Finite Group Databasebeta

← C2×#22603122 #32911296

Subgroups — C2×#22603122 #32911296

Order 18176.

10794 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986834C211yesmaximal, characteristic, complemented
2C2×2−1+4×D71C211yesmaximal, characteristic, complemented
3#22603122C2132yesmaximal, direct product factor
4C2×#17986816C211yesmaximal, characteristic, complemented
5C2×#17986815C213yesmaximal, complemented
6C2×#17986814C211yesmaximal, characteristic, complemented
7C2×#17986813C213yesmaximal, complemented
8C2×#17986810C211yesmaximal, characteristic, complemented
9C2×#17986809C213yesmaximal, complemented
10C2×#17986805C213yesmaximal, complemented
11C2×#17986796C213yesmaximal, complemented
12C2×#17986795C213yesmaximal, complemented
13C22×#14556157C213yesmaximal, complemented
14C2×#137×D71C213yesmaximal, complemented
15C2×#17986764C211yesmaximal, characteristic, complemented
16C2×#577×C71C211yesmaximal, characteristic, complemented
17#17986834—28no—
18#17986834C22116yescomplemented
19C2×#14556176—21no—
20C2×#14556176C2213yescomplemented
21C2×#14556175—23no—
22C2×#14556175—21no—
23C2×#14556175C2211yescharacteristic, complemented
24C2×#14556175C2211yescharacteristic, complemented
25C2×#14556175C2213yescomplemented
26C2×#14556175C2213yescomplemented
272−1+4×D71—28no—
282−1+4×D71C22116yescomplemented
29C2×#14556173—23no—
30C2×#14556173C2213yescomplemented
31C22×#11765864—23no—
32C22×#11765864C2213yes—
33C2×#41×D71—21no—
34C2×#41×D71—23no—
35C2×#41×D71C2213yes—
36C2×#41×D71C2211yescharacteristic
37C2×#41×D71C2213yescomplemented
38C22×Q8×D71—21no—
39C22×Q8×D71C2213yescomplemented
40#17986816C22116yescomplemented
41#17986815C22148yescomplemented
42#17986814C22116yescomplemented
43#17986813C22148yescomplemented
44#17986810C22116yescomplemented
45#17986809C22148yescomplemented
46#17986805C22148yescomplemented
47#17986796C22148yescomplemented
48#17986795C22148yescomplemented
49C2×#14556161C2213yescomplemented
50C2×#14556161C2213yescomplemented
51C2×#14556160C2213yescomplemented
52C2×#14556160C2213yescomplemented
53C2×#14556159C2213yescomplemented
54C2×#14556158C2213yescomplemented
55C2×#14556158C2213yescomplemented
56C2×#14556157C2216yescomplemented
57C2×#14556157C2213yescomplemented
58C2×#14556157C2216yescomplemented
59C2×#14556157C2216yescomplemented
60C2×#14556157C2213yescomplemented
61C2×#14556157C22148yescomplemented
62#137×D71C22148yescomplemented
63C2×#14556155C2211yescharacteristic, complemented
64C2×#14556155C2213yescomplemented
65C2×#14556154C2213yescomplemented
66C2×#14556152C2213yescomplemented
67C2×#14556152C2213yescomplemented
68C2×#14556150C2213yescomplemented
69C2×#14556149C2216yescomplemented
70C2×#14556148C2213yescomplemented
71C2×#14556148C2213yescomplemented
72C2×#14556147C2216yescomplemented
73C22×Dic284C2213yescomplemented
74C22×#11765855C2213yescomplemented
75C2×Q16×D71C2216yescomplemented
76C22×#11765853C2213yescomplemented
77C2×SD16×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
92#14556176—216no—
93#14556176—212no—
94#14556176C23124yescomplemented
95#14556175—212no—
96#14556175—212no—
97#14556175—248no—
98#14556175—216no—
99#14556175—24no—
100#14556175—24no—
101#14556175C2318yescomplemented
102#14556175C2318yescomplemented
103#14556175C23124yescomplemented
104#14556175C23124yescomplemented
105#14556173—212no—
106#14556173—248no—
107#14556173C23124yescomplemented
108C2×#11765866—23no—
109C2×#11765866D411yescharacteristic
110C2×#11765866C2311yescharacteristic
