Finite Group Databasebeta

← C2×#14542401 #17941416

Subgroups — C2×#14542401 #17941416

Order 4352.

7706 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#14542401C2132yesmaximal, direct product factor
2C2×#11763535C211yesmaximal, characteristic, complemented
3C2×#11763531C213yesmaximal, complemented
4C2×#11763500C213yesmaximal, complemented
5C2×#11763494C213yesmaximal, complemented
6C2×Q8×C22⋊D17C211yesmaximal, characteristic, complemented
7C2×#11763471C211yesmaximal, characteristic, complemented
8C2×#11763470C211yesmaximal, characteristic, complemented
9C2×#11763460C213yesmaximal, complemented
10C2×#11763363C213yesmaximal, complemented
11C2×#11763346C213yesmaximal, complemented
12C2×#11763343C213yesmaximal, complemented
13C2×C4×#63256C211yesmaximal, characteristic, complemented
14C2×C4×#63252C213yesmaximal, complemented
15C2×C4×Q8×D17C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C17C211yesmaximal, characteristic, complemented
17C22×#63256C2211yescharacteristic
18C22×#63252C2213yes—
19C22×Q8×D17C2211yescharacteristic
20#11763535C22116yescomplemented
21#11763531C22148yescomplemented
22#11763500C22148yescomplemented
23#11763494C22148yescomplemented
24Q8×C22⋊D17C22116yescomplemented
25#11763471C22116yescomplemented
26#11763470C22116yescomplemented
27#11763460C22148yescomplemented
28#11763363C22148yescomplemented
29C2×#10587574C2213yes—
30C2×#10587630C2213yes—
31#11763346C22148yescomplemented
32#11763343C22148yescomplemented
33C2×#10587584C2216yes—
34C2×#10587562C2216yes—
35C2×#10587556C2213yes—
36C2×#10587576C2213yes—
37C2×#10587575C2216yes—
38C2×#10587633C2213yes—
39C2×#10587561C2213yes—
40C2×#10587580C2216yes—
41C2×#10587615C2216yes—
42C2×#10587583C2213yes—
43C2×#10587610C2213yes—
44C2×#10587582C2216yes—
45C2×#10587632C2213yes—
46C2×#10587632C2213yes—
47C2×#10587581C2213yes—
48C2×#10587616C2213yes—
49C4×#63256C22116yescomplemented
50C4×#63252C22148yescomplemented
51C2×Q8×Dic17C2211yescharacteristic
52C2×Q8×Dic17C2211yescharacteristic
53C2×C4×Dic34C2213yes—
54C2×C4×Dic34C2213yes—
55C2×C4×Dic34C2213yes—
56C2×#10587573C2213yes—
57C4×Q8×D17C22116yescomplemented
58C2×C4×D68C2213yes—
59C2×C4×D68C2213yes—
60C2×C4×D68C2213yes—
61C2×#10587579C2213yes—
62C2×C4×C22⋊D17C2211yescharacteristic
63C2×C4×C22⋊D17C2213yes—
64C2×C4×C22⋊D17C2213yes—
65C2×C4×C22⋊D17C2213yes—
66C2×#10587612C2213yes—
67C2×#10587578C2213yes—
68C2×#10587558C2213yes—
69C2×#10587558C2213yes—
70C2×#10587558C2216yes—
71C2×C4⋊C4×D17C2213yes—
72C2×C42×D17C2213yes—
