Finite Group Databasebeta

← C2×#22603118 #32911291

Subgroups — C2×#22603118 #32911291

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×#17986836C211yesmaximal, characteristic, complemented
2C2×H(5,𝔽2)×D71C211yesmaximal, characteristic, complemented
3#22603118C2132yesmaximal, direct product factor
4C2×#17986808C213yesmaximal, complemented
5C2×#17986807C211yesmaximal, characteristic, complemented
6C2×#17986805C213yesmaximal, complemented
7C2×#17986804C211yesmaximal, characteristic, complemented
8C2×#17986803C213yesmaximal, complemented
9C2×#17986802C211yesmaximal, characteristic, complemented
10C2×#17986801C213yesmaximal, complemented
11C2×#17986798C213yesmaximal, complemented
12C2×#17986796C213yesmaximal, complemented
13C22×#14556155C213yesmaximal, complemented
14C2×AGL(1,ℤ/8)×D71C213yesmaximal, complemented
15C2×#17986764C211yesmaximal, characteristic, complemented
16C2×#577×C71C211yesmaximal, characteristic, complemented
17#17986836—28no—
18#17986836C22116yescomplemented
19C2×#14556176—21no—
20C2×#14556176C2213yescomplemented
21C2×#14556174—21no—
22C2×#14556174—23no—
23C2×#14556174C2211yescharacteristic, complemented
24C2×#14556174C2211yescharacteristic, complemented
25C2×#14556174C2213yescomplemented
26C2×#14556174C2213yescomplemented
27C2×#14556173—23no—
28C2×#14556173C2213yescomplemented
29H(5,𝔽2)×D71—28no—
30H(5,𝔽2)×D71C22116yescomplemented
31C22×#11765866—21no—
32C22×#11765866C2213yescomplemented
33C2×#41×D71—23no—
34C2×#41×D71—21no—
35C2×#41×D71C2211yescharacteristic
36C2×#41×D71C2213yescomplemented
37C2×#41×D71C2213yescomplemented
38C22×D4×D71—23no—
39C22×D4×D71C2213yescomplemented
40#17986808C22148yescomplemented
41#17986807C22116yescomplemented
42#17986805C22148yescomplemented
43#17986804C22116yescomplemented
44#17986803C22148yescomplemented
45#17986802C22116yescomplemented
46#17986801C22148yescomplemented
47#17986798C22148yescomplemented
48#17986796C22148yescomplemented
49C2×#14556160C2213yescomplemented
50C2×#14556160C2213yescomplemented
51C2×#14556159C2213yescomplemented
52C2×#14556157C2211yescharacteristic, complemented
53C2×#14556157C2213yescomplemented
54C2×#14556156C2213yescomplemented
55C2×#14556156C2213yescomplemented
56C2×#14556155C2216yescomplemented
57C2×#14556155C2213yescomplemented
58C2×#14556155C2216yescomplemented
59C2×#14556155C2216yescomplemented
60C2×#14556155C2213yescomplemented
61C2×#14556155C22148yescomplemented
62C2×#14556154C2213yescomplemented
63C2×#14556153C2213yescomplemented
64C2×#14556153C2213yescomplemented
65C2×#14556152C2213yescomplemented
66C2×#14556152C2213yescomplemented
67AGL(1,ℤ/8)×D71C22148yescomplemented
68C2×#14556151C2216yescomplemented
69C2×#14556150C2213yescomplemented
70C2×#14556149C2216yescomplemented
71C2×#14556148C2213yescomplemented
72C2×#14556148C2213yescomplemented
73C22×#11765852C2213yescomplemented
74C2×SD16×D71C2216yescomplemented
75C22×D568C2213yescomplemented
76C22×#11765850C2213yescomplemented
77C2×D8×D71C2216yescomplemented
78#17986764C22116yescomplemented
79C2×#14556136C2213yescomplemented
80C2×#14556135C2211yescharacteristic, complemented
81C2×#14556134C2213yescomplemented
82C22×#11765848C2213yescomplemented
83C2×M16×D71C2213yescomplemented
84C2×2−1+4×C71C2211yescharacteristic, complemented
85C2×H(5,𝔽2)×C71C2211yescharacteristic, complemented
86#577×C71C22116yescomplemented
87C2×#137×C71C2213yescomplemented
88C2×AGL(1,ℤ/8)×C71C2213yescomplemented
89C2×#135×C71C2213yescomplemented
90C22×SD16×C71C2213yescomplemented
91C2×#131×C71C2211yescharacteristic, complemented
92C24×D71—23no—
93#14556176—212no—
94#14556176—216no—
95#14556176C23124yescomplemented
96#14556174—216no—
97#14556174—212no—
98#14556174—212no—
99#14556174—248no—
100#14556174—24no—
101#14556174—24no—