111C2×#11765866C2313yes—
112C2×#11765865—23no—
113C2×#11765865—23no—
114C2×#11765865—26no—
115C2×#11765865—23no—
116C2×#11765865—23no—
117C2×#11765865C2313yes—
118C2×#11765865C2313yes—
119C2×#11765865C2313yes—
120C2×#11765864—248no—
121C2×#11765864—23no—
122C2×#11765864—26no—
123C2×#11765864—26no—
124C2×#11765864—23no—
125C2×#11765864—23no—
126C2×#11765864—23no—
127C2×#11765864—23no—
128C2×#11765864—212no—
129C2×#11765864—23no—
130C2×#11765864—23no—
131C2×#11765864D413yes—
132C2×#11765864C2313yes—
133C2×#11765864C2313yes—
134C2×#11765864C2316yes—
135C2×#11765864C23124yes—
136#41×D71—216no—
137#41×D71—248no—
138#41×D71—212no—
139#41×D71—212no—
140#41×D71D418yes—
141#41×D71C23124yes—
142#41×D71C2318yes—
143#41×D71C23124yescomplemented
144C22×Dic142—23no—
145C22×Dic142—23no—
146C22×Dic142—23no—
147C22×Dic142C2313yes—
148C22×Dic142C2313yes—
149C2×Q8×D71—23no—
150C2×Q8×D71—216no—
151C2×Q8×D71—23no—
152C2×Q8×D71—212no—
153C2×Q8×D71—23no—
154C2×Q8×D71—21no—
155C2×Q8×D71—21no—
156C2×Q8×D71D411yescharacteristic
157C2×Q8×D71C2313yes—
158C2×Q8×D71C2316yes—
159C2×Q8×D71C2313yes—
160C2×Q8×D71C23124yescomplemented
161C22×C22⋊D71—23no—
162C22×C22⋊D71—26no—
163C2×D4×D71—23no—
164C2×D4×D71—23no—
165C2×D4×D71—23no—
166C2×D4×D71D413yes—
167C2×D4×D71C2313yes—
168C2×D4×D71C2311yescharacteristic
169C23×Dic71—23no—
170C22×C4×D71—23no—
171C22×C4×D71—23no—
172C22×C4×D71—23no—
173C22×C4×D71C2313yes—
174#14556161C23124yescomplemented
175#14556161C23124yescomplemented
176#14556160C23124yescomplemented
177#14556160C23124yescomplemented
178#14556159C23124yescomplemented
179#14556158C23124yescomplemented
180#14556158C23124yescomplemented
181#14556157C23148yescomplemented
182#14556157C23124yescomplemented
183#14556157C23148yescomplemented
184#14556157C23148yescomplemented
185#14556157C23124yescomplemented
186#14556155C2318yescomplemented
187#14556155C23124yescomplemented
188#14556154C23124yescomplemented
189#14556152C23124yescomplemented
190#14556152C23124yescomplemented
191#14556150C23124yescomplemented
192#14556149C23148yescomplemented
193#14556148C23124yescomplemented
194#14556148C23124yescomplemented
195#14556147C23148yescomplemented
196C2×Dic284C2316yes—
197C2×Dic284C2313yes—
198C2×Dic284C23124yescomplemented
199C2×#11765855C2313yes—
200C2×#11765855C2316yes—
201C2×#11765855C2313yes—
202C2×#11765855C23124yescomplemented
203Q16×D71C23148yescomplemented
204C2×#11765854C2313yes—
205C2×#11765854C2313yes—
206C2×#11765853C2316yes—
207C2×#11765853C2313yes—
208C2×#11765853C2313yes—
209C2×#11765853C23124yescomplemented
210C2×#11765852C2313yes—
211C2×#11765852C2311yescharacteristic
212SD16×D71C23148yescomplemented
213C2×D568C2311yescharacteristic
214C2×#11765850C2311yescharacteristic
215C2×#11765850C2313yes—
216#14556136C23124yescomplemented
217#14556135C2318yescomplemented
218#14556134C23124yescomplemented
219C2×#11765849C2313yes—
220C2×#11765848C2313yes—
221C2×#11765848C2311yescharacteristic
222C2×#11765848C2313yes—
223C2×#11765848C2313yes—
224C2×#11765848C23124yescomplemented
225M16×D71C23124yescomplemented
226C22×C71⋊C8C2313yes—
227C2×C8×D71C2316yes—
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×C71C2313yes—
236C2×#41×C71C2311yescharacteristic
237C22×Q8×C71—21no—
238C22×Q8×C71C2313yes—
239C22×D4×C71—23no—
240C22×D4×C71C2313yes—
241#137×C71C23124yescomplemented
242AGL(1,ℤ/8)×C71C23124yescomplemented
243#135×C71C23124yescomplemented
244C2×Q16×C71C2313yes—
245C2×SD16×C71C2313yes—