73C2×C42×D17C2213yes—
74C23×Q8×C17C2211yescharacteristic
75C2×C4×Q8×C17C2211yescharacteristic
76C2×C4×Q8×C17C2211yescharacteristic
77C2×C4×Q8×C17C2213yes—
78C2×C4×Q8×C17C2213yes—
79C2×C4×Q8×C17C22116yescomplemented
80C22×C4⋊C4×C17C2213yes—
81C22×C42×C17C2213yes—
82C22×Q8×C17—28no—
83C22×Q8×C17C2318yes—
84C22×Q8×C17C2313yes—
85C22×Q8×C17C2311yescharacteristic
86C23×C4×C17C2311yescharacteristic
87C23×C4×C17C2313yes—
88C23×C4×C17C2313yes—
89C22×C22⋊D17C2313yes—
90C22×C22⋊D17C2311yescharacteristic
91C2×#63256—28no—
92C2×#63256C2318yes—
93C2×Q8×D17—28no—
94C2×Q8×D17C2318yes—
95C2×#63252—224no—
96C2×#63252C23124yes—
97C22×D68C2313yes—
98C22×D68C2313yes—
99C22×C4×D17C2311yescharacteristic
100C22×C4×D17C2313yes—
101C22×C4×D17C2313yes—
102C22×C4×D17C2313yes—
103C22×C4×D17C2313yes—
104C22×C4×D17C2313yes—
105C22×Dic34C2313yes—
106C22×Dic34C2313yes—
107C4×Q8×C17C2318yes—
108C4×Q8×C17C23124yes—
109C4×Q8×C17C2318yes—
110C4×Q8×C17C23124yes—
111C2×C4⋊C4×C17C23124yes—
112C2×C4⋊C4×C17C2313yes—
113C2×C4⋊C4×C17C2313yes—
114C2×C4⋊C4×C17C2316yes—
115C2×C42×C17C2313yes—
116C2×C42×C17C2313yes—
117C2×C42×C17C2313yes—
118C2×C42×C17C2313yes—
119C2×C42×C17C23124yes—
120C2×C22⋊Dic17C2311yescharacteristic
121C2×C22⋊Dic17C2313yes—
122#10587633C23124yes—
123#10587632C23124yes—
124#10587632C23124yes—
125Q8×Dic17C2318yes—
126Q8×Dic17C2318yes—
127#10587630C23124yes—
128#10587616C23124yes—
129#10587615C23148yes—
130C4×C22⋊D17C23124yes—
131C4×C22⋊D17C23124yes—
132C4×C22⋊D17C2318yes—
133C4×C22⋊D17C23124yes—
134C2×#63227C2311yescharacteristic
135C2×#63227C2313yes—
136C2×#63227C2313yes—
137C2×#63227C2313yes—
138C2×#63227C2316yes—
139C2×#63227C2316yes—
140C2×#63227C2316yes—
141#10587612C23124yes—
142C2×C4⋊Dic17C2313yes—
143C2×C4⋊Dic17C2313yes—
144C2×C4⋊Dic17C2313yes—
145C2×C4⋊Dic17C2313yes—
146#10587610C23124yes—
147C2×#63225C2316yes—
148C2×#63225C2311yescharacteristic
149C2×#63225C2313yes—
150C2×#63225C2313yes—
151C2×#63225C2313yes—
152C2×#63225C2316yes—
153C2×#63225C2316yes—
154C2×C4×Dic17C2311yescharacteristic
155C2×C4×Dic17C2313yes—
156C2×C4×Dic17C2313yes—
157C2×C4×Dic17C2313yes—
158C2×C4×Dic17C2313yes—
159C2×C4×Dic17C2313yes—
160#10587584C23148yes—
161#10587583C23124yes—
162#10587582C23148yes—
163#10587581C23124yes—
164#10587580C23148yes—
165#10587579C23124yes—
166#10587578C23124yes—
167C4⋊C4×D17C23124yes—
168#10587576C23124yes—
169#10587575C23148yes—
170#10587574C23124yes—
171#10587573C23124yes—
172#10587562C23148yes—
173#10587561C23124yes—
174C4×D68C23124yes—
175C4×D68C23124yes—
