Finite Group Databasebeta

← C2×#21455547 #30547417

Subgroups — C2×#21455547 #30547417

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×#16840560C211yesmaximal, characteristic, complemented
2C22×#14519805C211yesmaximal, characteristic, complemented
3C22×#14519802C211yesmaximal, characteristic, complemented
4#21455547C2116yesmaximal, direct product factor
5C2×#16840032C214yesmaximal, complemented
6C2×#16840025C214yesmaximal, complemented
7C2×#16839811C211yesmaximal, characteristic, complemented
8C2×#16839744C211yesmaximal, characteristic, complemented
9C22×#14519693C211yesmaximal, characteristic, complemented
10C2×C61×#568C211yesmaximal, characteristic, complemented
11C22×#11758222C2211yescharacteristic
12C23×D244C2211yescharacteristic
13#16840560—24no—
14#16840560C2218yescomplemented
15C2×#14519808—21no—
16C2×#14519807C2212yescomplemented
17C2×#14519805—22no—
18C2×#14519805—22no—
19C2×#14519805—24no—
20C2×#14519805C2218yescomplemented
21C2×#14519803—21no—
22C2×#14519802—22no—
23C2×#14519802—24no—
24C2×#14519802C2214yes—
25C2×#14519802C2218yescomplemented
26C2×#14519802C2212yescomplemented
27C2×#14519797—22no—
28C22×#11758190C2212yescomplemented
29C22×#11758201—21no—
30C22×D488C2212yescomplemented
31C22×#11758199—21no—
32C22×#11758194C2211yescharacteristic
33C22×#11758194C2211yescharacteristic
34#16840032C22132yescomplemented
35#16840025C22132yescomplemented
36#16839811C2218yescomplemented
37C2×#14519713C2214yescomplemented
38#16839744C2218yescomplemented
39C2×#14519695C2212yescomplemented
40C2×#14519693C2214yescomplemented
41C2×#14519693C2212yescomplemented
42C2×#14519693C2218yescomplemented
43C22×#41×C61C2211yescharacteristic
44C61×#568—24no—
45C61×#568C2218yescomplemented
46C2×#131×C61—22no—
47C2×#131×C61C2214yescomplemented
48C22×M16×C61—22no—
49C22×M16×C61C2211yescharacteristic
50C22×M16×C61C2211yescharacteristic
51C24×D61—21no—
52C2×#11758222—22no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—22no—
58C2×#11758222—22no—
59C2×#11758222C2314yes—
60C22×Dic122C2311yescharacteristic
61C22×D244—21no—
62C22×D244—21no—
63C22×D244—22no—
64C22×D244—21no—
65C22×D244—21no—
66C22×D244—22no—
67C22×D244—21no—
68C22×D244—22no—
69C22×D244C2311yescharacteristic
70C22×D244C2312yes—
71C22×D244C2314yes—
72C22×C22⋊D61—21no—
73C22×C4×D61—21no—
74#14519808—28no—
75#14519807—24no—
76#14519807C2318yescomplemented
77#14519805—216no—
78#14519805—216no—
79#14519803—28no—
80#14519802—28no—
81#14519802—216no—
82#14519802—24no—
83#14519802C23116yes—
84#14519802C2318yescomplemented
85#14519797—216no—
86C2×#11758202—22no—
87C2×#11758190—24no—
88C2×#11758190—24no—
89C2×#11758190C2318yescomplemented
90C2×#11758200—22no—
91C2×#11758201—24no—
92C2×#11758201—28no—
93C2×#11758201—22no—
94C2×D488—24no—
95C2×D488—24no—
96C2×D488C2318yescomplemented
97C2×#11758199—24no—
98C2×#11758199—28no—
99C2×#11758199—22no—
100C2×#11758194—21no—
