Finite Group Databasebeta

← C2×#21446297 #29681876

Subgroups — C2×#21446297 #29681876

Order 15616.

1782 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519802C211yesmaximal, characteristic
2C2×#16840529C211yesmaximal, characteristic, complemented
3C2×#16839766C211yesmaximal, characteristic, complemented
4C22×#14519693C211yesmaximal, characteristic, complemented
5#21446297C218yesmaximal, direct product factor
6C2×#16839532C211yesmaximal, characteristic, complemented
7C2×#16839520C211yesmaximal, characteristic, complemented
8C2×C61×#421C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C2×#14519802—22no—
11C2×#14519802—22no—
12C2×#14519802—22no—
13C2×#14519802—22no—
14C2×#14519802C414yescomplemented
15C2×#14519802C2214yes—
16C22×#11758201C412yescomplemented
17C22×#11758199C412yescomplemented
18#16840529—22no—
19#16840529—22no—
20#16840529—22no—
21#16840529C2214yescomplemented
22C2×#14519784—22no—
23C2×#14519784—22no—
24C22×#11758194—22no—
25C22×#11758194C2211yescharacteristic
26C22×#11758194C2211yescharacteristic
27C22×#11758194C2211yescharacteristic
28#16839766—22no—
29#16839766C2214yescomplemented
30C2×#14519697—22no—
31C2×#14519693—22no—
32C2×#14519693—22no—
33C2×#14519693C2214yescomplemented
34#16839532C2214yescomplemented
35#16839520C2214yescomplemented
36C22×#41×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C2×#117×C61C2211yescharacteristic
39C61×#421—22no—
40C61×#421C2214yescomplemented
41C2×#104×C61—22no—
42C24×D61—21no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—21no—
48C22×D244—21no—
49C22×D244—21no—
50C22×D244—21no—
51C22×D244—21no—
52C22×D244—21no—
53C22×D244—21no—
54C22×D244C2×C412yes—
55C22×D244C2×C412yes—
56C22×D244C2312yes—
57#14519802—28no—
58#14519802—28no—
59#14519802—28no—
60#14519802—28no—
61C2×#11758201—24no—
62C2×#11758201—24no—
63C2×#11758201C2×C418yescomplemented
64C2×#11758199—24no—
65C2×#11758199—24no—
66C2×#11758199C2×C418yescomplemented
67#14519784—28no—
68#14519784—28no—
69#14519784—28no—
70#14519784—28no—
71C2×#11758194—24no—
72C2×#11758194—28no—
73C2×#11758194—21no—
74C2×#11758194—21no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C2×#11758194—21no—
83C2×#11758194—21no—
84C2×#11758194—28no—
85C2×#11758194C2×C412yes—
86C2×#11758194D412yes—
87C2×#11758194D412yes—
88C2×#11758194D412yes—
89C2×#11758194C2312yes—
90C2×#11758194C2312yes—
91C2×#11758194C2312yes—
92C22×#92418—24no—
93C22×#92418—21no—
94C22×#92418C2×C412yes—
95C22×#92418D412yes—
96#14519697—28no—
97#14519693—28no—
98C2×#41×C61—21no—
99C2×#41×C61—21no—
100C2×#41×C61—21no—
101C2×#41×C61—21no—
102C2×#41×C61—21no—
103C2×#41×C61—21no—
104C2×#41×C61C2×C412yes—
105C2×#41×C61D412yes—
106C2×#41×C61D412yes—
107C2×#41×C61D412yes—
108C2×#41×C61D412yes—
109C2×#41×C61C2312yes—
110C22×Q8×C61C2×C411yescharacteristic
111C22×D4×C61—21no—
112C22×D4×C61C2×C411yescharacteristic
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61—21no—
120C2×M16×C61C2312yes—
121C22×C8×C61—21no—
122#117×C61—21no—
123#117×C61—21no—
124#117×C61—21no—
125#117×C61C2312yes—
126C2×C4⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C42×C61—21no—
129#104×C61—28no—
130C24×C61—21no—
131C24×C61#4111yescharacteristic
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—41no—
136C23×D61—41no—
137C23×D61—41no—
138C23×D61—41no—
139C23×D61—84no—
140#41×C61—22no—
141#41×C61—22no—
142#41×C61—22no—