102#14556174C2318yescomplemented
103#14556174C2318yescomplemented
104#14556174C23124yescomplemented
105#14556174C23124yescomplemented
106#14556173—212no—
107#14556173—248no—
108#14556173C23124yescomplemented
109C2×#11765866—216no—
110C2×#11765866—23no—
111C2×#11765866—23no—
112C2×#11765866—23no—
113C2×#11765866—212no—
114C2×#11765866—21no—
115C2×#11765866—21no—
116C2×#11765866D411yescharacteristic
117C2×#11765866C2313yes—
118C2×#11765866C2313yes—
119C2×#11765866C2316yescomplemented
120C2×#11765866C23124yescomplemented
121C2×#11765865—23no—
122C2×#11765865—23no—
123C2×#11765865—26no—
124C2×#11765865—23no—
125C2×#11765865—23no—
126C2×#11765865C2313yes—
127C2×#11765865C2313yes—
128C2×#11765865C2313yescomplemented
129C2×#11765864—23no—
130C2×#11765864—23no—
131C2×#11765864—23no—
132C2×#11765864D413yes—
133C2×#11765864C2311yescharacteristic
134C2×#11765864C2313yes—
135#41×D71—248no—
136#41×D71—216no—
137#41×D71—212no—
138#41×D71—212no—
139#41×D71D418yes—
140#41×D71C2318yes—
141#41×D71C23124yescomplemented
142#41×D71C23124yescomplemented
143C2×Q8×D71—23no—
144C2×Q8×D71D411yescharacteristic
145C2×Q8×D71C2311yescharacteristic
146C2×Q8×D71C2313yescomplemented
147C22×D284—23no—
148C22×D284—23no—
149C22×D284—23no—
150C22×D284C2313yes—
151C22×D284C2313yescomplemented
152C22×C22⋊D71—26no—
153C22×C22⋊D71—23no—
154C2×D4×D71—23no—
155C2×D4×D71—23no—
156C2×D4×D71—23no—
157C2×D4×D71—26no—
158C2×D4×D71—26no—
159C2×D4×D71—248no—
160C2×D4×D71—23no—
161C2×D4×D71—212no—
162C2×D4×D71—23no—
163C2×D4×D71—23no—
164C2×D4×D71—23no—
165C2×D4×D71D413yes—
166C2×D4×D71C2313yes—
167C2×D4×D71C2316yes—
168C2×D4×D71C23124yescomplemented
169C2×D4×D71C2313yescomplemented
170C22×C4×D71—23no—
171C22×C4×D71—23no—
172C22×C4×D71—23no—
173C22×C4×D71C2313yes—
174#14556160C23124yescomplemented
175#14556160C23124yescomplemented
176#14556159C23124yescomplemented
177#14556157C2318yescomplemented
178#14556157C23124yescomplemented
179#14556156C23124yescomplemented
180#14556156C23124yescomplemented
181#14556155C23148yescomplemented
182#14556155C23124yescomplemented
183#14556155C23148yescomplemented
184#14556155C23148yescomplemented
185#14556155C23124yescomplemented
186#14556154C23124yescomplemented
187#14556153C23124yescomplemented
188#14556153C23124yescomplemented
189#14556152C23124yescomplemented
190#14556152C23124yescomplemented
191#14556151C23148yescomplemented
192#14556150C23124yescomplemented
193#14556149C23148yescomplemented
194#14556148C23124yescomplemented
195#14556148C23124yescomplemented
196C2×Dic284C2311yescharacteristic, complemented
197C2×#11765855C2311yescharacteristic, complemented
198C2×#11765855C2313yescomplemented
199C2×#11765854C2313yescomplemented
200C2×#11765854C2313yescomplemented
201C2×#11765853C2313yescomplemented
202C2×#11765853C2311yescharacteristic, complemented
203C2×#11765852C2316yescomplemented
204C2×#11765852C2313yescomplemented
205C2×#11765852C2313yescomplemented
206C2×#11765852C23124yescomplemented
207SD16×D71C23148yescomplemented
208C2×D568C2316yescomplemented
209C2×D568C2313yescomplemented
210C2×D568C23124yescomplemented
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
2282−1+4×C71—24no—
2292−1+4×C71C2318yescomplemented
230H(5,𝔽2)×C71—24no—
231H(5,𝔽2)×C71C2318yescomplemented
232C2×#41×C71—21no—
233C2×#41×C71—23no—
234C2×#41×C71C2313yes—
235C2×#41×C71C2311yescharacteristic
236C2×#41×C71C2313yescomplemented
237C22×Q8×C71—21no—
238C22×Q8×C71C2313yescomplemented
239C22×D4×C71—23no—
240C22×D4×C71C2313yes—
241#137×C71C23124yescomplemented
242AGL(1,ℤ/8)×C71C23124yescomplemented
243#135×C71C23124yescomplemented
244C2×Q16×C71C2313yescomplemented
245C2×SD16×C71C2313yescomplemented
246C2×SD16×C71C2316yescomplemented
247C2×SD16×C71C2311yescharacteristic, complemented
248C2×SD16×C71C23124yescomplemented