246C2×SD16×C71C2316yes—
247C2×SD16×C71C2311yescharacteristic
248C2×SD16×C71C23124yescomplemented
249C2×D8×C71C2313yes—
250#131×C71C2318yescomplemented
251C2×M16×C71C2313yes—
252C22×C8×C71C2313yes—
253C23×D71—21no—
254C23×D71—23no—
255C23×D71C2×D413yes—
256#11765866—224no—
257#11765866—22no—
258#11765866—26no—
259#11765866C2×D418yes—
260#11765866C2414yes—
261#11765866C24112yes—
262#11765865—26no—
263#11765865—26no—
264#11765865—248no—
265#11765865—224no—
266#11765865—224no—
267#11765865—224no—
268#11765865—224no—
269#11765865C2×D4112yes—
270#11765865C24112yes—
271#11765865C24112yes—
272#11765865C24112yes—
273#11765864—224no—
274#11765864—224no—
275#11765864—248no—
276#11765864—248no—
277#11765864—224no—
278#11765864—224no—
279#11765864—224no—
280#11765864—26no—
281#11765864—26no—
282#11765864—224no—
283#11765864—212no—
284#11765864—224no—
285#11765864C2×D4124yes—
286#11765864C24112yes—
287#11765864C24112yes—
288#11765864C24124yes—
289C2×Dic142—23no—
290C2×Dic142—26no—
291C2×Dic142—23no—
292C2×Dic142—26no—
293C2×Dic142—23no—
294C2×Dic142—26no—
295C2×Dic142—224no—
296C2×Dic142—23no—
297C2×Dic142—224no—
298C2×Dic142—224no—
299C2×Dic142C2×D413yes—
300C2×Dic142C24112yes—
301C2×Dic142C24112yes—
302C2×Dic142C2413yes—
303C2×Dic142C2413yes—
304Q8×D71—28no—
305Q8×D71—28no—
306Q8×D71—26no—
307Q8×D71—224no—
308Q8×D71—212no—
309Q8×D71—224no—
310Q8×D71—26no—
311Q8×D71—224no—
312Q8×D71C2×D418yes—
313Q8×D71C24112yes—
314Q8×D71C24112yes—
315Q8×D71C24124yes—
316C2×D284—21no—
317C2×D284—23no—
318C2×D284C2×D413yes—
319C2×D284C2411yescharacteristic
320C2×D284C2411yescharacteristic
321C2×C22⋊D71—23no—
322C2×C22⋊D71—23no—
323C2×C22⋊D71—23no—
324C2×C22⋊D71—26no—
325C2×C22⋊D71—23no—
326C2×C22⋊D71—224no—
327C2×C22⋊D71—248no—
328C2×C22⋊D71—23no—
329C2×C22⋊D71—21no—
330C2×C22⋊D71C2×D416yes—
331D4×D71—224no—
332D4×D71—224no—
333D4×D71—224no—
334D4×D71—22no—
335D4×D71—26no—
336D4×D71C2×D4124yes—
337D4×D71C24112yes—
338D4×D71C2414yes—
339C22×Dic71—23no—
340C22×Dic71—23no—
341C22×Dic71—23no—
342C22×Dic71—23no—
343C22×Dic71—26no—
344C22×Dic71—224no—
345C22×Dic71C2×D413yes—
346C2×C4×D71—23no—
347C2×C4×D71—23no—
348C2×C4×D71—26no—
349C2×C4×D71—224no—
350C2×C4×D71—23no—
351C2×C4×D71—23no—
352C2×C4×D71—21no—
353C2×C4×D71—23no—
354C2×C4×D71—224no—
355C2×C4×D71—224no—
356C2×C4×D71C2×D413yes—
357C2×C4×D71C2×D413yes—
358C2×C4×D71C2×D4112yes—
359C2×C4×D71C2411yescharacteristic
360C2×C4×D71C2413yes—
361C2×C4×D71C24112yes—
362Dic284C24124yes—
363Dic284C24112yes—
364#11765855C24112yes—
365#11765855C24112yes—
366#11765855C24124yes—
367#11765854C24112yes—
368#11765854C24112yes—
369#11765853C24124yes—
370#11765853C24112yes—
371#11765853C24112yes—
372#11765852C2414yes—
373#11765852C24112yes—
374D568C2414yes—
375#11765850C2414yes—
376#11765850C24112yes—
377#11765849C24112yes—
378#11765848C24112yes—
379#11765848C24112yes—
380#11765848C2414yes—
381#11765848C24112yes—
382C2×C71⋊C8C2413yes—
383C2×C71⋊C8C2411yescharacteristic
384C2×C71⋊C8C24112yes—
385C8×D71C24124yes—
386C24×C71—23no—
387#41×C71—28no—
388#41×C71—224no—
389#41×C71—26no—
390#41×C71—26no—
391#41×C71C2×D414yes—
392#41×C71C24112yes—
393#41×C71C24112yes—
394#41×C71C2414yes—
395C2×Q8×C71—28no—
396C2×Q8×C71—23no—
397C2×Q8×C71—26no—
398C2×Q8×C71C2×D411yescharacteristic
399C2×Q8×C71C2413yes—
400C2×Q8×C71C2411yescharacteristic
401C2×Q8×C71C24112yes—
402C2×D4×C71—23no—
403C2×D4×C71—23no—
404C2×D4×C71—224no—
405C2×D4×C71—23no—
406C2×D4×C71—26no—
407C2×D4×C71C2×D413yes—
