Finite Group Databasebeta

← C2×#21447091 #29707842

Subgroups — C2×#21447091 #29707842

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×#14519803C211yesmaximal, characteristic
2C2×#16839811C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic, complemented
4C2×#16839767C211yesmaximal, characteristic, complemented
5C2×#16839744C211yesmaximal, characteristic, complemented
6#21447091C218yesmaximal, direct product factor
7C2×#16839533C211yesmaximal, characteristic, complemented
8C22×#100×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C2×#14519803—22no—
11C2×#14519803—22no—
12C2×#14519803—22no—
13C2×#14519803—22no—
14C2×#14519803—22no—
15C2×#14519803C2214yes—
16C22×#11758200—21no—
17C22×#11758199—21no—
18C22×#11758194C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16839811—22no—
22#16839811C2214yescomplemented
23C2×#14519713—22no—
24#16839778—22no—
25#16839778C2214yescomplemented
26C2×#14519703—22no—
27#16839767—22no—
28#16839767C2214yescomplemented
29C2×#14519698—22no—
30#16839744—22no—
31#16839744C2214yescomplemented
32C2×#14519695—21no—
33C2×#14519693—21no—
34#16839533C2214yescomplemented
35C23×D4×C61C2211yescharacteristic
36C22×M16×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C2×#100×C61—22no—
39C2×#100×C61—22no—
40C2×#100×C61C2214yescomplemented
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222—21no—
51C2×#11758222D412yes—
52C2×#11758222C2312yes—
53C22×Dic122D411yescharacteristic
54C22×D244D411yescharacteristic
55C22×C22⋊D61—21no—
56C22×C4×D61—21no—
57#14519803—28no—
58#14519803—28no—
59#14519803—28no—
60#14519803—28no—
61C2×#11758200—24no—
62C2×#11758200—24no—
63C2×#11758200—24no—
64C2×#11758199—24no—
65C2×#11758199—24no—
66C2×#11758199—24no—
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194—21no—
70C2×#11758194—21no—
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758194—21no—
74C2×#11758194—21no—
75C2×#11758194D412yes—
76C2×#11758194D412yes—
77C2×#11758194C2312yes—
78C2×#11758194C2312yes—
79C22×#92418—21no—
80C22×#92418—21no—
81#14519736—21no—
82#14519736—21no—
83#14519736—21no—
84#14519736C2312yes—
85C2×C4⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C4×Dic61—21no—
88#14519713—28no—
89#14519703—28no—
90#14519698—28no—
91#14519695—24no—
92#14519693—24no—
93C25×C61—21no—
94C22×D4×C61—21no—
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61—21no—
98C22×D4×C61—21no—
99C22×D4×C61—21no—
100C22×D4×C61—21no—
101C22×D4×C61—21no—
102C22×D4×C61—21no—
103C22×D4×C61—21no—
104C22×D4×C61—21no—
105C22×D4×C61D412yes—
106C22×D4×C61D412yes—
107C22×D4×C61C2312yes—
108C23×C4×C61C2311yescharacteristic
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×C61D412yes—
118C2×M16×C61D412yes—
119C2×M16×C61C2312yes—
120C2×M16×C61C2312yes—
121C22×C8×C61—21no—
122C22×C8×C61—21no—
123#100×C61—28no—
124C24×C61—22no—
125C24×C61—22no—
126C24×C61—22no—
127C24×C61—41no—
128C24×C61—41no—
129C24×C61—41no—
130C24×C61—41no—
131C24×C61—84no—
132C24×C61#4111yescharacteristic
133C23×D61—21no—
134C2×D4×C61—22no—
135C2×D4×C61—22no—
136C2×D4×C61—22no—
137C2×D4×C61—22no—
138C2×D4×C61—22no—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—22no—
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61—41no—
159C2×D4×C61—41no—
160C2×D4×C61—41no—
161C2×D4×C61C2×D414yes—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×C4×C61C2×D411yescharacteristic
170C22×C4×C61#4111yescharacteristic
171C22×C4×C61#4111yescharacteristic
172C22×C4×C61#4111yescharacteristic
173C22×C4×C61#4111yescharacteristic
174C22×C4×C61#4111yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C2×C22⋊D61—22no—