101C2×#11758194—22no—
102C2×#11758194—21no—
103C2×#11758194—22no—
104C2×#11758194C2312yes—
105C2×#11758194C2314yes—
106C2×#11758194C2312yes—
107C2×#11758194C2314yes—
108C22×#92418—21no—
109C22×#92418—21no—
110#14519713C23116yescomplemented
111#14519695C2318yescomplemented
112#14519693C23116yescomplemented
113#14519693C2318yescomplemented
114C2×#41×C61—21no—
115C2×#41×C61—22no—
116C2×#41×C61—21no—
117C2×#41×C61—22no—
118C2×#41×C61D412yes—
119C2×#41×C61D414yes—
120C2×#41×C61C2312yes—
121C2×#41×C61C2314yes—
122C22×Q8×C61D411yescharacteristic
123C22×D4×C61—21no—
124C22×D4×C61D411yescharacteristic
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127#131×C61—216no—
128#131×C61—28no—
129#131×C61C23116yescomplemented
130C2×M16×C61—21no—
131C2×M16×C61—22no—
132C2×M16×C61—216no—
133C2×M16×C61—24no—
134C2×M16×C61D412yes—
135C2×M16×C61D412yes—
136C2×M16×C61D414yes—
137C2×M16×C61C2312yes—
138C2×M16×C61C2314yes—
139C2×M16×C61C2314yes—
140C22×C8×C61—21no—
141C22×C8×C61—24no—
142C22×C8×C61C2312yes—
143C24×C61—21no—
144C24×C61#4111yescharacteristic
145C23×D61—21no—
146C23×D61—22no—
147C23×D61—24no—
148C23×D61—41no—
149C23×D61—41no—
150C23×D61—42no—
151C23×D61—84no—
152#41×C61—24no—
153#41×C61—24no—
154#41×C61—24no—
155#41×C61—24no—
156#41×C61—22no—
157#41×C61—22no—
158#41×C61—24no—
159#41×C61C2×D418yes—
160#41×C61C2×D414yes—
161#41×C61C2414yes—
162C2×Q8×C61—21no—
163C2×Q8×C61—22no—
164C2×Q8×C61C2×D414yes—
165C2×Q8×C61C2×D412yes—
166C2×D4×C61—22no—
167C2×D4×C61—24no—
168C2×D4×C61—22no—
169C2×D4×C61—24no—
170C2×D4×C61—21no—
171C2×D4×C61—22no—
172C2×D4×C61C2×D412yes—
173C2×D4×C61C2×D414yes—
174C22×C4×C61—21no—
175C22×C4×C61—22no—
176C22×C4×C61—24no—
177C22×C4×C61—22no—
178C22×C4×C61—24no—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D412yes—
185C22×C4×C61#4111yescharacteristic
186C22×C4×C61#4112yes—
187C22×C4×C61C2411yescharacteristic
188C22×C4×C61C2412yes—
189C2×C22⋊D61—24no—
190C2×C22⋊D61—41no—
191C2×C22⋊D61—41no—
192C2×C22⋊D61—42no—
193C22×Dic61—21no—
194#11758222—24no—
195#11758222—24no—
196#11758222—24no—
197#11758222—24no—
198#11758222—42no—
199#11758222—42no—
200#11758222—42no—
201#11758222—42no—
202C2×D244—22no—
203C2×D244—24no—
204C2×D244—22no—
205C2×D244—22no—
206C2×D244—24no—
207C2×D244—22no—
208C2×D244—24no—
209C2×D244—24no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—22no—
215C2×D244—24no—
216C2×D244—21no—
217C2×D244—41no—
218C2×D244—41no—
219C2×D244—42no—
220C2×D244—42no—
221C2×D244—42no—
222C2×D244—42no—
223C2×D244—42no—
224C2×D244C2414yes—
225C2×D244C2412yes—
226C2×C4×D61—24no—
227C2×C4×D61—41no—
228C2×C4×D61—41no—
229C2×C4×D61—42no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122C2412yes—
236M16×C61—24no—
237M16×C61—22no—
238M16×C61—216no—
239M16×C61C2×D418yes—
240M16×C61C2×D418yes—
241M16×C61C2414yes—
242C2×C8×C61—22no—
243C2×C8×C61—24no—
244C2×C8×C61—216no—
245C2×C8×C61C2×D414yes—
246C2×C8×C61C2×D414yes—
