Finite Group Databasebeta

← C2×#21447092 #29707843

Subgroups — C2×#21447092 #29707843

Order 15616.

1450 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519802C211yesmaximal, characteristic
2C2×#16839810C211yesmaximal, characteristic, complemented
3C2×#16839779C211yesmaximal, characteristic, complemented
4C2×#16839768C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic, complemented
6#21447092C218yesmaximal, direct product factor
7C2×#16839533C211yesmaximal, characteristic, complemented
8C2×C61×#413C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C2×#14519802—22no—
11C2×#14519802—22no—
12C2×#14519802—22no—
13C2×#14519802—22no—
14C2×#14519802—22no—
15C2×#14519802C2214yes—
16C22×#11758201—21no—
17C22×#11758199—21no—
18C22×#11758194C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16839810—22no—
22#16839810C2214yescomplemented
23C2×#14519712—22no—
24#16839779—22no—
25#16839779C2214yescomplemented
26C2×#14519704—22no—
27#16839768—22no—
28#16839768C2214yescomplemented
29C2×#14519699—22no—
30C2×#14519693—22no—
31C2×#14519693—22no—
32C2×#14519693C2214yescomplemented
33#16839533C2214yescomplemented
34C22×#41×C61C2211yescharacteristic
35C22×M16×C61C2211yescharacteristic
36C22×M16×C61C2211yescharacteristic
37C61×#413—22no—
38C61×#413C2214yescomplemented
39C2×#101×C61—21no—
40C2×#100×C61—21no—
41C24×D61—21no—
42C22×D244—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×D244D412yes—
54C22×D244D412yes—
55C22×D244C2312yes—
56#14519802—28no—
57#14519802—28no—
58#14519802—28no—
59#14519802—28no—
60C2×#11758201—24no—
61C2×#11758201—24no—
62C2×#11758201—24no—
63C2×#11758199—24no—
64C2×#11758199—24no—
65C2×#11758199—24no—
66C2×#11758194—21no—
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194—21no—
70C2×#11758194—21no—
71C2×#11758194—21no—
72C2×#11758194D412yes—
73C2×#11758194D412yes—
74C2×#11758194D412yes—
75C2×#11758194D412yes—
76C2×#11758194C2312yes—
77C2×#11758194C2312yes—
78C22×#92418—21no—
79C22×#92418—21no—
80#14519736—21no—
81#14519736—21no—
82#14519736—21no—
83#14519736C2312yes—
84C2×C4⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C4×Dic61—21no—
87#14519712—28no—
88#14519704—28no—
89#14519699—28no—
90#14519693—28no—
91C2×#41×C61—21no—
92C2×#41×C61—21no—
93C2×#41×C61—21no—
94C2×#41×C61—21no—
95C2×#41×C61—21no—
96C2×#41×C61—21no—
97C2×#41×C61—21no—
98C2×#41×C61—21no—
99C2×#41×C61—21no—
100C2×#41×C61—21no—
101C2×#41×C61D412yes—
102C2×#41×C61C2312yes—
103C22×Q8×C61D411yescharacteristic
104C22×D4×C61—21no—
105C22×D4×C61D411yescharacteristic
106C23×C4×C61—21no—
107C23×C4×C61C2311yescharacteristic
108C2×M16×C61—21no—
109C2×M16×C61—21no—
110C2×M16×C61—21no—
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×C61C2312yes—
119C2×M16×C61C2312yes—
120C22×C8×C61—21no—
121C22×C8×C61—21no—
122#101×C61—24no—
123#100×C61—24no—
124C24×C61—21no—
125C24×C61#4111yescharacteristic
126C23×D61—22no—
127C23×D61—22no—
128C23×D61—22no—
129C23×D61—41no—
130C23×D61—41no—
131C23×D61—41no—
132C23×D61—41no—
133C23×D61—84no—
134#41×C61—22no—
135#41×C61—22no—
136#41×C61—22no—
137#41×C61—22no—
138#41×C61—22no—
139#41×C61—22no—
140#41×C61—22no—
141#41×C61—22no—
142#41×C61—41no—
143#41×C61—41no—
144#41×C61—41no—
145#41×C61—41no—
146#41×C61—41no—
147#41×C61—41no—
148#41×C61—41no—
149#41×C61—41no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61C2×D412yes—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—41no—
164C2×D4×C61—41no—
165C2×D4×C61—41no—
166C2×D4×C61—41no—
167C2×D4×C61C2×D412yes—
168C22×C4×C61—21no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—41no—
172C22×C4×C61—41no—
173C22×C4×C61—41no—
174C22×C4×C61—41no—
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61#4111yescharacteristic
184C22×C4×C61#4111yescharacteristic
185C22×C4×C61#4111yescharacteristic
