Finite Group Databasebeta

← C2×#22603115 #32911288

Subgroups — C2×#22603115 #32911288

Order 18176.

11138 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986834C211yesmaximal, characteristic, complemented
2C2×H(5,𝔽2)×D71C211yesmaximal, characteristic, complemented
3#22603115C2132yesmaximal, direct product factor
4C2×#17986811C211yesmaximal, characteristic, complemented
5C2×#17986810C211yesmaximal, characteristic, complemented
6C2×#17986809C213yesmaximal, complemented
7C2×#17986806C213yesmaximal, complemented
8C2×#17986803C213yesmaximal, complemented
9C2×#17986802C211yesmaximal, characteristic, complemented
10C2×#17986800C213yesmaximal, complemented
11C2×#17986796C213yesmaximal, complemented
12C2×#17986795C213yesmaximal, complemented
13C22×#14556152C213yesmaximal, complemented
14C2×AGL(1,ℤ/8)×D71C213yesmaximal, complemented
15C2×#17986764C211yesmaximal, characteristic, complemented
16C2×#576×C71C211yesmaximal, characteristic, complemented
17#17986834—28no—
18#17986834C22116yescomplemented
19C2×#14556175—21no—
20C2×#14556175C2211yescharacteristic, complemented
21C2×#14556175C2213yescomplemented
22C2×#14556174—21no—
23C2×#14556174C2211yescharacteristic, complemented
24C2×#14556174C2213yescomplemented
25C2×#14556173—23no—
26C2×#14556173—23no—
27C2×#14556173C2213yescomplemented
28C2×#14556173C2213yescomplemented
29H(5,𝔽2)×D71—28no—
30H(5,𝔽2)×D71C22116yescomplemented
31C22×#11765864—23no—
32C22×#11765864C2213yescomplemented
33C2×#41×D71—21no—
34C2×#41×D71—21no—
35C2×#41×D71C2211yescharacteristic
36C2×#41×D71C2213yescomplemented
37C2×#41×D71C2213yescomplemented
38C22×D4×D71—23no—
39C22×D4×D71C2213yescomplemented
40#17986811C22116yescomplemented
41#17986810C22116yescomplemented
42#17986809C22148yescomplemented
43#17986806C22148yescomplemented
44#17986803C22148yescomplemented
45#17986802C22116yescomplemented
46#17986800C22148yescomplemented
47#17986796C22148yescomplemented
48#17986795C22148yescomplemented
49C2×#14556161C2213yescomplemented
50C2×#14556160C2211yescharacteristic, complemented
51C2×#14556160C2213yescomplemented
52C2×#14556158C2213yescomplemented
53C2×#14556157C2213yescomplemented
54C2×#14556157C2213yescomplemented
55C2×#14556156C2213yescomplemented
56C2×#14556155C2213yescomplemented
57C2×#14556155C2213yescomplemented
58C2×#14556154C2213yescomplemented
59C2×#14556154C2213yescomplemented
60C2×#14556153C2213yescomplemented
61C2×#14556152C2216yescomplemented
62C2×#14556152C2213yescomplemented
63C2×#14556152C2216yescomplemented
64C2×#14556152C2216yescomplemented
65C2×#14556152C2213yescomplemented
66C2×#14556152C22148yescomplemented
67AGL(1,ℤ/8)×D71C22148yescomplemented
68C2×#14556150C2213yescomplemented
69C2×#14556149C2216yescomplemented
70C2×#14556148C2213yescomplemented
71C2×#14556148C2213yescomplemented
72C2×#14556147C2216yescomplemented
73C22×#11765854C2213yescomplemented
74C22×#11765853C2213yescomplemented
75C2×SD16×D71C2216yescomplemented
76C22×#11765850C2213yescomplemented
77C2×D8×D71C2216yescomplemented
78#17986764C22116yescomplemented
79C2×#14556136C2213yescomplemented
80C2×#14556135C2211yescharacteristic, complemented
81C2×#14556134C2213yescomplemented
82C22×#11765848C2213yescomplemented
83C2×M16×D71C2213yescomplemented
84C2×H(5,𝔽2)×C71C2211yescharacteristic, complemented
85C2×H(5,𝔽2)×C71C2211yescharacteristic, complemented
86#576×C71C22116yescomplemented
87C2×AGL(1,ℤ/8)×C71C2213yescomplemented
88C2×AGL(1,ℤ/8)×C71C2213yescomplemented
89C2×#135×C71C2213yescomplemented
90C22×D8×C71C2213yescomplemented
91C2×#131×C71C2211yescharacteristic, complemented
92C24×D71—23no—
93#14556175—212no—
94#14556175—216no—
95#14556175—24no—
96#14556175C2318yescomplemented
97#14556175C23124yescomplemented
98#14556174—216no—
99#14556174—212no—
100#14556174—24no—
101#14556174C2318yescomplemented
102#14556174C23124yescomplemented
103#14556173—212no—
104#14556173—212no—
105#14556173—248no—
106#14556173—248no—
107#14556173C23124yescomplemented
108#14556173C23124yescomplemented
109C2×#11765866—21no—
110C2×#11765866D411yescharacteristic
111C2×#11765866C2311yescharacteristic
112C2×#11765866C2313yes—
113C2×#11765865—23no—