176C4×D68C23124yes—
177#10587558C23124yes—
178#10587558C23124yes—
179#10587558C23148yes—
180C42×D17C23124yes—
181C42×D17C23124yes—
182#10587556C23124yes—
183C4×Dic34C23124yes—
184C4×Dic34C23124yes—
185C4×Dic34C23124yes—
186C24×C17C2411yescharacteristic
187C23×D17C2413yes—
188C23×D17C2411yescharacteristic
189C2×Q8×C17—232no—
190C2×Q8×C17—212no—
191C2×Q8×C17#4118yescomplemented
192C2×Q8×C17C24112yes—
193C2×Q8×C17C2414yes—
194C22×C4×C17—212no—
195C22×C4×C17—212no—
196C22×C4×C17—24no—
197C22×C4×C17C2413yes—
198C22×C4×C17C2413yes—
199C22×C4×C17C24112yes—
200C22×C4×C17C2413yes—
201C22×C4×C17C24112yes—
202C22×C4×C17C2411yescharacteristic
203C22×C4×C17C2414yes—
204C22×C4×C17C2413yes—
205C22×C4×C17C2411yescharacteristic
206C2×C22⋊D17—212no—
207C2×C22⋊D17#4118yescomplemented
208C2×C22⋊D17C24112yes—
209C2×C22⋊D17C2414yes—
210C22×Dic17C2413yes—
211C22×Dic17C2413yes—
212C22×Dic17C2411yescharacteristic
213C22×Dic17C2411yescharacteristic
214C22×Dic17C2413yes—
215C22×Dic17C2411yescharacteristic
216#63256—232no—
217Q8×D17—232no—
218#63252—296no—
219C2×D68—212no—
220C2×D68—212no—
221C2×D68C24112yes—
222C2×D68C24112yes—
223C2×C4×D17—212no—
224C2×C4×D17—212no—
225C2×C4×D17—212no—
226C2×C4×D17—24no—
227C2×C4×D17—212no—
228C2×C4×D17—212no—
229C2×C4×D17C24112yes—
230C2×C4×D17C24112yes—
231C2×C4×D17C24112yes—
232C2×C4×D17C24112yes—
233C2×C4×D17C2414yes—
234C2×C4×D17C24112yes—
235C2×Dic34—212no—
236C2×Dic34—212no—
237C2×Dic34C24112yes—
238C2×Dic34C24112yes—
239C4⋊C4×C17C24112yes—
240C4⋊C4×C17C24112yes—
241C4⋊C4×C17C24124yes—
242C42×C17C24112yes—
243C42×C17C24112yes—
244C42×C17C24112yes—
245C42×C17C24112yes—
246C22⋊Dic17C24112yes—
247C22⋊Dic17C2414yes—
248#63227C2414yes—
249#63227C24112yes—
250#63227C24112yes—
251#63227C24112yes—
252#63227C24124yes—
253#63227C24124yes—
254#63227C24124yes—
255C4⋊Dic17C24112yes—
256C4⋊Dic17C24112yes—
257C4⋊Dic17C24112yes—
258C4⋊Dic17C24112yes—
259#63225C2414yes—
260#63225C24112yes—
261#63225C24112yes—
262#63225C24112yes—
263#63225C24124yes—
264#63225C24124yes—
265#63225C24124yes—
266C4×Dic17C2414yes—
267C4×Dic17C24112yes—
268C4×Dic17C24112yes—
269C4×Dic17C24112yes—
270C4×Dic17C24112yes—
271C4×Dic17C24112yes—
272C2×#3482—171nomaximal, Sylow
273C23×C17—22no—
274C23×C17—22no—
275C23×C17C2×#4114yes—
276C23×C17C2512yes—
277C23×C17C2511yescharacteristic
278C22×D17—22no—
279C22×D17—22no—
280C22×D17—26no—
281C22×D17—26no—
282C22×D17—26no—
283C22×D17C2×#4114yes—
284C22×D17C2516yes—
285C22×D17C2512yes—
286Q8×C17—224no—
287Q8×C17C2×#41116yescomplemented