143#41×C61—22no—
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—22no—
147#41×C61—22no—
148#41×C61—22no—
149#41×C61—22no—
150#41×C61—22no—
151#41×C61—22no—
152#41×C61C22⋊C414yes—
153#41×C61C22⋊C414yes—
154#41×C61C2×D414yes—
155#41×C61C2×D414yes—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C22⋊C412yes—
160C2×Q8×C61C22⋊C412yes—
161C2×Q8×C61C22×C412yes—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61C22⋊C412yes—
172C2×D4×C61C22⋊C412yes—
173C2×D4×C61C22×C412yes—
174C22×C4×C61—21no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—41no—
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61#4111yescharacteristic
193C22×C4×C61#4111yescharacteristic
194C22×C4×C61#4111yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×D244—22no—
197C2×D244—22no—
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—22no—
202C2×D244—22no—
203C2×D244—22no—
204C2×D244—22no—
205C2×D244—22no—
206C2×D244—22no—
207C2×D244—22no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—22no—
211C2×D244—41no—
212C2×D244—41no—
213C2×D244—41no—
214C2×D244—41no—
215C2×D244—41no—
216C2×D244—41no—
217C2×D244—41no—
218C2×D244—41no—
219C2×D244—41no—
220C2×D244—41no—
221C2×D244—41no—
222C2×D244—41no—
223C2×D244C22×C414yes—
224M16×C61—22no—
225M16×C61—22no—
226M16×C61—41no—
227M16×C61—41no—
228C2×C8×C61—22no—
229C2×C8×C61—41no—
230C2×C8×C61—41no—
231C4⋊C4×C61—22no—
232C4⋊C4×C61—41no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—41no—
235C42×C61—22no—
236C42×C61—41no—
237#11758201—216no—
238#11758199—216no—
239#11758194—216no—
240#11758194—22no—
241#11758194—22no—
242#11758194—22no—
243#11758194—22no—
244#11758194—22no—
245#11758194—22no—
246#11758194—22no—
247#11758194—22no—
248#11758194—22no—
249#11758194—22no—
250#11758194—22no—
251#11758194C2×D414yes—
252C2×#92418—216no—
253C2×#92418—22no—
254C2×#92418—22no—
255C2×#92418—22no—
256C2×#92418—22no—
257C2×#92418—22no—
258C2×#92418—22no—
259C2×#92418—22no—
260C2×#92418C22×C414yes—
261C2×#92418C2×D414yes—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—42no—
266C23×C61—82no—
267C23×C61C4×D411yescharacteristic
268C23×C61C4×D411yescharacteristic
269C23×C61#12111yescharacteristic
270C23×C61#12111yescharacteristic
271C23×C61#12311yescharacteristic
272C23×C61#12311yescharacteristic
273C23×C61C2×#4111yescharacteristic
274C22×D61—24no—
275C22×D61—42no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—42no—
280C22×D61—42no—
281C22×D61—84no—
282C22×D61—84no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288Q8×C61—22no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61C2×C22⋊C414yes—
292D4×C61—24no—
293D4×C61—24no—
294D4×C61—24no—
295D4×C61—24no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—22no—
299D4×C61C2×C22⋊C414yes—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—24no—
304C2×C4×C61—24no—
305C2×C4×C61—24no—
306C2×C4×C61—24no—
307C2×C4×C61—42no—
308C2×C4×C61—82no—
309C2×C4×C61C2×C22⋊C411yescharacteristic
310C2×C4×C61C2×C22⋊C411yescharacteristic
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C4×D411yescharacteristic
314C2×C4×C61C4×D411yescharacteristic
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C4×D411yescharacteristic
317C2×C4×C61C4×D411yescharacteristic
318C2×C4×C61C4×D411yescharacteristic
319C2×C4×C61#12011yescharacteristic
320C2×C4×C61#12011yescharacteristic
321C2×C4×C61#12011yescharacteristic
