Finite Group Databasebeta

← C2×#21455439 #30547160

Subgroups — C2×#21455439 #30547160

Order 15616.

3242 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519805C211yesmaximal, characteristic, complemented
2C22×M16×D61C211yesmaximal, characteristic, complemented
3C2×#16840274C211yesmaximal, characteristic, complemented
4C22×#14519752C211yesmaximal, characteristic, complemented
5#21455439C2116yesmaximal, direct product factor
6C2×#16840016C212yesmaximal, complemented
7C2×#16840009C212yesmaximal, complemented
8C2×#16839999C212yesmaximal, complemented
9C2×#16839992C212yesmaximal, complemented
10C2×#16839761C211yesmaximal, characteristic, complemented
11C2×#16839766C211yesmaximal, characteristic, complemented
12C2×C61×#428C211yesmaximal, characteristic, complemented
13C22×#11758222C2211yescharacteristic
14C23×D244—21no—
15C23×D244C2211yescharacteristic
16C23×C4×D61C2211yescharacteristic
17C2×#14519805—28no—
18C2×#14519805C2218yescomplemented
19C22×#11758190C2212yescomplemented
20C22×D488C2212yescomplemented
21C22×#11758194C2211yescharacteristic
22C22×#11758189C2212yescomplemented
23C2×M16×D61—28no—
24C2×M16×D61C2218yescomplemented
25C22×C8×D61C2212yescomplemented
26#16840274—24no—
27#16840274C2218yescomplemented
28C2×#14519761—21no—
29C2×#14519757C2211yescharacteristic, complemented
30C2×#14519757C2211yescharacteristic, complemented
31C2×#14519752—21no—
32C2×#14519752—21no—
33C2×#14519752—24no—
34C2×#14519752C2212yes—
35C2×#14519752C2212yes—
36C2×#14519752C2218yescomplemented
37C2×#14519752C2211yescharacteristic, complemented
38C2×#14519752C2211yescharacteristic, complemented
39C2×#14519747—21no—
40C2×C4×D244—21no—
41C2×C4×D244—21no—
42C22×#11758198—21no—
43#16840016C22116yescomplemented
44#16840009C22116yescomplemented
45#16839999C22116yescomplemented
46#16839992C22116yescomplemented
47#16839766C2218yescomplemented
48#16839761C2218yescomplemented
49C2×#14519700C2212yescomplemented
50C2×#14519697C2212yescomplemented
51C2×#14519697C2212yescomplemented
52C2×#14519697C2212yescomplemented
53C22×M16×C61C2211yescharacteristic
54C2×#117×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C61×#428C2218yescomplemented
57C2×#107×C61C2212yescomplemented
58C2×#106×C61C2212yescomplemented
59C24×D61—21no—
60C24×D61D411yescharacteristic
61C2×#11758222—22no—
62C2×#11758222—24no—
63C2×#11758222—24no—
64C2×#11758222C2314yes—
65C22×Dic122C2311yescharacteristic
66C22×D244—24no—
67C22×D244—24no—
68C22×D244—21no—
69C22×D244—21no—
70C22×D244—22no—
71C22×D244—22no—
72C22×D244—28no—
73C22×D244—21no—
74C22×D244—22no—
75C22×D244—48no—
76C22×D244C2312yes—
77C22×D244C2311yescharacteristic
78C22×D244C2314yes—
79C22×C22⋊D61—21no—
80C23×Dic61D411yescharacteristic
81C22×C4×D61—24no—
82C22×C4×D61—24no—
83C22×C4×D61—21no—
84C22×C4×D61D411yescharacteristic
85C22×C4×D61D411yescharacteristic
86C22×C4×D61D414yes—
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C22×C4×D61C2314yes—
90#14519805—232no—
91C2×#11758190—28no—
92C2×#11758190C2318yescomplemented
93C2×D488—28no—
94C2×D488C2318yescomplemented