249C2×D8×C71C2313yescomplemented
250#131×C71C2318yescomplemented
251C2×M16×C71C2313yescomplemented
252C22×C8×C71C2313yescomplemented
253C23×D71—23no—
254C23×D71—23no—
255C23×D71—23no—
256C23×D71—23no—
257C23×D71—224no—
258C23×D71—26no—
259C23×D71—812no—
260C23×D71C2×D413yes—
261#11765866—28no—
262#11765866—28no—
263#11765866—224no—
264#11765866—26no—
265#11765866—224no—
266#11765866—26no—
267#11765866—224no—
268#11765866—212no—
269#11765866C2×D418yes—
270#11765866C24112yes—
271#11765866C24112yes—
272#11765866C24124yescomplemented
273#11765865—26no—
274#11765865—26no—
275#11765865—248no—
276#11765865—224no—
277#11765865—224no—
278#11765865—224no—
279#11765865—224no—
280#11765865C2×D4112yes—
281#11765865C24112yes—
282#11765865C24112yes—
283#11765865C24112yescomplemented
284#11765864—224no—
285#11765864—224no—
286#11765864—22no—
287#11765864—26no—
288#11765864—224no—
289#11765864C2×D4124yes—
290#11765864C2414yes—
291#11765864C24112yes—
292C2×Dic142—23no—
293C2×Dic142—21no—
294C2×Dic142C2×D413yes—
295C2×Dic142C2411yescharacteristic
296C2×Dic142C2411yescharacteristic
297Q8×D71—22no—
298Q8×D71—26no—
299Q8×D71—224no—
300Q8×D71C2×D418yes—
301Q8×D71C2414yes—
302Q8×D71C24112yescomplemented
303C2×D284—23no—
304C2×D284—23no—
305C2×D284—26no—
306C2×D284—224no—
307C2×D284—23no—
308C2×D284—26no—
309C2×D284—23no—
310C2×D284—26no—
311C2×D284—224no—
312C2×D284—224no—
313C2×D284C2×D413yes—
314C2×D284C2413yes—
315C2×D284C24112yes—
316C2×D284C2413yes—
317C2×D284C24112yescomplemented
318C2×C22⋊D71—23no—
319C2×C22⋊D71—23no—
320C2×C22⋊D71—23no—
321C2×C22⋊D71—21no—
322C2×C22⋊D71—248no—
323C2×C22⋊D71—23no—
324C2×C22⋊D71—26no—
325C2×C22⋊D71—23no—
326C2×C22⋊D71—224no—
327C2×C22⋊D71C2×D416yes—
328D4×D71—224no—
329D4×D71—224no—
330D4×D71—224no—
331D4×D71—224no—
332D4×D71—248no—
333D4×D71—248no—
334D4×D71—224no—
335D4×D71—26no—
336D4×D71—224no—
337D4×D71—212no—
338D4×D71—224no—
339D4×D71—26no—
340D4×D71C2×D4124yes—
341D4×D71C24112yes—
342D4×D71C24124yes—
343D4×D71C24112yescomplemented
344C22×Dic71—21no—
345C22×Dic71—23no—
346C22×Dic71C2×D413yes—
347C2×C4×D71—21no—
348C2×C4×D71—23no—
349C2×C4×D71—23no—
350C2×C4×D71—23no—
351C2×C4×D71—23no—
352C2×C4×D71—23no—
353C2×C4×D71—26no—
354C2×C4×D71—224no—
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—
363Dic284C2414yescomplemented
364#11765855C2414yescomplemented
365#11765855C24112yescomplemented
366#11765854C24112yescomplemented
367#11765854C24112yescomplemented
368#11765853C24112yescomplemented
369#11765853C2414yescomplemented
370#11765852C24112yescomplemented
371#11765852C24112yescomplemented
372#11765852C24124yescomplemented
373D568C24124yescomplemented
374D568C24112yescomplemented
375#11765850C24112yescomplemented
376#11765850C24124yescomplemented
377#11765850C24112yescomplemented
378#11765849C24112yescomplemented
379#11765848C24112yes—
380#11765848C2414yes—
381#11765848C24112yescomplemented
382#11765848C24112yescomplemented
383C2×C71⋊C8C2413yes—
384C2×C71⋊C8C2411yescharacteristic
385C2×C71⋊C8C24112yescomplemented
386C8×D71C24124yescomplemented
387C24×C71—23no—
388#41×C71—28no—
389#41×C71—224no—
390#41×C71—26no—
391#41×C71—26no—
392#41×C71C2×D414yes—
393#41×C71C24112yes—
394#41×C71C2414yes—
395#41×C71C24112yescomplemented
396C2×Q8×C71—28no—
397C2×Q8×C71—23no—
398C2×Q8×C71—26no—
399C2×Q8×C71C2×D411yescharacteristic
400C2×Q8×C71C2411yescharacteristic
401C2×Q8×C71C2413yes—
402C2×Q8×C71C24112yescomplemented
403C2×D4×C71—23no—
404C2×D4×C71—23no—
405C2×D4×C71—224no—
406C2×D4×C71—23no—
407C2×D4×C71—26no—
408C2×D4×C71C2×D413yes—
409C2×D4×C71C2413yes—
410C2×D4×C71C2411yescharacteristic
411C2×D4×C71C24112yes—
412C22×C4×C71—23no—
413C22×C4×C71—23no—
414C22×C4×C71—23no—
415C22×C4×C71C2413yes—
416Q16×C71C24112yescomplemented
