Finite Group Databasebeta

← C2×#14542860 #17942532

Subgroups — C2×#14542860 #17942532

Order 4352.

7758 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542860C2132yesmaximal, direct product factor
2C2×#11763541C213yesmaximal, complemented
3C2×Q8×Dic34C211yesmaximal, characteristic, complemented
4C2×#11763517C213yesmaximal, complemented
5C2×#11763478C211yesmaximal, characteristic, complemented
6C2×#11763470C211yesmaximal, characteristic, complemented
7C2×#11763463C213yesmaximal, complemented
8C2×#11763459C213yesmaximal, complemented
9C2×#11763432C213yesmaximal, complemented
10C2×#11763428C213yesmaximal, complemented
11C2×#11763354C213yesmaximal, complemented
12C2×#11763339C213yesmaximal, complemented
13C2×#11763292C211yesmaximal, characteristic, complemented
14C2×#11763291C211yesmaximal, characteristic, complemented
15C22×Q8×Dic17C211yesmaximal, characteristic, complemented
16C2×C17×#548C211yesmaximal, characteristic, complemented
17C22×#63256C2211yescharacteristic
18C22×#63254C2216yes—
19#11763541C22148yescomplemented
20Q8×Dic34C22116yescomplemented
21#11763517C22148yescomplemented
22#11763478C22116yescomplemented
23#11763470C22116yescomplemented
24#11763463C22148yescomplemented
25#11763459C22148yescomplemented
26#11763432C22148yescomplemented
27#11763428C22148yescomplemented
28#11763354C22148yescomplemented
29C2×#10587555C2213yes—
30C2×#10587574C2213yes—
31C2×#10587574C2213yes—
32C2×#10587626C2213yes—
33#11763339C22148yescomplemented
34C2×#10587584C2213yes—
35C2×#10587565C2213yes—
36C2×#10587575C2213yes—
37C2×#10587633C2213yes—
38C2×#10587571C2213yes—
39C2×#10587571C2216yes—
40C2×#10587572C2216yes—
41C2×#10587572C2213yes—
42C2×#10587569C2216yes—
43C2×#10587621C2213yes—
44C2×#10587583C2216yes—
45C2×#10587564C2216yes—
46C2×#10587564C2211yescharacteristic
47C2×#10587632C2213yes—
48C2×#10587616C2213yes—
49C2×#10587616C2213yes—
50C2×#10587625C2213yes—
51C2×#10587624C2213yes—
52#11763292C22116yescomplemented
53#11763291C22116yescomplemented
54C2×Q8×Dic17C2211yescharacteristic
55C2×Q8×Dic17C2211yescharacteristic
56C2×Q8×Dic17C2213yes—
57C2×Q8×Dic17C2213yes—
58C2×Q8×Dic17C2211yescharacteristic
59C2×Q8×Dic17C22116yescomplemented
60C2×C4×Dic34C2213yes—
61C2×C4×D68C2213yes—
62C2×D4×Dic17C2213yes—
63C2×D4×Dic17C2213yes—
64C2×#10587579C2213yes—
65C2×C4×C22⋊D17C2213yes—
66C2×C4×C22⋊D17C2213yes—
67C2×#10587567C2216yes—
68C2×#10587612C2213yes—
69C2×#10587558C2213yes—
70C22×C4⋊Dic17C2213yes—
71C22×C4⋊Dic17C2213yes—
72C2×C4⋊C4×D17C2213yes—