408C2×D4×C71C2411yescharacteristic
409C2×D4×C71C2413yes—
410C2×D4×C71C24112yes—
411C22×C4×C71—23no—
412C22×C4×C71—23no—
413C22×C4×C71—23no—
414C22×C4×C71C2413yes—
415Q16×C71C24112yes—
416SD16×C71C24112yes—
417SD16×C71C24124yes—
418SD16×C71C2414yes—
419D8×C71C24112yes—
420M16×C71C24112yes—
421C2×C8×C71C2411yescharacteristic
422C2×C8×C71C2413yes—
423C2×C8×C71C24112yes—
424C23×C71—21no—
425C23×C71—23no—
426C23×C71—212no—
427C23×C71—86no—
428C23×C71C22×D413yes—
429C22×D71—21no—
430C22×D71—21no—
431C22×D71—24no—
432C22×D71—212no—
433C22×D71—46no—
434C22×D71—44no—
435C22×D71—86no—
436C22×D71C22×D411yescharacteristic
437C22×D71C22×D413yes—
438C22×D71C22×D4112yes—
439Q8×C71—23no—
440Q8×C71—212no—
441Q8×C71—21no—
442Q8×C71C22×D414yes—
443Q8×C71C2516yes—
444Q8×C71C2512yes—
445D4×C71—212no—
446D4×C71—212no—
447D4×C71—23no—
448D4×C71—212no—
449D4×C71—21no—
450D4×C71C22×D4112yes—
451D4×C71C2512yes—
452D4×C71C2516yes—
453C2×C4×C71—21no—
454C2×C4×C71—23no—
455C2×C4×C71—212no—
456C2×C4×C71—212no—
457C2×C4×C71—212no—
458C2×C4×C71C22×D413yes—
459C2×C4×C71C22×D416yes—
460C2×C4×C71C2511yescharacteristic
461C2×C4×C71C2516yes—
462C22⋊D71—212no—
463C22⋊D71—212no—
464C22⋊D71—212no—
465C22⋊D71—224no—
466C22⋊D71—212no—
467C22⋊D71—212no—
468C22⋊D71—24no—
469C22⋊D71C22×D4124yes—
470C2×Dic71—23no—
471C2×Dic71—23no—
472C2×Dic71—212no—
473C2×Dic71—212no—
474C2×Dic71—212no—
475C2×Dic71—212no—
476C2×Dic71—224no—
477C2×Dic71C22×D411yescharacteristic
478C2×Dic71C22×D413yes—
479C2×Dic71C22×D4112yes—
480D284—24no—
481D284—212no—
482D284—21no—
483D284—21no—
484D284C22×D4112yes—
485D284C2512yes—
486D284C2512yes—
487C4×D71—212no—
488C4×D71—212no—
489C4×D71—224no—
490C4×D71—212no—
491C4×D71—212no—
492C4×D71—24no—
493C4×D71—212no—
494C4×D71C22×D4112yes—
495C4×D71C22×D4112yes—
496C4×D71C22×D412yes—
497C4×D71C22×D416yes—
498C4×D71C2516yes—
499C4×D71C2512yes—
500Dic142—23no—
501Dic142—212no—
502Dic142—23no—
503Dic142—212no—
504Dic142—224no—
505Dic142—212no—
506Dic142—212no—
507Dic142C22×D4112yes—
508Dic142C2516yes—
509Dic142C2516yes—
510C8×C71C2512yes—
511C8×C71C2516yes—
512C71⋊C8C2516yes—
513C71⋊C8C2512yes—
514C22×C71—26no—
515C22×C71—22no—
516C22×C71—26no—
517C22×C71—42no—
518C22×C71—46no—
519C22×C71—812no—
520C22×C71C23×D416yes—
521C22×C71C23×D411yescharacteristic
522C2×D71—22no—
523C2×D71—26no—
524C2×D71—22no—
525C2×D71—22no—
526C2×D71—412no—
527C2×D71—48no—
528C2×D71—42no—
529C2×D71—42no—
530C2×D71—812no—
531C2×D71C23×D412yes—
532C2×D71C23×D416yes—
533C4×C71—22no—
534C4×C71—26no—
535C4×C71C23×D411yescharacteristic
536C4×C71C23×D416yes—
537C4×C71C2611yescharacteristic
538Dic71—26no—
539Dic71—26no—
540Dic71C23×D416yes—
541Dic71C23×D412yes—
542C2×#3586—711nomaximal, Sylow
543C2×C71—26no—
544C2×C71—42no—
545C2×C71—46no—
546C2×C71#358612yescomplemented
547C2×C71C24×D411yescharacteristic
548D71—22no—
549D71—26no—
550D71—42no—
551D71—42no—
552C2×#585—711no—
553C22×2−1+4—711no—
554#3586—7132no—
555C2×#578—711no—
556C2×#578—713no—
557C2×#578—713no—
558C2×#578—711no—
559C2×#577—711no—
560C2×#577—713no—
561C2×#577—713no—
562C2×#577D7111yescharacteristic, complemented
563C2×#575—713no—
564C2×#575—713no—
565C22×#137—713no—
566C22×#137—713no—
567C2×#568—711no—
568C71C2×#358611yescharacteristic, complemented, Sylow
569#585—7116no—
570#585—1428no—
571C2×2−1+4—7116no—
572C2×2−1+4—713no—
573C2×2−1+4—713no—
574C2×2−1+4—711no—
575C2×2−1+4—711no—
576C2×2−1+4—713no—
577C2×2−1+4—1421no—
578C2×2−1+4—1421no—
579C2×2−1+4—1423no—
580C2×2−1+4—1428no—
