Finite Group Databasebeta

← #29696010

Subgroups — #29696010

Order 15616.

1346 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840573C211yesmaximal, characteristic
2C2×#16839881C211yesmaximal, characteristic, complemented
3#21454690C211yesmaximal, characteristic, complemented
4#21454350C211yesmaximal, characteristic, complemented
5#21454345C211yesmaximal, characteristic, complemented
6#21446719C211yesmaximal, characteristic, complemented
7#21446699C211yesmaximal, characteristic, complemented
8#21446332C211yesmaximal, characteristic, complemented
9#21446324C211yesmaximal, characteristic, complemented
10#21446198C211yesmaximal, characteristic, complemented
11#21446186C211yesmaximal, characteristic, complemented
12#21445881C211yesmaximal, characteristic, complemented
13#21445779C211yesmaximal, characteristic, complemented
14#21445664C211yesmaximal, characteristic, complemented
15C61×#1792C211yesmaximal, characteristic, complemented
16C2×#14519824C2211yescharacteristic
17#16840573—24no—
18#16840573C418yescomplemented
19C2×#14519807—21no—
20C2×#14519807C2211yescharacteristic
21C2×#14519803—21no—
22C2×#14519803C2211yescharacteristic
23C2×#14519797—21no—
24C2×#14519797C2211yescharacteristic
25C22×#11758200—21no—
26C22×#11758200C2211yescharacteristic
27C2×#14519785C2211yescharacteristic, complemented
28C2×#14519784C2211yescharacteristic
29C2×#14519784C2211yescharacteristic
30#16840245C2211yescharacteristic
31#16840243C2211yescharacteristic, complemented
32#16839881—24no—
33#16839865—21no—
34#16839859—21no—
35#16839854—21no—
36#16839842—21no—
37C2×#14519712C2211yescharacteristic, complemented
38C2×#14519710C2211yescharacteristic, complemented
39C2×#14519705C2211yescharacteristic, complemented
40#16839772C2211yescharacteristic, complemented
41#16839769—21no—
42#16839767—21no—
43#16839767C2211yescharacteristic
44#16839764C2211yescharacteristic, complemented
45#16839763—21no—
46#16839763C2211yescharacteristic
47#16839760—21no—
48#16839758—21no—
49#16839758C2211yescharacteristic
50#16839755—21no—
51C2×#14519700C2211yescharacteristic, complemented
52#103×D61—21no—
53C2×#14519698—21no—
54C2×#14519698C2211yescharacteristic
55C2×#14519695C2211yescharacteristic, complemented
56#16839720C2211yescharacteristic, complemented
57C2×#14519688C2211yescharacteristic, complemented
58#16839668C2211yescharacteristic, complemented
59#16839531C2211yescharacteristic, complemented
60#16839530C2211yescharacteristic, complemented
61#16839526C2211yescharacteristic, complemented
62#16839522C2211yescharacteristic, complemented
63C2×H(5,𝔽2)×C61C2211yescharacteristic
64C2×#104×C61C2211yescharacteristic
65C2×#104×C61C2211yescharacteristic
66C61×#417C2211yescharacteristic
67C61×#417C2211yescharacteristic
68C2×#100×C61C2211yescharacteristic
69C61×#390C2211yescharacteristic
70#14519824—22no—
71#14519824—22no—
72#14519824—41no—
73#14519824C2×C414yescomplemented
74C2×#11758222—21no—
75C2×#11758222C2311yescharacteristic
76C2×#11758224—21no—
77C2×#11758224—41no—
78C22×Dic122—21no—
79C22×Dic122C2311yescharacteristic
80C2×Q8×D61—21no—
81#14519807—22no—
82#14519807—28no—
83#14519807C2×C414yescomplemented
84#14519803—22no—
85#14519803—28no—
86#14519803C2×C414yescomplemented
87#14519797—28no—
88#14519797C2×C414yes—
89#14519797D414yes—
90C2×#11758202—21no—
91C2×#11758202D411yescharacteristic
92C2×#11758200—21no—
93C2×#11758200—21no—
94C2×#11758200—28no—
95C2×#11758200—21no—
96C2×#11758200—21no—
97C2×#11758200—22no—
