Finite Group Databasebeta

← #30621791

Subgroups — #30621791

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×#16840805C211yesmaximal, characteristic, complemented
2#21462554C211yesmaximal, characteristic, complemented
3C2×#16840760C211yesmaximal, characteristic, complemented
4#21462407C211yesmaximal, characteristic, complemented
5#21461975C211yesmaximal, characteristic, complemented
6#21461913C211yesmaximal, characteristic, complemented
7#21461901C211yesmaximal, characteristic, complemented
8#21461838C211yesmaximal, characteristic, complemented
9#21461811C211yesmaximal, characteristic, complemented
10#21461808C211yesmaximal, characteristic, complemented
11#21461786C211yesmaximal, characteristic, complemented
12#21461773C211yesmaximal, characteristic, complemented
13#21461598C211yesmaximal, characteristic, complemented
14#21461550C211yesmaximal, characteristic, complemented
15#21455038C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic, complemented
17C2×#14519864C2211yescharacteristic
18C2×#14519864C2211yescharacteristic
19C2×D61⋊M16C2211yescharacteristic
20C2×#14519856C2211yescharacteristic
21#16840805—24no—
22#16840795—21no—
23#16840794—21no—
24#16840792—21no—
25#16840790—21no—
26C2×#14519848C2211yescharacteristic, complemented
27C2×#14519847C2211yescharacteristic, complemented
28#16840769C2211yescharacteristic, complemented
29#16840760—24no—
30C2×#14519842C2211yescharacteristic, complemented
31C2×#14519842C2211yescharacteristic, complemented
32C2×#14519841C2211yescharacteristic
33C2×#14519841C2211yescharacteristic
34C2×#14519841C2211yescharacteristic
35C2×#14519841C2211yescharacteristic
36#16840737C2211yescharacteristic, complemented
37#16840736C2211yescharacteristic
38#16840736C2211yescharacteristic
39#16840735—21no—
40#16840735—21no—
41#16840733C2211yescharacteristic
42#16840732—21no—
43D61⋊(C22⋊C8)C2211yescharacteristic
44C2×C22⋊#92420—21no—
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
54C22×#11758224C2211yescharacteristic
55C2×#14519798C2211yescharacteristic
56C2×#14519798C2211yescharacteristic
57#16840275C2211yescharacteristic
58#16839921C411yescharacteristic, complemented
59#16839921C411yescharacteristic, complemented
60#16839917C411yescharacteristic, complemented
61#16839908C411yescharacteristic, complemented
62#16839908C411yescharacteristic, complemented
63#16839903C411yescharacteristic, complemented
64#16839896C411yescharacteristic, complemented
65#16839755C2211yescharacteristic
66#16839755C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#450C411yescharacteristic, complemented
69#14519865—22no—
70#14519865—41no—
71#14519864—22no—
72#14519864—22no—
73#14519864—41no—
74#14519864—41no—
75C2×#11758213—21no—
76C2×#11758213C2311yescharacteristic
77C2×#11758213C2311yescharacteristic
78C2×#11758213C2311yescharacteristic
79C2×#11758213C2311yescharacteristic
80D61⋊M16—22no—
81D61⋊M16—41no—
82C2×#11758217—21no—
83C2×#11758217—21no—
84C2×#11758217—21no—
85C2×D61⋊C8—21no—
86C2×D61⋊C8—21no—
87C2×D61⋊C8C2311yescharacteristic
88C2×D61⋊C8C2311yescharacteristic
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—41no—
98#14519847—22no—
99#14519844—21no—
100C4⋊#92420—21no—
101#14519842—22no—
102#14519842—41no—
103#14519841—22no—
104#14519841—22no—
105#14519841—22no—
106#14519841D414yescomplemented
107#14519834—21no—
108#14519834—21no—
109#14519834—21no—
110#14519834D411yescharacteristic
111#14519834D411yescharacteristic
112C22⋊#92420—21no—
113C22⋊#92420—21no—
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×#11758224—22no—
125C2×#11758224—22no—
126C2×#11758224—21no—
127C2×#11758224—21no—
128C2×#11758224—41no—
129C2×#11758224—41no—
130C2×#11758224C2×C411yescharacteristic
131C2×#11758224C2×C411yescharacteristic
132C2×#11758224C2311yescharacteristic
133C2×#11758224C2311yescharacteristic
134C22×Dic122C2×C411yescharacteristic
135C22×C22⋊D61—21no—
136C23×Dic61—21no—
137C22×C4×D61C2311yescharacteristic
138#14519798—22no—
139#14519798—22no—
140#14519798—41no—
141#14519798—41no—
142C2×#11758202C2×C411yescharacteristic
143C2×#11758202C2×C411yescharacteristic
144C2×#11758190C2×C411yescharacteristic
145C2×#11758190C2×C411yescharacteristic
