Finite Group Databasebeta

← C2×#21446365 #29682035

Subgroups — C2×#21446365 #29682035

Order 15616.

1862 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2C2×#16840331C211yesmaximal, characteristic
3C2×#16839744C211yesmaximal, characteristic, complemented
4C22×#14519693C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic, complemented
6#21446365C218yesmaximal, direct product factor
7C2×#16839532C211yesmaximal, characteristic, complemented
8C2×C61×#344C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×D244C2211yescharacteristic
11#16840528—22no—
12#16840528—22no—
13#16840528—22no—
14#16840528C2214yescomplemented
15C2×#14519785—22no—
16C2×#14519783—22no—
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×M16×D61—22no—
20#16840331—22no—
21#16840331—22no—
22#16840331C414yes—
23#16840331C2214yes—
24C2×#14519774—21no—
25C2×#14519765—21no—
26C2×#14519752—22no—
27C2×#14519747C414yes—
28#16839744—22no—
29#16839744C2214yescomplemented
30C2×#14519695—21no—
31C2×#14519693—22no—
32C2×#14519693—22no—
33C2×#14519693—22no—
34C2×#14519693—22no—
35C2×#14519693—21no—
36C2×#14519693C2214yescomplemented
37C2×#14519693C2214yescomplemented
38#16839532C2214yescomplemented
39C22×M16×C61C2211yescharacteristic
40C22×M16×C61C2211yescharacteristic
41C2×#117×C61C2211yescharacteristic
42C61×#344C2214yescomplemented
43C24×D61C2×C412yes—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222C2×C412yes—
53C2×#11758222D412yes—
54C2×#11758222D412yes—
55C2×#11758222C2312yes—
56C22×Dic122D411yescharacteristic
57C22×D244—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244—21no—
64C22×D244—21no—
65C22×D244—21no—
66C22×D244—21no—
67C22×D244—21no—
68C22×D244—21no—
69C22×D244—24no—
70C22×D244C2×C412yes—
71C22×D244D411yescharacteristic
72C22×D244C2312yes—
73C22×C22⋊D61C2×C412yes—
74C22×C4×D61D412yes—
75#14519785—28no—
76#14519785—28no—
77#14519783—28no—
78#14519783—28no—
79C2×#11758194—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C2×#11758194—21no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194—21no—
87C2×#11758194D412yescomplemented
88C2×#11758194D412yescomplemented
89C2×#11758194C2312yes—
90C2×#11758194C2312yes—
91C2×#11758189—24no—
92M16×D61—28no—
93M16×D61—28no—
94C22×#92418—21no—
95C22×#92418—21no—
96C2×C8×D61—24no—
97#14519774—24no—
98#14519774—24no—
99#14519765—24no—
100#14519765—24no—
101#14519752—28no—
102#14519752—28no—
103#14519747—28no—
104#14519747C2×C4116yes—
105C2×#11758198—24no—
106#14519695—24no—
107#14519693—24no—
108#14519693—28no—
109#14519693—28no—
110C23×C4×C61C2311yescharacteristic
111C2×M16×C61—21no—
112C2×M16×C61—21no—
113C2×M16×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61D412yescomplemented
120C2×M16×C61D412yescomplemented
121C2×M16×C61C2312yes—
122C2×M16×C61C2312yes—
123C22×C8×C61—21no—
124C22×C8×C61—21no—
125#117×C61—21no—
126#117×C61—21no—
127#117×C61C2×C412yes—
128#117×C61C2312yes—
129C2×C4⋊C4×C61—21no—
130C2×C22⋊C4×C61C2×C412yes—
131C2×C42×C61—21no—
132C24×C61C22×C411yescharacteristic
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—84no—
140C23×D61C22⋊C412yes—
141C23×D61C22×C414yes—
142C22×C4×C61—22no—
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C22×C4×C61#4111yescharacteristic
156C22×C4×C61C2411yescharacteristic