73C22×C4×Dic17C2213yes—
74C22×#41×C17C2211yescharacteristic
75C23×Q8×C17C2211yescharacteristic
76C17×#548C22116yescomplemented
77C2×C17×#124C2213yes—
78C2×C17×C22⋊Q8C2213yes—
79C2×C17×#121C2213yes—
80C2×C4×Q8×C17C2211yescharacteristic
81C2×C4×D4×C17C2213yes—
82C2×#41×C17—28no—
83C2×#41×C17C2318yes—
84C22×Q8×C17—28no—
85C22×Q8×C17C2318yes—
86C22×Q8×C17C2313yes—
87C22×Q8×C17C2311yescharacteristic
88C22×D4×C17C2313yes—
89C22×D4×C17C2313yes—
90C23×C4×C17C2313yes—
91C23×C4×C17C2313yes—
92C22×C22⋊D17C2313yes—
93C22×C22⋊D17C2313yes—
94C22×C22⋊D17C2316yes—
95C23×Dic17C2311yescharacteristic
96C23×Dic17C2313yes—
97C23×Dic17C2316yes—
98C2×#63256—28no—
99C2×#63256C2318yes—
100C2×#63254—424no—
101C2×#63254C23148yes—
102C22×D68C2313yes—
103C22×C4×D17C2313yes—
104C22×C4×D17C2316yes—
105C22×Dic34C2311yescharacteristic
106C22×Dic34C2316yes—
107C17×#124C23124yes—
108C17×C22⋊Q8C23124yes—
109C17×#121C23124yes—
110C4×Q8×C17C2318yes—
111C4×D4×C17C23124yes—
112C2×C4⋊C4×C17C2313yes—
113C2×C4⋊C4×C17C2313yes—
114C2×C22⋊C4×C17C2311yescharacteristic
115C2×C22⋊C4×C17C2313yes—
116C2×C22⋊C4×C17C2316yes—
117C2×C42×C17C2313yes—
118C2×C22⋊Dic17C2313yes—
119C2×C22⋊Dic17C2313yes—
120C2×C22⋊Dic17C2311yescharacteristic
121C2×C22⋊Dic17C2313yes—
122#10587633C23124yes—
123#10587632C23124yes—
124Q8×Dic17C2318yes—
125Q8×Dic17C2318yes—
126Q8×Dic17C23124yes—
127Q8×Dic17C2318yes—
128Q8×Dic17C23124yes—
129#10587626C23124yes—
130#10587625C23124yes—
131#10587624C23124yes—
132#10587621C23124yes—
133D4×Dic17C23124yes—
134D4×Dic17C23124yes—
135#10587616C23124yes—
136#10587616C23124yes—
137C4×C22⋊D17C23124yes—
138C4×C22⋊D17C23124yes—
139C2×#63227C2313yes—
140C2×#63227C2313yes—
141C2×#63227C2316yes—
142C2×#63227C2313yes—
143C2×#63227C2313yes—
144#10587612C23124yes—
145C2×C4⋊Dic17C23124yes—
146C2×C4⋊Dic17C23124yes—
147C2×C4⋊Dic17C2313yes—
148C2×C4⋊Dic17C2313yes—
149C2×C4⋊Dic17C2313yes—
150C2×C4⋊Dic17C2313yes—
151C2×C4⋊Dic17C2316yes—
152C2×C4⋊Dic17C2311yescharacteristic
153C2×C4⋊Dic17C2313yes—
154C2×#63225C2313yes—
155C2×#63225C2311yescharacteristic
156C2×#63225C2313yes—
157C2×#63225C2311yescharacteristic
158C2×#63225C2313yes—
159C2×#63225C2313yes—
160C2×C4×Dic17C2313yes—
161C2×C4×Dic17C2313yes—
162C2×C4×Dic17C2313yes—
163C2×C4×Dic17C2313yes—
164C2×C4×Dic17C23124yes—
165C2×C4×Dic17C2313yes—
166#10587584C23124yes—
167#10587583C23148yes—
168#10587579C23124yes—
169C4⋊C4×D17C23124yes—
170#10587575C23124yes—
171#10587574C23124yes—
172#10587574C23124yes—
173#10587572C23124yes—
