Finite Group Databasebeta

← C2×#21455548 #30547418

Subgroups — C2×#21455548 #30547418

Order 15616.

2746 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840562C211yesmaximal, characteristic, complemented
2C22×#14519805C211yesmaximal, characteristic, complemented
3C22×#14519805C211yesmaximal, characteristic, complemented
4C2×#16840528C211yesmaximal, characteristic, complemented
5#21455548C2116yesmaximal, direct product factor
6C2×#16840033C214yesmaximal, complemented
7C2×#16840026C214yesmaximal, complemented
8C2×#16839744C211yesmaximal, characteristic, complemented
9C22×#14519693C211yesmaximal, characteristic, complemented
10C2×C61×#430C211yesmaximal, characteristic, complemented
11C22×#11758222C2211yescharacteristic
12C22×#11758222C2211yescharacteristic
13C23×D244C2211yescharacteristic
14#16840562—24no—
15#16840562C2218yescomplemented
16C2×#14519810—21no—
17C2×#14519810C2212yescomplemented
18C2×#14519805—22no—
19C2×#14519805—22no—
20C2×#14519805—24no—
21C2×#14519805—22no—
22C2×#14519805—24no—
23C2×#14519805—21no—
24C2×#14519805C2214yes—
25C2×#14519805C2218yescomplemented
26C2×#14519805C2212yescomplemented
27C2×#14519805C2218yescomplemented
28C2×#14519799—22no—
29C22×#11758190—21no—
30C22×#11758190C2212yescomplemented
31C22×D488—21no—
32C22×D488C2212yescomplemented
33#16840528—24no—
34#16840528C2218yescomplemented
35C2×#14519785—22no—
36C2×#14519783C2214yescomplemented
37C22×#11758194C2211yescharacteristic
38C2×M16×D61—22no—
39#16840033C22132yescomplemented
40#16840026C22132yescomplemented
41#16839744C2218yescomplemented
42C2×#14519695C2212yescomplemented
43C2×#14519693C2214yescomplemented
44C2×#14519693C2212yescomplemented
45C2×#14519693C2218yescomplemented
46C22×M16×C61C2211yescharacteristic
47C22×M16×C61C2211yescharacteristic
48C22×M16×C61C2211yescharacteristic
49C61×#430C2218yescomplemented
50C2×#108×C61C2214yescomplemented
51C24×D61—21no—
52C2×#11758222—21no—
53C2×#11758222—22no—
54C2×#11758222—21no—
55C2×#11758222—22no—
56C2×#11758222—22no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—22no—
61C2×#11758222—21no—
62C2×#11758222—22no—
63C2×#11758222D412yes—
64C2×#11758222D414yes—
65C2×#11758222C2312yes—
66C2×#11758222C2314yes—
67C2×#11758222C2314yes—
68C22×Dic122D411yescharacteristic
69C22×Dic122C2311yescharacteristic
70C22×D244—21no—
71C22×D244—21no—
72C22×D244—21no—
73C22×D244—22no—
74C22×D244—21no—
75C22×D244—22no—
76C22×D244—21no—
77C22×D244—22no—
78C22×D244D411yescharacteristic
79C22×D244C2311yescharacteristic
80C22×D244C2312yes—
81C22×D244C2314yes—
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86#14519810—24no—
87#14519810—28no—
88#14519810C2318yescomplemented
89#14519805—28no—
90#14519805—216no—
91#14519805—24no—
92#14519805—28no—
93#14519805—216no—
94#14519805—216no—
95#14519805C23116yes—
96#14519805C2318yescomplemented
97#14519799—216no—
98C2×Dic244—22no—
99C2×#11758190—22no—
100C2×#11758190—24no—
101C2×#11758190—28no—
102C2×#11758190—22no—
