Finite Group Databasebeta

← #30621785

Subgroups — #30621785

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840804C211yesmaximal, characteristic, complemented
2#21462549C211yesmaximal, characteristic, complemented
3C2×#16840759C211yesmaximal, characteristic, complemented
4#21462409C211yesmaximal, characteristic, complemented
5#21461975C211yesmaximal, characteristic, complemented
6#21461912C211yesmaximal, characteristic, complemented
7#21461903C211yesmaximal, characteristic, complemented
8#21461839C211yesmaximal, characteristic, complemented
9#21461810C211yesmaximal, characteristic, complemented
10#21461808C211yesmaximal, characteristic, complemented
11#21461786C211yesmaximal, characteristic, complemented
12#21461771C211yesmaximal, characteristic, complemented
13#21461598C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic, complemented
15#21455034C211yesmaximal, characteristic
16C2×#14519864C2211yescharacteristic
17C2×#14519864C2211yescharacteristic
18C2×#14519864C2211yescharacteristic, complemented
19C22×#11758213C2211yescharacteristic
20C2×#14519856C2211yescharacteristic
21#16840804—24no—
22#16840795—21no—
23#16840793—21no—
24#16840791—21no—
25D4×#92420—21no—
26C2×#14519848C2211yescharacteristic, complemented
27C2×#14519848C2211yescharacteristic, complemented
28#16840769C2211yescharacteristic, complemented
29#16840759—24no—
30C2×#14519842C2211yescharacteristic
31C2×#14519842C2211yescharacteristic
32C2×#14519841C2211yescharacteristic
33C2×#14519841C2211yescharacteristic
34C2×#14519841C2211yescharacteristic, complemented
35C2×#14519841C2211yescharacteristic, complemented
36#16840737C2211yescharacteristic
37#16840737C2211yescharacteristic
38#16840736C2211yescharacteristic, complemented
39#16840735—21no—
40#16840735—21no—
41#16840734—21no—
42#16840733C2211yescharacteristic
43C2×#14519834—21no—
44D61⋊(C22⋊C8)C2211yescharacteristic
45#16840727C2211yescharacteristic, complemented
46C2×#14519831C2211yescharacteristic, complemented
47C2×C8×#6923C2211yescharacteristic, complemented
48#16840638C2211yescharacteristic, complemented
49#16840638C2211yescharacteristic, complemented
50#16840632C2211yescharacteristic, complemented
51#16840632C2211yescharacteristic, complemented
52(C2×#6923)⋊C8C2211yescharacteristic, complemented
53(C2×#6923)⋊C8C2211yescharacteristic, complemented
54C2×#41×D61C2211yescharacteristic
55C2×#14519798C2211yescharacteristic
56C2×#14519796C2211yescharacteristic
57#16840272C2211yescharacteristic
58#16839926C411yescharacteristic, complemented
59#16839924C411yescharacteristic, complemented
60#16839919C411yescharacteristic, complemented
61#16839914C411yescharacteristic, complemented
62#16839905C411yescharacteristic, complemented
63#16839899C411yescharacteristic, complemented
64#16839894C411yescharacteristic, complemented
65#16839757C2211yescharacteristic
66#16839755C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#449C411yescharacteristic, complemented
69#14519864—22no—
70#14519864—22no—
71#14519864—22no—
72#14519864—41no—
73#14519864—41no—
74#14519864—41no—
75C2×#11758213—22no—
76C2×#11758213—21no—
77C2×#11758213—41no—
78C2×#11758213C2311yescharacteristic
79C2×#11758213C2311yescharacteristic
80C2×#11758213C2311yescharacteristic
81C2×#11758213C2311yescharacteristic
82C2×#11758217—21no—
83C2×#11758217—21no—
84C2×#11758217—21no—
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C22×#92420—21no—
88C22×#92420—21no—
89C22×#92420—21no—
90C22×#92420—21no—
91#14519856—22no—
92#14519856—41no—
93C2×C4⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C4×#6923C2311yescharacteristic
96C2×C4×#6923C2311yescharacteristic
97#14519848—22no—