177C2×C22⋊D61—22no—
178C2×C22⋊D61—41no—
179C2×C22⋊D61—41no—
180C2×C22⋊D61—41no—
181C2×C22⋊D61—41no—
182C22×Dic61—21no—
183C22×Dic61—41no—
184#11758222—22no—
185#11758222—22no—
186#11758222—22no—
187#11758222—22no—
188#11758222—22no—
189#11758222—22no—
190#11758222—22no—
191#11758222—22no—
192#11758222—41no—
193#11758222—41no—
194#11758222—41no—
195#11758222—41no—
196#11758222—41no—
197#11758222—41no—
198#11758222—41no—
199#11758222—41no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244C2×D412yes—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—41no—
209C2×C4×D61—41no—
210C2×C4×D61—41no—
211C2×C4×D61—41no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122C2×D412yes—
218M16×C61—22no—
219M16×C61—22no—
220M16×C61—22no—
221M16×C61—22no—
222M16×C61—22no—
223M16×C61—41no—
224M16×C61—41no—
225M16×C61C2×D414yes—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C2×C8×C61—22no—
230C2×C8×C61—41no—
231C2×C8×C61—41no—
232C22⋊Dic61—22no—
233C22⋊Dic61—41no—
234#11758200—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—41no—
246#11758194—41no—
247#11758194C2×D414yes—
248C2×#92418—22no—
249C2×#92418—22no—
250C2×#92418—22no—
251C2×#92418—22no—
252C2×#92418—41no—
253C2×#92418—41no—
254C23×C61—24no—
255C23×C61—42no—
256C23×C61—42no—
257C23×C61—42no—
258C23×C61—42no—
259C23×C61—42no—
260C23×C61—42no—
261C23×C61—42no—
262C23×C61—84no—
263C23×C61—84no—
264C23×C61—84no—
265C23×C61—84no—
266C23×C61—84no—
267C23×C61—84no—
268C23×C61—84no—
269C23×C61#12111yescharacteristic
270C23×C61#12111yescharacteristic
271C23×C61#12311yescharacteristic
272C23×C61#12311yescharacteristic
273C23×C61#12411yescharacteristic
274C23×C61#12411yescharacteristic
275C23×C61C2×#4111yescharacteristic
276C22×D61—22no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—82no—
280D4×C61—24no—
281D4×C61—24no—
282D4×C61—42no—
283D4×C61—42no—
284D4×C61—42no—
285D4×C61—42no—
286D4×C61—42no—
287D4×C61—42no—
288C2×C4×C61#12011yescharacteristic
289C2×C4×C61#12011yescharacteristic
290C2×C4×C61#12011yescharacteristic
291C2×C4×C61#12011yescharacteristic
292C2×C4×C61#12111yescharacteristic
293C2×C4×C61#12111yescharacteristic
294C2×C4×C61#12111yescharacteristic
295C2×C4×C61#12111yescharacteristic
296C2×C4×C61#12111yescharacteristic
297C2×C4×C61#12111yescharacteristic
298C2×C4×C61#12111yescharacteristic
299C2×C4×C61#12111yescharacteristic
300C2×C4×C61#12111yescharacteristic
301C2×C4×C61#12111yescharacteristic
302C2×C4×C61#12311yescharacteristic
303C2×C4×C61#12311yescharacteristic
304C2×C4×C61#12311yescharacteristic
305C2×C4×C61#12311yescharacteristic
306C2×C4×C61#12311yescharacteristic
307C2×C4×C61#12311yescharacteristic
308C2×C4×C61#12411yescharacteristic
309C2×C4×C61#12411yescharacteristic
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C22⋊D61—42no—
317C22⋊D61—42no—
318C22⋊D61—42no—
319C22⋊D61—42no—
320C2×Dic61—22no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—42no—
324C2×Dic61—82no—
325D244—22no—
326D244—22no—
327D244—41no—
328D244—41no—
329C4×D61—42no—
330C4×D61—42no—
331C4×D61—42no—
332C4×D61—42no—
333Dic122—22no—
334Dic122—22no—
335Dic122—41no—
336Dic122—41no—
337C8×C61—24no—
338C8×C61—42no—
339#92418—24no—
340#92418—42no—
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—44no—
350C22×C61—84no—
351C22×C61—84no—
352C22×C61—84no—
353C22×C61—84no—
354C22×C61—84no—
355C22×C61—84no—
356C22×C61—84no—
357C22×C61#39411yescharacteristic
358C22×C61#39411yescharacteristic
359C22×C61#39411yescharacteristic
360C22×C61#39411yescharacteristic
361C22×C61C2×#12111yescharacteristic