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61C22⋊C414yes—
162C2×C22⋊D61C22×C414yes—
163C22×Dic61C22⋊C412yes—
164#11758222—22no—
165#11758222—22no—
166#11758222—22no—
167#11758222—22no—
168#11758222—22no—
169#11758222—22no—
170#11758222—22no—
171#11758222—22no—
172#11758222—22no—
173#11758222—22no—
174#11758222—22no—
175#11758222—22no—
176#11758222—22no—
177#11758222—22no—
178#11758222—22no—
179#11758222—22no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—22no—
196C2×D244—216no—
197C2×D244—41no—
198C2×D244—41no—
199C2×D244—41no—
200C2×D244—41no—
201C2×D244—41no—
202C2×D244—41no—
203C2×D244—41no—
204C2×D244—41no—
205C2×D244—41no—
206C2×D244—41no—
207C2×D244—41no—
208C2×D244—41no—
209C2×D244—41no—
210C2×D244—41no—
211C2×D244—41no—
212C2×D244—41no—
213C2×D244—88no—
214C2×D244C22⋊C412yes—
215C2×D244C2×D412yes—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61C22⋊C414yes—
221C2×C4×D61C2×D414yes—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122C22⋊C412yes—
227C2×Dic122C2×D412yes—
228M16×C61—22no—
229M16×C61—22no—
230M16×C61—22no—
231M16×C61—22no—
232M16×C61—22no—
233M16×C61—41no—
234M16×C61—41no—
235M16×C61C2×D414yescomplemented
236C2×C8×C61—22no—
237C2×C8×C61—22no—
238C2×C8×C61—22no—
239C2×C8×C61—22no—
240C2×C8×C61—41no—
241C2×C8×C61—41no—
242C4⋊C4×C61—22no—
243C4⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61C22×C414yes—
246C42×C61—22no—
247C42×C61—22no—
248#11758198—216no—
249#11758194—22no—
250#11758194—22no—
251#11758194—22no—
252#11758194—22no—
253#11758194—22no—
254#11758194—41no—
255#11758194—41no—
256#11758194C2×D414yescomplemented
257C2×#92418—22no—
258C2×#92418—22no—
259C2×#92418—22no—
260C2×#92418—22no—
261C2×#92418—41no—
262C2×#92418—41no—
263#11758189—216no—
264C8×D61—216no—
265C23×C61—42no—
266C23×C61C2×C22⋊C411yescharacteristic
267C23×C61C2×C22⋊C411yescharacteristic
268C23×C61C4×D411yescharacteristic
269C23×C61C4×D411yescharacteristic
270C23×C61C4×D411yescharacteristic
271C23×C61C4×D411yescharacteristic
272C23×C61C23×C411yescharacteristic
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—44no—
279C22×D61—48no—
280C22×D61—42no—
281C22×D61—42no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61C2×C22⋊C414yes—
291C2×C4×C61—24no—
292C2×C4×C61—44no—
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61#12011yescharacteristic
300C2×C4×C61#12011yescharacteristic
301C2×C4×C61#12011yescharacteristic
302C2×C4×C61#12011yescharacteristic
303C2×C4×C61#12111yescharacteristic
304C2×C4×C61#12111yescharacteristic
305C2×C4×C61#12111yescharacteristic
306C2×C4×C61#12111yescharacteristic
307C2×C4×C61#12111yescharacteristic
308C2×C4×C61#12111yescharacteristic
309C2×C4×C61#12111yescharacteristic
310C2×C4×C61#12111yescharacteristic
311C2×C4×C61#12311yescharacteristic
312C2×C4×C61#12311yescharacteristic
313C2×C4×C61#12311yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C22×D411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C2×#4111yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C22⋊D61—24no—
322C22⋊D61—24no—
323C22⋊D61—24no—
324C22⋊D61—24no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61C2×C22⋊C414yes—
328D244—22no—
329D244—22no—
330D244—22no—
331D244—22no—
332D244—42no—
333D244—42no—
334D244—42no—
335D244—42no—
336D244—42no—