146C2×#11758199C2×C411yescharacteristic
147C2×#11758199C2×C411yescharacteristic
148C2×C8×D61C2311yescharacteristic
149C2×C8×D61C2311yescharacteristic
150#14519762—21no—
151#14519753C2×C411yescharacteristic
152#14519752C2×C411yescharacteristic
153#14519751C2×C411yescharacteristic
154#14519747—21no—
155#14519739—21no—
156#14519737—21no—
157#14519735C2311yescharacteristic
158#14519702C2×C411yescharacteristic
159#14519702C2×C411yescharacteristic
160#14519700C2×C411yescharacteristic
161#14519700C2×C411yescharacteristic
162#14519698C2×C411yescharacteristic
163#14519698C2×C411yescharacteristic
164C22⋊#92418C2×C411yescharacteristic
165#14519689C2×C411yescharacteristic
166#14519689C2×C411yescharacteristic
167C22×D4×C61C2×C411yescharacteristic
168C2×SD16×C61C2×C411yescharacteristic
169C2×SD16×C61C2×C411yescharacteristic
170C22⋊Q8×C61C2×C411yescharacteristic
171#102×C61C2×C411yescharacteristic
172#102×C61C2×C411yescharacteristic
173C22⋊C8×C61C2×C411yescharacteristic
174C24×C61—21no—
175C23×D61#4111yescharacteristic
176C22×#6923—21no—
177C22×#6923—21no—
178C2×Q8×C61C22×C411yescharacteristic
179C2×D4×C61—22no—
180C2×D4×C61—21no—
181C2×D4×C61—41no—
182C2×D4×C61C22×C411yescharacteristic
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C2×C22⋊D61—21no—
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61—42no—
198C22×Dic61—42no—
199C22×Dic61C2×D411yescharacteristic
200#11758226—21no—
201#11758226—21no—
202#11758226—21no—
203#11758226—21no—
204#11758224—22no—
205#11758224—21no—
206#11758224—21no—
207#11758224—21no—
208#11758224—21no—
209#11758224—21no—
210#11758224—21no—
211#11758224—22no—
212#11758224—41no—
213#11758224—41no—
214#11758224—42no—
215#11758224—42no—
216#11758224—42no—
217#11758224—42no—
218#11758224C2×D412yes—
219#11758224#4112yes—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244C22×C411yescharacteristic
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61C22×C411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61#4111yescharacteristic
231C2×C4×D61C2411yescharacteristic
232C2×Dic122—22no—
233C2×Dic122—21no—
234C2×Dic122—41no—
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×#92420C2×D411yescharacteristic
248C2×#92420C2×D411yescharacteristic
249C2×#92420C2×D411yescharacteristic
250C2×#92420C2×D411yescharacteristic
251C4⋊#6923—42no—
252C4×#6923—21no—
253C4×#6923—21no—
254C4×#6923—21no—
255C4×#6923C2×D412yes—
256#11758213—21no—
257#11758213—21no—
258#11758213—21no—
259#11758213—21no—
260#11758213—21no—
261#11758213—21no—
262#11758213—21no—
263#11758213—42no—
264#11758213C2×D412yes—
265D61⋊C8—21no—
266D61⋊C8—21no—
267D61⋊C8—21no—
268D61⋊C8—21no—
269D61⋊C8—42no—
270D61⋊C8—42no—
271SD16×C61—22no—
272SD16×C61—41no—
273C2×C8×C61C22×C411yescharacteristic
274C2×C8×C61C22×C411yescharacteristic
275C4⋊C4×C61—21no—
276C4⋊C4×C61C22×C411yescharacteristic
277C22⋊C4×C61—21no—
278#11758202—22no—
279#11758202—41no—
280#11758199—22no—
281#11758199—41no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286C4⋊Dic61C22×C411yescharacteristic
287#11758196—21no—
288C4×Dic61—21no—
289C2×#92418C22×C411yescharacteristic
290C2×#92418C22×C411yescharacteristic
291#11758190—22no—
292#11758190—41no—
293C8×D61—21no—
294C8×D61—21no—
295C8×D61—21no—
296C8×D61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—81no—
302C23×C61C4×D411yescharacteristic
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—41no—
307C22×D61—41no—
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×C61C4×D412yes—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61C4×D411yescharacteristic
328C2×C4×C61C23×C411yescharacteristic
329C22⋊D61—22no—
330C22⋊D61—22no—
331C22⋊D61—42no—
332C22⋊D61—42no—
333C22⋊D61—41no—
334C22⋊D61—41no—
335C22⋊D61—81no—
336C2×Dic61—21no—
337C2×Dic61—22no—
338C2×Dic61—21no—
339C2×Dic61—22no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—42no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61C4×D411yescharacteristic
349C2×Dic61C22×D411yescharacteristic
350D244—21no—
351D244—21no—
352D244—42no—
353D244—41no—
354D244—41no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
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—21no—