98#14519848—41no—
99#14519844—21no—
100C4⋊#92420—21no—
101#14519842—22no—
102#14519842—22no—
103#14519841—22no—
104#14519841—22no—
105#14519841—41no—
106#14519841D414yescomplemented
107#14519834—21no—
108#14519834—21no—
109#14519834—21no—
110#14519834—21no—
111#14519834—21no—
112#14519834D411yescharacteristic
113#14519834D411yescharacteristic
114C22⋊#92420—21no—
115C22⋊#92420—21no—
116C22⋊#92420—21no—
117C22⋊#92420D411yescharacteristic
118C22⋊#92420D411yescharacteristic
119#14519832—21no—
120#14519831—41no—
121C4×#92420—21no—
122C8×#6923—22no—
123C2×#11758226C2311yescharacteristic
124C2×#11758222—21no—
125C2×#11758222C2×C411yescharacteristic
126C2×#11758224—21no—
127C2×#11758224C2311yescharacteristic
128C2×#11758224C2311yescharacteristic
129#41×D61—22no—
130#41×D61—22no—
131#41×D61—41no—
132#41×D61—41no—
133C2×Q8×D61C2×C411yescharacteristic
134C2×D4×D61—21no—
135C2×D4×D61C2×C411yescharacteristic
136C22×C4×D61—21no—
137C22×C4×D61C2311yescharacteristic
138#14519798—41no—
139#14519798—41no—
140#14519796—22no—
141#14519796—22no—
142C2×Dic244C2×C411yescharacteristic
143C2×#11758202C2×C411yescharacteristic
144C2×#11758190C2×C411yescharacteristic
145C2×#11758200C2×C411yescharacteristic
146C2×#11758200C2×C411yescharacteristic
147C2×#11758199C2×C411yescharacteristic
148C2×C8×D61C2311yescharacteristic
149C2×C8×D61C2311yescharacteristic
150#14519759—21no—
151#14519757C2×C411yescharacteristic
152#14519756C2×C411yescharacteristic
153#14519748C2×C411yescharacteristic
154#14519745—21no—
155D4×Dic61—21no—
156#14519737—21no—
157#14519735C2311yescharacteristic
158#14519702C2×C411yescharacteristic
159#14519701C2×C411yescharacteristic
160#14519700C2×C411yescharacteristic
161#14519699C2×C411yescharacteristic
162#14519698C2×C411yescharacteristic
163#14519697C2×C411yescharacteristic
164C22⋊#92418C2×C411yescharacteristic
165#14519689C2×C411yescharacteristic
166#14519689C2×C411yescharacteristic
167C2×#41×C61C2×C411yescharacteristic
168C2×SD16×C61C2×C411yescharacteristic
169C2×D8×C61C2×C411yescharacteristic
170#121×C61C2×C411yescharacteristic
171#103×C61C2×C411yescharacteristic
172#102×C61C2×C411yescharacteristic
173C22⋊C8×C61C2×C411yescharacteristic
174C23×D61—21no—
175C23×D61#4111yescharacteristic
176C22×#6923—21no—
177C22×#6923—21no—
178#41×C61—22no—
179#41×C61—41no—
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61C22×C411yescharacteristic
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61C2×D411yescharacteristic
195#11758226—21no—
196#11758226—21no—
197#11758226—21no—
198#11758226—21no—
199Q8×D61—22no—
200Q8×D61—41no—
201#11758224—21no—
202#11758224—21no—
203#11758224—21no—
204#11758224—21no—
205#11758224—21no—
206#11758224—21no—
207#11758224—42no—
208#11758224—42no—
209#11758224C2×D412yes—
210#11758224#4112yes—
211D4×D61—22no—
212D4×D61—41no—
213D4×D61—42no—
214D4×D61—42no—
215#11758222—22no—
216#11758222—41no—
217#11758222—42no—
218#11758222—42no—
219C2×D244—21no—
220C2×D244C22×C411yescharacteristic
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61#4111yescharacteristic
233C2×C4×D61C2411yescharacteristic
234C2×Dic122—21no—
235C2×Dic122C22×C411yescharacteristic
236C2×Dic122C22×C411yescharacteristic
237C22⋊#6923—42no—
238#11758217—42no—
239#11758217—42no—
240#11758217—42no—
241C2×#92420—21no—
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—42no—
246C2×#92420—42no—
247C2×#92420—42no—
248C2×#92420—42no—
249C2×#92420C2×D411yescharacteristic
250C2×#92420C2×D411yescharacteristic
251C2×#92420C2×D411yescharacteristic
252C2×#92420C2×D411yescharacteristic
253C4⋊#6923—42no—
254C4×#6923—21no—
255C4×#6923—21no—
256C4×#6923—21no—
257C4×#6923C2×D412yes—
258#11758213—21no—