322C2×C4×C61#12011yescharacteristic
323C2×C4×C61#12111yescharacteristic
324C2×C4×C61#12111yescharacteristic
325C2×C4×C61#12111yescharacteristic
326C2×C4×C61#12111yescharacteristic
327C2×C4×C61#12111yescharacteristic
328C2×C4×C61#12111yescharacteristic
329C2×C4×C61#12311yescharacteristic
330C2×C4×C61#12311yescharacteristic
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337D244—24no—
338D244—24no—
339D244—42no—
340D244—42no—
341D244—42no—
342D244—42no—
343D244—42no—
344D244—42no—
345C8×C61—42no—
346#92418—24no—
347#92418—24no—
348#92418—24no—
349C2×#1903—611nomaximal, Sylow
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—24no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—44no—
359C22×C61—82no—
360C22×C61—82no—
361C22×C61#38611yescharacteristic
362C22×C61#38611yescharacteristic
363C22×C61#38611yescharacteristic
364C22×C61#38611yescharacteristic
365C22×C61C2×C4×D411yescharacteristic
366C22×C61C2×#12111yescharacteristic
367C22×C61C2×#12311yescharacteristic
368C2×D61—44no—
369C2×D61—84no—
370C2×D61—84no—
371C2×D61—84no—
372C2×D61—84no—
373C2×D61—84no—
374C2×D61—84no—
375C2×D61—84no—
376C4×C61—24no—
377C4×C61—82no—
378C4×C61#38611yescharacteristic
379C4×C61#38611yescharacteristic
380C4×C61#38611yescharacteristic
381C4×C61#38611yescharacteristic
382C4×C61C22×C22⋊C411yescharacteristic
383C4×C61C2×C4×D411yescharacteristic
384C4×C61C2×#12011yescharacteristic
385C4×C61C2×#12111yescharacteristic
386C22×AGL(1,ℤ/8)—611no—
387C2×#568—611no—
388C2×#421D6111yescharacteristic, complemented
389C2×#418—611no—
390C22×#100—611no—
391#1903—618no—
392C2×#344—611no—
393C2×#338—611no—
394C2×C61—21no—
395C2×C61—21no—
396C2×C61—21no—
397C2×C61—21no—
398C2×C61—21no—
399C2×C61—21no—
400C2×C61—44no—
401C2×C61#190312yescomplemented
402C2×C61C2×#38611yescharacteristic
403D61—84no—
404C22×#41C2×D6111yescharacteristic
405C23×D4—611no—
406C2×AGL(1,ℤ/8)—614no—
407C2×AGL(1,ℤ/8)—614no—
408C2×AGL(1,ℤ/8)—1222no—
409C2×AGL(1,ℤ/8)—1222no—
410C2×AGL(1,ℤ/8)—1222no—
411C2×AGL(1,ℤ/8)—1222no—
412C22×SD16—612no—
413C22×D8—612no—
414#568—614no—
415#568—1222no—
416#568—1222no—
417#568—1222no—
418C2×#131—1222no—
419C2×#131—1222no—
420C22×M16—611no—
421C22×M16—611no—
422C22×M16—611no—
423C22×M16—1222no—
424C22×M16C2×D6111yescharacteristic
425C2×#117C2×D6111yescharacteristic
426#421—22no—
427#421C2×D6114yescomplemented
428C2×#104—22no—
429#418—614no—
430#418—1222no—
431C2×#102—1222no—
432C2×#100—614no—
433C2×#100—1222no—
434C2×#100—1222no—
435#344—614no—
436#338—614no—
437C61C2×#190311yescharacteristic, complemented, Sylow
438C25—1221no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41C4×D6112yes—
446C2×#41D24412yes—
447C2×#41D24412yes—
448C2×#41C22⋊D6112yes—
449C2×#41C22⋊D6112yes—
450C2×#41C22×D6112yes—
451C22×Q8C4×D6111yescharacteristic
452C22×D4—21no—
453C22×D4—612no—
454C22×D4—612no—
455C22×D4—612no—
456C22×D4—1221no—
457C22×D4—1221no—
458C22×D4—1221no—
459C22×D4—1221no—
460C22×D4—1221no—
461C22×D4—1221no—
462C22×D4—1221no—
463C22×D4—1221no—
464C22×D4—1221no—
465C22×D4—1221no—
466C22×D4—1221no—
467C22×D4C4×D6111yescharacteristic
468C23×C4—21no—
469C23×C4C22×D6111yescharacteristic
470AGL(1,ℤ/8)—1228no—
471AGL(1,ℤ/8)—1228no—
472AGL(1,ℤ/8)—1228no—
473AGL(1,ℤ/8)—1228no—
474C2×SD16—618no—
475C2×SD16—1224no—
476C2×SD16—1224no—
477C2×D8—618no—
478C2×D8—1224no—
479C2×D8—1224no—
480#131—1228no—
481#131—1228no—
482#131—1228no—