114C2×#11765865—23no—
115C2×#11765865—23no—
116C2×#11765865—23no—
117C2×#11765865C2313yes—
118C2×#11765865C2313yes—
119C2×#11765865C2313yescomplemented
120C2×#11765864—248no—
121C2×#11765864—23no—
122C2×#11765864—23no—
123C2×#11765864—26no—
124C2×#11765864—23no—
125C2×#11765864—23no—
126C2×#11765864—23no—
127C2×#11765864—23no—
128C2×#11765864—212no—
129C2×#11765864—23no—
130C2×#11765864D413yes—
131C2×#11765864C2313yes—
132C2×#11765864C2313yes—
133C2×#11765864C2316yescomplemented
134C2×#11765864C23124yescomplemented
135#41×D71—216no—
136#41×D71—216no—
137#41×D71—212no—
138#41×D71—212no—
139#41×D71D418yes—
140#41×D71C2318yes—
141#41×D71C23124yescomplemented
142#41×D71C23124yescomplemented
143C22×Dic142—23no—
144C22×Dic142C2313yescomplemented
145C2×Q8×D71—21no—
146C2×Q8×D71D411yescharacteristic
147C2×Q8×D71C2311yescharacteristic
148C2×Q8×D71C2313yescomplemented
149C22×D284—23no—
150C22×D284C2313yes—
151C22×C22⋊D71—23no—
152C22×C22⋊D71—26no—
153C22×C22⋊D71—26no—
154C22×C22⋊D71—23no—
155C2×D4×D71—23no—
156C2×D4×D71—23no—
157C2×D4×D71—23no—
158C2×D4×D71—23no—
159C2×D4×D71—26no—
160C2×D4×D71—248no—
161C2×D4×D71—23no—
162C2×D4×D71—212no—
163C2×D4×D71—23no—
164C2×D4×D71—23no—
165C2×D4×D71D413yes—
166C2×D4×D71C2313yes—
167C2×D4×D71C2316yes—
168C2×D4×D71C23124yescomplemented
169C2×D4×D71C2313yescomplemented
170C23×Dic71—23no—
171C22×C4×D71—23no—
172C22×C4×D71—23no—
173C22×C4×D71C2313yes—
174#14556161C23124yescomplemented
175#14556160C2318yescomplemented
176#14556160C23124yescomplemented
177#14556158C23124yescomplemented
178#14556157C23124yescomplemented
179#14556157C23124yescomplemented
180#14556156C23124yescomplemented
181#14556155C23124yescomplemented
182#14556155C23124yescomplemented
183#14556154C23124yescomplemented
184#14556154C23124yescomplemented
185#14556153C23124yescomplemented
186#14556152C23148yescomplemented
187#14556152C23124yescomplemented
188#14556152C23148yescomplemented
189#14556152C23148yescomplemented
190#14556152C23124yescomplemented
191#14556150C23124yescomplemented
192#14556149C23148yescomplemented
193#14556148C23124yescomplemented
194#14556148C23124yescomplemented
195#14556147C23148yescomplemented
196C2×Dic284C2313yescomplemented
197C2×#11765855C2311yescharacteristic, complemented
198C2×#11765855C2313yescomplemented
199C2×#11765854C2316yescomplemented
200C2×#11765854C2313yescomplemented
201C2×#11765854C2311yescharacteristic, complemented
202C2×#11765854C23124yescomplemented
203C2×#11765853C2316yescomplemented
204C2×#11765853C2313yescomplemented
205C2×#11765853C2313yescomplemented
206C2×#11765853C23124yescomplemented
207C2×#11765852C2313yescomplemented
208C2×#11765852C2311yescharacteristic, complemented
209SD16×D71C23148yescomplemented
210C2×D568C2313yescomplemented
211C2×#11765850C2313yescomplemented
212C2×#11765850C2316yescomplemented
213C2×#11765850C2313yescomplemented
214C2×#11765850C23124yescomplemented
215D8×D71C23148yescomplemented
216#14556136C23124yescomplemented
217#14556135C2318yescomplemented
218#14556134C23124yescomplemented
219C2×#11765849C2313yescomplemented
220C2×#11765848C2313yes—
221C2×#11765848C2311yescharacteristic
222C2×#11765848C2313yescomplemented
223C2×#11765848C2313yescomplemented
224C2×#11765848C23124yescomplemented
225M16×D71C23124yescomplemented
226C22×C71⋊C8C2313yescomplemented
227C2×C8×D71C2316yescomplemented
228H(5,𝔽2)×C71—24no—
229H(5,𝔽2)×C71—24no—
230H(5,𝔽2)×C71C2318yescomplemented
231H(5,𝔽2)×C71C2318yescomplemented
232C2×#41×C71—21no—
233C2×#41×C71—21no—
234C2×#41×C71C2313yes—
235C2×#41×C71C2311yescharacteristic
236C2×#41×C71C2313yescomplemented
237C22×D4×C71—23no—
238C22×D4×C71—23no—
239C22×D4×C71C2313yes—
240C22×D4×C71C2313yescomplemented
241AGL(1,ℤ/8)×C71C23124yescomplemented
242AGL(1,ℤ/8)×C71C23124yescomplemented
243#135×C71C23124yescomplemented
244C2×Q16×C71C2311yescharacteristic, complemented
245C2×SD16×C71C2313yescomplemented
246C2×SD16×C71C2313yescomplemented
247C2×D8×C71C2313yescomplemented
248C2×D8×C71C2316yescomplemented
249C2×D8×C71C23124yescomplemented
250#131×C71C2318yescomplemented
251C2×M16×C71C2313yescomplemented
252C22×C8×C71C2313yescomplemented