259#11758213—21no—
260#11758213—21no—
261#11758213—21no—
262#11758213—21no—
263#11758213—21no—
264#11758213—21no—
265#11758213—42no—
266#11758213C2×D412yes—
267D61⋊C8—21no—
268D61⋊C8—21no—
269D61⋊C8—21no—
270D61⋊C8—21no—
271SD16×C61—41no—
272D8×C61—22no—
273C2×C8×C61C22×C411yescharacteristic
274C2×C8×C61C22×C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C22⋊C4×C61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279#11758202—41no—
280#11758200—22no—
281#11758200—22no—
282#11758199—41no—
283#11758198—21no—
284#11758198—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61C22×C411yescharacteristic
287#11758196—21no—
288C4×Dic61—21no—
289C2×#92418C22×C411yescharacteristic
290C2×#92418C22×C411yescharacteristic
291Dic244—22no—
292#11758190—41no—
293C8×D61—21no—
294C8×D61—21no—
295C8×D61—21no—
296C8×D61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61C4×D411yescharacteristic
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—81no—
308C22×D61C4×D411yescharacteristic
309C22×D61C2×#4111yescharacteristic
310C2×#6923—22no—
311C2×#6923—41no—
312C2×#6923—41no—
313C2×#6923—41no—
314C2×#6923—41no—
315C2×#6923—41no—
316Q8×C61—21no—
317Q8×C61—21no—
318D4×C61—21no—
319D4×C61—21no—
320D4×C61—21no—
321D4×C61—42no—
322D4×C61—42no—
323D4×C61C4×D412yes—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—42no—
329C2×C4×C61C4×D411yescharacteristic
330C2×C4×C61C23×C411yescharacteristic
331C22⋊D61—22no—
332C22⋊D61—22no—
333C22⋊D61—42no—
334C22⋊D61—42no—
335C22⋊D61—41no—
336C22⋊D61—41no—
337C22⋊D61—81no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61C4×D411yescharacteristic
348C2×Dic61C22×D411yescharacteristic
349D244—21no—
350D244—21no—
351D244—41no—
352D244—41no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61C22×D411yescharacteristic
364C4×D61C2×#4111yescharacteristic
365C4×D61H(5,𝔽2)11yescharacteristic
366C4×D61H(5,𝔽2)11yescharacteristic
367Dic122—21no—
368Dic122—21no—
369Dic122—21no—
370Dic122—42no—
371Dic122C4×D412yes—
372#92420—21no—
373#92420—21no—
374#92420—22no—
375#92420—21no—
376#92420—21no—
377#92420—41no—
378#92420—41no—
379#92420—41no—
380C8×C61—21no—
381C8×C61—21no—
382#92418—21no—
383#92418—21no—
384#22889—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61C2×C4×D411yescharacteristic
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—81no—
404C2×D61—81no—
405C2×D61—84no—
406C2×D61#54611yescharacteristic
407C2×D61#55111yescharacteristic
408#6923—42no—
409#6923—81no—
410C4×C61—21no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61C2×C4×D411yescharacteristic
414C4×C61#51811yescharacteristic
415Dic61—22no—
416Dic61—21no—
417Dic61—41no—
418Dic61—41no—
419Dic61D4211yescharacteristic
420Dic61#54611yescharacteristic
421#3002—611no—
422C2×#443—611no—
423#2933—611no—
424C2×#421—611no—
425#2880—611no—
426#1975—611no—
427#1937—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876—611no—
432#1866—611no—
433#1855—611no—
434#1765—611no—
435#1750—611no—
436C2×C61—41no—
437C2×C61—42no—
438C2×C61—81no—
439C2×C61#235811yescharacteristic
440C2×C61#295511yescharacteristic
441C2×C61#295711yescharacteristic
442D61—21no—
443D61—21no—
444D61—41no—
445D61—81no—
446C22×#41—611no—
447C2×#135—611no—
448C2×#135—611no—
449C2×#131—611no—
450C2×#131—611no—
451C2×#131—611no—
452C22×M16—611no—
453#525—611no—
454C2×#117—611no—
455#452—611no—
456#452—611no—
457#451—611no—
458#450—611no—
459#449—611no—
460#449#692311yescharacteristic, complemented
461#448—611no—
462#447—611no—
463#443—1224no—
464#436—1221no—
465#435—1221no—
466#435—1221no—
467C8×D4—1221no—
468C2×#108—611no—
469C2×#108—611no—
470#424—611no—
471#421—1224no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104—611no—
