Finite Group Databasebeta

← #29696007

Subgroups — #29696007

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×#16840570C211yesmaximal, characteristic
2C2×#16839882C211yesmaximal, characteristic, complemented
3#21454692C211yesmaximal, characteristic, complemented
4#21454341C211yesmaximal, characteristic, complemented
5#21446721C211yesmaximal, characteristic, complemented
6#21446697C211yesmaximal, characteristic, complemented
7#21446337C211yesmaximal, characteristic, complemented
8#21446327C211yesmaximal, characteristic, complemented
9#21446195C211yesmaximal, characteristic, complemented
10#21446185C211yesmaximal, characteristic, complemented
11#21445881C211yesmaximal, characteristic, complemented
12#21445778C211yesmaximal, characteristic, complemented
13#21445771C211yesmaximal, characteristic, complemented
14#21445666C211yesmaximal, characteristic, complemented
15C61×#2898C211yesmaximal, characteristic, complemented
16C2×#14519823C2211yescharacteristic
17#16840570—24no—
18#16840570C418yescomplemented
19C2×#14519808—21no—
20C2×#14519808C2211yescharacteristic
21C2×#14519802—21no—
22C2×#14519802C2211yescharacteristic
23C2×#14519797—21no—
24C2×#14519797C2211yescharacteristic
25C22×#11758201—21no—
26C22×#11758201C2211yescharacteristic
27C2×#14519784C2211yescharacteristic
28C2×#14519783C2211yescharacteristic
29#16840242C2211yescharacteristic
30#16839882—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
40#16839766C2211yescharacteristic
41#16839765—21no—
42#16839763C2211yescharacteristic
43#16839763C2211yescharacteristic, complemented
44#16839762—21no—
45#16839761C2211yescharacteristic
46#16839757—21no—
47C2×#14519699C2211yescharacteristic
48#102×D61—21no—
49C2×#14519696C2211yescharacteristic, complemented
50C2×#14519693C2211yescharacteristic
51#16839718C2211yescharacteristic, complemented
52C2×#14519687C2211yescharacteristic, complemented
53#16839669C2211yescharacteristic, complemented
54#16839663C2211yescharacteristic
55#16839531C2211yescharacteristic, complemented
56#16839530C2211yescharacteristic, complemented
57#16839527C2211yescharacteristic, complemented
58#16839521C2211yescharacteristic, complemented
59C2×2−1+4×C61C2211yescharacteristic
60C2×#131×C61C2211yescharacteristic, complemented
61C61×#520C2211yescharacteristic, complemented
62C61×#419—21no—
63C61×#419C2211yescharacteristic, complemented
64C61×#417—21no—
65C61×#417C2211yescharacteristic
66C61×#416—21no—
67C61×#416C2211yescharacteristic
68C2×#103×C61—21no—
69C2×#103×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#14519808—22no—
82#14519808—28no—
83#14519808C2×C414yescomplemented
84#14519802—22no—
85#14519802—28no—
86#14519802C2×C414yescomplemented
87#14519797—28no—
88#14519797C2×C414yes—
89#14519797D414yes—
90C2×#11758202—21no—
91C2×#11758202D411yescharacteristic
92C2×#11758200D411yescharacteristic
93C2×#11758201—21no—
94C2×#11758201—21no—
95C2×#11758201—28no—
96C2×#11758201—21no—
97C2×#11758201—21no—
98C2×#11758201—22no—
99C2×#11758201C2×C414yescomplemented
100C2×#11758201D411yescharacteristic
101C2×#11758199—21no—
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×#11758198—41no—
122C2×C4×Dic61C2311yescharacteristic
123#14519712—22no—
124#14519710—21no—
125#14519710—21no—
126#14519704—22no—
127#14519704—22no—
128#14519703—22no—
129#14519701—21no—
130#14519701—21no—
131#14519700—21no—
132#14519699—21no—
133#14519699—21no—
134#14519698—21no—
135#14519698—21no—
136#14519697—21no—
137#14519697—21no—
138#14519697—21no—
139#14519696—41no—
140#14519693—41no—
141#14519688—21no—
142#14519687—22no—
143C4×#92418—21no—
144#14519684—41no—
1452−1+4×C61—22no—
1462−1+4×C61—22no—
1472−1+4×C61—41no—
1482−1+4×C61C2×C414yescomplemented
149C2×#41×C61—21no—
150C2×#41×C61—21no—
151C2×#41×C61—41no—
152C2×#41×C61C2311yescharacteristic
153C2×#41×C61C2311yescharacteristic
154C22×Q8×C61—21no—
155C22×Q8×C61—21no—
156C22×Q8×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×C61—21no—
172#103×C61—21no—
173#103×C61—21no—
174#103×C61—21no—