95C2×#11758194—24no—
96C2×#11758194C2314yes—
97C2×#11758189—28no—
98C2×#11758189C2318yescomplemented
99M16×D61—232no—
100C22×#92418C2312yes—
101C2×C8×D61—28no—
102C2×C8×D61C2318yescomplemented
103#14519761—28no—
104#14519757—22no—
105#14519757—22no—
106#14519757C2314yescomplemented
107#14519757C2314yescomplemented
108#14519752—24no—
109#14519752—24no—
110#14519752—28no—
111#14519752—28no—
112#14519752—22no—
113#14519752—22no—
114#14519752C2318yes—
115#14519752C2318yes—
116#14519752C2314yescomplemented
117#14519752C2314yescomplemented
118#14519747—28no—
119C4×D244—28no—
120C4×D244—28no—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198—22no—
126C2×#11758198—22no—
127C2×#11758198—28no—
128C2×#11758198—21no—
129C2×#11758198—21no—
130#14519700C2318yescomplemented
131#14519697C2318yescomplemented
132#14519697C2318yescomplemented
133#14519697C2318yescomplemented
134C23×C4×C61—21no—
135C23×C4×C61C2311yescharacteristic
136C2×M16×C61D418yescomplemented
137C2×M16×C61C2314yes—
138C22×C8×C61C2312yes—
139#117×C61—22no—
140#117×C61C2314yes—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61—22no—
143C2×C4⋊C4×C61C2312yes—
144C2×C4⋊C4×C61C2314yes—
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—21no—
148C2×C42×C61—21no—
149#107×C61C2318yescomplemented
150#106×C61C2318yescomplemented
151C24×C61C2×D411yescharacteristic
152C23×D61—24no—
153C23×D61—24no—
154C23×D61—21no—
155C23×D61—24no—
156C23×D61—22no—
157C23×D61—42no—
158C23×D61—44no—
159C23×D61—44no—
160C23×D61—44no—
161C23×D61C2×D411yescharacteristic
162C23×D61C2×D414yes—
163C23×D61C2×D411yescharacteristic
164C22×C4×C61—24no—
165C22×C4×C61—22no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—44no—
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61C2×D412yes—
171C22×C4×C61C2×D414yes—
172C22×C4×C61#4114yes—
173C22×C4×C61C2411yescharacteristic
174C22×C4×C61C2412yes—
175C2×C22⋊D61—24no—
176C2×C22⋊D61—44no—
177C22×Dic61—24no—
178C22×Dic61—21no—
179C22×Dic61C2×D411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D414yes—
182#11758222—28no—
183#11758222—28no—
184#11758222—48no—
185C2×D244—24no—
186C2×D244—28no—
187C2×D244—22no—
188C2×D244—24no—
189C2×D244—28no—
190C2×D244—22no—
191C2×D244—28no—
192C2×D244—28no—
193C2×D244—24no—
194C2×D244—24no—
195C2×D244—24no—
196C2×D244—22no—
197C2×D244—21no—
198C2×D244—44no—
199C2×D244—48no—
200C2×D244—432no—
201C2×D244—44no—
202C2×D244—48no—
203C2×D244—44no—
204C2×D244—48no—
205C2×D244C2414yes—
206C2×D244C2412yes—
207C2×C4×D61—24no—
208C2×C4×D61—24no—
209C2×C4×D61—216no—
210C2×C4×D61—22no—
211C2×C4×D61—28no—
212C2×C4×D61—22no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—28no—
216C2×C4×D61—24no—
217C2×C4×D61—44no—
218C2×C4×D61C2×D414yes—
219C2×C4×D61C2×D414yes—
220C2×C4×D61C2×D412yes—
221C2×C4×D61C2×D412yes—
222C2×C4×D61C2412yes—
223C2×C4×D61C2412yes—
224C2×Dic122—22no—
225C2×Dic122—22no—
226C2×Dic122—21no—
227C2×Dic122C2412yes—
228M16×C61C2×D4116yescomplemented
229C2×C8×C61C2×D418yescomplemented
230C2×C8×C61C2414yes—