186C22×C4×C61#4111yescharacteristic
187C22×C4×C61#4111yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C22×Dic61—41no—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—22no—
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—41no—
206C2×D244—41no—
207C2×D244—41no—
208C2×D244—41no—
209C2×D244—41no—
210C2×D244—41no—
211C2×D244—41no—
212C2×D244—41no—
213C2×D244—41no—
214C2×D244—41no—
215C2×D244—41no—
216C2×D244—41no—
217C2×D244C2×D414yes—
218M16×C61—22no—
219M16×C61—22no—
220M16×C61—22no—
221M16×C61—22no—
222M16×C61—41no—
223M16×C61—41no—
224M16×C61—41no—
225M16×C61—41no—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C2×C8×C61—41no—
229C2×C8×C61—41no—
230C2×C8×C61—41no—
231C2×C8×C61—41no—
232C22⋊Dic61—22no—
233C22⋊Dic61—41no—
234#11758201—216no—
235#11758199—216no—
236C4⋊Dic61—22no—
237C4⋊Dic61—41no—
238C4×Dic61—22no—
239C4×Dic61—41no—
240#11758194—22no—
241#11758194—22no—
242#11758194—22no—
243#11758194—22no—
244#11758194—22no—
245#11758194—22no—
246#11758194C2×D414yes—
247#11758194C2×D414yes—
248C2×#92418—22no—
249C2×#92418—22no—
250C2×#92418—22no—
251C2×#92418—22no—
252C2×#92418—22no—
253C2×#92418—22no—
254C23×C61—22no—
255C23×C61—42no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—82no—
259C23×C61#12111yescharacteristic
260C23×C61#12111yescharacteristic
261C23×C61#12311yescharacteristic
262C23×C61#12311yescharacteristic
263C23×C61#12411yescharacteristic
264C23×C61#12411yescharacteristic
265C23×C61C2×#4111yescharacteristic
266C22×D61—24no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—42no—
270C22×D61—42no—
271C22×D61—42no—
272C22×D61—42no—
273C22×D61—84no—
274C22×D61—84no—
275C22×D61—84no—
276C22×D61—84no—
277C22×D61—84no—
278C22×D61—84no—
279C22×D61—84no—
280Q8×C61—22no—
281Q8×C61—22no—
282Q8×C61—41no—
283Q8×C61—41no—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—42no—
287D4×C61—42no—
288D4×C61—42no—
289D4×C61—42no—
290D4×C61—41no—
291D4×C61—41no—
292C2×C4×C61—22no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
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#12111yescharacteristic
312C2×C4×C61#12111yescharacteristic
313C2×C4×C61#12311yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61#12311yescharacteristic
316C2×C4×C61#12311yescharacteristic
317C2×C4×C61#12311yescharacteristic
318C2×C4×C61#12311yescharacteristic
319C2×C4×C61#12411yescharacteristic
320C2×C4×C61#12411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C2×C4×C61C22×D411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C2×#4111yescharacteristic
326C2×C4×C61C2×#4111yescharacteristic
327C2×Dic61—42no—
328C2×Dic61—82no—
329D244—24no—
330D244—24no—
331D244—42no—
332D244—42no—
333D244—42no—
334D244—42no—
335D244—42no—
336D244—42no—
337C8×C61—42no—
338C8×C61—42no—
339#92418—24no—
340#92418—24no—
341C2×#2048—611nomaximal, Sylow
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—42no—
350C22×C61—82no—
351C22×C61—82no—
352C22×C61—82no—
353C22×C61#39411yescharacteristic
354C22×C61#39411yescharacteristic
355C22×C61#39411yescharacteristic
356C22×C61#39411yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C22×C61C2×#12311yescharacteristic
359C22×C61C2×#12411yescharacteristic
360C2×D61—44no—
361C2×D61—84no—
362C2×D61—84no—
363C2×D61—84no—
364C2×D61—84no—
365C2×D61—84no—
366C2×D61—84no—
367C2×D61—84no—
368C4×C61—42no—
369C4×C61#39411yescharacteristic
370C4×C61#39411yescharacteristic
371C4×C61#39411yescharacteristic
372C4×C61#39411yescharacteristic
373C4×C61C2×#12011yescharacteristic
374C4×C61C2×#12111yescharacteristic
375C4×C61C2×#12111yescharacteristic
376C4×C61C2×#12311yescharacteristic
377Dic61—82no—
378C22×AGL(1,ℤ/8)—611no—
379C2×#430—611no—
380C2×#421—611no—
381C2×#418—611no—
382C2×#413D6111yescharacteristic, complemented