478#416—611no—
479#416—611no—
480#408—611no—
481#408—611no—
482#408—611no—
483#408—1221no—
484#408—1221no—
485#407—611no—
486#407—1221no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—611no—
489C2×C22⋊C8—1221no—
490#405—611no—
491C2×#97—611no—
492C2×C4×C8—611no—
493#341—611no—
494#341—611no—
495#339—611no—
496#339—611no—
497#336—611no—
498#336—611no—
499C61#2288911yescharacteristic, complemented, Sylow
500C2×#41—611no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—611no—
504C2×#41—1221no—
505C2×#41—1221no—
506C2×#41—1222no—
507C2×#41—1222no—
508C2×#41—2441no—
509C2×#41—2441no—
510C2×#41C2×#692311yescharacteristic
511C22×Q8—611no—
512C22×D4—611no—
513C22×D4—1221no—
514C23×C4—611no—
515C23×C4—1221no—
516#135—1222no—
517#135—1222no—
518#135—2441no—
519#135—2441no—
520C2×Q16—611no—
521C2×Q16—611no—
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16—611no—
525C2×SD16C2×#692311yescharacteristic
526C2×D8—611no—
527C2×D8C2×#692311yescharacteristic
528#131—1222no—
529#131—1222no—
530#131—1222no—
531#131—2441no—
532#131—2441no—
533#131—2441no—
534C2×M16—611no—
535C2×M16—611no—
536C2×M16—611no—
537C2×M16—611no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1222no—
543C2×M16—2441no—
544C22×C8—611no—
545C22×C8—611no—
546C22×C8—611no—
547C22×C8—611no—
548C22×C8—1221no—
549C22×C8—1221no—
550C22×C8—1221no—
551C22×C8—1221no—
552#123—1221no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555#121—611no—
556#121C2×#692311yescharacteristic
557#120—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560#117—611no—
561#117—1222no—
562#117—2441no—
563C2×C4⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—611no—
566C2×C42—611no—
567#108—1222no—
568#108—2441no—
569C4⋊C8—1221no—
570C4⋊C8—1221no—
571#104—614no—
572#104—1222no—
573#104—1222no—
574#104—1222no—
575#104—1222no—
576#104—2441no—
577#103—611no—
578#103—611no—
579#103—611no—
580#103C2×#692311yescharacteristic
581#102—611no—
582#102—611no—
583#102—611no—
584#102C2×#692311yescharacteristic
585C22⋊C8—611no—
586C22⋊C8—611no—
587C22⋊C8—611no—
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—1221no—
593C22⋊C8—1221no—
594C22⋊C8—1221no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8C2×#692311yescharacteristic
601#97—1221no—
602#97—2441no—
603C4×C8—1222no—
604C4×C8—1221no—
605C24—611no—
606C24—1221no—
607#41—22no—
608#41—41no—
609#41—612no—
610#41—612no—
611#41—1222no—
612#41—1221no—
613#41—1221no—
614#41—1221no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—1221no—
622#41—2441no—
623#41—2442no—
624#41—2442no—
625#41—2442no—
626#41—2442no—
627C2×Q8—611no—
628C2×Q8—611no—
629C2×Q8—1221no—
630C2×Q8—1222no—
631C2×Q8—2441no—
632C2×Q8C22×#692311yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—611no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1222no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—2441no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4C22×#692311yescharacteristic
647C2×D4C22×#692311yescharacteristic
648C22×C4—21no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4C22×#692311yescharacteristic
668Q16—1222no—
669Q16—2441no—
670SD16—41no—
671SD16—1222no—
672SD16—1222no—
673SD16—2441no—
674D8—22no—
675D8—2441no—
676M16—612no—
677M16—1221no—
678M16—1221no—
679M16—1221no—
680M16—1221no—
681M16—1221no—
682M16—1221no—
683M16—1221no—
684M16—2442no—
685M16—2442no—
686M16—2442no—
687M16—2442no—
688C2×C8—611no—
689C2×C8—611no—
690C2×C8—611no—
691C2×C8—611no—
692C2×C8—611no—
693C2×C8—611no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—2442no—
707C2×C8—2442no—
708C2×C8—2442no—
709C2×C8—2442no—
710C2×C8C22×#692311yescharacteristic