253C23×D71—23no—
254C23×D71—23no—
255C23×D71—23no—
256C23×D71—224no—
257C23×D71—26no—
258C23×D71—812no—
259C23×D71C2×D413yes—
260#11765866—28no—
261#11765866—22no—
262#11765866—26no—
263#11765866C2×D418yes—
264#11765866C2414yes—
265#11765866C24112yes—
266#11765865—26no—
267#11765865—26no—
268#11765865—224no—
269#11765865—224no—
270#11765865—224no—
271#11765865—224no—
272#11765865C2×D4112yes—
273#11765865C24112yes—
274#11765865C24112yes—
275#11765865C24112yescomplemented
276#11765864—224no—
277#11765864—248no—
278#11765864—224no—
279#11765864—224no—
280#11765864—26no—
281#11765864—224no—
282#11765864—26no—
283#11765864—212no—
284#11765864—224no—
285#11765864—224no—
286#11765864—224no—
287#11765864C2×D4124yes—
288#11765864C24112yes—
289#11765864C24112yes—
290#11765864C24124yescomplemented
291C2×Dic142—23no—
292C2×Dic142—26no—
293C2×Dic142—21no—
294C2×Dic142—23no—
295C2×Dic142—224no—
296C2×Dic142C2×D413yes—
297C2×Dic142C2411yescharacteristic
298C2×Dic142C2413yes—
299C2×Dic142C24112yescomplemented
300Q8×D71—28no—
301Q8×D71—22no—
302Q8×D71—26no—
303Q8×D71C2×D418yes—
304Q8×D71C2414yes—
305Q8×D71C24112yescomplemented
306C2×D284—23no—
307C2×D284—21no—
308C2×D284—23no—
309C2×D284—26no—
310C2×D284—224no—
311C2×D284C2×D413yes—
312C2×D284C2413yes—
313C2×D284C2411yescharacteristic
314C2×D284C24112yes—
315C2×C22⋊D71—23no—
316C2×C22⋊D71—23no—
317C2×C22⋊D71—23no—
318C2×C22⋊D71—23no—
319C2×C22⋊D71—26no—
320C2×C22⋊D71—224no—
321C2×C22⋊D71—248no—
322C2×C22⋊D71—248no—
323C2×C22⋊D71—23no—
324C2×C22⋊D71—26no—
325C2×C22⋊D71—224no—
326C2×C22⋊D71—23no—
327C2×C22⋊D71C2×D416yes—
328D4×D71—224no—
329D4×D71—224no—
330D4×D71—224no—
331D4×D71—248no—
332D4×D71—224no—
333D4×D71—224no—
334D4×D71—26no—
335D4×D71—224no—
336D4×D71—212no—
337D4×D71—224no—
338D4×D71—26no—
339D4×D71C2×D4124yes—
340D4×D71C24112yes—
341D4×D71C24124yes—
342D4×D71C24112yescomplemented
343C22×Dic71—23no—
344C22×Dic71—23no—
345C22×Dic71—23no—
346C22×Dic71—26no—
347C22×Dic71—224no—
348C22×Dic71C2×D413yes—
349C2×C4×D71—21no—
350C2×C4×D71—23no—
351C2×C4×D71—23no—
352C2×C4×D71—23no—
353C2×C4×D71—21no—
354C2×C4×D71—23no—
355C2×C4×D71—224no—
356C2×C4×D71—224no—
357C2×C4×D71C2×D413yes—
358C2×C4×D71C2×D413yes—
359C2×C4×D71C2×D4112yes—
360C2×C4×D71C2411yescharacteristic
361C2×C4×D71C2413yes—
362C2×C4×D71C24112yes—
363Dic284C24112yescomplemented
364#11765855C2414yescomplemented
365#11765855C24112yescomplemented
366#11765854C24112yescomplemented
367#11765854C2414yescomplemented
368#11765854C24124yescomplemented
369#11765853C24124yescomplemented
370#11765853C24112yescomplemented
371#11765853C24112yescomplemented
372#11765852C24112yescomplemented
373#11765852C2414yescomplemented
374D568C24112yescomplemented
375#11765850C24112yescomplemented
376#11765850C24124yescomplemented
377#11765850C24112yescomplemented
378#11765849C24112yescomplemented
379#11765848C2414yes—
380#11765848C24112yes—
381#11765848C24112yescomplemented
382#11765848C24112yescomplemented
383C2×C71⋊C8C2413yes—
384C2×C71⋊C8C2411yescharacteristic
385C2×C71⋊C8C24112yescomplemented
386C8×D71C24124yescomplemented
387C24×C71—23no—
388C24×C71—23no—
389#41×C71—28no—
390#41×C71—28no—
391#41×C71—26no—
392#41×C71—26no—
393#41×C71C2×D414yes—
394#41×C71C24112yes—
395#41×C71C2414yes—
396#41×C71C24112yescomplemented
397C2×Q8×C71C2×D411yescharacteristic
398C2×Q8×C71C2411yescharacteristic
399C2×Q8×C71C2411yescharacteristic
400C2×D4×C71—23no—
401C2×D4×C71—23no—
402C2×D4×C71—224no—
403C2×D4×C71—224no—
404C2×D4×C71—23no—
405C2×D4×C71—26no—
406C2×D4×C71—23no—
407C2×D4×C71—26no—
408C2×D4×C71C2×D413yes—
409C2×D4×C71C2413yes—
410C2×D4×C71C24112yes—
411C2×D4×C71C2413yes—
412C2×D4×C71C24112yescomplemented
413C22×C4×C71—23no—
414C22×C4×C71—23no—
415C22×C4×C71C2413yes—
416Q16×C71C2414yescomplemented
417SD16×C71C24112yescomplemented
418SD16×C71C24112yescomplemented
419D8×C71C24112yescomplemented
420D8×C71C24124yescomplemented
421M16×C71C24112yescomplemented
422C2×C8×C71C2411yescharacteristic
423C2×C8×C71C2413yes—
424C2×C8×C71C24112yescomplemented
425C23×C71—23no—
426C23×C71—23no—
427C23×C71—212no—
428C23×C71—212no—
429C23×C71—86no—
