Finite Group Databasebeta

← #29696025

Subgroups — #29696025

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×#16839876C211yesmaximal, characteristic, complemented
3#21454690C211yesmaximal, characteristic, complemented
4#21454345C211yesmaximal, characteristic, complemented
5#21454343C211yesmaximal, characteristic, complemented
6#21446726C211yesmaximal, characteristic, complemented
7#21446684C211yesmaximal, characteristic, complemented
8#21446325C211yesmaximal, characteristic, complemented
9#21446324C211yesmaximal, characteristic, complemented
10#21446198C211yesmaximal, characteristic, complemented
11#21446193C211yesmaximal, characteristic, complemented
12#21445881C211yesmaximal, characteristic, complemented
13#21445774C211yesmaximal, characteristic, complemented
14#21445657C211yesmaximal, characteristic, complemented
15C61×#1792C211yesmaximal, 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×#14519785C2211yescharacteristic, complemented
28C2×#14519784C2211yescharacteristic
29C2×#14519784C2211yescharacteristic, complemented
30#16840245C2211yescharacteristic, complemented
31#16840243C2211yescharacteristic, complemented
32#16839876—24no—
33#16839865—21no—
34#16839859—21no—
35#16839854—21no—
36#16839842—21no—
37C2×#14519712C2211yescharacteristic, complemented
38C2×#14519710C2211yescharacteristic, complemented
39C2×#14519705C2211yescharacteristic, complemented
40#16839768C2211yescharacteristic, complemented
41#16839767—21no—
42#16839767C2211yescharacteristic, complemented
43#16839765—21no—
44#16839764C2211yescharacteristic, complemented
45#16839763—21no—
46#16839763C2211yescharacteristic
47#16839762—21no—
48#16839758—21no—
49#16839758C2211yescharacteristic
50#16839757—21no—
51C2×#14519698—21no—
52C2×#14519698C2211yescharacteristic, complemented
53C2×#14519697C2211yescharacteristic, complemented
54#102×D61—21no—
55C2×#14519693C2211yescharacteristic, complemented
56#16839720C2211yescharacteristic, complemented
57C2×C4×#92418C2211yescharacteristic, complemented
58#16839664C2211yescharacteristic, complemented
59#16839531C2211yescharacteristic, complemented
60#16839530C2211yescharacteristic, complemented
61#16839526C2211yescharacteristic, complemented
62#16839522C2211yescharacteristic, complemented
63C2×H(5,𝔽2)×C61C2211yescharacteristic
64C2×#104×C61C2211yescharacteristic
65C2×#104×C61C2211yescharacteristic, complemented
66C61×#417C2211yescharacteristic
67C61×#417C2211yescharacteristic, complemented
68C2×#100×C61C2211yescharacteristic, complemented
69C61×#390C2211yescharacteristic, 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#14519785—22no—
104#14519785—41no—
105#14519784—22no—
106#14519784—22no—
107#14519784—41no—
108#14519784C2×C414yescomplemented
109C2×#11758194—21no—
110C2×#11758194—21no—
111C2×#11758194C2311yescharacteristic
112C2×#11758194C2311yescharacteristic
113C2×#11758189—21no—
114C22×#92418—21no—
115C22×#92418—21no—
116C22×#92418C2311yescharacteristic
117C22×#92418C2311yescharacteristic
118C2×C8×D61—21no—
119Q8×Dic61—21no—
120#14519742—21no—
121D4×Dic61—21no—
122D4×Dic61—41no—
123#14519739—21no—
124C4×C22⋊D61—41no—
125#14519736—21no—
126#14519736C2311yescharacteristic
127#14519735—21no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61C2311yescharacteristic
130C4⋊C4×D61—21no—
131C2×#11758198—41no—
132#14519712—22no—
133#14519710—21no—
134#14519710—21no—
135#14519705—22no—
136#14519702—21no—
137#14519701—21no—
138#14519701D411yescharacteristic
139#14519701D411yescharacteristic
140#14519699—21no—
141#14519699—21no—
142#14519699—21no—
143#14519698—21no—
144#14519698—21no—
145#14519698—21no—
146#14519698—21no—
147#14519698—21no—
148#14519698D411yescharacteristic
149#14519698D411yescharacteristic
150#14519697—21no—
151#14519697—21no—
152#14519693—41no—
153#14519687—21no—
154C4×#92418—22no—
155C8×Dic61—21no—
156H(5,𝔽2)×C61—22no—
157H(5,𝔽2)×C61—22no—
158H(5,𝔽2)×C61—41no—
159H(5,𝔽2)×C61C2×C414yescomplemented
160C2×#41×C61—21no—
161C2×#41×C61—21no—
162C2×#41×C61C2311yescharacteristic
163C2×#41×C61C2311yescharacteristic
164C22×D4×C61—21no—
165C22×D4×C61—21no—
166C22×D4×C61—41no—
167C22×D4×C61C2311yescharacteristic
168C2×M16×C61C2311yescharacteristic
169C2×M16×C61C2311yescharacteristic
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C22⋊C4×C61—41no—
172C2×C42×C61C2311yescharacteristic
173#104×C61—22no—
174#104×C61—22no—
175#103×C61—21no—
176#103×C61—21no—
177#102×C61—21no—
178#102×C61—21no—
179#100×C61—41no—
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—21no—
220C22×C4×C61—41no—
221C22×C4×C61C2411yescharacteristic
222C2×C22⋊D61—21no—
223C2×C22⋊D61—41no—
224C22×Dic61—21no—
225C22×Dic61—41no—
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—21no—
255M16×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C22⋊C4×C61—82no—
261C42×C61—21no—
262C42×C61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—41no—
265#11758202C22⋊C414yescomplemented
266#11758201—24no—
267#11758201C22⋊C414yescomplemented
268#11758200—24no—
269#11758200C22⋊C414yescomplemented
270#11758199—24no—
271#11758199—24no—
272#11758199—24no—
273#11758199—24no—
274#11758199C22⋊C414yescomplemented
275#11758198—41no—
276#11758198—82no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—41no—
280C4⋊Dic61C2×D411yescharacteristic
281C4⋊Dic61C2×D411yescharacteristic
282#11758196—41no—
283C4×Dic61—21no—
284C4×Dic61—41no—
285C4×Dic61—41no—
286#11758194—21no—
287#11758194—24no—
288#11758194—21no—
289#11758194—21no—
290#11758194—42no—
291#11758194C22×C412yes—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—24no—