288C2×C4×C17—26no—
289C2×C4×C17—26no—
290C2×C4×C17—224no—
291C2×C4×C17—26no—
292C2×C4×C17—22no—
293C2×C4×C17—224no—
294C2×C4×C17—28no—
295C2×C4×C17C2×#41112yes—
296C2×C4×C172−1+414yes—
297C2×C4×C17C2512yes—
298C2×C4×C17C2516yes—
299C2×C4×C17C2516yes—
300C2×C4×C17C2516yes—
301C2×C4×C17C2516yes—
302C2×C4×C17C2512yes—
303C22⋊D17—224no—
304C22⋊D17C2×#41116yescomplemented
305C2×Dic17—26no—
306C2×Dic17—26no—
307C2×Dic17—22no—
308C2×Dic17—22no—
309C2×Dic17—26no—
310C2×Dic17C2×#4114yes—
311C2×Dic17C2516yes—
312C2×Dic17C2512yes—
313C2×Dic17C2512yes—
314C2×Dic17C2516yes—
315C2×Dic17C2516yes—
316C2×Dic17C2512yes—
317D68—224no—
318D68—224no—
319C4×D17—224no—
320C4×D17—224no—
321C4×D17—224no—
322C4×D17—28no—
323C4×D17—224no—
324C4×D17—224no—
325Dic34—224no—
326Dic34—224no—
327#3482—1732no—
328C2×#557—171no—
329C2×#556—173no—
330C2×#552—173no—
331C2×#552—173no—
332C2×D4×Q8—171no—
333C2×#548—171no—
334C2×#548—171no—
335C2×#547—173no—
336C2×#533—173no—
337C2×#529—173no—
338C2×#529—173no—
339C2×C4×#41—173no—
340C2×C4×#41—171no—
341C22×C4×Q8—171no—
342C22×C4×Q8D1711yescharacteristic, complemented
343C22×C17—22no—
344C22×C17—22no—
345C22×C17—28no—
346C22×C17C22×#4114yes—
347C22×C17C22×#4112yes—
348C22×C17C22×#4112yes—
349C22×C17C2×2−1+412yes—
350C22×C17C2611yescharacteristic
351C2×D17—22no—
352C2×D17—22no—
353C2×D17—28no—
354C2×D17—26no—
355C2×D17—26no—
356C2×D17—26no—
357C2×D17—412no—
358C2×D17C22×#4114yes—
359C4×C17—26no—
360C4×C17—26no—
361C4×C17—26no—
362C4×C17—22no—
363C4×C17C22×#41112yes—
364C4×C17C2×2−1+414yes—
365Dic17—26no—
366Dic17—26no—
367Dic17—22no—
368Dic17—22no—
369Dic17—26no—
370Dic17C22×#4114yes—
371C22×#41—171no—
372C22×#41—173no—
373C23×Q8—171no—
374C23×Q8C2×D1711yescharacteristic
375#557—1716no—
376#556—1748no—
377#552—1748no—
378#552—1748no—
379D4×Q8—1716no—
380#548—1716no—
381#548—1716no—
382#547—1748no—
383#533—1748no—
384C2×C4⋊Q8—173no—
385C2×C4⋊Q8—173no—
386#529—1748no—
387#529—1748no—
388C2×#126—176no—
389C2×#126—176no—
390C2×#125—173no—
391C2×#125—176no—
392C2×#125—173no—
393C2×#124—173no—
394C2×#124—173no—
395C2×#123—176no—
396C2×#123—176no—
397C2×C22⋊Q8—173no—
398C2×C22⋊Q8—173no—
399C2×C22⋊Q8—173no—
400C2×C22⋊Q8—176no—
401C2×C22⋊Q8—173no—
402C2×#121—173no—
403C2×#121—173no—
404C4×#41—1716no—
405C4×#41—1748no—
406C2×C4×Q8—171no—
407C2×C4×Q8—171no—
408C2×C4×Q8—1716no—
409C2×C4×Q8—173no—
410C2×C4×Q8—173no—
411C2×C4×Q8—173no—
412C2×C4×Q8—173no—
413C2×C4×Q8C2×D1711yescharacteristic
414C2×C4×Q8C2×D1713yes—