383C22×#100—611no—
384#2048—618no—
385C2×#344—611no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—21no—
391C2×C61—21no—
392C2×C61—82no—
393C2×C61#204812yescomplemented
394C2×C61C2×#39411yescharacteristic
395D61—84no—
396C22×#41C2×D6111yescharacteristic
397C23×D4—611no—
398C2×AGL(1,ℤ/8)—614no—
399C2×AGL(1,ℤ/8)—1222no—
400C2×AGL(1,ℤ/8)—1222no—
401C2×AGL(1,ℤ/8)—1222no—
402C2×AGL(1,ℤ/8)—1222no—
403C2×AGL(1,ℤ/8)—1222no—
404C22×SD16—1221no—
405C22×D8—1221no—
406C22×M16—611no—
407C22×M16—611no—
408C22×M16C2×D6111yescharacteristic
409C22×M16C2×D6111yescharacteristic
410C2×#117—611no—
411#430—614no—
412#430—1222no—
413C2×#108—1222no—
414#421—614no—
415#421—1222no—
416C2×#104—1222no—
417#418—614no—
418#418—1222no—
419C2×#102—1222no—
420#413—22no—
421#413C2×D6114yescomplemented
422C2×#101—21no—
423C2×#100—21no—
424C2×#100—614no—
425C2×#100—1222no—
426C2×#100—1222no—
427#344—614no—
428C61C2×#204811yescharacteristic, complemented, Sylow
429C25—1221no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41C22⋊D6112yes—
441C2×#41C22×D6112yes—
442C22×Q8C22⋊D6111yescharacteristic
443C22×D4—21no—
444C22×D4—612no—
445C22×D4—612no—
446C22×D4—612no—
447C22×D4—1221no—
448C22×D4—1221no—
449C22×D4—1221no—
450C22×D4—1221no—
451C22×D4—1221no—
452C22×D4—1221no—
453C22×D4—1221no—
454C22×D4—1221no—
455C22×D4—1221no—
456C22×D4—1221no—
457C22×D4—1221no—
458C22×D4C22⋊D6111yescharacteristic
459C23×C4—21no—
460C23×C4C22×D6111yescharacteristic
461AGL(1,ℤ/8)—1228no—
462AGL(1,ℤ/8)—1228no—
463AGL(1,ℤ/8)—1228no—
464AGL(1,ℤ/8)—1228no—
465C2×SD16—1224no—
466C2×SD16—1224no—
467C2×SD16—1224no—
468C2×D8—1224no—
469C2×D8—1224no—
470C2×D8—1224no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—21no—
481C2×M16—612no—
482C2×M16—612no—
483C2×M16—612no—
484C2×M16—612no—
485C2×M16—612no—
486C2×M16—612no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16—1221no—
491C2×M16—1221no—
492C2×M16—1221no—
493C2×M16C22×D6112yes—
494C2×M16C22×D6112yes—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—1221no—
498C22×C8—1221no—
499#117—612no—
500#117—1221no—
501#117—1221no—
502#117—1221no—
503C2×C4⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C42—1221no—
506#108—1228no—
507#104—1228no—
508#102—1228no—
509#101—24no—
510#100—24no—
511#100—1228no—
512C24—21no—
513C24—1222no—
514C24—1222no—
515C24—1222no—
516C24—4884no—
517C24—2441no—
518C24—2441no—
519C24—2441no—
520C24—2441no—
521C24#1175822211yescharacteristic
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—22no—
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—41no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C22⋊D6112yes—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—614no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—2441no—
572C2×D4—2441no—
573C2×D4—2441no—
574C2×D4—2441no—
575C2×D4—2441no—
576C2×D4—2441no—
577C2×D4—2441no—
578C2×D4—2441no—
579C2×D4—2441no—
580C2×D4—2441no—
581C2×D4—2441no—
582C2×D4—2441no—
583C2×D4C2×C22⋊D6112yes—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—2441no—
592C22×C4#1175822211yescharacteristic
593C22×C4#1175822211yescharacteristic
594C22×C4#1175822211yescharacteristic
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4D4×D6111yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4#1175822411yescharacteristic
602C22×C4#1175822411yescharacteristic
603C22×C4C2×C22⋊D6111yescharacteristic
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C23×D6111yescharacteristic
606SD16—12216no—
607D8—12216no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—614no—
617M16—614no—
618M16—1222no—
619M16—1222no—
620M16—1222no—
621M16—1222no—
622M16—1222no—
623M16—1222no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—1222no—
631C2×C8—1222no—
632C2×C8—1222no—
633C2×C8—1222no—
634C2×C8—1222no—
