Finite Group Databasebeta

← #29696028

Subgroups — #29696028

Order 15616.

1384 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840565C211yesmaximal, characteristic
2C2×#16839877C211yesmaximal, characteristic, complemented
3#21454692C211yesmaximal, characteristic, complemented
4#21454341C211yesmaximal, characteristic, complemented
5#21446728C211yesmaximal, characteristic, complemented
6#21446682C211yesmaximal, characteristic, complemented
7#21446330C211yesmaximal, characteristic, complemented
8#21446327C211yesmaximal, characteristic, complemented
9#21446195C211yesmaximal, characteristic, complemented
10#21446192C211yesmaximal, characteristic, complemented
11#21445881C211yesmaximal, characteristic, complemented
12#21445773C211yesmaximal, characteristic, complemented
13#21445771C211yesmaximal, characteristic, complemented
14#21445659C211yesmaximal, characteristic, complemented
15C61×#2897C211yesmaximal, characteristic, complemented
16C2×#14519823C2211yescharacteristic
17#16840565—24no—
18#16840565C418yescomplemented
19C2×#14519803—21no—
20C2×#14519803C2211yescharacteristic
21C2×#14519802—21no—
22C2×#14519802C2211yescharacteristic
23C2×#14519797—21no—
24C2×#14519797C2211yescharacteristic
25C22×#11758199—21no—
26C22×#11758199C2211yescharacteristic
27C2×#14519784C2211yescharacteristic
28C2×#14519783C2211yescharacteristic, complemented
29#16840242C2211yescharacteristic, complemented
30#16839877—24no—
31#16839862—21no—
32#16839860—21no—
33C4×#11758202—21no—
34C4×#11758199—21no—
35C2×#14519712C2211yescharacteristic, complemented
36C2×#14519710C2211yescharacteristic, complemented
37C2×#14519704C2211yescharacteristic
38C2×#14519704C2211yescharacteristic, complemented
39C2×#14519703C2211yescharacteristic, complemented
40#16839766C2211yescharacteristic, complemented
41#16839765—21no—
42#16839763C2211yescharacteristic
43#16839763C2211yescharacteristic, complemented
44#16839762—21no—
45#16839761C2211yescharacteristic, complemented
46#16839757—21no—
47C2×#14519699C2211yescharacteristic, complemented
48#102×D61—21no—
49C2×#14519694C2211yescharacteristic, complemented
50C2×#14519693C2211yescharacteristic, complemented
51#16839718C2211yescharacteristic, complemented
52C2×C8×Dic61C2211yescharacteristic, complemented
53#16839665C2211yescharacteristic, complemented
54#16839663C2211yescharacteristic, complemented
55#16839531C2211yescharacteristic, complemented
56#16839530C2211yescharacteristic, complemented
57#16839527C2211yescharacteristic, complemented
58#16839521C2211yescharacteristic, complemented
59C2×H(5,𝔽2)×C61C2211yescharacteristic
60C2×#131×C61C2211yescharacteristic, complemented
61C61×#520C2211yescharacteristic, complemented
62C61×#418—21no—
63C61×#418C2211yescharacteristic, complemented
64C61×#417—21no—
65C61×#417C2211yescharacteristic
66C61×#416—21no—
67C61×#416C2211yescharacteristic
68C2×#102×C61—21no—
69C2×#102×C61C2211yescharacteristic, complemented
70#14519823—22no—
71#14519823—22no—
72#14519823—41no—
73#14519823C2×C414yescomplemented
74C2×#11758226—21no—
75C2×#11758222—21no—
76C2×#11758222C2311yescharacteristic
77C22×D244—21no—
78C22×D244C2311yescharacteristic
79C2×D4×D61—21no—
80C2×D4×D61—41no—
81#14519803—22no—
82#14519803—28no—
83#14519803C2×C414yescomplemented
84#14519802—22no—
85#14519802—28no—
86#14519802C2×C414yescomplemented
87#14519797—28no—
88#14519797C2×C414yes—
89#14519797D414yes—
90C2×#11758202D411yescharacteristic