581C2×2−1+4C2×D7111yescharacteristic, complemented
582C2×H(5,𝔽2)—713no—
583C2×H(5,𝔽2)—1423no—
584C2×H(5,𝔽2)C2×D7111yescharacteristic, complemented
585C22×#41—711no—
586C22×#41—713no—
587C22×#41—713no—
588C22×#41—713no—
589C22×#41—1423no—
590C22×#41—1423no—
591C22×#41—1421no—
592C23×Q8—713no—
593C23×Q8—1421no—
594#578—7116no—
595#578—7148no—
596#578—7148no—
597#578—7116no—
598#577—7116no—
599#577—7148no—
600#577—7148no—
601#577C2×D71116yescomplemented
602#575—7148no—
603#575—7148no—
604C2×#137—713no—
605C2×#137—713no—
606C2×#137—713no—
607C2×#137—7148no—
608C2×#137—713no—
609C2×#137—713no—
610C2×#137—716no—
611C2×#137—713no—
612C2×#137—716no—
613C2×#137—716no—
614C2×#137—713no—
615C2×#137—7148no—
616C2×#137—713no—
617C2×#137—713no—
618C2×#137C2×D7113yescomplemented
619C2×AGL(1,ℤ/8)—713no—
620C2×AGL(1,ℤ/8)—711no—
621C2×AGL(1,ℤ/8)—713no—
622C2×AGL(1,ℤ/8)—713no—
623C2×AGL(1,ℤ/8)—713no—
624C2×AGL(1,ℤ/8)C2×D7113yescomplemented
625C2×#135—713no—
626C2×#135—713no—
627C2×#135—716no—
628C2×#135—716no—
629C2×#135—713no—
630C2×#135C2×D7113yescomplemented
631C22×Q16—713no—
632C22×Q16—716no—
633C22×Q16—713no—
634C22×SD16—713no—
635C22×SD16—716no—
636C22×SD16C2×D7113yescomplemented
637#568—7116no—
638C2×#131—711no—
639C2×#131—713no—
640C2×#131—713no—
641C2×#131C2×D7111yescharacteristic, complemented
642C22×M16—713no—
643C22×M16—713no—
6442−1+4—24no—
6452−1+4—7124no—
6462−1+4—718no—
6472−1+4—7124no—
6482−1+4—718no—
6492−1+4—7124no—
6502−1+4—14216no—
6512−1+4—14212no—
6522−1+4—14216no—
6532−1+4—14248no—
6542−1+4—14212no—
6552−1+4—14212no—
6562−1+4—1424no—
6572−1+4—1424no—
6582−1+4C22×D7118yescomplemented
659H(5,𝔽2)—24no—
660H(5,𝔽2)—7124no—
661H(5,𝔽2)—14248no—
662H(5,𝔽2)—14212no—
663H(5,𝔽2)C22×D7118yescomplemented
664C2×#41—21no—
665C2×#41—23no—
666C2×#41—718no—
667C2×#41—718no—
668C2×#41—711no—
669C2×#41—713no—
670C2×#41—713no—
671C2×#41—7124no—
672C2×#41—7124no—
673C2×#41—713no—
674C2×#41—711no—
675C2×#41—713no—
676C2×#41—716no—
677C2×#41—713no—
678C2×#41—7124no—
679C2×#41—713no—
680C2×#41—713no—
681C2×#41—1423no—
682C2×#41—1423no—
683C2×#41—1423no—
684C2×#41—1426no—
685C2×#41—1423no—
686C2×#41—1423no—
687C2×#41—1423no—
688C2×#41—1423no—
689C2×#41—1423no—
690C2×#41—14212no—
691C2×#41—14212no—
692C2×#41—14212no—
693C2×#41—1426no—
694C2×#41—1426no—
695C2×#41—1423no—
696C2×#41—14248no—
697C2×#41—1423no—
698C2×#41—14248no—
699C2×#41—14216no—
700C2×#41—1423no—
701C2×#41—1423no—
702C2×#41C22×D7113yes—
703C2×#41C22×D7113yes—
704C2×#41C22×D7111yescharacteristic
705C22×Q8—21no—
706C22×Q8—711no—
707C22×Q8—716no—
708C22×Q8—713no—
709C22×Q8—713no—
710C22×Q8—7124no—
711C22×Q8—713no—
712C22×Q8—713no—
713C22×Q8—1423no—
714C22×Q8—1423no—
715C22×Q8—1423no—
716C22×Q8—1423no—
717C22×Q8—1423no—
718C22×Q8—14212no—
719C22×Q8—14216no—
720C22×Q8—1423no—
721C22×Q8—1421no—
722C22×Q8—1421no—
723C22×Q8C22×D7113yes—
724C22×D4—23no—
725C22×D4—713no—
726C22×D4—713no—
727C22×D4—711no—
728C22×D4—1423no—
729C22×D4—1423no—
730C22×D4—1423no—
731C22×D4—1426no—
732C22×D4—1423no—
733C22×D4C22×D7113yes—
734C23×C4—713no—
735C23×C4—1423no—
736C23×C4—1423no—
737C23×C4—1423no—
738C23×C4—1423no—
739#137—7124no—
740#137—7124no—
741#137—7124no—
742#137—7124no—
743#137—7124no—
744#137—7148no—
745#137—7124no—
746#137—7148no—
747#137—7148no—
748#137—7124no—
749#137—7124no—
750#137—7124no—
751#137C22×D71124yescomplemented
752AGL(1,ℤ/8)—7124no—
753AGL(1,ℤ/8)—718no—
754AGL(1,ℤ/8)—7124no—
755AGL(1,ℤ/8)—7124no—
756AGL(1,ℤ/8)—7124no—