103C2×#11758190—24no—
104C2×#11758190—24no—
105C2×#11758190C2318yescomplemented
106C2×D488—24no—
107C2×D488—28no—
108C2×D488—22no—
109C2×D488—24no—
110C2×D488—24no—
111C2×D488C2318yescomplemented
112#14519785—216no—
113#14519783—28no—
114#14519783C23116yescomplemented
115C2×#11758194—21no—
116C2×#11758194—22no—
117C2×#11758194C2312yes—
118C2×#11758194C2314yes—
119C2×#11758189—24no—
120M16×D61—216no—
121C22×#92418—21no—
122C2×C8×D61—24no—
123#14519695C2318yescomplemented
124#14519693C23116yescomplemented
125#14519693C2318yescomplemented
126C23×C4×C61C2311yescharacteristic
127C2×M16×C61—21no—
128C2×M16×C61—22no—
129C2×M16×C61—21no—
130C2×M16×C61—22no—
131C2×M16×C61D412yes—
132C2×M16×C61D412yes—
133C2×M16×C61D414yes—
134C2×M16×C61C2312yes—
135C2×M16×C61C2314yes—
136C2×M16×C61C2312yes—
137C2×M16×C61C2314yes—
138C2×M16×C61C2314yes—
139C22×C8×C61—21no—
140C22×C8×C61—21no—
141C22×C8×C61C2312yes—
142#108×C61C23116yescomplemented
143C24×C61#4111yescharacteristic
144C23×D61—21no—
145C23×D61—21no—
146C23×D61—22no—
147C23×D61—24no—
148C23×D61—41no—
149C23×D61—41no—
150C23×D61—42no—
151C23×D61—84no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D412yes—
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61#4112yes—
160C22×C4×C61C2411yescharacteristic
161C22×C4×C61C2412yes—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—24no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—24no—
166C2×C22⋊D61—24no—
167C2×C22⋊D61—41no—
168C2×C22⋊D61—41no—
169C2×C22⋊D61—42no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172#11758222—24no—
173#11758222—24no—
174#11758222—24no—
175#11758222—22no—
176#11758222—24no—
177#11758222—22no—
178#11758222—24no—
179#11758222—24no—
180#11758222—24no—
181#11758222—24no—
182#11758222—24no—
183#11758222—42no—
184#11758222—42no—
185#11758222—42no—
186#11758222—42no—
187#11758222C2×D414yes—
188#11758222C2×D418yes—
189#11758222C2414yes—
190C2×D244—21no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—24no—
194C2×D244—22no—
195C2×D244—22no—
196C2×D244—24no—
197C2×D244—22no—
198C2×D244—24no—
199C2×D244—24no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—22no—
205C2×D244—24no—
206C2×D244—21no—
207C2×D244—41no—
208C2×D244—42no—
209C2×D244—41no—
210C2×D244—42no—
211C2×D244—42no—
212C2×D244—42no—
213C2×D244—42no—
214C2×D244C2×D412yes—
215C2×D244C2×D414yes—
216C2×D244C2414yes—
217C2×D244C2412yes—
218C2×C4×D61—22no—
219C2×C4×D61—24no—
220C2×C4×D61—22no—
221C2×C4×D61—24no—
222C2×C4×D61—24no—
223C2×C4×D61—41no—
224C2×C4×D61—41no—
225C2×C4×D61—42no—
226C2×Dic122—21no—
227C2×Dic122—22no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122C2×D414yes—
234C2×Dic122C2×D412yes—
235C2×Dic122C2412yes—
236M16×C61—24no—
237M16×C61—22no—
238M16×C61—24no—
239M16×C61—22no—
240M16×C61C2×D418yes—
241M16×C61C2×D418yes—
242M16×C61C2414yes—
243M16×C61C2414yes—
244C2×C8×C61—22no—
245C2×C8×C61—24no—
246C2×C8×C61—22no—
247C2×C8×C61—24no—
248C2×C8×C61C2×D414yes—
249C2×C8×C61C2×D414yes—