231C4⋊C4×C61—24no—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61C2412yes—
236C4⋊C4×C61C2414yes—
237C4⋊C4×C61C2412yes—
238C22⋊C4×C61—24no—
239C42×C61—24no—
240#11758198—24no—
241#11758198—24no—
242#11758198—28no—
243#11758198—28no—
244#11758198—24no—
245#11758198—24no—
246C4⋊Dic61—24no—
247C4⋊Dic61—24no—
248#11758194—28no—
249C2×#92418—24no—
250C2×#92418C2414yes—
251D488—216no—
252#11758190—216no—
253#11758189—216no—
254C8×D61—216no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61#12114yes—
258C23×C61C22×D412yes—
259C23×C61C22×D411yescharacteristic
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—28no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—28no—
267C22×D61—22no—
268C22×D61—24no—
269C22×D61—44no—
270C22×D61—416no—
271C22×D61—48no—
272C22×D61—48no—
273C22×D61—42no—
274C22×D61—48no—
275C22×D61—44no—
276C22×D61—44no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—44no—
280C22×D61—816no—
281C22×D61AGL(1,ℤ/8)14yescomplemented
282C22×D61C22×D412yes—
283C22×D61C22×D412yes—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—24no—
287C2×C4×C61—48no—
288C2×C4×C61—44no—
289C2×C4×C61—42no—
290C2×C4×C61—42no—
291C2×C4×C61#12114yes—
292C2×C4×C61#12118yes—
293C2×C4×C61C22×D412yes—
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C22×D412yes—
296C2×C4×C61C22×D414yes—
297C2×C4×C61C2×#4112yes—
298C2×C4×C61C2×#4114yes—
299C2×C4×C61C2511yescharacteristic
300C22⋊D61—48no—
301C2×Dic61—28no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—42no—
306C2×Dic61C22×D412yes—
307C2×Dic61C22×D412yes—
308D244—24no—
309D244—22no—
310D244—24no—
311D244—22no—
312D244—48no—
313D244—416no—
314D244—48no—
315D244—416no—
316D244—44no—
317D244—48no—
318D244—42no—
319C4×D61—24no—
320C4×D61—24no—
321C4×D61—28no—
322C4×D61—28no—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—48no—
328Dic122—22no—
329Dic122—22no—
330Dic122—42no—
331C8×C61C22×D418yescomplemented
332#92418—24no—
333C2×#3055—611nomaximal, Sylow
334C22×C61—28no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61C2×#12114yes—
338C22×C61C2×#12112yes—
339C22×C61C2×AGL(1,ℤ/8)12yes—
340C22×C61#57512yes—
341C22×C61C23×D411yescharacteristic
342C2×D61—22no—
343C2×D61—28no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—416no—
349C2×D61—44no—
350C2×D61—42no—
351C2×D61—44no—
352C2×D61—44no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—44no—
356C2×D61—816no—
357C2×D61—84no—
358C2×D61—88no—
359C2×D61C2×AGL(1,ℤ/8)14yescomplemented
360C4×C61—44no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61C2×#12112yes—
364C4×C61C2×#12114yes—
365C4×C61C23×D411yescharacteristic
366C4×C61C22×#4111yescharacteristic
367Dic61—22no—
368Dic61—22no—
369Dic61—42no—
370C22×AGL(1,ℤ/8)—611no—
371C23×M16—611no—
372C2×#525—611no—
373C22×#121—611no—
374#3055—6116no—
375C2×#469—612no—
376C2×#468—612no—
377C2×#466—612no—
378C2×#465—612no—
379C2×#428D6111yescharacteristic, complemented
380C2×#417—611no—
381C2×#418—611no—
382C2×C61—24no—
383C2×C61#305514yescomplemented
384C2×C61C22×#12111yescharacteristic