417SD16×C71C24112yescomplemented
418SD16×C71C24124yescomplemented
419SD16×C71C2414yescomplemented
420D8×C71C24112yescomplemented
421M16×C71C24112yescomplemented
422C2×C8×C71C2411yescharacteristic
423C2×C8×C71C2413yes—
424C2×C8×C71C24112yescomplemented
425C23×C71—21no—
426C23×C71—23no—
427C23×C71—212no—
428C23×C71—86no—
429C23×C71C22×D413yes—
430C22×D71—23no—
431C22×D71—23no—
432C22×D71—212no—
433C22×D71—212no—
434C22×D71—212no—
435C22×D71—212no—
436C22×D71—224no—
437C22×D71—46no—
438C22×D71—412no—
439C22×D71—86no—
440C22×D71—812no—
441C22×D71—848no—
442C22×D71—86no—
443C22×D71—86no—
444C22×D71C22×D411yescharacteristic
445C22×D71C22×D413yes—
446C22×D71C22×D4112yes—
447Q8×C71—23no—
448Q8×C71—212no—
449Q8×C71—21no—
450Q8×C71C22×D414yes—
451Q8×C71C2516yes—
452Q8×C71C2512yes—
453D4×C71—212no—
454D4×C71—212no—
455D4×C71—23no—
456D4×C71—212no—
457D4×C71—21no—
458D4×C71C22×D4112yes—
459D4×C71C2512yes—
460D4×C71C2516yes—
461C2×C4×C71—21no—
462C2×C4×C71—23no—
463C2×C4×C71—212no—
464C2×C4×C71—212no—
465C2×C4×C71—212no—
466C2×C4×C71C22×D413yes—
467C2×C4×C71C22×D416yes—
468C2×C4×C71C2511yescharacteristic
469C2×C4×C71C2516yes—
470C22⋊D71—212no—
471C22⋊D71—212no—
472C22⋊D71—212no—
473C22⋊D71—24no—
474C22⋊D71—224no—
475C22⋊D71—212no—
476C22⋊D71—212no—
477C22⋊D71C22×D4124yes—
478C2×Dic71—21no—
479C2×Dic71—21no—
480C2×Dic71—24no—
481C2×Dic71—212no—
482C2×Dic71C22×D411yescharacteristic
483C2×Dic71C22×D413yes—
484C2×Dic71C22×D4112yes—
485D284—212no—
486D284—212no—
487D284—224no—
488D284—23no—
489D284—212no—
490D284—23no—
491D284—212no—
492D284C22×D4112yes—
493D284C2516yes—
494D284C2516yes—
495C4×D71—24no—
496C4×D71—212no—
497C4×D71—212no—
498C4×D71—212no—
499C4×D71—212no—
500C4×D71—212no—
501C4×D71—224no—
502C4×D71C22×D4112yes—
503C4×D71C22×D4112yes—
504C4×D71C22×D412yes—
505C4×D71C22×D416yes—
506C4×D71C2516yes—
507C4×D71C2512yes—
508Dic142—21no—
509Dic142—21no—
510Dic142—212no—
511Dic142—24no—
512Dic142C22×D4112yes—
513Dic142C2512yes—
514Dic142C2512yes—
515C8×C71C2512yes—
516C8×C71C2516yes—
517C71⋊C8C2516yes—
518C71⋊C8C2512yes—
519C22×C71—26no—
520C22×C71—22no—
521C22×C71—26no—
522C22×C71—46no—
523C22×C71—42no—
524C22×C71—812no—
525C22×C71C23×D416yes—
526C22×C71C23×D411yescharacteristic
527C2×D71—22no—
528C2×D71—26no—
529C2×D71—26no—
530C2×D71—26no—
531C2×D71—412no—
532C2×D71—424no—
533C2×D71—46no—
534C2×D71—46no—
535C2×D71—812no—
536C2×D71—824no—
537C2×D71—812no—
538C2×D71—812no—
539C2×D71C23×D412yes—
540C2×D71C23×D416yes—
541C4×C71—22no—
542C4×C71—26no—
543C4×C71C23×D411yescharacteristic
544C4×C71C23×D416yes—
545C4×C71C2611yescharacteristic
546Dic71—22no—
547Dic71—22no—
548Dic71C23×D416yes—
549Dic71C23×D412yes—
550C2×#3585—711nomaximal, Sylow
551C2×C71—26no—
552C2×C71—46no—
553C2×C71—42no—
554C2×C71#358512yescomplemented
555C2×C71C24×D411yescharacteristic
556D71—22no—
557D71—26no—
558D71—46no—
559D71—46no—
560C2×#585—711no—
561C22×H(5,𝔽2)—711no—
562#3585—7132no—
563C2×#577—711no—
564C2×#577—713no—
565C2×#577—713no—
566C2×#577D7111yescharacteristic, complemented
567C2×#576—711no—
568C2×#576—713no—
569C2×#576—713no—
570C2×#576—711no—
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—713no—
580C2×2−1+4—1421no—
581C2×2−1+4C2×D7111yescharacteristic, complemented
582C2×H(5,𝔽2)—7116no—
583C2×H(5,𝔽2)—713no—
584C2×H(5,𝔽2)—711no—
585C2×H(5,𝔽2)—711no—
586C2×H(5,𝔽2)—713no—
587C2×H(5,𝔽2)—713no—
588C2×H(5,𝔽2)—1423no—
589C2×H(5,𝔽2)—1423no—
590C2×H(5,𝔽2)—1421no—
591C2×H(5,𝔽2)—1428no—
592C2×H(5,𝔽2)C2×D7111yescharacteristic, complemented
593C22×#41—711no—
594C22×#41—713no—
595C22×#41—713no—
596C22×#41—713no—
597C22×#41—1421no—
598C22×#41—1421no—
599C22×#41—1423no—
600C23×D4—713no—
601C23×D4—1423no—
602#577—7116no—
603#577—7148no—
604#577—7148no—
605#577C2×D71116yescomplemented