91C2×#11758200—21no—
92C2×#11758200D411yescharacteristic
93C2×#11758201—21no—
94C2×#11758201D411yescharacteristic
95C2×#11758199—21no—
96C2×#11758199—21no—
97C2×#11758199—28no—
98C2×#11758199—21no—
99C2×#11758199—21no—
100C2×#11758199—22no—
101C2×#11758199C2×C414yescomplemented
102C2×#11758199D411yescharacteristic
103#14519784—22no—
104#14519784C2×C414yescomplemented
105#14519783—22no—
106#14519783—41no—
107C2×#11758194—21no—
108C2×#11758194C2311yescharacteristic
109C2×#11758194C2311yescharacteristic
110C2×#11758194C2311yescharacteristic
111C2×#11758189—21no—
112C22×#92418—21no—
113C22×#92418C2311yescharacteristic
114C2×C8×D61—21no—
115C4×Dic122—21no—
116C4×D244—21no—
117#14519737—41no—
118#14519735—21no—
119C2×C4⋊Dic61C2311yescharacteristic
120C4⋊C4×D61—21no—
121C2×C22⋊Dic61—41no—
122C2×#11758198—41no—
123C2×C4×Dic61C2311yescharacteristic
124#14519712—22no—
125#14519710—21no—
126#14519710—21no—
127#14519704—22no—
128#14519704—22no—
129#14519703—22no—
130#14519701—21no—
131#14519701—21no—
132#14519700—21no—
133#14519699—21no—
134#14519699—21no—
135#14519698—21no—
136#14519698—21no—
137#14519697—21no—
138#14519697—21no—
139#14519697—21no—
140#14519694—41no—
141#14519693—41no—
142#14519688—21no—
143C4×#92418—21no—
144C8×Dic61—22no—
145H(5,𝔽2)×C61—22no—
146H(5,𝔽2)×C61—22no—
147H(5,𝔽2)×C61—41no—
148H(5,𝔽2)×C61C2×C414yescomplemented
149C2×#41×C61—21no—
150C2×#41×C61—21no—
151C2×#41×C61C2311yescharacteristic
152C2×#41×C61C2311yescharacteristic
153C22×D4×C61—21no—
154C22×D4×C61—21no—
155C22×D4×C61—41no—
156C22×D4×C61C2311yescharacteristic
157#131×C61—22no—
158#131×C61—41no—
159C2×M16×C61—21no—
160C2×M16×C61C2311yescharacteristic
161C22×C8×C61—21no—
162C22×C8×C61C2311yescharacteristic
163C4×Q8×C61—21no—
164C4×D4×C61—21no—
165C4×D4×C61—41no—
166#117×C61—21no—
167#117×C61C2311yescharacteristic
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61C2311yescharacteristic
170#103×C61—21no—
171#103×C61D411yescharacteristic
172#103×C61D411yescharacteristic
173#102×C61—21no—
174#102×C61—21no—
175#102×C61—21no—
176#102×C61—21no—
177#102×C61—21no—
178#102×C61D411yescharacteristic
179#102×C61D411yescharacteristic
180C24×C61—21no—
181C24×C61—41no—
182C23×D61—21no—
183C23×D61—41no—
184#41×C61—21no—
185#41×C61—21no—
186#41×C61—21no—
187#41×C61—21no—
188#41×C61—24no—
189#41×C61—24no—
190#41×C61—42no—
191#41×C61—42no—
192#41×C61C22×C412yes—
193#41×C61C22×C412yes—
194#41×C61C2×D412yes—
195#41×C61#4112yes—
196C2×Q8×C61C2×D411yescharacteristic
197C2×Q8×C61C2×D411yescharacteristic
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—24no—
201C2×D4×C61—24no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
209C2×D4×C61—41no—
210C2×D4×C61—41no—
211C2×D4×C61—44no—
212C2×D4×C61—44no—
213C2×D4×C61C22×C412yes—
214C2×D4×C61C2×D411yescharacteristic
215C2×D4×C61C2×D411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—41no—
220C22×C4×C61—41no—
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61—41no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226#11758226—24no—
227#11758226—42no—
228D4×D61—24no—
229D4×D61—42no—
230D4×D61—44no—
231D4×D61—44no—
232#11758222—21no—
233#11758222—21no—
234#11758222—24no—
235#11758222—42no—
236#11758222C22×C412yes—
237#11758222C2×D412yes—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244—21no—
241C2×D244—21no—
242C2×D244—24no—
243C2×D244—21no—
244C2×D244—42no—
245C2×D244—41no—
246C2×D244C22×C412yes—