98C2×#11758200C2×C414yescomplemented
99C2×#11758200D411yescharacteristic
100C2×#11758201D411yescharacteristic
101C2×#11758199—21no—
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—
131#14519712—22no—
132#14519710—21no—
133#14519710—21no—
134#14519705—22no—
135#14519702—21no—
136#14519702—21no—
137#14519702—21no—
138#14519701—21no—
139#14519701D411yescharacteristic
140#14519701D411yescharacteristic
141#14519700—21no—
142#14519700—21no—
143#14519699—21no—
144#14519698—21no—
145#14519698—21no—
146#14519698—21no—
147#14519698—21no—
148#14519698—21no—
149#14519698D411yescharacteristic
150#14519698D411yescharacteristic
151#14519695—41no—
152#14519688—22no—
153#14519687—21no—
154C8×Dic61—21no—
155#14519684—41no—
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—
182#41×C61—21no—
183#41×C61—21no—
184#41×C61—21no—
185#41×C61—21no—
186#41×C61—24no—
187#41×C61—24no—
188#41×C61—42no—
189#41×C61—42no—
190#41×C61C22×C412yes—
191#41×C61C22×C412yes—
192#41×C61C2×D412yes—
193#41×C61#4112yes—
194C2×Q8×C61C2×D411yescharacteristic
195C2×Q8×C61C2×D411yescharacteristic
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—24no—
199C2×D4×C61—24no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—41no—
208C2×D4×C61—41no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61C22×C412yes—
212C2×D4×C61C2×D411yescharacteristic
213C2×D4×C61C2×D411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—41no—
219C22×C4×C61C2411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—41no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—41no—
225C22×Dic61—41no—
226Q8×D61—24no—
227Q8×D61—42no—
228#11758224—24no—
229#11758224—42no—
230#11758224—44no—
231#11758224—44no—
232#11758222—21no—
233#11758222—21no—
234#11758222—24no—
235#11758222—42no—
236#11758222C22×C412yes—
237#11758222C2×D412yes—
238C2×D244C2×D411yescharacteristic
239C2×C4×D61—21no—
240C2×C4×D61—41no—
241C2×C4×D61—41no—
242C2×Dic122—21no—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—24no—
247C2×Dic122—21no—
248C2×Dic122—42no—
249C2×Dic122—41no—
250C2×Dic122C22×C412yes—
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#11758202—24no—
266#11758202C22⋊C414yescomplemented
267#11758201C22⋊C414yescomplemented
268#11758200—24no—
269#11758200—24no—
270#11758200—24no—
271#11758200—24no—
272#11758200C22⋊C414yescomplemented
273#11758199—24no—
274#11758199C22⋊C414yescomplemented
275#11758198—41no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—41no—
279C4⋊Dic61C2×D411yescharacteristic
280C4⋊Dic61C2×D411yescharacteristic
281#11758196—41no—
282C4×Dic61—21no—
283C4×Dic61—41no—
284C4×Dic61—41no—
285#11758194—21no—
286#11758194—24no—
287#11758194—21no—
288#11758194—21no—
289#11758194—42no—
290#11758194C22×C412yes—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—24no—
295C2×#92418—21no—
296C2×#92418—42no—
297C2×#92418C22×C412yes—
298C2×#92418C2×D411yescharacteristic
299C2×#92418C2×D411yescharacteristic
300C2×#92418C2×D411yescharacteristic
301C2×#92418C2×D411yescharacteristic
302C2×#92418C2×D412yes—
303#11758189—42no—
304C8×D61—42no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—22no—
308C23×C61—44no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—81no—
312C23×C61—81no—
313C23×C61—161no—
314C23×C61—161no—
315C23×C61H(5,𝔽2)11yescharacteristic
316C22×D61—21no—
317Q8×C61—21no—
318Q8×C61—21no—
319Q8×C61C2×C22⋊C412yes—
320Q8×C61C4×D412yes—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—22no—
327D4×C61—21no—
328D4×C61—21no—
329D4×C61—44no—