175#103×C61D411yescharacteristic
176#103×C61D411yescharacteristic
177#102×C61—21no—
178#102×C61D411yescharacteristic
179#102×C61D411yescharacteristic
180C23×D61—21no—
181C23×D61—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—44no—
189#41×C61—42no—
190#41×C61—42no—
191#41×C61—44no—
192#41×C61C22×C412yes—
193#41×C61C22×C412yes—
194#41×C61C2×D412yes—
195#41×C61#4112yes—
196C2×Q8×C61—21no—
197C2×Q8×C61—24no—
198C2×Q8×C61—24no—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—21no—
202C2×Q8×C61—21no—
203C2×Q8×C61—41no—
204C2×Q8×C61—42no—
205C2×Q8×C61—42no—
206C2×Q8×C61C22×C412yes—
207C2×Q8×C61C2×D411yescharacteristic
208C2×Q8×C61C2×D411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—41no—
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×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—
270#11758202—24no—
271#11758202C22⋊C414yescomplemented
272#11758201—24no—
273#11758201—24no—
274#11758201—24no—
275#11758201—24no—
276#11758201C22⋊C414yescomplemented
277#11758200C22⋊C414yescomplemented
278#11758199—24no—
279#11758199C22⋊C414yescomplemented
280#11758198—41no—
281#11758198—82no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284#11758196—41no—
285C4×Dic61—21no—
286C4×Dic61—21no—
287C4×Dic61—41no—
288#11758194—21no—
289#11758194—24no—
290#11758194—21no—
291#11758194—21no—
292#11758194—21no—
293#11758194—21no—
294#11758194C22×C412yes—
295C2×#92418—21no—
296C2×#92418—24no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418C22×C412yes—
300C2×#92418C2×D411yescharacteristic
301C2×#92418C2×D412yes—
302C2×#92418C2×D411yescharacteristic
303#11758189—42no—
304C8×D61—42no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61H(5,𝔽2)11yescharacteristic
308C22×D61—21no—
309C22×D61—22no—
310C22×D61—44no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—81no—
314C22×D61—81no—
315C22×D61—161no—
316C22×D61—161no—
317Q8×C61—21no—
318Q8×C61—21no—
319Q8×C61—22no—
320Q8×C61—22no—
321Q8×C61—44no—
322Q8×C61—41no—
323Q8×C61—41no—
324Q8×C61C2×C22⋊C412yes—
325Q8×C61C4×D412yes—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—21no—
331D4×C61—21no—
332D4×C61—44no—
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—22no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—44no—
345C2×C4×C61—44no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—81no—
350C2×C4×C61—161no—
351C2×C4×C61C23×C411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C2×#4111yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C22⋊D61—22no—
358C22⋊D61—22no—
359C22⋊D61—44no—
360C2×Dic61—21no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—81no—
366D244—22no—
367D244—22no—
368D244—21no—
369D244—44no—
370D244—41no—
371D244—41no—
372D244C2×C22⋊C412yes—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—44no—
376C4×D61—161no—
377Dic122—21no—
378Dic122C2×C22⋊C412yes—
379C8×C61—21no—
380C8×C61—21no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
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#51811yescharacteristic
397C22×C61D4211yescharacteristic
398C22×C61#54611yescharacteristic
399C2×D61—22no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—42no—
403C2×D61—81no—
404C2×D61—81no—
405C2×D61—82no—
406C2×D61—164no—
407C2×D61—161no—
408C4×C61—22no—
409C4×C61—22no—
410C4×C61—42no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61—81no—
414C4×C61C22×C22⋊C411yescharacteristic
415C4×C61C2×C4×D411yescharacteristic
416C4×C61D4211yescharacteristic
417C4×C61#54611yescharacteristic
418Dic61—22no—
419Dic61—81no—
420Dic61—81no—
421C2×#577—611no—
422C2×#444—611no—
423#2951—611no—
424#2898D6111yescharacteristic, complemented
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#1792—611no—
435#1765—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—42no—
439C2×C61—42no—
440C2×C61D4×C22⋊C411yescharacteristic
441C2×C61#328811yescharacteristic
442C2×C61#328911yescharacteristic
443D61—42no—
444D61—82no—
445C2×2−1+4C2×D6111yescharacteristic
446C2×H(5,𝔽2)—611no—
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×#131C2×D6111yescharacteristic, complemented