247C2×D244C2×D411yescharacteristic
248C2×C4×D61—21no—
249C2×C4×D61—41no—
250C2×C4×D61—41no—
251C2×Dic122C2×D411yescharacteristic
252M16×C61—21no—
253M16×C61—21no—
254M16×C61—42no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—42no—
259C2×C8×C61C2×D411yescharacteristic
260C2×C8×C61C2×D411yescharacteristic
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—41no—
264C4⋊C4×C61C2×D411yescharacteristic
265C4⋊C4×C61C2×D411yescharacteristic
266C22⋊C4×C61—21no—
267C22⋊C4×C61—41no—
268C42×C61—21no—
269C42×C61—41no—
270C22⋊Dic61—82no—
271#11758202C22⋊C414yescomplemented
272#11758201—24no—
273#11758201C22⋊C414yescomplemented
274#11758200—24no—
275#11758200C22⋊C414yescomplemented
276#11758199—24no—
277#11758199—24no—
278#11758199—24no—
279#11758199—24no—
280#11758199C22⋊C414yescomplemented
281#11758198—41no—
282#11758198—82no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285#11758196—41no—
286C4×Dic61—21no—
287C4×Dic61—21no—
288C4×Dic61—41no—
289#11758194—21no—
290#11758194—24no—
291#11758194—21no—
292#11758194—21no—
293#11758194—21no—
294#11758194—21no—
295#11758194C22×C412yes—
296C2×#92418—21no—
297C2×#92418—24no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418C22×C412yes—
301C2×#92418C2×D412yes—
302C2×#92418C2×D411yescharacteristic
303C2×#92418C2×D411yescharacteristic
304#11758189—42no—
305C8×D61—42no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—22no—
309C23×C61—44no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—81no—
313C23×C61—81no—
314C23×C61—161no—
315C23×C61—161no—
316C23×C61H(5,𝔽2)11yescharacteristic
317C22×D61—21no—
318C22×D61—22no—
319C22×D61—44no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—81no—
323C22×D61—81no—
324C22×D61—161no—
325C22×D61—161no—
326Q8×C61—21no—
327Q8×C61—21no—
328Q8×C61C2×C22⋊C412yes—
329Q8×C61C4×D412yes—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—22no—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—21no—
337D4×C61—21no—
338D4×C61—44no—
339D4×C61—44no—
340D4×C61—41no—
341D4×C61—41no—
342D4×C61C2×C22⋊C412yes—
343D4×C61C4×D412yes—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—21no—
351C2×C4×C61—21no—
352C2×C4×C61—44no—
353C2×C4×C61—41no—
354C2×C4×C61—81no—
355C2×C4×C61—161no—
356C2×C4×C61C23×C411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C2×#4111yescharacteristic
361C2×C4×C61H(5,𝔽2)11yescharacteristic
362C22⋊D61—22no—
363C22⋊D61—22no—
364C22⋊D61—44no—
365C2×Dic61—21no—
366C2×Dic61—22no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—81no—
371D244—22no—
372D244—22no—
373D244—21no—
374D244—44no—
375D244—41no—
376D244—41no—
377D244C2×C22⋊C412yes—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—44no—
381C4×D61—161no—
382Dic122—21no—
383Dic122C2×C22⋊C412yes—
384C8×C61—21no—
385C8×C61—21no—
386C8×C61—41no—
387#92418—22no—
388#92418—41no—
389#92418—41no—
390#92418C2×C22⋊C412yes—
391#92418C2×C22⋊C412yes—
392#22466—611nomaximal, Sylow
393C22×C61—21no—
394C22×C61—21no—
395C22×C61—22no—
396C22×C61—22no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—42no—
402C22×C61—82no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—161no—
406C22×C61—164no—
407C22×C61#51811yescharacteristic
408C22×C61D4211yescharacteristic
409C22×C61#54611yescharacteristic
410C2×D61—22no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—42no—
414C2×D61—81no—
415C2×D61—81no—
416C2×D61—82no—
417C2×D61—164no—
418C2×D61—161no—
419C4×C61—22no—