247C2×C8×C61C2414yes—
248#11758202—28no—
249#11758201—28no—
250#11758201—216no—
251#11758200—28no—
252#11758199—216no—
253#11758199—28no—
254#11758194—24no—
255#11758194—24no—
256#11758194—22no—
257#11758194—22no—
258#11758194C2414yes—
259#11758194C2414yes—
260C2×#92418—22no—
261C2×#92418—24no—
262C2×#92418—22no—
263C2×#92418—24no—
264D488—216no—
265#11758190—216no—
266C23×C61—22no—
267C23×C61—24no—
268C23×C61—42no—
269C23×C61—82no—
270C23×C61#12111yescharacteristic
271C23×C61#12111yescharacteristic
272C23×C61#12112yes—
273C23×C61C2×#4111yescharacteristic
274C23×C61C2×#4112yes—
275C22×D61—22no—
276C22×D61—24no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—44no—
280C22×D61—42no—
281C22×D61—44no—
282C22×D61—42no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—88no—
286C22×D61—82no—
287C22×D61—84no—
288C22×D61—88no—
289Q8×C61—22no—
290Q8×C61—24no—
291Q8×C61C22×D414yes—
292D4×C61—24no—
293D4×C61—28no—
294D4×C61—24no—
295D4×C61—22no—
296D4×C61—24no—
297D4×C61C22×D414yes—
298C2×C4×C61—24no—
299C2×C4×C61—22no—
300C2×C4×C61—24no—
301C2×C4×C61—28no—
302C2×C4×C61—24no—
303C2×C4×C61#12111yescharacteristic
304C2×C4×C61#12111yescharacteristic
305C2×C4×C61#12112yes—
306C2×C4×C61#12112yes—
307C2×C4×C61#12112yes—
308C2×C4×C61#12112yes—
309C2×C4×C61#12112yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×D412yes—
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D412yes—
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C22×D412yes—
316C2×C4×C61C22×D412yes—
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C2×#4111yescharacteristic
319C2×C4×C61C2×#4112yes—
320C2×C4×C61C2511yescharacteristic
321C22⋊D61—44no—
322C22⋊D61—44no—
323C2×Dic61—22no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326D244—24no—
327D244—22no—
328D244—24no—
329D244—22no—
330D244—42no—
331D244—42no—
332D244—44no—
333D244—44no—
334D244—41no—
335D244—41no—
336C4×D61—44no—
337C4×D61—44no—
338Dic122—22no—
339Dic122—22no—
340Dic122—41no—
341Dic122—41no—
342C8×C61—24no—
343C8×C61C22×D418yes—
344#92418—24no—
345#92418—24no—
346C2×#3068—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—24no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—44no—
354C22×C61—84no—
355C22×C61C2×#12111yescharacteristic
356C22×C61C2×#12112yes—
357C22×C61C2×#12112yes—
358C22×C61C2×#12111yescharacteristic
359C22×C61C22×#4111yescharacteristic
360C2×D61—42no—
361C2×D61—44no—
362C2×D61—82no—
363C2×D61—88no—
364C2×D61—84no—
365C2×D61—88no—
366C2×D61—82no—
367C2×D61—84no—
368C2×D61—82no—
369C2×D61—84no—
370C4×C61—24no—
371C4×C61C2×#12111yescharacteristic
372C4×C61C2×#12111yescharacteristic
373C4×C61C2×#12112yes—
374C4×C61C2×#12112yes—
375C4×C61C23×D411yescharacteristic
376C4×C61C23×D411yescharacteristic
377Dic61—42no—
378C2×#575—611no—
379C22×AGL(1,ℤ/8)—611no—
380C22×AGL(1,ℤ/8)—611no—
381C2×#568D6111yescharacteristic, complemented
382#3068—6116no—
383C2×#472—614no—