250C2×C8×C61C2414yes—
251#11758194—24no—
252#11758194—22no—
253#11758194C2414yes—
254C2×#92418—22no—
255C2×#92418—24no—
256Dic244—28no—
257D488—216no—
258D488—28no—
259D488—216no—
260#11758190—28no—
261#11758190—28no—
262#11758190—216no—
263#11758190—216no—
264#11758189—216no—
265C8×D61—216no—
266C23×C61—42no—
267C23×C61#12111yescharacteristic
268C23×C61#12111yescharacteristic
269C23×C61#12112yes—
270C23×C61C2×#4111yescharacteristic
271C23×C61C2×#4112yes—
272C22×D61—22no—
273C22×D61—24no—
274C22×D61—22no—
275C22×D61—24no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—44no—
279C22×D61—44no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—82no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—88no—
286C22×D61—82no—
287C22×D61—84no—
288C22×D61—88no—
289C2×C4×C61#12111yescharacteristic
290C2×C4×C61#12112yes—
291C2×C4×C61#12111yescharacteristic
292C2×C4×C61#12112yes—
293C2×C4×C61#12112yes—
294C2×C4×C61#12112yes—
295C2×C4×C61#12112yes—
296C2×C4×C61C22×D411yescharacteristic
297C2×C4×C61C22×D412yes—
298C2×C4×C61C22×D412yes—
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D412yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D412yes—
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4112yes—
306C2×C4×C61C2511yescharacteristic
307C22⋊D61—24no—
308C22⋊D61—28no—
309C22⋊D61—24no—
310C22⋊D61—44no—
311C22⋊D61—44no—
312C2×Dic61—24no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317D244—22no—
318D244—24no—
319D244—24no—
320D244—24no—
321D244—22no—
322D244—22no—
323D244—42no—
324D244—44no—
325D244—42no—
326D244—44no—
327D244—41no—
328D244—41no—
329D244C22×D414yes—
330C4×D61—24no—
331C4×D61—28no—
332C4×D61—24no—
333C4×D61—44no—
334C4×D61—44no—
335Dic122—22no—
336Dic122—24no—
337Dic122—22no—
338Dic122—22no—
339Dic122—41no—
340Dic122—41no—
341Dic122C22×D414yes—
342C8×C61—24no—
343C8×C61—24no—
344C8×C61C22×D418yes—
345#92418—24no—
346C2×#3068—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61C2×#12112yes—
353C22×C61C2×#12111yescharacteristic
354C22×C61C2×#12112yes—
355C22×C61C2×#12111yescharacteristic
356C22×C61C22×#4111yescharacteristic
357C2×D61—24no—
358C2×D61—44no—
359C2×D61—42no—
360C2×D61—44no—
361C2×D61—84no—
362C2×D61—82no—
363C2×D61—88no—
364C2×D61—88no—
365C2×D61—84no—
366C2×D61—82no—
367C2×D61—84no—
368C2×D61—82no—
369C2×D61—84no—
370C4×C61C2×#12111yescharacteristic
371C4×C61C2×#12112yes—
372C4×C61C2×#12111yescharacteristic
373C4×C61C2×#12112yes—
374C4×C61C23×D411yescharacteristic
375C4×C61C23×D411yescharacteristic
376Dic61—24no—
377Dic61—42no—
378C2×#575—611no—
379C22×AGL(1,ℤ/8)—611no—
380C22×AGL(1,ℤ/8)—611no—
381C2×#568—611no—
382#3068—6116no—
383C2×#472—614no—
384C2×#471—614no—
385C2×#430D6111yescharacteristic, complemented
386C2×#413—611no—
387C22×#100—611no—
388C2×C61—22no—
389C2×C61—21no—
390C2×C61—21no—
391C2×C61—22no—
392C2×C61#306812yescomplemented
393C2×C61C22×#12111yescharacteristic
394D61—44no—
395D61—82no—
396D61—84no—
397C22×#41—611no—