420C4×C61—22no—
421C4×C61—41no—
422C4×C61—41no—
423C4×C61—81no—
424C4×C61C22×C22⋊C411yescharacteristic
425C4×C61C2×C4×D411yescharacteristic
426C4×C61D4211yescharacteristic
427C4×C61#54611yescharacteristic
428Dic61—22no—
429Dic61—42no—
430Dic61—81no—
431C2×#576—611no—
432C2×#443—611no—
433#2951—611no—
434#2897—611no—
435#2897D6111yescharacteristic, complemented
436#1978—611no—
437#1970—611no—
438#1907—611no—
439#1907—611no—
440#1883—611no—
441#1883—611no—
442#1816—611no—
443#1792—611no—
444#1792—611no—
445#1764—611no—
446C2×C61—21no—
447C2×C61—21no—
448C2×C61—42no—
449C2×C61—42no—
450C2×C61—82no—
451C2×C61D4×C22⋊C411yescharacteristic
452C2×C61#329011yescharacteristic
453C2×C61#329211yescharacteristic
454D61—42no—
455D61—82no—
456C2×H(5,𝔽2)—611no—
457C2×H(5,𝔽2)C2×D6111yescharacteristic
458#576—618no—
459#576—1224no—
460C2×AGL(1,ℤ/8)—611no—
461C2×AGL(1,ℤ/8)—611no—
462C2×AGL(1,ℤ/8)—1221no—
463C2×AGL(1,ℤ/8)—1221no—
464C2×#135—611no—
465C2×#135—1221no—
466C22×D8—611no—
467C22×D8—1221no—
468C2×#131—611no—
469C2×#131—611no—
470C2×#131C2×D6111yescharacteristic, complemented
471#520—611no—
472#520C2×D6111yescharacteristic, complemented
473#443—1224no—
474#440—1221no—
475#440—1221no—
476C4×Q16—1221no—
477C4×D8—1221no—
478C2×#108—611no—
479C2×#107—611no—
480C2×#104—611no—
481C2×#104—611no—
482C2×#104—611no—
483#418—21no—
484#418—611no—
485#418—1221no—
486#418C2×D6111yescharacteristic, complemented
487#417—21no—
488#417—611no—
489#417—611no—
490#417—611no—
491#417—1221no—
492#417C2×D6111yescharacteristic
493#416—21no—
494#416—1221no—
495#416C2×D6111yescharacteristic
496C2×#102—21no—
497C2×#102—611no—
498C2×#102—1221no—
499C2×#102C2×D6111yescharacteristic, complemented
500C2×#100—611no—
501C2×#100—611no—
502#405—611no—
503C2×C4×C8—611no—
504#390—611no—
505#390—611no—
506#343—611no—
507#343—611no—
508#341—611no—
509#339—611no—
510C61#2246611yescharacteristic, complemented, Sylow
511H(5,𝔽2)—22no—
512H(5,𝔽2)—22no—
513H(5,𝔽2)—41no—
514H(5,𝔽2)—614no—
515H(5,𝔽2)—1222no—
516H(5,𝔽2)—1222no—
517H(5,𝔽2)—2441no—
518H(5,𝔽2)C4×D6114yescomplemented
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—611no—
522C2×#41—1221no—
523C2×#41—1221no—
524C2×#41C22×D6111yescharacteristic
525C2×#41C22×D6111yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—41no—
529C22×D4—611no—
530C22×D4—1221no—
531C22×D4—1221no—
532C22×D4—2441no—
533C22×D4C22×D6111yescharacteristic
534AGL(1,ℤ/8)—614no—
535AGL(1,ℤ/8)—614no—
536AGL(1,ℤ/8)—1228no—
537AGL(1,ℤ/8)—1228no—
538AGL(1,ℤ/8)—1222no—
539AGL(1,ℤ/8)—1222no—
540#135—614no—
541#135—614no—
542#135—1228no—
543C2×Q16—611no—
544C2×SD16—611no—
545C2×SD16—611no—
546C2×SD16—1221no—
547C2×SD16—1221no—
548C2×D8—611no—
549C2×D8—614no—
550C2×D8—1221no—
551C2×D8—1221no—
552C2×D8—1222no—
553C2×D8—1228no—
554C2×D8—1221no—
555C2×D8—1221no—
556#131—22no—
557#131—41no—
558#131—614no—
559#131—1222no—
560#131—1222no—
561#131—2441no—
562C2×M16—21no—
563C2×M16—611no—
564C2×M16—611no—
565C2×M16—611no—
566C2×M16—1221no—
567C2×M16—1221no—
568C2×M16C22×D6111yescharacteristic
569C22×C8—21no—
570C22×C8—611no—
571C22×C8—1221no—
572C22×C8—1221no—
573C22×C8C22×D6111yescharacteristic
574C4×Q8—21no—
575C4×Q8—1221no—
576C4×D4—21no—
577C4×D4—41no—
578C4×D4—1221no—
579C4×D4—2441no—
580#117—21no—
581#117—1221no—
582#117C22×D6111yescharacteristic
583C2×C4⋊C4—21no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—1221no—
586C2×C4⋊C4C22×D6111yescharacteristic