174#10587572C23148yes—
175#10587571C23124yes—
176#10587571C23148yes—
177#10587569C23148yes—
178#10587567C23148yes—
179#10587565C23124yes—
180#10587564C23148yes—
181#10587564C2318yes—
182C4×D68C23124yes—
183#10587558C23124yes—
184#10587555C23124yes—
185C4×Dic34C23124yes—
186C24×C17C2413yes—
187C24×C17C2411yescharacteristic
188C23×D17C2413yes—
189#41×C17—232no—
190C2×Q8×C17—232no—
191C2×Q8×C17—212no—
192C2×Q8×C17#4118yescomplemented
193C2×Q8×C17C24112yes—
194C2×Q8×C17C2414yes—
195C2×D4×C17—212no—
196C2×D4×C17—212no—
197C2×D4×C17C24112yes—
198C2×D4×C17C24112yes—
199C22×C4×C17—212no—
200C22×C4×C17—212no—
201C22×C4×C17C24112yes—
202C22×C4×C17C2413yes—
203C22×C4×C17C2411yescharacteristic
204C22×C4×C17C2411yescharacteristic
205C22×C4×C17C2413yes—
206C22×C4×C17C24112yes—
207C22×C4×C17C2413yes—
208C2×C22⋊D17—212no—
209C2×C22⋊D17—212no—
210C2×C22⋊D17—412no—
211C2×C22⋊D17C24112yes—
212C2×C22⋊D17C24112yes—
213C2×C22⋊D17C24124yes—
214C22×Dic17—212no—
215C22×Dic17—24no—
216C22×Dic17—412no—
217C22×Dic17C2413yes—
218C22×Dic17C2413yes—
219C22×Dic17C2411yescharacteristic
220C22×Dic17C2411yescharacteristic
221C22×Dic17C2413yes—
222C22×Dic17C24112yes—
223C22×Dic17C2414yes—
224C22×Dic17C2411yescharacteristic
225C22×Dic17C24124yes—
226C22×Dic17C2411yescharacteristic
227#63256—232no—
228#63254—496no—
229C2×D68—212no—
230C2×D68C24112yes—
231C2×C4×D17—212no—
232C2×C4×D17—412no—
233C2×C4×D17C24112yes—
234C2×C4×D17C24124yes—
235C2×Dic34—24no—
236C2×Dic34—412no—
237C2×Dic34C2414yes—
238C2×Dic34C24124yes—
239C4⋊C4×C17C24112yes—
240C4⋊C4×C17C24112yes—
241C22⋊C4×C17C24124yes—
242C22⋊C4×C17C24112yes—
243C22⋊C4×C17C2414yes—
244C42×C17C24112yes—
245C22⋊Dic17C24112yes—
246C22⋊Dic17C2414yes—
247C22⋊Dic17C24112yes—
248C22⋊Dic17C24112yes—
249#63227C24112yes—
250#63227C24112yes—
251#63227C24124yes—
252#63227C24112yes—
253#63227C24112yes—
254C4⋊Dic17C24112yes—
255C4⋊Dic17C24112yes—
256C4⋊Dic17C24112yes—
257C4⋊Dic17C24112yes—
258C4⋊Dic17C24124yes—
259C4⋊Dic17C2414yes—
260C4⋊Dic17C24112yes—
261#63225C24112yes—
262#63225C24112yes—
263#63225C2414yes—
264#63225C24112yes—
265#63225C24112yes—
266#63225C2414yes—
267C4×Dic17C24112yes—
268C4×Dic17C24112yes—
269C4×Dic17C24112yes—
270C4×Dic17C24112yes—
271C4×Dic17C24112yes—
272C2×#3522—171nomaximal, Sylow
273C23×C17—22no—
274C23×C17—22no—
275C23×C17—26no—
276C23×C17—26no—
277C23×C17—26no—
278C23×C17H(5,𝔽2)14yes—
279C23×C17C2516yes—
280C23×C17C2512yes—
281C23×C17C2511yescharacteristic
282C22×D17—26no—
283C22×D17—26no—
284C22×D17—26no—