384C2×#471—614no—
385C2×#430—611no—
386C2×#413—611no—
387C22×#100—611no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—22no—
391C2×C61—22no—
392C2×C61—44no—
393C2×C61#306812yescomplemented
394C2×C61C22×#12111yescharacteristic
395D61—82no—
396D61—84no—
397C22×#41—611no—
398C22×#41C2×D6111yescharacteristic
399C23×D4—611no—
400#575—618no—
401#575—1224no—
402C2×#137—612no—
403C2×#137—1221no—
404C2×AGL(1,ℤ/8)—614no—
405C2×AGL(1,ℤ/8)—612no—
406C2×AGL(1,ℤ/8)—618no—
407C2×AGL(1,ℤ/8)—618no—
408C2×AGL(1,ℤ/8)—1222no—
409C2×AGL(1,ℤ/8)—1224no—
410C2×AGL(1,ℤ/8)—1221no—
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—24no—
420#568C2×D6118yescomplemented
421C2×#131—22no—
422C2×#131C2×D6114yescomplemented
423C22×M16—22no—
424C22×M16—611no—
425C22×M16—611no—
426C22×M16C2×D6111yescharacteristic
427C22×M16C2×D6111yescharacteristic
428#472—6132no—
429#471—6132no—
430#430—618no—
431C2×#108—614no—
432#413—618no—
433C2×#101—612no—
434C2×#100—614no—
435C2×#100—618no—
436C2×#100—612no—
437C61C2×#306811yescharacteristic, complemented, Sylow
438C25—1221no—
439C2×#41—21no—
440C2×#41—22no—
441C2×#41—21no—
442C2×#41—22no—
443C2×#41—614no—
444C2×#41—1222no—
445C2×#41—1221no—
446C2×#41—1221no—
447C2×#41—1222no—
448C2×#41—1221no—
449C2×#41—1221no—
450C2×#41—1222no—
451C2×#41D24412yes—
452C2×#41D24414yes—
453C2×#41C22×D6112yes—
454C2×#41C22×D6114yes—
455C22×Q8—611no—
456C22×Q8D24411yescharacteristic
457C22×D4—21no—
458C22×D4—611no—
459C22×D4—612no—
460C22×D4—614no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4—1221no—
464C22×D4—1222no—
465C22×D4—1221no—
466C22×D4—1222no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1222no—
470C22×D4D24411yescharacteristic
471C23×C4—21no—
472C23×C4—1221no—
473C23×C4C22×D6111yescharacteristic
474#137—618no—
475#137—1224no—
476#137—1228no—
477AGL(1,ℤ/8)—6116no—
478AGL(1,ℤ/8)—618no—
479AGL(1,ℤ/8)—12216no—
480AGL(1,ℤ/8)—1228no—
481AGL(1,ℤ/8)—1224no—
482AGL(1,ℤ/8)—1228no—
483AGL(1,ℤ/8)—12216no—
484AGL(1,ℤ/8)—12216no—
485#135—12216no—
486C2×Q16—1222no—
487C2×SD16—618no—
488C2×SD16—1224no—
489C2×SD16—1228no—
490C2×SD16—1222no—
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—216no—
501#131—28no—
502#131C22×D61116yescomplemented
503C2×M16—21no—
504C2×M16—22no—
505C2×M16—216no—
506C2×M16—24no—
507C2×M16—612no—
508C2×M16—614no—
509C2×M16—612no—
510C2×M16—614no—
511C2×M16—1221no—
512C2×M16—1222no—
513C2×M16—1221no—
514C2×M16—1222no—
515C2×M16C22⋊D6112yes—
516C2×M16C22⋊D6112yes—
517C2×M16C22⋊D6114yes—
518C2×M16C22×D6112yes—
519C2×M16C22×D6114yes—
520C2×M16C22×D6114yes—
521C22×C8—21no—
522C22×C8—24no—
523C22×C8—1221no—
524C22×C8—1221no—
525C22×C8C22×D6112yes—
526#108—6116no—
527#101—618no—
528#100—6116no—
529#100—618no—
530C24—21no—
531C24—1221no—
532C24—1222no—
533C24—1224no—
534C24—4884no—
535C24—2441no—
536C24—2441no—
537C24—2442no—
538C24#1175822211yescharacteristic
539#41—24no—
540#41—22no—
541#41—24no—