606#576—7116no—
607#576—7148no—
608#576—7148no—
609#576—7116no—
610#575—7148no—
611#575—7148no—
612C2×#137—713no—
613C2×#137—713no—
614C2×#137—713no—
615C2×#137—711no—
616C2×#137—713no—
617C2×#137C2×D7113yescomplemented
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)—7148no—
623C2×AGL(1,ℤ/8)—716no—
624C2×AGL(1,ℤ/8)—713no—
625C2×AGL(1,ℤ/8)—716no—
626C2×AGL(1,ℤ/8)—716no—
627C2×AGL(1,ℤ/8)—713no—
628C2×AGL(1,ℤ/8)—713no—
629C2×AGL(1,ℤ/8)—713no—
630C2×AGL(1,ℤ/8)—713no—
631C2×AGL(1,ℤ/8)—713no—
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×SD16C2×D7113yescomplemented
642C22×D8—713no—
643C22×D8—716no—
644C22×D8—713no—
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—24no—
6542−1+4—7124no—
6552−1+4—14216no—
6562−1+4—14212no—
6572−1+4C22×D7118yescomplemented
658H(5,𝔽2)—24no—
659H(5,𝔽2)—718no—
660H(5,𝔽2)—7124no—
661H(5,𝔽2)—718no—
662H(5,𝔽2)—7124no—
663H(5,𝔽2)—7124no—
664H(5,𝔽2)—14248no—
665H(5,𝔽2)—14212no—
666H(5,𝔽2)—14248no—
667H(5,𝔽2)—14216no—
668H(5,𝔽2)—14212no—
669H(5,𝔽2)—14212no—
670H(5,𝔽2)—1424no—
671H(5,𝔽2)—1424no—
672H(5,𝔽2)C22×D7118yescomplemented
673C2×#41—21no—
674C2×#41—23no—
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—713no—
684C2×#41—716no—
685C2×#41—7124no—
686C2×#41—713no—
687C2×#41—711no—
688C2×#41—713no—
689C2×#41—713no—
690C2×#41—1423no—
691C2×#41—1423no—
692C2×#41—1426no—
693C2×#41—1423no—
694C2×#41—1423no—
695C2×#41—1423no—
696C2×#41—1423no—
697C2×#41—1423no—
698C2×#41—1423no—
699C2×#41—14212no—
700C2×#41—14212no—
701C2×#41—14212no—
702C2×#41—1423no—
703C2×#41—1423no—
704C2×#41—14216no—
705C2×#41—14216no—
706C2×#41—14248no—
707C2×#41—1421no—
708C2×#41—1421no—
709C2×#41C22×D7113yes—
710C2×#41C22×D7111yescharacteristic
711C2×#41C22×D7113yescomplemented
712C22×Q8—21no—
713C22×Q8—711no—
714C22×Q8—711no—
715C22×Q8—713no—
716C22×Q8—1423no—
717C22×Q8C22×D7113yescomplemented
718C22×D4—23no—
719C22×D4—713no—
720C22×D4—716no—
721C22×D4—713no—
722C22×D4—713no—
723C22×D4—7124no—
724C22×D4—713no—
725C22×D4—713no—
726C22×D4—1423no—
727C22×D4—1423no—
728C22×D4—1423no—
729C22×D4—1423no—
730C22×D4—1423no—
731C22×D4—14212no—
732C22×D4—1423no—
733C22×D4—1426no—
734C22×D4—14248no—
735C22×D4—1423no—
736C22×D4—1426no—
737C22×D4—1423no—
738C22×D4—1423no—
739C22×D4—1426no—
740C22×D4—1423no—
741C22×D4—1423no—
742C22×D4C22×D7113yes—
743C23×C4—713no—
744C23×C4—1423no—
745C23×C4—1423no—
746C23×C4—1423no—
747#137—7124no—
748#137—7124no—
749#137—7124no—
750#137—718no—
751#137—7124no—
752#137C22×D71124yescomplemented
753AGL(1,ℤ/8)—7124no—
754AGL(1,ℤ/8)—7124no—
755AGL(1,ℤ/8)—7124no—
756AGL(1,ℤ/8)—7148no—
757AGL(1,ℤ/8)—7124no—
758AGL(1,ℤ/8)—7148no—
759AGL(1,ℤ/8)—7148no—
760AGL(1,ℤ/8)—7124no—
761AGL(1,ℤ/8)—7124no—
762AGL(1,ℤ/8)—7124no—
763AGL(1,ℤ/8)—7124no—
764AGL(1,ℤ/8)—7124no—
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—711no—
773C2×Q16—713no—
774C2×Q16—711no—
775C2×Q16C22×D7113yescomplemented
776C2×SD16—713no—
777C2×SD16—716no—
778C2×SD16—713no—
779C2×SD16—7124no—
780C2×SD16—713no—
781C2×SD16—711no—
782C2×SD16—7148no—
783C2×SD16—713no—
784C2×SD16—713no—
785C2×SD16C22×D7116yescomplemented
786C2×SD16C22×D7113yescomplemented
787C2×SD16C22×D7111yescharacteristic, complemented
788C2×SD16C22×D71124yescomplemented
789C2×D8—713no—
790C2×D8—716no—
791C2×D8—713no—
792C2×D8—7124no—
793C2×D8—7148no—
794C2×D8—716no—
795C2×D8—713no—
796C2×D8—7124no—
797C2×D8C22×D7113yescomplemented
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—56812no—
815C24—713no—
816C24—1423no—
817C24—1423no—
818C24—1426no—
819C24—14224no—
820C24—1423no—
821C24—1423no—
822#41—28no—
823#41—224no—
824#41—26no—
825#41—26no—
826#41—718no—
827#41—7124no—
828#41—7112no—
829#41—7112no—
830#41—7112no—
831#41—7112no—
832#41—7124no—
833#41—7112no—
834#41—714no—
835#41—7112no—
836#41—7112no—