460#520—611no—
461#520C2×D6111yescharacteristic, complemented
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×#104—611no—
471C2×#104—611no—
472#419—21no—
473#419C2×D6111yescharacteristic, complemented
474#418—611no—
475#418—1221no—
476#417—21no—
477#417—611no—
478#417—611no—
479#417—611no—
480#417—1221no—
481#417C2×D6111yescharacteristic
482#416—21no—
483#416—1221no—
484#416C2×D6111yescharacteristic
485C2×#103—21no—
486C2×#103C2×D6111yescharacteristic, complemented
487C2×#102—611no—
488C2×#102—1221no—
489C2×#101—611no—
490C2×#100—611no—
491#405—611no—
492C2×#97—611no—
493#391—611no—
494#390—611no—
495#343—611no—
496#343—611no—
497#341—611no—
498#339—611no—
499C61#2246411yescharacteristic, complemented, Sylow
5002−1+4—22no—
5012−1+4—22no—
5022−1+4—41no—
5032−1+4C4×D6114yescomplemented
504H(5,𝔽2)—614no—
505H(5,𝔽2)—1222no—
506H(5,𝔽2)—1222no—
507H(5,𝔽2)—2441no—
508C2×#41—21no—
509C2×#41—21no—
510C2×#41—41no—
511C2×#41—611no—
512C2×#41—1221no—
513C2×#41—1221no—
514C2×#41C22×D6111yescharacteristic
515C2×#41C22×D6111yescharacteristic
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8C22×D6111yescharacteristic
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4—1221no—
522C22×D4—2441no—
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—22no—
546#131—41no—
547#131—614no—
548#131—1222no—
549#131—1222no—
550#131—2441no—
551C2×M16—21no—
552C2×M16—611no—
553C2×M16—611no—
554C2×M16—611no—
555C2×M16—1221no—
556C2×M16—1221no—
557C2×M16C22×D6111yescharacteristic
558C22×C8—21no—
559C22×C8—611no—
560C22×C8—1221no—
561C22×C8—1221no—
562C22×C8C22×D6111yescharacteristic
563C4×Q8—21no—
564C4×Q8—1221no—
565C4×D4—21no—
566C4×D4—41no—
567C4×D4—1221no—
568C4×D4—2441no—
569#117—21no—
570#117—1221no—
571#117C22×D6111yescharacteristic
572C2×C4⋊C4—21no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4C22×D6111yescharacteristic
576C2×C22⋊C4—2441no—
577C2×C42—611no—
578#108—1222no—
579#107—1221no—
580#107—1221no—
581#104—1222no—
582#104—1222no—
583#104—1222no—
584#103—21no—
585#103—21no—
586#103—21no—
587#103—21no—
588#103—21no—
589#103—1221no—
590#103—1221no—
591#103—1221no—
592#103C22⋊D6111yescharacteristic
593#103C22⋊D6111yescharacteristic
594#102—21no—
595#102—1221no—
596#102—1221no—
597#102—1221no—
598#102—1221no—
599#102—1221no—
600#102—1221no—
601#102—1221no—
602#102C22⋊D6111yescharacteristic
603#102C22⋊D6111yescharacteristic
604#101—2441no—
605#100—2441no—
606#97—1221no—
607#97—1222no—
608C4×C8—1221no—
609#95—2441no—
610C24—1221no—
611C24—2441no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—24no—
617#41—24no—
618#41—44no—
619#41—42no—
620#41—42no—
621#41—44no—
622#41—612no—
623#41—612no—
624#41—1224no—
625#41—1221no—
626#41—1221no—
627#41—1224no—
628#41—2442no—
629#41—2442no—
630#41C2×C4×D6112yes—
631#41C2×C4×D6112yes—
632#41#1175822212yes—
633#41D4×D6112yes—
634C2×Q8—21no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—41no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—611no—
645C2×Q8C2×C4×D6112yes—
646C2×Q8D4×D6111yescharacteristic
647C2×Q8C2×C22⋊D6111yescharacteristic
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—41no—
651C2×D4—612no—
652C2×D4—611no—
653C2×D4—1224no—
654C2×D4—1221no—
655C2×D4—1224no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1221no—
661C2×D4—2442no—
662C2×D4—2441no—
663C2×D4—2442no—
664C2×D4—2441no—
665C2×D4—2444no—
666C2×D4—2444no—
667C2×D4D4×D6111yescharacteristic
668C2×D4C2×C22⋊D6111yescharacteristic
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
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—42no—
695M16—612no—
696M16—1224no—
697M16—1221no—
698M16—1221no—
699M16—1221no—
700M16—1221no—
701M16—1221no—
702M16—2442no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—42no—
707C2×C8—612no—
708C2×C8—611no—
709C2×C8—611no—
710C2×C8—612no—
711C2×C8—1224no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—2442no—
716C2×C8C2×C22⋊D6111yescharacteristic