711C2×C8C22×#692311yescharacteristic
712C4⋊C4—611no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—2442no—
716C4⋊C4C22×#692311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—2442no—
723C42—612no—
724C42—1221no—
725C42—1221no—
726C42—1221no—
727C42—1221no—
728C23—21no—
729C23—21no—
730C23—611no—
731C23—611no—
732C23—1221no—
733C23—1221no—
734C23—1221no—
735C23—4881no—
736C23—2441no—
737C23—2441no—
738C23—2442no—
739C23—2442no—
740C23D4×#692311yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—612no—
744Q8—1221no—
745Q8—1221no—
746Q8—1221no—
747Q8—2442no—
748D4—21no—
749D4—21no—
750D4—21no—
751D4—42no—
752D4—42no—
753D4—1222no—
754D4—1222no—
755D4—1221no—
756D4—1221no—
757D4—4881no—
758D4—2441no—
759D4—2441no—
760D4—2442no—
761D4—2442no—
762D4—2441no—
763D4—2441no—
764D4D4×#692312yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—42no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1222no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—2442no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2442no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4D4×#692311yescharacteristic
802C2×C4C23×#692311yescharacteristic
803C8—21no—
804C8—21no—
805C8—1221no—
806C8—1221no—
807C8—1221no—
808C8—1221no—
809C8—1222no—
810C8—1221no—
811C8—1221no—
812C8—2441no—
813C8—2441no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—22no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—611no—
825C22—611no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—1221no—
831C22—4881no—
832C22—4881no—
833C22—4884no—
834C22—2441no—
835C22—2441no—
836C22—2441no—
837C22C2×D4×#692311yescharacteristic
838C4—21no—
839C4—41no—
840C4—41no—
841C4—611no—
842C4—611no—
843C4—1221no—
844C4—1222no—
845C4—4881no—
846C4—2442no—
847C4—2441no—
848C4—2441no—
849C4C2×D4×#692311yescharacteristic
850C4#1684082911yescharacteristic
851C2—41no—
852C2—42no—
853C2—81no—
854C2—1221no—
855C2—1221no—
856C2—4881no—
857C2—2441no—
858C2#2146234111yescharacteristic
859C2#2146259111yescharacteristic
860C2#2146259611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#449C4
socleC22×C61C2×C4×D4
prime radical#21455034C2
cosocleC2×C4×D61C24
hypercenter#449#6923
hypocenterC61#22889
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#16840804C2semidirect
2. #21462549C2semidirect
3. C2×#16840759C2semidirect
4. #21462409C2semidirect
5. #21461975C2semidirect
6. #21461912C2semidirect
7. #21461903C2semidirect
8. #21461839C2semidirect
9. #21461810C2semidirect
10. #21461808C2semidirect
11. #21461786C2semidirect
12. #21461771C2semidirect
13. #21461598C2semidirect
14. #21461550C2semidirect
18. C2×#14519864C22semidirect
26. C2×#14519848C22semidirect
27. C2×#14519848C22semidirect
28. #16840769C22semidirect
34. C2×#14519841C22semidirect
35. C2×#14519841C22semidirect
38. #16840736C22semidirect
45. #16840727C22semidirect
46. C2×#14519831C22semidirect
47. C2×C8×#6923C22semidirect
48. #16840638C22semidirect
49. #16840638C22semidirect
50. #16840632C22semidirect
51. #16840632C22semidirect
52. (C2×#6923)⋊C8C22semidirect
53. (C2×#6923)⋊C8C22semidirect
58. #16839926C4semidirect
59. #16839924C4semidirect
60. #16839919C4semidirect
61. #16839914C4semidirect
62. #16839905C4semidirect
63. #16839899C4semidirect
64. #16839894C4semidirect
68. C61×#449C4semidirect
106. #14519841D4semidirect
460. #449#6923semidirect
499. C61#22889semidirect

Maximal subgroups

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

subgroupindex
C2×#168408042
#214625492
C2×#168407592
#214624092
#214619752
#214619122
#214619032
#214618392
#214618102
#214618082
#214617862
#214617712
#214615982
#214615502
#214550342
#2288961