362C22×C61C2×#12311yescharacteristic
363C22×C61C2×#12411yescharacteristic
364C2×D61—42no—
365C2×D61—82no—
366C2×D61—82no—
367C2×D61—82no—
368C4×C61#39411yescharacteristic
369C4×C61#39411yescharacteristic
370C4×C61#39411yescharacteristic
371C4×C61#39411yescharacteristic
372C4×C61C2×#12011yescharacteristic
373C4×C61C2×#12111yescharacteristic
374C4×C61C2×#12111yescharacteristic
375C4×C61C2×#12311yescharacteristic
376Dic61—42no—
377Dic61—82no—
378C22×AGL(1,ℤ/8)—611no—
379C2×#430—611no—
380C2×#421—611no—
381C2×#418—611no—
382C2×#413—611no—
383C22×#100D6111yescharacteristic, complemented
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—84no—
393C2×C61#204812yescomplemented
394C2×C61C2×#39411yescharacteristic
395D61—82no—
396C22×#41—611no—
397C23×D4C2×D6111yescharacteristic
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—614no—
421#413—1222no—
422C2×#101—1221no—
423C2×#100—22no—
424C2×#100—22no—
425C2×#100—1221no—
426C2×#100C2×D6114yescomplemented
427#344—614no—
428C61C2×#204811yescharacteristic, complemented, Sylow
429C25—21no—
430C2×#41—612no—
431C2×#41—612no—
432C2×#41—1221no—
433C2×#41—1221no—
434C2×#41—1221no—
435C2×#41—1221no—
436C2×#41—1221no—
437C2×#41—1221no—
438C2×#41—1221no—
439C2×#41—1221no—
440C2×#41—1221no—
441C2×#41—1221no—
442C22×Q8—611no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—611no—
455C22×D4—1221no—
456C22×D4D24412yes—
457C22×D4D24412yes—
458C22×D4C22×D6112yes—
459C23×C4—1221no—
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—612no—
480C2×M16—612no—
481C2×M16—612no—
482C2×M16—612no—
483C2×M16—1221no—
484C2×M16—1221no—
485C2×M16—1221no—
486C2×M16—1221no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16—1221no—
491C2×M16C22⋊D6112yes—
492C2×M16C22⋊D6112yes—
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—1224no—
510#100—28no—
511#100—1224no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—41no—
516C24—41no—
517C24—41no—
518C24—41no—
519C24—84no—
520C24—1221no—
521C24#1175822211yescharacteristic
522#41—1222no—
523#41—1222no—
524#41—1222no—
525#41—1222no—
526#41—1222no—
527#41—1222no—
528#41—1222no—
529#41—1222no—
530#41—2441no—
531#41—2441no—
532#41—2441no—
533#41—2441no—
534#41—2441no—
535#41—2441no—
536#41—2441no—
537#41—2441no—
538C2×Q8—612no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—1221no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—612no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C2×D4—1221no—
579C2×D4—2441no—
580C2×D4—2441no—
581C2×D4—2441no—
582C2×D4—2441no—
583C2×D4C2×D24414yes—
584C22×C4—1221no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—2441no—
588C22×C4—2441no—
589C22×C4—2441no—
590C22×C4—2441no—
591C22×C4—2441no—
592C22×C4C2×D24411yescharacteristic
593C22×C4C2×D24411yescharacteristic
594C22×C4#1175822211yescharacteristic
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4#1175822411yescharacteristic
600C22×C4#1175822411yescharacteristic
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—22no—
613M16—41no—
614M16—41no—
615M16—614no—
616M16—1222no—
617M16—1222no—
618M16—1222no—
619M16—1222no—
620M16—1222no—
621M16—2441no—
622M16—2441no—
623M16C2×C22⋊D6114yes—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—1222no—
631C2×C8—1222no—
632C2×C8—1222no—
633C2×C8—1222no—
634C2×C8—2441no—
635C2×C8—2441no—
636C4⋊C4—1222no—
637C4⋊C4—2441no—
638C22⋊C4—1222no—
639C22⋊C4—2441no—
640C42—1222no—
641C42—2441no—
642C23—24no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—1222no—
658C23—4882no—
659C23—2441no—
660C23—2441no—
661C23#1451975111yescharacteristic