837#41—14224no—
838#41—14224no—
839#41—14248no—
840#41—14224no—
841#41—14224no—
842#41—14224no—
843#41—1422no—
844#41—14224no—
845#41—1426no—
846#41—1426no—
847#41—14224no—
848#41—1426no—
849#41—14224no—
850#41—14212no—
851#41—14224no—
852#41—14224no—
853#41—1428no—
854#41—1428no—
855#41—1426no—
856#41—1426no—
857#41D4×D7114yes—
858#41C23×D71112yes—
859#41C23×D7114yes—
860#41C23×D71112yescomplemented
861C2×Q8—28no—
862C2×Q8—23no—
863C2×Q8—26no—
864C2×Q8—718no—
865C2×Q8—713no—
866C2×Q8—714no—
867C2×Q8—7112no—
868C2×Q8—711no—
869C2×Q8—711no—
870C2×Q8—1423no—
871C2×Q8—1421no—
872C2×Q8—1422no—
873C2×Q8—1426no—
874C2×Q8—14224no—
875C2×Q8D4×D7111yescharacteristic
876C2×Q8C23×D7113yes—
877C2×Q8C23×D7111yescharacteristic
878C2×Q8C23×D71112yescomplemented
879C2×D4—23no—
880C2×D4—23no—
881C2×D4—224no—
882C2×D4—23no—
883C2×D4—26no—
884C2×D4—716no—
885C2×D4—7124no—
886C2×D4—7124no—
887C2×D4—7112no—
888C2×D4—7112no—
889C2×D4—713no—
890C2×D4—713no—
891C2×D4—713no—
892C2×D4—7112no—
893C2×D4—7112no—
894C2×D4—14224no—
895C2×D4—14224no—
896C2×D4—1423no—
897C2×D4—1423no—
898C2×D4—1426no—
899C2×D4—14224no—
900C2×D4—1426no—
901C2×D4—14224no—
902C2×D4—14224no—
903C2×D4—14212no—
904C2×D4—1426no—
905C2×D4—1423no—
906C2×D4—1426no—
907C2×D4—1423no—
908C2×D4—14224no—
909C2×D4—14248no—
910C2×D4—14224no—
911C2×D4—14248no—
912C2×D4—14224no—
913C2×D4—14224no—
914C2×D4—14248no—
915C2×D4—1423no—
916C2×D4—1421no—
917C2×D4—1423no—
918C2×D4—1423no—
919C2×D4—14224no—
920C2×D4—14224no—
921C2×D4—1423no—
922C2×D4—1423no—
923C2×D4—1426no—
924C2×D4—1426no—
925C2×D4D4×D7113yes—
926C2×D4C23×D7111yescharacteristic
927C2×D4C23×D7113yes—
928C2×D4C23×D71112yes—
929C22×C4—23no—
930C22×C4—23no—
931C22×C4—23no—
932C22×C4—713no—
933C22×C4—713no—
934C22×C4—713no—
935C22×C4—7112no—
936C22×C4—713no—
937C22×C4—711no—
938C22×C4—7112no—
939C22×C4—1423no—
940C22×C4—1423no—
941C22×C4—14224no—
942C22×C4—1426no—
943C22×C4—14224no—
944C22×C4—14224no—
945C22×C4—1421no—
946C22×C4—1423no—
947C22×C4—1421no—
948C22×C4—1423no—
949C22×C4—1423no—
950C22×C4—1423no—
951C22×C4C23×D7113yes—
952Q16—714no—
953Q16—7112no—
954Q16—714no—
955Q16C23×D71112yescomplemented
956SD16—7112no—
957SD16—7124no—
958SD16—7112no—
959SD16—7112no—
960SD16—714no—
961SD16—7112no—
962SD16—7112no—
963SD16C23×D71124yescomplemented
964SD16C23×D71112yescomplemented
965SD16C23×D7114yescomplemented
966D8—7124no—
967D8—7112no—
968D8—7112no—
969D8—7124no—
970D8—7112no—
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—21no—
986C23—23no—
987C23—212no—
988C23—86no—
989C23—2846no—
990C23—28412no—
991C23—5686no—
992C23—5686no—
993C23—56812no—
994C23—5686no—
995C23—56848no—
996C23—7112no—
997C23—711no—
998C23—713no—
999C23—14212no—
1000C23—14212no—
1001C23—14224no—
1002C23—1423no—
1003C23—1423no—
1004C23—14212no—
1005C23—14212no—
1006C23C2×D4×D7113yes—
1007Q8—23no—
1008Q8—212no—
1009Q8—21no—
1010Q8—7112no—
1011Q8—712no—
1012Q8—712no—
1013Q8—14212no—
1014Q8—1424no—
1015Q8—1421no—
1016Q8—1421no—
1017Q8C2×D4×D7114yes—
1018Q8C24×D7116yes—
1019Q8C24×D7112yes—
1020D4—212no—
1021D4—212no—
1022D4—212no—
1023D4—23no—
1024D4—21no—
1025D4—7124no—
1026D4—7112no—
1027D4—716no—
1028D4—716no—
1029D4—14212no—
1030D4—14212no—
1031D4—14224no—
1032D4—14212no—
1033D4—14224no—
1034D4—14212no—
1035D4—14212no—
1036D4—1424no—
1037D4—14212no—
1038D4—14212no—
1039D4—14212no—
1040D4—1423no—
1041D4—14212no—
1042D4—1423no—
1043D4C2×D4×D71112yes—
1044D4C24×D7112yes—
1045D4C24×D7116yes—
1046C2×C4—212no—
1047C2×C4—21no—
1048C2×C4—23no—
1049C2×C4—212no—
1050C2×C4—212no—
1051C2×C4—7112no—
1052C2×C4—711no—
1053C2×C4—713no—
1054C2×C4—712no—
1055C2×C4—7112no—
1056C2×C4—7112no—
1057C2×C4—716no—
1058C2×C4—716no—
1059C2×C4—712no—
1060C2×C4—14212no—
1061C2×C4—14212no—
1062C2×C4—14224no—