757AGL(1,ℤ/8)C22×D71124yescomplemented
758#135—7124no—
759#135—7124no—
760#135—7148no—
761#135—7148no—
762#135—7124no—
763#135C22×D71124yescomplemented
764C2×Q16—713no—
765C2×Q16—713no—
766C2×Q16—716no—
767C2×Q16—7124no—
768C2×Q16—7148no—
769C2×Q16—716no—
770C2×Q16—713no—
771C2×Q16—7124no—
772C2×Q16C22×D7113yes—
773C2×SD16—713no—
774C2×SD16—711no—
775C2×SD16—713no—
776C2×SD16—716no—
777C2×SD16—7124no—
778C2×SD16—713no—
779C2×SD16—7148no—
780C2×SD16—713no—
781C2×SD16—713no—
782C2×SD16C22×D7116yes—
783C2×SD16C22×D7113yes—
784C2×SD16C22×D7111yescharacteristic
785C2×SD16C22×D71124yescomplemented
786C2×D8—713no—
787C2×D8—711no—
788C2×D8—711no—
789C2×D8C22×D7113yes—
790#131—718no—
791#131—7124no—
792#131—7124no—
793#131C22×D7118yescomplemented
794C2×M16—713no—
795C2×M16—7124no—
796C2×M16—713no—
797C2×M16—711no—
798C2×M16—713no—
799C2×M16—713no—
800C2×M16—7124no—
801C2×M16C22×D7113yes—
802C22×C8—713no—
803C22×C8—716no—
804C22×C8C22×D7113yes—
805C24—23no—
806C24—713no—
807C24—1421no—
808C24—1423no—
809#41—28no—
810#41—224no—
811#41—26no—
812#41—26no—
813#41—718no—
814#41—7124no—
815#41—7112no—
816#41—7112no—
817#41—7112no—
818#41—714no—
819#41—7112no—
820#41—7124no—
821#41—7112no—
822#41—7112no—
823#41—7112no—
824#41—14224no—
825#41—14224no—
826#41—14224no—
827#41—14248no—
828#41—14224no—
829#41—14224no—
830#41—1426no—
831#41—14224no—
832#41—14224no—
833#41—14212no—
834#41—14224no—
835#41—1426no—
836#41—1422no—
837#41—1426no—
838#41—14248no—
839#41—14248no—
840#41—14224no—
841#41—14224no—
842#41—14224no—
843#41—14224no—
844#41—1426no—
845#41—1426no—
846#41D4×D7114yes—
847#41C23×D71112yes—
848#41C23×D71112yes—
849#41C23×D7114yes—
850C2×Q8—28no—
851C2×Q8—23no—
852C2×Q8—26no—
853C2×Q8—718no—
854C2×Q8—713no—
855C2×Q8—7124no—
856C2×Q8—7112no—
857C2×Q8—7112no—
858C2×Q8—713no—
859C2×Q8—713no—
860C2×Q8—7112no—
861C2×Q8—7112no—
862C2×Q8—1423no—
863C2×Q8—1426no—
864C2×Q8—1423no—
865C2×Q8—14224no—
866C2×Q8—14224no—
867C2×Q8—14224no—
868C2×Q8—1426no—
869C2×Q8—14224no—
870C2×Q8—14224no—
871C2×Q8—14212no—
872C2×Q8—1426no—
873C2×Q8—14224no—
874C2×Q8—1428no—
875C2×Q8—1428no—
876C2×Q8—1423no—
877C2×Q8—1423no—
878C2×Q8—1426no—
879C2×Q8—1426no—
880C2×Q8D4×D7111yescharacteristic
881C2×Q8C23×D7113yes—
882C2×Q8C23×D7111yescharacteristic
883C2×Q8C23×D71112yes—
884C2×D4—23no—
885C2×D4—23no—
886C2×D4—224no—
887C2×D4—23no—
888C2×D4—26no—
889C2×D4—716no—
890C2×D4—7124no—
891C2×D4—7112no—
892C2×D4—714no—
893C2×D4—713no—
894C2×D4—711no—
895C2×D4—711no—
896C2×D4—1421no—
897C2×D4—1423no—
898C2×D4—1422no—
899C2×D4—1426no—
900C2×D4—1423no—
901C2×D4—1421no—
902C2×D4—14224no—
903C2×D4—14224no—
904C2×D4—14224no—
905C2×D4—14248no—
906C2×D4—1423no—
907C2×D4—1426no—
908C2×D4—1423no—
909C2×D4—14224no—
910C2×D4—1423no—
911C2×D4—1423no—
912C2×D4D4×D7113yes—
913C2×D4C23×D7111yescharacteristic
914C2×D4C23×D7113yes—
915C2×D4C23×D71112yes—
916C22×C4—23no—
917C22×C4—23no—
918C22×C4—23no—
919C22×C4—713no—
920C22×C4—713no—
921C22×C4—713no—
922C22×C4—7112no—
923C22×C4—713no—
924C22×C4—711no—
925C22×C4—7112no—
926C22×C4—1421no—
927C22×C4—1423no—
928C22×C4—14224no—
929C22×C4—14224no—
930C22×C4—1423no—
931C22×C4—1423no—
932C22×C4—14224no—
933C22×C4—1426no—
934C22×C4—1423no—
935C22×C4—1426no—
936C22×C4—1423no—
937C22×C4—14224no—
938C22×C4—1423no—
939C22×C4—1423no—
940C22×C4—1423no—
941C22×C4—1423no—
942C22×C4C23×D7113yes—
943Q16—7112no—
944Q16—7112no—
945Q16—7124no—
946Q16—7124no—
947Q16—7112no—
948Q16C23×D71112yes—
949SD16—7112no—
950SD16—714no—