430C23×C71—86no—
431C23×C71C22×D413yes—
432C22×D71—21no—
433C22×D71—23no—
434C22×D71—212no—
435C22×D71—212no—
436C22×D71—212no—
437C22×D71—224no—
438C22×D71—46no—
439C22×D71—412no—
440C22×D71—86no—
441C22×D71—812no—
442C22×D71—848no—
443C22×D71—86no—
444C22×D71C22×D411yescharacteristic
445C22×D71C22×D413yes—
446C22×D71C22×D4112yes—
447Q8×C71—21no—
448Q8×C71—21no—
449Q8×C71C22×D414yes—
450Q8×C71C2512yes—
451Q8×C71C2512yes—
452D4×C71—212no—
453D4×C71—212no—
454D4×C71—23no—
455D4×C71—212no—
456D4×C71—23no—
457D4×C71—212no—
458D4×C71C22×D4112yes—
459D4×C71C2516yes—
460D4×C71C2516yes—
461C2×C4×C71—21no—
462C2×C4×C71—21no—
463C2×C4×C71—212no—
464C2×C4×C71—212no—
465C2×C4×C71C22×D413yes—
466C2×C4×C71C22×D416yes—
467C2×C4×C71C2511yescharacteristic
468C2×C4×C71C2516yes—
469C22⋊D71—212no—
470C22⋊D71—212no—
471C22⋊D71—212no—
472C22⋊D71—212no—
473C22⋊D71—224no—
474C22⋊D71—224no—
475C22⋊D71—212no—
476C22⋊D71—212no—
477C22⋊D71C22×D4124yes—
478C2×Dic71—21no—
479C2×Dic71—23no—
480C2×Dic71—212no—
481C2×Dic71—212no—
482C2×Dic71—212no—
483C2×Dic71—224no—
484C2×Dic71C22×D411yescharacteristic
485C2×Dic71C22×D413yes—
486C2×Dic71C22×D4112yes—
487D284—212no—
488D284—24no—
489D284—23no—
490D284—212no—
491D284—21no—
492D284C22×D4112yes—
493D284C2512yes—
494D284C2516yes—
495C4×D71—24no—
496C4×D71—212no—
497C4×D71—212no—
498C4×D71—212no—
499C4×D71—24no—
500C4×D71—212no—
501C4×D71C22×D4112yes—
502C4×D71C22×D4112yes—
503C4×D71C22×D412yes—
504C4×D71C22×D416yes—
505C4×D71C2516yes—
506C4×D71C2512yes—
507Dic142—23no—
508Dic142—212no—
509Dic142—21no—
510Dic142—24no—
511Dic142—212no—
512Dic142C22×D4112yes—
513Dic142C2516yes—
514Dic142C2512yes—
515C8×C71C2512yes—
516C8×C71C2516yes—
517C71⋊C8C2516yes—
518C71⋊C8C2512yes—
519C22×C71—26no—
520C22×C71—26no—
521C22×C71—26no—
522C22×C71—46no—
523C22×C71—46no—
524C22×C71—812no—
525C22×C71—812no—
526C22×C71C23×D416yes—
527C22×C71C23×D411yescharacteristic
528C2×D71—22no—
529C2×D71—26no—
530C2×D71—22no—
531C2×D71—26no—
532C2×D71—412no—
533C2×D71—424no—
534C2×D71—46no—
535C2×D71—42no—
536C2×D71—812no—
537C2×D71—824no—
538C2×D71—812no—
539C2×D71C23×D412yes—
540C2×D71C23×D416yes—
541C4×C71—22no—
542C4×C71—22no—
543C4×C71C23×D411yescharacteristic
544C4×C71C23×D416yes—
545C4×C71C2611yescharacteristic
546Dic71—26no—
547Dic71—22no—
548Dic71C23×D416yes—
549Dic71C23×D412yes—
550C2×#3585—711nomaximal, Sylow
551C2×C71—26no—
552C2×C71—46no—
553C2×C71—46no—
554C2×C71#358512yescomplemented
555C2×C71C24×D411yescharacteristic
556D71—22no—
557D71—26no—
558D71—46no—
559D71—42no—
560C2×#585—711no—
561C22×H(5,𝔽2)—711no—
562#3585—7132no—
563C2×#577—711no—
564C2×#577—713no—
565C2×#577—713no—
566C2×#577—711no—
567C2×#576—711no—
568C2×#576—713no—
569C2×#576—713no—
570C2×#576D7111yescharacteristic, complemented
571C2×#575—713no—
572C2×#575—713no—
573C22×AGL(1,ℤ/8)—713no—
574C22×AGL(1,ℤ/8)—713no—
575C2×#568—711no—
576C71C2×#358511yescharacteristic, complemented, Sylow
577#585—7116no—
578#585—1428no—
579C2×2−1+4—711no—
580C2×2−1+4—713no—
581C2×2−1+4—1421no—
582C2×H(5,𝔽2)—7116no—
583C2×H(5,𝔽2)—713no—
584C2×H(5,𝔽2)—711no—
585C2×H(5,𝔽2)—713no—
586C2×H(5,𝔽2)—713no—
587C2×H(5,𝔽2)—1423no—
588C2×H(5,𝔽2)—1423no—
589C2×H(5,𝔽2)—1421no—
590C2×H(5,𝔽2)—1428no—
591C2×H(5,𝔽2)C2×D7111yescharacteristic, complemented
592C2×H(5,𝔽2)C2×D7111yescharacteristic, complemented
593C22×#41—711no—
594C22×#41—713no—
595C22×#41—713no—
596C22×#41—713no—
597C22×#41—1423no—
598C22×#41—1421no—
599C22×#41—1421no—
600C23×D4—713no—
601C23×D4—1423no—
602#577—7116no—
603#577—7148no—
604#577—7148no—
605#577—7116no—
606#576—7116no—
607#576—7148no—
608#576—7148no—
609#576C2×D71116yescomplemented
610#575—7148no—
611#575—7148no—
612C2×#137—713no—
613C2×#137—711no—
614C2×#137—713no—
615C2×#137—713no—
616C2×#137—713no—
617C2×#137—713no—
618C2×AGL(1,ℤ/8)—713no—
619C2×AGL(1,ℤ/8)—713no—
620C2×AGL(1,ℤ/8)—713no—
621C2×AGL(1,ℤ/8)—7148no—
622C2×AGL(1,ℤ/8)—713no—
623C2×AGL(1,ℤ/8)—713no—
624C2×AGL(1,ℤ/8)—7148no—
625C2×AGL(1,ℤ/8)—716no—
626C2×AGL(1,ℤ/8)—713no—
627C2×AGL(1,ℤ/8)—716no—
628C2×AGL(1,ℤ/8)—716no—
629C2×AGL(1,ℤ/8)—713no—
630C2×AGL(1,ℤ/8)—713no—
631C2×AGL(1,ℤ/8)C2×D7113yescomplemented