483#131—1228no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—612no—
490C2×M16—612no—
491C2×M16—612no—
492C2×M16—612no—
493C2×M16—612no—
494C2×M16—612no—
495C2×M16—612no—
496C2×M16—1228no—
497C2×M16—1224no—
498C2×M16—1228no—
499C2×M16—1221no—
500C2×M16—1221no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16—1221no—
507C2×M16—1221no—
508C2×M16—1221no—
509C2×M16—1221no—
510C2×M16C22×D6112yes—
511C22×C8—21no—
512C22×C8—612no—
513C22×C8—612no—
514C22×C8—1224no—
515C22×C8—1221no—
516#117—21no—
517#117—21no—
518#117—21no—
519#117C22×D6112yes—
520C2×C4⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C42—21no—
523#104—28no—
524#102—1228no—
525#100—1228no—
526C24—21no—
527C24—1222no—
528C24—1222no—
529C24—1222no—
530C24—4884no—
531C24—2441no—
532C24—2441no—
533C24—2441no—
534C24—2441no—
535C24#1175822411yescharacteristic
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41#1175819814yes—
549#41#1175819814yes—
550#41C2×D24414yes—
551#41C2×C22⋊D6114yes—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8#1175819812yes—
556C2×Q8#1175819812yes—
557C2×Q8C2×C4×D6112yes—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—614no—
568C2×D4—1222no—
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—2441no—
584C2×D4—2441no—
585C2×D4—2441no—
586C2×D4—2441no—
587C2×D4—2441no—
588C2×D4—2441no—
589C2×D4—2441no—
590C2×D4—2441no—
591C2×D4—2441no—
592C2×D4—2441no—
593C2×D4—2441no—
594C2×D4—2441no—
595C2×D4#1175819812yes—
596C2×D4#1175819812yes—
597C2×D4C2×C4×D6112yes—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—41no—
606C22×C4C2×C4×D6111yescharacteristic
607C22×C4C2×C4×D6111yescharacteristic
608C22×C4C2×D24411yescharacteristic
609C22×C4C2×D24411yescharacteristic
610C22×C4D4×D6111yescharacteristic
611C22×C4D4×D6111yescharacteristic
612C22×C4D4×D6111yescharacteristic
613C22×C4D4×D6111yescharacteristic
614C22×C4#1175822411yescharacteristic
615C22×C4#1175822411yescharacteristic
616C22×C4#1175822411yescharacteristic
617C22×C4C2×C22⋊D6111yescharacteristic
618C22×C4C2×C22⋊D6111yescharacteristic
619C22×C4C23×D6111yescharacteristic
620SD16—12216no—
621D8—12216no—
622M16—22no—
623M16—22no—
624M16—41no—
625M16—41no—
626M16—614no—
627M16—12216no—
628M16—1222no—
629M16—1222no—
630M16—1222no—
631M16—1222no—
632M16—1222no—
633M16—1222no—
634M16—1222no—
635M16—1222no—
636M16—1222no—
637M16—1222no—
638M16—1222no—
639C2×C8—22no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—614no—
643C2×C8—614no—
644C2×C8—12216no—
645C2×C8—1222no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—1222no—
649C2×C8—1222no—
650C2×C8—1222no—
651C2×C8—1222no—
652C4⋊C4—22no—
653C4⋊C4—41no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C42—22no—
657C42—41no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—42no—
662C23—82no—
663C23—1224no—
664C23—4884no—
665C23—4884no—
666C23—4884no—
667C23—4884no—
668C23—4884no—
669C23—4884no—
670C23—4884no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23—2442no—
675C23—2442no—
676C23—2442no—
677C23#1451973711yescharacteristic
678C23#1451973711yescharacteristic
679C23#1451974911yescharacteristic
680C23#1451974911yescharacteristic
681C23#1451976111yescharacteristic
682C23#1451976111yescharacteristic
683C23C2×#1175822411yescharacteristic
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8C2×#1175819814yes—
688D4—24no—
689D4—24no—
690D4—24no—