398C22×#41—611no—
399C23×D4—611no—
400#575—618no—
401#575—1224no—
402C2×#137—612no—
403C2×#137—1221no—
404C2×AGL(1,ℤ/8)—618no—
405C2×AGL(1,ℤ/8)—614no—
406C2×AGL(1,ℤ/8)—612no—
407C2×AGL(1,ℤ/8)—618no—
408C2×AGL(1,ℤ/8)—1221no—
409C2×AGL(1,ℤ/8)—1222no—
410C2×AGL(1,ℤ/8)—1224no—
411C2×AGL(1,ℤ/8)—1222no—
412C2×AGL(1,ℤ/8)—1222no—
413C2×AGL(1,ℤ/8)—1224no—
414C2×#135—1222no—
415C22×SD16—612no—
416C22×SD16—1221no—
417C22×D8—612no—
418C22×D8—1221no—
419#568—618no—
420#568—1224no—
421C2×#131—614no—
422C2×#131—1222no—
423C22×M16—611no—
424C22×M16—1222no—
425C22×M16C2×D6111yescharacteristic
426C22×M16C2×D6111yescharacteristic
427C22×M16C2×D6111yescharacteristic
428#472—6132no—
429#471—6132no—
430#430C2×D6118yescomplemented
431C2×#108C2×D6114yescomplemented
432#413—618no—
433C2×#101—612no—
434C2×#100—614no—
435C2×#100—618no—
436C2×#100—612no—
437C61C2×#306811yescharacteristic, complemented, Sylow
438C25—1221no—
439C2×#41—612no—
440C2×#41—614no—
441C2×#41—612no—
442C2×#41—614no—
443C2×#41—614no—
444C2×#41—1221no—
445C2×#41—1222no—
446C2×#41—1221no—
447C2×#41—1222no—
448C2×#41—1222no—
449C2×#41—1221no—
450C2×#41—1221no—
451C2×#41—1222no—
452C2×#41—1221no—
453C2×#41—1221no—
454C2×#41—1222no—
455C22×Q8—611no—
456C22×Q8—611no—
457C22×D4—611no—
458C22×D4—611no—
459C22×D4—612no—
460C22×D4—614no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4—1221no—
464C22×D4—1221no—
465C22×D4—1222no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1222no—
469C22×D4—1221no—
470C22×D4—1222no—
471C23×C4—1221no—
472C23×C4—1221no—
473C23×C4C22×D6111yescharacteristic
474#137—618no—
475#137—1228no—
476#137—1224no—
477AGL(1,ℤ/8)—6116no—
478AGL(1,ℤ/8)—618no—
479AGL(1,ℤ/8)—1228no—
480AGL(1,ℤ/8)—12216no—
481AGL(1,ℤ/8)—1228no—
482AGL(1,ℤ/8)—1224no—
483AGL(1,ℤ/8)—12216no—
484AGL(1,ℤ/8)—12216no—
485#135—12216no—
486C2×Q16—1222no—
487C2×SD16—618no—
488C2×SD16—1222no—
489C2×SD16—1224no—
490C2×SD16—1228no—
491C2×SD16—1222no—
492C2×SD16—1224no—
493C2×SD16—1224no—
494C2×D8—618no—
495C2×D8—1224no—
496C2×D8—1228no—
497C2×D8—1222no—
498C2×D8—1224no—
499C2×D8—1224no—
500#131—6116no—
501#131—12216no—
502#131—1228no—
503C2×M16—21no—
504C2×M16—22no—
505C2×M16—21no—
506C2×M16—22no—
507C2×M16—612no—
508C2×M16—614no—
509C2×M16—1221no—
510C2×M16—1222no—
511C2×M16—12216no—
512C2×M16—1224no—
513C2×M16D24412yes—
514C2×M16D24412yes—
515C2×M16D24414yes—
516C2×M16C22×D6112yes—
517C2×M16C22×D6114yes—
518C2×M16C22×D6112yes—
519C2×M16C22×D6114yes—
520C2×M16C22×D6114yes—
521C22×C8—21no—
522C22×C8—21no—
523C22×C8—1221no—
524C22×C8—1224no—
525C22×C8C22×D6112yes—
526#108C22×D61116yescomplemented
527#101—618no—
528#100—6116no—
529#100—618no—
530C24—1221no—
531C24—1221no—
532C24—1222no—
533C24—1224no—
534C24—4884no—
535C24—2441no—
536C24—2441no—
537C24—2442no—
538C24#1175822611yescharacteristic
539#41—618no—
540#41—614no—
541#41—614no—
542#41—1224no—
543#41—1222no—
544#41—1224no—
545#41—1222no—
546#41—1224no—
547#41—1224no—
548#41—1224no—
549#41—1224no—