415C2×C4×Q8C2×D1711yescharacteristic
416C2×C4×Q8C2×D1713yes—
417C2×C4×Q8C2×D17116yescomplemented
418C2×C4×D4—171no—
419C2×C4×D4—173no—
420C2×C4×D4—173no—
421C2×C4×D4—173no—
422C2×C4×D4—173no—
423C2×C4×D4—173no—
424C2×C4×D4—173no—
425C2×C4×D4—173no—
426C2×#117—173no—
427C2×#117—173no—
428C2×#117—173no—
429C2×#117—173no—
430C2×#117—176no—
431C22×C4⋊C4—173no—
432C22×C4⋊C4C2×D1713yes—
433C22×C42—173no—
434C22×C42—173no—
435C22×C42C2×D1713yes—
436C2×C17—24no—
437C2×C17#348214yescomplemented
438C2×C17C23×#4111yescharacteristic
439C2×C17C23×#4111yescharacteristic
440C2×C17C22×2−1+411yescharacteristic
441D17—24no—
442D17—46no—
443C2×#41—178no—
444C2×#41—1724no—
445C2×#41—3424no—
446C2×#41—348no—
447C22×Q8—28no—
448C22×Q8—178no—
449C22×Q8—173no—
450C22×Q8—173no—
451C22×Q8—348no—
452C22×Q8C22×D1713yes—
453C22×Q8C22×D1718yes—
454C22×Q8C22×D1711yescharacteristic
455C22×D4—171no—
456C22×D4—173no—
457C22×D4—173no—
458C22×D4—173no—
459C23×C4—173no—
460C23×C4—173no—
461C23×C4—173no—
462C23×C4—173no—
463C23×C4—173no—
464C23×C4—171no—
465C23×C4C22×D1713yes—
466C23×C4C22×D1713yes—
467C23×C4C22×D1711yescharacteristic
468C4⋊Q8—1724no—
469C4⋊Q8—1724no—
470#126—1748no—
471#126—1748no—
472#125—1724no—
473#125—1748no—
474#125—1724no—
475#124—1724no—
476#124—1724no—
477#123—1748no—
478#123—1748no—
479C22⋊Q8—1724no—
480C22⋊Q8—1724no—
481C22⋊Q8—1724no—
482C22⋊Q8—1748no—
483C22⋊Q8—1724no—
484#121—1724no—
485#121—1724no—
486C4×Q8—178no—
487C4×Q8—178no—
488C4×Q8—1724no—
489C4×Q8—1724no—
490C4×Q8—1724no—
491C4×Q8—1724no—
492C4×Q8C22×D1718yes—
493C4×Q8C22×D17124yes—
494C4×Q8C22×D1718yes—
495C4×Q8C22×D17124yes—
496C4×D4—178no—
497C4×D4—1724no—
498C4×D4—1724no—
499C4×D4—1724no—
500C4×D4—1724no—
501C4×D4—1724no—
502C4×D4—1724no—
503C4×D4—1724no—
504#117—1724no—
505#117—1724no—
506#117—1724no—
507#117—1724no—
508#117—1748no—
509C2×C4⋊C4—173no—
510C2×C4⋊C4—176no—
511C2×C4⋊C4—171no—
512C2×C4⋊C4—173no—
513C2×C4⋊C4—173no—
514C2×C4⋊C4—173no—
515C2×C4⋊C4—173no—
516C2×C4⋊C4—173no—
517C2×C4⋊C4—173no—
518C2×C4⋊C4—176no—
519C2×C4⋊C4—176no—
520C2×C4⋊C4—1724no—
521C2×C4⋊C4C22×D1713yes—
522C2×C4⋊C4C22×D1713yes—
523C2×C4⋊C4C22×D1716yes—
524C2×C4⋊C4C22×D17124yes—
525C2×C22⋊C4—171no—
526C2×C22⋊C4—173no—
527C2×C22⋊C4—171no—
528C2×C22⋊C4—173no—
529C2×C22⋊C4—176no—
530C2×C22⋊C4—173no—
531C2×C22⋊C4—173no—
532C2×C22⋊C4—176no—
533C2×C22⋊C4—176no—
534C2×C42—173no—
535C2×C42—173no—
536C2×C42—173no—
537C2×C42—173no—
538C2×C42—173no—
539C2×C42—171no—
540C2×C42—1724no—
541C2×C42—1724no—
542C2×C42C22×D1713yes—