691D4—24no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—1224no—
696D4—1224no—
697D4—2442no—
698D4—2442no—
699D4—2442no—
700D4—2442no—
701D4—2442no—
702D4—2442no—
703D4C2×#1175819814yes—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—82no—
713C2×C4C2×#1175819811yescharacteristic
714C2×C4C2×#1175819811yescharacteristic
715C2×C4C2×#1175819811yescharacteristic
716C2×C4C2×#1175819811yescharacteristic
717C2×C4#1451973711yescharacteristic
718C2×C4#1451973711yescharacteristic
719C2×C4#1451973711yescharacteristic
720C2×C4#1451973711yescharacteristic
721C2×C4#1451973711yescharacteristic
722C2×C4#1451973711yescharacteristic
723C2×C4#1451974711yescharacteristic
724C2×C4#1451974711yescharacteristic
725C2×C4#1451974711yescharacteristic
726C2×C4#1451974711yescharacteristic
727C2×C4#1451974911yescharacteristic
728C2×C4#1451974911yescharacteristic
729C2×C4#1451974911yescharacteristic
730C2×C4#1451974911yescharacteristic
731C2×C4#1451974911yescharacteristic
732C2×C4#1451974911yescharacteristic
733C2×C4#1451976111yescharacteristic
734C2×C4#1451976111yescharacteristic
735C2×C4C22×C4×D6111yescharacteristic
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4C2×D4×D6111yescharacteristic
738C2×C4C22×C22⋊D6111yescharacteristic
739C2×C4C22×D24411yescharacteristic
740C2×C4C2×#1175822411yescharacteristic
741C8—42no—
742C8—1224no—
743C8—1224no—
744C8—1224no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—24no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—44no—
754C22—82no—
755C22—82no—
756C22—4884no—
757C22—4884no—
758C22—4884no—
759C22—4884no—
760C22—4884no—
761C22—4884no—
762C22—4884no—
763C22—2444no—
764C22#1683963911yescharacteristic
765C22#1683963911yescharacteristic
766C22#1683963911yescharacteristic
767C22#1683963911yescharacteristic
768C22C2×#1451973711yescharacteristic
769C22C2×#1451974911yescharacteristic
770C22C2×#1451976111yescharacteristic
771C4—24no—
772C4—82no—
773C4#1683963911yescharacteristic
774C4#1683963911yescharacteristic
775C4#1683963911yescharacteristic
776C4#1683963911yescharacteristic
777C4C22×#1175819811yescharacteristic
778C4C2×#1451973711yescharacteristic
779C4C2×#1451974711yescharacteristic
780C4C2×#1451974911yescharacteristic
781C2—21no—
782C2—21no—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—44no—
788C2—4884no—
789C2#2144629712yesdirect product factor
790C2C2×#1683963911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61#386
prime radicalC22×#14519802C2
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61C2×#1903
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16840529C2semidirect
3. C2×#16839766C2semidirect
4. C22×#14519693C2semidirect
5. #21446297C2direct (N × H)
6. C2×#16839532C2semidirect
7. C2×#16839520C2semidirect
8. C2×C61×#421C2semidirect
14. C2×#14519802C4semidirect
16. C22×#11758201C4semidirect
17. C22×#11758199C4semidirect
21. #16840529C22semidirect
29. #16839766C22semidirect
33. C2×#14519693C22semidirect
34. #16839532C22semidirect
35. #16839520C22semidirect
40. C61×#421C22semidirect
63. C2×#11758201C2×C4semidirect
66. C2×#11758199C2×C4semidirect
388. C2×#421D61semidirect
401. C2×C61#1903semidirect
427. #421C2×D61semidirect
437. C61C2×#1903semidirect
789. C2#21446297direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198022
C2×#168405292
C2×#168397662
C22×#145196932
#214462972
C2×#168395322
C2×#168395202
C2×C61×#4212
C2×#190361