330D4×C61—44no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61C2×C22⋊C412yes—
334D4×C61C4×D412yes—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—44no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—81no—
347C2×C4×C61C23×C411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C2×#4111yescharacteristic
352C2×C4×C61H(5,𝔽2)11yescharacteristic
353C22⋊D61—22no—
354C22⋊D61—22no—
355C22⋊D61—44no—
356C2×Dic61—21no—
357C2×Dic61—22no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—44no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—81no—
365C2×Dic61—161no—
366D244—21no—
367D244C2×C22⋊C412yes—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—44no—
371C4×D61—161no—
372Dic122—21no—
373Dic122—22no—
374Dic122—22no—
375Dic122—44no—
376Dic122—41no—
377Dic122—41no—
378Dic122C2×C22⋊C412yes—
379C8×C61—41no—
380C8×C61—41no—
381#92418—22no—
382#92418—21no—
383#92418—21no—
384#92418—41no—
385#92418C2×C22⋊C412yes—
386#92418C2×C22⋊C412yes—
387#22464—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—42no—
397C22×C61—82no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61—161no—
401C22×C61—164no—
402C22×C61#51811yescharacteristic
403C22×C61D4211yescharacteristic
404C22×C61#54611yescharacteristic
405C2×D61—22no—
406C2×D61—41no—
407C2×D61—41no—
408C4×C61—22no—
409C4×C61—22no—
410C4×C61—81no—
411C4×C61—81no—
412C4×C61C22×C22⋊C411yescharacteristic
413C4×C61C2×C4×D411yescharacteristic
414C4×C61D4211yescharacteristic
415C4×C61#54611yescharacteristic
416Dic61—22no—
417Dic61—42no—
418Dic61—41no—
419Dic61—41no—
420Dic61—81no—
421C2×#577—611no—
422C2×#444—611no—
423#2951—611no—
424#2898—611no—
425#2897—611no—
426#1977—611no—
427#1973—611no—
428#1908—611no—
429#1907—611no—
430#1883—611no—
431#1882—611no—
432#1816—611no—
433#1793—611no—
434#1792D6111yescharacteristic, complemented
435#1765—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—42no—
439C2×C61—42no—
440C2×C61—82no—
441C2×C61D4×C22⋊C411yescharacteristic
442C2×C61#328811yescharacteristic
443C2×C61#328911yescharacteristic
444D61—42no—
445C2×2−1+4—611no—
446C2×H(5,𝔽2)C2×D6111yescharacteristic
447#577—618no—
448#577—1224no—
449C2×#137—611no—
450C2×#137—1221no—
451C2×AGL(1,ℤ/8)—611no—
452C2×AGL(1,ℤ/8)—1221no—
453C2×#135—611no—
454C2×#135—1221no—
455C22×SD16—611no—
456C22×SD16—1221no—
457C2×#131—611no—
458C2×#131—611no—
459C2×#131—611no—
460#520—611no—
461#520—611no—
462#444—1224no—
463#440—1221no—
464#440—1221no—
465C4×Q16—1221no—
466C4×D8—1221no—
467C2×#108—611no—
468C2×#107—611no—
469C2×#104—611no—
470C2×#104C2×D6111yescharacteristic
471C2×#104C2×D6111yescharacteristic
472#419—611no—
473#419—1221no—
474#418—611no—
475#418—1221no—
476#417—611no—
477#417—611no—
478#417—1221no—
479#417—1221no—
480#417C2×D6111yescharacteristic
481#417C2×D6111yescharacteristic
482#416—611no—
483#416—1221no—
484#416—1221no—
485C2×#103—611no—
486C2×#103—1221no—
487C2×#102—611no—
488C2×#102—1221no—
489C2×#101—611no—
490C2×#100C2×D6111yescharacteristic
491#405—611no—
492C2×#97—611no—
493#391—611no—
494#390C2×D6111yescharacteristic
495#343—611no—
496#343—611no—
497#341—611no—
498#339—611no—
499C61#2246411yescharacteristic, complemented, Sylow
5002−1+4—614no—
5012−1+4—1222no—
5022−1+4—1222no—
5032−1+4—2441no—
504H(5,𝔽2)—22no—
505H(5,𝔽2)—22no—
506H(5,𝔽2)—41no—
507H(5,𝔽2)C4×D6114yescomplemented
508C2×#41—21no—
509C2×#41—21no—
510C2×#41—611no—
511C2×#41—1221no—
512C2×#41—1221no—
513C2×#41—2441no—
514C2×#41C22×D6111yescharacteristic