337D244—42no—
338D244—42no—
339D244—42no—
340D244—816no—
341C4×D61—24no—
342C4×D61—24no—
343C4×D61—24no—
344C4×D61—24no—
345Dic122—22no—
346Dic122—22no—
347Dic122—22no—
348Dic122—22no—
349C8×C61—24no—
350C8×C61—42no—
351#92418—24no—
352#92418—42no—
353C2×#1914—611nomaximal, Sylow
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61#38611yescharacteristic
362C22×C61#38611yescharacteristic
363C22×C61#38611yescharacteristic
364C22×C61#38611yescharacteristic
365C22×C61C22×C22⋊C411yescharacteristic
366C22×C61C2×C4×D411yescharacteristic
367C22×C61C2×C4×D411yescharacteristic
368C2×D61—24no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—48no—
372C2×D61—44no—
373C2×D61—82no—
374C2×D61—84no—
375C2×D61—84no—
376C2×D61—84no—
377C2×D61—84no—
378C2×D61—84no—
379C2×D61—84no—
380C4×C61—44no—
381C4×C61#38611yescharacteristic
382C4×C61#38611yescharacteristic
383C4×C61#38611yescharacteristic
384C4×C61#38611yescharacteristic
385C4×C61C2×#12011yescharacteristic
386C4×C61C2×#12111yescharacteristic
387C4×C61C2×#12111yescharacteristic
388C4×C61C2×#12311yescharacteristic
389Dic61—24no—
390C2×#568—611no—
391C2×#535—611no—
392C2×#413—611no—
393C22×#100—611no—
394C22×#100—611no—
395#1914—618no—
396C2×#344—611no—
397C2×#344D6111yescharacteristic, complemented
398C2×C61—21no—
399C2×C61—21no—
400C2×C61—21no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—21no—
404C2×C61#191412yescomplemented
405C2×C61C2×#38611yescharacteristic
406D61—44no—
407D61—84no—
408C22×#41—611no—
409C23×D4—611no—
410#568—614no—
411#568—1222no—
412#568—1222no—
413#568—1222no—
414C2×#131—1222no—
415C2×#131—1222no—
416C22×M16—611no—
417C22×M16—611no—
418C22×M16—1222no—
419C22×M16C2×D6111yescharacteristic
420C22×M16C2×D6111yescharacteristic
421#535—614no—
422#535—614no—
423#535—1222no—
424#535—1222no—
425C2×#127—1221no—
426C2×#124—1221no—
427C2×#121—1222no—
428C2×#120—614no—
429C2×#117C2×D6111yescharacteristic
430#413—614no—
431#413—1222no—
432C2×#101—1221no—
433C2×#100—614no—
434C2×#100—614no—
435C2×#100—1222no—
436C2×#100—1222no—
437C2×#100—1221no—
438C2×#100—1222no—
439C2×#100—1222no—
440#344—614no—
441#344C2×D6114yescomplemented
442C61C2×#191411yescharacteristic, complemented, Sylow
443C25—612no—
444C2×#41—612no—
445C2×#41—612no—
446C2×#41—612no—
447C2×#41—612no—
448C2×#41—1221no—
449C2×#41—1221no—
450C2×#41—1221no—
451C2×#41—1221no—
452C2×#41—1221no—
453C2×#41—1221no—
454C2×#41—1221no—
455C2×#41—1221no—
456C22×Q8—611no—
457C22×D4—612no—
458C22×D4—612no—
459C22×D4—611no—
460C22×D4—612no—
461C22×D4—1224no—
462C22×D4—1221no—
463C22×D4—1221no—
464C22×D4—1221no—
465C22×D4—1221no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C23×C4—612no—
475C23×C4C22×D6111yescharacteristic
476#131—1228no—
477#131—1228no—
478#131—1228no—
479#131—1228no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—612no—
489C2×M16—612no—
490C2×M16—612no—
491C2×M16—612no—
492C2×M16—1224no—
493C2×M16—1228no—
494C2×M16—1228no—
495C2×M16—1221no—
496C2×M16—1221no—
497C2×M16—1221no—
498C2×M16—1221no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16D24412yescomplemented
504C2×M16D24412yescomplemented
505C2×M16C22×D6112yes—
506C2×M16C22×D6112yes—
507C22×C8—21no—
508C22×C8—21no—
509C22×C8—1224no—
510C22×C8—1221no—
511C22×C8—1221no—
512#127—1224no—