550#41—1224no—
551#41—1224no—
552#41—1224no—
553#41—2442no—
554#41—2442no—
555#41—2442no—
556#41—2442no—
557C2×Q8—612no—
558C2×Q8—614no—
559C2×Q8—612no—
560C2×Q8—1221no—
561C2×Q8—1222no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8—1221no—
567C2×D4—612no—
568C2×D4—614no—
569C2×D4—612no—
570C2×D4—614no—
571C2×D4—1224no—
572C2×D4—1222no—
573C2×D4—1224no—
574C2×D4—1222no—
575C2×D4—1224no—
576C2×D4—1224no—
577C2×D4—1222no—
578C2×D4—1221no—
579C2×D4—1224no—
580C2×D4—1222no—
581C2×D4—1221no—
582C2×D4—1221no—
583C2×D4—1221no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1224no—
587C2×D4—1224no—
588C2×D4—1224no—
589C2×D4—1222no—
590C2×D4—1221no—
591C2×D4—1222no—
592C2×D4—1221no—
593C2×D4—2442no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2442no—
597C2×D4—2442no—
598C2×D4—2442no—
599C2×D4—2442no—
600C2×D4—2442no—
601C2×D4—2441no—
602C2×D4—2441no—
603C22×C4—1221no—
604C22×C4—1222no—
605C22×C4—1224no—
606C22×C4—1224no—
607C22×C4—1222no—
608C22×C4—1221no—
609C22×C4—1224no—
610C22×C4—2442no—
611C22×C4—2441no—
612C22×C4—2441no—
613C22×C4C2×D24411yescharacteristic
614C22×C4C2×D24411yescharacteristic
615C22×C4C2×D24412yes—
616C22×C4D4×D6111yescharacteristic
617C22×C4D4×D6111yescharacteristic
618C22×C4D4×D6112yes—
619C22×C4#1175822611yescharacteristic
620C22×C4#1175822612yes—
621C22×C4C23×D6111yescharacteristic
622C22×C4C23×D6112yes—
623Q16—1228no—
624SD16—1228no—
625SD16—12216no—
626SD16—1228no—
627SD16—12216no—
628D8—12216no—
629D8—1228no—
630D8—12216no—
631M16—24no—
632M16—22no—
633M16—24no—
634M16—22no—
635M16—614no—
636M16—1224no—
637M16—1222no—
638M16—12216no—
639M16C2×D24418yes—
640M16C2×D24418yes—
641M16C23×D6114yes—
642M16C23×D6114yes—
643C2×C8—24no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—24no—
647C2×C8—1222no—
648C2×C8—1224no—
649C2×C8—12216no—
650C2×C8C2×D24414yes—
651C2×C8C2×D24414yes—
652C2×C8C23×D6114yes—
653C23—42no—
654C23—1224no—
655C23—1222no—
656C23—1222no—
657C23—1224no—
658C23—4882no—
659C23—4884no—
660C23—4884no—
661C23—4884no—
662C23—4882no—
663C23—4888no—
664C23—4888no—
665C23—2441no—
666C23—2444no—
667C23—2442no—
668C23—2444no—
669C23—2441no—
670C23—2442no—
671C23#1451975211yescharacteristic
672C23#1451975211yescharacteristic
673C23#1451975212yes—
674C23C2×#1175822611yescharacteristic
675C23C2×#1175822612yes—
676Q8—614no—
677Q8—1224no—
678Q8—1222no—
679Q8—1222no—
680Q8—1222no—
681Q8—2441no—
682Q8—2441no—
683D4—614no—
684D4—1224no—
685D4—1228no—
686D4—1224no—
687D4—1224no—
688D4—1222no—
689D4—1224no—
690D4—1222no—
691D4—1222no—
692D4—1224no—
693D4—2444no—
694D4—2444no—
695D4—2444no—
696D4—2442no—
697D4—2444no—
698D4—2442no—
699D4—2441no—
700D4—2441no—
701C2×C4—1224no—
702C2×C4—1222no—
703C2×C4—1228no—
704C2×C4—1224no—
705C2×C4—1224no—
706C2×C4—1222no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2444no—
710C2×C4—2444no—
711C2×C4#1451975212yes—
712C2×C4#1451975212yes—
713C2×C4#1451975212yes—
714C2×C4#1451975212yes—
715C2×C4#1451975212yes—