385C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
386C2×C61C2×#57511yescharacteristic
387D61—24no—
388D61—42no—
389D61—82no—
390D61—84no—
391C22×#41—611no—
392C23×D4—611no—
393C23×D4—1221no—
394C24×C4—611no—
395C2×AGL(1,ℤ/8)—618no—
396C2×AGL(1,ℤ/8)—1228no—
397C22×SD16—612no—
398C22×D8—612no—
399C22×M16—611no—
400C22×M16—618no—
401C22×M16—612no—
402C22×M16—1228no—
403C22×M16C2×D6111yescharacteristic
404C23×C8—612no—
405#525—618no—
406#525—1224no—
407C2×#123—1221no—
408C2×C22⋊Q8—611no—
409C2×C22⋊Q8—611no—
410C2×#121—612no—
411C2×#121—612no—
412C2×#121—618no—
413C2×#121—611no—
414C2×#121—611no—
415C2×#121—1221no—
416C2×#121—1221no—
417C2×#121—1224no—
418C2×#120—1221no—
419C2×C4×D4—1221no—
420C2×C4×D4—1221no—
421C2×#117C2×D6111yescharacteristic
422C22×C4⋊C4C2×D6111yescharacteristic
423C22×C22⋊C4—1221no—
424#469—6116no—
425#468—6116no—
426#466—6116no—
427#465—6116no—
428#428C2×D6118yescomplemented
429C2×#107C2×D6112yescomplemented
430C2×#106C2×D6112yescomplemented
431#418—618no—
432#417—618no—
433C2×#103—612no—
434C2×#102—612no—
435C2×#102—612no—
436C2×#102—612no—
437C61C2×#305511yescharacteristic, complemented, Sylow
438C25—611no—
439C25—1221no—
440C2×#41—614no—
441C2×#41—1222no—
442C2×#41—1224no—
443C2×#41—1224no—
444C22×Q8—611no—
445C22×D4—611no—
446C22×D4—612no—
447C22×D4—614no—
448C22×D4—1221no—
449C22×D4—1221no—
450C22×D4—1228no—
451C22×D4—1222no—
452C22×D4—1222no—
453C22×D4—1221no—
454C22×D4—1224no—
455C22×D4—1222no—
456C22×D4—1221no—
457C22×D4—1224no—
458C22×D4—2448no—
459C23×C4—21no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—614no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—614no—
467C23×C4—1224no—
468C23×C4—1224no—
469C23×C4—1221no—
470C23×C4C22×D6111yescharacteristic
471AGL(1,ℤ/8)—12232no—
472C2×SD16—618no—
473C2×SD16—1228no—
474C2×D8—618no—
475C2×D8—1228no—
476C2×M16—614no—
477C2×M16—618no—
478C2×M16—1224no—
479C2×M16—12232no—
480C2×M16—1228no—
481C2×M16D24418yescomplemented
482C2×M16C22×D6114yes—
483C22×C8—612no—
484C22×C8—618no—
485C22×C8—1228no—
486C22×C8C22×D6112yes—
487#123—1228no—
488C22⋊Q8—614no—
489C22⋊Q8—614no—
490C22⋊Q8—1222no—
491C22⋊Q8—1222no—
492#121—618no—
493#121—618no—
494#121—614no—
495#121—614no—
496#121—1228no—
497#121—1228no—
498#121—1224no—
499#121—1224no—
500#121—1222no—
501#121—1222no—
502#120—1228no—
503C4×D4—1228no—
504C4×D4—1228no—
505#117—22no—
506#117C22×D6114yes—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4C22×D6112yes—
512C2×C4⋊C4C22×D6114yes—
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—1228no—
517C2×C22⋊C4—1222no—
518C2×C22⋊C4—1222no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4—1221no—
523C2×C42—21no—
524#107C22×D6118yescomplemented
525#106C22×D6118yescomplemented
526#103—618no—
527#102—618no—
528#102—618no—
529#102—618no—
530C24—611no—
531C24—611no—
532C24—614no—
533C24—1224no—
534C24—1224no—
535C24—1224no—
536C24—1221no—
537C24—1222no—
538C24—2442no—
539C24—2444no—
540C24—2444no—
541C24—2444no—
542C24D4×D6111yescharacteristic
543#41—1228no—
544#41—1228no—
545#41—2448no—
546C2×Q8—612no—