515C2×#41C22×D6111yescharacteristic
516C22×Q8—611no—
517C22×Q8—1221no—
518C22×Q8—1221no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—41no—
522C22×D4C22×D6111yescharacteristic
523#137—614no—
524#137—1228no—
525#137—1222no—
526AGL(1,ℤ/8)—614no—
527AGL(1,ℤ/8)—1228no—
528AGL(1,ℤ/8)—1222no—
529#135—614no—
530#135—614no—
531#135—1228no—
532C2×Q16—611no—
533C2×Q16—1221no—
534C2×SD16—611no—
535C2×SD16—611no—
536C2×SD16—614no—
537C2×SD16—1221no—
538C2×SD16—1221no—
539C2×SD16—1222no—
540C2×SD16—1228no—
541C2×SD16—1221no—
542C2×SD16—1221no—
543C2×D8—611no—
544C2×D8—1221no—
545#131—614no—
546#131—1222no—
547#131—1222no—
548#131—1222no—
549#131—2441no—
550#131—2441no—
551C2×M16—611no—
552C2×M16—611no—
553C2×M16—1221no—
554C2×M16—1221no—
555C2×M16—1221no—
556C2×M16C22×D6111yescharacteristic
557C2×M16C22×D6111yescharacteristic
558C22×C8—611no—
559C22×C8—611no—
560C22×C8—1221no—
561C22×C8—1221no—
562C22×C8—1221no—
563C4×Q8—1221no—
564C4×Q8—1221no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—2441no—
568C4×D4—2441no—
569#117—611no—
570#117—1221no—
571#117—1221no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4C22×D6111yescharacteristic
576C2×C22⋊C4—41no—
577C2×C42C22×D6111yescharacteristic
578#108—1222no—
579#107—1221no—
580#107—1221no—
581#104—22no—
582#104—22no—
583#104—1222no—
584#103—21no—
585#103—21no—
586#103—611no—
587#103—611no—
588#103—1221no—
589#103—1221no—
590#103—1221no—
591#103—1221no—
592#103—1221no—
593#103—1221no—
594#102—21no—
595#102—21no—
596#102—611no—
597#102—611no—
598#102—1221no—
599#102—1221no—
600#102—1221no—
601#102—1221no—
602#102—1221no—
603#102—1221no—
604#101—2441no—
605#100—41no—
606#97—1222no—
607#97—1221no—
608C4×C8—1221no—
609#95—2441no—
610C24—21no—
611C24—41no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—24no—
617#41—24no—
618#41—42no—
619#41—42no—
620#41—612no—
621#41—612no—
622#41—1224no—
623#41—1221no—
624#41—1221no—
625#41—1224no—
626#41—2442no—
627#41—2444no—
628#41—2442no—
629#41—2444no—
630#41C2×C4×D6112yes—
631#41C2×C4×D6112yes—
632#41D4×D6112yes—
633#41#1175822412yes—
634C2×Q8—612no—
635C2×Q8—611no—
636C2×Q8—1224no—
637C2×Q8—1221no—
638C2×Q8—1224no—
639C2×Q8—1221no—
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×Q8—1221no—
643C2×Q8—2441no—
644C2×Q8—2442no—
645C2×Q8—2442no—
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—611no—
664C2×D4—1221no—
665C2×D4—2441no—
666C2×D4C2×C4×D6112yes—
667C2×D4D4×D6111yescharacteristic
668C2×D4D4×D6111yescharacteristic
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—41no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—2441no—
678C22×C4—2441no—
679C22×C4—2441no—
680C22×C4—2441no—
681C22×C4C23×D6111yescharacteristic
682Q16—614no—
683Q16—1224no—
684SD16—614no—
685SD16—614no—
686SD16—1224no—
687SD16—1224no—
688SD16—1224no—
689SD16—1224no—
690D8—614no—
691D8—1224no—
692M16—21no—
693M16—21no—
694M16—21no—
695M16—21no—
696M16—612no—
697M16—1224no—
698M16—1221no—
699M16—1221no—
700M16—1221no—
701M16—2442no—
702M16—2442no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—612no—
706C2×C8—611no—
707C2×C8—611no—
708C2×C8—612no—
709C2×C8—611no—
710C2×C8—611no—
711C2×C8—1224no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—2442no—
717C2×C8—2442no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—2441no—
725C4⋊C4—2441no—
726C22⋊C4—82no—
727C22⋊C4—1221no—
728C22⋊C4—2441no—
729C22⋊C4—2441no—
730C42—21no—
731C42—21no—
732C42—1221no—
733C42—2441no—
734C42—2441no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—44no—