296C2×#92418—21no—
297C2×#92418—42no—
298C2×#92418C22×C412yes—
299C2×#92418C2×D411yescharacteristic
300C2×#92418C2×D411yescharacteristic
301C2×#92418C2×D411yescharacteristic
302C2×#92418C2×D412yes—
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—22no—
351C2×C4×C61—44no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—81no—
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—21no—
367C2×Dic61—21no—
368C2×Dic61—41no—
369C2×Dic61—81no—
370C2×Dic61—161no—
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—41no—
385C8×C61—41no—
386#92418—22no—
387#92418—21no—
388#92418—21no—
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—42no—
422C4×C61—81no—
423C4×C61C22×C22⋊C411yescharacteristic
424C4×C61C2×C4×D411yescharacteristic
425C4×C61D4211yescharacteristic
426C4×C61#54611yescharacteristic
427Dic61—22no—
428Dic61—41no—
429Dic61—41no—
430Dic61—81no—
431C2×#576—611no—
432C2×#443—611no—
433#2951—611no—
434#2897—611no—
435#2897—611no—
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#1792D6111yescharacteristic, complemented
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×#131—611no—
471#520—611no—
472#520—611no—
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×#104C2×D6111yescharacteristic
482C2×#104C2×D6111yescharacteristic, complemented
483#418—611no—
484#418—611no—
485#418—1221no—
486#418—1221no—
487#417—611no—
488#417—611no—
489#417—1221no—
490#417—1221no—
491#417C2×D6111yescharacteristic
492#417C2×D6111yescharacteristic, complemented
493#416—611no—
494#416—1221no—
495#416—1221no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—1221no—
499C2×#102—1221no—
500C2×#100—611no—
501C2×#100C2×D6111yescharacteristic, complemented
502#405—611no—
503C2×C4×C8—611no—
504#390—611no—
505#390C2×D6111yescharacteristic, complemented
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—614no—
557#131—1222no—
558#131—1222no—
559#131—1222no—
560#131—2441no—
561#131—2441no—
562C2×M16—611no—
563C2×M16—611no—
564C2×M16—1221no—
565C2×M16—1221no—
566C2×M16—1221no—
567C2×M16C22×D6111yescharacteristic
568C2×M16C22×D6111yescharacteristic
569C22×C8—611no—
570C22×C8—611no—
571C22×C8—1221no—
572C22×C8—1221no—
573C22×C8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×D4—1221no—
577C4×D4—1221no—
578C4×D4—2441no—
579C4×D4—2441no—
580#117—611no—
581#117—1221no—
582#117—1221no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—1221no—
585C2×C4⋊C4—1221no—
586C2×C4⋊C4C22×D6111yescharacteristic
587C2×C22⋊C4—41no—
588C2×C22⋊C4—2441no—
589C2×C42C22×D6111yescharacteristic
590#108—1222no—
591#107—1221no—
592#107—1221no—
593#104—22no—
594#104—22no—
595#104—1222no—
596#103—21no—
597#103—21no—
598#103—611no—
599#103—611no—
600#103—1221no—
601#103—1221no—
602#102—21no—
603#102—21no—
604#102—611no—
605#102—611no—
606#102—1221no—
607#102—1221no—
608#102—1221no—
609#102—1221no—
610#102—1221no—
611#102—1221no—
612#102—1221no—
613#102—1221no—
614#102—1221no—
615#102—1221no—
616#100—41no—
617#100—2441no—
618#97—1221no—
619C4×C8—1222no—
620C4×C8—1221no—
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#41D4×D6112yes—
644#41#1175822412yes—
645C2×Q8—611no—
646C2×Q8D4×D6111yescharacteristic
647C2×Q8D4×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×D4D4×D6111yescharacteristic
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—41no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—2441no—
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—21no—
706M16—21no—
707M16—612no—
708M16—1224no—
709M16—1221no—
710M16—1221no—
711M16—1221no—
712M16—2442no—
713M16—2442no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—612no—
717C2×C8—611no—
718C2×C8—612no—
719C2×C8—611no—
720C2×C8—611no—
721C2×C8—611no—
722C2×C8—1224no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—2442no—
728C2×C8—2442no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—2441no—
736C4⋊C4—2441no—
737C22⋊C4—82no—
738C22⋊C4—1221no—
739C22⋊C4—4882no—
740C22⋊C4—2441no—
741C22⋊C4—2441no—
742C42—21no—
743C42—21no—
744C42—1221no—
745C42—2441no—
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—
772Q8#1451973712yes—
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—
796D4#1451973712yes—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—44no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—81no—
809C2×C4—1221no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—9761no—
815C2×C4—9761no—
816C2×C4—4881no—
817C2×C4—2444no—
818C2×C4—2441no—
819C2×C4C22×C4×D6111yescharacteristic
820C2×C4C2×D4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4C2×#1175822411yescharacteristic
824C2×C4#1451982211yescharacteristic
825C8—41no—
826C8—41no—
827C8—612no—
828C8—612no—
829C8—1222no—
830C8—1221no—
831C8—1221no—
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
857C22#1684039411yescharacteristic
858C22#1684039911yescharacteristic
859C4—22no—
860C4—22no—
861C4—42no—
862C4—81no—
863C4—1222no—
864C4—4881no—
865C4—2441no—
866C4—2441no—
867C4C2×C22⋊C4×D6111yescharacteristic
868C4C2×#1451973711yescharacteristic
869C4#1684039411yescharacteristic
870C4#1684039911yescharacteristic
871C2—21no—
872C2—21no—
873C2—42no—
874C2—42no—
875C2—82no—
876C2—4882no—
877C2—2442no—
878C2#2144863511yescharacteristic
879C2#2145760311yescharacteristic
880C2#2145761511yescharacteristic
subgroupG/H
centerC22#16840394
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1792C2
socleC22×C61D42
prime radicalC2×#16840565C2
cosocleC22×C4×C61C24
hypercenter#1792D61
hypocenterC61#22466
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1792