285C22×D17C2516yes—
286Q8×C17—224no—
287Q8×C17C2×#41116yescomplemented
288D4×C17—224no—
289D4×C17—224no—
290C2×C4×C17—22no—
291C2×C4×C17—26no—
292C2×C4×C17—26no—
293C2×C4×C17—22no—
294C2×C4×C17—224no—
295C2×C4×C17—224no—
296C2×C4×C17C2×#41112yes—
297C2×C4×C17C2512yes—
298C2×C4×C17C2516yes—
299C2×C4×C17C2516yes—
300C2×C4×C17C2512yes—
301C2×C4×C17C2516yes—
302C22⋊D17—224no—
303C22⋊D17—224no—
304C22⋊D17—424no—
305C2×Dic17—22no—
306C2×Dic17—26no—
307C2×Dic17—26no—
308C2×Dic17—26no—
309C2×Dic17—224no—
310C2×Dic17—22no—
311C2×Dic17—22no—
312C2×Dic17—28no—
313C2×Dic17—424no—
314C2×Dic172−1+414yes—
315C2×Dic17C2512yes—
316C2×Dic17C2512yes—
317C2×Dic17C2512yes—
318C2×Dic17C2516yes—
319C2×Dic17C2516yes—
320C2×Dic17C2516yes—
321C2×Dic17C2512yes—
322D68—224no—
323C4×D17—224no—
324C4×D17—424no—
325Dic34—28no—
326Dic34—424no—
327#3522—1732no—
328C2×#559—173no—
329C2×Q82—171no—
330C2×#554—173no—
331C2×#550—171no—
332C2×#548—171no—
333C2×#548D1711yescharacteristic, complemented
334C2×#547—173no—
335C2×#547—173no—
336C2×#542—173no—
337C2×#542—173no—
338C2×#532—173no—
339C2×#529—173no—
340C2×#520—171no—
341C2×#520—171no—
342C22×C4×Q8—171no—
343C22×C17—22no—
344C22×C17—22no—
345C22×C17—28no—
346C22×C17—26no—
347C22×C17—26no—
348C22×C17—26no—
349C22×C17—412no—
350C22×C17C22×#4112yes—
351C22×C17C2×H(5,𝔽2)14yes—
352C22×C17C2×H(5,𝔽2)12yes—
353C22×C17C2×2−1+412yes—
354C22×C17C2611yescharacteristic
355C2×D17—26no—
356C2×D17—26no—
357C2×D17—26no—
358C2×D17—412no—
359C4×C17—22no—
360C4×C17—26no—
361C4×C17—26no—
362C4×C17—22no—
363C4×C17C22×#41112yes—
364Dic17—22no—
365Dic17—26no—
366Dic17—26no—
367Dic17—26no—
368Dic17—22no—
369Dic17—22no—
370Dic17C2×2−1+414yes—
371C22×#41—171no—
372C22×#41—176no—
373C22×#41C2×D1711yescharacteristic
374C23×Q8C2×D1711yescharacteristic
375#559—1748no—
376Q82—1716no—
377#554—1748no—
378#550—1716no—
379#548—1716no—
380#548C2×D17116yescomplemented
381#547—1748no—
382#547—1748no—
383#542—1748no—
384#542—1748no—
385#532—1748no—
386C2×C4⋊Q8—173no—
387C2×C4⋊Q8—173no—
388C2×C4⋊Q8—173no—
389C2×#127—173no—
390#529—1748no—
391C2×#126—173no—
392C2×#126—173no—
393C2×#125—173no—
394C2×#124—173no—
395C2×#124—173no—
396C2×#124—176no—
397C2×#124C2×D1713yes—
398C2×#123—173no—
399C2×#123—173no—
400C2×#123—176no—
401C2×#123—176no—
402C2×C22⋊Q8—173no—
403C2×C22⋊Q8—176no—
404C2×C22⋊Q8—171no—
405C2×C22⋊Q8—176no—
406C2×C22⋊Q8C2×D1713yes—
407C2×#121—173no—
408C2×#121—173no—
409C2×#121—173no—
410C2×#121—173no—
411C2×#121C2×D1713yes—
412#520—1716no—