632C2×AGL(1,ℤ/8)C2×D7113yescomplemented
633C2×#135—713no—
634C2×#135—713no—
635C2×#135—716no—
636C2×#135—716no—
637C2×#135—713no—
638C2×#135C2×D7113yescomplemented
639C22×SD16—713no—
640C22×SD16—716no—
641C22×SD16—713no—
642C22×D8—713no—
643C22×D8—716no—
644C22×D8C2×D7113yescomplemented
645#568—7116no—
646C2×#131—711no—
647C2×#131—713no—
648C2×#131—713no—
649C2×#131C2×D7111yescharacteristic, complemented
650C22×M16—713no—
651C22×M16—713no—
652C25—1423no—
6532−1+4—718no—
6542−1+4—7124no—
6552−1+4—14216no—
6562−1+4—14212no—
6572−1+4—1424no—
658H(5,𝔽2)—24no—
659H(5,𝔽2)—24no—
660H(5,𝔽2)—7124no—
661H(5,𝔽2)—718no—
662H(5,𝔽2)—7124no—
663H(5,𝔽2)—7124no—
664H(5,𝔽2)—14248no—
665H(5,𝔽2)—14248no—
666H(5,𝔽2)—14212no—
667H(5,𝔽2)—14212no—
668H(5,𝔽2)—14216no—
669H(5,𝔽2)—14212no—
670H(5,𝔽2)—1424no—
671H(5,𝔽2)C22×D7118yescomplemented
672H(5,𝔽2)C22×D7118yescomplemented
673C2×#41—21no—
674C2×#41—21no—
675C2×#41—718no—
676C2×#41—718no—
677C2×#41—711no—
678C2×#41—713no—
679C2×#41—713no—
680C2×#41—7124no—
681C2×#41—7124no—
682C2×#41—713no—
683C2×#41—711no—
684C2×#41—713no—
685C2×#41—713no—
686C2×#41—716no—
687C2×#41—7124no—
688C2×#41—713no—
689C2×#41—713no—
690C2×#41—1423no—
691C2×#41—1423no—
692C2×#41—1423no—
693C2×#41—1423no—
694C2×#41—1423no—
695C2×#41—1423no—
696C2×#41—1423no—
697C2×#41—1423no—
698C2×#41—14212no—
699C2×#41—14212no—
700C2×#41—14212no—
701C2×#41—1426no—
702C2×#41—1423no—
703C2×#41—1423no—
704C2×#41—14248no—
705C2×#41—14216no—
706C2×#41—14216no—
707C2×#41—1421no—
708C2×#41—1423no—
709C2×#41C22×D7113yes—
710C2×#41C22×D7111yescharacteristic
711C2×#41C22×D7113yescomplemented
712C22×Q8—711no—
713C22×Q8—711no—
714C22×Q8—713no—
715C22×Q8—713no—
716C22×Q8—1423no—
717C22×Q8—1421no—
718C22×D4—23no—
719C22×D4—23no—
720C22×D4—713no—
721C22×D4—716no—
722C22×D4—713no—
723C22×D4—713no—
724C22×D4—7124no—
725C22×D4—713no—
726C22×D4—1423no—
727C22×D4—1423no—
728C22×D4—1423no—
729C22×D4—14212no—
730C22×D4—1423no—
731C22×D4—1426no—
732C22×D4—14248no—
733C22×D4—1423no—
734C22×D4—1423no—
735C22×D4—1423no—
736C22×D4—1423no—
737C22×D4—1426no—
738C22×D4—1426no—
739C22×D4—1423no—
740C22×D4—1423no—
741C22×D4C22×D7113yes—
742C22×D4C22×D7113yescomplemented
743C23×C4—713no—
744C23×C4—1423no—
745C23×C4—1423no—
746C23×C4—1423no—
747#137—7124no—
748#137—718no—
749#137—7124no—
750#137—7124no—
751#137—7124no—
752#137—7124no—
753AGL(1,ℤ/8)—7124no—
754AGL(1,ℤ/8)—7124no—
755AGL(1,ℤ/8)—7124no—
756AGL(1,ℤ/8)—7124no—
757AGL(1,ℤ/8)—7124no—
758AGL(1,ℤ/8)—7148no—
759AGL(1,ℤ/8)—7124no—
760AGL(1,ℤ/8)—7148no—
761AGL(1,ℤ/8)—7148no—
762AGL(1,ℤ/8)—7124no—
763AGL(1,ℤ/8)—7124no—
764AGL(1,ℤ/8)C22×D71124yescomplemented
765AGL(1,ℤ/8)C22×D71124yescomplemented
766#135—7124no—
767#135—7124no—
768#135—7148no—
769#135—7148no—
770#135—7124no—
771#135C22×D71124yescomplemented
772C2×Q16—713no—
773C2×Q16—711no—
774C2×Q16—713no—
775C2×Q16C22×D7111yescharacteristic, complemented
776C2×SD16—713no—
777C2×SD16—711no—
778C2×SD16—713no—
779C2×SD16—716no—
780C2×SD16—7124no—
781C2×SD16—713no—
782C2×SD16—7148no—
783C2×SD16—716no—
784C2×SD16—713no—
785C2×SD16—711no—
786C2×SD16—7124no—
787C2×SD16C22×D7113yescomplemented
788C2×SD16C22×D7113yescomplemented
789C2×D8—713no—
790C2×D8—713no—
791C2×D8—716no—
792C2×D8—7124no—
793C2×D8—7148no—
794C2×D8—713no—
795C2×D8C22×D7116yescomplemented
796C2×D8C22×D7113yescomplemented
797C2×D8C22×D71124yescomplemented
798#131—718no—
799#131—7124no—
800#131—7124no—
801#131C22×D7118yescomplemented
802C2×M16—713no—
803C2×M16—7124no—
804C2×M16—713no—
805C2×M16—711no—
806C2×M16—713no—
807C2×M16—713no—
808C2×M16—7124no—
809C2×M16C22×D7113yescomplemented
810C22×C8—713no—
811C22×C8—716no—
812C22×C8C22×D7113yescomplemented
813C24—23no—
814C24—23no—
815C24—56812no—
816C24—713no—
817C24—1423no—
818C24—1423no—
819C24—1426no—
820C24—14224no—
821C24—1423no—
822#41—28no—
823#41—28no—
824#41—26no—
825#41—26no—
826#41—718no—
827#41—7124no—
828#41—7112no—
829#41—7112no—
830#41—7112no—
831#41—714no—
832#41—7112no—
833#41—7112no—
834#41—7124no—
835#41—7112no—
836#41—7112no—
837#41—14224no—
838#41—14224no—
839#41—14224no—
840#41—14224no—
841#41—14224no—
842#41—1426no—