542#41—22no—
543#41—24no—
544#41—24no—
545#41—24no—
546#41—1224no—
547#41—1224no—
548#41—1224no—
549#41—1224no—
550#41—2442no—
551#41—2442no—
552#41—2442no—
553#41—2442no—
554#41C2×D24418yes—
555#41C2×D24414yes—
556#41C23×D6114yes—
557C2×Q8—22no—
558C2×Q8—21no—
559C2×Q8—612no—
560C2×Q8—1221no—
561C2×Q8—1221no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8C2×D24412yes—
566C2×Q8C2×D24414yes—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—612no—
574C2×D4—614no—
575C2×D4—1224no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—1224no—
581C2×D4—1224no—
582C2×D4—1224no—
583C2×D4—1222no—
584C2×D4—1221no—
585C2×D4—1224no—
586C2×D4—1222no—
587C2×D4—1221no—
588C2×D4—1224no—
589C2×D4—1222no—
590C2×D4—1221no—
591C2×D4—2442no—
592C2×D4—2441no—
593C2×D4—2441no—
594C2×D4—2442no—
595C2×D4—2442no—
596C2×D4—2442no—
597C2×D4—2442no—
598C2×D4—2442no—
599C2×D4—2441no—
600C2×D4—2441no—
601C2×D4C2×D24412yes—
602C2×D4C2×D24414yes—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—22no—
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×C4#1175822211yescharacteristic
617C22×C4#1175822212yes—
618C22×C4C2×C22⋊D6111yescharacteristic
619C22×C4C2×C22⋊D6111yescharacteristic
620C22×C4C2×C22⋊D6112yes—
621C22×C4C23×D6111yescharacteristic
622C22×C4C23×D6112yes—
623Q16—1228no—
624SD16—12216no—
625SD16—1228no—
626SD16—1228no—
627SD16—12216no—
628D8—12216no—
629D8—1228no—
630D8—12216no—
631M16—24no—
632M16—22no—
633M16—216no—
634M16—614no—
635M16—614no—
636M16—1224no—
637M16—1222no—
638M16—1224no—
639M16—1222no—
640M16C2×C22⋊D6118yes—
641M16C2×C22⋊D6118yes—
642M16C23×D6114yes—
643C2×C8—22no—
644C2×C8—24no—
645C2×C8—216no—
646C2×C8—1224no—
647C2×C8—1222no—
648C2×C8—1222no—
649C2×C8—1224no—
650C2×C8C2×C22⋊D6114yes—
651C2×C8C2×C22⋊D6114yes—
652C2×C8C23×D6114yes—
653C23—22no—
654C23—24no—
655C23—42no—
656C23—82no—
657C23—1222no—
658C23—1224no—
659C23—4882no—
660C23—4884no—
661C23—4884no—
662C23—4884no—
663C23—4888no—
664C23—4888no—
665C23—2441no—
666C23—2444no—
667C23—2442no—
668C23—2444no—
669C23—2441no—
670C23—2442no—
671C23#1451975111yescharacteristic
672C23#1451975111yescharacteristic
673C23#1451975112yes—
674C23C2×#1175822211yescharacteristic
675C23C2×#1175822212yes—
676Q8—24no—
677Q8—22no—
678Q8—1222no—
679Q8—1222no—
680Q8—2441no—
681Q8—2441no—
682Q8C22×D24414yes—
683D4—24no—
684D4—28no—
685D4—24no—
686D4—24no—
687D4—22no—
688D4—1222no—
689D4—1224no—
690D4—1224no—
691D4—1222no—
692D4—2444no—
693D4—2444no—
694D4—2444no—
695D4—2442no—
696D4—2444no—
697D4—2442no—
698D4—2441no—
699D4—2441no—
700D4C22×D24414yes—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—28no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—1222no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2444no—
710C2×C4—2444no—
711C2×C4#1451975112yes—
712C2×C4#1451975112yes—
713C2×C4#1451975112yes—
714C2×C4#1451975112yes—
715C2×C4#1451975112yes—