716C2×C4#1451975211yescharacteristic
717C2×C4#1451975211yescharacteristic
718C2×C4C2×D4×D6112yes—
719C2×C4C2×D4×D6112yes—
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C2×D4×D6111yescharacteristic
722C2×C4C22×D24412yes—
723C2×C4C22×D24411yescharacteristic
724C2×C4C22×D24412yes—
725C2×C4C22×D24411yescharacteristic
726C2×C4C2×#1175822612yes—
727C2×C4C2×#1175822611yescharacteristic
728C2×C4C24×D6111yescharacteristic
729C8—24no—
730C8—24no—
731C8—1224no—
732C8C22×D24418yes—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—42no—
737C22—42no—
738C22—1224no—
739C22—4882no—
740C22—4884no—
741C22—4884no—
742C22—4888no—
743C22—4888no—
744C22—4882no—
745C22—4884no—
746C22—4884no—
747C22—4882no—
748C22—2442no—
749C22—2444no—
750C22—2444no—
751C22C2×#1451975212yes—
752C22C2×#1451975211yescharacteristic
753C22C2×#1451975212yes—
754C22C2×#1451975211yescharacteristic
755C22C22×#1175822611yescharacteristic
756C4—1224no—
757C4—2442no—
758C4C2×#1451975212yes—
759C4C2×#1451975211yescharacteristic
760C4C2×#1451975212yes—
761C4C2×#1451975211yescharacteristic
762C4C22×D4×D6111yescharacteristic
763C4C23×D24411yescharacteristic
764C2—21no—
765C2—22no—
766C2—21no—
767C2—22no—
768C2—4884no—
769C2—4882no—
770C2—2444no—
771C2#2145554812yesdirect product factor
772C2C22×#1451975211yescharacteristic
subgroupG/H
centerC22C2×#14519752
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#430C2
socleC22×C61C2×#121
hypercenterC2×#430D61
hypocenterC61C2×#3068
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
1. C2×#16840562C2semidirect
2. C22×#14519805C2semidirect
3. C22×#14519805C2semidirect
4. C2×#16840528C2semidirect
5. #21455548C2direct (N × H)
6. C2×#16840033C2semidirect
7. C2×#16840026C2semidirect
8. C2×#16839744C2semidirect
9. C22×#14519693C2semidirect
10. C2×C61×#430C2semidirect
15. #16840562C22semidirect
17. C2×#14519810C22semidirect
25. C2×#14519805C22semidirect
26. C2×#14519805C22semidirect
27. C2×#14519805C22semidirect
30. C22×#11758190C22semidirect
32. C22×D488C22semidirect
34. #16840528C22semidirect
36. C2×#14519783C22semidirect
39. #16840033C22semidirect
40. #16840026C22semidirect
41. #16839744C22semidirect
42. C2×#14519695C22semidirect
43. C2×#14519693C22semidirect
44. C2×#14519693C22semidirect
45. C2×#14519693C22semidirect
49. C61×#430C22semidirect
50. C2×#108×C61C22semidirect
88. #14519810C23semidirect
96. #14519805C23semidirect
105. C2×#11758190C23semidirect
111. C2×D488C23semidirect
114. #14519783C23semidirect
123. #14519695C23semidirect
124. #14519693C23semidirect
125. #14519693C23semidirect
142. #108×C61C23semidirect
385. C2×#430D61semidirect
392. C2×C61#3068semidirect
430. #430C2×D61semidirect
431. C2×#108C2×D61semidirect
437. C61C2×#3068semidirect
526. #108C22×D61semidirect
771. C2#21455548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405622
C22×#145198052
C2×#168405282
#214555482
C2×#168400332
C2×#168400262
C2×#168397442
C22×#145196932
C2×C61×#4302
C2×#306861