547C2×Q8—1221no—
548C2×Q8—1222no—
549C2×Q8—1222no—
550C2×D4—612no—
551C2×D4—614no—
552C2×D4—1224no—
553C2×D4—1224no—
554C2×D4—1228no—
555C2×D4—1228no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—1222no—
559C2×D4—1221no—
560C2×D4—1222no—
561C2×D4—1224no—
562C2×D4—1228no—
563C2×D4—1224no—
564C2×D4—1228no—
565C2×D4—1222no—
566C2×D4—2448no—
567C2×D4—2444no—
568C2×D4—24432no—
569C2×D4—2448no—
570C2×D4—2444no—
571C2×D4—2444no—
572C2×D4—2444no—
573C2×D4—2448no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—44no—
579C22×C4—614no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—614no—
583C22×C4—614no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—1224no—
589C22×C4—1222no—
590C22×C4—1228no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1228no—
595C22×C4—1224no—
596C22×C4—1224no—
597C22×C4—12216no—
598C22×C4—1221no—
599C22×C4—1224no—
600C22×C4—2444no—
601C22×C4C2×D24414yes—
602C22×C4D4×D6112yes—
603C22×C4D4×D6111yescharacteristic
604C22×C4#1175822614yes—
605C22×C4C23×D6112yes—
606C22×C4C23×D6111yescharacteristic
607SD16—12216no—
608D8—12216no—
609M16—1228no—
610M16—12216no—
611M16C2×D244116yescomplemented
612C2×C8—614no—
613C2×C8—1224no—
614C2×C8—12216no—
615C2×C8C2×D24418yescomplemented
616C2×C8C23×D6114yes—
617C4⋊C4—24no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4C23×D6112yes—
624C4⋊C4C23×D6112yes—
625C4⋊C4C23×D6114yes—
626C22⋊C4—24no—
627C22⋊C4—1228no—
628C22⋊C4—1228no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C22⋊C4—1224no—
633C42—24no—
634C23—22no—
635C23—22no—
636C23—614no—
637C23—612no—
638C23—612no—
639C23—1228no—
640C23—1222no—
641C23—1222no—
642C23—1228no—
643C23—1222no—
644C23—1222no—
645C23—1222no—
646C23—1222no—
647C23—1224no—
648C23—48816no—
649C23—2444no—
650C23—24416no—
651C23—2448no—
652C23—2448no—
653C23—2442no—
654C23—2448no—
655C23—2444no—
656C23—2444no—
657C23—2442no—
658C23—2442no—
659C23—2444no—
660C23#1451975214yes—
661C23C2×D4×D6112yes—
662C23C2×D4×D6111yescharacteristic
663Q8—1222no—
664Q8—1222no—
665Q8—2442no—
666D4—1222no—
667D4—1224no—
668D4—1224no—
669D4—1222no—
670D4—2448no—
671D4—24416no—
672D4—2448no—
673D4—24416no—
674D4—2448no—
675D4—2448no—
676D4—2444no—
677D4—2442no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—48no—
682C2×C4—44no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—1228no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1228no—
691C2×C4—1228no—
692C2×C4—1224no—
693C2×C4—1224no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—2442no—
700C2×C4—2448no—
701C2×C4#1451975214yes—
702C2×C4#1451975218yes—
703C2×C4C2×D4×D6112yes—
704C2×C4C2×D4×D6111yescharacteristic
705C2×C4C22×D24412yes—
706C2×C4C22×D24414yes—
707C2×C4C2×#1175822612yes—
708C2×C4C2×#1175822614yes—
709C2×C4C24×D6111yescharacteristic
710C8—1224no—
711C8C22×D24418yescomplemented
712C22—22no—
713C22—28no—
714C22—22no—
715C22—614no—
716C22—1228no—
717C22—1222no—
718C22—1222no—
719C22—1222no—
720C22—1222no—
721C22—1222no—
722C22—48816no—
723C22—4888no—
724C22—4884no—
725C22—24416no—
726C22—2444no—