951SD16—7124no—
952SD16—7112no—
953SD16—7112no—
954SD16—7112no—
955SD16—7112no—
956SD16C23×D71124yes—
957SD16C23×D71112yes—
958SD16C23×D7114yes—
959D8—7112no—
960D8—714no—
961D8—714no—
962D8C23×D71112yes—
963M16—7112no—
964M16—7112no—
965M16—714no—
966M16—7112no—
967M16—7112no—
968M16C23×D71112yes—
969C2×C8—713no—
970C2×C8—711no—
971C2×C8—7112no—
972C2×C8—7124no—
973C2×C8C23×D7113yes—
974C2×C8C23×D7111yescharacteristic
975C2×C8C23×D71112yes—
976C23—21no—
977C23—23no—
978C23—212no—
979C23—86no—
980C23—2846no—
981C23—2844no—
982C23—5686no—
983C23—7112no—
984C23—711no—
985C23—713no—
986C23—1424no—
987C23—14212no—
988C23—1421no—
989C23—1421no—
990C23C2×D4×D7113yes—
991Q8—212no—
992Q8—23no—
993Q8—21no—
994Q8—7112no—
995Q8—716no—
996Q8—716no—
997Q8—14212no—
998Q8—14224no—
999Q8—14212no—
1000Q8—14212no—
1001Q8—1423no—
1002Q8—14212no—
1003Q8—1423no—
1004Q8C2×D4×D7114yes—
1005Q8C24×D7116yes—
1006Q8C24×D7112yes—
1007D4—212no—
1008D4—212no—
1009D4—212no—
1010D4—23no—
1011D4—21no—
1012D4—7124no—
1013D4—7112no—
1014D4—712no—
1015D4—712no—
1016D4—1424no—
1017D4—14212no—
1018D4—14212no—
1019D4—1424no—
1020D4—14212no—
1021D4—14224no—
1022D4—14212no—
1023D4—14212no—
1024D4—14212no—
1025D4—1421no—
1026D4—1421no—
1027D4C2×D4×D71112yes—
1028D4C24×D7112yes—
1029D4C24×D7116yes—
1030C2×C4—212no—
1031C2×C4—21no—
1032C2×C4—23no—
1033C2×C4—212no—
1034C2×C4—212no—
1035C2×C4—7112no—
1036C2×C4—711no—
1037C2×C4—713no—
1038C2×C4—712no—
1039C2×C4—7112no—
1040C2×C4—7112no—
1041C2×C4—716no—
1042C2×C4—716no—
1043C2×C4—712no—
1044C2×C4—1424no—
1045C2×C4—14212no—
1046C2×C4—14212no—
1047C2×C4—14212no—
1048C2×C4—14224no—
1049C2×C4—14212no—
1050C2×C4—14224no—
1051C2×C4—14212no—
1052C2×C4—14212no—
1053C2×C4—14212no—
1054C2×C4—1423no—
1055C2×C4—1423no—
1056C2×C4—14212no—
1057C2×C4—14212no—
1058C2×C4C2×D4×D7116yes—
1059C2×C4C2×D4×D7113yes—
1060C2×C4C24×D7116yes—
1061C2×C4C24×D7111yescharacteristic
1062C8—712no—
1063C8—716no—
1064C8C24×D7116yes—
1065C8C24×D7112yes—
1066C22—26no—
1067C22—22no—
1068C22—26no—
1069C22—46no—
1070C22—42no—
1071C22—812no—
1072C22—28412no—
1073C22—2848no—
1074C22—2842no—
1075C22—2842no—
1076C22—56812no—
1077C22—712no—
1078C22—716no—
1079C22—1422no—
1080C22—1422no—
1081C22—1422no—
1082C22—1426no—
1083C22C22×D4×D7116yes—
1084C22C22×D4×D7111yescharacteristic
1085C4—22no—
1086C4—26no—
1087C4—712no—
1088C4—716no—
1089C4—1426no—
1090C4—1426no—
1091C4C22×D4×D7116yes—
1092C4C22×D4×D7111yescharacteristic
1093C4C25×D7111yescharacteristic
1094C2—26no—
1095C2—46no—
1096C2—42no—
1097C2—2842no—
1098C2—2842no—
1099C2—1422no—
1100C2—1426no—
1101C2#2260312212yesdirect product factor
1102C2C23×D4×D7111yescharacteristic
subgroupG/H
centerC22C22×D4×D71
commutator, cosocleC4×C71C26
FrattiniC4C25×D71
FittingC2×#577×C71C2
socleC22×C71C23×D4
hypercenterC2×#577D71
hypocenterC71C2×#3586
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×#17986834C2semidirect
2. C2×2−1+4×D71C2semidirect
3. #22603122C2direct (N × H)
4. C2×#17986816C2semidirect
5. C2×#17986815C2semidirect
6. C2×#17986814C2semidirect
7. C2×#17986813C2semidirect
8. C2×#17986810C2semidirect
9. C2×#17986809C2semidirect
10. C2×#17986805C2semidirect
11. C2×#17986796C2semidirect
12. C2×#17986795C2semidirect
13. C22×#14556157C2semidirect
14. C2×#137×D71C2semidirect
15. C2×#17986764C2semidirect
16. C2×#577×C71C2semidirect
18. #17986834C22semidirect
20. C2×#14556176C22semidirect
23. C2×#14556175C22semidirect
24. C2×#14556175C22semidirect
25. C2×#14556175C22semidirect