587C2×C22⋊C4—2441no—
588C2×C22⋊C4—2441no—
589C2×C42—611no—
590#108—1222no—
591#107—1221no—
592#107—1221no—
593#104—1222no—
594#104—1222no—
595#104—1222no—
596#103—21no—
597#103—1221no—
598#103—1221no—
599#103—1221no—
600#103C22⋊D6111yescharacteristic
601#103C22⋊D6111yescharacteristic
602#102—21no—
603#102—21no—
604#102—21no—
605#102—21no—
606#102—21no—
607#102—1221no—
608#102—1221no—
609#102—1221no—
610#102—1221no—
611#102—1221no—
612#102—1221no—
613#102—1221no—
614#102C22⋊D6111yescharacteristic
615#102C22⋊D6111yescharacteristic
616#100—2441no—
617#100—2441no—
618#97—1221no—
619C4×C8—1221no—
620C4×C8—1222no—
621C24—21no—
622C24—41no—
623C24—1221no—
624C24—2441no—
625#41—21no—
626#41—21no—
627#41—21no—
628#41—21no—
629#41—24no—
630#41—24no—
631#41—42no—
632#41—42no—
633#41—612no—
634#41—612no—
635#41—1224no—
636#41—1221no—
637#41—1221no—
638#41—1224no—
639#41—2442no—
640#41—2442no—
641#41C2×C4×D6112yes—
642#41C2×C4×D6112yes—
643#41#1175822212yes—
644#41D4×D6112yes—
645C2×Q8—611no—
646C2×Q8D4×D6111yescharacteristic
647C2×Q8C2×C22⋊D6111yescharacteristic
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—41no—
660C2×D4—41no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4—612no—
664C2×D4—611no—
665C2×D4—1224no—
666C2×D4—1221no—
667C2×D4—1224no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—2442no—
674C2×D4—2441no—
675C2×D4—2442no—
676C2×D4—2441no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4C2×C4×D6112yes—
680C2×D4D4×D6111yescharacteristic
681C2×D4C2×C22⋊D6111yescharacteristic
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—41no—
686C22×C4—41no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—2441no—
691C22×C4—2441no—
692C22×C4C23×D6111yescharacteristic
693Q16—614no—
694SD16—614no—
695SD16—614no—
696SD16—1224no—
697SD16—1224no—
698D8—614no—
699D8—1224no—
700D8—1224no—
701D8—1224no—
702D8—1224no—
703M16—21no—
704M16—21no—
705M16—42no—
706M16—612no—
707M16—1224no—
708M16—1221no—
709M16—1221no—
710M16—1221no—
711M16—1221no—
712M16—1221no—
713M16—2442no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—42no—
718C2×C8—612no—
719C2×C8—611no—
720C2×C8—612no—
721C2×C8—611no—
722C2×C8—1224no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—2442no—
727C2×C8C2×C22⋊D6111yescharacteristic
728C2×C8C2×C22⋊D6111yescharacteristic
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—41no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—2441no—
735C4⋊C4C2×C22⋊D6111yescharacteristic
736C4⋊C4C2×C22⋊D6111yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—41no—
739C22⋊C4—4882no—
740C22⋊C4—4882no—
741C22⋊C4—2441no—
742C42—21no—
743C42—41no—
744C42—1221no—
745C42—1221no—
746C42—2441no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—44no—
751C23—41no—
752C23—41no—
753C23—81no—
754C23—81no—
755C23—161no—
756C23—161no—
757C23—1221no—
758C23—1222no—
759C23—9761no—
760C23—9761no—
761C23—4881no—
762C23—4881no—
763C23—2444no—
764C23—2441no—
765C23—2441no—
766C23#1451982211yescharacteristic
767Q8—21no—
768Q8—21no—
769Q8—612no—
770Q8—1221no—
771Q8C22⋊C4×D6112yes—
772Q8C4×C22⋊D6112yes—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—21no—
780D4—21no—
781D4—44no—
782D4—44no—
783D4—41no—
784D4—41no—
785D4—612no—
786D4—1222no—
787D4—1222no—
788D4—1222no—
789D4—1222no—
790D4—1221no—
791D4—2444no—
792D4—2444no—
793D4—2441no—
794D4—2441no—
795D4C22⋊C4×D6112yes—
796D4C4×C22⋊D6112yes—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—44no—