716C2×C4#1451975111yescharacteristic
717C2×C4#1451975111yescharacteristic
718C2×C4C22×C22⋊D6112yes—
719C2×C4C22×C22⋊D6111yescharacteristic
720C2×C4C22×C22⋊D6112yes—
721C2×C4C22×C22⋊D6111yescharacteristic
722C2×C4C22×D24412yes—
723C2×C4C22×D24412yes—
724C2×C4C22×D24411yescharacteristic
725C2×C4C22×D24411yescharacteristic
726C2×C4C2×#1175822212yes—
727C2×C4C2×#1175822211yescharacteristic
728C2×C4C24×D6111yescharacteristic
729C8—24no—
730C8—1224no—
731C8—1224no—
732C8C22×C22⋊D6118yes—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—24no—
737C22—42no—
738C22—42no—
739C22—44no—
740C22—84no—
741C22—4882no—
742C22—4884no—
743C22—4888no—
744C22—4884no—
745C22—4888no—
746C22—4882no—
747C22—4884no—
748C22—4882no—
749C22—2442no—
750C22—2444no—
751C22C2×#1451975112yes—
752C22C2×#1451975111yescharacteristic
753C22C2×#1451975112yes—
754C22C2×#1451975111yescharacteristic
755C22C22×#1175822211yescharacteristic
756C4—24no—
757C4—2442no—
758C4C2×#1451975112yes—
759C4C2×#1451975111yescharacteristic
760C4C2×#1451975112yes—
761C4C2×#1451975111yescharacteristic
762C4C23×C22⋊D6111yescharacteristic
763C4C23×D24411yescharacteristic
764C2—22no—
765C2—21no—
766C2—21no—
767C2—22no—
768C2—44no—
769C2—4884no—
770C2—4882no—
771C2#2145554712yesdirect product factor
772C2C22×#1451975111yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#568C2
socleC22×C61C2×#121
hypercenterC2×#568D61
hypocenterC61C2×#3068
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
1. C2×#16840560C2semidirect
2. C22×#14519805C2semidirect
3. C22×#14519802C2semidirect
4. #21455547C2direct (N × H)
5. C2×#16840032C2semidirect
6. C2×#16840025C2semidirect
7. C2×#16839811C2semidirect
8. C2×#16839744C2semidirect
9. C22×#14519693C2semidirect
10. C2×C61×#568C2semidirect
14. #16840560C22semidirect
16. C2×#14519807C22semidirect
20. C2×#14519805C22semidirect
25. C2×#14519802C22semidirect
26. C2×#14519802C22semidirect
28. C22×#11758190C22semidirect
30. C22×D488C22semidirect
34. #16840032C22semidirect
35. #16840025C22semidirect
36. #16839811C22semidirect
37. C2×#14519713C22semidirect
38. #16839744C22semidirect
39. C2×#14519695C22semidirect
40. C2×#14519693C22semidirect
41. C2×#14519693C22semidirect
42. C2×#14519693C22semidirect
45. C61×#568C22semidirect
47. C2×#131×C61C22semidirect
76. #14519807C23semidirect
84. #14519802C23semidirect
89. C2×#11758190C23semidirect
96. C2×D488C23semidirect
110. #14519713C23semidirect
111. #14519695C23semidirect
112. #14519693C23semidirect
113. #14519693C23semidirect
129. #131×C61C23semidirect
381. C2×#568D61semidirect
393. C2×C61#3068semidirect
420. #568C2×D61semidirect
422. C2×#131C2×D61semidirect
437. C61C2×#3068semidirect
502. #131C22×D61semidirect
771. C2#21455547direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405602
C22×#145198052
C22×#145198022
#214555472
C2×#168400322
C2×#168400252
C2×#168398112
C2×#168397442
C22×#145196932
C2×C61×#5682
C2×#306861