543C2×C42C22×D1713yes—
544C2×C42C22×D17124yes—
545C2×C42C22×D1713yes—
546C2×C42C22×D1713yes—
547C17C2×#348211yescharacteristic, complemented, Sylow
548C24—171no—
549C24—173no—
550C24C23×D1711yescharacteristic
551#41—3496no—
552#41—3432no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—1712no—
556C2×Q8—1712no—
557C2×Q8—3412no—
558C2×Q8—3432no—
559C2×Q8—3412no—
560C2×Q8#6325218yescomplemented
561C2×Q8C23×D17112yes—
562C2×Q8C23×D1714yes—
563C2×D4—178no—
564C2×D4—174no—
565C2×D4—1712no—
566C2×D4—1712no—
567C2×D4—1712no—
568C2×D4—3412no—
569C2×D4—3412no—
570C2×D4—3412no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—171no—
575C22×C4—171no—
576C22×C4—171no—
577C22×C4—173no—
578C22×C4—173no—
579C22×C4—173no—
580C22×C4—174no—
581C22×C4—1712no—
582C22×C4—1712no—
583C22×C4—1712no—
584C22×C4—1712no—
585C22×C4—1712no—
586C22×C4—3412no—
587C22×C4—3412no—
588C22×C4—3412no—
589C22×C4—3412no—
590C22×C4—344no—
591C22×C4—3412no—
592C22×C4C23×D1713yes—
593C22×C4C23×D1711yescharacteristic
594C22×C4C23×D1714yes—
595C22×C4C23×D1713yes—
596C22×C4C23×D1713yes—
597C22×C4C23×D17112yes—
598C22×C4C23×D17112yes—
599C22×C4C23×D1713yes—
600C22×C4C23×D1711yescharacteristic
601C4⋊C4—1712no—
602C4⋊C4—1724no—
603C4⋊C4—174no—
604C4⋊C4—1712no—
605C4⋊C4—1712no—
606C4⋊C4—1712no—
607C4⋊C4—1712no—
608C4⋊C4—1712no—
609C4⋊C4—1712no—
610C4⋊C4—1724no—
611C4⋊C4—1724no—
612C4⋊C4C23×D17112yes—
613C4⋊C4C23×D17112yes—
614C4⋊C4C23×D17124yes—
615C22⋊C4—174no—
616C22⋊C4—1712no—
617C22⋊C4—174no—
618C22⋊C4—1712no—
619C22⋊C4—1724no—
620C22⋊C4—1712no—
621C22⋊C4—1712no—
622C22⋊C4—1724no—
623C22⋊C4—1724no—
624C42—174no—
625C42—1712no—
626C42—1712no—
627C42—1712no—
628C42—1712no—
629C42—1712no—
630C42C23×D17112yes—
631C42C23×D17112yes—
632C42C23×D17112yes—
633C42C23×D17112yes—
634C23—22no—
635C23—22no—
636C23—174no—
637C23—172no—
638C23—176no—
639C23—342no—
640C23—342no—
641C23—346no—
642C23—346no—
643C23—346no—
644C23#41×D1714yes—
645C23C24×D1712yes—
646C23C24×D1711yescharacteristic
647Q8—224no—
648Q8—3424no—
649Q8—3424no—
650Q8C2×#63252116yescomplemented
651D4—1716no—
652D4—3424no—
653D4—3424no—
654D4—3424no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—224no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—174no—
663C2×C4—172no—
664C2×C4—172no—
665C2×C4—172no—
666C2×C4—176no—
667C2×C4—176no—
668C2×C4—176no—
669C2×C4—3424no—
670C2×C4—3424no—
671C2×C4—346no—
672C2×C4—342no—
673C2×C4—346no—
674C2×C4—342no—
675C2×C4—346no—
676C2×C4—3424no—
677C2×C4—3424no—
678C2×C4—348no—
679C2×C4—3424no—