806C2×C4—41no—
807C2×C4—81no—
808C2×C4—161no—
809C2×C4—1221no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—9761no—
814C2×C4—4881no—
815C2×C4—2444no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4C22×C4×D6111yescharacteristic
820C2×C4C2×D4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C22×C22⋊D6111yescharacteristic
823C2×C4C2×#1175822211yescharacteristic
824C2×C4#1451982211yescharacteristic
825C8—21no—
826C8—21no—
827C8—41no—
828C8—612no—
829C8—612no—
830C8—1222no—
831C8—2441no—
832C8—2441no—
833C22—21no—
834C22—21no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22—161no—
846C22—164no—
847C22—1222no—
848C22—9761no—
849C22—9764no—
850C22—4882no—
851C22—4881no—
852C22—4881no—
853C22—2442no—
854C22—2441no—
855C22—2441no—
856C22#1684023511yescharacteristic
857C22D4×C22⋊D6111yescharacteristic
858C22#1684040211yescharacteristic
859C4—22no—
860C4—22no—
861C4—41no—
862C4—41no—
863C4—81no—
864C4—1222no—
865C4—4881no—
866C4—2442no—
867C4C2×C22⋊C4×D6111yescharacteristic
868C4C2×C4×C22⋊D6111yescharacteristic
869C4D4×C22⋊D6111yescharacteristic
870C4#1684040211yescharacteristic
871C2—21no—
872C2—21no—
873C2—42no—
874C2—42no—
875C2—82no—
876C2—4882no—
877C2—2442no—
878C2C22⋊C4×C22⋊D6111yescharacteristic
879C2#2145759911yescharacteristic
880C2#2145761611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2897C2
socleC22×C61D42
prime radicalC2×#16840565C2
cosocleC22×C4×C61C24
hypercenter#2897D61
hypocenterC61#22466
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2897

Complements

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

NH ≅ G/Ntype
2. C2×#16839877C2semidirect
3. #21454692C2semidirect
4. #21454341C2semidirect
5. #21446728C2semidirect
6. #21446682C2semidirect
7. #21446330C2semidirect
8. #21446327C2semidirect
9. #21446195C2semidirect
10. #21446192C2semidirect
11. #21445881C2semidirect
12. #21445773C2semidirect
13. #21445771C2semidirect
14. #21445659C2semidirect
15. C61×#2897C2semidirect
18. #16840565C4semidirect
28. C2×#14519783C22semidirect
29. #16840242C22semidirect
35. C2×#14519712C22semidirect
36. C2×#14519710C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519703C22semidirect
40. #16839766C22semidirect
43. #16839763C22semidirect
45. #16839761C22semidirect
47. C2×#14519699C22semidirect
49. C2×#14519694C22semidirect
50. C2×#14519693C22semidirect
51. #16839718C22semidirect
52. C2×C8×Dic61C22semidirect
53. #16839665C22semidirect
54. #16839663C22semidirect
55. #16839531C22semidirect
56. #16839530C22semidirect
57. #16839527C22semidirect
58. #16839521C22semidirect
60. C2×#131×C61C22semidirect
61. C61×#520C22semidirect
63. C61×#418C22semidirect
69. C2×#102×C61C22semidirect
73. #14519823C2×C4semidirect
83. #14519803C2×C4semidirect
86. #14519802C2×C4semidirect
101. C2×#11758199C2×C4semidirect
104. #14519784C2×C4semidirect
148. H(5,𝔽2)×C61C2×C4semidirect
271. #11758202C22⋊C4semidirect
273. #11758201C22⋊C4semidirect
275. #11758200C22⋊C4semidirect
280. #11758199C22⋊C4semidirect
435. #2897D61semidirect
470. C2×#131C2×D61semidirect
472. #520C2×D61semidirect
486. #418C2×D61semidirect
499. C2×#102C2×D61semidirect
510. C61#22466semidirect
518. H(5,𝔽2)C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405652
C2×#168398772
#214546922
#214543412
#214467282
#214466822
#214463302
#214463272
#214461952
#214461922
#214458812
#214457732
#214457712
#214456592
C61×#28972
#2246661