413#520—1716no—
414C2×C4×Q8—171no—
415C2×C4×Q8—173no—
416C2×C4×Q8—171no—
417C2×C4×Q8—173no—
418C2×C4×Q8—171no—
419C2×C4×Q8—1716no—
420C2×C4×Q8—173no—
421C2×C4×Q8C2×D1711yescharacteristic
422C2×C4×D4—173no—
423C2×C4×D4—173no—
424C2×C4×D4—173no—
425C2×C4×D4—173no—
426C2×C4×D4—173no—
427C2×C4×D4—176no—
428C2×C4×D4—173no—
429C2×C4×D4C2×D1713yes—
430C2×#117—173no—
431C2×#117—173no—
432C22×C4⋊C4—173no—
433C22×C4⋊C4—173no—
434C22×C4⋊C4—173no—
435C22×C42—173no—
436C2×C17—24no—
437C2×C17—46no—
438C2×C17#352214yescomplemented
439C2×C17C23×#4111yescharacteristic
440C2×C17C22×H(5,𝔽2)11yescharacteristic
441C2×C17C22×2−1+411yescharacteristic
442D17—46no—
443C2×#41—28no—
444C2×#41—178no—
445C2×#41—1748no—
446C2×#41—348no—
447C2×#41—6824no—
448C2×#41C22×D1718yes—
449C22×Q8—28no—
450C22×Q8—171no—
451C22×Q8—176no—
452C22×Q8C22×D1713yes—
453C22×Q8C22×D1718yes—
454C22×Q8C22×D1711yescharacteristic
455C22×D4—173no—
456C22×D4—173no—
457C22×D4—176no—
458C22×D4—173no—
459C22×D4C22×D1713yes—
460C22×D4C22×D1713yes—
461C23×C4—173no—
462C23×C4—171no—
463C23×C4—176no—
464C23×C4—173no—
465C23×C4—176no—
466C23×C4C22×D1713yes—
467C23×C4C22×D1713yes—
468C4⋊Q8—1724no—
469C4⋊Q8—1724no—
470C4⋊Q8—1724no—
471#127—1724no—
472#126—1724no—
473#126—1724no—
474#125—1724no—
475#124—1724no—
476#124—1724no—
477#124—1748no—
478#124C22×D17124yes—
479#123—1724no—
480#123—1724no—
481#123—1748no—
482#123—1748no—
483C22⋊Q8—1724no—
484C22⋊Q8—1748no—
485C22⋊Q8—178no—
486C22⋊Q8—1748no—
487C22⋊Q8C22×D17124yes—
488#121—1724no—
489#121—1724no—
490#121—1724no—
491#121—1724no—
492#121C22×D17124yes—
493C4×Q8—178no—
494C4×Q8—1724no—
495C4×Q8—178no—
496C4×Q8—1724no—
497C4×Q8—178no—
498C4×Q8—1724no—
499C4×Q8C22×D1718yes—
500C4×D4—1724no—
501C4×D4—1724no—
502C4×D4—1724no—
503C4×D4—1724no—
504C4×D4—1724no—
505C4×D4—1748no—
506C4×D4—1724no—
507C4×D4C22×D17124yes—
508#117—1724no—
509#117—1724no—
510C2×C4⋊C4—173no—
511C2×C4⋊C4—173no—
512C2×C4⋊C4—173no—
513C2×C4⋊C4—173no—
514C2×C4⋊C4—173no—
515C2×C4⋊C4—176no—
516C2×C4⋊C4—1724no—
517C2×C4⋊C4—1724no—
518C2×C4⋊C4—171no—
519C2×C4⋊C4—171no—
520C2×C4⋊C4—171no—
521C2×C4⋊C4—173no—
522C2×C4⋊C4—173no—
523C2×C4⋊C4—173no—
524C2×C4⋊C4—173no—
525C2×C4⋊C4—1724no—
526C2×C4⋊C4C22×D1713yes—
527C2×C4⋊C4C22×D1713yes—
528C2×C22⋊C4—173no—
529C2×C22⋊C4—173no—
530C2×C22⋊C4—171no—
531C2×C22⋊C4—173no—
532C2×C22⋊C4—173no—
533C2×C22⋊C4—173no—
534C2×C22⋊C4—173no—
535C2×C22⋊C4—176no—
536C2×C22⋊C4—173no—
537C2×C22⋊C4C22×D1716yes—
538C2×C22⋊C4C22×D1711yescharacteristic