680C2×C4C2×#63252112yes—
681C2×C4#1058769414yes—
682C2×C4C24×D1716yes—
683C2×C4C24×D1712yes—
684C2×C4C24×D1716yes—
685C2×C4C24×D1716yes—
686C2×C4C24×D1716yes—
687C2×C4C24×D1712yes—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—174no—
692C22—348no—
693C22—342no—
694C22—342no—
695C22—346no—
696C22—346no—
697C22—346no—
698C22—6812no—
699C22C2×#41×D1714yes—
700C22C2×#41×D1712yes—
701C22C22×#6325212yes—
702C22C2×#1058769412yes—
703C22C25×D1711yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—174no—
709C4—346no—
710C4—342no—
711C4—346no—
712C4—342no—
713C4—346no—
714C4C22×#63252112yes—
715C4C2×#1058769414yes—
716C2—24no—
717C2—344no—
718C2—686no—
719C2#1454240114yesdirect product factor
720C2C22×#41×D1711yescharacteristic
721C2C23×#6325211yescharacteristic
722C2C22×#1058769411yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC22×C4×Q8×C17C2
socleC23×C17C25
hypercenterC22×C4×Q8D17
hypocenterC17C2×#3482
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #14542401C2direct (N × H)
2. C2×#11763535C2semidirect
3. C2×#11763531C2semidirect
4. C2×#11763500C2semidirect
5. C2×#11763494C2semidirect
6. C2×Q8×C22⋊D17C2semidirect
7. C2×#11763471C2semidirect
8. C2×#11763470C2semidirect
9. C2×#11763460C2semidirect
10. C2×#11763363C2semidirect
11. C2×#11763346C2semidirect
12. C2×#11763343C2semidirect
13. C2×C4×#63256C2semidirect
14. C2×C4×#63252C2semidirect
15. C2×C4×Q8×D17C2semidirect
16. C22×C4×Q8×C17C2semidirect
20. #11763535C22semidirect
21. #11763531C22semidirect
22. #11763500C22semidirect
23. #11763494C22semidirect
24. Q8×C22⋊D17C22semidirect
25. #11763471C22semidirect
26. #11763470C22semidirect
27. #11763460C22semidirect
28. #11763363C22semidirect
31. #11763346C22semidirect
32. #11763343C22semidirect
49. C4×#63256C22semidirect
50. C4×#63252C22semidirect
57. C4×Q8×D17C22semidirect
79. C2×C4×Q8×C17C22semidirect
191. C2×Q8×C17#41semidirect
207. C2×C22⋊D17#41semidirect
287. Q8×C17C2×#41semidirect
304. C22⋊D17C2×#41semidirect
342. C22×C4×Q8D17semidirect
417. C2×C4×Q8C2×D17semidirect
437. C2×C17#3482semidirect
547. C17C2×#3482semidirect
560. C2×Q8#63252semidirect
650. Q8C2×#63252semidirect
719. C2#14542401direct (N × H)

Maximal subgroups

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

subgroupindex
#145424012
C2×#117635352
C2×#117635312
C2×#117635002
C2×#117634942
C2×Q8×C22⋊D172
C2×#117634712
C2×#117634702
C2×#117634602
C2×#117633632
C2×#117633462
C2×#117633432
C2×C4×#632562
C2×C4×#632522
C2×C4×Q8×D172
C22×C4×Q8×C172
C2×#348217