662C23#1451975111yescharacteristic
663C23#1451975911yescharacteristic
664C23#1451975911yescharacteristic
665C23#1451976311yescharacteristic
666C23#1451976311yescharacteristic
667C23C2×#1175822211yescharacteristic
668Q8—1222no—
669Q8—1222no—
670Q8—2441no—
671Q8—2441no—
672D4—24no—
673D4—24no—
674D4—42no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—1222no—
681D4—1222no—
682D4—2442no—
683D4—2442no—
684D4—2442no—
685D4—2442no—
686D4—2441no—
687D4—2441no—
688C2×C4—1222no—
689C2×C4—4882no—
690C2×C4—2442no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4#1451974711yescharacteristic
698C2×C4#1451974711yescharacteristic
699C2×C4#1451974711yescharacteristic
700C2×C4#1451974711yescharacteristic
701C2×C4#1451974811yescharacteristic
702C2×C4#1451974811yescharacteristic
703C2×C4#1451974811yescharacteristic
704C2×C4#1451974811yescharacteristic
705C2×C4#1451974911yescharacteristic
706C2×C4#1451974911yescharacteristic
707C2×C4#1451974911yescharacteristic
708C2×C4#1451974911yescharacteristic
709C2×C4#1451975111yescharacteristic
710C2×C4#1451975111yescharacteristic
711C2×C4#1451975911yescharacteristic
712C2×C4#1451975911yescharacteristic
713C2×C4#1451976111yescharacteristic
714C2×C4#1451976111yescharacteristic
715C2×C4#1451976111yescharacteristic
716C2×C4#1451976111yescharacteristic
717C2×C4#1451976311yescharacteristic
718C2×C4#1451976311yescharacteristic
719C2×C4C2×D4×D6111yescharacteristic
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C22×C22⋊D6111yescharacteristic
722C2×C4C22×D24411yescharacteristic
723C2×C4C2×#1175822411yescharacteristic
724C2×C4C2×#1175822411yescharacteristic
725C8—24no—
726C8—42no—
727C8—1224no—
728C8—2442no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—44no—
737C22—84no—
738C22—84no—
739C22—84no—
740C22—84no—
741C22—84no—
742C22—84no—
743C22—84no—
744C22—4882no—
745C22—4882no—
746C22—4882no—
747C22—2442no—
748C22#1683967811yescharacteristic
749C22#1683967811yescharacteristic
750C22#1683967811yescharacteristic
751C22#1683967811yescharacteristic
752C22C2×#1451975111yescharacteristic
753C22C2×#1451975911yescharacteristic
754C22C2×#1451976311yescharacteristic
755C4—4882no—
756C4—2442no—
757C4#1683967811yescharacteristic
758C4#1683967811yescharacteristic
759C4#1683967811yescharacteristic
760C4#1683967811yescharacteristic
761C4C2×#1451974711yescharacteristic
762C4C2×#1451974811yescharacteristic
763C4C2×#1451974911yescharacteristic
764C4C2×#1451976111yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—84no—
772C2—4882no—
773C2#2144709112yesdirect product factor
774C2C2×#1683967811yescharacteristic
subgroupG/H
centerC22#16839678
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#100×C61C2
socleC22×C61#394
prime radicalC22×#14519803C2
hypercenterC22×#100D61
hypocenterC61C2×#2048
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#100

Complements

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

NH ≅ G/Ntype
2. C2×#16839811C2semidirect
3. C2×#16839778C2semidirect
4. C2×#16839767C2semidirect
5. C2×#16839744C2semidirect
6. #21447091C2direct (N × H)
7. C2×#16839533C2semidirect
8. C22×#100×C61C2semidirect
22. #16839811C22semidirect
25. #16839778C22semidirect
28. #16839767C22semidirect
31. #16839744C22semidirect
34. #16839533C22semidirect
40. C2×#100×C61C22semidirect
383. C22×#100D61semidirect
393. C2×C61#2048semidirect
426. C2×#100C2×D61semidirect
428. C61C2×#2048semidirect
773. C2#21447091direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198032
C2×#168398112
C2×#168397782
C2×#168397672
C2×#168397442
#214470912
C2×#168395332
C22×#100×C612
C2×#204861