843#41—14224no—
844#41—14224no—
845#41—1426no—
846#41—14224no—
847#41—14212no—
848#41—1422no—
849#41—1426no—
850#41—14248no—
851#41—14224no—
852#41—14224no—
853#41—1428no—
854#41—14224no—
855#41—1426no—
856#41—1426no—
857#41D4×D7114yes—
858#41C23×D71112yes—
859#41C23×D7114yes—
860#41C23×D71112yescomplemented
861C2×Q8—718no—
862C2×Q8—713no—
863C2×Q8—714no—
864C2×Q8—7112no—
865C2×Q8—713no—
866C2×Q8—711no—
867C2×Q8—7112no—
868C2×Q8—1423no—
869C2×Q8—1421no—
870C2×Q8—14224no—
871C2×Q8—1422no—
872C2×Q8—1426no—
873C2×Q8—1428no—
874C2×Q8—1423no—
875C2×Q8—1426no—
876C2×Q8D4×D7111yescharacteristic
877C2×Q8C23×D7111yescharacteristic
878C2×Q8C23×D7111yescharacteristic
879C2×D4—23no—
880C2×D4—23no—
881C2×D4—224no—
882C2×D4—224no—
883C2×D4—23no—
884C2×D4—23no—
885C2×D4—26no—
886C2×D4—26no—
887C2×D4—716no—
888C2×D4—7124no—
889C2×D4—7124no—
890C2×D4—7112no—
891C2×D4—7112no—
892C2×D4—713no—
893C2×D4—711no—
894C2×D4—713no—
895C2×D4—7112no—
896C2×D4—14224no—
897C2×D4—1423no—
898C2×D4—1421no—
899C2×D4—1426no—
900C2×D4—14224no—
901C2×D4—14224no—
902C2×D4—14212no—
903C2×D4—1426no—
904C2×D4—1423no—
905C2×D4—1426no—
906C2×D4—1423no—
907C2×D4—14224no—
908C2×D4—14248no—
909C2×D4—14224no—
910C2×D4—14224no—
911C2×D4—14224no—
912C2×D4—14224no—
913C2×D4—14248no—
914C2×D4—14248no—
915C2×D4—1423no—
916C2×D4—1423no—
917C2×D4—1426no—
918C2×D4—14224no—
919C2×D4—1423no—
920C2×D4—1423no—
921C2×D4—14224no—
922C2×D4—1423no—
923C2×D4—1426no—
924C2×D4D4×D7113yes—
925C2×D4C23×D7113yes—
926C2×D4C23×D7113yes—
927C2×D4C23×D71112yes—
928C2×D4C23×D71112yescomplemented
929C22×C4—23no—
930C22×C4—23no—
931C22×C4—713no—
932C22×C4—713no—
933C22×C4—713no—
934C22×C4—7112no—
935C22×C4—713no—
936C22×C4—711no—
937C22×C4—7112no—
938C22×C4—1421no—
939C22×C4—1423no—
940C22×C4—14224no—
941C22×C4—14224no—
942C22×C4—1421no—
943C22×C4—1423no—
944C22×C4—1423no—
945C22×C4—1423no—
946C22×C4—1426no—
947C22×C4—14224no—
948C22×C4—1423no—
949C22×C4—1423no—
950C22×C4—1423no—
951C22×C4C23×D7113yes—
952Q16—7112no—
953Q16—714no—
954Q16—7112no—
955Q16C23×D7114yescomplemented
956SD16—7112no—
957SD16—714no—
958SD16—7124no—
959SD16—7112no—
960SD16—7112no—
961SD16—7124no—
962SD16—7112no—
963SD16—714no—
964SD16C23×D71112yescomplemented
965SD16C23×D71112yescomplemented
966D8—7112no—
967D8—7124no—
968D8—7112no—
969D8—7112no—
970D8C23×D71124yescomplemented
971D8C23×D71112yescomplemented
972M16—7112no—
973M16—7112no—
974M16—714no—
975M16—7112no—
976M16—7112no—
977M16C23×D71112yescomplemented
978C2×C8—713no—
979C2×C8—711no—
980C2×C8—7112no—
981C2×C8—7124no—
982C2×C8C23×D7113yes—
983C2×C8C23×D7111yescharacteristic
984C2×C8C23×D71112yescomplemented
985C23—23no—
986C23—23no—
987C23—212no—
988C23—212no—
989C23—86no—
990C23—86no—
991C23—2846no—
992C23—28412no—
993C23—5686no—
994C23—56812no—
995C23—5686no—
996C23—56848no—
997C23—7112no—
998C23—711no—
999C23—713no—
1000C23—14212no—
1001C23—14212no—
1002C23—14224no—
1003C23—1421no—
1004C23—1423no—
1005C23—14212no—
1006C23C2×D4×D7113yes—
1007Q8—21no—
1008Q8—21no—
1009Q8—7112no—
1010Q8—716no—
1011Q8—712no—
1012Q8—14212no—
1013Q8—1424no—
1014Q8—14212no—
1015Q8—1423no—
1016Q8—1421no—
1017Q8C2×D4×D7114yes—
1018Q8C24×D7112yes—
1019Q8C24×D7112yes—
1020D4—212no—
1021D4—212no—
1022D4—212no—
1023D4—23no—
1024D4—23no—
1025D4—212no—
1026D4—7124no—
1027D4—7112no—
1028D4—712no—
1029D4—716no—
1030D4—14212no—
1031D4—1424no—
1032D4—14212no—
1033D4—14224no—
1034D4—14212no—
1035D4—14212no—
1036D4—14212no—
1037D4—14224no—
1038D4—14212no—
1039D4—14212no—
1040D4—14212no—
1041D4—1423no—
1042D4—1421no—
1043D4C2×D4×D71112yes—
1044D4C24×D7116yes—
1045D4C24×D7116yes—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—212no—
1049C2×C4—212no—
1050C2×C4—7112no—
1051C2×C4—711no—
1052C2×C4—713no—
1053C2×C4—712no—
1054C2×C4—7112no—
1055C2×C4—7112no—
1056C2×C4—716no—
1057C2×C4—716no—
1058C2×C4—712no—
1059C2×C4—1424no—
1060C2×C4—14212no—
1061C2×C4—1424no—
1062C2×C4—14212no—
1063C2×C4—14212no—
1064C2×C4—14212no—
1065C2×C4—14224no—
1066C2×C4—14212no—
1067C2×C4—1421no—
1068C2×C4—1423no—
1069C2×C4—14212no—
1070C2×C4—14212no—
1071C2×C4C2×D4×D7116yes—
1072C2×C4C2×D4×D7113yes—