Complements

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

NH ≅ G/Ntype
2. C2×#16839876C2semidirect
3. #21454690C2semidirect
4. #21454345C2semidirect
5. #21454343C2semidirect
6. #21446726C2semidirect
7. #21446684C2semidirect
8. #21446325C2semidirect
9. #21446324C2semidirect
10. #21446198C2semidirect
11. #21446193C2semidirect
12. #21445881C2semidirect
13. #21445774C2semidirect
14. #21445657C2semidirect
15. C61×#1792C2semidirect
18. #16840565C4semidirect
27. C2×#14519785C22semidirect
29. C2×#14519784C22semidirect
30. #16840245C22semidirect
31. #16840243C22semidirect
37. C2×#14519712C22semidirect
38. C2×#14519710C22semidirect
39. C2×#14519705C22semidirect
40. #16839768C22semidirect
42. #16839767C22semidirect
44. #16839764C22semidirect
52. C2×#14519698C22semidirect
53. C2×#14519697C22semidirect
55. C2×#14519693C22semidirect
56. #16839720C22semidirect
57. C2×C4×#92418C22semidirect
58. #16839664C22semidirect
59. #16839531C22semidirect
60. #16839530C22semidirect
61. #16839526C22semidirect
62. #16839522C22semidirect
65. C2×#104×C61C22semidirect
67. C61×#417C22semidirect
68. C2×#100×C61C22semidirect
69. C61×#390C22semidirect
73. #14519823C2×C4semidirect
83. #14519803C2×C4semidirect
86. #14519802C2×C4semidirect
101. C2×#11758199C2×C4semidirect
108. #14519784C2×C4semidirect
159. H(5,𝔽2)×C61C2×C4semidirect
265. #11758202C22⋊C4semidirect
267. #11758201C22⋊C4semidirect
269. #11758200C22⋊C4semidirect
274. #11758199C22⋊C4semidirect
444. #1792D61semidirect
482. C2×#104C2×D61semidirect
492. #417C2×D61semidirect
501. C2×#100C2×D61semidirect
505. #390C2×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×#168398762
#214546902
#214543452
#214543432
#214467262
#214466842
#214463252
#214463242
#214461982
#214461932
#214458812
#214457742
#214456572
C61×#17922
#2246661