1063C2×C4—1424no—
1064C2×C4—14212no—
1065C2×C4—1424no—
1066C2×C4—14212no—
1067C2×C4—1421no—
1068C2×C4—1421no—
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—22no—
1081C22—26no—
1082C22—46no—
1083C22—42no—
1084C22—812no—
1085C22—28412no—
1086C22—28424no—
1087C22—2846no—
1088C22—2846no—
1089C22—56812no—
1090C22—56812no—
1091C22—56824no—
1092C22—56812no—
1093C22—712no—
1094C22—716no—
1095C22—1426no—
1096C22—1426no—
1097C22—1422no—
1098C22—1426no—
1099C22C22×D4×D7116yes—
1100C22C22×D4×D7111yescharacteristic
1101C4—22no—
1102C4—26no—
1103C4—712no—
1104C4—716no—
1105C4—1422no—
1106C4—1422no—
1107C4C22×D4×D7116yes—
1108C4C22×D4×D7111yescharacteristic
1109C4C25×D7111yescharacteristic
1110C2—26no—
1111C2—46no—
1112C2—42no—
1113C2—2846no—
1114C2—2846no—
1115C2—1422no—
1116C2—1426no—
1117C2#2260311812yesdirect product factor
1118C2C23×D4×D7111yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC4×C71C26
FrattiniC4C25×D71
FittingC2×#577×C71C2
socleC22×C71C23×D4
hypercenterC2×#577D71
hypocenterC71C2×#3585
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#17986836C2semidirect
2. C2×H(5,𝔽2)×D71C2semidirect
3. #22603118C2direct (N × H)
4. C2×#17986808C2semidirect
5. C2×#17986807C2semidirect
6. C2×#17986805C2semidirect
7. C2×#17986804C2semidirect
8. C2×#17986803C2semidirect
9. C2×#17986802C2semidirect
10. C2×#17986801C2semidirect
11. C2×#17986798C2semidirect
12. C2×#17986796C2semidirect
13. C22×#14556155C2semidirect
14. C2×AGL(1,ℤ/8)×D71C2semidirect
15. C2×#17986764C2semidirect
16. C2×#577×C71C2semidirect
18. #17986836C22semidirect
20. C2×#14556176C22semidirect
23. C2×#14556174C22semidirect
24. C2×#14556174C22semidirect
25. C2×#14556174C22semidirect
26. C2×#14556174C22semidirect
28. C2×#14556173C22semidirect
30. H(5,𝔽2)×D71C22semidirect
32. C22×#11765866C22semidirect
36. C2×#41×D71C22semidirect
37. C2×#41×D71C22semidirect
39. C22×D4×D71C22semidirect
40. #17986808C22semidirect
41. #17986807C22semidirect
42. #17986805C22semidirect
43. #17986804C22semidirect
44. #17986803C22semidirect
45. #17986802C22semidirect
46. #17986801C22semidirect
47. #17986798C22semidirect
48. #17986796C22semidirect
49. C2×#14556160C22semidirect
50. C2×#14556160C22semidirect
51. C2×#14556159C22semidirect
52. C2×#14556157C22semidirect
53. C2×#14556157C22semidirect
54. C2×#14556156C22semidirect
55. C2×#14556156C22semidirect
56. C2×#14556155C22semidirect
57. C2×#14556155C22semidirect
58. C2×#14556155C22semidirect
59. C2×#14556155C22semidirect
60. C2×#14556155C22semidirect
61. C2×#14556155C22semidirect
62. C2×#14556154C22semidirect
63. C2×#14556153C22semidirect
64. C2×#14556153C22semidirect
65. C2×#14556152C22semidirect
66. C2×#14556152C22semidirect
67. AGL(1,ℤ/8)×D71C22semidirect
68. C2×#14556151C22semidirect
69. C2×#14556150C22semidirect
70. C2×#14556149C22semidirect
71. C2×#14556148C22semidirect
72. C2×#14556148C22semidirect
73. C22×#11765852C22semidirect
74. C2×SD16×D71C22semidirect
75. C22×D568C22semidirect
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. C2×2−1+4×C71C22semidirect
85. C2×H(5,𝔽2)×C71C22semidirect
86. #577×C71C22semidirect
87. C2×#137×C71C22semidirect
88. C2×AGL(1,ℤ/8)×C71C22semidirect
89. C2×#135×C71C22semidirect
90. C22×SD16×C71C22semidirect
91. C2×#131×C71C22semidirect
95. #14556176C23semidirect
102. #14556174C23semidirect
103. #14556174C23semidirect
104. #14556174C23semidirect
105. #14556174C23semidirect
108. #14556173C23semidirect
119. C2×#11765866C23semidirect
120. C2×#11765866C23semidirect
128. C2×#11765865C23semidirect
141. #41×D71C23semidirect
142. #41×D71C23semidirect
146. C2×Q8×D71C23semidirect
151. C22×D284C23semidirect
168. C2×D4×D71C23semidirect
169. C2×D4×D71C23semidirect
174. #14556160C23semidirect
175. #14556160C23semidirect
176. #14556159C23semidirect