386C22×C61—22no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—84no—
395C22×C61C2×C4×D411yescharacteristic
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—81no—
405C2×D61—81no—
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#692311yescharacteristic, complemented
459#449—611no—
460#449—611no—
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—611no—
505C2×#41—1221no—
506C2×#41—1221no—
507C2×#41—1222no—
508C2×#41—1222no—
509C2×#41—2441no—
510C2×#41—2441no—
511C22×Q8—611no—
512C22×D4—1221no—
513C22×D4C2×#692311yescharacteristic
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×SD16C2×#692311yescharacteristic
525C2×SD16C2×#692311yescharacteristic
526C2×D8—611no—
527C2×D8—611no—
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⋊Q8C2×#692311yescharacteristic
555#121—611no—
556#121—611no—
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#103—611no—
581#102—611no—
582#102—611no—
583#102C2×#692311yescharacteristic
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—21no—
606C24—611no—
607#41—612no—
608#41—612no—
609#41—1221no—
610#41—1221no—
611#41—1221no—
612#41—1221no—
613#41—1221no—
614#41—1221no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—1222no—
620#41—1222no—
621#41—2442no—
622#41—2442no—
623#41—2441no—
624#41—2441no—
625#41—2442no—
626#41—2442no—
627C2×Q8—611no—
628C2×Q8—611no—
629C2×Q8—1222no—
630C2×Q8—1221no—
631C2×Q8—2441no—
632C2×Q8C22×#692311yescharacteristic
633C2×D4—22no—
634C2×D4—21no—
635C2×D4—41no—
636C2×D4—611no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4C22×#692311yescharacteristic
647C2×D4C22×#692311yescharacteristic
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—1221no—
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—22no—
671SD16—41no—
672SD16—1222no—
673SD16—2441no—
674D8—1222no—
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—21no—
713C4⋊C4—611no—
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—42no—
731C23—42no—
732C23—81no—
733C23—611no—
734C23—611no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—2441no—
739C23—2441no—
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—1222no—
753D4—1222no—
754D4—1221no—
755D4—1221no—
756D4—4881no—
757D4—2441no—
758D4—2441no—
759D4—2442no—
760D4—2442no—
761D4—2442no—
762D4—2441no—
763D4—2441no—
764D4D4×#692312yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—611no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1222no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4—2442no—
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—22no—
818C22—21no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—84no—
825C22—611no—
826C22—611no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—1221no—
831C22—1221no—
832C22—4881no—
833C22—4881no—
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#2146259711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#450C4
socleC22×C61C2×C4×D4
prime radical#21455038C2
cosocleC2×C4×D61C24
hypercenter#450#6923
hypocenterC61#22889
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#16840805C2semidirect
2. #21462554C2semidirect
3. C2×#16840760C2semidirect
4. #21462407C2semidirect
5. #21461975C2semidirect
6. #21461913C2semidirect
7. #21461901C2semidirect
8. #21461838C2semidirect
9. #21461811C2semidirect
10. #21461808C2semidirect
11. #21461786C2semidirect
12. #21461773C2semidirect
13. #21461598C2semidirect
14. #21461550C2semidirect
16. C2×#14519865C22semidirect
26. C2×#14519848C22semidirect
27. C2×#14519847C22semidirect
28. #16840769C22semidirect
30. C2×#14519842C22semidirect
31. C2×#14519842C22semidirect
36. #16840737C22semidirect
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. #16839921C4semidirect
59. #16839921C4semidirect
60. #16839917C4semidirect
61. #16839908C4semidirect
62. #16839908C4semidirect
63. #16839903C4semidirect
64. #16839896C4semidirect
68. C61×#450C4semidirect
106. #14519841D4semidirect
458. #450#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×#168408052
#214625542
C2×#168407602
#214624072
#214619752
#214619132
#214619012
#214618382
#214618112
#214618082
#214617862
#214617732
#214615982
#214615502
#214550382
#2288961