539C2×C22⋊C4C22×D1713yes—
540C2×C42—173no—
541C2×C42—173no—
542C2×C42—173no—
543C2×C42—173no—
544C2×C42—173no—
545C2×C42—1724no—
546C2×C42C22×D1713yes—
547C17C2×#352211yescharacteristic, complemented, Sylow
548C24—173no—
549C24C23×D1713yes—
550C24C23×D1711yescharacteristic
551#41—232no—
552#41—3432no—
553#41—6896no—
554C2×Q8—232no—
555C2×Q8—212no—
556C2×Q8—174no—
557C2×Q8—1724no—
558C2×Q8—344no—
559C2×Q8—6812no—
560C2×Q8#6325418yescomplemented
561C2×Q8C23×D17112yes—
562C2×Q8C23×D1714yes—
563C2×D4—212no—
564C2×D4—212no—
565C2×D4—1712no—
566C2×D4—1712no—
567C2×D4—1724no—
568C2×D4—1712no—
569C2×D4—3412no—
570C2×D4—3412no—
571C2×D4—3412no—
572C2×D4—6812no—
573C2×D4C23×D17112yes—
574C2×D4C23×D17112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—171no—
578C22×C4—174no—
579C22×C4—1712no—
580C22×C4—171no—
581C22×C4—171no—
582C22×C4—173no—
583C22×C4—173no—
584C22×C4—173no—
585C22×C4—171no—
586C22×C4—1724no—
587C22×C4—1712no—
588C22×C4—1724no—
589C22×C4—344no—
590C22×C4—3412no—
591C22×C4—3412no—
592C22×C4—6812no—
593C22×C4—6812no—
594C22×C4C23×D17112yes—
595C22×C4C23×D17112yes—
596C22×C4C23×D1713yes—
597C22×C4C23×D1711yescharacteristic
598C22×C4C23×D1713yes—
599C22×C4C23×D1711yescharacteristic
600C22×C4C23×D1713yes—
601C4⋊C4—1712no—
602C4⋊C4—1712no—
603C4⋊C4—1712no—
604C4⋊C4—1712no—
605C4⋊C4—1712no—
606C4⋊C4—1724no—
607C4⋊C4—174no—
608C4⋊C4—174no—
609C4⋊C4—174no—
610C4⋊C4—1712no—
611C4⋊C4—1712no—
612C4⋊C4—1712no—
613C4⋊C4—1712no—
614C4⋊C4C23×D17112yes—
615C4⋊C4C23×D17112yes—
616C22⋊C4—1712no—
617C22⋊C4—1712no—
618C22⋊C4—174no—
619C22⋊C4—1712no—
620C22⋊C4—1712no—
621C22⋊C4—1712no—
622C22⋊C4—1712no—
623C22⋊C4—1724no—
624C22⋊C4—1712no—
625C22⋊C4C23×D17124yes—
626C22⋊C4C23×D1714yes—
627C22⋊C4C23×D17112yes—
628C42—1712no—
629C42—1712no—
630C42—1712no—
631C42—1712no—
632C42—1712no—
633C42C23×D17112yes—
634C23—22no—
635C23—22no—
636C23—26no—
637C23—26no—
638C23—26no—
639C23—176no—
640C23—346no—
641C23—346no—
642C23—346no—
643C23#1058769614yes—
644C23C24×D1716yes—
645C23C24×D1712yes—
646C23C24×D1711yescharacteristic
647Q8—224no—
648Q8—348no—
649Q8—6824no—
650Q8C2×#63254116yescomplemented
651D4—224no—
652D4—224no—
653D4—3424no—
654D4—3424no—
655D4—3424no—
656D4—6824no—
657C2×C4—22no—
658C2×C4—26no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—174no—
664C2×C4—172no—
665C2×C4—172no—
666C2×C4—172no—
667C2×C4—176no—
668C2×C4—176no—
669C2×C4—176no—
670C2×C4—172no—
671C2×C4—348no—
672C2×C4—342no—
673C2×C4—346no—
674C2×C4—346no—
675C2×C4—3424no—