739C23—41no—
740C23—41no—
741C23—81no—
742C23—81no—
743C23—161no—
744C23—161no—
745C23—1221no—
746C23#1451982211yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—612no—
750Q8—1221no—
751Q8—1222no—
752Q8—1222no—
753Q8—2444no—
754Q8—2441no—
755Q8—2441no—
756Q8C22⋊C4×D6112yes—
757Q8#1451973712yes—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—21no—
765D4—21no—
766D4—44no—
767D4—44no—
768D4—41no—
769D4—41no—
770D4—612no—
771D4—1222no—
772D4—1222no—
773D4—1221no—
774D4—2444no—
775D4C22⋊C4×D6112yes—
776D4#1451973712yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—44no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—81no—
789C2×C4—1221no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—9761no—
796C2×C4—9761no—
797C2×C4—4881no—
798C2×C4—2444no—
799C2×C4—2444no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4C2×D4×D6111yescharacteristic
807C2×C4C2×#1175822411yescharacteristic
808C2×C4#1451982211yescharacteristic
809C8—41no—
810C8—41no—
811C8—612no—
812C8—612no—
813C8—1222no—
814C8—1221no—
815C8—1221no—
816C8—2441no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—82no—
827C22—81no—
828C22—81no—
829C22—161no—
830C22—164no—
831C22—1222no—
832C22—2441no—
833C22—2441no—
834C22#1684023511yescharacteristic
835C22#1684039411yescharacteristic
836C22#1684039911yescharacteristic
837C4—22no—
838C4—22no—
839C4—81no—
840C4—81no—
841C4—1222no—
842C4—4881no—
843C4—2441no—
844C4—2442no—
845C4—2441no—
846C4C2×C22⋊C4×D6111yescharacteristic
847C4C2×#1451973711yescharacteristic
848C4#1684039411yescharacteristic
849C4#1684039911yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—42no—
854C2—82no—
855C2—2442no—
856C2#2144863511yescharacteristic
857C2#2145758011yescharacteristic
858C2#2145759711yescharacteristic
subgroupG/H
centerC22#16840394
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1792C2
socleC22×C61D42
prime radicalC2×#16840573C2
cosocleC22×C4×C61C24
hypercenter#1792D61
hypocenterC61#22464
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×#16839881C2semidirect
3. #21454690C2semidirect
4. #21454350C2semidirect
5. #21454345C2semidirect
6. #21446719C2semidirect
7. #21446699C2semidirect
8. #21446332C2semidirect
9. #21446324C2semidirect
10. #21446198C2semidirect
11. #21446186C2semidirect
12. #21445881C2semidirect
13. #21445779C2semidirect
14. #21445664C2semidirect
15. C61×#1792C2semidirect
18. #16840573C4semidirect
27. C2×#14519785C22semidirect
31. #16840243C22semidirect
37. C2×#14519712C22semidirect
38. C2×#14519710C22semidirect
39. C2×#14519705C22semidirect
40. #16839772C22semidirect
44. #16839764C22semidirect
51. C2×#14519700C22semidirect
55. C2×#14519695C22semidirect
56. #16839720C22semidirect
57. C2×#14519688C22semidirect
58. #16839668C22semidirect
59. #16839531C22semidirect
60. #16839530C22semidirect
61. #16839526C22semidirect
62. #16839522C22semidirect
73. #14519824C2×C4semidirect
83. #14519807C2×C4semidirect
86. #14519803C2×C4semidirect
98. C2×#11758200C2×C4semidirect
108. #14519784C2×C4semidirect
159. H(5,𝔽2)×C61C2×C4semidirect
266. #11758202C22⋊C4semidirect
267. #11758201C22⋊C4semidirect
272. #11758200C22⋊C4semidirect
274. #11758199C22⋊C4semidirect
434. #1792D61semidirect
499. C61#22464semidirect
507. 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×#168405732
C2×#168398812
#214546902
#214543502
#214543452
#214467192
#214466992
#214463322
#214463242
#214461982
#214461862
#214458812
#214457792
#214456642
C61×#17922
#2246461