1073C2×C4C24×D7116yes—
1074C2×C4C24×D7111yescharacteristic
1075C8—712no—
1076C8—716no—
1077C8C24×D7116yes—
1078C8C24×D7112yes—
1079C22—26no—
1080C22—26no—
1081C22—26no—
1082C22—46no—
1083C22—46no—
1084C22—812no—
1085C22—812no—
1086C22—28412no—
1087C22—28424no—
1088C22—2846no—
1089C22—2842no—
1090C22—56812no—
1091C22—56824no—
1092C22—56812no—
1093C22—712no—
1094C22—716no—
1095C22—1422no—
1096C22—1426no—
1097C22—1422no—
1098C22—1426no—
1099C22C22×D4×D7116yes—
1100C22C22×D4×D7111yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—712no—
1104C4—716no—
1105C4—1422no—
1106C4—1426no—
1107C4C22×D4×D7116yes—
1108C4C22×D4×D7111yescharacteristic
1109C4C25×D7111yescharacteristic
1110C2—26no—
1111C2—46no—
1112C2—46no—
1113C2—2846no—
1114C2—2842no—
1115C2—1422no—
1116C2—1426no—
1117C2#2260311512yesdirect product factor
1118C2C23×D4×D7111yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC4×C71C26
FrattiniC4C25×D71
FittingC2×#576×C71C2
socleC22×C71C23×D4
hypercenterC2×#576D71
hypocenterC71C2×#3585
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#576

Complements

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

NH ≅ G/Ntype
1. C2×#17986834C2semidirect
2. C2×H(5,𝔽2)×D71C2semidirect
3. #22603115C2direct (N × H)
4. C2×#17986811C2semidirect
5. C2×#17986810C2semidirect
6. C2×#17986809C2semidirect
7. C2×#17986806C2semidirect
8. C2×#17986803C2semidirect
9. C2×#17986802C2semidirect
10. C2×#17986800C2semidirect
11. C2×#17986796C2semidirect
12. C2×#17986795C2semidirect
13. C22×#14556152C2semidirect
14. C2×AGL(1,ℤ/8)×D71C2semidirect
15. C2×#17986764C2semidirect
16. C2×#576×C71C2semidirect
18. #17986834C22semidirect
20. C2×#14556175C22semidirect
21. C2×#14556175C22semidirect
23. C2×#14556174C22semidirect
24. C2×#14556174C22semidirect
27. C2×#14556173C22semidirect
28. C2×#14556173C22semidirect
30. H(5,𝔽2)×D71C22semidirect
32. C22×#11765864C22semidirect
36. C2×#41×D71C22semidirect
37. C2×#41×D71C22semidirect
39. C22×D4×D71C22semidirect
40. #17986811C22semidirect
41. #17986810C22semidirect
42. #17986809C22semidirect
43. #17986806C22semidirect
44. #17986803C22semidirect
45. #17986802C22semidirect
46. #17986800C22semidirect
47. #17986796C22semidirect
48. #17986795C22semidirect
49. C2×#14556161C22semidirect
50. C2×#14556160C22semidirect
51. C2×#14556160C22semidirect
52. C2×#14556158C22semidirect
53. C2×#14556157C22semidirect
54. C2×#14556157C22semidirect
55. C2×#14556156C22semidirect
56. C2×#14556155C22semidirect
57. C2×#14556155C22semidirect
58. C2×#14556154C22semidirect
59. C2×#14556154C22semidirect
60. C2×#14556153C22semidirect
61. C2×#14556152C22semidirect
62. C2×#14556152C22semidirect
63. C2×#14556152C22semidirect
64. C2×#14556152C22semidirect
65. C2×#14556152C22semidirect
66. C2×#14556152C22semidirect
67. AGL(1,ℤ/8)×D71C22semidirect
68. C2×#14556150C22semidirect
69. C2×#14556149C22semidirect
70. C2×#14556148C22semidirect
71. C2×#14556148C22semidirect
72. C2×#14556147C22semidirect
73. C22×#11765854C22semidirect
74. C22×#11765853C22semidirect
75. C2×SD16×D71C22semidirect
76. C22×#11765850C22semidirect
77. C2×D8×D71C22semidirect
78. #17986764C22semidirect
79. C2×#14556136C22semidirect
80. C2×#14556135C22semidirect
81. C2×#14556134C22semidirect
82. C22×#11765848C22semidirect
83. C2×M16×D71C22semidirect
84. C2×H(5,𝔽2)×C71C22semidirect
85. C2×H(5,𝔽2)×C71C22semidirect
86. #576×C71C22semidirect
87. C2×AGL(1,ℤ/8)×C71C22semidirect
88. C2×AGL(1,ℤ/8)×C71C22semidirect
89. C2×#135×C71C22semidirect
90. C22×D8×C71C22semidirect
91. C2×#131×C71C22semidirect
96. #14556175C23semidirect
97. #14556175C23semidirect
101. #14556174C23semidirect
102. #14556174C23semidirect
107. #14556173C23semidirect
108. #14556173C23semidirect
119. C2×#11765865C23semidirect
133. C2×#11765864C23semidirect
134. C2×#11765864C23semidirect
141. #41×D71C23semidirect
142. #41×D71C23semidirect
144. C22×Dic142C23semidirect
148. C2×Q8×D71C23semidirect
168. C2×D4×D71C23semidirect
169. C2×D4×D71C23semidirect
174. #14556161C23semidirect
175. #14556160C23semidirect
176. #14556160C23semidirect
177. #14556158C23semidirect
178. #14556157C23semidirect
179. #14556157C23semidirect