177. #14556157C23semidirect
178. #14556157C23semidirect
179. #14556156C23semidirect
180. #14556156C23semidirect
181. #14556155C23semidirect
182. #14556155C23semidirect
183. #14556155C23semidirect
184. #14556155C23semidirect
185. #14556155C23semidirect
186. #14556154C23semidirect
187. #14556153C23semidirect
188. #14556153C23semidirect
189. #14556152C23semidirect
190. #14556152C23semidirect
191. #14556151C23semidirect
192. #14556150C23semidirect
193. #14556149C23semidirect
194. #14556148C23semidirect
195. #14556148C23semidirect
196. C2×Dic284C23semidirect
197. C2×#11765855C23semidirect
198. C2×#11765855C23semidirect
199. C2×#11765854C23semidirect
200. C2×#11765854C23semidirect
201. C2×#11765853C23semidirect
202. C2×#11765853C23semidirect
203. C2×#11765852C23semidirect
204. C2×#11765852C23semidirect
205. C2×#11765852C23semidirect
206. C2×#11765852C23semidirect
207. SD16×D71C23semidirect
208. C2×D568C23semidirect
209. C2×D568C23semidirect
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
229. 2−1+4×C71C23semidirect
231. H(5,𝔽2)×C71C23semidirect
236. C2×#41×C71C23semidirect
238. C22×Q8×C71C23semidirect
241. #137×C71C23semidirect
242. AGL(1,ℤ/8)×C71C23semidirect
243. #135×C71C23semidirect
244. C2×Q16×C71C23semidirect
245. C2×SD16×C71C23semidirect
246. C2×SD16×C71C23semidirect
247. C2×SD16×C71C23semidirect
248. C2×SD16×C71C23semidirect
249. C2×D8×C71C23semidirect
250. #131×C71C23semidirect
251. C2×M16×C71C23semidirect
252. C22×C8×C71C23semidirect
272. #11765866C24semidirect
283. #11765865C24semidirect
302. Q8×D71C24semidirect
317. C2×D284C24semidirect
343. D4×D71C24semidirect
363. Dic284C24semidirect
364. #11765855C24semidirect
365. #11765855C24semidirect
366. #11765854C24semidirect
367. #11765854C24semidirect
368. #11765853C24semidirect
369. #11765853C24semidirect
370. #11765852C24semidirect
371. #11765852C24semidirect
372. #11765852C24semidirect
373. D568C24semidirect
374. D568C24semidirect
375. #11765850C24semidirect
376. #11765850C24semidirect
377. #11765850C24semidirect
378. #11765849C24semidirect
381. #11765848C24semidirect
382. #11765848C24semidirect
385. C2×C71⋊C8C24semidirect
386. C8×D71C24semidirect
395. #41×C71C24semidirect
402. C2×Q8×C71C24semidirect
416. Q16×C71C24semidirect
417. SD16×C71C24semidirect
418. SD16×C71C24semidirect
419. SD16×C71C24semidirect
420. D8×C71C24semidirect
421. M16×C71C24semidirect
424. C2×C8×C71C24semidirect
554. C2×C71#3585semidirect
566. C2×#577D71semidirect
576. C71C2×#3585semidirect
581. C2×2−1+4C2×D71semidirect
592. C2×H(5,𝔽2)C2×D71semidirect
605. #577C2×D71semidirect
617. C2×#137C2×D71semidirect
632. C2×AGL(1,ℤ/8)C2×D71semidirect
638. C2×#135C2×D71semidirect
641. C22×SD16C2×D71semidirect
649. C2×#131C2×D71semidirect
657. 2−1+4C22×D71semidirect
672. H(5,𝔽2)C22×D71semidirect
711. C2×#41C22×D71semidirect
717. C22×Q8C22×D71semidirect
752. #137C22×D71semidirect
765. AGL(1,ℤ/8)C22×D71semidirect
771. #135C22×D71semidirect
775. C2×Q16C22×D71semidirect
785. C2×SD16C22×D71semidirect
786. C2×SD16C22×D71semidirect
787. C2×SD16C22×D71semidirect
788. C2×SD16C22×D71semidirect
797. C2×D8C22×D71semidirect
801. #131C22×D71semidirect
809. C2×M16C22×D71semidirect
812. C22×C8C22×D71semidirect
860. #41C23×D71semidirect
878. C2×Q8C23×D71semidirect
955. Q16C23×D71semidirect
963. SD16C23×D71semidirect
964. SD16C23×D71semidirect
965. SD16C23×D71semidirect
971. D8C23×D71semidirect
977. M16C23×D71semidirect
984. C2×C8C23×D71semidirect
1117. C2#22603118direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179868362
C2×H(5,𝔽2)×D712
#226031182
C2×#179868082
C2×#179868072
C2×#179868052
C2×#179868042
C2×#179868032
C2×#179868022
C2×#179868012
C2×#179867982
C2×#179867962
C22×#145561552
C2×AGL(1,ℤ/8)×D712
C2×#179867642
C2×#577×C712
C2×#358571