26. C2×#14556175C22semidirect
28. 2−1+4×D71C22semidirect
30. C2×#14556173C22semidirect
37. C2×#41×D71C22semidirect
39. C22×Q8×D71C22semidirect
40. #17986816C22semidirect
41. #17986815C22semidirect
42. #17986814C22semidirect
43. #17986813C22semidirect
44. #17986810C22semidirect
45. #17986809C22semidirect
46. #17986805C22semidirect
47. #17986796C22semidirect
48. #17986795C22semidirect
49. C2×#14556161C22semidirect
50. C2×#14556161C22semidirect
51. C2×#14556160C22semidirect
52. C2×#14556160C22semidirect
53. C2×#14556159C22semidirect
54. C2×#14556158C22semidirect
55. C2×#14556158C22semidirect
56. C2×#14556157C22semidirect
57. C2×#14556157C22semidirect
58. C2×#14556157C22semidirect
59. C2×#14556157C22semidirect
60. C2×#14556157C22semidirect
61. C2×#14556157C22semidirect
62. #137×D71C22semidirect
63. C2×#14556155C22semidirect
64. C2×#14556155C22semidirect
65. C2×#14556154C22semidirect
66. C2×#14556152C22semidirect
67. C2×#14556152C22semidirect
68. C2×#14556150C22semidirect
69. C2×#14556149C22semidirect
70. C2×#14556148C22semidirect
71. C2×#14556148C22semidirect
72. C2×#14556147C22semidirect
73. C22×Dic284C22semidirect
74. C22×#11765855C22semidirect
75. C2×Q16×D71C22semidirect
76. C22×#11765853C22semidirect
77. C2×SD16×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
94. #14556176C23semidirect
101. #14556175C23semidirect
102. #14556175C23semidirect
103. #14556175C23semidirect
104. #14556175C23semidirect
107. #14556173C23semidirect
143. #41×D71C23semidirect
160. C2×Q8×D71C23semidirect
174. #14556161C23semidirect
175. #14556161C23semidirect
176. #14556160C23semidirect
177. #14556160C23semidirect
178. #14556159C23semidirect
179. #14556158C23semidirect
180. #14556158C23semidirect
181. #14556157C23semidirect
182. #14556157C23semidirect
183. #14556157C23semidirect
184. #14556157C23semidirect
185. #14556157C23semidirect
186. #14556155C23semidirect
187. #14556155C23semidirect
188. #14556154C23semidirect
189. #14556152C23semidirect
190. #14556152C23semidirect
191. #14556150C23semidirect
192. #14556149C23semidirect
193. #14556148C23semidirect
194. #14556148C23semidirect
195. #14556147C23semidirect
198. C2×Dic284C23semidirect
202. C2×#11765855C23semidirect
203. Q16×D71C23semidirect
209. C2×#11765853C23semidirect
212. SD16×D71C23semidirect
216. #14556136C23semidirect
217. #14556135C23semidirect
218. #14556134C23semidirect
224. C2×#11765848C23semidirect
225. M16×D71C23semidirect
229. 2−1+4×C71C23semidirect
231. H(5,𝔽2)×C71C23semidirect
241. #137×C71C23semidirect
242. AGL(1,ℤ/8)×C71C23semidirect
243. #135×C71C23semidirect
248. C2×SD16×C71C23semidirect
250. #131×C71C23semidirect
546. C2×C71#3586semidirect
562. C2×#577D71semidirect
568. C71C2×#3586semidirect
581. C2×2−1+4C2×D71semidirect
584. C2×H(5,𝔽2)C2×D71semidirect
601. #577C2×D71semidirect
618. C2×#137C2×D71semidirect
624. C2×AGL(1,ℤ/8)C2×D71semidirect
630. C2×#135C2×D71semidirect
636. C22×SD16C2×D71semidirect
641. C2×#131C2×D71semidirect
658. 2−1+4C22×D71semidirect
663. H(5,𝔽2)C22×D71semidirect
751. #137C22×D71semidirect
757. AGL(1,ℤ/8)C22×D71semidirect
763. #135C22×D71semidirect
785. C2×SD16C22×D71semidirect
793. #131C22×D71semidirect
1101. C2#22603122direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179868342
C2×2−1+4×D712
#226031222
C2×#179868162
C2×#179868152
C2×#179868142
C2×#179868132
C2×#179868102
C2×#179868092
C2×#179868052
C2×#179867962
C2×#179867952
C22×#145561572
C2×#137×D712
C2×#179867642
C2×#577×C712
C2×#358671