180. #14556156C23semidirect
181. #14556155C23semidirect
182. #14556155C23semidirect
183. #14556154C23semidirect
184. #14556154C23semidirect
185. #14556153C23semidirect
186. #14556152C23semidirect
187. #14556152C23semidirect
188. #14556152C23semidirect
189. #14556152C23semidirect
190. #14556152C23semidirect
191. #14556150C23semidirect
192. #14556149C23semidirect
193. #14556148C23semidirect
194. #14556148C23semidirect
195. #14556147C23semidirect
196. C2×Dic284C23semidirect
197. C2×#11765855C23semidirect
198. C2×#11765855C23semidirect
199. C2×#11765854C23semidirect
200. C2×#11765854C23semidirect
201. C2×#11765854C23semidirect
202. C2×#11765854C23semidirect
203. C2×#11765853C23semidirect
204. C2×#11765853C23semidirect
205. C2×#11765853C23semidirect
206. C2×#11765853C23semidirect
207. C2×#11765852C23semidirect
208. C2×#11765852C23semidirect
209. SD16×D71C23semidirect
210. C2×D568C23semidirect
211. C2×#11765850C23semidirect
212. C2×#11765850C23semidirect
213. C2×#11765850C23semidirect
214. C2×#11765850C23semidirect
215. D8×D71C23semidirect
216. #14556136C23semidirect
217. #14556135C23semidirect
218. #14556134C23semidirect
219. C2×#11765849C23semidirect
222. C2×#11765848C23semidirect
223. C2×#11765848C23semidirect
224. C2×#11765848C23semidirect
225. M16×D71C23semidirect
226. C22×C71⋊C8C23semidirect
227. C2×C8×D71C23semidirect
230. H(5,𝔽2)×C71C23semidirect
231. H(5,𝔽2)×C71C23semidirect
236. C2×#41×C71C23semidirect
240. C22×D4×C71C23semidirect
241. AGL(1,ℤ/8)×C71C23semidirect
242. AGL(1,ℤ/8)×C71C23semidirect
243. #135×C71C23semidirect
244. C2×Q16×C71C23semidirect
245. C2×SD16×C71C23semidirect
246. C2×SD16×C71C23semidirect
247. C2×D8×C71C23semidirect
248. C2×D8×C71C23semidirect
249. C2×D8×C71C23semidirect
250. #131×C71C23semidirect
251. C2×M16×C71C23semidirect
252. C22×C8×C71C23semidirect
275. #11765865C24semidirect
290. #11765864C24semidirect
299. C2×Dic142C24semidirect
305. Q8×D71C24semidirect
342. D4×D71C24semidirect
363. Dic284C24semidirect
364. #11765855C24semidirect
365. #11765855C24semidirect
366. #11765854C24semidirect
367. #11765854C24semidirect
368. #11765854C24semidirect
369. #11765853C24semidirect
370. #11765853C24semidirect
371. #11765853C24semidirect
372. #11765852C24semidirect
373. #11765852C24semidirect
374. D568C24semidirect
375. #11765850C24semidirect
376. #11765850C24semidirect
377. #11765850C24semidirect
378. #11765849C24semidirect
381. #11765848C24semidirect
382. #11765848C24semidirect
385. C2×C71⋊C8C24semidirect
386. C8×D71C24semidirect
396. #41×C71C24semidirect
412. C2×D4×C71C24semidirect
416. Q16×C71C24semidirect
417. SD16×C71C24semidirect
418. SD16×C71C24semidirect
419. D8×C71C24semidirect
420. D8×C71C24semidirect
421. M16×C71C24semidirect
424. C2×C8×C71C24semidirect
554. C2×C71#3585semidirect
570. C2×#576D71semidirect
576. C71C2×#3585semidirect
591. C2×H(5,𝔽2)C2×D71semidirect
592. C2×H(5,𝔽2)C2×D71semidirect
609. #576C2×D71semidirect
631. C2×AGL(1,ℤ/8)C2×D71semidirect
632. C2×AGL(1,ℤ/8)C2×D71semidirect
638. C2×#135C2×D71semidirect
644. C22×D8C2×D71semidirect
649. C2×#131C2×D71semidirect
671. H(5,𝔽2)C22×D71semidirect
672. H(5,𝔽2)C22×D71semidirect
711. C2×#41C22×D71semidirect
742. C22×D4C22×D71semidirect
764. AGL(1,ℤ/8)C22×D71semidirect
765. AGL(1,ℤ/8)C22×D71semidirect
771. #135C22×D71semidirect
775. C2×Q16C22×D71semidirect
787. C2×SD16C22×D71semidirect
788. C2×SD16C22×D71semidirect
795. C2×D8C22×D71semidirect
796. C2×D8C22×D71semidirect
797. C2×D8C22×D71semidirect
801. #131C22×D71semidirect
809. C2×M16C22×D71semidirect
812. C22×C8C22×D71semidirect
860. #41C23×D71semidirect
928. C2×D4C23×D71semidirect
955. Q16C23×D71semidirect
964. SD16C23×D71semidirect
965. SD16C23×D71semidirect
970. D8C23×D71semidirect
971. D8C23×D71semidirect
977. M16C23×D71semidirect
984. C2×C8C23×D71semidirect
1117. C2#22603115direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179868342
C2×H(5,𝔽2)×D712
#226031152
C2×#179868112
C2×#179868102
C2×#179868092
C2×#179868062
C2×#179868032
C2×#179868022
C2×#179868002
C2×#179867962
C2×#179867952
C22×#145561522
C2×AGL(1,ℤ/8)×D712
C2×#179867642
C2×#576×C712
C2×#358571