635C2×C8—1222no—
636C4⋊C4—1222no—
637C4⋊C4—2441no—
638C22⋊C4—1222no—
639C22⋊C4—2441no—
640C42—1222no—
641C42—2441no—
642C23—22no—
643C23—42no—
644C23—41no—
645C23—41no—
646C23—82no—
647C23—1224no—
648C23—4884no—
649C23—4884no—
650C23—4884no—
651C23—4884no—
652C23—4884no—
653C23—4884no—
654C23—4884no—
655C23—2442no—
656C23—2442no—
657C23—2442no—
658C23—2442no—
659C23—2442no—
660C23—2442no—
661C23#1451975011yescharacteristic
662C23#1451975011yescharacteristic
663C23#1451976011yescharacteristic
664C23#1451976011yescharacteristic
665C23#1451976311yescharacteristic
666C23#1451976311yescharacteristic
667C23C2×#1175822211yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—41no—
679D4—41no—
680D4—1224no—
681D4—1224no—
682D4—2442no—
683D4—2442no—
684D4—2442no—
685D4—2442no—
686D4—2442no—
687D4—2442no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—4882no—
696C2×C4—2442no—
697C2×C4#1451974511yescharacteristic
698C2×C4#1451974511yescharacteristic
699C2×C4#1451974511yescharacteristic
700C2×C4#1451974511yescharacteristic
701C2×C4#1451974911yescharacteristic
702C2×C4#1451974911yescharacteristic
703C2×C4#1451974911yescharacteristic
704C2×C4#1451974911yescharacteristic
705C2×C4#1451975011yescharacteristic
706C2×C4#1451975011yescharacteristic
707C2×C4#1451975011yescharacteristic
708C2×C4#1451975011yescharacteristic
709C2×C4#1451975011yescharacteristic
710C2×C4#1451975011yescharacteristic
711C2×C4#1451975911yescharacteristic
712C2×C4#1451975911yescharacteristic
713C2×C4#1451975911yescharacteristic
714C2×C4#1451975911yescharacteristic
715C2×C4#1451976011yescharacteristic
716C2×C4#1451976011yescharacteristic
717C2×C4#1451976311yescharacteristic
718C2×C4#1451976311yescharacteristic
719C2×C4C2×D4×D6111yescharacteristic
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C2×D4×D6111yescharacteristic
722C2×C4C22×C22⋊D6111yescharacteristic
723C2×C4C2×#1175822411yescharacteristic
724C2×C4C2×#1175822211yescharacteristic
725C8—42no—
726C8—42no—
727C8—1224no—
728C8—1224no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—4884no—
741C22—4884no—
742C22—4884no—
743C22—4884no—
744C22—4884no—
745C22—4884no—
746C22—4884no—
747C22—2444no—
748C22#1683967711yescharacteristic
749C22#1683967711yescharacteristic
750C22#1683967711yescharacteristic
751C22#1683967711yescharacteristic
752C22C2×#1451975011yescharacteristic
753C22C2×#1451976011yescharacteristic
754C22C2×#1451976311yescharacteristic
755C4—42no—
756C4—4882no—
757C4#1683967711yescharacteristic
758C4#1683967711yescharacteristic
759C4#1683967711yescharacteristic
760C4#1683967711yescharacteristic
761C4C2×#1451974511yescharacteristic
762C4C2×#1451974911yescharacteristic
763C4C2×#1451975011yescharacteristic
764C4C2×#1451975911yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—82no—
772C2—4884no—
773C2#2144709212yesdirect product factor
774C2C2×#1683967711yescharacteristic
subgroupG/H
centerC22#16839677
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#413C2
socleC22×C61#394
prime radicalC22×#14519802C2
hypercenterC2×#413D61
hypocenterC61C2×#2048
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#16839810C2semidirect
3. C2×#16839779C2semidirect
4. C2×#16839768C2semidirect
5. C22×#14519693C2semidirect
6. #21447092C2direct (N × H)
7. C2×#16839533C2semidirect
8. C2×C61×#413C2semidirect
22. #16839810C22semidirect
25. #16839779C22semidirect
28. #16839768C22semidirect
32. C2×#14519693C22semidirect
33. #16839533C22semidirect
38. C61×#413C22semidirect
382. C2×#413D61semidirect
393. C2×C61#2048semidirect
421. #413C2×D61semidirect
428. C61C2×#2048semidirect
773. C2#21447092direct (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×#168398102
C2×#168397792
C2×#168397682
C22×#145196932
#214470922
C2×#168395332
C2×C61×#4132
C2×#204861