676C2×C4—346no—
677C2×C4—342no—
678C2×C4—342no—
679C2×C4—3424no—
680C2×C4—6824no—
681C2×C4—6824no—
682C2×C4C2×#63254112yes—
683C2×C4C24×D1716yes—
684C2×C4C24×D1712yes—
685C2×C4C24×D1716yes—
686C2×C4C24×D1712yes—
687C2×C4C24×D1716yes—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—26no—
692C22—26no—
693C22—26no—
694C22—412no—
695C22—346no—
696C22—346no—
697C22—346no—
698C22—6812no—
699C22C22×#6325412yes—
700C22C2×#1058769614yes—
701C22C2×#1058769612yes—
702C222−1+4×D1712yes—
703C22C25×D1711yescharacteristic
704C4—22no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—174no—
709C4—342no—
710C4—346no—
711C4—346no—
712C4—346no—
713C4—342no—
714C4—342no—
715C4C22×#63254112yes—
716C2—24no—
717C2—46no—
718C2—686no—
719C2#1454286014yesdirect product factor
720C2C23×#6325411yescharacteristic
721C2C22×#1058769611yescharacteristic
722C2C2×2−1+4×D1711yescharacteristic
subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×#548C2
socleC23×C17C25
hypercenterC2×#548D17
hypocenterC17C2×#3522
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #14542860C2direct (N × H)
2. C2×#11763541C2semidirect
3. C2×Q8×Dic34C2semidirect
4. C2×#11763517C2semidirect
5. C2×#11763478C2semidirect
6. C2×#11763470C2semidirect
7. C2×#11763463C2semidirect
8. C2×#11763459C2semidirect
9. C2×#11763432C2semidirect
10. C2×#11763428C2semidirect
11. C2×#11763354C2semidirect
12. C2×#11763339C2semidirect
13. C2×#11763292C2semidirect
14. C2×#11763291C2semidirect
15. C22×Q8×Dic17C2semidirect
16. C2×C17×#548C2semidirect
19. #11763541C22semidirect
20. Q8×Dic34C22semidirect
21. #11763517C22semidirect
22. #11763478C22semidirect
23. #11763470C22semidirect
24. #11763463C22semidirect
25. #11763459C22semidirect
26. #11763432C22semidirect
27. #11763428C22semidirect
28. #11763354C22semidirect
33. #11763339C22semidirect
52. #11763292C22semidirect
53. #11763291C22semidirect
59. C2×Q8×Dic17C22semidirect
76. C17×#548C22semidirect
192. C2×Q8×C17#41semidirect
287. Q8×C17C2×#41semidirect
333. C2×#548D17semidirect
380. #548C2×D17semidirect
438. C2×C17#3522semidirect
547. C17C2×#3522semidirect
560. C2×Q8#63254semidirect
650. Q8C2×#63254semidirect
719. C2#14542860direct (N × H)

Maximal subgroups

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

subgroupindex
#145428602
C2×#117635412
C2×Q8×Dic342
C2×#117635172
C2×#117634782
C2×#117634702
C2×#117634632
C2×#117634592
C2×#117634322
C2×#117634282
C2×#117633542
C2×#117633392
C2×#117632922
C2×#117632912
C22×Q8×Dic172
C2×C17×#5482
C2×#352217