513#127—1224no—
514#124—1224no—
515#124—1224no—
516#121—1228no—
517#121—1228no—
518#120—6116no—
519#120—1228no—
520#117—21no—
521#117—21no—
522#117C4×D6112yes—
523#117C22×D6112yes—
524C2×C4⋊C4—21no—
525C2×C22⋊C4—1224no—
526C2×C22⋊C4C4×D6112yes—
527C2×C42—21no—
528#101—1224no—
529#100—1228no—
530#100—1224no—
531#100—1228no—
532C24—612no—
533C24—614no—
534C24—1222no—
535C24—1222no—
536C24—1222no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—4884no—
541C24C2×C4×D6111yescharacteristic
542#41—1222no—
543#41—1222no—
544#41—1222no—
545#41—1222no—
546#41—1222no—
547#41—1222no—
548#41—1222no—
549#41—1222no—
550#41—1222no—
551#41—1222no—
552#41—1222no—
553#41—1222no—
554#41—1222no—
555#41—1222no—
556#41—1222no—
557#41—1222no—
558C2×Q8—612no—
559C2×Q8—612no—
560C2×Q8—1221no—
561C2×Q8—1221no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×D4—614no—
565C2×D4—614no—
566C2×D4—612no—
567C2×D4—612no—
568C2×D4—12216no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—4888no—
590C2×D4—2441no—
591C2×D4—2441no—
592C2×D4—2441no—
593C2×D4—2441no—
594C2×D4—2441no—
595C2×D4—2441no—
596C2×D4—2441no—
597C2×D4—2441no—
598C2×D4—2441no—
599C2×D4—2441no—
600C2×D4—2441no—
601C2×D4—2441no—
602C2×D4—2441no—
603C2×D4—2441no—
604C2×D4—2441no—
605C2×D4—2441no—
606C22×C4—22no—
607C22×C4—612no—
608C22×C4—614no—
609C22×C4—614no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4C2×C4×D6111yescharacteristic
615C22×C4C2×D24411yescharacteristic
616C22×C4C2×D24411yescharacteristic
617C22×C4#1175822211yescharacteristic
618C22×C4#1175822211yescharacteristic
619C22×C4D4×D6111yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4D4×D6111yescharacteristic
622C22×C4D4×D6111yescharacteristic
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4#1175822611yescharacteristic
626C22×C4#1175822611yescharacteristic
627C22×C4C23×D6111yescharacteristic
628M16—22no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—22no—
633M16—41no—
634M16—41no—
635M16—614no—
636M16—12216no—
637M16—1222no—
638M16—1222no—
639M16—1222no—
640M16—1222no—
641M16—1222no—
642M16—2441no—
643M16—2441no—
644M16C2×D24414yescomplemented
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—12216no—
652C2×C8—1222no—
653C2×C8—1222no—
654C2×C8—1222no—
655C2×C8—1222no—
656C2×C8—2441no—
657C2×C8—2441no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—12216no—
662C22⋊C4C2×C4×D6114yes—
663C42—22no—
664C42—22no—
665C23—42no—
666C23—614no—
667C23—1222no—
668C23—1222no—
669C23—1224no—
670C23—1224no—
671C23—1224no—
672C23—4884no—
673C23—4884no—
674C23—4884no—
675C23—4884no—
676C23—4884no—
677C23—4884no—
678C23—2448no—
679C23—2444no—
680C23—2442no—
681C23—2442no—
682C23—2442no—
683C23—2442no—
684C23C22⋊C4×D6111yescharacteristic
685C23C22⋊C4×D6111yescharacteristic
686C23#1451973911yescharacteristic
687C23#1451973911yescharacteristic
688C23C4×D24411yescharacteristic
689C23C4×D24411yescharacteristic
690C23C22×C4×D6111yescharacteristic
691Q8—1222no—
692Q8—1222no—
693Q8—1222no—
694Q8—1222no—
695D4—1224no—
696D4—1224no—
697D4—1224no—
698D4—1224no—
699D4—1222no—
700D4—1222no—
701D4—1222no—
702D4—1222no—
703D4—48816no—
704D4—2442no—
705D4—2442no—
706D4—2442no—
707D4—2442no—
708D4—2442no—
709D4—2442no—
710D4—2442no—