717C2×C8C2×C22⋊D6111yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—41no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—2441no—
724C4⋊C4C2×C22⋊D6111yescharacteristic
725C4⋊C4C2×C22⋊D6111yescharacteristic
726C22⋊C4—21no—
727C22⋊C4—41no—
728C22⋊C4—4882no—
729C22⋊C4—2441no—
730C42—21no—
731C42—41no—
732C42—1221no—
733C42—1221no—
734C42—2441no—
735C23—21no—
736C23—21no—
737C23—1221no—
738C23—1222no—
739C23—9761no—
740C23—9761no—
741C23—4881no—
742C23—4881no—
743C23—2444no—
744C23—2441no—
745C23—2441no—
746C23#1451982211yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—22no—
750Q8—22no—
751Q8—44no—
752Q8—41no—
753Q8—41no—
754Q8—612no—
755Q8—1221no—
756Q8C22⋊C4×D6112yes—
757Q8C4×C22⋊D6112yes—
758D4—22no—
759D4—22no—
760D4—22no—
761D4—22no—
762D4—21no—
763D4—21no—
764D4—44no—
765D4—612no—
766D4—1222no—
767D4—1222no—
768D4—1222no—
769D4—1222no—
770D4—1221no—
771D4—2444no—
772D4—2444no—
773D4—2441no—
774D4—2441no—
775D4C22⋊C4×D6112yes—
776D4C4×C22⋊D6112yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—81no—
792C2×C4—161no—
793C2×C4—1221no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—9761no—
797C2×C4—4881no—
798C2×C4—2444no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4C22×C4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4C22×C22⋊D6111yescharacteristic
807C2×C4C2×#1175822211yescharacteristic
808C2×C4#1451982211yescharacteristic
809C8—21no—
810C8—21no—
811C8—41no—
812C8—612no—
813C8—612no—
814C8—1222no—
815C8—2441no—
816C8—2441no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—1222no—
826C22—9761no—
827C22—9764no—
828C22—4882no—
829C22—4881no—
830C22—4881no—
831C22—2442no—
832C22—2441no—
833C22—2441no—
834C22#1684023511yescharacteristic
835C22D4×C22⋊D6111yescharacteristic
836C22#1684040211yescharacteristic
837C4—22no—
838C4—22no—
839C4—41no—
840C4—41no—
841C4—42no—
842C4—81no—
843C4—1222no—
844C4—4881no—
845C4—4881no—
846C4C2×C22⋊C4×D6111yescharacteristic
847C4C2×C4×C22⋊D6111yescharacteristic
848C4D4×C22⋊D6111yescharacteristic
849C4#1684040211yescharacteristic
850C2—21no—
851C2—21no—
852C2—42no—
853C2—42no—
854C2—4882no—
855C2—2442no—
856C2C22⋊C4×C22⋊D6111yescharacteristic
857C2#2145758111yescharacteristic
858C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2898C2
socleC22×C61D42
prime radicalC2×#16840570C2
cosocleC22×C4×C61C24
hypercenter#2898D61
hypocenterC61#22464
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2898

Complements

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

NH ≅ G/Ntype
2. C2×#16839882C2semidirect
3. #21454692C2semidirect
4. #21454341C2semidirect
5. #21446721C2semidirect
6. #21446697C2semidirect
7. #21446337C2semidirect
8. #21446327C2semidirect
9. #21446195C2semidirect
10. #21446185C2semidirect
11. #21445881C2semidirect
12. #21445778C2semidirect
13. #21445771C2semidirect
14. #21445666C2semidirect
15. C61×#2898C2semidirect
18. #16840570C4semidirect
35. C2×#14519712C22semidirect
36. C2×#14519710C22semidirect
38. C2×#14519704C22semidirect
43. #16839763C22semidirect
49. C2×#14519696C22semidirect
51. #16839718C22semidirect
52. C2×#14519687C22semidirect
53. #16839669C22semidirect
55. #16839531C22semidirect
56. #16839530C22semidirect
57. #16839527C22semidirect
58. #16839521C22semidirect
60. C2×#131×C61C22semidirect
61. C61×#520C22semidirect
63. C61×#419C22semidirect
69. C2×#103×C61C22semidirect
73. #14519823C2×C4semidirect
83. #14519808C2×C4semidirect
86. #14519802C2×C4semidirect
99. C2×#11758201C2×C4semidirect
104. #14519784C2×C4semidirect
148. 2−1+4×C61C2×C4semidirect
271. #11758202C22⋊C4semidirect
276. #11758201C22⋊C4semidirect
277. #11758200C22⋊C4semidirect
279. #11758199C22⋊C4semidirect
424. #2898D61semidirect
459. C2×#131C2×D61semidirect
461. #520C2×D61semidirect
473. #419C2×D61semidirect
486. C2×#103C2×D61semidirect
499. C61#22464semidirect
503. 2−1+4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405702
C2×#168398822
#214546922
#214543412
#214467212
#214466972
#214463372
#214463272
#214461952
#214461852
#214458812
#214457782
#214457712
#214456662
C61×#28982
#2246461