727C22—2442no—
728C22—2442no—
729C22—2444no—
730C22—2442no—
731C22—2444no—
732C22—2444no—
733C22C2×#1451975214yes—
734C22C2×#1451975212yes—
735C22AGL(1,ℤ/8)×D6112yes—
736C22#1684056112yes—
737C22C22×D4×D6111yescharacteristic
738C4—44no—
739C4—42no—
740C4—42no—
741C4—1222no—
742C4—1222no—
743C4—2442no—
744C4C2×#1451975214yes—
745C4C2×#1451975212yes—
746C4C23×D24411yescharacteristic
747C4C22×#1175822611yescharacteristic
748C2—24no—
749C2—1224no—
750C2—4884no—
751C2—4882no—
752C2—2442no—
753C2#2145543914yesdirect product factor
754C2C22×#1451975211yescharacteristic
755C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
756C2C2×#1684056111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#428C2
socleC23×C61C22×D4
hypercenterC2×#428D61
hypocenterC61C2×#3055
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C22×#14519805C2semidirect
2. C22×M16×D61C2semidirect
3. C2×#16840274C2semidirect
4. C22×#14519752C2semidirect
5. #21455439C2direct (N × H)
6. C2×#16840016C2semidirect
7. C2×#16840009C2semidirect
8. C2×#16839999C2semidirect
9. C2×#16839992C2semidirect
10. C2×#16839761C2semidirect
11. C2×#16839766C2semidirect
12. C2×C61×#428C2semidirect
18. C2×#14519805C22semidirect
19. C22×#11758190C22semidirect
20. C22×D488C22semidirect
22. C22×#11758189C22semidirect
24. C2×M16×D61C22semidirect
25. C22×C8×D61C22semidirect
27. #16840274C22semidirect
29. C2×#14519757C22semidirect
30. C2×#14519757C22semidirect
36. C2×#14519752C22semidirect
37. C2×#14519752C22semidirect
38. C2×#14519752C22semidirect
43. #16840016C22semidirect
44. #16840009C22semidirect
45. #16839999C22semidirect
46. #16839992C22semidirect
47. #16839766C22semidirect
48. #16839761C22semidirect
49. C2×#14519700C22semidirect
50. C2×#14519697C22semidirect
51. C2×#14519697C22semidirect
52. C2×#14519697C22semidirect
56. C61×#428C22semidirect
57. C2×#107×C61C22semidirect
58. C2×#106×C61C22semidirect
92. C2×#11758190C23semidirect
94. C2×D488C23semidirect
98. C2×#11758189C23semidirect
102. C2×C8×D61C23semidirect
106. #14519757C23semidirect
107. #14519757C23semidirect
116. #14519752C23semidirect
117. #14519752C23semidirect
130. #14519700C23semidirect
131. #14519697C23semidirect
132. #14519697C23semidirect
133. #14519697C23semidirect
136. C2×M16×C61D4semidirect
149. #107×C61C23semidirect
150. #106×C61C23semidirect
228. M16×C61C2×D4semidirect
229. C2×C8×C61C2×D4semidirect
281. C22×D61AGL(1,ℤ/8)semidirect
331. C8×C61C22×D4semidirect
359. C2×D61C2×AGL(1,ℤ/8)semidirect
379. C2×#428D61semidirect
383. C2×C61#3055semidirect
428. #428C2×D61semidirect
429. C2×#107C2×D61semidirect
430. C2×#106C2×D61semidirect
437. C61C2×#3055semidirect
481. C2×M16D244semidirect
524. #107C22×D61semidirect
525. #106C22×D61semidirect
611. M16C2×D244semidirect
615. C2×C8C2×D244semidirect
711. C8C22×D244semidirect
753. C2#21455439direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198052
C22×M16×D612
C2×#168402742
C22×#145197522
#214554392
C2×#168400162
C2×#168400092
C2×#168399992
C2×#168399922
C2×#168397612
C2×#168397662
C2×C61×#4282
C2×#305561