711D4—2442no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—614no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1224no—
718C2×C4—1224no—
719C2×C4—1224no—
720C2×C4—1224no—
721C2×C4C22⋊C4×D6111yescharacteristic
722C2×C4C22⋊C4×D6111yescharacteristic
723C2×C4#1451973911yescharacteristic
724C2×C4#1451973911yescharacteristic
725C2×C4C4×D24411yescharacteristic
726C2×C4C4×D24411yescharacteristic
727C2×C4#1451974711yescharacteristic
728C2×C4#1451974711yescharacteristic
729C2×C4#1451974711yescharacteristic
730C2×C4#1451974711yescharacteristic
731C2×C4#1451975011yescharacteristic
732C2×C4#1451975011yescharacteristic
733C2×C4#1451975011yescharacteristic
734C2×C4#1451975011yescharacteristic
735C2×C4#1451975211yescharacteristic
736C2×C4#1451975211yescharacteristic
737C2×C4#1451975211yescharacteristic
738C2×C4#1451975211yescharacteristic
739C2×C4#1451976211yescharacteristic
740C2×C4#1451976211yescharacteristic
741C2×C4#1451976211yescharacteristic
742C2×C4#1451976211yescharacteristic
743C2×C4C2×D4×D6111yescharacteristic
744C2×C4C2×D4×D6111yescharacteristic
745C2×C4C2×D4×D6111yescharacteristic
746C2×C4C22×D24411yescharacteristic
747C2×C4C2×#1175822211yescharacteristic
748C2×C4C2×#1175822611yescharacteristic
749C8—24no—
750C8—42no—
751C8—1224no—
752C8—2442no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—1224no—
761C22—4884no—
762C22—4884no—
763C22—4884no—
764C22—4884no—
765C22—4884no—
766C22—4882no—
767C22—4884no—
768C22—2448no—
769C22—2444no—
770C22—2444no—
771C22—2444no—
772C22#1683964011yescharacteristic
773C22#1683964011yescharacteristic
774C22#1683964011yescharacteristic
775C22#1683964011yescharacteristic
776C22C2×C22⋊C4×D6111yescharacteristic
777C22C2×#1451973911yescharacteristic
778C22C2×C4×D24411yescharacteristic
779C4—44no—
780C4—1224no—
781C4#1683964011yescharacteristic
782C4#1683964011yescharacteristic
783C4#1683964011yescharacteristic
784C4#1683964011yescharacteristic
785C4C2×#1451974711yescharacteristic
786C4C2×#1451975011yescharacteristic
787C4C2×#1451975211yescharacteristic
788C4C2×#1451976211yescharacteristic
789C2—21no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—4884no—
796C2—2444no—
797C2#2144636512yesdirect product factor
798C2C2×#1683964011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#344C2
socleC22×C61#386
prime radicalC2×#16840331C2
cosocleC22×C4×C61C24
hypercenterC2×#344D61
hypocenterC61C2×#1914
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839744C2semidirect
4. C22×#14519693C2semidirect
5. C22×#14519693C2semidirect
6. #21446365C2direct (N × H)
7. C2×#16839532C2semidirect
8. C2×C61×#344C2semidirect
14. #16840528C22semidirect
29. #16839744C22semidirect
36. C2×#14519693C22semidirect
37. C2×#14519693C22semidirect
38. #16839532C22semidirect
42. C61×#344C22semidirect
87. C2×#11758194D4semidirect
88. C2×#11758194D4semidirect
119. C2×M16×C61D4semidirect
120. C2×M16×C61D4semidirect
235. M16×C61C2×D4semidirect
256. #11758194C2×D4semidirect
397. C2×#344D61semidirect
404. C2×C61#1914semidirect
441. #344C2×D61semidirect
442. C61C2×#1914semidirect
503. C2×M16D244semidirect
504. C2×M16D244semidirect
644. M16C2×D244semidirect
797. C2#21446365direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405282
C2×#168403312
C2×#168397442
C22×#145196932
#214463652
C2×#168395322
C2×C61×#3442
C2×#191461