirect
155. #10587625C23semidirect
156. #10587624C23semidirect
157. #10587624C23semidirect
159. #10587622C23semidirect
161. C4×C22⋊D17C23semidirect
171. #10587610C23semidirect
172. #10587610C23semidirect
180. #10587583C23semidirect
182. #10587580C23semidirect
183. #10587579C23semidirect
184. C4⋊C4×D17C23semidirect
185. C4⋊C4×D17C23semidirect
187. #10587570C23semidirect
188. #10587569C23semidirect
189. #10587569C23semidirect
190. #10587569C23semidirect
193. #10587564C23semidirect
194. #10587564C23semidirect
196. C4×D68C23semidirect
197. #10587558C23semidirect
198. #10587555C23semidirect
245. #63256C2×D4semidirect
327. C22×D172−1+4semidirect
382. C2×#548D17semidirect
416. C2×D17C2×2−1+4semidirect
441. C23×Q8C2×D17semidirect
447. #548C2×D17semidirect
457. C2×#124C2×D17semidirect
472. C2×C22⋊Q8C2×D17semidirect
478. C2×#121C2×D17semidirect
483. C2×C4×Q8C2×D17semidirect
489. C2×C4×D4C2×D17semidirect
496. C2×C17#3489semidirect
532. C22×Q8C22×D17semidirect
560. #124C22×D17semidirect
573. C22⋊Q8C22×D17semidirect
579. #121C22×D17semidirect
583. C4×Q8C22×D17semidirect
589. C4×D4C22×D17semidirect
618. C17C2×#3489semidirect
835. C2#14542463direct (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×#41×D172
#145424632
C2×Q8×D682
C2×Q8×C22⋊D172
C2×#117634662
C2×#117634642
C2×#117634612
C2×#117634562
C2×#117634522
C2×#117633882
C2×#117633792
C2×#117633182
C2×C22⋊Q8×D172
C2×#117632912
C2×C17×#5482
C2×#348917